Behavioral and Brain Sciences, Volume 32, Issue 3-4, June-August 2009

An International journal of current research and theory with open peer commentary Volume 32 | Issue 3/4 | June/August 2009 | ISSN: 0140-525X

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Editorial Board Atypical Neurodevelopment Simon Baron-Cohen/Cambridge U. Behavioral Neurogenetics Wim E. Crusio/CNRS UMR Cognition and Artificial Intelligence Zenon Pylyshyn/Rutgers U. Cognitive and Decision Sciences Nick Chater/University College London Cognitive Development Annette Karmiloff-Smith/Birbeck College Cognitive Neuroscience Moshe Bar/Harvard Medical School Computational Neuroscience Nestor A. Schmajuk/Duke U. Evolution of Brain and Cognition Dean Falk/Florida State U. Evolution of Cognition Celia Heyes/Oxford U. Experimental Analysis of Behavior A. Charles Catania/U. Maryland, Baltimore County Language and Language Disorders Max Coltheart/Macquarie U. Linguistics Robert A. Freidin/Princeton U. Perception Bruce Bridgeman/U. of California, Santa Cruz Philosophy of Science Massimo Piattelli-Palmarini/U. of Arizona Primate Cognition Laurie R. Santos/Yale U. Social Cognition Mahzarin R. Banaji/Harvard U. Social Cognitive Neuroscience Rebecca Saxe/MIT Vision, Language and Computation Shimon Edelman/Cornell U.

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Contents

Volume 32:(3/4)

June/August 2009

Archer, J. Does sexual selection explain human sex differences in aggression? Open Peer Commentary Bailey, D. H., Oxford, J. K. & Geary, D. C. Ultimate and proximate influences on human sex differences Behme, C. Does sexual selection explain why human aggression peaks in early childhood? Benenson, J. F. Dominating versus eliminating the competition: Sex differences in human intrasexual aggression Boden, J. M. Sex differences in the developmental antecedents of aggression Browne, K. R. Sex differences in aggression: Origins and implications for sexual integration of combat forces Buss, D. M. The multiple adaptive problems solved by human aggression Campbell, A. What kind of selection? Cashdan, E. Sex differences in aggression: What does evolutionary theory predict? Corr, P. J. & Perkins, A. M. Differentiating defensive and predatory aggression: Neuropsychological systems and personality in sex differences Dickins, T. E. & Sergeant, M. J. T. Two more things for consideration: Sexual orientation and conduct disorder Eagly, A. H. & Wood, W. Sexual selection does not provide an adequate theory of sex differences in aggression Figueredo, A. J., Gladden, P. R. & Brumbach, B. H. Sex, aggression, and life history strategy Finkel, E. J. & Slotter, E. B. An I3 Theory analysis of human sex differences in aggression Gaulin, S. J. C. Biophobia breeds unparsimonious exceptionalism

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Johnson, D. D. P. & van Vugt, M. A history of war: The role of inter-group conflict in sex differences in aggression Kaighobadi, F. & Shackelford, T. K. Suspicions of female infidelity predict men’s partner-directed violence Kempenaers, B. & Forstmeier, W. A quantitative genetic approach to understanding aggressive behavior Kenrick, D. T. & Griskevicius, V. More holes in social roles Pellegrini, A. D. Moderators of sex differences in sexual selection theory Pound, N., Daly, M. & Wilson, M. There’s no contest: Human sex differences are sexually selected Schredl, M. Sex differences in dream aggression Sefcek, J. A. & Sacco, D. F. Human sexual dimorphism, fitness display, and ovulatory cycle effects Sell, A. Standards of evidence for designed sex differences Terburg, D., Peper, J. S., Morgan, B. & van Honk, J. Sex differences in human aggression: The interaction between early developmental and later activational testosterone Tremblay, R. E. & Coˆte´, S. M. Development of sex differences in physical aggression: The maternal link to epigenetic mechanisms van den Berghe, P. L. Sexual selection and social roles: Two models or one? Author’s Response Archer, J. Refining the sexual selection explanation within an ethological framework

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Cohen Kadosh, R. & Walsh, V. Numerical representation in the parietal lobes: Abstract or not abstract? Open Peer Commentary Algom, D. Slippery platform: The role of automatic and intentional processes in testing the effect of notation Ansari, D. Are non-abstract brain representations of number developmentally plausible? Campbell, J. I. D. & Metcalfe, A. W. S. Numerical abstractness and elementary arithmetic Cantlon, J. F., Cordes, S., Libertus, M. E. & Brannon, E. M. Numerical abstraction: It ain’t broke Cohen, D. J. Numerical representations are neither abstract nor automatic Dehaene, S. The case for a notation-independent representation of number Falter, C. M., Noreika, V., Kiverstein, J. & Mo¨lder, B. Concrete magnitudes: From numbers to time Freeman, W. J. & Kozma, R. Brain neural activity patterns yielding numbers are operators, not representations Ganor-Stern, D. Automatic numerical processing is based on an abstract representation Grabner, R. H. Expertise in symbol-referent mapping Houde´, O. Abstract after all? Abstraction through inhibition in children and adults Kucian, K. & Kaufmann, L. A developmental model of number representation Lindemann, O., Rueschemeyer, S.-A. & Bekkering, H. Symbols in numbers: From numerals to magnitude information Mayo, J. P. Inactivation and adaptation of number neurons Myachykov, A., Platenburg, W. P. A. & Fischer, M. H. Non-abstractness as mental simulation in the representation of number

328 329 330 331 332 333 335 336 337 338 339 340 341

Nu´n˜ez, R. E. Numbers and numerosities: Absence of abstract neural realization doesn’t mean non-abstraction Orban, G. A. The discussion of methodological limitations in number representation studies is incomplete Pease, A., Smaill, A. & Guhe, M. Abstract or not abstract? Well, it depends . . . Pesenti, M. & Andres, M. Common mistakes about numerical representations Peters, E. & Castel, A. Numerical representation, math skills, memory, and decision-making Piazza, M. & Izard, V. What is an (abstract) neural representation of quantity? Reynvoet, B. & Notebaert, K. Abstract or not? Insights from priming Rosenberg-Lee, M., Tsang, J. M. & Menon, V. Symbolic, numeric, and magnitude representations in the parietal cortex Santens, S., Fias, W. & Verguts, T. Abstract representations of number: What interactions with number form do not prove and priming effects do Szu´´cs, D., Solte´sz, F. & Goswami, U. Beyond format-specificity: Is analogue magnitude really the core abstract feature of the cultural number representation? Tzelgov, J. & Pinhas, M. In search of non-abstract representation of numbers: Maybe on the right track, but still not there Vallar, G. & Girelli, L. Numerical representations: Abstract or supramodal? Some may be spatial Wiefel, A., Pauen, S. & Dueck, M. Do infants count like scientists?

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Authors’ Response: Cohen Kadosh, R. & Walsh, V. Non-abstract numerical representations in the IPS: Further support, challenges, and clarifications

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BEHAVIORAL AND BRAIN SCIENCES (2009) 32, 249 –311 Printed in the United States of America

doi:10.1017/S0140525X09990951

Does sexual selection explain human sex differences in aggression? John Archer School of Psychology, University of Central Lancashire, Preston PR1 2HE, United Kingdom [email protected] http://www.uclan.ac.uk/scitech/research/rae2008/psychology/ staff_profiles/jarcher.php

Abstract: I argue that the magnitude and nature of sex differences in aggression, their development, causation, and variability, can be better explained by sexual selection than by the alternative biosocial version of social role theory. Thus, sex differences in physical aggression increase with the degree of risk, occur early in life, peak in young adulthood, and are likely to be mediated by greater male impulsiveness, and greater female fear of physical danger. Male variability in physical aggression is consistent with an alternative life history perspective, and context-dependent variability with responses to reproductive competition, although some variability follows the internal and external influences of social roles. Other sex differences, in variance in reproductive output, threat displays, size and strength, maturation rates, and mortality and conception rates, all indicate that male aggression is part of a sexually selected adaptive complex. Physical aggression between partners can be explained using different evolutionary principles, arising from the conflicts of interest between males and females entering a reproductive alliance, combined with variability following differences in societal gender roles. In this case, social roles are particularly important since they enable both the relatively equality in physical aggression between partners from Western nations, and the considerable cross-national variability, to be explained. Keywords: aggression; partner violence; sex differences; sexual selection; social role theory

1. Introduction Darwin (1859/1911; 1871/1901) regarded the greater proneness to physical aggression by men than women as part of a general mammalian pattern, which can be explained by one aspect of sexual selection, inter-male competition. Within the social sciences there is a long tradition of explaining sex differences in social behavior, including aggression, in human-centered terms, as a consequence of social influences. In this article, I argue that sexual selection provides a better explanation for human sex differences in aggression than the main contemporary social science approach, the social role theory. Aggression is typically defined as behavior intended to harm another individual, and its study was originally restricted to direct physical and verbal forms. Psychologists began systematically documenting human sex differences in these types of aggression in the 1920s, and studies have continued to the present time. The forms of aggression now include indirect (or “relational”1) aggression, which Feshbach (1969) and Lagerspetz et al. (1988) found to be more typical of girls than boys. They suggested that the sex difference, hitherto characterized as involving “aggression,” was more accurately viewed as involving its form. Contemporary studies include both direct and indirect aggression. A separate extensive literature documents sex differences (or similarities) in physical aggression between partners, although this is not usually considered in discussions of sex differences in aggression. I do consider the evolutionary and social forces underlying aggression between # 2009 Cambridge University Press

0140-525X/09 $40.00

partners in this article, so as to provide a comprehensive explanation of sex differences in aggression. Nevertheless, most of the discussion is devoted to within-sex differences, the main concern of sexual selection and social role accounts. In assessing the evidence, I address the issues of ultimate origins, development, mediating variables, and sources of individual differences, in relation to predictions derived from the two theories. I argue that sexual selection provides the more complete explanation of the origins of sex differences in aggression, and that these differences are linked to a range of other features indicting the operation of sexual selection in humans. Although reformulations of social role theory do encompass some evolved differences, they are restricted to physical attributes, which form only part of the sexual selection view.

JOHN ARCHER , Professor of Psychology at the University of Central Lancashire, Preston, United Kingdom, is the author of more than 100 articles, in a wide range of journals, in the areas of animal aggression and emotionality, testosterone and behavior, human sex differences, human aggression, grief and loss, and evolutionary psychology. He is also the author of several books, including The Behavioural Biology of Aggression (1988), The Nature of Grief (1999), and Sex and Gender (2nd edition, 2002). He is a former President of the International Society for Research on Aggression (ISRA), and is a Fellow of the British Psychological Society.

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Archer: Sex differences in aggression 2. Aggression between same-sex individuals 2.1. Sexual selection as an explanatory framework for human aggression 2.1.1. Principles of sexual selection. Sexual selection

involves the choice of members of one sex by the other, and competition by members of one sex for access to the other (Darwin 1871/1901). The more competitive and aggressive sex is usually the male, particularly in mammals. Sexual selection forms a basis for understanding sex differences in aggression in animals, although it is not the only explanation (Ralls 1976; Selander 1972). Trivers (1972) proposed that the reason why males are typically the more competitive sex is their lower parental investment, defined as any contribution by a parent that increases an offspring’s chances of survival and reproduction, while reducing the parents’ ability to produce further offspring. Examples include the energy expended in gamete production (Bateman 1948), and feeding or guarding the young. The initial greater contribution by the female to the gametes will make desertion to seek access to other mates a more beneficial option for males than for females, providing that one parent can care for the offspring.2 The sex showing higher parental investment becomes a limiting resource, the other sex competing for reproductive access. Competition can take forms other than direct aggression, for example, sperm competition, or features that aid mate attraction, or securing a dispersed resource (Andersson 1994, pp. 10–13; Archer 1988, pp. 106–107). When parental care by both sexes is required, inter-male competition will be countered by the male’s greater paternal investment, as occurs in monogamous birds. Where the female can leave the male to brood the eggs and care for the young alone, as occurs in polyandrous wading birds, females will be the more competitive, and the larger and more aggressive, sex (Jenni 1974). This reversal of the usual sex differences provides crucial support for Trivers’ theory. In mammals, fertilization is internal and the female feeds the developing offspring, so that parental investment is further female-biased, and polygyny is the usual outcome. In terrestrial mammals, this is typically associated with inter-male aggression, accompanied by large size and musculature, and a greater variation in male than female reproductive success (Andersson 1994). Differential reproductive rate can be regarded as a more fundamental principle driving sexual selection than parental investment (Clutton-Brock & Vincent 1991). It reflects the rates at which males and females are able to mate again, after producing offspring (and therefore is closely related to parental investment). Differences in reproductive rate were associated with sex differences in mating competition in 29 species where the male shows some parental care (Clutton-Brock & Vincent 1991), and females had higher reproductive rates than males when the usual sex difference was reversed (i.e. when females were larger and more competitive than males). The basic principles of sexual selection are complicated by ecological constraints on the degree to which one sex can compete for, and monopolize, access to the other sex (Emlen & Oring 1977). Where resources that are important for reproduction are located in one place, there will be accentuated competition for access to the sex with the lowest reproductive rate, usually the female, and polygyny is more likely. Where resources are widely 250

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distributed, the potential for reproductive competition is less, and monogamy is more likely. These principles also apply to variation within a species. For example, the mating system of the dunnock (Prunella vulgaris) varies from polygyny to monogamy to polyandry (Davies & Hartley 1996; Davies & Lundberg 1984), depending on the food distribution, which affects female range size. Underlying these associations is the ability of males to control access to females, or more precisely, the concept of operational sex ratio (OSR; Emlen & Oring 1977) – the ratio of sexually active males to fertilizable females at any given time and place. This will be biased in the female direction as a consequence of males being excluded from the breeding group by higher mortality, or being ejected as a result of competition, or maturing more slowly (Clutton-Brock & Harvey 1977), and in the male direction if females only gradually become fertile or available to males (e.g., Smuts 1987b). The OSR is essentially an index of the degree of male competition for mates, and is associated with greater variance in male than female reproductive success. Pomiankowski and Møller (1995) found greater variability in sexually selected than non-sexually selected traits in males than females from a range of species, and they attributed this to sexual selection producing traits exaggerated beyond those that were optimal for survival. An alternative explanation in species where there is some degree of paternal care is that males of many monogamous species retain traits associated with polygynous mating, and can therefore be regarded as facultatively polygynous (Andersson 1994, pp. 157– 58; Trivers 1972). The degree to which this occurs depends both on the context (e.g., the availability of alternative mates) and the individual (e.g., the ability to attract alternative mates). Such individual differences are said to arise from the extent to which reproductive effort is concentrated on parental or mating effort, which is termed a conditional reproductive strategy (Gross 1996). It would lead to greater variation in sexually selected traits among males than among females. 2.1.2. Sexual selection applied to human aggression.

Because gestation in female mammals is internal, males must show a higher potential reproductive rate than females, and this is associated with being the competitive sex. The necessity of biparental care in some species will counter this and reduce the degree of sexual dimorphism. The extent to which this applies to humans is a matter of contention (Geary 2000), and humans have been regarded as basically monogamous or polygynous (sect. 2.1). However, even males of monogamous species are likely to be facultatively polygynous (Trivers 1972), and therefore reproductive competition is likely to be higher in men than women, irrespective of the basic human mating pattern. Daly and Wilson (1988; 1990) applied the principles of sexual selection to human homicide, which they regarded as indicative of the strength of aggressive dispositions in different individuals and under different circumstances. They viewed the much higher frequency of male than female same-sex homicides, and the concentration of these among men with few resources (sect. 1.8), as consequences of sexual selection. An alternative evolutionary view (Campbell 1999) explained the lower incidence of women’s engagement in risky and violent aggression in terms of their relatively greater parental investment,

Archer: Sex differences in aggression which increases the importance of remaining alive to rear their offspring. As a consequence, women have evolved a psychological disposition to be more risk-averse. This can be viewed as either an alternative to the sexual selection view, which concentrates on male competition, or as complementary. It is still derived from unequal parental investment, and it generates very similar predictions to sexual selection. The basic principle underlying all evolutionary explanations of aggression, including sexual selection, is a cost-benefit analysis, in which the costs and benefits of behavior are determined by natural selection. For male aggression, the benefits will be successful reproduction, and the costs those resulting from injury. For men with few resources, successful reproduction may only be possible if they challenge other men and risk injury in escalated encounters (Daly & Wilson 1988; 1990): consistent with this, an evolutionary simulation demonstrated the increasing payoffs for risky (dangerous) tactics as the value of victory increased (Daly & Wilson 1988, pp. 164 –65). For women, access to a mate is less dependent on within-sex competition, and they typically have more to lose in terms of reproductive fitness from potentially damaging confrontations (Campbell 1999). The emphasis in these explanations is on higher potential reproductive benefits for males, and higher potential costs for females, of damaging aggressive encounters. It follows that the sex difference would be largest for dangerous forms of physical aggression, and be greater for physical than for direct verbal aggression. Indirect aggression is less dangerous in terms of inviting immediate retaliation, and has therefore been viewed as a lower-cost form of aggression, typically used more by females (Bjo¨rkqvist 1994; Geary 1998; Hess & Hagen 2006). The cost-benefit analysis locates the source of the sex difference in the damaging nature of physically aggressive encounters and would not predict a difference in features of aggressive motivation, such as the ease with which the two sexes are aroused to anger. Typically, evolved dispositions such as those underlying a sex difference in aggression should not have to rely on socialization practices that could vary from culture to culture. How and when they first occur in development is an issue that is not precisely specified by a functional explanation, which primarily addresses adaptive significance. As Darwin (1871/1901) noted, sex differences may be small or minimal before reproductive maturity. The sex difference in size and strength conforms to this pattern, developing at puberty under the control of testosterone (Tanner 1989). Some researchers have suggested that testosterone controls the greater male physical aggression in humans (e.g., Book et al. 2001), following the link found in many mammals and birds (Archer 1988, pp. 135 –42). An alternative is that the sex difference in direct aggression begins early in life (Bjorklund & Pellegrini 2000), before the cumulative impact of gendered social influences, possibly as a result of a direct or indirect effect of prenatal androgens (Berenbaum & Resnick 1997; Pasterski et al. 2007). It would be associated with other early-developing dispositional sex differences, such as those in activity (Archer & Lloyd 2002, p. 74; Campbell & Eaton 1999; Eaton & Enns 1986), and social preferences for larger competitive groups rather than smaller, more supportive ones (Geary et al. 2003). Since sex-segregation, and the relationship styles

accompanying this, occur early in life (Archer 1992a; Maccoby 1988; 1998; Pellegrini 2004), we would expect sex differences in aggression to occur then too. A further possibility, not necessarily inconsistent with an early emergence of sex differences, arises from the finding that males of many polygynous species delay risky encounters with older males until they are large enough to compete effectively with them (Andersson 1994). If this applied to humans, the peak years for high-risk confrontations would be when young adults become physically mature and enter the mating arena (Geary 2002). Overall, the most likely prediction from a sexual selection perspective is an early emergence of sex differences in aggression combined with a peak in risky competition during young adulthood, with a possible influence of pubertal testosterone. Just as the course of development cannot be precisely specified from an evolutionary explanation, nor can the precise mechanisms underlying human sex differences in aggression. Sexual selection does, however, imply the following: (1) that the sex differences are not wholly the result of a general-purpose learning mechanism, although this is likely to be involved; (2) that there are sexually dimorphic neuroendocrine mechanisms underlying aggression, accompanying other aspects of sexual dimorphism, such as size and strength; (3) that the mechanism is unlikely to reside in a general sex difference in responses to frustration or in ease of arousal to anger; (4) that the sex difference is more likely to involve either greater risktaking by males or more fear of physical danger by females: either or both of these would represent the way that the motivational system underlying aggression had responded to evolutionary costs and benefits. These would represent basic predispositions that could be modified in development (sect. 2.5), or overridden by environmental contingencies (sect. 2.8). Based on Trivers’ analysis (sect. 2.1.1), sexual selection theory can also predict individual differences among men according to their relative specialization for mating or parental effort. One prediction is that there should be a coherent set of individual differences associated with mating or parental effort; a second is that variability in sexually selected traits such as physical aggression should be greater in men than in women, whereas traits that are not sexually selected, such as anger, should not show sex differences in variability. Sexual selection theory also predicts variability in sex differences in aggression as a consequence of social conditions affecting the cost-benefit contingencies of reproductive competition. For example, inter-male competition will be accentuated where resources are scarce, and where there are fewer females than males of reproductive age; that is, where the OSR is high. Where the OSR is in the other direction, with fewer males, we would expect greater female competition and overt aggression. Table 1 provides a summary of the main points of the predictions set out in this section, together with the sections that consider the evidence relating to them. 2.2. Social role theory as an explanatory framework for human aggression 2.2.1. Principles of social role theory. The main alterna-

tive explanation of the origins of human sex differences in social behavior is the “biosocial”3 reformulation (Wood & BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Archer: Sex differences in aggression Table 1. Summary of predictions about sex differences in aggression from sexual selection and social role theories Relevant section

Sexual selection theory

Social role/biosocial theory

Magnitude and nature of the sex difference

2.4

Magnitude will be modest; larger difference for physical than for psychological aggression (verbal and indirect). Presumably, no difference for anger.

Development

2.5

In accordance with the degree of physical danger, the largest differences will be in physical aggression, followed by direct verbal, with indirect aggression showing no difference or more by females; no difference for anger. Early emergence of sex difference in direct aggression; peak in damaging and risky competition during young adulthood.

Mediators

2.6

These will reflect functional principles, for example, greater risk-taking by males or greater fear of physical danger by females, or both.

Individual differences

2.7

Variability in response to environmental conditions

2.8

There will be a coherent set of individual differences (including in aggression) among males, reflecting greater or lesser emphasis on mating than parental effort. A consequence of these differences will be greater male than female variability in physical aggression. Variability across local conditions, cultures and nations is expected to reflect resources that are important for reproduction, principally access to the mates and the status and resources important in this process.

Eagly 2002) of social role theory (Eagly 1987; Eagly et al. 2000). The basic tenet of social role theory is that sex differences in behavior arise “from the societal division of labor between the sexes” (Eagly 1997, p. 1381). Although it is primarily the societal positions of men and women, as breadwinner and homemaker, and in the workforce of modern societies, that are important, social role theory acknowledges that the roles of men and women are complex. Thus, more specific roles, such as those in the family (e.g., father, grandmother) and in occupations (e.g., police officer, nurse) also contribute to sex differences in social behavior and to within-sex variations. The biosocial reformulation of social role theory (Wood & Eagly 2002) represents an extension of the earlier accounts to address issues raised in exchanges with evolutionary theorists (e.g., Archer 1996; Buss 1996; Eagly & Wood 1999), specifically the origins of sex differences, and the principles through which men and women are distributed in societal roles. It is also wider in scope, incorporating evidence from social and physical anthropology. 252

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Sex difference should start small and increase with age through childhood, coincident with the cumulative influence of socialization. Internal mediators should follow from the characteristics of gender roles (e.g., empathy, fear of retaliation, guilt, anxiety associated with aggression). They arise from general learning mechanisms associated with gender roles. Biosocial model indicates that roles can vary in response to role-related costs and benefits. Consistent individual differences would arise from differences in internalization of gender roles, and from the influence of specific roles; no consideration of possible sex differences in variability.

There should be variations in women’s level of aggressiveness accompanying: (1) changes in role salience; (2) cross-cultural variations in women’s relative emancipation; and (3) changes over historical time in women’s roles and status.

The biosocial account explains how recurrent forms of the division of labor based on sex arose from an interaction between the requirements of the social and physical environment and constraints imposed by the mammalian method of reproduction and sex differences in size and strength. Thus, women’s childbearing and nursing of infants, and men’s greater size and strength, make it easier for women to perform certain activities and men to perform others. This explains the cross-cultural consistency in gender roles. The interaction between these biological differences and particular ecological, social, economic, and technological forces, explains the variability in gender roles. The behavior associated with the specific sex-typed social roles that emerge from these interactions form the basis of behavioral sex differences, including those in aggression. Social roles are therefore viewed as being rooted in human history, but they originate from phylogenetic history in the form of reproductive and physical sex differences. Nevertheless, Wood and Eagly (2002) stated that

Archer: Sex differences in aggression their biosocial model does not assume a major role for sexual selection in producing psychological sex differences such as those in aggression. Their argument rested on two points: (1) that sexual selection operates “primarily” in polygynous mating systems; and (2) that other indications of sexual dimorphism in humans, such as size and canine teeth, are low compared with other primates. I return to these issues in section 3. The notion that certain activities are more efficient under particular circumstances implies cost-benefit maximization. Although this is superficially similar to the reasoning in evolutionary explanations (sect. 2.1.2), no explicit connection is made with reproductive success in the biosocial account (Wood & Eagly 2002, p. 704). Instead, the terms “cost” and “benefit” refer to individual utility maximization (Wood & Eagly 2002, p. 719), which is more in line with their meaning in the social sciences, to indicate that individuals are behaving according to their own estimation of the outcomes of their actions (e.g., Kirkpatrick & Epstein 1992; Tedeschi & Felson 1994). The developmental processes identified in social role explanations are largely those described in social learning accounts of how socialization produces sex-typed behavior. This was the initial focus of psychological explanations of sex differences in behavior, and gender roles were an important feature of these (e.g., Maccoby & Jacklin 1974; Sears et al. 1965). Social role theory incorporated social learning (e.g., Bandura 1973; Bussey & Bandura 1999; Perry & Bussey 1979) as one of one of several processes underlying the social transmission of gender roles (Eagly 1987, p. 31; Eagly et al. 2004, p. 270; Wood & Eagly 2002, p. 717). According to social learning theory, gender-typed behavior occurs as a result of the incremental effects of influences by parents, teachers, peers, and the media on the children’s developing self-concepts, beliefs, and motives (Leaper & Friedman 2007). A variety of processes studied by social psychologists have been identified as underlying the way that shared characteristics of roles influence men’s and women’s behavior (Eagly et al. 2004). These can be regarded as the proximate causes of sex differences in social behavior. They include expectancies, situational contingencies, incorporation into self-concepts, and the acquisition of different skills and beliefs. One straightforward way that gender roles may influence behavior is through the internalization of gender-stereotypic traits (Eagly 1987), whose content is derived from roles, in the form of feminine communal traits (e.g., helpful, kind, nurturant), and masculine agentic traits (e.g., dominant, self-reliant, aggressive). The traits are not only internalized but also operate externally as expectations of behavior by men and women. Later versions of social role theory (Eagly et al. 2004, p. 280; Wood & Eagly 2002, pp. 701– 702) also included neuroendocrine mechanisms. It is known that a range of hormones, principally those concerned with reproduction, and with stress reactions, are responsive to inputs from the social environment. For example, testosterone levels respond to sexual stimuli, the outcomes of competition, and fatherhood (Archer 2006b). Wood and Eagly (2002) interpreted these as reactions to the demands of social roles. In social role accounts, within-sex variations in sextyped behavior can arise in several ways. One of these is through differences in the extent to which individuals

internalize the gender roles of their society (Eagly et al. 2004, p. 280). Another is through the operation of specific roles, for example, family and occupational roles. Social role accounts also predict when external circumstances would accentuate or diminish sex differences. When gender roles are made more salient, the magnitude of the difference should increase. We would also expect sex differences to be influenced by variations in gender roles across cultures or historical times. Eagly and Wood (1999) found that sex differences in mate preferences were larger in nations where gender roles were more traditional. Attitudes among college students changed from 1970 to 1995, in the direction of more frequent endorsement of equal rights for women (Twenge 1997a), and in accordance with this, women’s own endorsement of agentic traits also increased over these years (Twenge 1997b). 2.2.2. Social role theory applied to human aggression.

According to the original social role theory (Eagly 1987, pp. 71 –73), sex differences in aggression occur because aggressiveness is a component of masculine roles, and because traditional feminine roles discourage it, although both sets of roles involve norms that encourage and discourage aggression under different circumstances. Specific masculine roles, such as the military, and training in skills for physical aggression, further accentuate the sex difference. The higher societal status of men provides another route to greater direct aggression, since people perceive higher status to be associated with agentic characteristics (Eagly & Steffen 1984). Social role analyses view status as one attribute of gender roles, although others distinguish between roles and status as influences on sex differences (e.g., Conway et al. 2005). The original social role theory (Eagly 1987) predicted that men should be more aggressive than women, to a moderate extent, consistent with other sex differences in social behavior. Although the main research on indirect aggression had not yet been published, Eagly (1987) distinguished physical from psychological aggression in relation to experimental studies. The first was defined as producing physical harm and the second psychological or social harm, including what was later termed indirect or relational aggression (Archer & Coyne 2005). Like sexual selection, social role theory predicts larger sex differences for physical than psychological aggression, on the basis that physical aggression is more clearly linked with masculine roles. Social role theory makes no specific predictions about anger, although the emphasis on sex differences in aggressive responses to anger-arousing situations implies that it predicts no difference in anger. There is usually no explicit treatment of when sex differences in aggression are first expected to appear in socialization accounts, and no indication of their subsequent progression, since the emphasis is on the mechanisms underlying gender-differentiated behavior. However, in view of the cumulative nature of the processes of learning, it is reasonable to expect, as others have (e.g., Baillargeon et al. 2007; Tremblay et al. 1999), that aggression should increase with age through childhood, and that this will be more marked for boys than for girls, leading to larger sex differences in aggression with age throughout childhood. From this, we would expect a gradual onset of sex differences, and aggression in general, during early BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Archer: Sex differences in aggression childhood, consistent with a gradual and cumulative learning process (Keenan & Shaw 1997; Tieger 1980). From social role theory, we would expect internal mediators of sex differences in aggression to follow general and specific features of gender roles. General features would be the internalization of masculine or agentic traits, which includes those associated with aggression. Variables such as empathy, fear of retaliation, and guilt and anxiety associated with the consequences of aggression, have been viewed as mediators of women’s lower levels of aggression, as consequences of internalized gender roles (Bettencourt & Miller 1996; Eagly & Steffen 1986). In the biosocial account, neuroendocrine mechanisms are viewed as playing a different role than in sexual selection explanations. They are the consequences of role-related activity, which may then help to orient men and women to role-related activities. In social role accounts, within-sex variability in aggression would arise from differences in the internalization of gender roles, and in the adoption of specific roles. Variability as a consequence of different environmental conditions would largely follow variations in the extent to which gender roles are operating. Decreasing the salience of gender roles should lead to a much reduced sex difference in aggression (Eagly & Steffen 1986; Lightdale & Prentice 1994). We would expect larger sex differences in nations with more traditional gender roles, and for the difference to have declined over the last 50 years in Western nations, in accordance with the increase in gender role equality. Table 1 also provides a summary of the main predictions set out in this section, together with the sections that consider the evidence relating to them. 2.3. Sources of evidence

Much of the evidence discussed in the following sections is taken from meta-analyses of sex differences in aggression, which provide systematic summaries of several hundred research reports, involving observations, and reports from self, peers, and teachers, of “real-world” aggression, and experimental studies, both laboratory and naturalistic. Self-reports and experimental studies mainly involve adults, whereas the other methods involve children. The findings are reported for the different types of aggression, and for different measurement methods (Table 2). The values are Cohen’s d, which is the difference between male and female mean values, standardized in units of the overall standard deviation. If positive, it represents a higher value for males, and if negative it represents a higher value for females. The types of aggression sampled in these analyses were physical, verbal, and indirect, and one analysis of self-reported trait anger (Table 2). The methods used in laboratory and field experiments are not directly comparable with those used in the “realworld” studies, and the effect sizes for the sex differences tend to be smaller (Archer 2004), but they provide a useful alternative to self-reports for adult ages where observations and peer reports are no longer practical options. Self-reports (194 samples: Archer 2004), typically involve young adults. Laboratory and field experimental studies (50 samples: Eagly & Steffen 1986; 107 samples: Bettencourt & Miller 1996) are likely to include a high proportion of college students. In Archer’s (2004) meta-analyses, there 254

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Table 2. Sex differences in types of aggression for different methods of assessment Method and study

Physical

Verbal

Indirect

Experimental (Eagly & Steffen 1986) Experimental (Bettencourt & Miller 1996) Self-reports (Archer 2004) Observations (Archer 2004) Peer-reports (Archer 2004) Teacher-reports (Archer 2004) Combinedb (Knight et al. 1996) Combinedb (Knight et al. 2002)

.40

.18

.48

.36

.59

.19

.55

.09

2.45

.80

.55

2.10

.33

.24

2.21

.91

.46

.59

.28

.05a

Anger

.035

2.07

Note: Values are weighted mean effect sizes (d). d values from Archer’s studies are those with outliers removed. a This value excludes values from the indirect hostility scale of the Buss-Durkee Hostility Inventory, which measures a composite of indirect and displaced aggression (see Archer 2004). b This category refers to a combination of measurement methods (all of those listed above, and projective methods in the case of the 1996 source). The 1996 source was a reanalysis and extension of a previous analysis (Hyde 1984; 1986).

are 64 samples using observations, with an age range of 1.8 to 13.2 years; 51 samples using peer reports, with an age range of 5 to 17 years; and 40 samples using teacher reports, with ages ranging from 3 to 15 years. Most studies are from the United States, although self-report studies come from 23 other countries. These summaries of sex differences in aggression refer to measures for which the sex of opponent is unspecified. Observational studies of children4 that do not specify the sex of the opponent are likely to involve same-sex encounters, since children tend to interact in sex-segregated groups (Archer 1992a; Maccoby 1988; 1998; Pellegrini 2004). Self-report methods for studying adults’ aggression do not typically specify the sex of the opponent. Where they do (Gergen 1990; Harris 1992; Hilton et al. 2000; Richardson & Green 1999), the values for same-sex physical aggression are very similar to those found in general questionnaires, and the values for opposite-sex encounters are in the female direction, consistent with findings for physical aggression to an opposite-sex partner (Archer 2000a). It is therefore reasonable to conclude that general questionnaires are largely measuring same-sex aggression (Archer 2000; 2000b; 2004).5 Meta-analyses have the advantage of precision, but they are limited to the data-bases used, which are typically from studies of aggression between individuals in Western societies. Evidence from other sources is therefore included, for example, criminological sources in relation to changes with age (sect. 2.5), and psychological studies for possible causal mechanisms (sect. 2.6).

Archer: Sex differences in aggression 2.4. Overall pattern of sex differences in aggression

The overall pattern of sex differences in aggression enables an assessment to be made of the prediction, from sexual selection, that the magnitude of the sex difference will follow the cost or danger involved. Thus, higher d values in the male direction are expected for physical aggression, a lower one in the male direction for verbal aggression, no sex difference or one in the female direction for indirect aggression, and no sex difference in anger. Table 2 shows the values for the three forms of aggression, for various measurement methods, and for trait anger. Across a range of measures at different ages, d values were higher for physical than for verbal aggression, which were still consistently in the male direction, whereas those for indirect aggression were in the female direction in childhood and adolescence, and very slightly in the male direction for adults. Values for the selfreported experience of anger were around zero, indicating no sex difference, which is consistent with the results for anger in a meta-analysis of temperament in childhood (Else-Quest et al. 2006). These findings support the view that the magnitude of sex differences follows the degree of immediate risk the actions entail (Archer 1994; Bjo¨rkqvist 1994). Statistics on the proportion of men and women using weapons, and killing members of their own sex, are also consistent with this position. In several surveys of United States youth, reported in Archer (2004), 80% of those who reported carrying a weapon were male. Aggregating data from 20 studies of nearly 14,000 same-sex homicides (Daly & Wilson 1990) showed an even higher sex difference, with 97% of the perpetrators being male. Of the meta-analyses listed in Table 2, only Archer (2004) sampled studies outside North America, and most studies in this analysis did come from the United States. There were, however, sufficient studies from other nations to show that the effect size was consistently in the male direction for physical aggression across 13 nations for self-reports, 9 for observations, and 5 for peer reports. Practically all the nations involved were industrial states with an effective rule of law. Historical evidence indicates that, in pre-industrial societies, men have the capacity for intense inter-male competition, which is likely to take a physical form, whereas in modern industrial states they typically use other ways of competing for resources6 (e.g., Courtwright 1996; Daly & Wilson 1988; 2001; Eisner 2004). Another limitation of the meta-analytic evidence is the emphasis on aggression between individuals. There is little systematic evidence on relative male and female involvement in coalitional aggression, which also occurs in chimpanzees (e.g., Wilson & Wrangham 2003). It has been greatly extended in humans, in the form of raiding parties, primitive warfare in pre-industrial societies (Keeley 1996), gangs, organized crime, and the military in modern nations. These are all activities typically involving men. Keeley (1996) concluded, from several extensive cross-cultural surveys, that in non-state societies, intergroup warfare typically occurred more or less continuously, involving the mobilization of up to 40% of the male population, and the death of around 30% of the young men. It is possible that, as a consequence of their participation in group aggression, men’s behavior and

cognition are more intergroup-oriented than women’s (van Vugt et al. 2007). Men (but not women) increased altruistic group contributions during intergroup competition (van Vugt et al. 2007), and they showed more risky decision choices when in the presence of other men (Daly & Wilson 2001). 2.5. Age trends in sex difference in physical aggression

In section 2.1.2, I indicated some broad predictions from sexual selection theory concerning the development of sex differences in aggression. They would not be solely determined by cultural learning throughout childhood; they would be subject to some biological developmental influence, either early in postnatal life, or at puberty; and they would be largest in young adulthood. From a socialization perspective, we would expect sex differences to be small or nonexistent at preschool ages (see Keenan & Shaw 1997), and to increase throughout childhood, reflecting the cumulative influences of gendered learning. Three lines of evidence show that the sex difference begins early in life, and can be substantial at young ages, supporting an evolutionary analysis (Bjorklund & Pellegrini 2000). First, individual observational studies (Table 3) show that sex differences in physical aggression are large early in life. Second, although Keenan and Shaw (1997) claimed that there was no sex difference in direct aggression for toddlers, on the basis of a narrative review of five observational studies, a meta-analysis of the same studies showed a significant difference (d ¼ .44; p ¼ .003: Archer & Coˆte´ 2005). Third, a longitudinal study of mother’s reports of children’s physical aggression at 17 and 29 months found sex differences at the first of these times, with no change in magnitude at 29 months (Baillargeon et al. 2007). The large-sample longitudinal study of Tremblay et al. (1999), represented in Figure 1 here, also found that the sex difference in physical aggression was present at 2 years of age, and that physical aggression showed a peak between 2 and 3 years of age, followed by a decline in the childhood years. They concluded that socialization must largely entail learning to inhibit physical aggression, rather than learning it from role models. A meta-analysis of age trends for self-reported physical aggression showed no increase from before to after puberty (6 – 11 years: d ¼ .56; 12– 17 years: d ¼ .46: Archer 2004), coincident with the action of testosterone on reproductive physiology and secondary sexual Table 3. Sex differences in physical aggression in four observational studies at young ages Study

Sample

Mean age (yr)

d value

Sears et al. (1965) McGrew (1972) Hay et al. (2000) Campbell et al. (2002)

40 30 66 56

4 4 2 2.3

1.27 1.29 .66 1.42a

Note: d values were calculated using DSTAT (Johnson 1989), and have previously been used for a meta-analysis (Archer 2004) or reported in a book chapter (Archer & Coˆte´ 2005). a This value was for “grabbing another child’s toy.”

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Archer: Sex differences in aggression

Figure 1. Changes in physical aggression of boys and girls with age (mothers’ reports). Source: Tremblay et al. (1999).

characteristics (Tanner 1989). Consistent with this, several longitudinal studies showed no increase in aggression for boys at puberty, and two others showed no link between testosterone levels and physical aggression at puberty (Archer 2006b). Crime figures from a variety of historical times and cultures (Courtwright 1996; Daly & Wilson 1990; 2001; Eisner 2003; Quetelet 1833/1984), show that men’s involvement in violent crimes, and in same-sex homicides, is highest between the ages 18 and 30 years. This is as expected if they represent reproductive competition that is delayed until men have attained optimum size and strength (sect. 2.1.2). Effect sizes for sex differences in self-reported physical aggression are also largest in the 18 –21 and 22 – 30 age categories (Archer 2004).

2.6. Mediators of sex differences in physical aggression

The implications of sexual selection for the mechanisms underlying sex differences in aggression are that they are likely to involve sexually dimorphic neuroendocrine mechanisms, and that they will be concerned with variables such as risk-taking, lack of inhibition, or fear of physical harm (sect. 2.1.2). The available evidence (sect. 2.5) did not support the view that male escalated aggression arises at puberty as a result of increased testosterone levels. Nevertheless, temporarily raising a woman’s level of testosterone to that of a man enhances her cardiac defense reflex to angry (but not other) faces, in a masked Stroop test (van Honk et al. 2001). The rationale behind this procedure is that a greater initial reaction to an angry face is associated with threat rather than appeasement responding (Putman et al. 2004). A subsequent functional MRI (fMRI) study (Hermans et al. 2008) showed that in response to an angry face there was extensive activity in a range of cortical and subcortical brain areas known to be associated with aggression in nonhuman mammals. Further, administering testosterone affected the responses in these areas, primarily by increasing the excitability of subcortical structures involved in regulating aggression. Further studies have shown that laboratory measures of two suggested mediators of the sex difference in aggression, fear and empathy, are also reduced by administering testosterone to women (Hermans et al. 256

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2006a; 2006b). These findings seem to indicate a direct influence of testosterone on brain mechanisms underlying aggression, at least in one specific aggression-related measure, and also an influence on two attributes that may mediate direct aggression. It is not easy to see how this research fits with the lack of a testosterone-induced increase in aggression at puberty, or the evidence that sex differences in aggression begin early in life. It may be that the brain areas are affected by pubertal testosterone, but that they only gradually manifest themselves in overt behavior over subsequent years. Evolutionary analyses (sect. 2.1.2) emphasize greater risk-taking by males than females as underlying the differences in their aggression. Overall, men show more risktaking than women (Byrnes et al. 1999), although the sex differences are greater for certain types of risk: Effect sizes are highest for risks such as driving, drug and alcohol use, gambling, and everyday risks such as crossing a road (Byrnes et al. 1999; Daly & Wilson 2001; Harris et al. 2006; Pawlowski et al. 2008; Zuckerman & Kuhlman 2000). A mediator of these differences may be a sex difference in a related characteristic, such as fear (Byrnes et al. 1999; Campbell 1999), impulsivity (Campbell 2006), or sensation-seeking (Wilson & Daly 2006; Zuckerman 1994; Zuckerman et al. 1993). A study by Harris et al. (2006) suggests that several variables may underlie men’s greater risk-taking: Men anticipated being less upset or harmed by possible negative outcomes; they judged negative consequences as being less likely to occur; and they reported higher enjoyment of risky activities. Applied to physical aggression, that would mean women anticipate greater harm from its consequences, which is highlighted in Campbell’s (1999) evolutionary analysis and in social role theory (Eagly & Steffen 1986). Women would also view such negative consequences as being more likely to occur, and show less enjoyment of physical aggression than men: This would fit the very large sex difference found for children’s enjoyment of physical aggression (Benenson et al. 2008). Campbell (1999; 2006) argued that higher levels of fear experienced by women in confrontational situations could mediate the sex difference in physical aggression. Consistent with this, the sex difference in fear occurs at an early age (Else-Quest et al. 2006), and is pronounced in situations involving physical danger. In experimental studies of adults (Bettencourt & Miller 1996; Eagly & Steffen 1986), the sex difference in aggression was higher under conditions of greater danger. Campbell (2006) also considered a related process, effortful control, as another possible mediator of sex differences in physical aggression. This is the ability to suppress a dominant (and immediately attractive) response in favor of a subdominant (and later beneficial) one. It shows a large sex difference in favor of girls from early in postnatal life (Else-Quest et al. 2006). Social role theory predicts that sex differences in aggression will vary according to a number of external and internal variables associated with gender roles. Both guilt and anxiety about others’ suffering, and exposure to danger to the self, are important aspects of internalized gender roles, corresponding to the fear and risk-taking identified in evolutionary analyses, and to empathy, which also features in evolutionary accounts. Eagly and Steffen (1986) found that women viewed their aggression as more likely to pose a danger to themselves than men

Archer: Sex differences in aggression did, and the extent of the perceived danger predicted the magnitude of the sex difference. Meta-analyses of experimental studies (Bettencourt & Kernahan 1997; Bettencourt & Miller 1996; Eagly & Steffen 1986) found that women showed more empathy with the victim of their aggression (i.e., more anxiety and guilt after aggressing), than men did. For empathy to act as a mediator of the sex difference in physical aggression, it would have to operate to a greater extent as the level of escalation increased, as indeed it could as the consequences for the other person will be greater. It would have to be minimized in cases of indirect aggression, where the victim’s emotional distress may be less apparent. It would also have to be lessened for aggression between partners where there is no sex difference in physical aggression in Western nations (sect. 4). This would be possible in cases where male suffering is minimized or disregarded (Felson 2002). Another aspect of social role theory concerns the expectancies associated with status differences between men and women. These expectancies can either be internalized or reside in the others’ expectations. Conway et al. (2005) found that expectancies for men’s and women’s aggression were similar to those for people differing in status. Lowstatus individuals were, like women, viewed as experiencing more guilt and anxiety, and causing less harm by aggressing, than were high-status individuals. Low-status individuals were also viewed as less physically aggressive. This study concerned the expectancies attributed to people by others. If they also represent internalized expectancies, as suggested by social role theory, they could guide the behavior of men and women, and therefore act as mediators of sex differences. One problem with this view is that cross-cultural and historical evidence has repeatedly shown that lowerstatus individuals with little to lose are those who are most inclined to engage in physical aggression (sect. 2.7). Possible mediators of sex differences in aggression need to be viewed in terms of their social and developmental context, as contributors to the outcome of a developmental sequence arising from the interaction of internal and external influences. Individual components coalesce to produce the typical outcome only when embedded in a typical male or female sequence of development. For example, it is possible that prenatal testosterone alters predispositions for fear of physical danger, and for activity and play preferences, which manifest themselves in overt behavior only through interactions with other boys. The behavior so produced would then become viewed in terms of the gender roles operating in that culture, which will themselves influence behavioral development. Similarly, testosterone secretion at puberty may produce the dispositions shown in laboratory studies, but these produce sex differences in escalated physical aggression only under the social conditions that are manifest in early adulthood. Such specific dispositions will also be subject to activating and inhibiting social influences operating throughout development. For example, a culture that emphasizes the need to respond to the slightest provocation (the “culture of honor”: sect. 2.8) is activating, and an effective rule of law is inhibiting. This perspective on mediators of sex differences in aggression involves social roles as both emerging from the interaction of dispositions and the social environment, and also feeding into this process.

2.7. Within-sex individual differences in physical aggression

A prediction derived from sexual selection is that, in species where there is parental investment, there will be individual differences among males reflecting a different emphasis on mating or parental effort. A number of studies show that individual differences in measures indicative of mating versus parental effort are associated with testosterone levels (Archer 2006b), and with a range of antisocial activities and behavioral and personality variables, including dominance and aggressiveness. These appear to be long-term dispositions, present before puberty. Such individual differences among males will lead to greater variability among males than females in traits such as physical aggression, but not in those on which the sexes do not differ, such as anger and self-esteem. Archer and Mehdikhani (2003) tested this prediction in a sample of questionnaire studies, and found that male variability was indeed significantly greater than female variability for physical aggression but not for anger or self-esteem. Although these findings are consistent with the hypothesis that individual differences reflect variability in male mating strategies, a more direct test is needed to establish whether this is the case. Social role theory makes no comparable predictions of differences in within-sex variability in aggression. It does identify a number of variables that will produce withinsex variability in both sexes. One is the different extent to which people internalize gender role norms (Eagly et al. 2004, p. 280). Consistent with this, self-reported physical aggression was highly correlated with agentic traits among a sample of men (Archer, submitted), and three other studies have found low to moderate associations between a measure highly related to self-reported aggression and endorsement of gender role traits (Campbell & Muncer 1994; Campbell et al. 1993; Thanzami & Archer 2005). Specific gender-related roles provide another influence on within-sex variability: Campbell and Muncer (1994) found that occupation (soldier or nurse) was a better predictor of a person’s attributions about his or her own aggression than was the person’s sex.

2.8. Variability in sex differences in aggression in response to environmental conditions

Sexual selection predicts variability in response to conditions that affect the extent of inter-male or interfemale competition, notably resources that are important for reproduction, such as access to mates, and the status and resources important in this process. Consistent with this, violence is higher among men who have few economic resources or prospects (Courtwright 1996; Daly & Wilson 1988; Eisner 2003), and is lower among married men than those who are single, divorced, or widowed (Daly & Wilson 2001). In an analysis of Japanese homicide figures, Hiraiwa-Hasegawa (2005) found that the rate of homicides by young males had declined considerably since 1955, and that this coincided with smaller families, an increase in GDP per person, and a high proportion of young adults in education, all indicators of greater resource availability. The annual rate of homicides for young males from 1960 to 1996 was inversely related to BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Archer: Sex differences in aggression college enrollment and the degree of financial equality in the society. These influences are very different from those found to account for the more limited decline in violent crime in the United States in the 1990s (Levitt 2004), but are similar to the likely causes of the longer-term large decline in violent crime since the fifteenth century in Europe (Eisner 2003). A simple prediction from the concept of Operational Sex Ratio (OSR; Emlen & Oring 1977), the ratio of sexually active males to fertilizable females in the population (sect. 2.1.1), is that inter-male competition will be intensified where there are a greater number of males of reproductive age. Hudson and Den Boer (2002; 2004) showed from historical records that where there had been high male-biased sex ratios (e.g., in nineteenth century China and medieval Portugal), there was social unrest, individual and collective violence, and expansionist military campaigns. The consequences of a low OSR were indicated by Campbell (1995), who reported localized high rates of physical aggression among young women where a large proportion of young men were not regarded as suitable mates as they had debilitating drug habits. Schuster (1983; 1985) also documented escalated female aggression in Zambia and in China when there was competition for desirable men. In these examples, environmental conditions accentuate the relative benefits of successful direct competition. In other cases, social forces operate in the opposite direction. One that has been particularly important in human history is the effectiveness of a rule of law. Where this makes men secure in their own safety and the security of their property, the costs of ignoring a challenge will be relatively low. There are also likely to be benefits from this course of action, such as avoiding injury and legal penalties. When there is no effective rule of law, and a man’s possessions and livelihood can readily be taken by force, the costs of ignoring a challenge will be high. Consequently, establishing a reputation for effective retaliatory power is necessary, and not to do so is to risk one’s personal safety, possessions, and family. A “culture of honor” (Nisbett & Cohen 1996) emerges under these circumstances. Social role theory predicts that there will be variations in sex differences in aggression accompanying differences in the salience or nature of men’s and women’s roles. Since provoked aggression is viewed as justified aggression, this justification was regarded as freeing women from the constraints normally imposed by gender roles (Bettencourt & Miller 1996). Consistent with this, experimental studies showed a smaller sex difference in aggression when participants were provoked (Bettencourt & Miller 1996). Another influence on the salience of roles is whether the behavior occurs in public or private settings, although the prediction that roles are more salient in public is complicated by the varied effects of different audiences: Experimental findings were ambiguous on this issue (Eagly & Steffen 1986). One particular study was regarded by its authors, and by Bettencourt and Miller (1996), as specifically supporting a social role explanation of sex differences in aggression. Lightdale and Prentice (1994) experimentally reduced role salience by creating a sense of anonymity and unaccountability regarding the opponent in a video-game task involving dropping bombs on an opponent following provocation. There was a striking reversal of the usual sex difference under these conditions (d ¼ 2.41, from the 258

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authors’ Table 3) compared with those in which opponents were identifiable and known to one another (d ¼ .92). A more recent study (Evers et al. 2005) reported similar findings, but explained them in terms of the social appraisal of emotions rather than role salience. Men showed a higher aggressive response than women did when they expected to meet the person who had angered them (d ¼ 2.42, from the authors’ Table 2), but there was no sex difference (d ¼ .11) when people believed they would not meet the person who had angered them. An alternative explanation for both findings would be that the aggression required under the anonymous condition is indirect aggression, involving a lesser likelihood of anticipated retaliation (Bjo¨rkqvist 1994). This would link the findings to a larger set of studies on indirect aggression (Archer & Coyne 2005), and to Campbell’s (1999) evolutionary view that emphasizes women’s greater anticipation of negative consequences for their direct (but not indirect) aggression. Social role theory predicts that sex differences will be larger when more traditional gender roles operate (e.g., Eagly & Wood 1999). Although sex differences in physical aggression are available for a variety of countries (Archer 2004), and all show a difference in the male direction, they could not be used to test this prediction as the measures and samples were inconsistent. Lippa (in press) assessed the association between the relative empowerment of women in different nations and sex differences in the personality trait agreeableness, which is inversely related to aggressiveness (Gleason et al. 2004; Sharpe & Desai 2001). He found lower sex differences where there were more traditional gender roles, the opposite of that expected if sex differences were accentuated by more pronounced gender roles. Another prediction from social role theory is that there would be a lowering in the magnitude of sex differences in physical aggression coinciding with changes in gender roles in North America since the 1960s (Twenge 1997a; 1997b). Although there is no direct evidence on this, sex differences in the related characteristics of assertiveness and dominance did decrease during this time period (Twenge 2001). Women’s assertiveness and dominance rose and fell over a longer time period, from 1931 to 1993, in accordance with changes in women’s status and roles. From 1968 to 1993, there was a change in the sex difference in assertiveness from a moderately higher level in men (d ¼ .40) to a slight female advantage (d ¼ 2.07). A direct investigation of changes over time in women’s aggression in relation to changing roles is hampered by the lack of consistent measures and the availability of studies throughout the whole time period. 2.9. Conclusions for sex differences in aggression between same-sex individuals

The evidence reviewed in section 2.4 supports the first prediction from a sexual selection analysis that sex differences in aggression will increase in magnitude as the form of aggression becomes potentially more costly. Thus, physical aggression shows a substantial effect size in the male direction; verbal aggression a smaller one in the male direction; indirect aggression shows no sex difference, or is in the female direction; and there is no difference in anger. Weapons use and homicide statistics show

Archer: Sex differences in aggression even larger sex differences. The social role prediction that sex differences in aggression should be modest applies only to its less damaging forms, although social role theory does predict differences in effect sizes between physical and indirect aggression. Sexual selection provides a better fit with the overall pattern of greater sex differences for more risky and costly forms of aggression. The finding that a sex difference in physical aggression occurs early in postnatal life, together with an increase in the magnitude of the sex difference in young adulthood, when there are also very large sex differences in violent crime and homicide, fits one of the two patterns expected from sexual selection. There is no evidence of an increase in aggression coinciding with puberty. The absence of a progressive increase in the size of the sex difference in physical aggression during childhood is inconsistent with an explanation in terms of the gradual differential learning of aggression by boys and girls, inferred from social learning accounts. From sexual selection, we would expect mediators of the sex difference in aggression to follow functional principles, such as greater risk-taking by males and/or greater fear of physical danger by females. Although there are currently no direct tests of these as possible mediators, indirect evidence showed sex differences in these variables, consistent with this prediction, and some evidence that they were influenced by testosterone. Both greater risk-taking by men and fear of physical danger by women also feature as possible mediators in social role accounts, in this instance connected to masculine and feminine roles. I have outlined a developmental perspective that encompasses biological dispositions interacting with the social environment, with the resulting outcomes being reflected in social roles, which in turn influence the process of development. There is evidence consistent with the prediction that there would be a coherent set of individual difference variables among males, reflecting greater specialization for mating versus parental effort. These variables are associated with testosterone levels. The greater variability in men’s than women’s physical aggression levels also supports this prediction. Social role theory does not predict greater variability for males than females. However, there is clear evidence that individual differences reflecting internalization of gender roles are associated with aggression-related measures, supporting predictions from social role theory. Context-dependent variability is approached differently by sexual selection and social role theory. A number of studies suggest that those with few resources are the most prone to physical aggression, and that differences in the operational sex ratio accentuate competition in the more numerous sex: both of these suggestions are consistent with sexual selection analyses. Social role theory predicts that sex differences in aggression will be absent when roles are not salient. Two experimental studies were apparently consistent with this prediction, although the findings could be explained in terms of aggression being indirect when the aggressor had no prospect of meeting the victim. A cross-cultural analysis of sex differences in the personality trait agreeableness (which is inversely related to aggression) produced findings opposite to those expected from social role theory. However, it is clear that agentic characteristics in general, and assertiveness in particular,

have changed in North America from the 1960s to the present, as gender attitudes became less traditional. 3. Evidence for an adaptive complex produced by inter-male competition 3.1. Overview

Section 2 indicated considerable evidence that was consistent with a sexual selection explanation of sex differences in aggression. In nonhuman mammals, greater male than female engagement in escalated aggression is typically accompanied by other sexually selected attributes, forming an adaptive complex associated with a polygynous mating system (Alexander et al. 1979; Clutton-Brock et al. 1977). This is characterized by higher male than female variance in reproductive success, which is equivalent to a measure of effective polygyny (Daly & Wilson 1983). I consider the evidence for this among humans in section 3.2. The adaptive complex (sects. 3.3 to 3.6), involves several features: (1) specializations for inter-male encounters, such as threat displays, involving visual and vocal signals; (2) larger size, musculature, and strength, among males than females; (3) longer maturation rates in males than females; (4) greater male than female mortality rates, during both immaturity and adulthood, accompanied by a greater number of males than females conceived. Section 3.7 concerns variability in mating systems in relation to the adaptive complex. 3.2. Polygyny and variance in reproductive output

From a comparative primatological perspective (Fuentes 1999), humans do not fit the criteria of a monogamous species, and cross-cultural surveys show the existence of polygyny in most pre-industrial societies (Alexander et al. 1979; Ford & Beach 1951; Murdock 1967). Alexander et al. (1979) argued that the widespread occurrence of monogamy in the world today is imposed on a more general pattern of polygyny, except in societies where ecological conditions are harsh. Betzig (1986; 1992) used historical sources to show that whenever there was political and economic inequality, as was generally the case in the large historical empires, mating was effectively polygynous, even if marriage was legally only monogamous. Thus, throughout recorded history, powerful men typically had a very high number of sexual partners (Betzig 1986; 1992), which until recent times was reflected in their numbers of offspring (Daly & Wilson 1988). This is maintained to some extent today. In modern Western nations where divorce is available, men who can afford a younger wife at the expense of an older one are likely to have the same effect on the variation in reproductive success as polygyny. In a study of a society where remarriage was common (Sweden), Forsberg and Tullberg (1995) found that remarriage produced increased numbers of offspring for men but not for women. Several studies of pre-industrial societies enable figures to be calculated for male and female variance in reproductive success. Variance ratios were: 3.1 for the Brazilian Xante Indians (Salzano et al. 1967); 1.77 for the Dobe !Kung (from Howell 1979, p. 269); from 2.02 to 4.69 for Yanomamo¨ (Chagnon 1979); and 2.76 for Aka pygmies (Hewlett 1988). All indicate effective polygyny. BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

259

Archer: Sex differences in aggression 3.3. Aggressive display features

Primate males typically show ritualized threat displays, and these are probably associated with the higher costs of male than female fights (Smuts 1987a). Throughout primates, male facial hair growth is associated with threat displays (Andersson 1994, p. 345), increasing the apparent size of the lower part of the face (Guthrie 1970). Consistent with this are suggestions that the male beard is the consequence of selection for competition over rank and resources (Darwin 1871/1901; Guthrie 1970; Tanner 1989). The few empirical studies of this suggestion support it. Addison (1989) found that college students rated bearded men significantly higher than beardless men on aggressiveness, dominance, masculinity, and strength. Muscarella and Cunningham (1996) manipulated facial stimuli, and found that facial hair increased perceptions of aggression, although such faces were rated as less attractive and lower on social maturity. Sell (2006) argued that the human angry face is an adaptation to accentuate facial cues indicating size and strength. Consistent with this, people can predict the lifting strength of young men from their faces (Sell et al. 2009). This applied to faces from their contemporaries, students from the University of California, Santa Barbara (r ¼ .39 and .45), and from two South American Amerindian groups (r ¼ .52 and .47). Two features of the human face show sexual dimorphism, the brow ridges and the chin. Both are exaggerated in the angry face (Sell 2006): Ratings of “angry” and “masculine” were increased by lowering the brow ridges in androgynous prototypical faces with emotionally neutral expressions (Becker et al., 2007). It is likely that other sexually dimorphic features, such as neck size, contribute to male threat displays (Guthrie 1970), and that these constitute “honest advertisements” (Clutton-Brock & Albon 1979) of fighting ability. Weston et al. (2004, p. 416) referred to the paradox between “marked body size dimorphism, suggestive of strong sexual selection” in the human line and the absence of larger male canines, the other feature associated with inter-male competition in primates. Their analysis of 14 species of New World monkeys and apes showed that canine dimorphism is negatively correlated with another sexually dimorphic feature, facial width-toheight ratio. They argued that contrary to the absence of canine dimorphism being a sign of weak sexual selection, it is associated with strong selection for this alternative feature. Their subsequent analysis of a series of human skulls from infancy to adulthood confirmed that this is a sexually dimorphic feature in humans (Weston et al. 2007). Their preferred explanation was in terms of female choice, but a subsequent study of three samples of young men (Carre´ & McCormick 2008) found that facial width-to-height ratio is associated with aggressiveness, suggesting that it may be a further cue for coercive power, or possibly for dispositional aggressiveness. A range of male vertebrates use vocalizations as threat displays (e.g., Clutton-Brock & Albon 1979; Davies & Halliday 1978; McElligott et al. 1999; Mager et al. 2007), and these generally indicate fighting ability, or Resource Holding Power (RHP; Parker 1974a), which can be used to decide whether or not to fight. In human males, two changes occur to the voice at puberty, a lowering of the fundamental frequency, and a descent of the larynx, 260

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resulting in lowered formants and less formant dispersal. Evans et al. (2006) found that the first was associated with measures of shoulder-to-hip ratio, and the second with body size and shape. Artificially lowering the pitch of a man’s voice increased ratings of his fighting ability by other men (Puts et al. 2006; 2007). Men who regarded themselves as physically dominant lowered their voice pitch in a competitive situation (Puts et al. 2006). These studies are consistent with the view that the deepness of the male voice is also an “honest advertisement” (Clutton-Brock & Albon 1979) of fighting ability. In a hunter-gatherer group, men with deeper voices had higher reproductive success than those with higherpitched voices (Apicella et al. 2007). 3.4. Size and strength

Although females are larger than males in most animals, larger male size is typical of mammals (Andersson 1994; Darwin 1871/1901; Lindenfors et al. 2007). Human males are on average taller, weigh more, and have greater strength and musculature than human females. Alexander et al. (1979) summarized data from 93 societies from the ethnographic record, in terms of the ratio of male-to-female height. On average, men were 7.6% taller than women, with a variation of 4.7% to 11.6% between societies. A large-scale study using data from North Indian migrant workers from 1842 to 1916 found values of 7% to 8% for ages 15 to 40 years (Brennan et al. 1997). Data from nineteenth century British Columbia produced values ranging from 6 to 10% for seven adult age categories (Hall 1978). More recent evidence shows similar differences in the United States, Switzerland, and China. Effect sizes calculated from these studies are very large (Hall 1978: d ¼ 2.67; Kyle et al. 2005: d ¼ 1.78 to 1.85; Lindle et al. 1997: d ¼ 1.14; Luk et al. 2003, d ¼ 5.95; Pheasant 1983: d ¼ 1.07; Xiao et al. 2005: d ¼ 2.24). Men are around 25% heavier than women of a similar age, and these are large differences when expressed as effect sizes (Kyle et al. 2005: d ¼ .87 to 1.79; Lindle et al. 1997: d ¼ .60; Luk et al. 2003, d ¼ .78; Pheasant 1983: d ¼ 1.15; Xiao et al. 2005: d ¼ 1.30). Sex differences in fat-free body mass are even larger, with effect sizes reaching d ¼ 2.36 for a U. S. sample and d ¼ 3.46 for a Swiss sample (Kyle et al. 2005), with the male-to-female ratios reaching 1.40 in the Swiss sample and 1.43 in the U. S. sample, Across 112 studies, Pheasant (1983) found that women’s mean strength was 61% of that of men. Other studies have found similar or higher values (e.g., Battie´ et al. 1989; Luk et al. 2003; Xiao et al. 2005), with d values from 1.45 to 3.09, depending on the sample and the strength measure (Battie´ et al. 1989; Xiao et al. 2005). Compared to women, men also have larger hearts and lungs, higher systolic blood pressure, lower resting heart rate, greater oxygen-carrying capacity, and greater ability to neutralize the products of muscular exertion (Tanner 1970). These studies indicate considerable sex differences in muscle mass and strength, although they are smaller than in highly polygynous primates, where the male-to-female body mass ratio is above 1.5 (Plavcan 2000, p. 331; Plavcan & Schaik 1997a). In humans, it is assumed that both paternal investment (Geary 2000) and male-male coalitions (Geary et al. 2003) have lessened the impact of inter-male competition, and with it the degree of dimorphism in strength

Archer: Sex differences in aggression and size, compared to more polygynous ancestral species. Estimates of the male-to-female body mass indices for Australopithecines range from the oldest, A. afarensis, at 1.52, to the more recent A. africanus, robustus, and boisei at 1.32, 1.26, and 1.40 (Plavcan 2000), which are similar to chimpanzees at 1.30 (Plavcan & Schaik 1997a), but not much more than modern humans. If, as McHenry and Coffing’s (2000) analysis indicates, the decreased dimorphism from Australopithecines to modern humans resulted from a relatively greater increase in female than male size, this suggests that it did not reflect a lessening of inter-male competition. However, all estimates of dimorphism in extinct hominids rely on fragmentary fossil remains (Plavcan & Schaik 1997a), and should therefore be treated with caution. 3.5. Maturation rates

A further characteristic of sexual selection is bimaturism, males starting to reproduce at a later age than females. Andersson (1994) suggested that this occurs where size is important for inter-male competition: by delaying reproduction, males can avoid risky fights with older, larger, males. This reduction in male competition will have the effect of reducing the OSR (sect. 2.8), one consequence of which is to increase the degree of polygynous mating (Clutton-Brock & Harvey 1977). Boys take around two years longer than girls to reach puberty (Tanner 1989), and a difference in maturation is apparent early in life: half-way through the fetal period, girls are three weeks ahead of boys (Tanner 1989). 3.6. Mortality and conception rates

Higher male than female mortality occurs in humans throughout life, both as result of greater male vulnerability to disease, stress, and injury, and higher risk-taking and violent behavior by men. Although the specific causes of death have changed throughout human history, and vary under different environmental conditions, the typical end result is greater male mortality (Kruger & Nesse 2006), through a combination of greater engagement in risky activities and higher disease susceptibility. Analyzing mortality rates in U. S. statistics for 2000, at five-year intervals throughout the lifespan, Kruger and Nesse (2006) found that the peak male-to-female mortality ratio (M:F MR) was in young adulthood (20 –24 years), when the overall value was 3.01, and it declined thereafter. The curve for changes in the M:F MR with age was very similar to that for the age-crime curve. The ratio tended to be higher throughout life for external causes, whose peak value was 4.03, again during the 20 –24 years age group. Kruger and Nesse also calculated M:F MR for a sample of chimpanzees and generally found higher values for males across the lifespan (1.43), again with a pronounced peak in young adulthood. Analysis of figures for Ache hunter-gatherers, where homicide was a major cause of death, showed an overall value of 1.77, with the peak more evenly distributed throughout adult life. Accompanying the greater male mortality throughout life is an unequal sex ratio at conception, leading to equal numbers of males and females in young adulthood. At conception, the ratio has been reported as between 110 and 160 human males for every 100 females, reduced to 105:100 at birth (Shettles 1961). Alexander et al. (1979)

suggested that the sex ratio at conception reflects a long history of selection based on greater male than female mortality before maturity. 3.7. Ecological influences on mating systems and sexual dimorphism

The analysis by Emlen and Oring (1977) of the impact of environmental resources on mating systems (sect. 2.1.1) was applied by Alexander et al. (1979) to human mating systems. These authors did find that monogamous societies occurred in marginal or extreme habitats, as predicted, but that they also occurred in large and complex societies where monogamy was imposed as a form of social control. Alexander et al. (1979) created three categories, ecologically imposed monogamy, socially imposed monogamy, and polygyny, and applied these to 93 societies from the standard cross-cultural sample (Murdock 1967). They assessed the hypothesis that in the first of these, where nutrition is likely to be suboptimal, men will pursue a reproductive strategy involving greater parental than mating effort, which will be accompanied by reduced size and hence physical dimorphism. Their analysis of the ratio of maleto-female height was consistent with this, with mediumsized differences (d ¼ .58 and .63, from the authors’ tables 15.4 to 15.6) between the first and the other two categories. However, a re-analysis of these data, and an analysis of a larger sample of 237 societies (Wolfe & Gray 1982), showed that geographical region, rather than mating system, could account for the variation in height dimorphism across the societies. There were also problems with the measure of polygyny: When they used the original codes from Murdock (1967) for the larger sample of 216 societies, Gray and Wolfe (1980) found no association between polygyny and sexual dimorphism. Low (1988) used multiple existing assessments of the degree of polygyny in a standardized cross-cultural sample of 93 societies, to test a proposed link between polygyny and pathogen stress (following Hamilton & Zuk 1982). The reasoning was that when pathogen stress is severe, heritable pathogen-resistance will be a highly selected male trait. Pathogen-resistant males will therefore attract a disproportionate number of females, resulting in polygyny. Consistent with this, Low (1988) found a positive association between polygyny and pathogen exposure. A subsequent study (Low 1990) found the same association for all 186 societies in the ethnographic atlas (Murdock 1967). Whether these variations in polygyny are associated with variations in sexually selected features, such as height and aggression, remains to be assessed. 3.8. Aggression and the sexually selected adaptive complex

There are therefore a number of other features, besides aggression, that indicate the operation of sexual selection in humans. Greater variance in reproductive success for males than females indicates effective polygyny. There are vocal and facial features that indicate adaptations for threat displays in men, there is greater male size and strength, longer male maturation, higher male mortality, and a male-biased conception ratio. Taken together, these indicate a coevolved adaptive complex, associated with inter-male competition. BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

261

Archer: Sex differences in aggression The view that sex differences in size and strength are an evolutionary consequence of inter-male competition can be traced back to Darwin (1871/1901), and it has been a widely accepted view since then. Nevertheless, in their biosocial model (sect. 2.2.1), Wood and Eagly (2002) argued that a variety of selection pressures operating on females as well as males could explain these differences. Although animals do show a range of influences on size dimorphism (Andersson 1994; Ralls 1976; Selander 1972), a systematic review demonstrated the link between greater male size and success in fights and dominance contests in many animals (Andersson 1994). Plavcan and van Schaik (1997b) analyzed data from 86 extant anthropoid primates (New World monkeys and apes), finding that greater male-to-female size is associated with higher levels of inter-male competition (rs ¼ .73). This shows a clear association between size dimorphism and inter-male competition across nonhuman primates. There is also evidence that size and strength are positively associated with men’s history of physical aggression (Archer & Thanzami 2007; Felson 1996; Sell 2005; Sell et al. 2005; Tremblay et al. 1998). In terms of effect sizes, sex differences in features such as size and strength, and mortality, are considerably larger than those reported for physical aggression (sect. 2.4). For example, 90% of people can be classified successfully as male or female on the basis of their shoulder-to-hip width (Tanner 1989), or their lifting strength (Pheasant 1983), but the corresponding values from measures of physical aggression would typically be 62 to 73% (calculated from Rosenthal 1984, p. 131). These lower values may be because they are taken from people living in states with an effective rule of law, and who have alternative methods of competing, and because legitimized forms of aggression – for example, in the military, or in sports contests – are not included in these analyses (see Geary [1998] for further discussion of this point). If this is correct, such studies underestimate the magnitude of sex differences in aggression in other contexts. 4. Physical aggression between opposite-sex partners 4.1. Explanatory frameworks

So far, I have considered same-sex aggression, the focus of sexual selection and social role theory. In section 2.3, I indicated that the findings are different for aggression between members of the opposite sex. Most of the available data on physical aggression between opposite-sex adults involves married, cohabiting, or dating partners. Two main explanations dominate the literature. The patriarchal framework emphasizes the male nature of partner violence and views it as derived from the societal power of men, which is rooted in history (e.g., Dobash & Dobash 1977– 78; 1980; Walker 1989). This is a more limited explanation than social role theory, which seeks to explain the behavior of both men and women. In contrast, family relations researchers have been informed by large-scale surveys indicating that both sexes can be perpetrators and victims. Their accounts (e.g., Straus 1999; Straus & Gelles 1988) therefore emphasize influences on both sexes, involving the frustrations of everyday living, a view that coincides with social psychological analyses 262

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(Berkowitz 1993). Although the evidence strongly supports the family relations perspective, the patriarchal view is widely accepted by policy makers in Western nations. In considering physical aggression between partners, I first present the evidence, and then consider explanations based on evolutionary and social role theory, which in this case can complement one another. 4.2. Sources of evidence

Three meta-analyses systematically examined the evidence on sex differences in physical aggression between partners, and their consequences. The first (Archer 2000a) concerned the acts of physical aggression between partners, from self- and partner-reports and from composites of the two. Its aim was to assess whether men and women differed in the occurrence and frequency of any form of physical aggression. Most studies used the Conflict Tactics Scales (CTS; Straus 1979), which asks men and women to rate the frequency with which they have used and received various forms of behavior, including acts of physical aggression, in solving relationship conflicts. A second meta-analysis (Archer 2002) examined these acts separately, and a third (Archer 2000a) their consequences, in terms of the frequency of injuries. This was undertaken to assess whether the CTS underestimates the impact of partner violence on women because it concentrates on acts of aggression rather than their consequences. 4.3. Acts of physical aggression and their consequences

The mean weighted effect size for the sex difference in physical aggression, for composites of self and partner reports, was d ¼ 2.05, a very small, but statistically significant, effect in the female direction (Archer 2000a). Only 19 of the 82 studies involved interval-level data, although effect sizes in these were similar to those involving categorical data. The value for self-reports was slightly larger (d ¼ 2.12), and from partner-reports it was near to zero (d ¼ 2.016). The important conclusion is that even partner reports – those that are less likely to be subject to bias (Archer 1999) – do not show a sex difference in the male direction. For students in dating relationships, the sex difference was more in the female direction (d ¼ 2.10; k ¼ 42) than it was in community samples (d ¼ 2.03; k ¼ 27). In two samples of women from refuges for female victims of partner violence, reporting on their own and their partner’s levels of aggression, the difference was, as expected, very high in the male direction (d ¼ .86). Thus, concentrating on samples involving victims of domestic violence produces a sex difference in the male direction, which is different from that found in community samples. The second meta-analysis (Archer 2002) examined each item of physical aggression on the CTS to answer the question of whether men were more likely than women to show more-damaging acts, and women less-damaging acts. The data (from 58 studies) were in the form of proportions of men and women showing (and/or receiving) specific acts of physical aggression. Table 4 shows the effect sizes, and the proportions of those who showed each act that were men. For self-reports, women were significantly more likely to commit most acts of physical aggression.

Archer: Sex differences in aggression Table 4. Effect sizes for sex differences in acts of physical aggression to partners Act of aggression towards partner Threw something at Pushed, grabbed or shoved Slapped Kicked, bit, or hit with fist Hit or tried to hit with something Beat up Threatened with a knife or gun Used a knife or gun

Self-reports

Partner-reports

2.18 [.37] 2.03 [.49]

2.08 [.44] .09 [.54]

2.27 [.33] 2.20 [.35] 2.15 [.36]

2.15 [.41] 2.09 [.44] 2.08 [.44]

.03 [.55] 2.003 [.48]

.13 [.68] 2.05 [.42]

.005 [.52]

.015 [.53]

Figures are mean weighted d values from 58 studies, with the proportion that were men given in square brackets (Archer 2002). The items are derived from the Conflict Tactics Scale (Straus 1979).

Partner reports altered these figures slightly in the male direction. However, even “beat up” showed a substantial proportion of women perpetrators (self: .32; partner: .45). A third meta-analysis (Archer 2000a) assessed whether women sustain more injuries from a partner’s physical aggression than men do (as predicted by Dobash et al. 1992). Injuries were, as expected, more common among women than men. Although in the male direction, the effect size was small (d ¼ .08). The proportion of all those injured who were women was .62 for injuries, and .65 for those requiring medical treatment (corrected for unequal sample sizes). Similar proportions were found in the 1996 British Crime Survey (Mirrlees-Black et al. 1998), again indicating a significant proportion of male injuries.

4.4. Conclusions from the meta-analyses

These meta-analyses clearly indicate that, in general samples, there is little difference in the proportion of each sex using any act of physical aggression. A composite of the range of acts and how often they are used also showed little sex difference. Attacks that inflicted injuries were more likely to be perpetrated by men than women, but a significant minority of injuries was caused by women. The findings are inconsistent with the assumption that partner violence only involves men’s aggression, and therefore with explanations involving only patriarchal values. They are compatible with “gender-inclusive” explanations (Hamel & Nicholls 2007; Straus 1999; Straus & Gelles 1988) that link partner violence more with the types of psychological processes investigated by social psychologists, such as frustration, poor impulse control, personality profiles, and attachment styles, all of which apply to both women and men. The conclusion from these studies seems to be that there are no appreciable sex differences in physical aggression to opposite-sex partners, and therefore there is no need to look for ultimate explanations or for mediators. While this may seem a reasonable conclusion, the available evidence is derived almost exclusively from people living

in the late twentieth century in technologically advanced Western nations. As indicated in section 4.5, these provide an unusual sample when considered from a cross-cultural and historical perspective. 4.5. Cross-national variability in physical aggression to partners

The meta-analyses of physical aggression to partners are limited by the data-base from which they are derived: 72 of 80 studies used in the first one (Archer 2000a) were from the United States, and another seven were from Canada or the United Kingdom; a large number of the studies involved young dating samples from the United States. Figure 2 shows the effect sizes for sex differences in physical aggression to partners from community samples in four non-Western nations (Efoghe 1989; Kim & Cho 1992; Kumagai & Straus 1983), along with the value for U. S. community studies (Archer 2000a) for comparison. The weighted mean for the United States is near to zero, whereas those for the other nations are in the male direction (d ¼ .15 to .30). A systematic analysis of cross-national variations, and their relation to the societal position of women in different nations, was undertaken (Archer 2006a). The Gender Empowerment Index (GEM; United Nations Development Programme Human Development Report 1997) 7 was used to measure women’s relative emancipation in different nations. Across 16 nations, sex differences in partner aggression were highly negatively correlated with GEM (r ¼ 2.79), and also with two measures of collectivism (r ¼ 2.87 and 2.81), which are highly associated with lack of gender empowerment. Thus, the lower that women’s power is in a nation, and the more collectivist the culture, the more in the male direction is the sex difference in physical aggression from community samples. Consistent with this, an analysis of partner violence in 90 societies, from the Human Relations Area Files (Levinson 1989), showed that participation in female work groups, which provide women with financial and social support, was inversely related to wife-beating (rs ¼ 2.30) and positively related to husband-beating (rs ¼ .36). A further analysis of the more extensive cross-national evidence on women’s victimization from their partners showed that this increased as the GEM for that nation decreased, for three sets of figures: previous year (r ¼ 2.63; N ¼ 25), current relationship (r ¼ 2.69; N ¼ 15), and lifetime (r ¼ 2.48; N ¼ 40). Collectivism

Figure 2. Effect sizes for sex differences in physical aggression to partners from studies in non-Western nations. Source: Archer (2006a). BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Archer: Sex differences in aggression showed similar correlations with victimization, which was also correlated with traditional gender attitudes and approval of a man slapping his wife (but not with national levels of violent crime). These associations suggest that gender attitudes, and attitudes towards men’s violence, may be mediators between societal-level gender empowerment, and men’s physical aggression to their partners. The findings support an extension of social role theory to cross-national differences in partner aggression, comparable with those found for mate choice (Eagly & Wood 1999; Eagly et al. 2004).8 4.6. Explaining sex differences in aggression between partners

The cross-national analysis has considerable implications for how sex differences (or their absence) in physical aggression are explained. Rather than seeking a single explanation, as in the case of within-sex aggression, both the typical pattern and variations across nations require explanations. Many contemporary nations have relatively low gender empowerment (United Nations Development Programme Human Development Report 1997; 2005) and strong patriarchal values. This is likely to have been the usual pattern for most human societies throughout history (Betzig 1986). It is therefore likely that the typical sex difference in physical aggression to partners is that found today in low empowerment nations: that is, in the male direction. The similarity between the sexes that is found in postfeminist Western societies is likely to be attributable to historically recent changes in the position of women. Higher male-to-female physical aggression can be explained in terms of evolutionary principles derived from sexual selection. Darwin (1871/1901) originally considered male competition and female choice, processes that occur prior to copulation. However, Trivers’ (1972) emphasis on unequal parental investment (sect. 2.1.1) led to an elaboration of the consequences of males and females investing in parental care at different rates subsequent to fertilisation. Consistent with this, some theoretical treatments of sexual selection have widened its scope to include conflict between the sexes at all stages in the reproductive process (e.g., Clutton-Brock & Parker 1995; Hosken & Snook 2005). This has led to a number of analyses whose starting point is the conflict of interest between a male and female entering into a reproductive alliance. Clutton-Brock and Parker (1995) set out theoretical models for the evolution of three forms of sexual coercion: forced copulation, harassment, and intimidation. Intimidation most closely fits the case of partner violence in humans. Males of a number of primate species physically punish females who refuse their mating attempts, or who consort, or mate, with more subordinate males (see Muller et al. 2007, for an empirical analysis of sexual coercion in chimpanzees). In most species where sexual coercion occurs, males are larger than females and can therefore physically dominate them. A game theory evolutionary model (Clutton-Brock & Parker 1995) showed that where one sex (usually the male) is assumed to be more powerful than the other (the female), who is unable to offer effective retaliation, an Evolutionarily Stable Strategy (ESS; Maynard Smith 1982) is punishment by the male and learned cooperation by the female. One consequence of male intimidation in social animals is 264

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that females will seek to pair with dominant males for protection from other males. Thus, mate guarding – often viewed only from the male perspective (Shackelford & Buss 1997; Wilson & Daly 1992) – is likely to have benefits for the female under such circumstances. Applying these evolutionary principles to humans, it is clear that the relatively greater size and strength of men (sect. 3.4), and their greater familiarity with physical aggression, would enable them to physically intimidate and coerce their female partners, who would as a consequence show learned cooperation. Smuts (1992) identified the following additional circumstances that would increase women’s vulnerability to being beaten by their husbands: weak female alliances; lack of support from natal kin; strong male alliances; less egalitarian male relationships; and control of resources by men. Although it was argued that these circumstances would have been common in human history, as a consequence of a general pattern of patrilocal residence in human societies (Geary et al. 2003; Smuts 1992), an analysis of foragers from the standard cross-cultural sample showed a typical pattern of mutual rather than patrilocal residence (Marlowe 2004). Other evidence, based on genetic markers (e.g., DestroBisol et al. 2004), does support the view that African hunter-gathers have a history of patrilocal residence. The situation where some men use physical aggression towards their wives is likely to be maintained unless there is a credible threat of retaliation, from the woman’s male kin, or from the law. Among a sample of Mexican men and women, Figueredo et al. (2001) found that for women, density of local male kin, combined with high family support, predicted lower victimization rates. Other ways in which women’s power is increased at a local level, such as female work-groups (Levinson 1989), also increase their ability to counter male domination. Increases in women’s empowerment at a national level, which are reflected in gender role attitudes, and in challenges to the legitimacy of men using physical aggression against women, were also shown to be associated with lower victimization rates cross-nationally (Archer 2006a). Both the impelling and the inhibiting forces just outlined form part of the calculus of anticipated costs and benefits of physical aggression against a partner. In societies where women have greater economic and political power, victimization rates are lessened for several reasons: Women are less economically reliant on their husbands, and can more easily escape abusive relationships; and partner violence becomes a public rather than a private issue (Felson 2002), increasing the legal and reputational costs that are imposed on violent men. These changes are accompanied by more negative attitudes towards men’s physical aggression to their partners, which will have an inhibiting effect on men who might, in other circumstances, have used such aggression to control their partners’ behavior. Similarly, some women will physically aggress against their partners if the fear of retaliation is lessened or is absent (Fiebert & Gonzalez 1997). 5. General conclusions I began by considering within-sex aggression. Meta-analyses of several different measurement methods showed the expected pattern of greater male than female direct

Archer: Sex differences in aggression physical, and to a lesser extent verbal, aggression when the opponent’s sex was unspecified, and these findings paralleled what was found when a same-sex opponent was specified. There were no sex differences in trait anger. Girls showed more indirect aggression than boys, although by adulthood the sex difference had disappeared. This overall pattern was consistent with a sexual selection analysis involving an increasing sex difference with more costly forms of aggression. The emergence of sex difference in physical aggression early in life, together with the very high levels of physical aggression in both sexes at age 2 years, and a decline throughout childhood, is difficult to explain in terms of gradual learning of aggressive responses through imitation and other processes. It better fits the view that physical aggression occurs as an innate pattern of behavior that is subsequently inhibited by social learning, to different extents in boys and girls. A large sex difference in damaging physical aggression occurs in young adulthood, the peak years of reproductive competition. Mediators of the sex differences in aggression, such as the greater physical risk-taking and lesser fear of physical danger among males, have been attributed to evolved dispositions or to social roles. An interactive developmental process was suggested in which early predispositions come to manifest themselves as sex differences in social behavior through interactions with same-sex others, and these behavioral differences become conceptualized in terms of gender roles. Variability in sex differences was explained from a sexual selection perspective in terms of alternative mating strategies and the greater variability in men’s than women’s physical aggression supported this. Differences in the internalization of role-related attributes were also related to variability in aggression. Different forms of context-dependent variability are predicted by sexual selection and social role theory. Findings on status and resources, and operational sex ratios, supported a sexual selection analysis. There was mixed support for social role predictions of changes in sex differences under different social role conditions, from experimental, cross-national and historical analyses. In section 3, I have considered broader evidence for the occurrence of sexual selection in humans. Greater male than female variance in reproductive success indicates effective polygyny. Men show vocal and visual features indicative of male displays, and there is greater male than female size and strength, slower male maturation, greater male mortality, and higher male conception rates, all indicative of sexual selection. I have argued that this, in conjunction with sex differences in aggression, represents an adaptive complex arising from sexual selection. Physical aggression to partners showed little or no sex difference, both overall and for most specific acts. The exceptions were beating up and causing injuries to a partner, although a considerable minority of men reported being beaten up or injured by a female partner. This relative equality between the sexes in acts of physical aggression was confined to nations where women have higher levels of societal power, patriarchal societies typically showing greater male than female physical aggression. The magnitude and direction of the sex difference followed a measure of societal gender empowerment and beliefs about gender roles. For both same- and between-sex physical aggression, theoretical models derived from sexual selection can

explain the basic pattern of sex differences, although the underlying principles are different. This follows not only the different evolutionary interests of the protagonists in the two cases, but also the different nature of the conflict that underlies their aggression. In the case of same-sex aggression, individuals are competing with others like themselves for mates, resources, or status that will ultimately enhance their chances of reproducing successfully. In the case of aggression to an opposite-sex partner, they are competing with individuals who have different reproductive strategies, and with whom they have to cooperate in shared parenting. In the first case, sex differences arise from the different nature of within-sex competition for the two sexes, and in the second from their evolved reproductive specializations. The evolutionary models applied to the two cases, although both characterized as “sexual selection,” are very different. Underlying all evolutionary models are the fitness costs and benefits of particular behavioral options (sect. 2.1.2). A broad principle derived from game theory models of animal fighting is that the probability of escalating a conflict to a more damaging level, for example by initiating physical aggression, is a function of the likely benefits divided by the costs (or P ¼ V/C; Maynard Smith 1982). Applied to within-sex aggression, inter-male competition can be viewed as altering the value of V so that males generally stand to gain more by fighting other males than females do by fighting other females. This is a consequence of males’ higher reproductive rate (CluttonBrock & Vincent 1991). In these evolutionary models, costs and benefits refer to those imposed by natural selection. They may be reflected in basic predispositions (sect. 2.1.2), representing their incorporation into the control of behavior across a phylogenetic time-scale. This is one of three ways in which animals make adaptive responses to their environments (Waddington 1957). The other two involve developmental flexibility, enabling the individual to adapt to conditions occurring during a single lifetime, and short-term flexibility, involving learning and neuroendocrine responses (Archer 1988; 2006b). Psychological frameworks derived from learning theory (e.g., Perry et al. 1989) incorporate short-term adaptive mechanisms in the form of cost-benefit principles – for example, by viewing expectancies about outcomes as causal agents of behavior. Later social role formulations (Eagly et al. 2004; Eagly & Wood 2006) viewed roles as establishing costs and benefits that influence behavior. Thus, for women, anticipation of fewer benefits and greater costs (in the form of negative self-evaluation and the disapproval of others) will decrease the likelihood of responding to provocation with overt aggression. Used in this sense, costs and benefits refer to those in the immediate environment as assessed by the individual. This can be fitted into Waddington’s evolutionary framework as a form of short-term flexibility. Both evolutionary (e.g., Gangestad et al. 2006a), and social role analyses (Eagly 1987; Eagly et al. 2000; 2004) emphasize variation according to the social context. Such variations in contingencies may act to accentuate, counteract, or reverse the typical sex difference. An example from section 1.8 is that when reproductive competition between women is high, their physical aggression is more common (Campbell 1995; Schuster 1983; 1985). Presumably, peer BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Commentary/Archer: Sex differences in aggression disapproval of direct aggression to other women is lessened, and beliefs about acceptable behavior for women are altered accordingly. In modern professional life, the costs of physically aggressing to a coworker are likely to be high, so that indirect aggression – which entails lower direct costs – will be used (Bjo¨rkqvist et al. 1994; Rutter & Hine 2005). In this context, beliefs about what is acceptable behavior for men are altered. These examples involve influences that tend to reduce the sex difference, but there are other influences, such as the culture of honor (sect. 2.8), that increase it. Sex differences in aggression between partners can also be viewed as following the immediate costs and benefits operating in particular social environments. Here the benefits will be control of the partner’s behavior, rather than resource or status acquisition as is the case for within-sex competition. The main evolutionary model covering aggression between sexual partners (Clutton-Brock & Parker 1995) involves compliance by the physically weaker sex as a result of force by the stronger sex. This situation, which arises from sex differences in size and strength, has been viewed as forming the evolutionary origin of patriarchal beliefs (Smuts 1995), which will in turn legitimize, accentuate, and to some extent control, men’s violence against their partners. The legitimacy of “wife beating” (Campbell 1992) is a feature of patriarchal societies (e.g., El-Zanty et al. 1995). Cultural attitudes associated with patriarchal values have undergone socially induced changes in Western nations, particularly over the last 40 years. These attitudinal changes have led to changes in the cost-benefit contingencies involved in partner violence. There are strong negative reputational costs attached to male violence towards women (Felson 2002), and when female victims have recourse to legal and social sanctions against violent men, female victimization decreases, and the level of male victimization increases (Archer 2006a). Overall, the evidence indicates a different operation of evolutionary and social forces according to the sex of the opponent. Sexual selection provides the more comprehensive explanation for same-sex aggression, and a mix of evolutionary conflicts of interest and social roles for between-sex aggression. The sexual selection account presented here for same-sex aggression incorporates both consideration of context-dependent variations in behavior and the operation of social roles. In this account, the proximal causes of social roles are viewed as being derived from a complex interaction between innate dispositions, social development, and context-dependent reactions. Social roles feed back into this process, affecting the contingencies influencing behavior. They are not viewed as guiding the process, as in social role theory (Eagly et al. 2004, p. 270). They have their ultimate origins in evolutionary history, one that involves a sexually selected adaptive complex, containing psychological dispositions as well as the physical sex differences emphasized in Eagly and Wood’s biosocial theory. ACKNOWLEDGMENT I thank Alice Eagly and Derek Heim for helpful comments on earlier drafts of this article. Correspondence should be addressed to John Archer, School of Psychology, University of Central Lancashire, Preston, PR1 2 HE, Lancashire, UK [e-mail: [email protected]].

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NOTES 1. Based on the features they have in common, Archer and Coyne (2005) concluded that the earlier term “indirect” and the later term “relational” aggression refer to the same activities, and sex differences are similar whichever term is used. I therefore use the original term “indirect” in this article. 2. Dawkins and Carlisle (1976) pointed out that emphasis on past investment determining which sex would desert involved the “sunk cost” fallacy, the crucial variable being the replacement cost of deserting. However, past investment usually provides an indication of the future investment needed to produce offspring to the same stage as those that were lost. 3. Wood and Eagly’s use of the term “bioscocial” differs from the typical use of this term, which is to refer to an approach that is specifically concerned with how genes and environment interact in development (e.g., Raine et al. 1997). 4. In these and all the studies of children mentioned in this article, play-fighting (“rough and tumble play”) is excluded from consideration, and has been studied separately, since it is motivationally distinct from physical aggression (Blurton Jones 1972; Boulton 1994). 5. If it were the case that men were answering with other men in mind and women with their male partners in mind, we should expect a standardized difference for general questionnaires that is mid-way between the values where the sex of the opponent is specified. It is not. This deduction needs to be tested directly in future studies by asking respondents which sex of opponent they had in mind when completing the questionnaire. 6. In simple hunter-gatherer societies, the rates of withingroup aggression are relatively low (Knauft 1991), although rates of between-group aggression may be high (Wrangham et al. 2006). 7. GEM is a national-level variable derived from a combination of: (1) the proportion of women in managerial, administrative, professional, and technical posts; (2) their share or earned income; and (3) their parliamentary representation. 8. These analyses are now contentious since a reanalysis controlling for income, latitude, and region found that mate preferences were then unrelated to gender empowerment (Gangestad et al. 2006a). Eagly and Wood (2006) argued that by controlling for these, variables closely related to the equality of the sexes were removed. However, these variables are not conceptually related to women’s empowerment, and consequently they can more reasonably be interpreted as ecological variables influencing mate choice (Gangestad et al. 2006b).

Open Peer Commentary Ultimate and proximate influences on human sex differences doi:10.1017/S0140525X09990483 Drew H. Bailey, Jonathan K. Oxford, and David C. Geary Department of Psychological Sciences, University of Missouri, Columbia, MO 65211. [email protected] [email protected] [email protected] http://web.missouri.edu/~gearyd/

Abstract: We agree with Archer that human sex differences in aggression are well explained by sexual selection, but note that “social learning” explanations of human behaviors are not logically mutually exclusive from “evolutionary” explanations and therefore should not be framed as such. We discuss why this type of framing hinders the development of both social learning and evolutionary theories of human behavior.

Commentary/Archer: Sex differences in aggression Debate regarding the origins or even existence of sex differences began with Darwin’s (1871/1901) seminal contribution and continues to this day. Denials of so-called biological influences on sex differences are less common than they once were, but arguments that such influences are trivial in relation to social-psychological ones are common (Hyde 2005). Evaluations of the relative influence of these mechanisms often pit “evolutionary” against “social learning” explanations (e.g., Wood & Eagly 2002). Archer proposes that, “the magnitude and nature of sex differences in aggression, their development, causation, and variability, can be better explained by sexual selection than by the alternative biosocial version of social role theory” (target article, Abstract; emphasis added). We argue that Archer’s review, along with many previous contributions to this debate, assume, either implicitly or explicitly, that sexual selection and social learning are alternative explanations – but in fact, they are not necessarily so. Progress in our understanding of evolutionary and social learning influences on expressed sex differences is hampered by mutually exclusive contrasts of these classes of theories. By focusing on proximate mechanisms and implicitly assuming these are alternatives to an ultimate mechanism, social learning researchers prevent themselves from integrating ultimate level influences on human behavior, including the capacity to socially learn, into their models. Understanding evolutionary influences on social learning can inform evolutionary and social learning researchers ¨ hman & Mineka 2001). Furthermore, evolutionary alike (e.g., O researchers who view social learning as an alternative to evolutionary theory might be missing many nuances in the ways in which evolved biases can be expressed in our species, and the evolved mechanisms that enable this variation in expression. We agree with many of Archer’s concerns about the social roles model of sex differences in intrasexual aggression, and agree that sexual selection provides a very powerful and parsimonious explanation, and that the social roles model struggles on many dimensions. However, we ask Archer and others to reframe these arguments in terms of explicitly stated ultimate and proximate mechanisms. Sexual selection is necessary, in our view, for a complete understanding of the sex differences in intrasexual aggression but does not provide sufficient explanation for the variation in how men’s competitive dominancestriving and behavioral aggression is expressed. Intrasexual, male-male competition is found throughout the world, but the ways in which it is expressed can differ substantively from one culture or historical period to the next. Irons’ (1979) concept of cultural success allows us to understand how ecology, cultural history, and current conditions influence how men express an evolved desire for status vis-a`-vis other men. Pastoral raiders who steal another tribe’s cattle to pay bride price and Wall Street raiders who seek hostile takeovers of competitor’s companies may seem different on the surface, but they are not: Each of these activities is an expression of men’s desire for control of the resources that affect their reproductive prospects and general well being in their culture. A Wall Street raider does not, of course, need that extra $10 million to attract a bride or live well, but as long as there are other raiders who make more than he does, our ambitious raider will continue the struggle. This said, we agree with Archer, that male-on-male behavioral aggression is a manifestation of our evolutionary history, and reflects a motivation to achieve social dominance and cultural status at a proximate level. But even the clearest indicators of an evolutionary history of male-male competition – the sex differences in physical size, other physical traits, and behavioral aggression – are expressed in more ways than are found in other species (Geary 1998). Because they represent different levels of analysis, different types of data would be required to falsify hypotheses based on social learning and sexual selection. To falsify a social learning model, one would need to assess the proposed proximate

mechanisms, not contrast the model with one that focuses on ultimate mechanisms. As one example, boys and girls who were not exposed to their respective “social roles” should not be as sextyped as their same-sex peers who were exposed to these roles. One type of evidence comes from children of parents who discourage sex-typing. These children have less sex-typed explicit beliefs about sex roles, in keeping with a social learning component, but have the same toy and play preferences as other children, inconsistent with a causal link between this knowledge and behavioral sex differences (Weisner & Wilson-Mitchell 1990). Male-typical behaviors in biological males raised as girls (Colapinto 2001; Reiner & Gearhart 2004) are especially difficult to reconcile with a strict social learning model of gender development. These results and others (e.g., Berenbaum & Hines 1992) suggest sex-typed activities are influenced by prenatal exposure to androgens, a proximate mechanism in the expression of sexually selected traits. Boys’ attraction to karate and baseball are consistent with male-male competition, but the fact that they are culturally specific variations of one-on-one and coalitional male-male competition suggests some forms of proximate social leaning mechanisms are operating. Like Archer, we do not believe these mechanisms are the same as those identified in the social roles model. Rather, the activities that capture children’s attention and that they wish to engage in, or not, are influenced by prenatal exposure to androgens, but the specifics of these activities (e.g., ice hockey) depend on exposure and the opportunity the activity affords for the expression of physical and social dominance and the formation of male coalitions (Geary et al. 2003). In short, we believe that Archer is correct in his conclusions that male-male aggression is well explained by sexual selection and poorly explained by social roles. Our point is that by framing the argument in terms of evolutionary mechanisms versus social leaning mechanisms, Archer and many others miss the opportunity to integrate these different levels of explanation. What are the proximate attentional, cognitive, motivational, and social learning mechanisms that enable boys and men to engage in sexually selected intrasexual competition in so many creative and varied ways?

Does sexual selection explain why human aggression peaks in early childhood? doi:10.1017/S0140525X09990471 Christina Behme Department of Philosophy, Dalhousie University, Halifax, Nova Scotia B3H 4P9, Canada. [email protected]

Abstract: Archer provides seemingly compelling evidence for his claim that sexual selection explains sex differences in human aggression better than social role theory. I challenge Archer’s interpretation of some of this evidence. I argue that the same evidence could be used to support the claim that what has been selected for is the ability to curb aggression and discuss implications for Archer’s theory.

Before turning to the main point of my commentary I want to note that Archer’s definition of sexual selection as involving “the choice of members of one sex by the other, and competition by members of one sex for access to the other” (target article, sect. 2.1.1) is not uncontested. Archer does not acknowledge, let alone resolve, the controversies surrounding historic and contemporary accounts of sexual selection (e.g., Andersson 1994; Cornwell & Perrett 2008; Cronin 1991; Darwin 1871/1901; Hubbard 1990; Johnstone 1995; Kirkpatrick & Ryan 1991; Leonard 2005; Miller 2006; Roughgarden et al. 2006; Stamos 2008; Wade & BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Commentary/Archer: Sex differences in aggression Shuster 2002; Wallace 1871; Williams 1975). Darwin held that modifications acquired through sexual selection are strongly pronounced and fully developed only at maturity. He did not attribute all differences between the sexes to sexual selection but only those differences that could not be explained based on natural selection alone (Darwin 1871/1901). Since Archer links aggression to endocrine mechanisms that also underwrite larger size and musculature in males he needs to show that these traits are not fitness-enhancing outside of the realm of reproduction. If that were the case, they (and subsequently aggression) could be explained based on natural (not sexual) selection. If we use Archer’s definition of sexual selection, several issues need to be resolved. First, Archer focuses on the differences in (physical and verbal) aggression between sexes. He provides compelling evidence that these differences arise at around 24 months and are greatest in adolescence and early adulthood. Because sex differences arise so early, Archer concludes that they cannot be based solely on cultural learning throughout childhood (sect. 2.2.1). However, he has not shown that sex differences exist already when aggressive behaviour first emerges. “Rage reactions” occur in neonates; aggressive behaviour has been documented in 4- to 6-month-old infants of both sexes (Parens 2008) and is well developed in 12-month-old infants (Holmberg 1980; Lewis et al. 1990; Sroufe 1995; Stenberg & Campos 1990; Stenberg et al. 1983). Alink et al. (2006) did not find sex differences in aggression in 12-month-olds. For Archer’s account it is important to uncover exactly when and why sex differences arise. It is well documented that physical aggression peaks in early childhood and decreases continually. Hartup (1974) reported that 4- to 6-year-olds are more aggressive than 6- to 7-yearolds. Cummings et al. (1989) found that frequency of physical aggression, initiation of aggression, and average length of aggression periods decreased in both sexes between 2 and 5 years of age. Tremblay et al. (1999, as cited in Fig. 1 of the target article; see sect. 2.5) and Tremblay et al. (2004) found that after a peak at age 2 to 3 years, aggression decreased steadily until age 11 in both sexes. This appears to be a problem for Archer’s account, because it is difficult to see how a theory of sexual selection can explain that the amount of aggressive behaviour decreases steadily throughout childhood. If aggressive behaviour (a) results in greater success in inter-male competition for mates, and/or (b) is considered by females to be an attractive characteristic of potential mates, we should expect the highest values of aggression – not only the greatest difference between the sexes – at the time when mating occurs. Instead, the peak of aggressive behaviour occurs more than 10 years before the time of mate-choice. This development is very different from that of the other sexually dimorphic traits that are part of Archer’s “adaptive complex” (see sects. 3.1. to 3.4). Sex differences in these traits (e.g., body height, absolute and fat-free body mass, strength, musculature, and “aggressive display features”) are usually most pronounced at the time of mating. However, we also find either a steady, “absolute” increase of these traits during childhood towards a maximum at late puberty/early adulthood (e.g., body height, body mass, strength), or a late onset (e.g., facial hair, lowering of the male voice). In no case do we have a decline in the absolute value of the trait similar to that observed in aggression. For these reasons, I suggest that it is implausible that aggression has been sexually selected for. To maintain an evolutionary explanatory framework one might argue that females select mates that are best able to curb aggression. This move could still account for the early onset of aggression and, if we assume that aggression is underwritten by sexually dimorphic neuroendocrine mechanisms as suggested by Archer (sect. 2.1.2) and the sex differences in aggression. In addition, it could account for the decline in aggression throughout childhood. Tremblay et al. (1999) suggest that we have to learn to inhibit aggression. It is not relevant here whether this learning

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is based on social or evolutionary mechanisms. Both processes could contribute to sex differences in aggression. Parental feedback can impact behaviour much earlier than learning based on explicit instruction (Alink et al. 2006; Coˆte´ et al. 2006). Parents and caregivers react differently to aggressive behaviour in boys and girls, and it has been shown that this differential reaction can increase initially small differences in behaviour (Bergeron & Schneider 2005; Fagot 1984; Fagot & Hagan 1985; Serbin et al. 1973). Ostrov and Keating (2004) speculate that from an early age onwards, boys gravitate toward contexts in which overt aggressive tactics are more appropriate, while girls are drawn to contexts in which relational aggression is more effective. On the other hand, Chen et al. (2002) suggest that aggression can be seen as reliable indicator for poor ability to exert self-control. Hinshaw (1992) suggests that aggression is associated with academic difficulties in school-age children. Arnold (1997) and Stevenson et al. (1985) reported associations between aggression and language deficits in preschool children. Finally, on Archer’s account, women would face a conflict in mate choice. On the one hand, they would be attracted to aggressive males. On the other hand, they would be interested in a longterm relationship with a provider. It seems that females who resolve this conflict by choosing a mate who is not likely to harm them or their offspring will leave more offspring than those who choose an overly aggressive mate. This would lead to selection against aggression. Much work remains to be done before we can understand the evolutionary history of aggression. As a longtime researcher of the field aptly put it: “We stand at the edge of the nest, then, regarding what we know about the development of aggression” (Hartup 2005, p. 19).

Dominating versus eliminating the competition: Sex differences in human intrasexual aggression doi:10.1017/S0140525X0999046X Joyce F. Benenson Department of Psychology, Emmanuel College, Boston, MA 02115; Department of Biological Anthropology, Harvard University, Cambridge, MA 02138. [email protected]

Abstract: Archer presents a traditional view of intrasexual competition. Knowledge of a species’ social structure provides a more complete picture. Human males compete against individuals with whom they may cooperate later in inter-group aggression. By contrast, females compete against individuals for a mate’s continued support. Females’ aggression may aim at eliminating the competition, whereas males simply may attempt to dominate others.

Archer argues that across most species, males’ greater intrasexual competition for mates accounts for their higher rates of aggression, with variation in paternal care elucidating the magnitude of the sex difference. Defining intrasexual competition as including not only mating contests but also breeding competition, however, provides a broader perspective (Clutton-Brock 2007; 2009). Breeding competition may include contests over food, territory, helpers, protection, and status, as well as other factors that enhance reproductive success within a particular ecology. A species’ social structure determines in part how these challenges are confronted, through delineating patterns of same-sex associations, asymmetries in sex-biased investment in both kin and non-kin, and functions of same-sex alliances and coalitions (Wrangham 1987). To understand more completely human sex differences in patterns of aggression, Archer could reach

Commentary/Archer: Sex differences in aggression beyond consideration of the benefits and costs of physical fighting to incorporate an understanding of a species’ social structure. Humans segregate themselves by sex early in the juvenile period (Maccoby 1988). Across varied cultures beginning in middle childhood and continuing into adulthood, human males interact in large, loosely structured, interconnected same-sex groups, whereas human females interact with one same-sex individual at a time (Benenson et al. 1997; Cairns et al. 1998; Markovits et al. 2001; 2006; Savin-Williams 1980). Additionally, human males invest more than females in, and exhibit more tolerance towards, same-sex peers (Benenson et al. 1998; 2008b; 2009). Sex differences in group versus individual investment extend to sexual partners. Like polygynously and monogamously mated primates, human females typically form a long-term bond to one sexual partner, whereas human males more frequently form bonds with multiple short- and longterm sexual partners. Unique facets of humans’ social structure should influence Archer’s conclusions regarding sex differences in aggression. More than in most other species, human females rely heavily on the investment of one mate to provision and protect themselves and their offspring (Lancaster & Lancaster 1983). Consequently, in contrast to other species, human females invest more in a mate to the exclusion of other individuals. Likewise, unlike males in virtually all primate species (with the exception of chimpanzees, Pan troglodytes), human males routinely engage in lethal coalitionary inter-group contests (LeBlanc & Register 2003; Wrangham 1999). Success in these contests heavily influences the survival and reproductive fitness of the entire community. Like male chimpanzees, human males therefore must balance intra-group competition for status and mates with cooperation with these same competitors during intergroup contests. Heavy investment in male peers combined with high tolerance for transgressions likely produce rapid reconciliation of within group conflicts during inter-group contests. By their nature, groups enhance competitive and aggressive behaviors, whereas one-on-one competition disguises competition with more placating behaviors, including signals of anxiety and depression – for both sexes (Bales & Borgatta 1955; Benenson et al. 2001; 2002). Groups enhance competition because fewer resources are available per individual and many individuals vie for rank. Because human males must maintain a group’s integrity given the perpetual threat of inter-group contests, however, group members likely dampen competitions’ adverse effects by providing mediators, allies, and alternate partners, and promoting loyalty to the larger group. A human male’s goal in intrasexual competition consequently becomes to dominate other individuals within the group without harming the group’s integrity. Within-group fighting then may be less important than between-group fighting in explaining sex differences. Human females’ competition occurs within a different structure. Isolated one-on-one competition without the support that a group provides jeopardizes the relationship’s survival. Human females’ same-sex dyadic relationships endure for shorter periods than those of males, most likely because of their lesser ability to resolve conflicts (Benenson & Christakos 2003). A human female must compete, however, not only to initiate a long-term bond with a high status mate who can enhance the survival and status of her offspring, but also to maintain her mate’s loyalty. She must fend off competitors for her mate’s resources and protection, or in the case of polygynous unions, for a greater share of her mate’s investment. Social exclusion of competitors provides the perfect mechanism. Because females’ same-sex relationships by their nature are not interconnected or group-based, exclusion of another female can occur seamlessly. Feshbach showed that compared to their male peers, females in both early childhood (Feshbach 1969) and adolescence (Feshbach & Sones 1971) were less welcoming to a same-sex newcomer. Likewise, in an experiment with limited resources, 4-year-old female triads were more likely than

male triads to exclude the one child who obtained a resource, whereas males competed individually for the resource while maintaining the integrity of the trio (Benenson et al. 2008a). Whereas Archer, using Campbell’s (1999) analysis, emphasizes that females gain less and lose more from overt fighting, he neglects to consider that females also may benefit far more than males from aggressively excluding one another. Smuts (1987a) argues that across primate species, males generally engage in sporadic but intense bouts of aggression for mates, whereas females engage in more chronic but low-grade aggression to attain resources. In humans, males compete for status and mates but they frequently retain these mates for long periods. The premium placed on virginal status and ensured paternity also means that once a male has successfully dominated his competitor to win a virginal female, losers will be less interested in the winner’s wives. Further, male winners and losers may serve as future partners in cooperative group endeavors, including lethal coalitionary inter-group aggression. Human females, by contrast, continually compete to initiate and maintain long-term bonds with a mate who can provide prolonged aid. Eliminating competitors provides continuous benefits. Archer’s perspective that sex differences in aggression result from human males’ confronting greater intrasexual competition for mates neglects the unique breeding challenges of each sex that human social structure likely evolved to satisfy.

Sex differences in the developmental antecedents of aggression doi:10.1017/S0140525X0900140X Joseph M. Boden Christchurch Health and Development Study, University of Otago, Christchurch School of Medicine and Health Sciences, PO Box 4345, Christchurch, New Zealand. [email protected] http://www.chmeds.ac.nz/research/chds/index.htm

Abstract: Archer examines sex differences in aggression, and argues that these differences may be better explained by sexual selection theory than by social role theory. This commentary examines sex differences in the developmental antecedents of aggression and violence, and presents a preliminary framework for examining whether the observed sex differences amongst these developmental antecedents can also be accounted for by sexual selection theory.

The target article examines sex differences in aggression, arguing that differences in aggressive behaviour may be better explained by sexual selection theory rather than social role theory. In this commentary I examine the related question of sex differences in the developmental antecedents of aggression, and show that these too may be better explained by sexual selection theory, rather than social role theory. Archer argues that the magnitude and nature of sex differences in aggression, which he defines as differences in aggression between same-sex individuals as well as between opposite-sex individuals, are better explained in terms of sexual selection than of social role. One of the key underpinnings of this argument is that evidence concerning the development of aggression suggests that physical aggression emerges early in life and tends to decline thereafter, suggesting that aggression is not a learned response. The developmental perspective on aggression has also underpinned studies examining the causal influence of early experience on later aggression. Several studies have examined the extent to which certain developmental factors, such as family functioning, socio-economic conditions, exposure to abuse, and other factors can account for aggression and violence later in life (Daigle et al. BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Commentary/Archer: Sex differences in aggression 2007; Fergusson et al. 2008; Howells & Rosenbaum 2008). One of the key findings common to these studies is that there may be reliable sex differences in the extent to which certain environmental or behavioural factors may be related to later aggression. While this is a somewhat different issue than that addressed by Archer, an examination of the pattern of sex differences in the developmental antecedents of aggression shows that these differences can also be better explained by sexual selection theory than by social role theory. Although a wide range of studies have examined the developmental processes that predispose individuals to aggression and violence (for reviews see, e.g., Emery & Billings-Laumann 1998; Loeber & Hay 1997; Tolan et al. 2006), relatively few studies have identified sex differences in the extent to which certain risk factors may have differential effects on males and females in terms of predicting later violence. One such study was conducted by Fergusson et al. (2008), using data from a longitudinal birth cohort. These researchers found that several factors predicted both perpetration of and victimization by intimate partner violence (IPV) in adulthood, including childhood conduct problems, exposure to family adversity, abuse exposure, and adolescent alcohol abuse/dependence. Importantly, however, they found that exposure to family adversity was more strongly predictive of later IPV involvement for males, whereas childhood conduct problems were more strongly predictive of later IPV for females. Fergusson et al. concluded that the data suggested a varied developmental pathway to IPV for males and females, although the precise mechanisms behind this pathway were unclear. Comparable findings were reported by Howells and Rosenbaum (2008) and by Daigle et al. (2007). Social role theory (e.g., Eagly 1997; Eagly & Steffen 1986) would predict that sex differences in the developmental antecedents of aggression and violence should reflect the differential sex-role socialization experienced by males and females. For example, under such an explanation we will expect males to be more influenced by exposure to violence or by affiliation with violent and aggressive peers (both features of the male sex role under social role theory). On the other hand, on the assumption that the socialization of females tends to move individuals away from violence and aggression, it may be expected that females will be more influenced by the weakening of social bonds via family dysfunction. The data on sex differences in the developmental antecedents of aggression do not seem to be congruent with this position, however. For example, Fergusson et al. (2008) found that a broad measure of family dysfunction predicted later IPV for males more strongly than females. This finding suggests that the weakening of social bonds caused by dysfunctional family processes increases the risks of violence among males relative to females, counter to what would be expected under social role theory. Furthermore, conduct-disordered behaviour in childhood predicts adult IPV involvement more strongly for females than males, suggesting that there are lower levels of continuity of aggressive behaviour across the lifespan among males than females, again counter to what would be expected under social role theory. The question then arises: Can sexual selection theory better explain the sex differences observed in the developmental antecedents of violence and aggression? Archer argues that sexual selection theory would view variability in aggression as reflecting resources important for reproduction. In the cohort studied by Fergusson et al. (2008), males at greater risk of later aggression were more likely to have come from dysfunctional homes in which they were at greater risk of exposure to a wide range of environmental stressors, including material deprivation. It could therefore be argued that exposure to family adversity increases violence and aggression in males by making salient resource limitations, engaging adaptive modules that serve the purpose of increasing access to resources (via aggression). Furthermore, in the study by Fergusson et al. males were less

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likely than females to show continuity of aggression, in terms of childhood conduct disorder being linked to adult IPV involvement. Again, this may be linked to Archer’s general argument that, under sexual selection theory, there should be greater variability among males than females in terms of the effect of local environmental conditions. If we extend “local environmental conditions” to include environmental conditions across the lifespan of the individual, the greater discontinuity in males relative to females might reflect adaptation to variable environmental influences on aggressive behaviour. In summary, I agree with Archer that an initial examination of the evidence pertaining to sex differences in the developmental antecedents of aggression appears to support the notion that aggression is primarily a product of sexual selection, rather than social role. Further research is needed to shed light on this question.

Sex differences in aggression: Origins and implications for sexual integration of combat forces doi:10.1017/S0140525X09990458 Kingsley R. Browne Wayne State University Law School, Detroit, MI 48202. [email protected] http://faculty.law.wayne. edu/browne/index.htm

Abstract: Sex differences in aggressive and risk-taking behaviors have practical implications for sexual integration of military combat units. The social-role theory implies that female soldiers will adapt to their role and display the same aggressive and risk-taking propensities as their male comrades. If sex differences reflect evolved propensities, however, adoption of the soldier’s role is unlikely to eliminate those differences.

The choice between the evolutionary approach advocated in the target article and the biosocial approach that it criticizes, is an important one that is of more than academic interest. In fact, it has direct application to a critical policy choice facing modern governments: whether women should be integrated into military combat units. A variety of sex differences are relevant to the integration question. Most obvious are differences in physical attributes – such as size, strength, speed, and endurance – which overwhelming evidence shows are primarily a consequence of sex hormones (Cheuvront et al. 2002). Differences in intragroup interactions between all-male and sexually integrated groups also bear on the question of integration, as issues of group cohesion, sexual relationships, male protectiveness toward women, among others, are of central importance (Browne 2001; 2007). Of specific relevance to the subject of the target article are sex differences in aggressiveness and physical risk-taking. The biosocial theory attributes sex differences in aggressiveness and risk-taking to “the distribution of women and men into different specific roles in societies” (Becker & Eagly 2004). Characteristics such as a propensity to engage in risky behavior are imputed to men because men are more likely to occupy roles requiring such action due to their greater physical prowess and the restrictions that childbearing places on the activities of women. A critical flaw in the biosocial theory is the lack of curiosity it exhibits over the origins of physical sex differences. The theory assumes that the evolutionary forces that left their imprint on human bodies had no similar effect on human minds, an assumption that is untenable if one reflects on where these physical differences came from. Because these differences are consistent with a common mammalian pattern – according to which sexual

Commentary/Archer: Sex differences in aggression size dimorphism appears to be an evolved consequence of malemale competition that has behavioral correlates – the principle of parsimony would, at least as a first cut, suggest common origins. Needless to say, a social-role explanation for behavioral sex differences throughout the mammal world is difficult to credit. If men exhibit greater aggressiveness and risk-taking simply because they have been placed in roles that demand, or at least reward, these attributes, then one might expect that placing women into the role of combat soldier will cause them to exhibit the same kinds of aggressiveness and risk-taking as male soldiers. Because women have not widely served in combat, there is no clear empirical evidence directly on point. However, there are some data to show that even female soldiers respond differently to combat risks than men do. A number of press reports from Iraq suggest that female soldiers are at least perceived as less aggressive than their male comrades. One story (in The Times of London), for example, described a female U. S. Army helicopter pilot who requested that the reporter use the term “neutralise,” rather than “kill,” because she did not want to create an erroneous impression that soldiers enjoyed killing. The reporter noted that “her sensitivity stands out in an army in which male soldiers talk of ‘smoking,’ ‘wasting,’ or ‘whacking’ the enemy” (Meo 2006, p. 46). Another newspaper story (in the Washington Post) profiled a different female helicopter pilot who objected to the bellicosity of her male comrades: “Everyone was like, ‘Yeah, get them’ and I was having trouble with that really aggressive attitude” (Tyson 2005, p. A-1). According to a Chicago Sun-Times article, a female National Guard gunner noted that women do not fire their weapons as much as men do because of their greater caution. She continued: Men are more aggressive and trigger-happy. We have a lot of younger guys – 18-, 19-year old guys – who can’t wait to get their first kill. Women don’t look at death that way. We would rather solve the situation. If somebody has to die, then nobody really wins. (Reed 2005, p. 4)

I concede these are anecdotal accounts and are not necessarily representative. However, there is little reason to believe that they present a false picture. Mere presence in a war zone is considerably more stressful to women than to men. Among male and female soldiers serving in non-combat positions during the Gulf War, women reported experiencing significantly more psychological stress than men, especially stress in anticipation of combat (Rosen et al. 1999). Reports from Iraq indicate that women are suffering posttraumatic stress disorder at approximately twice the rate of men, and suffering from more severe forms, despite the fact that women are exposed to considerably less combat danger (Scharnberg 2005, p. C-1). These reports are consistent with the view articulated in the target article that women exhibit higher fear levels than men. The target article notes that studies typically find no sex difference in anger. However, there are sex differences in the correlates of anger that are likely to facilitate physically aggressive behavior in men and to be of importance in combat. Fessler et al. (2004) have shown that anger increases risk-taking among men but does not do so for women. On the other hand, disgust inhibits risk-taking among women but not among men. Because the battlefield provides ample opportunity for both anger and disgust to operate, patterned differences between men and women in combat performance are predictable. Average differences between the sexes are not necessarily a reason to exclude women from combat. In theory, soldiers could be selected based upon their individual attributes, including aggressiveness and risk-taking. One problem is that, as the target article notes, sex differences in naturalistic settings are generally greater than those exhibited in labs and on paperand-pencil tests. Moreover, unlike strength, which can be easily

and cheaply screened for, future courage under fire cannot be readily measured. A consistent theme in the combat-behavior literature is that one never knows who is going to be an effective soldier until the shooting starts, and the identity of the good fighters often turns out to be a surprise (Braun et al. 1991; Browne 2007, p. 111). The question of whether to integrate the sexes in combat forces is an important one, with many lives potentially hanging in the balance. Knowledge of the origins of sex differences in aggression and risk-taking does not by itself determine appropriate military manpower policy. However, any policy adopted is more likely to succeed if it is grounded in accurate factual assumptions.

The multiple adaptive problems solved by human aggression doi:10.1017/S0140525X09990343 David M. Buss Department of Psychology, A8000, University of Texas, Austin, TX 78712. [email protected] www.davidbuss.com

Abstract: Human psychology contains adaptations to deploy aggression as one solution to many distinct adaptive problems. These include expropriating resources, defending against incursions, establishing encroachment-deterring reputations, inflicting costs on rivals, ascending dominance hierarchies, dissuading partner defection, eliminating fitnessdraining offspring, and obtaining new mates. Aggression is not a singular strategy. Comprehensive theories must identify the “design features” of multiple adaptations for aggression.

Archer makes a compelling case – conceptually and empirically – that many patterns of human sex differences in aggression, and adaptations that contributed to an aggressive strategy, have arisen by the evolutionary process of sexual selection. Alternative theories that assume a sexually monomorphic evolved mind, such as social role theory, are implausible on conceptual grounds and have so much empirical evidence against them that they can safely be consigned to a footnote in the history of psychology. I suggest that the case for sexual selection in explaining sex-differentiated patterns of aggression is even stronger than that presented in Archer’s target article, and that progress in understanding human aggression will be advanced by a more detailed consideration of the adaptive problems solved by implementation of an aggressive strategy. Hypotheses about adaptive problems solved by aggression lead to predictions about psychological and behavioral “design features” of adaptations for aggression. Archer alludes to some of the broad classes when he suggests that contingent use of aggression evolved to solve adaptive problems of competing for mates, resources, and status; and he details some of the attendant anatomical and physiological features that accompany adaptations for aggression. The specific ways in which competitions occur provide a deeper understanding of aggression, as well as powerful evidence supporting Archer’s overarching claim. Many theorists have proposed that aggression evolved as a context-contingent solution to a host of adaptive problems, including: appropriating the resources of others; reacquiring resources previously appropriated by competitors; preemptively defending against attack; establishing a reputation that deters aggression from others; inflicting costs on intrasexual rivals that damages their ability to retaliate; ascending dominance hierarchies; dissuading romantic partners from infidelity; aggressive stalking to acquire new mates or regain former mates; eliminating fitness-draining offspring; and obtaining sexual access to the otherwise inaccessible (Buss 2005; Buss & Duntley 2006; 2008; BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Commentary/Archer: Sex differences in aggression Buss & Shackelford 1997b; Campbell 1995; 2002; Duntley & Shackelford 2008; Smith 2007; van der Dennen 1995). Examination of a few of these reveals details about adaptations for aggression, and renders the case for sexual selection origins stronger. Consider war, a particularly dramatic a form of aggression. Mythology aside, there exists not a single case in which women formed same-sex coalitions to kill other female coalitions for the purpose of purloining resources, territory, and mates. Yet history is replete with evidence that men routinely wage war for precisely these purposes (Buss 2005; Chagnon 1983; Tooby & Cosmides 1988; Smith 2007; van der Dennen 1995). Identifying adaptations for this specific form of aggression reveals additional evidence in support of the sexual selection origins. Among the Yanomamo of Venezuela, unokai men (those who have killed) have more wives and children than those who have not killed (Chagnon 1988). The paleontological evidence brims with findings of male skulls and skeletons, with injuries corresponding in size and shape to weaponry existing at the time, and an otherwise inexplicable dearth of female skulls and skeletons (Grauer & StuartMacadam 1998). DNA studies of genetic signatures suggest that warriors who vanquished other groups of men sired many progeny (Zerjal et al. 2003), pointing directly to the sexually selective benefits of aggression. Ascending status hierarchies is almost certainly one evolved function of physical aggression, as is using aggression to maintain positions attained. History is replete with influential leaders such as Joseph Stalin of Russia, Pol Pot of Cambodia, Saddam Hussein of Iraq, Idi Amin of Uganda, Franc¸ois Duvalier of Haiti, Benito Mussolini of Italy, Ion Antonescue of Romania, Mao Zedong of China, Kim Il Sung of North Korea, Ferdinand Marcos of the Philippines, Slobodan Milosevic of the former Serbia, Ne Win of Burma, and Pablo Escobar of Colombia – all of whom murdered to get to the top, and continued to murder to quash competitors in order to maintain their status positions (Buss 2005). Most turned their positions of power into mating opportunities, again supporting a sexual selection explanation. Although these examples might imply that men have a monopoly on aggression, examination of other adaptive problems and their evolved solutions suggest a more nuanced depiction. Evidence points to differently designed infanticidal adaptations in women and men. Women are more inclined to kill their infant when they have many years of future reproduction ahead of them, or when the infant lacks an investing father or is congenitally deformed (Daly & Wilson 1988). Men are more inclined to kill infants when there is suspicion of knowledge of a lack of paternity (Daly & Wilson 1988). Less gruesome forms of aggression, such as derogation of competitors, show sex-differentiated design features. Women derogate rivals along the dimensions of sexual promiscuity, sexual fidelity, and physical appearance (Buss & Dedden 1990; Campbell 2002). Men are more likely to derogate rivals along the dimensions of resources, future resource trajectories, physical strength, and athletic prowess (Buss & Dedden 1990; Schmitt & Buss 1996). These findings suggest a complex way in which sexual selection has influenced human aggression. The domains of intrasexual competition (one component of sexual selection) are dictated by the mate preferences of the opposite sex (the second component of sexual selection) (Buss 1988b). Sexual selection, in short, provides a powerful overarching theory of the origins of human aggression, but not solely in explaining the broadly based sex differences in physical aggression. Sexual selection theory also explains many forms of female aggression. Perhaps most important, identifying with greater specificity the adaptive problems for which aggression evolved as one context-contingent solution provides a key to future scientific advances. In this sense, aggression is not singular

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in nature, but rather is an overarching term for a collection of context-specific cost-inflicting strategies.

What kind of selection? doi:10.1017/S0140525X09990446 Anne Campbell Psychology Department, Durham University, Durham DH1 3LE, United Kingdom. [email protected]

Abstract: Supporting a mediating role for fear in inhibiting female aggression, a recent study shows that aversion to “risky” impulsivity completely mediates the sex difference in direct aggression but not in angry acts where dangerous retaliation is unlikely. A more inclusive use of the term “sexual selection” to encompass reproductive advantage would recognise females’ crucial role in nurturing and protecting offspring.

A perplexing paradox for aggression researchers is the marked sex difference in same-sex aggression and its absence in partner-directed aggression. Archer is well placed to take on the explanatory challenge, given his impressive output of metaanalyses in this area. In discussing fear and risk-taking as candidate mediators of the sex difference in aggression, Archer notes that “there are currently no direct tests of these.” However, a colleague and I recently conducted such a study (Campbell & Muncer, in press). We developed a scale of “risky impulsivity” – defined as a tendency to act spontaneously and without deliberation, where the act has potentially dangerous consequences. We purposely omitted any reference to hostile interchanges. We also measured direct physical and verbal aggression, both of which involve potentially injurious retaliation by the victim, and two forms of anger expression that do not involve confrontation and are therefore unlikely to excite retaliation. One form was what we called “defusing” anger (taking actions that reduce anger intensity, such as retreating from the scene or discussing the incident with a third party) and the other was “explosive” anger (discharging acute physical or verbal anger when alone, e.g., by hitting walls or shouting). Sex differences in physical and verbal aggression were eliminated when risky impulsivity was controlled. This complete mediation of sex differences was restricted to the two direct forms of aggression, those carrying the risk of retaliation. Archer uses the term “sexual selection” to describe the evolution of sex-differentiated traits, but there has recently been heated controversy about the scope and interpretation of this term (Kavanagh 2006; Roughgarden et al. 2006). Darwin himself (1871/2004, p. 245) left the door open to such debate when, with disarming honesty, he acknowledged that, “in most cases . . . it is impossible to distinguish between the effects of natural and sexual selection.” Evolutionary psychologists have mainly restricted “sexual selection” to intrasexual or intersexual competition for mating opportunities. When male variance in reproductive success exceeds that of females, there is effective polygyny and intensified male competition. Daly and Wilson’s (1988) account of sex differences in aggression clearly identifies these mating opportunities as the driver of male competition and, in extremis, aggression. Under monogamy, there is two-way selection and researchers have now begun to address women’s intersexual competition for mates. One popular topic is male preference for female body shape, with debate focusing on the relative importance of waist-to-hip ratio and body mass index, and the universality of these male preferences (Tovee & Cornelissen 1999; Yu & Shepard 1999).

Commentary/Archer: Sex differences in aggression But what if female waist-hip ratio evolved, not with men’s preferences, but with women’s reproductive success, in mind? Bipedal locomotion, combined with pregnancy and infant carrying, meant that a lower relative centre of body mass increased women’s stability and this shift corresponds with a lower waist-hip ratio (Pawlowski & Grabarczyk 2003). Or a lower waist-hip ratio may have resulted from foetal developmental demands: The supply of long-chain polyunsaturated fatty acids needed for neurodevelopment is optimised where the mother’s lower body fat exceeds upper body fat. Waisthip ratio, a proxy for this fat distribution, is positively associated with children’s cognitive test scores (Lassek & Gaulin 2008). This is not to deny men’s preference for female body shapes but to suggest that the selective advantage for women was not obtaining a better mate but producing more surviving, high-quality children. This suggests a second, more inclusive interpretation of sexual selection – “the advantage which certain individuals have over others of the same sex and species solely in respect of reproduction” (Darwin 1871/2004, p. 243). Because Darwin focused chiefly on males, with their typically lower parental investment, his notion of reproduction was largely restricted to mating opportunities. Yet, as Hrdy (1999, p. 81) emphasises, “Unless mating results in the production of offspring who themselves survive infancy and the juvenile years and position themselves so as to reproduce, sex is only so much sound and undulation signifying nothing.” And in the vast majority of mammals, mothers take this responsibility. It might therefore be argued that any female trait that confers an advantage over competitors in reproduction (in this broader sense beyond mate competition) should be considered a sexually selected trait. In my own proposal (Campbell 1999; 2002) for a psychological mediator of sex differences in aggression, this would include a lower threshold for experiencing fear. In summarising my proposal, Archer accepts that it derives from unequal parental investment but describes it as an “alternative to the sexual selection view” of Daly and Wilson, thus implying the action of natural selection. And Darwin might agree with him: When . . . the two sexes differ in structure in relation to different habits of life, they have no doubt been modified through natural selection, and by inheritance, limited to one and the same sex . . . those individuals which generated or nourished their offspring best, would leave, ceteris paribus, the greatest number to inherit their superiority. (Darwin 1871/2004, p. 243)

Certainly from the infant’s viewpoint, maternal care is about its own survival and hence about natural selection. But from the mother’s viewpoint, her care is about increasing her reproductive success relative to her competitors. So we can see heightened female fear in the service of offspring survival as a sexually selected trait defined in this more inclusive sense. But if sexual selection refers narrowly to competition for copulations it will predominantly apply to males. This means that traits that increase competitive ability are more likely to be attributed to males than females (Clutton-Brock 2007), and this narrow usage devalues women’s parenting effort, which is so crucial to infant survival and female reproductive success. Carranza (2009, p. 750) suggests the term “sex dependent selection” to capture “those natural selection forces that operate differently in males and females because of the different reproductive strategies of the two sexes.” Specifically, fear evolved in both sexes under natural selection but was hyper-selected in females because of its association with increased reproductive success in females but not males. In that sense, men’s heightened competitive risk-taking and women’s lower threshold for fear are both examples of sexdependent selection.

Sex differences in aggression: What does evolutionary theory predict? doi:10.1017/S0140525X09990318 Elizabeth Cashdan Department of Anthropology, University of Utah, Salt Lake City, UT 84112-0060. [email protected] http://www.anthro.utah.edu/people/faculty/elizabeth-cashdan.html

Abstract: The target article claims that evolutionary theory predicts the emergence of sex differences in aggression in early childhood, and that there will be no sex difference in anger. It also finds an absence of sex differences in spousal abuse in Western societies. All three are puzzling from an evolutionary perspective and warrant further discussion.

I agree with Archer that “Social roles . . . have their ultimate origins in evolutionary history” (target article, sect. 5, last para.) and think that the difference in levels of explanation between evolutionary theory and social role theory is responsible for some of the confusion surrounding this debate. Archer’s review of these theories as they apply to sex differences in same-sex aggression is very helpful, but a few of the evolutionary predictions raise additional questions. Most of Archer’s evolutionary predictions regarding same-sex conflict are clear, but two are puzzling. One is the claim that evolutionary theory predicts the early emergence of sex differences in direct aggression. If this is a sexually selected trait, why should it appear before it is needed in mating competition? Most sexually selected traits appear at puberty, so an additional argument is required to support this prediction. Also puzzling is Archer’s assertion that evolutionary theory would not predict a sex difference in anger. Emotions motivate behavior and are affected by selection only if they affect behavior. If theory predicts a sex difference in aggressive behavior, why would it not also predict a sex difference in the emotion that motivates it? The answer may help us understand the evolutionary reasons for greater male same-sex aggression. As Archer notes, two arguments have been proposed: (1) greater benefit to males because of greater variance in male reproductive success (the usual argument), and (2) greater cost to females, due to their greater parental investment (Campbell 1999). If the first of these is driving sex differences in aggression, we should expect reduced anger in women, to motivate their less intense aggressive competition. The second argument, in contrast, would predict equally intense competition but would temper anger with fear, thereby leading to less costly, but not less emotionally-intense, forms of aggression. This seems more consistent with the data showing that women and men experience similar degrees of anger, although they may express it differently. My chief concern with this otherwise valuable target article lies in its treatment of partner violence. Evolutionary theory provides a robust explanation for the finding that males are more likely to control sexual access to females than the converse, and often use aggression to enforce it. In view of this, Archer’s claim that there is no sex difference in spousal abuse in Western nations is surprising and deserves another look. The claim of sexual symmetry ignores much contradictory evidence, ignores sex differences in motive, and relies heavily on studies using the problematic (Dobosh et al. 1992) Conflict Tactics Scale (CTS). Johnson (2006) has shown that violence involving proprietariness and control (“intimate terrorism”) is heavily male-biased, unlike the disputes picked up by the CTS, which arise chiefly from conflicts of daily life (“situational couple violence”). The former also causes far more harm, both physically and psychologically, than more sexually symmetrical altercations (Johnson & Leone 2005). Evolutionary theory that addresses male sexual proprietariness and concern over cuckoldry provides a phylogenetically broad explanation for this more serious type of male-biased BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Commentary/Archer: Sex differences in aggression violence, and leads to predictions that distinguish it from violence arising from conflicts of interest in other domains (Daly & Wilson 1988; Wilson & Daly 1996).

Differentiating defensive and predatory aggression: Neuropsychological systems and personality in sex differences doi:10.1017/S0140525X09990434 Philip J. Corra and Adam M. Perkinsb a School of Social Work and Psychology, Faculty of Social Sciences, University of East Anglia, Norwich NR4 7TJ, United Kingdom; bDepartment of Psychology, School of Human Sciences, Swansea University, Singleton Park, Swansea SA2 8PP, United Kingdom. [email protected] [email protected]

Abstract: We draw a distinction between defensive and predatory forms of aggression, and how these forms relate to basic neuropsychological systems, especially the Fight-Flight-Freeze-System (FFFS; putatively related to defensive aggression), and the Behavioural Approach System (BAS; putatively related to predatory aggression). These systems may help further to account for proximal brain processes and personality influences in the context of sex differences. 1. Behaviour as a product of evolutionary processes. Twentiethcentury psychologists devoted considerable attention to the hypothesis that behaviour is learnt, and tended to downplay, or even completely deny, the possibility that behaviour has a heritable basis (e.g., Watson 1919). A plethora of evidence, from across mammalian species, challenges this viewpoint. For example, rodents innately display species-typical defensive behaviour when exposed to a predator for the first time (Blanchard 1997); and, in humans, studies of twins have revealed that a wide range of behavioural traits are substantially heritable (e.g., Plomin et al. 2001). One by-product of the emerging consensus that mammalian behaviour patterns are partly innate is a growing interest in explanations as to the mechanism by which behaviour becomes coded in the genome. By far the most prominent theory is that innate behaviours, such as aggression, evolved by similar processes to those that are widely accepted to have shaped anatomical features (Darwin 1859/1911). Following Darwin, Archer presents a detailed argument that human sex differences in aggression evolved primarily as a result of selection pressure that placed less aggressive males at a competitive disadvantage in the struggle for mating opportunities. Archer is careful to note, however, that the greater propensity to aggressive behaviour in males is limited to attacks on male competitors. In situations where violence occurs between heterosexual couples or in situations of provocation, Archer cites studies that show males and females display similar levels of aggression (e.g., Archer 2000a; Bettencourt & Kernahan 1997). We argue that Archer’s already convincing argument could be further strengthened by supplementation with certain principles drawn from the work of Jeffrey Gray on defensive/ predatory behaviours and personality (Gray & McNaughton 2000; updated by McNaughton & Corr 2004; 2008; for a summary, see Corr 2008). 2. Reinforcing stimuli as mediators of aggression. Gray’s approach postulates that the various classes of emotional behaviour displayed by animals are dependent upon the interplay of three major neuropsychological systems. Threat stimuli activate a Fight-Flight-Freeze-System (FFFS), leading to avoidance/escape and the emotions of fear and panic/rage (depending on the level of threat perceived) – this system is specifically related to defensive aggression. Reward stimuli activate a Behavioural Approach System (BAS), leading to

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approach behaviour and the emotion of hopeful anticipation, optimism, and so forth – this system may be related to predatory aggression (see below). Ambiguous and conflicting stimuli (e.g., approach-avoidance conflict) activate a Behavioural Inhibition System (BIS), leading to risk assessing cautious behaviour and the emotion of anxiety (reflecting the apprehension that something bad may occur at any moment) – activation of this system should be expected to inhibit aggression. Applied to personality, this theory maintains that major traits (e.g., extraversion and neuroticism) originate in individual differences in the sensitivity of these brain systems to their adequately eliciting stimuli. This theoretical perspective suggests that Archer’s theme – that competitive aggression is predominantly a male phenomenon, whereas provoked aggression is equally common in males and females – may be explained by sex differences in functioning of these brain systems. For example, a male who assaults another male with the intention of improving his own mating prospects is displaying appetitively motivated predatory aggression (in this case, by the prospect of sexual intercourse) that is hypothetically mediated by the BAS. In support of this view, there is now mounting evidence that anger/aggression is, at least in part, elicited by BAS activity (Carver 2004; Carver & Harmon-Jones 2009; Corr 2002). The defensive-versus-predatory and negative-versus-positive distinctions receive additional support from findings that rats seek out opportunities to perpetrate predatory aggression – as if it were appetitive – yet they try to avoid perpetrating defensive aggression – as if it were unpleasant (Panksepp 1971). If, over time, predatory aggression boosts male fecundity, then this trait would spread throughout the male population by standard evolutionary means. As explained by Archer, the mechanics of mammalian reproduction mean that women face little or no selection pressure to harm or kill female rivals, and so a trait for predatory aggression should not be expected to proliferate in the female population. Given that individual variations are observed in the functioning of the FFFS, BAS, and BIS, personality differences, both within and between the sexes, should be expected in defensive and predatory aggression. For example, a personality dimension, such as impulsiveunsocialised-sensation seeking (often labelled “psychoticism”; Eysenck & Eysenck 1991) would be a promising candidate for a measure of predatory tendencies. This idea is supported by males typically scoring higher on these traits (e.g., Diaz & Pickering 1993). With regard to defensive aggression, an evolutionary view, such as that advanced by Archer, would predict there should be little significant difference between the sexes, as both sexes face selection pressure to defend themselves against aggressive conspecifics and other species. This idea is supported by evidence that females are as likely as males to be aggressive when provoked (Bettencourt & Kernahan 1997), which is further supported by study of human defence reactions using a threat scenario questionnaire approach (Blanchard et al. 2001). This questionnaire requires participants to select their preferred defensive response to each of 12 threat scenarios from a list of 10 defensive options (e.g., fight, run away). Typically, preferred defensive reactions to scenarios describing especially close or inescapable threats consist of explosive behaviour and aggression (e.g., yell, scream, attack, struggle), and this is equally likely for men and women (e.g., Perkins & Corr 2006). If the distinction between defensive and predatory aggression is valid, then a dissociation should exist in human preferences for exhibiting aggression, with both sexes seeking to avoid situations that require defensive aggression, but males (especially those who score high on traits such as psychoticism) preferentially seeking opportunities to perpetrate predatory aggression. This hypothesis has yet to be tested in humans, but it is supported anecdotally by the predominantly male enjoyment of, and

Commentary/Archer: Sex differences in aggression participation in, rough or violent sports such as boxing, rugby, and American football. It would be valuable to know the importance Archer attaches to the defensive-versus-predatory distinction, and the role played by personality factors in aggressive behaviours; we would be interested in learning about the possible evolutionary pressures on the variation of aggression seen within the sexes.

Two more things for consideration: Sexual orientation and conduct disorder doi:10.1017/S0140525X09990252 Thomas Edmund Dickinsa and Mark James Timothy Sergeantb a School of Psychology, University of East London, London E15 4LZ, United Kingdom, and Centre for Philosophy of Natural and Social Science, London School of Economics, London WC2A 2AE, United Kingdom; bSchool of Social Sciences, Nottingham Trent University, Nottingham NG1 4BU, United Kingdom. [email protected]; [email protected] [email protected] http://www.uel.ac.uk/psychology/staff/tomdickins.htm http://www.lse.ac.uk/collections/CPNSS/people/centre_research_ associatesinResidence.htm http://www.ntu.ac.uk/research/school_research/social/staff/ 54063gp.html

Abstract: We add to Archer’s review with mention of sexual orientation differences in aggression and empathy, which suggest a biological basis for the mediating role of empathy. We also note that Archer’s view of sex differences will illuminate discussion of conduct disorder, which can only be of help to researchers in this field.

As Archer has made clear, intrasexual competition among males is a consequence of operational sex ratios (OSR). Male gametes are more numerous and cheaper to produce than those of females, and in many species paternal care is relatively low. This results in a situation where there are more reproductively available males than females, and females are thus a scarce resource to be striven for; and consequently, males enter into competition with one another. Those males with heritable traits that enable competitive success reproduce more and those traits go to fixation. The literature abounds with examples of male phenotypes designed for aggressive display and combat, and these dimorphisms are the consequence of this intrasexual selection. Although Archer is asking whether sexual selection accounts for sex differences in aggression, he is really adding to the evidence for sexual selection in his detailed overview of this literature. We want to add two more considerations to the discussion. One line of enquiry that Archer does not pursue is that of the influence of sexual orientation on aggression. Organizational hormones, important in the process of sexual differentiation, are strongly implicated in the aetiology of male homosexuality. Specifically, the regime of organizational hormones appears to be different in homosexual compared with heterosexual males. These hormones are thought to alter a number of behaviours, somatic features, and cognitive dispositions, including sexual preference (see Wilson & Rahman 2005). A number of studies have now also drawn a tentative link between the actions of these organizational hormones and the levels of physical aggression displayed by individuals (Bailey & Hurd 2005; Berenbaum & Resnick 1997; Fink et al. 2007; Pasterski et al. 2007). Sergeant et al. (2006) and Dickins and Sergeant (2008) have recently tested specific hypotheses about homosexual male aggression at an individual level and the coalitional psychology underpinning group-level aggression. Both papers

report that homosexual males display significantly lower levels of physical aggression than heterosexual males. No differences were recorded in either study for sexual orientation – related differences in verbal aggression, anger, hostility, or several forms of indirect or relational aggression. These findings are in accord with the sex differences described by Archer. Furthermore, both papers documented significantly higher levels of empathy among homosexual males compared to heterosexual males. Empathy is identified by Archer as possible mediator of aggression, associated with the “biosocial” approach (Bettencourt & Miller 1996; Eagly & Steffen 1986), and as being reduced among women through the administration of exogenous testosterone (Hermans et al. 2006b). Interestingly, the levels of empathy displayed by individuals have been tentatively linked to organizational hormone exposure (Knickmeyer et al. 2005). Thus, there appears to be a relationship not only between organizational hormones, sexual orientation, and the process of sexual differentiation, but also between levels of physical aggression and empathy. Although Archer clearly talks about less-than-desirable traits in his paper, he does not mention disorders associated with aggression. For the most part this is unsurprising, for dysfunction is not the focus of his argument. However, conduct disorder might be an exception to this. The American Psychiatric Association describes conduct disorder as “a repetitive and persistent pattern of behaviour in which the basic rights of others or major age-appropriate societal norms or rules are violated” (DSM-IV Diagnostic Criteria 312.8, American Psychiatric Association 2000). To be diagnosed with conduct disorder a person must exhibit three or more behaviours from a list of 15 during the course of one year, with at least one in the past six months. Seven of these behaviours are aggressive and include intimidation, physical fights, and sexual coercion. Males are two-and-a-half times more likely to have conduct disorder than females. Meltzer et al. (2000), in a survey of the mental health of children and adolescents (from 5 to 15 years old) in Great Britain, reported that conduct disorder was overrepresented in low socioeconomic status boys between 11 and 15 years of age. It is not unreasonable to assume that boys of low socioeconomic status are under-resourced and face more risks than wealthier boys. Given that the former are entering sexual maturity from some point after age 11 years, and their endocrine profile is changing accordingly, the full impact of their local OSR will begin to be felt. As Archer has noted, males from such backgrounds are more likely to be heavy future-discounters and more prone to aggressive conflict, irrespective of a conduct disorder diagnosis (Wilson & Daly 1997). Finally, it is worth noting that girls with conduct disorder have higher levels of free testosterone (Pajer et al. 2006) and are more likely to have precocious menarche (Burt et al. 2006). Early menarche is also associated with high-risk environments, lower socioeconomic status and early fertility (Belsky et al. 1991; Chisholm 1999; Dickins 2006). As Clutton-Brock (2007) notes, in a recent discussion of advances in sexual selection theory, females of some species do compete aggressively for breeding opportunities, and they can exhibit more masculine anatomical, physiological, and behavioural profiles. This kind of female competition can emerge, even when the OSR is as discussed by Archer. Taking sexual selection seriously, as Archer does, thus provides us with a possible research programme with regard to conduct disorder. It would be of great value to collect data on the local ecologies in which conduct disorder arises, tracking resources and OSR as well as fertility profiles. The relationship between early fertility, or teenage pregnancy, and male aggression is well known (Wilson & Daly 1997), but sexual selection theory should throw new light on the facultative psychology underpinning these patterns. BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Sexual selection does not provide an adequate theory of sex differences in aggression doi:10.1017/S0140525X09990264 Alice H. Eaglya and Wendy Woodb a Department of Psychology, Northwestern University, Evanston, IL 602084609; bDepartment of Psychology and Neuroscience, Duke University, Durham, NC 27708. [email protected] [email protected] http://www.wcas.northwestern.edu/psych/people/faculty/faculty_ individual_pages/eagly.htm http://www.duke.edu/~wwood

Abstract: Our social role/biosocial theory provides a more adequate account of aggression sex differences than does Archer’s sexual selection theory. In our theory, these sex differences arise flexibly from sociocultural and ecological forces in interaction with humans’ biology, as defined by female and male physical attributes and reproductive activities. Our comments elaborate our theory’s explanations for the varied phenomena that Archer presents.

John Archer’s stimulating article compares our social role/biosocial theory (see Wood & Eagly 2002) with his own version of sexual selection theory as accounts for sex differences in aggressive behavior. We are delighted to see the increasing importance he gives in his own theory to men’s and women’s social roles and to understanding the dynamic biosocial interactions that produce sex differences in behavior. A central difference, however, remains between our perspective and his – we allocate greater causal power to social structural determinants of male and female aggression and less to sex-differentiated aggressive dispositions presumed to be built into human psychology through sexual selection. Additionally, Archer fails to acknowledge empirical evidence that challenges the sexual selection aspects of his theory, and he misses key points in presenting our work. Human evolution yields behavioral flexibility. Any evolutionary analysis of human sex differences has to account for humans’ behavioral flexibility. This flexibility in response to local circumstances is a characteristic feature of the human species. It reflects their evolution in diverse environments with changeable conditions that impinged in differing ways on survival and reproductive outcomes (Wood & Eagly 2002; in press). For example, in human history, particularly in the late Pleistocene era, climate appears to have been highly changeable. Also, humans and their ancestors engaged in extensive niche construction, meaning that their activities produced changes in the environments in which they lived. Accommodating to such changes required behavioral flexibility, enabled by an evolved capacity for innovating and sharing of information through social learning, yielding a cumulation of culture (Richerson & Boyd 2005). Humans’ flexibility is evident in their various novel solutions to the problems of reproduction and survival, including tolerance for a wide range of foods, ecologies, and living arrangements. This flexibility in behavior is at the heart of our evolutionary analysis. Sex differences in behavior arise flexibly from a biosocial interaction, in particular from sociocultural and ecological forces in interaction with humans’ biology as defined by female and male physical attributes and reproductive activities (Wood & Eagly 2002). Women bear and nurse children, and men possess greater size, speed, and upper-body strength. These attributes serve as constraints on behavior such that certain activities are more efficiently accomplished in certain societies by one sex than by the other. Consequently, the sexes participate in a division of labor. Some behaviors tend to be performed by one sex across most societies and time periods, but even these behaviors can be influenced by particular societal circumstances.

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In vivid illustration of the flexibility of sex differences in human aggression, women sometimes, although rarely, engage in organized combat in world societies. A prominent example is the “Amazon Corps” of the Dahomey Kingdom of West Africa in the eighteenth and nineteenth centuries. Because endemic warfare had reduced the supply of male warriors, survival of the kingdom required military service by women. These women were trained for combat and fought with distinction in all-female units (e.g., Alpern 1998). A prominent twentieth century example is: the women soldiers of Eritrea. These women fought successfully alongside men in mixed units in the long-term and eventually victorious struggle of the Eritrean People’s Liberation Front to win Eritrea’s independence from Ethiopia (Bernal 2000). Eritrean women’s military service was apparently ideologically driven by the revolutionary movement’s modernist rejection of traditional gender relations. These societies overcame the constraints of female reproduction in different ways – in Dahomey by forbidding women warriors to have sex with men, and in Eritrea by providing community childcare. The potential military disadvantages of lesser female physical prowess were surmounted through training and the provision of weapons. In both societies, the female warriors’ psychology proved adequate for full participation in highly aggressive combat activity. Also indicative of flexibility in aggressive behavior is the evidence that women in a small percentage of world societies regularly hunted large game (see Wood & Eagly 2002). Division of labor produces sex differences in human behavior. Archer has left out the key link in our theory

between the division of labor and gender roles, which explains how these roles and associated behaviors change over time and circumstance. Consistent with the social psychological principle of correspondent inference (Gilbert 1998), people infer the traits of men and women from observations of their behavior. To the extent that people observe men and women engaging in different types of behaviors, they regard them as psychologically different. These observations underlie gender roles, which form a shared knowledge structure specifying what men and women usually do and what they should do in a society. These gender roles, as well as specific social roles such as daughter, boss, and friend, influence behavior through a trio of interacting proximal causes of sex differences and similarities: Roles influence behavior through chemical signals of hormonal changes in interaction with individuals’ personal gender identity and others’ stereotypic expectations. Our position that the activating influence of hormones is mainly to facilitate role behavior reflects Archer’s excellent meta-analysis (Archer 2006b). Specifically, testosterone rose in men anticipating and playing sports and highly competitive games, especially among the contest winners, but did not rise in the absence of social roles or provocations calling for aggressive, dominant behavior. Although women have substantially less testosterone than do men, female athletes also recruit testosterone before a competition (see Wood & Eagly, in press). But Archer’s (2006b) meta-analysis did not show the reverse causal relation: Studies that experimentally injected men with testosterone or related synthetic androgens found no systematic rise in anger, aggression, or hostility resulting. Along with hormonal changes, internalized gender roles produce gender identities that act as trait-like determinants of aggressive behaviors. Others’ expectations also foster behavior consistent with gender roles. Unfortunately, Archer misinterpreted one of the best-designed experiments demonstrating that aggression is influenced by others’ expectations (Lightdale & Prentice 1994). This study did not confound the directness of aggression with its normative manipulation, as he claimed, and thus demonstrated how sex differences in aggression depend on the salience of social norms. Nonetheless, Archer is correct in recognizing our theory’s trio of psychological mechanisms (hormonal activation, gender identity, others’ expectations)

Commentary/Archer: Sex differences in aggression that can yield differences between men and women in aggressive behaviors as well as differences between individuals within each sex. Sexual selection provides an inadequate account of human bodily dimorphism. Archer maintains that men’s size and

strength and other physical attributes were sculpted by sexual selection pressures in which ancestral males who were larger and stronger had better fitness outcomes because they were able to compete with other males for access to many mates. Sexual selection pressures presumably also organized human psychology, making men more aggressive than women. Comparative research with primates, however, suggests that bodily dimorphism requires a more complex explanation. Despite the bodily metrics that Archer presents, when evaluated in relation to other anthropoid primate species, humans have relatively low male-female dimorphism in both body weight and canines, and presumably in other bodily attributes as well (Plavcan & van Schaik 1997a, p. 351). Even though across all primate species, greater bodily dimorphism was associated with polygynous mating and male-male competition, dimorphism at the low levels existing in humans “can be found among species with a wide variety of mating systems and competition levels” (Plavcan 2000, p. 338). In addition, compared with most other primate species, humans have a low operational sex ratio (e.g., Wrangham et al. 1999), which also is compatible with low male-male competition. We are puzzled by Archer’s failure to acknowledge that, when compared with other primates, the relatively small amount of human size dimorphism does not imply sexual selection through malemale competition. Also undermining Archer’s one-dimensional sexual selection account is evidence that bodily dimorphism was likely influenced by selection on females as well as males. Selection pressures on females are plausible, given that the decreasing size dimorphism as hominids evolved from the earlier Australopithecus to Homo was due to an increase in the size of females relative to males (as Archer notes). For this and other reasons, experts have abandoned Archer’s one-sided sexual selection argument in favor of a richer set of possibilities. These newer ideas include not only selection pressures on females but also more varied principles for understanding the cooperative and competitive relations between males and the niche construction of males and females in varied environments (e.g., Plavcan 2000; Plavcan & van Schaik 1997a; 2005). Now consider the real predictions of the social role/biosocial theory. It is troubling that Archer claims that we believe that sex

differences in aggression are “modest” (see his Table 1). Our analysis yields no a priori hypotheses about the size of sex differences but instead anticipates that they pattern in a society according to the trio of proximal causes noted above. In addition, as we explain in the next paragraphs, Archer has freely invented (and then disproved) a social role prediction about developmental changes in aggression sex differences and failed to recognize an obvious social role alternative prediction for greater male than female variability in aggressiveness. He also oversimplifies the social role predictions for cross-cultural comparisons of sex differences. Archer maintains that our position on developmental changes should be that, “Sex difference should start small and increase with age through childhood, coincident with the cumulative influence of socialization” (see Table 1 of the target article). This naı¨ve prediction assumes that socialization pressures cumulate in some simple way across development, and furthermore, that they overwhelmingly encourage boys’ aggressiveness – that they are composed of cheering sections of mothers, fathers, teachers, siblings, and peers, all urging aggressive behavior. On the contrary, boys encounter both discouragement of aggression (e.g., in the classroom) and encouragement (e.g., in sports, selfdefense). Prohibitions against physical aggression increase as boys mature, with violence disallowed in the overwhelming

majority of employment settings and disparaged in close relationships with friends, family, and romantic partners. Given these complexities, boys learn to express aggression contextually and in patterned ways. We have not made the claim that Archer suggests but instead have remained silent on age trends in aggression because prediction demands close study of the pressures that foster and discourage aggression as boys and girls mature. With respect to within-sex variability in aggressive behavior, our theory offers an obvious alternative explanation to sexual selection theory. Societies have often provided more opportunities for boys than girls to learn aggression (e.g., in gangs and contact sports). Because some boys and young men avail themselves of these opportunities and others do not, their aggressiveness should be more variable than that of women and girls. Men’s greater power and resources in society also bring some men protection from retaliation, and other, subordinate men greater vulnerability to retaliation. Women’s more restricted opportunities are consistent with their lesser variability in these behaviors. Finally, we note that many cross-national comparisons of sex differences, although seemingly an attractive way of testing social role and evolutionary hypotheses, are plagued by ambiguity. Our theory generally predicts a lessening of sex differences with greater gender equality – and this is what Archer (2000a) found with greater male physical aggression to partners in countries marked by lesser gender equality. Yet, gender equality is not the only feature of men’s and women’s roles that influence sex differences across cultures. Other aspects of roles influence subjective ratings of personality attributes and abilities. In particular, the extent of segregation of men and women can influence the comparison standard that they use to evaluate themselves and others. In traditional cultures in which occupational and other roles tend to be segregated by sex, men and women would judge their own and others’ psychological attributes through comparisons with salient others, who would mainly be of the same sex. Thus, a man might rate himself as only moderately aggressive because he is comparing himself with other men, who are generally somewhat aggressive in his society. In contrast, in societies with less segregated roles, a man might compare himself with individuals of both sexes and conclude that he is relatively aggressive. The result of this shifting comparison standard is that sex differences can appear to be smaller in less egalitarian, more hierarchical societies, in which individuals compare themselves to their own sex (Guimond et al. 2007). Therefore, cross-national comparative data based on subjective trait ratings (e.g., Schmitt et al. 2008) cannot be taken at face value. Overcoming such confounds requires common-rule (or more objective) measures that disallow standard shifts (Biernat 2003). The reports of behavioral frequencies in the research on intimate partner aggression are an instance of common-rule measures, thus allowing for confirmation of our social role prediction in Archer’s (2000a) metaanalysis. In conclusion, the debate between sexual selection theories of the origins of human sex differences and our social role/ biosocial theory will no doubt continue as proponents of each theory hone their views in response to newly emerging empirical evidence. We are encouraged by Archer’s extension of standard evolutionary psychology models to include social roles, but we think an adequate theory of sex differences in aggression would take more seriously the flexibility in behavior that follows from a social role analysis.

ACKNOWLEDGMENT The authors thank Paul Eastwick for his comments on a draft of this commentary.

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Commentary/Archer: Sex differences in aggression

Sex, aggression, and life history strategy doi:10.1017/S0140525X09990422 Aurelio Jose´ Figueredo,a Paul Robert Gladden,a and Barbara Hagenah Brumbachb a

Department of Psychology, University of Arizona, Tucson, AZ 85721-0068; Department of Psychology, Northern Arizona University, P. O. Box 15106, Flagstaff, AZ 86011-5036. [email protected] www.u.arizona.edu/~ajf [email protected] [email protected] b

Abstract: We agree that sexual selection is a more comprehensive explanation for sex differences in direct aggression than social role theory, which is an unparsimonious and vestigial remnant of human exceptionalism. Nevertheless, Archer misses several opportunities to put the theoretical predictions made by himself and by others into direct competition in a way that would further the interests of strong inference.

Archer argues that sexual selection is a more comprehensive explanation for sex differences in direct aggression than social role theory. We concur completely with this assessment. Indeed, we find it hard to believe that social role theory, even the “biosocial” version, retains any scientific credibility at all in the twenty-first century. To us, social role theory is a vestigial remnant of human exceptionalism. Given the overwhelming preponderance of comparative evidence for sexually selected sex differences in intraspecific aggression across such a broad diversity of species, it does great violence to the principle of parsimony to invent a special explanation for exactly the same phenomenon in our own species. Surely, such special pleading cannot be considered sound scientific theorizing. Although we agree that sexual selection theory is essential for explaining sex differences in aggression, Archer seems indecisive regarding the relationship between sexual selection theory and the influence of social roles. Archer suggests that evolved dispositions typically do not rely on socialization practices that could vary from culture to culture (sect. 2.1.2). However, he acknowledges that several ecological and social conditions (e.g., scarcity of resources, operational sex ratio, and culture of honor) are predicted to modify the sex difference magnitude according to the sexual selection view. Here, Archer’s argument would have been aided by emphasizing that evolved dispositions and the influence of social context are not in competition with one another. Further, Archer’s analysis of intrasexual aggression would have been strengthened by specifying why the sexual selection theory of sex differences in aggression is consistent with epigenetic sensitivity to particular environmental conditions, rather than emphasizing insensitivity to those specified by social role theory. This emphasis becomes more difficult to understand in the light of the discussion of intersexual aggression in which sexual selection theory and social role theory are treated as complementary explanations. This leaves the reader confused about why parts of the social role explanation, or at least similar social conditions, could not be integrated with the sexual selection explanation. The analysis would have been further strengthened by specifying the differences between the two theories at both the ultimate and proximate levels of explanation. Advocates on both sides of this debate should attempt to explicitly specify what their theories imply about both levels, because there is a tendency to contrast the ultimate level of sexual selection theory with the proximate level of social role theory. Although Archer does present proximate level mediators specified by each theory, it might have been helpful to examine what social role theory implicitly implies about the

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ultimate level. Each theory implies some differences at both levels, and an effort should be made to translate the two models into the language of each level to allow more thorough examination. Archer acknowledges there is evidence for an association between “internalization of gender roles” and measures of aggression (sect. 2.9). However, in our own lab, we have found evidence that individual differences in both mating effort and life history (LH) strategy are associated with both sexual aggression (Gladden et al. 2008) and negative androcentrism (bias against women; Figueredo et al., in preparation), suggesting that sexual selected LH strategies may account for the association between so-called gender roles and aggression. Future work should attempt to put the sexual selection and social role models in direct competition. The use of path-analytic modeling may suggest which model fits the data best. Although Archer’s primary point was to discuss sex differences in physical aggression, we would suggest that expanding a discussion of sex differences in indirect aggression could have strengthened his argument that sexual selection plays an important role in determining both between and within sex differences in aggression. The difference between males and females in indirect aggression may not be as substantial as that of physical aggression; however, the evidence he presents on effect size clearly indicates that indirect aggression is employed more by females than by males (sect. 2.8). Why is this? Archer’s use of sexual selection theory for explaining sex differences in physical aggression could be applied equally well for examining sex differences in indirect aggression. The following are just a few examples of how this logic could be applied. Archer suggests that, “Overall, the most likely prediction from a sexual selection perspective is an early emergence of sex differences in aggression combined with a peak in risky competition during young adulthood” (sect. 2.1.2, para. 3). One could make the same prediction focusing on indirect rather than physical aggression. More specifically, one could predict the following: (1) females will begin engaging in indirect aggression at an early age (e.g., grade-school girls negotiating social networks at recess), and (2) female indirect aggression will increase into adolescence and young adulthood (e.g., junior-high girls gossiping about rivals at lunch). Archer also addresses context and within-sex competition, “Sexual selection predicts variability in response to conditions that affect the extent of inter-male or inter-female competition, notably resources that are important for reproduction, such as access to mates, and the status and resources important in this process” (sect. 2.8, para. 1). The same logic could be used to further predict differences in indirect aggression among females. For example, one could predict that: (1) there should be less indirect aggression from females who have formed satisfactory and relatively secure long-term pair bonds or secured adequate resources; (2) there should be more indirect aggression from females who pursue short-term mating strategies (fast LH strategy) and less indirect aggression from females who pursue long-term mating strategies (slow LH strategy), especially once a secure pair bond is established (i.e., the less secure the bond, the more incidents of indirect aggression); and (3) female indirect aggression should focus on issues of contested resources, relative fertility, and paternity certainty. In short, Archer misses several opportunities for putting the theoretical predictions made by both himself and others into direct competition in a way that would further the interests of strong inference (Platt 1964). Hence, although essentially correct, in our view his critique did not go far enough in demolishing the antiquated and obsolete alternative hypotheses reviewed.

Commentary/Archer: Sex differences in aggression

An I3 Theory analysis of human sex differences in aggression doi:10.1017/S0140525X09990410 Eli J. Finkel and Erica B. Slotter Department of Psychology, Northwestern University, Evanston, IL 60208. [email protected] [email protected] http://faculty.wcas.northwestern.edu/eli-finkel/

Abstract: According to I3 Theory, individuals enact aggressive behaviors when (a) instigating triggers are severe, (b) impelling forces are strong, and/ or (c) inhibiting forces are weak. Archer’s analysis of human sex differences in aggression could be bolstered by a careful analysis of male-female discrepancies in reactivity (or exposure) to instigating triggers, proneness toward impelling forces, and/or proneness toward inhibiting forces.

Any comprehensive theory of human sex differences in aggression must accomplish the following three tasks (among others). First, it must establish the presence and magnitude of these sex differences. Second, it must discern which specific mediators (e.g., risk-taking, fear of danger) account for these differences. And third, it must identify the specific mechanism by which these mediators translate into behavior (e.g., by strengthening aggressive urges, by weakening the restraint of such urges). Archer’s impressive review, which does not purport to be a comprehensive theory of sex differences in aggression, focuses on the first and the second of these tasks. Regarding the first, relative to women, men are considerably more physical aggressive (in Archer’s Table 2, average d ¼ .58, range ¼ .33–.91) and somewhat more verbally aggressive (average d ¼ .29, range ¼ .09– .55), although women are slightly more indirectly aggressive (average d ¼ 2.16, range ¼ 2.45–.05). Regarding the second, sex differences in aggression appear to be driven in large part by male-female discrepancies in factors such as risk-taking (men are higher) and fear of physical danger (women are higher). We believe Archer’s analysis could be bolstered by a careful analysis of the third task. According to I3 Theory (pronounced “ICubed Theory”), scholars can determine whether an individual will engage in aggressive behavior in a given situation by discerning the strength of the relevant instigating triggers, impelling forces, and inhibiting forces (Finkel 2007; 2008; Slotter & Finkel, in press). Instigating triggers refer to discrete, situational events or circumstances that induce rudimentary action tendencies toward physical aggression (e.g., provocation, goal obstruction, opportunities for personal gain). Impelling forces refer to the collective power of factors that increase the strength of individuals’ tendencies to experience aggressive urges in response to an instigating trigger (e.g., high dispositional anger, elevated testosterone, previous exposure to violent media). Individuals tend to experience more powerful aggressive urges when impelling forces are strong than when they are weak, especially when instigating triggers are severe. Inhibiting forces refer to the collective power of factors that increase the strength of individuals’ tendencies to override aggressive urges rather than acting upon them (e.g., high dispositional self-control, strong relationship commitment, sobriety). Inhibiting forces function as a threshold: Individuals will enact aggressive behavior only when aggressive urges are stronger than inhibiting forces. Archer suggests that the tendency for males to be more aggressive than females is likely to be mediated by greater male risktaking (for reproductive advantage) and greater female fear of physical danger. From the perspective of I3 Theory, the former could plausibly function as an impelling factor causing men to experience stronger aggressive urges than women because access to mates is so enticing, whereas the latter could plausibly function as an inhibiting factor causing women to experience stronger restraint of aggressive urges than men because of the elevated costs of acting upon these urges. If so, men are more aggressive than women because men experience both stronger impelling tendencies toward aggressive urges and weaker inhibiting tendencies to restrain these urges than women do. Establishing

definitively whether risk-taking is an impelling factor and whether fear of physical danger is an inhibiting factor, however, is an important direction for additional empirical research. Regarding instigating triggers, Archer argues that the sexual selection analysis implies that the mechanism underlying sex differences in aggression “is unlikely to reside in a general sex difference in response to frustration or ease of arousal to anger” (sect. 2.1.2, para. 5). It is not immediately obvious to us why sexual selection would have built men to be (a) more (directly) aggressive than women while simultaneously (b) no more anger-prone in general or reactive to instigating triggers in particular. Many scholars argue that anger is an emotion that evolved in large part for its aggression-related consequences (e.g., Fischer & Roseman 2007; Frijda et al. 1989), so the disconnect between anger and aggression in Archer’s model (implying that the link between anger and aggression differs for men and women) requires further elaboration. The I3 Theory emphasis on instigating triggers, impelling forces, and inhibiting forces is also relevant to cases where male/female levels of aggression are comparable. One such instance is physical aggression in heterosexual romantic relationships. According to Archer’s review, “there are no appreciable sex differences in physical aggression to opposite-sex partners, and therefore there is no need to look for ultimate explanations or for mediators” (sect. 4.4, para. 2). From the perspective of I3 Theory, this latter conclusion may be premature. It seems plausible that there could be ultimate explanations (and also proximal explanations) for sex differences in reactivity (or exposure) to instigating triggers, in the experience of impelling forces, and/or in the experience of inhibiting forces that trend in opposite directions and consequently neutralize one another. For example, perhaps sexual selection has caused men to experience stronger impelling tendencies to aggress physically toward an opposite-sex romantic partner (consistent with men’s tendency to be more physically aggressive in general), but this effect is neutralized by stronger inhibiting tendencies for men to restrain these urges (particularly in cultural contexts where boys and men are socialized that it is inappropriate to be physically aggressive toward girls and women). Future research could productively explore whether sex-differentiated tendencies across the I3 Theory components could account for the lack of appreciable sex differences in the frequency of physical aggression toward opposite-sex partners. In sum, although Archer’s analysis of human sex differences in aggression is timely and valuable, it could benefit from greater elaboration of the psychological mechanisms driving these differences. Identifying mediators like risk-taking and fear of physical danger is a step in the right direction, but doing so does not establish whether the sex differences result from male-female discrepancies in reactivity (or exposure) to instigating triggers, proneness toward impelling forces, and/or proneness toward inhibiting forces. ACKNOWLEDGMENTS The preparation of this commentary was supported in part by the National Science Foundation (Grant No. 719780). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. We thank Paul Eastwick for his constructive feedback on an earlier draft.

Biophobia breeds unparsimonious exceptionalism doi:10.1017/S0140525X0999029X Steven J. C. Gaulin Department of Anthropology and Center for Evolutionary Psychology, University of California, Santa Barbara, Santa Barbara, CA 93106-3210. [email protected]

Abstract: With respect to aggressiveness it is not enough to say that humans are “like other mammals.” We resemble only those species BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Commentary/Archer: Sex differences in aggression where males have higher maximum reproductive rates than females. In such species males evolve a set of hormonally mediated competitive traits via sexual selection. Because humans match the predictions of this general evolutionary model, attempts to (re)explain men’s aggressiveness in sociological terms are superfluous and misleading.

Archer compares sexual selection (Darwin 1871/1901) and social role theory (Eagly 1987) as explanations for human sex differences in aggressiveness. Archer’s empirical claims are grounded, but his case is weakened because he fails to emphasize two related metamethodological points: the power of the comparative approach and the parsimony it provides. Greater male aggressiveness is neither uniquely human nor universal among animals. It exhibits a particular cross-species distribution, being present in some species and absent in others. That distribution strongly constrains its functional explanation. Unfortunately, social role theory neglects this powerful source of insight. It examines sex differences in aggression in a zoological vacuum, naively treating the human case as unique. As a result of its narrow focus, social role theory fails to shed new light on sex differences in human aggression. Like many models in the social sciences, it is a case of special pleading where none is required. Darwin (1871/1901) defined sexual selection as an evolutionary process that regularly produces differences between the females and males of a species, and he enumerated the reproductive differentials that drive it. Subsequently, twentieth-century biologists (Andersson 1994; Clutton-Brock & Vincent 1991; Trivers 1972) explained the forces that give sexual selection its polarity. It is this polarity – which sex is more aggressive – that both sexual selection and social role theory seek to explain. Scientific theories explain relevant variance. Thus, social role theory would have some traction if there were cultures where women are more aggressive than men. For better or worse, no such cultures exist (Brown 1991; Daly & Wilson 1988). So, where is the theory-testing variance? To find it one must escape anthropocentric Durkheimian biophobia and look across species. Sexual selection theory provides a general explanation of sex differences that applies to all sexual species. It predicts the distribution of sex differences in aggression: which species will evolve greater male aggressiveness, which species will exhibit no such sex differences, and which will show greater female aggressiveness. According to sexual selection theory, aggressiveness is not a function of sex per se, but of sex differences in maximum reproductive rate (Clutton-Brock & Vincent 1991), arising out of sex differences in parental investment (Trivers 1972). To illustrate, because only female mammals gestate and lactate, a male could have many more offspring than a female. Every reproductive venture requires one male and one female; thus the slower sex is in short supply and worth competing for. (In this example reproductive physiology determines reproductive rates but aspects of the mating system may also be important.) Sexual selection theory’s accuracy in predicting the distribution of sex differences across species makes it logically prior to ad hoc explanations of sex differences in any particular species, unless that species fails to match its predictions. Thus, a baseline question for social role theorists is, do humans constitute an exception to sexual selection theory? Men have, and have had for thousands of generations, higher maximum reproductive rates than women. This implies that men will have found women in short supply and consequently evolved a suite of competitive tactics for acquiring mates, including aggression. What remains for social role theory to explain? Its proponents might say “development.” But, whatever ontogenetic influences social scientists imagine for gender roles, their hypotheses will have to contend with a thick cross-species literature on the developmental effects of androgens. Wherever sexual selection has produced more aggressive males, androgens orchestrate the development of that sex difference. As a functional viewpoint would suggest, the very same hormones also shape the anatomical components of the male-competition complex. Compared

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to women, men are much stronger and more muscular in the upper body (the region most engaged in physical aggression). The effect size for these sex differences is approximately 3.0, with 99.9% of women falling below the male mean; individual differences in muscle mass still reliably predict male mating success in the United States (Lassek & Gaulin, in press). Thus, sexual selection simultaneously explains both anatomical and behavioral sex differences and their joint hormonal mediation. Social role theory cannot approach this level of explanatory integration. But the explanation gap is wider still. The male-competition complex has many evolved manifestations. Bimaturism, sexually differentiated mortality rates, and sex differences in navigational ability are well-described human traits; and again, the crossspecies distribution of these traits strongly implicates sexual selection. Delayed sexual maturity of males is limited to species where they have higher reproductive rates than females (Leigh 1992, Leigh & Shea 1995). Controlled within-genus comparisons suggest that searching for mates drives the evolution of male navigational ability, but again, only where they have higher reproductive rates (Gaulin 1992). Both bimaturism and navigational ability are developmentally linked to the same androgenic hormones that organize aggressive structures and behaviors. Many aspects of the male-competition complex entail costs reflected in higher male mortality rates: In both birds and mammals sex differences in mortality are not universal but proportionate to the intensity of sexual selection (Promislow 1992, Promislow et al. 1992). These costs are not limited to combat-related mortality but include higher male susceptibility to infection that: (a) closely tracks the intensity of sexual selection across species (Moore & Wilson 2002), (b) manifests prominently in humans (Owens 2002), and (c) is probably related to androgens’ immunosuppressant effects (Folstad & Karter 1992) because castration removes the sex difference in infection rates and hormone replacement reinstates it (Zuk & McKean 1996). It is not the existence of these traits but their patterned, cross-species association that social role theory must confront. In sum, humans exhibit a suite of traits – elevated male aggressiveness, greater male muscularity and strength, later male maturation, superior male navigational ability, and higher male mortality, all underpinned by an androgen-based developmental system – that they share only with species where male reproductive rates can significantly exceed those of females. The coherent distribution of these traits strongly suggests they were jointly produced by sexual selection. This patterning, revealed by cross-species comparison, supports the causal primacy of sexual selection. In the absence of a significant misfit with the predictions of sexual selection, any attempts to (re)explain men’s greater aggressiveness in purely sociological terms constitute unparsimonious exceptionalism and have little scientific promise.

A history of war: The role of inter-group conflict in sex differences in aggression doi:10.1017/S0140525X09990409 Dominic D. P. Johnsona and Mark van Vugtb a Department of Politics and International Relations, University of Edinburgh, Edinburgh, EH8 9LD, Scotland, United Kingdom; bDepartment of Psychology, University of Kent at Canterbury, Canterbury CT2 7NP, England, United Kingdom. [email protected] http://www.dominicdpjohnson.com/ [email protected] http://www.kent.ac.uk/psychology/department/people/van-vugtm/

Abstract: Human aggression has two important dimensions: withingroup aggression and between-group aggression. Archer offers an

Commentary/Archer: Sex differences in aggression excellent treatment of the former only. A full explanation of sex differences in aggression will fail without accounting for our history of inter-group aggression, which has deep evolutionary roots and specific psychological adaptations. The causes and consequences of inter-group aggression are dramatically different for males and females.

Human aggression takes two very different forms: (1) intra-group aggression (between individuals); and (2) inter-group aggression (between groups of individuals, such as coalitions, gangs, warriors, armies). Archer argues that observed sex differences in aggression are best explained by sexual selection theory, but this is based on an exclusive focus on intra-group aggression, ignoring the potential explanatory (or confounding) role of inter-group aggression. We suggest that the inter-group dimension is vital to understanding sex differences in aggression: If inter-group processes explain some of the variance in sex differences in aggression, then Archer may have overestimated the role of sexual selection in accounting for the observed sex differences, and may also have underestimated sex differences in aggression overall (since they may be even higher in inter-group contexts). Inter-group aggression has arguably been a major force in human evolution. There is evidence that warfare was frequent and severe throughout human history (Gat 2006; Guilaine & Zammit 2004; Keeley 1996; LeBlanc & Register 2003) and has deep roots in human evolution (Alexander 1987; Thayer 2004; Wrangham & Peterson 1996). Warfare has been a significant cause of male deaths (13 – 15% in the archeological and ethnographic record; Bowles 2006), suggesting a strong selection pressure on adaptations for inter-group aggression. Studies of warfare differ in many respects but are in agreement on one thing: it is almost exclusively a male phenomenon (Potts & Hayden 2008; Wrangham & Peterson 1996). Although women commonly aid in war efforts of various kinds, they generally do not participate as warriors. Legends of Amazons and female warriors are so rare (or unsubstantiated) as to serve as exceptions that prove the rule. The introduction of women into combat units in modern militaries has also been problematic (Browne 2007). We should, therefore, expect significant sex differences in adaptations to inter-group aggression. Inter-group aggression introduces at least two complexities to Archer’s analysis. First, as noted above, some variance in sex differences in aggression is likely to derive from inter-group processes, not sexual selection. Second, inter-group aggression can often be a cause of reduced aggression between males of the same group – uniting to fight a common enemy. Indeed, extraordinary cooperation (even self-sacrifice) can emerge in the context of inter-group aggression (McNeill 1995; Rielly 2000). Sex-differentiated aggression in inter-group contexts is as much about intermale cooperation as it is about inter-male aggression. Empirical evidence supports two key predictions of this “male warrior hypothesis” (van Vugt et al. 2007). First, in situations of inter-group threat, men should display more aggression than women. This is a robust finding in both experimental and realworld studies (Johnson et al. 2006; McDermott & Cowden 2001; Wrangham & Wilson 2004). Second, in situations of intergroup threat, men should increase their cooperation with the in-group in order to more effectively defend and aggress against the out-group. This is supported by experiments in which cooperation in collective action games increases in the presence of rival groups, but only among men (van Vugt et al. 2007). An inter-group perspective raises the question of interactions between sexual selection and inter-group aggression: what is the impact of sexual selection on aggression between members of different groups? Indeed, inter-group aggression may actually be rooted in sexual selection. For example, performance in intergroup warfare may bring status or rewards that increase individual reproductive success (Chagnon 1988). Or, since a primary function of wars in pre-industrial societies is the capture of women (Keeley 1996), warfare may represent competition for reproductive access fought between coalitions rather than

between individuals. Finally, inter-group aggression may even be a method of displacing sexual competition from the ingroup to the out-group, serving to minimize within-group conflict (and its associated costs). An inter-group perspective also raises the question of the role of women in aggression. If women have been beneficiaries and victims of inter-group aggression, we would expect selection pressures on response strategies. For example, there is some evidence that women find military men more sexually attractive, but only if they are observed in battle (Leunissen & van Vugt, unpublished). Women also show an aversion to out-group males at peak fertility in their menstrual cycle (Navarrete et al. 2009). Women might even support inter-group aggression if they (or their offspring and kin) will benefit from the consequences. Keeley reports that among the Apache, “when the meat supply of a band began to run low, an older woman would complain publicly and suggest that a raid be mounted to obtain a fresh supply” (Keeley 1996, p. 135). An inter-group perspective is also important for Archer’s analysis of intersexual (male on female) aggression. Archer focuses primarily on aggression among partners. However, differences in male and female aggression is likely to be highly dependent on group membership. As noted above, a common objective of pre-industrial warfare is the capture of women, and the occurrence of rape in wartime is widely documented even among modern societies (Naimark 1995; Potts & Hayden 2008). Therefore, male aggression against women is likely to be significantly underestimated if we look only at data on partners – men and women who typically chose to be together in the first place, or at least come from the same in-group. An inter-group perspective does at least support Archer’s rejection of social role theory. Briefly, differences in intergroup behavior between boys and girls also appear at a young age and follow a fairly stable developmental trajectory across contexts (Ellis et al. 2008), suggesting an evolutionary explanation. For example, boys more often play team games involving larger groups and have more transient friendships, whereas girls have more exclusive friendships. Boys are also angrier about rulebreaking behavior in such games. To summarize, inter-group aggression might seem to have little bearing on Archer’s core claims – perhaps just representing a different research question. However, we suggest that the omission of an inter-group dimension is significant, because: (1) it underestimates overall sex differences in aggression; and (2) observed sex differences in aggression may derive from some third factor other than sexual selection – in particular intergroup psychology. Thus, even if the evidence that Archer examines is correct, we cannot tell whether it derives from an evolutionary history of sexual selection or from an evolutionary history of inter-group aggression (or some combination thereof). Sex differences in aggression between groups remains an important research area for the future with implications for understanding, predicting, and intervening in human aggression within both domestic and international contexts.

Suspicions of female infidelity predict men’s partner-directed violence doi:10.1017/S0140525X09990392 Farnaz Kaighobadi and Todd K. Shackelford Department of Psychology, Florida Atlantic University, Davie, FL 33314. [email protected] [email protected] http://www.toddkshackelford.com/

Abstract: Archer’s argument regarding sex differences in partner violence rests on a general account of between-sex differences in BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Commentary/Archer: Sex differences in aggression reproductive strategies and in social roles. However, men’s partnerdirected violence often is predicted by perceived risk of female infidelity. We hypothesize that men’s partner-directed violence is produced by psychological mechanisms evolved to solve the adaptive problem of paternity uncertainty.

Archer presents a comprehensive account of between-sex aggression from an evolutionary perspective built on sexual selection theory. We appreciate Archer’s argument that sex differences in reproductive strategy are responsible for sexual conflict and for between-sex aggression. Sexual selection explains sex differences in aggression, in general. We contend, however, that there is a particular area of work that deserves more attention in research on violence in intimate relationships. There is a large body of research investigating men’s partner-directed violence as an evolved solution to the adaptive problems of female infidelity and paternity uncertainty. Over the course of human evolutionary history, men have faced the adaptive problem of female sexual infidelity and subsequent cuckoldry – or the unwitting investment in genetically unrelated offspring. The reproductive costs of cuckoldry, including loss of time, energy, resources, and alternative mating opportunities are potentially so great that men are hypothesized to have evolved psychological mechanisms that function to motivate anticuckoldry tactics. The problem of paternity uncertainty is hypothesized to have selected for the emotion of male sexual jealousy, which in turn motivates men’s anti-cuckoldry tactics such as nonviolent and violent mate retention behaviors. Considerable evidence indicates that men’s perceptions of their female partner’s infidelity predict men’s partner-directed insults, sexual coercion, and partner-directed violence. Male sexual jealousy is one of the most frequently cited causes of men’s partner-directed violence, both physical and sexual (e.g., Buss 2000; Daly & Wilson 1988; Daly et al. 1982; Dobash & Dobash 1979; Dutton 1998; Frieze 1983; Gage & Hutchinson 2006; Russell 1982; Walker 1979). The frequency with which men perform nonviolent mate retention behaviors predicts the frequency with which they inflict physical violence against their partners, arguably because both classes of behavior are outputs of sexual jealousy (Shackelford et al. 2005a). Men who directly accuse their partners of sexual infidelity also are more likely to inflict partner-directed violence (Kaighobadi et al. 2008). Sexual coercion also is hypothesized to function as an anticuckoldry tactic (Lalumie`re et al. 2005; Thornhill & Thornhill 1992; Wilson & Daly 1992; see also Goetz & Shackelford 2006). Instances of forced in-pair copulation (FIPC) have been documented in avian species that form long-term pair-bonds (Bailey et al. 1978; Barash 1977; Birkhead et al. 1989; Cheng et al. 1983; Goodwin 1955; McKinney et al. 1984). FIPC is hypothesized to be a form of post-copulatory male-male competition – that is, a sperm-competition tactic (Barash 1977; Cheng et al. 1983; Lalumie`re et al. 2005; McKinney et al. 1984), because it often follows a female partner’s extra-pair copulation or intrusions by rival males (e.g., Bailey et al. 1978; Barash 1977; Birkhead et al. 1989; Cheng et al. 1983; Goodwin 1955; McKinney et al. 1983; McKinney & Stolen 1982; Valera et al. 2003). Sperm competition occurs when a female copulates with and is inseminated by more than one male in a sufficiently brief period of time (Parker 1970). Thus, by forcing the female to copulate shortly after the increased risk of insemination by a rival, males place their sperm in competition with any sperm deposited into their partner by a rival male (Birkhead et al. 1989; Cheng et al. 1983). Observations of sperm competition in nonhuman species offer a framework with which to consider similar adaptations in humans, who also form long-term socially (but not genetically) monogamous pair-bonds. Recent evidence suggests that sperm competition has been a recurrent feature of human evolutionary history and that men have physiological and psychological mechanisms that may have evolved to solve related adaptive problems (Baker & Bellis 1993; Gallup et al. 2003; Goetz et al. 2005;

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Kilgallon & Simmons 2005; Pound 2002; Shackelford & Goetz 2007; Shackelford & Pound 2006; Shackelford et al. 2002; 2005b; Smith 1984). It has been hypothesized that, by forcing their partners to have sex, men who are suspicious of their partner’s infidelity introduce their own sperm into their partner’s reproductive tract and thereby decrease the risk of cuckoldry. Thornhill and Thornhill (1992) argued that women who resist or avoid copulating with their partners might thereby be signaling to their partners a recent sexual infidelity; hence, forced copulation might function to decrease men’s paternity uncertainty. And the fact that rape of a woman is more likely to occur during or after a breakup (when men’s concerns about women’s infidelities are greatest) may provide preliminary support for this hypothesis (see Thornhill & Thornhill 1992). A number of studies have documented a positive relationship between men’s sexual jealousy and men’s sexual coercion of their partners. For example, Frieze (1983) and Gage and Hutchinson (2006) found that men who sexually coerced their wives are more sexually jealous than men who did not. Previous research has found a direct positive relationship between men’s suspicions and accusations of partner infidelity and men’s sexual coercion of their partners (Starratt et al. 2008). In two studies securing data from men’s self-reports and women’s partner-reports, Goetz and Shackelford (2006) found that men’s sexual coercion correlated positively with women’s past and future likelihood of engaging in sexual infidelity. We recognize that sex differences in intimate partner violence can be explained by sex differences in reproductive strategies and by social roles, as Archer argues; however, men’s partnerdirected violence can be more specifically predicted by perceived risk of female infidelity and male sexual jealousy. A large body of empirical evidence supports the hypothesis that men’s partnerdirected sexual coercion and violence might sometimes be a product of evolved psychological mechanisms designed to prevent or punish female infidelity. The relevant evolved mechanisms interact with stable dispositions and situational factors to produce manifest behavior. Future research might benefit by using an evolutionary perspective to build models of intimate partner violence that include stable dispositions such as personality traits, environmental factors such as social roles, and situational factors such as perceived risk of partner infidelity.

A quantitative genetic approach to understanding aggressive behavior doi:10.1017/S0140525X09990380 Bart Kempenaers and Wolfgang Forstmeier Behavioural Ecology and Evolutionary Genetics, Max Planck Institute for Ornithology, D-82305 Starnberg (Seewiesen), Germany. [email protected] http://www.orn.mpg.de/kempenaers/abtkempenaers_en.html [email protected] http://www.orn.mpg.de/mitarbeiter/forstm.html

Abstract: Quantitative genetic studies of human aggressive behavior only partly support the claim of social role theory that individual differences in aggressive behavior are learnt rather than innate. As to its heritable component, future studies on the genetic architecture of aggressive behavior across different contexts could shed more light on the evolutionary origins of male-female versus male-male aggression.

Archer’s review explores the extent to which human sex differences in aggression can be explained by (1) sexual selection theory versus (2) social role theory. From the perspective of a behavioral ecologist and evolutionary geneticist this seems like a highly unequal comparison. While sexual selection theory

Commentary/Archer: Sex differences in aggression provides ultimate explanations (“Why has it evolved?”) based on principles that universally apply to the entire animal kingdom, social role theory provides a proximate explanation (“How does it come about?”) that is limited to at best a small range of higher taxa. Social role theory argues that sex differences in aggressiveness are learnt rather than innate, a proposition that may be best explored using quantitative genetic methods. The extent to which individual differences in aggressiveness (within each sex) are genetically determined, as opposed to affected by the rearing environment, should also shed some light on the relative importance of innate versus social factors that could act on the between-sex difference in aggressiveness. A large meta-analysis of genetic versus environmental influences on human aggressive and criminal behavior (Rhee & Waldman 2002) suggests that there indeed are some effects of the family rearing environment (explaining 16% of the variance). However, this is considerably less than the joint additive and non-additive genetic effects, which explain 41% of the observed variation. Hence, humans seem to show both – a certain level of genetic polymorphism with regard to aggressive behavior (within both sexes), as well as a certain amount of behavioral flexibility allowing humans to adjust their behavior in response to their environment (i.e., the perceived costs and benefits of aggressiveness). This flexibility may underlie the observation that male aggression against female partners declines with the Gender Empowerment Index (Archer’s Fig. 2), which may reflect increasing reputational costs to male perpetrators and increasing risk of retaliation by the female partner (e.g., risk of being sued, risk of being divorced). While behavioral flexibility often seems adaptive, sexual selection theory per se does not predict whether differences in behavior will result from genetically fixed (innate) strategies or individually flexible reactions to environmental cues. However, sexual selection theory does differentiate according to the ultimate goals of aggressive behavior. Here we take issue with the definition of aggression as a “behavior intended to harm another individual” (see target article, sect. 1, para. 2). We argue that this definition emphasizes a possible – but not necessary – consequence of the behavior, instead of focusing on its aim, which is to defend or obtain a resource. Ultimately, aggression serves to secure reproductive success (Darwinian fitness), which can be achieved by securing or defending resources. Therefore, in the context of Archer’s review, it seems useful to differentiate among different types of conflicts over resources that may lead to variation in sex differences in aggression. Sexual selection theory can make predictions about the following: 1. Variation in male aggression against a female partner as a form of paternity protection. Indeed, if promiscuity occurs, males may risk losing paternity (i.e., the limited resource of fertilizable eggs). 2. Variation in male sexual aggression (against partner or nonmate), including forced copulations, to obtain paternity. 3. Variation in aggression towards conspecifics of the same sex to obtain or defend resources that give access to mates (e.g., food, territory) or to obtain or defend the mate(s) themselves. 4. Variation in aggression towards heterospecific individuals to obtain or defend resources (e.g., food, nest sites). 5. Variation in aggression towards conspecifics (not necessarily sex-dependent) or towards heterospecific individuals to defend offspring (e.g., protection against predation or infanticide). Hence, aggression can be both a component of mating effort and of parental effort. Differentiating between them seems important because they might be caused by different proximate mechanisms, and because sex differences may have different underlying causes. Interestingly, the question whether aggressive behavior is genetically correlated among different contexts remains hugely underexplored.

As to the issue of male aggression directed towards the female mate, the important question to ask (in Archer’s Table 4) would have been the percentage of women versus men who avoid having an extramarital affair due to fear their husband/wife could seriously injure them if they found out. It seems possible that the evolutionary origin of violence by males against their female partners has its roots in paternity insurance (Valera et al. 2003), rather than being a byproduct (a genetic corollary) of greater male strength that evolved due to male-male competition. This could be tested by estimating the genetic correlation between male aggressiveness against their partner and aggressiveness against rival males. In any case, the fact that most women show strong preferences for tall and physically strong partners (e.g. Pawlowski & Koziel 2002; Frederick & Haselton 2007) suggests that over evolutionary times women benefited more from their partners’ protection than they suffered from their men’s physical superiority. Further insights could be gained by considering species that show a partial sex-role reversal, as occurs in some birds or fish. In these species, male parental investment is larger than that of females, and females have a higher potential reproductive rate than males. Hence, males tend to be choosy while females compete among each other for access to males (Eens & Pinxten 2000). Increased competition among females led to a stronger selective pressure on females to win in physical fights, and thereby to the evolution of larger and more aggressive females compared to the relatively small and peaceful males (Dale et al. 2007). One would predict that these females show hardly any aggression against their male partners, since maternity (as opposed to paternity) is never uncertain. Support for this prediction would then suggest that the larger and more competitive sex does not principally dominate the smaller and less competitive sex, but rather, that within-pair aggression by males evolved as a specific adaptation to paternity insurance. In contrast, a strong positive genetic correlation between intra- and inter-sexual aggressiveness would suggest that male aggression against the partner could arise as a genetic corollary (i.e., a possibly even maladaptive byproduct) of intense male-male competition.

More holes in social roles doi:10.1017/S0140525X09990331 Douglas T. Kenricka and Vladas Griskeviciusb a

Department of Psychology, Arizona State University, Tempe, AZ, 852871104; bCarlson School of Management, University of Minnesota, Minneapolis, MN 55455. [email protected] [email protected] www.carlsonschool.umn.edu/marketinginstitute/vgriskevicius

Abstract: Given the strength of Archer’s case for a sexual selection account, he is too accommodating of the social roles alternative. We present data on historical changes in violent crime contradicting that perspective, and discuss recent evidence showing how an evolutionary perspective predicts sex similarities and differences responding in a flexible and functional manner to adaptively relevant triggers across different domains.

Archer argues that sex differences in within-sex aggression are better explained by sexual selection than by the alternative biosocial version of social role theory. Although Archer presents solid theoretical and empirical evidence against the social role account of sex differences in aggression, he unnecessarily pulls his punches. Social role theorists have positioned their account of sex differences as antithetical to evolutionary psychologists’ accounts. For example, in a recent exposition of their theory, Wood and Eagly BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Commentary/Archer: Sex differences in aggression (2007) claim: “Evolutionary psychologists have observed sex differences in modern, patriarchal societies and inappropriately concluded that humans evolved sex-typed psychological dispositions in ancestral times” (p. 389). Wood and Eagly predict a “demise of many sex differences with increasing gender equality” (p. 390). To argue that biological sex differences originate below the neck (in women’s child-bearing capacities and men’s greater muscular strength), and to suggest those differences would simply disappear if society treated men and women alike, is to argue for a Blank Slate. After presenting solid evidence against the social role account of sex differences in aggression, Archer concedes that: “the similarity between the sexes that is found in post-feminist Western societies is likely to be attributable to historically recent changes in the position of women” (sect. 4.6, para. 1). But with regard to the target topic of aggression, the hardest evidence – statistics on violent crime since the liberalization of sex roles in the 1970s – do not show the changes expected by sex-role theories (see our Table 1). Cultural variations are not arbitrary. The social roles accounts debated by Archer have repeatedly taken cultural variations as evidence against an evolutionary perspective, perpetuating the misconception that universal predispositions produce phenotypic invariance in behavior across societies and across time-periods. However, numerous evolution-inspired research programs indicate that such variations can be ecologically triggered by biologically meaningful factors (e.g., Gangestad et al. 2006a; Schaller & Murray 2008). Consider cultural variations in age preferences (Kenrick & Keefe 1992). Eagly and Wood (1999) argued that these stem from sex differences in social power, citing cross-cultural correlations between female power and magnitude of age preferences. Yet they fail to note that “sex differences in modern, patriarchal societies” do not disappear in non-Western societies, but instead get larger. Why are these larger sex differences in nonWestern societies? One possible explanation is linked to the fact that women in those societies have more children and therefore increase in apparent age more rapidly than women in European and North American countries. Thus, what appear to be “cultural variations” may instead be products of biologically meaningful variations in fertility cues, and not arbitrary role assignments (Kenrick & Keefe 1992). Young men’s preferences provide one way to distinguish the two explanations. Developmental studies reveal teenage boys to be highly sex-typed. Hence, they should manifest the roletypical desire for younger, less powerful, partners. But instead, teenage boys are attracted to college-age women (Kenrick et al. 1996). This and many other findings are consistent with an attraction to fertility cues. Tiwi society, in which young men marry older widows, seems at first glance to contradict evolutionary explanations. Is this Eagly and Wood’s imagined egalitarian society, in which women have more power and patriarchy is reversed? Hardly:

Tiwi society is highly patriarchal and polygynous, and Tiwi women have little say in who they marry. Instead, Tiwi patriarchs enforce a rule that all females (but not all males) must be married. The elder patriarchs marry all the young females, and are not interested in older widows. By marrying an elder widow, a young man acquires rights to determine who her young daughters remarry, and establishes himself as a potential recipient of a younger wife (Hart & Pillig 1960). So, even in a society where one aspect of typical sex-specific behavior is reversed by socially enforced caveat, evolved mating preferences do not reverse at all (Kenrick et al. 2010). Evolutionary hypotheses are based on a comparative nomological network. A misconception advanced by Eagly and Wood and other critics is that evolutionary models depend on hard-to-observe behaviors among ancestral humans. In reality, sexual selection models, as Archer makes clear, are derived not from observations of Western patriarchal societies alone but from an immense comparative literature on still-living species. This poses a problem for sex-roles explanations, since many sex differences found among humans in Western societies are shared not only with people in other societies, but with all other mammals, and most other vertebrates. As Archer notes, when sex-role reversals are found in some species, they further support the clear link between parental investment and sexual selection. Evolutionary psychology examines functional responses to adaptive contexts. As Archer notes, an evolutionary approach to human behavior derives hypotheses from comparative and cross-cultural data, not from observations of Western patriarchal society. From this powerful nomological network of research and theory, evolutionary psychologists derive hypotheses about how behavior varies flexibly – and functionally – in response to adaptively relevant environmental triggers. Consistent with Archer’s analysis of sexual selection and aggression, activating status motives leads men but not women to desire to aggress in a

Table 1 (Kenrick & Griskevicius). Percentage of homicides committed by women. [Statistics based on FBI Uniform Crime Reports.] 1961– 1965 1966– 1970 1971– 1975 1976– 1980 1981– 1985 1986– 1990 1991– 1995 1996– 2000 2001– 2007

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15 14 13 13 14 12 9 10 10

Figure 1 (Kenrick & Griskevicius). Self-protection and mating motives have distinct consequences for conformity behaviors of men and women. Both men and women tend to be more conforming when feeling threat. Activating mating motives leads men to become less conforming and, as discussed in the text, more creative and showy in other ways. (Adapted from Griskevicius et al. 2006b)

Commentary/Archer: Sex differences in aggression direct manner (face-to-face confrontation). And consistent with other domain-sensitive evolutionary accounts, resource threat leads women to respond in a manner more similar to men (Griskevicius et al. 2009). Ultimately, aggression for both men and women appears to function as a tactic for enhancing reproductive success. Men and women also show sex-specific and functionally strategic differences and similarities when different goals are activated. For example, consistent with theories of sexual selection and differential parental investment, mating motives lead men – but not women – to engage in conspicuous, attentionattracting, displays, including conspicuous consumption and creative flair (Griskevicius et al. 2006a; 2007). Such findings are not merely demonstrations of arousal enhancing sex-role typical behavior. For instance, activating mating motives leads men to go against group opinion, whereas mating motives lead women to conform more (Griskevicius et al. 2006b). However, activating self-protective motives eliciting similar levels of arousal do not lead men to act in “macho” ways as might be expected. Instead, self-protective motives lead both men and women to become more conforming and group-oriented (see our Fig. 1). Research generated from an evolutionary-psychological perspective is not designed to test hypotheses about historical evolution (a persistent misconception), but to consider proximate causes of human behavior in ways consistent with functional analyses. This approach has generated abundant evidence showing that men and women do not randomly remember and then forget their sex-roles, but instead respond in adaptively flexible ways to functionally relevant environmental cues (Griskevicius et al. 2009; Kenrick & Sheets 1993). Archer’s target article does an excellent job dispelling some of these misconceptions, pointing to strong theoretical and empirical evidence supporting a sexual selection account of sex differences in within-sex aggression.

Moderators of sex differences in sexual selection theory doi:10.1017/S0140525X09990379 Anthony D. Pellegrini Department of Educational Psychology, University of Minnesota, Twin Cities Campus, Minneapolis, MN 55405. [email protected]

Abstract: Archer recognizes that sexual selection theory is sensitive to the effects of ecologies on sex differences, yet he does not explain the impact of such variation. For example, to what degree are there sex differences in aggression in polygynous and monogamous societies? I demonstrate how differences in mating perceptions affect the traditional dichotomy that males compete for and females choose mates.

Archer’s review is an important addition to the continuing debate around sex differences in human behavior, generally, and aggression, more specifically. Concerning the wider debate, a recent review (Hyde 2005) minimized the importance of sex differences in human behavior. One dimension of that argument was based on tallying the number of studies showing sex differences in relation to those not showing differences. That method presents an interesting issue: Do we judge the importance of differences based on the number of differences tallied across all observed behavior and traits, or should judgments be guided by testing for specific differences specified by a theory where differences between certain behaviors and traits are more important than others? My bias is with the latter approach. Archer also takes this tack by evaluating the extant literature in relation to hypotheses for sex differences in aggression generated by Darwin’s (1871/1901) sexual selection theory and social role

theory (Eagly 1997). This is a debate with a lively and healthy history; the very sort of debate that helps advance science. Focus on the degree to which aggression is intersexual, or primarily directed on members of the other sex, specifically males aggressing against females, or intrasexual, male-male or femalefemale, is crucial to the debate. Traditional versions of sexual selection theory (Darwin 1871/1901) as well as revised versions (e.g., Clutton-Brock 2009) posit that males’ and females’ competition should be primarily intrasexual; and that males, more than females, should compete with each other for mates using direct aggression, and females compete less directly with each other for resources. That within-sex aggression is greater than that between sexes, even among preschoolers (Pellegrini et al. 2007b) and middle school youngsters (Pellegrini & Long 2003), and among adults, as shown in this review, highlights the robustness of the finding. Recently scholars have begun to recognize the importance of females’ intrasexual competition (e.g., Campbell 1999), and this has lead to the reformulation of sexual selection theory (Carranza 2009; Clutton-Brock 2009). In contrast to males, females’ intrasexual competition should be aimed at accessing and maintaining resources related to raising and provisioning offspring and should result in the selection of a phenotype that maximizes social support, in the forms of alliance formation, manipulation, and indirect aggression (Hrdy 2005). An important aspect of this reformulation is that the expression of any behavior is moderated by the ecological niche in which individuals are embedded, a position consistent with both Darwin (1871/1901) and his predecessor John Hunter (Hunter 1780; cf. Clutton-Brock 2009). This is not to say that phylogenetic history is irrelevant. Instead, this history probably canalizes (Hinde & Stevenson-Hinde 1973) the behaviors and strategies to be learned (during ontogeny) in the context of social groupings (Crook 1989). Variations in different ecologies, in turn, result in individuals’ developing alternative strategies in the course of ontogeny (Caro & Bateson 1986). Experiences early in ontogeny alert the organism to the environment in which they will function so as to maximize their adaptation to that niche. Different phenotypes develop during childhood in sexually segregated groups during childhood, to prepare boys and girls for adult roles. Briefly, ecologies labeled as “abundant” (Bateson & Martin 1999) should be characterized by polygynous mating patterns and males, relative to females, being more competitive and active. This high level of activity should result in segregated juvenile groups with males being characterized by physically activity and aggressive behavior and females by more sedentary and nurturing behavior (Pellegrini 2004). More severe ecologies should witness more “thrifty phenotypes” (Bateson & Martin 1999), resulting in monogamous or cooperative breeding and less difference between the sexes in competition and activity. Consequently, peer groups should be less segregated, resulting in fewer sex differences in aggression. Archer himself acknowledges the role of such variation, yet he does not go into sufficient detail to explain variation in different ecologies. For example, sexual selection theory predicts that sex differences in size and aggression should be most pronounced in polygynous societies. To what degree does this occur? Traditional sexual selection theory also posits that more intense male-male competition should result in corresponding sex differences in body size, with males being physically larger than females. This review, however, has not explained the reliable sex difference is physical aggression during early and middle childhood when there are no differences in dimorphism for physical size. Why is that? One argument holds that the sex differences in physical activity (Pellegrini et al. 2007a) and locomotor play (Pellegrini & Smith 1998) during early childhood reflect the differences necessary to shape males’ and females’ skeletal and muscular systems that differ in adulthood. Further, contextual variation associated with males’ uses of within-sex aggression to attract mates within an evolutionary BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Commentary/Archer: Sex differences in aggression framework has been addressed in a recent and very provocative paper by Buston and Emlen (2003). They suggest that mate choice, at least among Cornell undergraduates, is not governed by mate “potential” attributes – for example, attractive women choosing strong, high-status males, and strong, high status men choosing attractive women. Instead, they found that individuals’ choices were based on their perceptions of the possible duration of the relationships. When there was expectation of a long term, stable relationship, individuals chose mates similar to themselves (on factors such as physical attractiveness, status, and commitment to family). Attractive women chose attractive men; they did not choose strong, aggressive men. Situations in which costs associated with mate switching is high, for example, where divorce is economically disruptive, would result in individuals choosing mates who are similar to themselves (see Borgerhoff Mulder 2004). By contrast, aggressive men (again, where aggression is intrasexual) were chosen by physically attractive women in situations in which the quality of available mates is low. In this latter case, male-male aggression would be reinforced by female choice and females would “sample” widely from available males for a strong mate who also protects and provisions her and her offspring. With these limitations stated, Archer’s target article makes an important contribution toward the theoretical integration of a wide and disparate literature. He has done the field an important service.

There’s no contest: Human sex differences are sexually selected doi:10.1017/S0140525X0999032X Nicholas Pound,a Martin Daly,b and Margo Wilsonb a Department of Psychology, School of Social Sciences, Brunel University, Uxbridge UB8 3PH, United Kingdom; bDepartment of Psychology, Neuroscience, and Behaviour (PNB), McMaster University, Hamilton, Ontario L8S 4K1, Canada. [email protected] [email protected] [email protected]

Abstract: An evolutionary psychological perspective drawing on sexual selection theory can better explain sex differences in aggression and violence than can social constructionist theories. Moreover, there is accumulating evidence that, in accordance with predictions derived from sexual selection theory, men modulate their willingness to engage in risky and violent confrontations in response to cues to fitness variance and future prospects.

In the target article, Archer argues persuasively that an evolutionary psychological perspective drawing on sexual selection theory can account for observed sex differences in aggression and violence more parsimoniously than social constructionist theories. In our view, however, the case for sexual selection’s role in the evolution of these sex differences is even stronger than Archer’s treatment suggests, and he concedes too much to advocates of the discredited null hypothesis that female and male psyches are undifferentiated. According to Archer (sect. 2.2.1), the “main alternative” to a selectionist explanation of the origins of the sex differences of interest is the “social role” theory of Eagly and Wood (1999; Wood & Eagly 2002). At best, these authors can be read as offering a partial account of ontogenetic processes in sexual differentiation, which, if upheld, would complement an evolutionary account. At worst, they can be read as proposing that the only evolved differences between women and men are “physical” (i.e., non-neural anatomical differences), and if this is indeed their meaning, they are simply uninformed (see, e.g., Kimura

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1999). In neither case have they provided a viable “alternative” to an account that gives centre stage to sexual selection. In explaining why sexual selection should have made men more intensely competitive than women, Archer (sect. 3.2) aptly cites anatomical, demographic, and behavioural evidence that Homo sapiens evolved as an effectively polygynous species in which male fitness variance exceeded female fitness variance. Recent genetic evidence (Wilder et al. 2004) reinforces this conclusion: In both our species as a whole and in discrete subpopulations thereof, the most recent common ancestor (MRCA) of mitochondrial DNA, inherited matrilineally, lived about twice as long ago as the MRCA of Y chromosomes, inherited patrilineally. These results provide strong evidence that individual men have consistently faced a higher risk of reproductive failure than individual women. Archer notes (sect. 2.8) that, consistent with sexual selection theory, there is evidence that males with limited access to reproductive opportunities, or the resources required to obtain such opportunities, are more likely to resort to violence. However, there is accumulating evidence to support a more specific prediction derived from the same theoretical perspective, namely that the prevalence of dangerous confrontations should vary predictably according to variations in the local intensity of intrasexual competition and that cues to higher fitness variance should lead males to modulate their willingness to engage in risky and violent interactions with other men (for review, see Wilson et al. 2002; 2009). In an effectively polygynous species, the intensity of male-male competition will in part depend on the extent to which the resources required to obtain reproductive opportunities are distributed equitably. Extreme inequity creates a situation where those at the bottom have little to lose if they escalate their tactics of competition, and much to gain. Consequently, cues to inequity should lead to facultative adjustments in men’s willingness to employ violent and risky tactics to gain status and resources, which are the means to fitness. Consistent with this, evidence indicates that relative deprivation (as indexed by income inequality) is typically a more powerful predictor of variation in male violence than other socioeconomic measures such as percent below the poverty line or average income (Daly & Wilson 2001). In both cross-national and more local comparisons, the Gini index of income inequality consistently outperforms most other socioeconomic predictors of homicide rates (e.g. Blau & Blau 1982; Daly et al. 2001). Increased willingness to resort to violence where resources are distributed inequitably is not uniquely predicted by sexual selection theory. However, in contrast to social constructionist accounts, an evolutionary psychological perspective treats such increased risk-proneness as a facultative adaptive response to situations where the distribution of resources is such that excessive risk-aversion will lead to substantially reduced expected fitness (Wilson et al. 2002; 2009). An evolutionary psychological approach based on sexual selection and life history theory also predicts that individuals should modulate their willingness to engage in risky and violent confrontations according to cues of future survival and hence reproductive prospects – in other words, when prospects are poor, organisms may be expected to discount the future steeply in the pursuit of more immediate goals (Daly & Wilson 2005). Archer notes (sect. 3.1) that greater male than female mortality is characteristic of the sexually selected “adaptive complex” generated by intense inter-male competition, but the target article could perhaps have examined the implications of this in more detail. It is not just that males are likely to discount the future more heavily than females as a consequence of the sex difference in mortality; moreover, future discounting and willingness to engage in risky escalation of social conflicts are expected to vary predictably in relation to future survival prospects. Where these are poor, men should become particularly risk prone and willing to risk death in violent altercations as they compete for

Commentary/Archer: Sex differences in aggression the resources required to obtain reproductive opportunities, and directly for the opportunities themselves. Consistent with this, Wilson and Daly (1997) found that across neighbourhoods in a major U.S. city (Chicago), the best statistical predictor of homicide rates was low male life expectancy (even with homicide as a cause of death removed). Finally, we do not understand Archer’s rationale for suggesting that a sexual selection approach warrants the “prediction” that the sexes will not differ in “aggression” or “anger,” but only in how they manifest these things. Sell’s research and theorizing (e.g., Sell et al. 2005), which Archer cites, clearly suggests that insofar as becoming angry entails an elevated risk of violent confrontation, we may expect people to differ adaptively in their readiness to anger. Why should this proposition not apply to sex differences? More fundamentally, what does it even mean to suggest that men and women do not differ in “aggression” or “anger,” but only in the manifestations thereof? We lack both consensual definitions and good metrics of these states, and finding that the sexes give the same mean answer on a selfreport scale of “aggression” or “anger” is uninformative. Consequently, evidence for the popular claim that men and women are equally aggressive, but that the former manifest their aggression “directly” (e.g., as violence) and the latter “indirectly” (e.g., as innuendo) is not convincing.

Sex differences in dream aggression doi:10.1017/S0140525X09990306 Michael Schredl Sleep Laboratory, Central Institute of Mental Health, J5, 68159 Mannheim, Germany. [email protected] www.dreamresearch.de

Abstract: Dream research shows sex differences in dream aggression that fit very well with the findings for waking-life aggressive behaviour. Dream studies are a valuable tool for investigating variables underlying the sex difference in aggression. One might argue that studying dream aggression might be even more promising because aggression in dreams is not socially labelled, as being aggressive in waking life is.

Since dreams reflect waking life experiences (the so-called continuity hypothesis of dreaming; Schredl 2003), dream studies can elucidate sex differences reported for waking behaviour. For example, it is a stable finding that men report more sexual dreams than do women (Schredl et al. 1998), which reflects the meta-analytic findings of higher frequency of masturbation and sexual fantasies in males compared to females (Oliver & Hyde 1993). Regarding aggression in dreams, the findings are in line with the meta-analysis reported by Archer: Men’s dreams included more physical aggression than women’s dreams did (Hall & Van de Castle 1966), whereas the amount of verbal aggression did not differ between the sexes (Schredl et al. 1998). The gender difference regarding the percentage of physical aggression (50% in men’s dreams vs. 34% in women’s dreams; Hall & Van de Castle 1966) is quite stable over time. The data collection period of Hall and Van de Castle (1966) ranged from the late 1940s to the early ’50s. Subsequent studies in the ’70s (Hall et al. 1982) and ’90s (Schredl et al. 2003), and very recent studies (Schredl & Keller 2008 –2009) replicated the higher prevalence of physical aggression in men’s dreams compared with total aggression. This means that cultural developments such as the women’s movement did not affect this sex difference in dreams. And this favours the sexual selection theory over the social role theory.

Another aspect of dream aggression fits the theory put forward by Archer: the higher difference in the aggression per male character compared to the aggression per female character in men (0.23 vs. 0.13 for men, 0.13 vs. 0.10 for women). That is, women experience aggressive interactions with both men and women in almost equal frequency in their dreams, whereas men’s dreams include same-sex aggression more often compared to opposite-sex aggression (Hall & Domhoff 1963). Also very interesting is the shift in the percentage of physical aggression over the life-span. Whereas children (younger than 11 years old) showed the typical gender difference of more physical aggression in boy’s dreams compared with girl’s dreams, the ratio of physical aggression in dreams is the same for both sexes in the age range from 12 to 17 years (Hall & Domhoff 1963; Oberst et al. 2005). This fits with Archer’s argument that males avoid risky encounters with older males prior to adulthood. The adults – as reported above – again showed the preponderance of physical aggression in men’s dreams. Domhoff (1996) reviews cross-cultural dreams studies. Whereas many Western countries showed higher prevalence rates of dream aggression in men compared to women, there where several exceptions. The Hopi Indians, for example, showed no gender differences in overall aggression and in the percentage of physical aggression (Domhoff 1996). The term Hopi can be translated into “peaceful ones” reflecting the lifestyle of these Pueblo Native Americans. But for some industrial countries, such as Switzerland and Japan, the ratios of physical dream aggression were not different between the sexes. This indicates that cultural factors modulate the amount of aggression in dream. In females, dream aggression was more often found in dreams of non-traditional women, indicating again the cultural effect on aggression pointed out by Archer. Unfortunately, these studies did not differentiate between same-sex aggression and opposite-sex aggression to enable us to test Archer’s claim that cultural factors might be more important in explaining the amount of opposite-sex aggression. Two studies, by Waterman et al. (1988) and Cohen (1973), investigated whether biological sex or feminine versus masculine sex role orientation explains differences in dream aggression. Whereas the finding of the first study was unambiguous (only biological sex was of importance), the second study showed effects of both variables on the amount of dream aggression. Again, it would have been fruitful to differentiate between same-sex and opposite-sex aggression. Another interesting gender difference can be found in the bad dreams and nightmares of children (Schredl & Pallmer 1998). In Table 1, the percentages of male and female aggressors are presented. Male characters threaten the dreamer most often whereas women are quite rarely aggressors in dreams. The ratio of male and female aggressors in dreams is similar for boys and girls, thus reflecting the preponderance of male aggression in mass media (news, films, etc.). It would be very interesting to study the gender of the aggressor in cross-cultural dream studies in more detail, for example, in societies without predominance of male aggression. If dream aggressors are still mostly male, one

Table 1 (Schredl). Human aggressors in children’s dreams

Aggressors

Total (n ¼ 111)

Boys (n ¼ 35)

Girls (n ¼ 76)

Male (unfamiliar) Female (unfamiliar) Male (familiar) Female (familiar)

49.7% 3.6% 27.8% 18.9%

51.4% 0.0% 31.4% 17.2%

48.7% 5.3% 26.2% 19.8%

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Commentary/Archer: Sex differences in aggression might argue that gender differences in aggression have hereditary aspects. To summarize, dream studies seem to be a valuable tool for studying sex differences in aggression, because the findings fit very well with the findings for waking-life aggressive behaviour. One might argue that studying dream aggression might be even more promising because aggression in dreams is not labelled socially the way being aggressive in waking life is. This is supported by the fact that aggression, even physical aggression, is quite common in dreams (Hall & Van de Castle 1966). For future studies, it would be very interesting to study the effect of mediator variables mentioned by Archer on the amount of dream aggression – for instance, the effects of empathy, risk-taking behaviour, and assertiveness, as well as physiological measures such as testosterone levels, size, and strength.

Human sexual dimorphism, fitness display, and ovulatory cycle effects doi:10.1017/S0140525X09990240 Jon A. Sefceka and Donald F. Saccob a

Department of Psychology, University of Arizona, Tucson, AZ 85721-0068; Department of Psychology, Miami University, Oxford, OH 45056. [email protected] [email protected] http://www.u.arizona.edu/~jons b

Abstract: Social roles theorists claim that differences between the sexes are of limited consequence. Such misperceptions lead to misunderstanding the important role of sexual selection in explaining phenotypic differences both between species and within humans. Countering these claims, we explain how sexual dimorphism in humans affect expressions of artistic display and patterns of male and female aggression across the ovulatory cycle.

We would like to applaud Archer for his target article, “Does sexual selection explain human sex differences in aggression?” The tone of the article title is reminiscent of the November 2004 National Geographic cover article that asked: “Was Darwin Wrong?” (With a resounding “NO!” answering the reader on the opening page). It’s no surprise that Archer has confidently proclaimed a resounding “YES!” to his own question. Archer effectively argues that social role theory fails to adequately explain the complexity of aggressive patterns found both within humans and across species by requiring that its adherents downplay the dramatic similarities that permeate the animal kingdom, underestimate cross-cultural similarities in human aggressive behavior, and disregard the impact of human sexual dimorphism. Here we would like to extend Archer’s critique of social role theory by looking at differences both between animal species and the human sexes. According to social role, or biosocial, theory (e.g., Eagly & Wood 1999; Wood & Eagly 2002), sex differences in social behavior result from the distribution of men and women into different social roles within society. These differences stem from sex differences in the physical attributes of the sexes as well as the changing local ecologies of humans. Despite acknowledging these dimorphisms as the starting point, this framework reduces the “role” of sexual selection in shaping these differences to little more than a historical footnote by failing to attend adequately to the variety of evolutionary forces integral in shaping the degree of sexual dimorphism within species. Largely due to parental investment and mating patterns, which themselves are largely determined by the local ecological conditions, dimorphisms may take the shape of physical attributes such as body size, or behavioral attributes such as behavioral fitness display (see Sefcek et al. 2006, for review). Specifically,

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social role theory argues that hominid sexual dimorphism is small in magnitude compared to other primates and driven as much by fluctuations in female body size as it is by intrasexual competition (Plavcan & van Schaik 1997b). We argue that the less-extreme dimorphism in humans is not evidence that the dimorphisms are not significant. Although the human sexes, which are approximately 15 – 20% different in body size, do not show the extreme dimorphisms of male and female gorillas or orangutans (e.g., these males being 50% larger in body size), they also do not show the remarkable similarity (monomorphism) in body size that gibbons and other socially monogamous primates do (Leutenegger 1982). That humans fall somewhere in-between suggests at least a moderate level of dimorphism as the result of a species-typical evolutionary history of moderate polygyny, cuckoldry, male parental investment, and male intrasexual competition, which leads to sex-typical differences in mating effort – that may manifest itself through aggression and other risky behaviors (Sefcek et al. 2006). One important difference in mating effort is illustrated through sex differences in fitness indicating, whereby an individual “shows-off” in an effort to display behavioral energy or genetic quality (Miller 2000). Such ornamental display is risky; it redirects metabolic resources away from survival and makes the individual conspicuous to intrasexual rivals and interspecies predators. Such advertisement may, however, yield a highpayoff. While humans do not display extreme physical ornaments like the peacocks tail, it is argued many products of the human mind and culture serve this fitness signaling function. Cultural artifacts produced through artistic expression (e.g., painting, musical production, poetic language, and humor) and scientific discovery are male-biased and are suggested to stem from intrasexual competition (Kanazawa 2000; Miller 2001). These patterns tend to show male-biased sexual dimorphism in public display, yet monomorphism in both public appreciation and private display. Furthermore, both men and women display cycle-specific dimorphic perceptual and behavioral changes related to aggression and self-protection that are in the service of enhancing reproductive fitness. For example, men perceive more dominance in male faces when their partner is ovulating, suggesting an evolved bias to identify the most likely intrasexual competitors in order to protect against potential cuckoldry (Burriss & Little 2006). Fertile females who rate their partners as sexually unattractive (a phenotypic sign of high mutation load) report greater extrapair flirtation and more partnerenacted mate guarding behavior, itself an aggression-based mating tactic (Haselton & Gangestad 2006). Finally, men report more use of sexual coercion in intimate relationships when they perceive that their partner has engaged in sexual infidelity (Goetz & Shackelford 2006), as well as report deeper and more vigorous penile thrusting (Gallup et al. 2003), and a higher sperm count per ejaculate (Baker & Bellis 1995) after periods of separation or alleged sexual infidelity. Conversely, fertile females become less aggressive and even though they report more attraction to male dominance, they engage in fewer risky behaviors – which suggests that women strategically avoid the types of activities that may increase their exposure to male aggression when fertile (Broder & Hohmann 2003). Furthermore, in response to sexually coercive scenarios, female handgrip strength increases at peak ovulation, an adaptation that may have evolved to protect females against sexually coercive male tactics (Petralia & Gallup 2002). That so much variability in men’s aggressive behaviors and female’s self-defense behaviors is contingent on fluctuations in female fertility and potential infidelity, strongly suggests that human aggression in its various forms may be better explained as solutions to reproductive problems, shaped via sexual selection, rather than simply as consequences of social roles. Although it is certainly the case that men and women often respond to the same cues with aggression, the fact that aggression, fertility, and

Commentary/Archer: Sex differences in aggression perceptions of infidelity are so intertwined suggests that sex differences in aggression are rooted in our evolutionary past. Because men and women, by dint of their biology have historically faced different adaptive challenges to reproductive success, those who inherited the most effective sexual strategies (e.g., Buss 1998) would be better equipped to effectively reproduce. It seems that one strategy for differentially improving reproduction includes sex-specific risky-behavioral tendencies, with women focusing on low-risk forms of aggression and males focusing on high-risk forms of aggression.

Standards of evidence for designed sex differences doi:10.1017/S0140525X09990276 Aaron Sell Department of Psychology, University of California, Santa Barbara, Santa Barbara, CA 93106-9660. [email protected] http://www.psych.ucsb.edu/research/cep/grads/Sell.html

Abstract: At the heart of the debate between social role theorists and evolutionary psychologists is whether natural selection has designed the minds of the sexes differently to some interesting extent. In this commentary I describe the standards of evidence for both the positive and negative claims. In my opinion, Archer has met the standard for designed sex differences in intrasexual conflict.

George Williams argued that natural selection results in three categories of features: adaptations, by-products and noise (Williams 1966). The same classifications hold for sex differences, and the debate between evolutionary psychologists and gender role theorists can be understood as a debate about which of two categories sex differences in aggression falls into. Because Williams was classifying features and not differences in features, some slight translation is necessary. Evolutionary psychologists tend to think that sex differences in aggression are adaptive differences; that is, they are sex differences resulting from adaptations designed differently in men and women by natural selection in response to differing ancestral selection pressures. Non-controversial examples include sex differences in body size and maturation rates. Gender role theorists tend to think of sex differences in aggression as learned byproducts, that is, as sex differences that result from learning mechanisms (which were designed by natural selection, of course) that are the same in men and women but create differences because of differential input. Non-controversial examples of this would be sex differences in car seat settings and fear of prostate cancer. Finally, there are arbitrary differences: these are sex differences that result from accidents of history and are not designed by natural selection but also do not stem from learning mechanisms in ways that lead to sensible outcomes. Non-controversial examples would be sex differences in styles of dress, the spelling of names (e.g., Aaron vs. Erin), and culturally agreed upon color symbols (e.g., pink for girls, blue for boys). The standard of proof for adaptive differences is parallel to those for adaptations. One has to show evidence of complex functional design, geared toward solving an adaptive problem that acted differently on the sexes. Archer has done this for sex differences in intrasexual aggression. He lays out a complex of features, all of which would result from a differential selection pressure (namely, sexual selection). They include, for males: greater variance in reproductive success, greater size and strength, longer maturation times, higher mortality and male-biased conception ratio. I would add that physical differences in size and strength are also supplemented by sex differences in basal metabolic

rates (Garn & Clark 1953), heart size, heat dissipation, hemoglobin, muscle-to-fat ratio, and bone density (Lassek & Gaulin, in press). Across all those variables the sex difference is in the direction of males being designed for physical aggression. Additionally, boys prefer rough-and-tumble play, a type of activity that is understood by evolutionary biologists to be practice for future combat (Symons 1978). This last point is particularly important because of the overwhelming evidence that sex differences in rough-and-tumble play are not caused by societal expectation. Girls born with congenital adrenal hyperplasia (CAH) as well as progestin-induced hermaphrodism (PIH) are typically raised as girls, and genetically are girls, but experience some heightened organizing effects of androgens during development. As a result, they engage in more boy-like play patterns, including rough-andtumble play (Daly & Wilson 1983). All of these coordinated features, each in the predicted direction, provide powerful evidence that natural selection designed males and females differently when it comes to aggressive tendencies. The evidence required to put sexual differences in aggression in the category of learned byproducts is as follows: (1) identify the adaptation (or adaptations) that aggressive differences result from, and (2) demonstrate why, as a byproduct of their design, those adaptations would lead to sex differences. Gender role theorists have taken steps in these directions, specifying that evolved physical differences in strength and size coupled with a cost-benefit analysis mechanism (and more traditional socialization mechanisms) will produce differences in aggressive tendencies (Wood & Eagly 2002). As Archer points out, however, the data are stacked against this theory. He mentions that aggression’s developmental trajectories are inconsistent with socialization theory, and the role of testosterone and operational sex ratio are difficult for gender theorists to explain. The data from CAH and PIH girls also contradicts the idea that gender roles lead to differential aggression, as the girls generally maintain a female identity even while increasing their aggressive play. Finally, from a theoretical point of view, one has to ask why natural selection would have selected genes that created sex differences in body size and strength if males and females were aggressing at equal rates. With regard to intersexual aggression, it is important to keep in mind that similarities between men and women on broad measures of aggression can hide sex differences in particulars. For example, men and women have similar rates of spousal homicide that are motivated by sexual jealousy, but it was male jealousy that resulted in both the killing of husbands, usually in defense, and wives, usually out of jealous anger (Daly & Wilson 1988). As Archer says, both evolutionary and social role perspectives predict that spousal aggression should vary with the relative power of the individuals. The question remains, however: Which perspective will be most useful for predicting and explaining currently unknown features of mate-directed aggression? By studying selection pressures and how they work, evolutionary biologists have been able to account not only for the origin of biological complexity, but the origin of sexual reproduction itself (Tooby 1982), the origin of sexes (Parker et al. 1972), the existence of maturation and senescence (Williams 1957), the origin of aggression (Maynard Smith & Price 1973), its major causes (Huntingford & Turner 1987), the existence and function of aggressive displays (Alcock 1998), the magnitude and constituent features of sexual dimorphism (Daly & Wilson 1983), and sexual differences in aggressive tendencies, homicide (Daly & Wilson 1988), and rough-and-tumble play (Symons 1978). Finally there is a massive amount of primatological data showing how natural selection has designed males and females of other species in ways consistent with the differing adaptive problems they faced ancestrally (Smuts et al. 1987). With all that in mind, it seems likely that natural selection played some important role in the differential design of male and female minds, particularly in domains defined by differential selection pressures such as aggression. BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Commentary/Archer: Sex differences in aggression

Sex differences in human aggression: The interaction between early developmental and later activational testosterone doi:10.1017/S0140525X09990367 David Terburg,a Jiska S. Peper,a Barak Morgan,b and Jack van Honka a Department of Psychology, Utrecht University, 3584 CS Utrecht, The Netherlands; bDepartment of Human Biology, University of Cape Town, Department of Human Biology, Cape Town, South Africa 7925. [email protected] [email protected] [email protected] [email protected]

Abstract: The relation between testosterone levels and aggressive behavior is well established. From an evolutionary viewpoint, testosterone can explain at least part of the sex differences found in aggressive behavior. This explanation, however, is mediated by factors such as prenatal testosterone levels and basal levels of cortisol. Especially regarding sex differences in aggression during adolescence, these mediators have great influence. Based on developmental brain structure research we argue that sex differences in aggression have a pre-pubertal origin and are maintained during adolescence. Evidence of prenatal, adolescent, and adult levels of testosterone in relation to aggression taken together, support Archer’s argument for sexual selection as the driver of sex differences in aggression.

John Archer makes a strong argument for an evolutionary basis of sex differences in aggression. His thesis is that, starting in early childhood, sex differences in aggressive behavior exist, and, although these are mediated by social influences, they are underlain by biological variables. One of these variables is the steroid hormone testosterone. Archer’s conclusions regarding testosterone and adolescence need some refinement. As Archer himself points out, data of self-reported aggression in male adolescents do not support findings in testosterone administration studies on aggression. He argues that, although exogenous testosterone seems to enhance proneness to aggression, the rising levels of testosterone in male adolescents are not reflected in self-reported aggression measures. However, behavioral studies suggest that testosterone is a mediator of adolescent aggression. James Dabbs and colleagues showed repeatedly, in a line of studies in the nineties, associations of testosterone and violent criminal behavior. Imprisoned young males with high salivary testosterone were substantially more frequently convicted for aggressive crimes like violence and rape, and they showed more violent behavior (Dabbs et al. 1995). This was also replicated in studies on women (Dabbs & Hargrove 1997). Interestingly, in late adolescent males the hormone cortisol mediated the correlation between testosterone and aggressive behavior, which was found only in imprisoned adolescents with low cortisol levels (Dabbs & Jurkovic 1991). More recently, Popma and colleagues (Popma et al. 2007) showed a correlation of testosterone and self-reported measures of violent behavior, but again, this was mediated by cortisol. Designed to investigate the relation between testosterone, cortisol, and aggression in early adolescence, their study pointed to an effect of testosterone on overt aggression only when cortisol levels were low. Confirming this, Hermans et al. (2008) found in an fMRI study increased activity in the hypothalamus, amygdala, and orbitofrontal cortex in response to angry facial expressions. This network of brain structures is considered vital in human reactive aggression. Importantly, activity in the subcortical part of this network, namely, the hypothalamus and amygdala, in response to angry faces proved to be related to the ratio between testosterone and cortisol. Based on these findings one should consider taking basal levels of cortisol into account when comparing groups on aggressive behavior. Especially during adolescence, a highly stressful period (as demonstrated hormonally by marked increases in HPA-activity [Gunnar et al. 2009] and, behaviorally, by the onset of several

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stress-related psychiatric illnesses [Paus et al. 2008]), the rise of testosterone levels (alone) in boys relative to girls will not necessarily result in a relative increase of aggressive behavior. Another issue of consideration is testosterone in early development. Bailey and Hurd (2005), for instance, have shown that prenatal levels of testosterone, reflected in the 2D:4D digit length ratio, may mediate testosterone-aggression relationships. In males, higher prenatal testosterone levels correlated with physical aggression in adulthood. Interestingly, recent evidence from testosterone administration research in humans suggests that high prenatal testosterone levels increase sensitivity to behavioral effects of testosterone in later life (van Honk 2009). Furthermore, during early puberty (mean age 11.9 years), clear volumetric sex differences were found in brain areas mediating aggression (i.e., amygdala, striatum, rostral anterior cingulate cortex, and superior temporal gyrus; male volume . female volume) (Peper et al. 2009). However, testosterone levels at this age could not explain these brain morphological sex differences. It might therefore be argued that a possible influence of testosterone on brain areas involved in aggression has a prenatal or early postnatal origin. In conclusion, testosterone is unmistakably involved in human aggression and contributes importantly to sex differences in aggressive behavior. These sex differences, however, seem to originate before puberty. The relative increase of testosterone levels in adolescent boys and its relation to aggressive behavior is obscured by at least two mediators: high testosterone-sensitivity due to high prenatal testosterone levels and, especially during adolescence, levels of basal cortisol. Taking these factors into account, increased levels of testosterone enhance aggressive behavior in both adolescent boys and girls. Thus, it seems that the link between testosterone and aggression in adolescents is maintained. The heredescribed relations between prenatal, adolescent and adult levels of testosterone, together with results found after testosterone administration, are in support of Archer’s hypothesis that sex differences in aggression are a result of sexual selection.

Development of sex differences in physical aggression: The maternal link to epigenetic mechanisms doi:10.1017/S0140525X09990288 Richard E. Tremblaya,c and Sylvana M. Coˆte´b,c a School of Public Health and Population Sciences, University College Dublin; Belfield Campus, Dublin 4, Ireland; bDepartment of Social and Preventive Medicine and St-Justine Hospital, University of Montreal, Montreal, Quebec H3T 1J7, Canada; cInternational Laboratory for Children’s Mental Health, University of Montreal, Montreal, Quebec H3T 1J7, Canada and INSERM, Paris, France. [email protected] [email protected] http://www.gripinfo.ca/Grip/Public/www/

Abstract: As Archer argues, recent developmental data on human physical aggression support the sexual selection hypothesis. However, sex differences are largely due to males on a chronic trajectory of aggression. Maternal characteristics of these males suggest that, in societies with low levels of physical violence, females with a history of behavior problems largely contribute to maintenance of physical aggression sex differences.

We agree with Archer that sex differences in physical aggression during infancy observed in recent longitudinal studies support the sexual selection theory rather than the social role/biosocial theory. We first emphasize that the physical aggression developmental trajectory trends observed in these studies are still more strongly at odds with the “social role/biosocial” and “social learning” theories of physical aggression. Second, we suggest that in societies with low levels of physical violence females may play a

Commentary/Archer: Sex differences in aggression more active role in maintaining physical aggression sex differences than generally concluded from sexual selection theory. Trends in physical aggression development. Results from large longitudinal studies on the development of anger and physical aggression during early childhood became available only recently. These studies clearly confirmed Darwin’s (1872/1989) observations that humans use physical aggression to fight for property as soon as they have the required motor control to push, slap, hit, and kick (Alink et al. 2006; Tremblay et al. 1999). As illustrated in our Figure 1, analyses of physical aggression developmental trajectories during early childhood showed that frequency of aggression increases dramatically for most children from its onset at the end of the first year after birth until it reaches a peak between the third and fourth year (Coˆte´ et al. 2007). If this general increase is driven by social learning of aggression (Bandura 1973), it is unlikely to be from imitation of virtual violent models. Still, it could be learned from parents, siblings, and peers. Yet, reliance on social learning theory of aggression poses major challenges to account for life-span sex differences. The main challenge comes from the observation, as illustrated in Figure 1, that the peak frequency of physical aggressions between 3 and 4 years is followed by a steadily decreasing trend for most children until adulthood (Coˆte´ et al. 2006; Loeber et al. 2005; Nagin & Tremblay 1999; National Institute of Child Health and Development [NICHD] 2004). Counterintuitively, the frequency of physical aggression declines during periods (middle childhood and adolescence) when exposure to physical aggression in the neighborhood and the media increases dramatically. This observation was totally unexpected from the “social learning of aggression” and “social role/biosocial” perspectives. Why would children suddenly reverse the developmental trend presumably set by their family environment during the first three years of life? To our knowledge no “social role” or “social learning” theorist has suggested that the majority of infants learn to aggress from their parents and unlearn from the mass media and the neighborhood. The fact that boys are more physically aggressive than girls by 17 months (Alink et al. 2006; Baillargeon et al. 2007) points to the powerful role of biological factors (Dionne et al. 2003), as Archer points out. However, these biological factors can be the product of early environmental conditions as well as genetic inheritance. Epigenetic effects of maternal care. Developmental trajectory studies from childhood to adulthood show that a small group of children maintain high frequencies of physical aggression (see Fig. 1). This exception to the rule is useful to search for the environmental and genetic differences between the majority who learn not to physically aggress from early childhood onwards and the minority that maintains an atypically high frequency of physical aggression. As argued by Archer, males are more likely to be on the high trajectory. There is also accumulating evidence that specific genetic profiles, especially for males, are involved in neurological deficits which handicap learning alternatives to physical aggression (Buckholtz & Meyer-Lindenberg 2008). However, much of the variance in physical aggression

is accounted for by environmental factors related to maternal characteristics such as the mother’s history of behavior problems during adolescence; low levels of education; childbearing during adolescence; smoking during pregnancy; depression; and coercive parenting early after birth (Coˆte´ et al. 2006; Nagin & Tremblay 1999; NICHD 2004). Research on nonhuman primates has shown the importance of early maternal care on the development of unregulated aggression (Suomi 2005), while rodent work on early maternal behavior shows differential sex effects on play-fighting, sexual behavior, and reproductive success (Cameron et al. 2008; Parent & Meaney 2008). There is also growing evidence from human studies of early environmental genetic programming effects which can explain differences in brain development and regulation of behavior, including aggression and suicide (McGowan et al. 2009 Tremblay 2008). From this perspective a key proximal mechanism for sex differences in aggression may be strongly based on maternal behavior during the perinatal period through its impact on infant gene expression, brain development, and behavior development, and eventually on the next generation through reproductive behavior (Gluckman & Hanson 2005; Meaney 2001). The link between maternal behavior and frequent male physical aggression appears important to understand the reason we observe relatively large physical aggression sex differences in modern societies despite the fact that the use of this form of aggression to resolve conflicts is largely condemned for males and females. Indeed, frequency of physical aggression is one of the best predictors of male school failure and exclusion from the labor market (Kokko & Pulkkinen 2000; Vitaro et al. 2005). Longitudinal studies of females with physical aggression problems during childhood show that, although they do not maintain high levels of physical aggression during adolescence and early adulthood, they tend to fail in school, suffer from depression, are likely to mate with behavior problem males, to become pregnant during adolescence, to smoke during pregnancy, and to use coercive behavior towards their children (Fontaine et al. 2008; Serbin et al. 1998). In other words, they have all the risk factors needed to place their male children on a trajectory of chronic physical aggression. From this perspective males who mate with well-adapted females should in the long run contribute to the reduction of physical aggression sex differences among humans. It can also be argued that helping maladjusted females adapt to the modern environment will increase the likelihood that their male children will be less physically aggressive and thus reduce sex differences in physical aggression.

Sexual selection and social roles: Two models or one? doi:10.1017/S0140525X09990355 Pierre L. van den Berghe Department of Sociology, University of Washington, Seattle, WA 98195-3340. [email protected]

Abstract: Nothing is gained by opposing “sexual selection” and “social roles,” or by proclaiming the supremacy of one over the other. Instead, we should develop a unitary model of gene-culture coevolution, allowing for the complex interaction of both, and varying importance of each, all within our double, species-specific, adaptive, evolutionary track.

Figure 1 (Tremblay & Coˆte´). Developmental trajectories of physical aggression from 17 months to 21 years based on two Que´bec population samples: 17 months to 5 years (N ¼ 1758), 6 to 21 years (N ¼ 2000).

Archer’s article is a useful survey of the evidence in support of the role of sexual selection in male-female differences in the expression of physical violence and risk-taking, combined with a weak and inconsistent conceptual framework. Archer begins by opposing two views of gender differences in the expression of aggression, “sexual selection theory” and “social role/biosocial theory,” and, after reviewing the evidence, proclaims the first a hands-down winner. Then, he turns to conflicts between mates, BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Response/Archer: Sex differences in aggression notes a lesser sex difference in aggression, and shifts gears to propose an economics-style model of conflict between selfish maximizers in a dyadic relationship. Even then, he concedes that cultural variation leaves a large, unexplained residual. All this conceptual confusion can be simply resolved by discarding the opposition between the two approaches, and adopting a unitary model of gene-culture coevolution. There is abundant evidence for the role of sexual selection in producing gender differences in behavior, including levels of aggression. But the same sexual selection model also explains sexually differentiated behavior between mates in a reproductive relationship. Indeed, that is the very core of sexual selection. No conceptual shift is needed at all. It is all one and the same. Now for cultural variation: It, too, obviously exists, but by now it is clear that the circular explanation of culture in terms of culture is bankrupt. “They do it so because it is their custom” is not an alternative model of behavior. It merely describes; it does not explain. Cultural variation is not random; most of it is adaptive, and linked to adaptation by natural selection. Humans are on a double evolutionary track: genetic and cultural, complexly intertwined. A single coevolution model explicating variations in gene-culture interactions is called for (Alexander 1979; Boyd & Richerson 1985; Chagnon & Irons 1979; Lumsden & Wilson 1981). In some instances, cultural variation is near zero. In others, it is considerable. That range of variation is the explanandum. Let us take the example of women’s participation in warfare. It ranges from negligible to considerable (Adams 1983; Lynn 2008). But a closer look reveals a near-zero variation in women’s direct participation in combat, while, in highly militarized societies (such as Israel), women play a large supporting role in scores of military duties, except combat. In short, nothing is gained by trying to show that sexual selection explains behavior better than “social role” or culture. Everything is gained by explaining the complex modalities of geneculture coevolution in terms of a double adaptive track. To deny the importance of either is untenable.

Author’s Response Refining the sexual selection explanation within an ethological framework doi:10.1017/S0140525X09990963 John Archer School of Psychology, University of Central Lancashire, Preston, Lancashire PR1 2HE, United Kingdom. [email protected] http://www.uclan.ac.uk/scitech/research/rae2008/psychology/ staff_profiles/jarcher.php

Abstract: My response is organized into three sections. The first revisits the theme of the target article, the explanatory power of sexual selection versus social role theory. The second considers the range and scope of sexual selection, and its application to human sex differences. Two topics are examined in more detail: (1) the paternity uncertainty theory of partner violence; (2) evolution of inter-group aggression. Section 4 covers ultimate and proximal explanations and their integration within an ethological approach. I consider the development of sex differences in aggression, and their causal mechanisms, within this framework.

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R1. Introduction I thank the commentators for an interesting and varied set of comments on my target article. Most of my responses are organized in terms of the following broad themes. The first is the central question in my target article, whether sex differences in aggression are better explained by sexual selection than social role theory. Most commentators agree that sexual selection is preferable, although a minority do not view the two as incompatible. The second issue concerns sexual selection. A number of commentators raise the issue of how broadly or narrowly sexual selection should be defined, and what other features of human sex differences might be covered by the concept. Some want me to go further than I had in expanding its scope, and offer their own varied and interesting suggestions as to how this could be achieved. Several of these are clearly advances on aspects of my target article, whereas others (in my opinion) are not. Arising out of this discussion of sexual selection are two issues that require longer treatment: violence between partners and inter-group aggression. The third main theme concerns ultimate and proximal explanations of human behavior. My preferred approach to evolutionary psychology is grounded in ethology, rather than the modular version. I outline the main differences between these two and then consider commentaries relating to development and causation within the ethological framework. R2. Sexual selection and social role theory Most commentators agree that sexual selection provides a more comprehensive explanation of sex differences in aggression than the social role theory alternative. Some (Buss; Figueredo, Gladden, & Brumbach [Figueredo et al.]; Gaulin; Kenrick & Griskevicius; and Pound, Daly, & Wilson [Pound et al.]) suggest that social role theory has very little merit in this context, and that the case for sexual selection is much stronger than I indicated. Only Eagly & Wood defend social role theory fully. Two other commentaries (from Bailey, Oxford, & Geary [Bailey et al.] and van den Berghe) regard the explanations as reconcilable, although neither explains how this might be achieved. Bailey et al. state: “We argue that Archer’s review, along with many previous contributions to this debate, assume, either implicitly or explicitly, that sexual selection and social learning are alternative explanations – but in fact, they are not necessarily so” (first para.; emphasis theirs). Subsequently, they refer to “social roles” rather than “social learning.” Yet I was careful to distinguish the older, more limited, social learning view from social role theory, and its updated biosocial version. Bailey et al. did not recognize these distinctions. They correctly state that social learning and sexual selection theories are not necessarily alternatives, since sexual selection is an ultimate explanation and social learning is one form of proximal mechanism. However, the appropriate alternative to sexual selection is the “biosocial” version of social role theory, which sets out a way in which sex differences could have arisen without sexual selection (or at least without a central role for it). Referring to their “biosocial” social role theory, Eagly & Wood state that “flexibility in behavior is at the heart of

Response/Archer: Sex differences in aggression our evolutionary analysis.” There are two issues raised by this statement: The first concerns flexibility, and the second the extent to which their analysis is evolutionary. The capacity for flexibility is an issue on which evolutionary psychologists and social role theorists can agree in principle, although their conceptualization is different. Gangestad et al. (2006a) put forward an evolutionarybased theory of the impact of ecology on culture (and consequently flexibility in behavior), which they explicitly contrasted with Eagly’s social role theory (see also Kenrick & Griskevicius). This approach has been further developed by others (Fincher et al. 2008; Schaller & Murray 2008; Thornhill et al. 2009). In the target article, I considered flexibility in relation to environmental conditions (sect. 2.8). Pound et al. developed this further in their commentary, with the prediction that cues to greater fitness variance in the local environment should result in more dangerous confrontations between men. They note some of the ways in which this argument could have been further developed in my target article, in particular important recent evidence linking inequality of resource distribution and violence proneness. To add to their suggestions is the comprehensive analysis by Wilkinson and Pickett (2009), linking societal inequality with not only violent crime, but also a range of indicators of health and well-being. This reasoning could also be linked with criminological evidence on the role of marriage, work, and fatherhood in lowering the prevalence of criminal offending (Laub et al. 1998; Skarðhamar & Lyngstad 2009). The second issue Eagly & Wood’s statement raises is that few evolutionary researchers would recognize their analysis as “evolutionary,” since they invoke evolution of the body but not the mind (as noted by Friedman et al. 2000; Lieberman 2006; and the commentaries by Browne and Kenrick & Griskevicius). Where Wood and Eagly (2002) invoked evolved capacities, they specified that these are “physical and reproductive” (p. 719), not psychological. This view of evolution is a crucial difference between an approach rooted in sexual selection and Wood and Eagly’s biosocial theory. Social role theory was originally a theory that (unlike evolution) was not concerned with ultimate origins (Eagly 1987). Later, following critiques by evolutionary psychologists (see target article), Wood and Eagly (2002) developed a version of social role theory that did include ultimate origins, one that involved constraints on what men and women could easily do in the light of their evolved physical differences. This recasting of social role theory seems to me to have been a fundamental error. Rather than seek to revise a theory with flawed assumptions (that men’s and women’s evolved psyches are similar), a more realistic strategy would be to acknowledge that there was an evolved origin for certain aspects of human sex differences, and to seek to incorporate social roles within that framework. As in a previous book chapter (Eagly et al. 2004), Eagly & Wood interpret findings on the hormonal responses to social events, such as insults, competition, and forthcoming fatherhood, as representing role demands. However, these specific reactions occur widely in other mammals, in birds and fish (Archer 1988; 2006b; see R.4), and even in cockroaches (Kou et al. 2008). It would seem more parsimonious to conceptualize them as part of a widespread pattern of adaptive responses, which have an ancient

phylogenetic history, rather than as role demands that are presumably specific to humans. As Gaulin notes, sexual selection is a theory that applies to all sexual species, and it is special pleading to argue that a different sort of theory can apply to humans, even with additions from the biological sciences, such as hormonal reactions. Indeed, this seems to do nothing but highlight fundamental problems with the theory. Sell’s commentary provides a lucid analysis of the requirements for adaptive features, or for learned byproducts. He assesses Wood and Eagly’s biosocial theory according to the second category, pointing out that it involves evolved sex differences in size and strength combined with a mechanism incorporating general cost-benefit analysis. He then asks why natural selection would have produced sex differences in size and strength if men and women were aggressing at similar rates. This is a telling question that is not addressed by social role theory. R3. Extending the concept and scope of sexual selection In this section, I consider a number of related issues, connected to the scope of sexual selection. The first subsection concerns the concept itself, its original scope and more recent extensions. This leads to a more detailed consideration of a specific evolutionary explanation that applies to post-copulatory competition: mate guarding arising from paternity uncertainty. I then consider suggestions for extending the original scope of sexual selection to other forms of behavior, and consider in more detail intergroup aggression. R3.1. The concept of sexual selection

After Trivers’ (1972) consideration of parental investment, it became logical to extend what we consider as sexual selection to processes following fertilization, although noting that this changes the original conception. I did so in the target article (sect. 4.6), and this was the theme of a recent article by Carranza (2009), a source cited in two commentaries (Campbell and Pellegrini). Specifically, I considered the application of the game theory model of Clutton-Brock and Parker (1995) to physical aggression between partners: again it should be stressed that models such as this one are quite different from classic sexual selection models (a point not appreciated by van den Berghe). Two commentaries (Cashdan and Kaighobadi & Shackelford) were concerned that I did not consider mate guarding derived from paternity uncertainty, the usual evolutionary explanation applied to partner violence. This is also a model that involves processes following fertilization. My reasons for omitting it in the target article are elaborated in section R3.2. Of the two original processes involved in sexual selection, I focused on male competition because it was most relevant to the topic of my article, sex differences in aggression. While recognizing that female choice was the other process, I did not cover this for reasons of relevance. However, one issue concerning female choice is raised in two commentaries (Behme and Kempenaers & Forstmeier). It concerns the conflict between choosing aggressive or non-aggressive mates, and forms part of the extensively investigated topic of when women prefer BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Response/Archer: Sex differences in aggression men who are likely to show more parental effort and when they prefer men who typically show mating effort, and with it higher physical attraction and more pronounced aggression. These alternative male reproductive strategies were mentioned in my target article (sect. 2.7), but not in relation to women’s preferences, which is another (extensive) topic. A full treatment of the evolution of sex differences in aggression would include this. A number of commentaries seek to extend my central argument, based on inter-male competition, in interesting and relevant ways. These include intrasexual competition by females, which has been the subject of recent articles on sexual selection in animals (considered by Campbell and Pellegrini). One of these, Clutton-Brock (2009), described instances where females compete for breeding territories and other resources necessary for reproduction, and for social rank: In some cases females can show a greater variance in reproductive rate than males. These and other examples of female competition are readily encompassed by traditional conceptions of sexual selection in terms of parental investment or reproductive rate (Trivers 1972; Clutton-Brock & Vincent 1991). They typically occur in polyandrous and monogamous species, or in eusocial breeders. Clutton-Brock (2009) also pointed out a fundamental distinction between competition in the two sexes, that male competition is typically for access to the other sex and female competition is typically for resources necessary for reproduction. This is likely to provide an additional reason why female aggression is usually escalated to a lesser extent than is male aggression. As Clutton-Brock (2004, p. 26) noted: “one of the problems in writing about sexual selection today is that the term is used in so many different ways.” Campbell’s consideration of her evolutionary explanation of less risky female aggression shows the difficulty of drawing the line in specific instances. I wonder whether it really is useful when considering sex differences in behavior to extend the concept of sexual selection to such an extent that, “We might say that, under this definition, almost all selection is sexual selection” (Carranza 2009, p. 750). Since I was mainly concerned in the target article with inter-male competition, a central part of the original conception of sexual selection (Darwin 1871/1901), it was clear what I was dealing with, and what I was not. Campbell makes a compelling case for considering other features that might not have arisen from inter-male competition, and yet which are relevant to sex differences in aggression. Behme suggests that larger male size and musculature may be fitness-enhancing outside the realms of reproduction: Of course, this may or may not be the case, but unlike Campbell’s example of greater female fear, no precise functions are suggested. Until they are, it is more parsimonious to regard the enhanced upper body musculature of the human male as part of a range of adaptive features that originated from intermale competition. Even those who propose a widening of the term sexual selection (e.g., Carranza 2009, cited by Campbell and Pellegrini) recognize the central importance of competition for mates in the process. Secondary differences, such as in feeding behavior or habitat use (Carranza 2009), may be relevant to sex differences associated with men’s specialization for hunting and women’s for gathering, although this arose much later in human evolution 294

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and, unlike male competition, is restricted to humans, rather than being widespread in many animals. It may well play a part in men’s adaptations for group-cooperation and out-group aggression (Browne and Johnson & van Vugt). In his cross-species analysis of sexual selection, CluttonBrock (2009) stated that sex differences in behavior are probably more flexible than is commonly realized. This highlights the importance of ecological conditions for variations in the sex differences. Pellegrini refers to the degree to which sex differences in behavior are moderated by different ecologies. Related to this, in section 3.7, I described a cross-cultural test of the hypothesis that sex differences in size would be more pronounced in polygynous societies (Alexander et al. 1979). The original claim that this was the case was undermined by later re-analyses. A related issue concerns the relationship between mating systems and the ecological conditions under which they occur. I also mentioned the finding that polygny was associated with higher degrees of pathogen stress across 186 societies (Low 1990). Low (1989) found that boys were taught to strive and compete more in polygynous societies. Thus, the degree of pathogen stress was related to the mating system, which in turn was related to the type of socialization. More recent studies have extended Low’s analysis to characteristics of the social structure of modern states, including gender empowerment (Thornhill et al. 2009). This is a particularly interesting line of research suggesting that social roles can be explained in terms of ecological adaptations. R3.2. Partner violence and paternity uncertainty

One particular evolutionary model involving post-copulatory conflicts of interest between the sexes has been used to explain male violence to women. This is viewed as a form of mate guarding, whose ultimate function is to ensure paternity. Since females do not have the adaptive problem of paternity uncertainty, they do not have this reason to mate-guard. This explanation is elaborated in two commentaries (Cashdan and Kaighobadi & Shackelford). The logic of mate-guarding and its widespread existence in nonhuman animals (e.g., Parker 1974b; Wilson & Daly 1992) is not disputed. It is likely to play a part in explaining men’s sexual coercion to their partners (as Kaighobadi & Shackelford argue), which might also be linked to sperm competition (widely found in insects and birds). However, I know of only one study that provides direct evidence for sperm competition in humans (Baker & Bellis 1993), and as far as I know this has not been replicated. I did not refer to the mate-guarding view as an explanation of sex differences in partner violence in my target article, although I was aware of work by Wilson and Daly (1992; 1996) and others. I like the logic of mateguarding, and the associated emotion (sexual jealousy) is clearly associated both with men’s violence to other men and with men’s violence to their own partners (Daly & Wilson 1988; 1990). It was in hindsight an omission not to have mentioned paternity uncertainty in relation to inter-male aggression motivated by sexual jealousy, since this would be in addition to the pre-copulatory intermale competition typically covered by sexual selection. The reason I did not mention paternity uncertainty in

Response/Archer: Sex differences in aggression relation to partner violence was not an oversight. It was because there are typically no sex differences in overall acts of physical aggression, at least in modern Western nations (Archer 2000a; 2002). There are sex differences in injuries, the consequences of these acts – a difference better explained by the size and strength differences of the two sexes than by mate-guarding. Faced with the evidence of similar proportions of male and female physical aggression to partners, it would seem reasonable to conclude that whatever part mate-guarding plays in the male psyche, this alone cannot explain partner violence. It would then be of interest to examine not only behavior used by males to increase their chances of paternity, but also behavior used by females to maximize their partner’s investment in the relationship. Buss’s studies of mate-retention tactics (Buss 1988a; Buss & Shackelford 1997a) and Flinn’s (1988) study of mateguarding in a Caribbean village did adopt such a “gender-inclusive” approach,” although others have only studied male-to-female violence (e.g., Buss et al. 2008; Shackelford et al. 2005a). A digression is necessary on the background to such selective studies that only consider partner violence as a one-way process. Selective studies are based on the assumption that most partner violence is male-to-female. I presented a considerable body of evidence from Western nations that this is incorrect (both in the target article and in previous reviews). The sources cited by Cashdan were ideologically biased, as are many in this area. Her source of criticism of the Conflict Tactics Scale (CTS), the measure used by family researchers to study conflict between partners, is a selective narrative review that is more a polemic than an objective review (Dobash et al. 1992). A more representative, quantitative assessment of the evidence for the accuracy and reliability of the CTS (Archer 1999) showed that it is much more reliable than Dobash et al. inferred from their review. Correlations between couples were r ¼ .55 and .53, for men and women, respectively, for an aggregate of six studies. This is comparable with values obtained for spousal ratings of personality (McCrae & Costa 1990) and does not take into account attenuation by measurement error. In their study of 350 couples in New Zealand, Moffit et al. (1997) found that correlations of r ¼ .58 and .54 were raised to .83 and .71 when latent correlations were derived from confirmatory factor analysis. Other evidence supports both the reliability and validity of the CTS and its modifications (Straus 1990; 2004), as does the similarity in the findings from this measure and other methods, such as crime victimization surveys (e.g., Laroche 2005; Mirrlees-Black et al. 1998). Cashdan also cites the influential but controversial work of Michael Johnson (see Dutton 2005; Dutton & Nicholls 2005). Again, I was aware of this, but chose not to cite it in the target article. Johnson (1995) argued from a qualitative review of studies involving general population samples and samples of women victims from shelters, that there were two “types” of partner violence, one (characteristically male) involving high levels of sustained violence and control, found in shelter samples, and the other mutual lower-level violence in the absence of overall control, found in general samples. He termed these, respectively, “patriarchal” (later “intimate”) terrorism,” and “common (later “situational”) couple” violence.

Johnson (2001) applied cluster analysis to two samples, a community sample and one selected for high levels of male-to-female violence, finding clusters corresponding to these samples. It is likely that these arose from the prior selection of the samples, which in turn corresponded to Johnson’s earlier classification. Johnson’s other empirical study (Johnson & Leone 2005) used a sample drawn from a “violence against women” survey that cannot be regarded as an unbiased sample of violence by both sexes (Archer 2000a; 2002; Straus 1999). In an analysis of a large-scale Canadian survey sampling physical aggression and controlling behavior by both sexes, LaRoche (2005) found that 38% of those who fitted Johnson’s “intimate terrorist” category (i.e., they were both violent and controlling) were women, again suggesting that the previous categorization was based on biased sampling. Using another sample not selected for high levels of victimization, and including reports by both men and women, Graham-Kevan and Archer (submitted) found that the “intimate terrorist” group contained similar proportions of men and women. Nonviolent victims – that is, those who do not use any physical aggression towards an “intimate terrorist” – were twice as likely to be men than women. These findings indicate that Johnson’s typology should be viewed with some skepticism, rather than the uncritical acceptance it enjoys at present, and that it requires further investigation. To return to paternity uncertainty, if this were a full explanation of partner violence, the following would be the case: (1) men but not women would show physical aggression to their partners; (2) the male-only nature of physical aggression would be consistent across cultures (since paternity uncertainty is universal); (3) males but not females would show controlling behavior to their partners; (4) male aggression but not female aggression (if and when it occurs) would be motivated by the desire to control the partner’s behavior; (5) males would show more sexual jealousy than females; (6) physical aggression to a partner would be linked to sexual jealousy in males but not in females (again if and when it occurs). The first of these expectations was mentioned above and was covered in the target article. Studies in Western nations show similar frequencies of acts of physical aggression among women and men, although women are more likely to be injured. The second was also covered in the target article, and as indicated, there is considerable and meaningful variability across nations, which is related to women’s degree of societal power and to gender attitudes (Archer 2006a). The third is refuted by a number of studies showing no sex differences in controlling behavior (Felson & Outlaw 2007; Graham-Kevan & Archer, in press; Walby & Allen 2004), or more control by women than men (Charles & Perreira 2007), all from large or representative samples. The fourth is refuted by evidence that control motives are linked to physical aggression in both sexes (Felson & Outlaw 2007; Graham-Kevan & Archer, in press). Regarding sex differences in sexual jealousy, some studies have found none (Bookwala et al. 1992; Felson 2002; Mullen & Martin 1994; White 1981), whereas others have found that women report more sexual jealousy than men (de Weerth & Kalma 1993; Felson & Outlaw 2007; Nannini & Meyers 2000; Webb 2007). Physical aggression has been found to be related to sexual jealousy in both sexes in some studies (Felson BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Response/Archer: Sex differences in aggression 1997; 2002; Haden & Hojjat 2006), or in men only (Archer & Webb 2006; Webb 2007), or in women more than in men (de Weerth & Kalma 1993). Altogether, the above findings are not what one would expect if male mate-guarding, derived from paternity uncertainty, were responsible for partner violence. However much I agree that the paternity uncertainty hypothesis makes evolutionary sense, the evidence from modern Western nations indicates that women are also seeking to control men. Having said this, I accept the view that paternity uncertainty is likely to be more important in relation to sexual aggression to partners (Kaighobadi & Shackelford), and that men’s mate-guarding is likely to show subtle changes in relation to the woman’s fertility (as indicated by Sefcek & Sacco). I also acknowledge a different point made by Johnson & van Vugt, about male aggression towards women, that it is underestimated if men’s aggression to out-group women, during warfare (and in other contexts), is ignored. R3.3. Extending the range of human behavior covered by sexual selection

Several commentaries seek to extend the range of human behavior that could be explained by sexual selection, without necessarily extending the concept itself. These included artistic and other displays (Sefcek & Sacco), the behavior of homosexual males (Dickins & Sergeant), and the large sex difference in “conduct disorders” (Dickins & Sergeant) – that is, antisocial disorders in children and adolescents, which are two and a half times more frequent in males than in females. All of these seem appropriate extensions of the scope of sexual selection in its original meaning. Schredl’s interesting and unusual commentary extends the scope of sexual selection to the content of dreams. He reports that dreams reflect real-life sex differences in not only sexual activity but also physical aggression. These findings parallel research on homicidal fantasies: Men report more of these than women do, and their fantasies are more frequent and persistent (Crabb 2000; Kenrick & Sheets 1993). Schredl also notes that the sex differences in dream content have been stable since the 1940s and were unchanged during the time when societal gender roles changed. Consistent with this, Kenrick & Griskevicius also note that homicide rates do not differ with changes in gender attitudes from 1960s onwards. The sex difference in physical aggression in dreams becomes pronounced from around 17 years of age, consistent with analyses of violent crimes. Several commentators suggest that my sexual selection analysis could have been further refined by paying attention to the particular forms of aggression that sexual selection would predict. Buss does so in relation to specific adaptive problems (associated with his modular framework: see sect. R4). Kempenaers & Forstmeier set out a number of specific predictions about male aggression derived from sexual selection. These provide useful hypotheses for future studies. Corr & Perkins raised the issue of whether the sexes differ in different forms of aggression, distinguishing between competitive and provoked (and also predatory) aggression. There have been many suggested subtypes of aggression, and these are discussed elsewhere (Gendreau 296

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& Archer 2005). The more commonly used distinction between proactive and reactive aggression (Vitaro & Brendgen 2005) is likely to correspond to Corr & Perkins’ competitive and provoked aggression. It would therefore be interesting to enquire whether men and women differ more in either proactive or reactive aggression. These forms are typically not distinguished in most of the available studies involving sex differences, although many of the items on the commonly used physical aggression scale of the Aggression Questionnaire (A.H. Buss & Perry 1992) do seem to refer to reactive forms of aggression. Studies specifying reactive and proactive aggression in adolescents and adults (Archer & Thanzami, in press; Raine et al. 2006) have involved only males. It is likely that men show more of both of these forms of aggression, and that it is its physical nature, rather than the presence or absence of an immediate provocation, that is important for the sex difference. Proactive and reactive aggression are often highly correlated, indicating that they co-occur in the same individuals (e.g., Brown et al. 1996; Dodge & Coie 1987; Raine et al. 2006), although they are related to different variables (Raine et al. 2006; Scarpa & Haden 2006). R3.4. Beyond sexual selection: Inter-group competition

One suggested extension of sexual selection that requires longer consideration is inter-group conflict. The principles of sexual selection apply to a range of species, and are therefore not specifically designed for the human case where inter-group competition is widespread. I mentioned inter-group competition as a limitation to the existing psychological and criminological evidence on male aggression. Recent research (e.g., van Vugt et al. 2007; Wilson & Wrangham 2003; Wrangham 1999; Wrangham & Wilson 2004) has considered coalitional aggression from an evolutionary viewpoint. Several commentators (e.g., Johnson & van Vugt) raise this issue as a limitation to a sexual selection view of sex differences in aggression that is based on aggression between individuals. How to integrate evolutionary approaches to inter-group and intra-group aggression is an important issue. Benenson argues that the contrasting structures of male and female social groups lead to a more complex consideration of sexual selection than that proposed in the target article. In particular, she characterizes males as oriented primarily towards inter-group competition, with mechanisms for minimizing within-group aggression; female competition is characterized as being aimed at removing rivals. This is a very interesting and elegant extension of my target article, but it has the drawback of being inconsistent with evidence on adult friendship patterns. Benenson’s argument involves the contrasting nature of male and female groups, which has been noted for some time in the developmental literature (e.g., Archer 1992a; Maccoby 1988; see also commentaries by Johnson & van Vugt and Pellegrini). Benenson extends this to claim that “human males invest more than females in, and exhibit more tolerance towards, same-sex peers.” She goes on to characterize males’ same-sex relationships as being interconnected or groupbased (in contrast to those of females, which are not). Benenson’s citations in support her position rely heavily on

Response/Archer: Sex differences in aggression child samples. Research on adult friendship patterns suggests a different female pattern to one characterized by the lack of a group basis, and fragile friendships. In many ways, both sexes have similarly patterned friendship networks, with certain reliable differences. Men’s friendships tend to be centered on shared activities whereas women’s involve shared feelings. In contrast to Benenson’s statement that “Human females’ same-sex dyadic relationships endure for shorter periods than those of males,” women’s dyadic pairs are found to be more intimate, disclosing, and satisfying than those of men (e.g., Caldwell & Peplau 1982; Dindia & Allen 1992; Rubin 1985; Wright 1988). The social exclusion Benenson mentions refers to the outcome of female aggression in young children. It is, however, advantageous for both sexes to exclude competitors, and in the nonhuman world social exclusion results from direct aggression. In rodents, it is typically the fate of those who are displaced following territorial disputes (Archer 1970). Disruptive young male rhesus monkeys may be driven from their social group before puberty by adult females (Suomi 2005). Throughout human history, social exclusion from a group has been used as a form of punishment (e.g., Ruff 2001). Exclusion is therefore a consequence of aggression, and not connected to one particular form, indirect (or relational) aggression, as Benenson indicates. I considered this type of aggression throughout my target article. It works better in the denser and more elaborate social groups found among women and girls (Green et al. 1996; Lagerspetz et al. 1988), than in the dyadic context that Benenson suggests is typical of female networks; here a different form of relational manipulation is found (Archer & Coyne 2005). In terms of immediate costs, such as physical retaliation, indirect aggression is less risky than direct aggression (Bjo¨rkqvist 1994), but it can indeed be effective in removing a competitor. Recent evidence suggests that women’s indirect aggression is targeted particularly at those viewed as posing a reproductive threat – that is, more overtly attractive women (Vaillancourt & Sharma 2008) – which is consistent with other analyses, including the perceptive evolutionary account of indirect aggression by Figueredo et al. To sum up, although Benenson’s commentary opens up an interesting avenue for future discussion and research, it conflicts with the present evidence on men’s and women’s social networks. Rather than seeking to characterize men’s conflicts as inter-group and women’s as within-group, it is more realistic to regard men as engaging in both inter- and intragroup conflicts, as Johnson & van Vugt do. These commentators suggest that I have underestimated the extent of sex differences in aggression by concentrating on within-group aggression. I did acknowledge inter-group aggression in passing, and I referred to some of the sources they cite, including warfare being the common cause of male deaths in pre-state societies. There still remains a considerable amount of human aggression that is within-group. It is this that is the major topic of psychological and criminological investigations, and can most readily be linked to sexual selection. Nevertheless, an additional section on inter-group conflict would undoubtedly have strengthened and extended the scope of my article. The magnitude of the sex difference is clearly much larger for inter-group aggression.

Male inter-group aggression is not readily explained in terms of classic sexual selection principles, but is likely to be based on sexually selected features (as Johnson & van Vugt suggest). Male sexually selected characteristics, such as upper body strength and willingness to escalate encounters to dangerous levels, form the basis of simple forms of inter-group violent contests. It is but a short step from the coalitional aggression found in nonhuman primates to the simpler forms of group violence characteristic of humans. Van Vugt et al. (2007) identified a further psychological adaptation for such inter-group conflicts in men: Men are more likely than women to cooperate in the face of inter-group competition (see also target article). On the face of it, this would tend to decrease intra-group male competition. Yet, higher levels of male than female aggression are nevertheless reported in individual-level studies. It has to be noted, however, that studies on sex differences in inter-group aggression and conflict are only just beginning, and their data base is as yet very small compared to that covering within-group aggression, and it largely consists of laboratory studies. There are other studies (see Kenrick & Griskevicius) indicating that activating mating motives can lead men to conform less to group norms. The full picture regarding intra- and inter-group conflict awaits clarification by future research. Browne’s commentary also concerns coalitional aggression, although not specifically about the nature of men’s and women’s groups. He argues that the sex differences outlined in the target article would prevent women from being as effective or as suited to combat as men. To be convincing, Browne’s argument needs to include the sort of “male warrior” adaptations discussed by Johnson & van Vugt. One finding that may be relevant in this context is the early sex difference in preferences for games and entertainments involving killing (Benenson et al. 2008). There is a counterargument to Browne’s position. Both physical and psychological sex differences – even those with large effect sizes such as upper body strength – overlap, so that there will always be some women who possess these characteristics more than some men do. As stated, Browne’s argument seems to neglect such individual variability, and the importance of motivation, general physical training, and specific combat training. Consequently, it may well be that most men are more fitted for combat than most women, but this still leaves the few exceptions. It is likely that throughout history gender attitudes have converted these overlapping differences into categorical ones by generalizing from the typical sex difference to one that is prescribed by social rules. The argument that women can form effective combat units is usually illustrated by the example of the fighting units of the West African Dahomey kingdom in the eighteenth and nineteenth centuries (as noted by Eagly & Wood). It is also likely that women have fought effectively alongside men, particularly in twentieth-century liberation armies. The position that women lack psychological adaptations for inter-group conflict could simply mean that it is more difficult, but not impossible, to integrate women as effectively as men into combat roles. How the infrequent cases discussed by Eagly & Wood, and more extensively by Goldstein (2001), have overcome such adaptations provides an interesting challenge for future evolutionary researchers in this field. BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Response/Archer: Sex differences in aggression R4. A framework for integrating ultimate and proximal explanations Although Buss and I agree in terms of the general position that sex differences in human aggression can be understood in terms of sexual selection, I welcome the opportunity to set out ways in which our general approaches differ. Implicit in my coverage of the relationship between evolutionary (ultimate) and immediate causal (proximal) explanations was an ethological framework. I shall now make this more explicit, in order to address the remaining commentaries. Based on Huxley’s “three major problems of biology” (to which he added a fourth), Tinbergen (1963) set out four questions that need to be addressed (and integrated) when we ask why behavior occurs. R4.1. Tinbergen’s four questions

The first question, regarding “survival value,” corresponds to the functional evolutionary explanations found in evolutionary psychology. As set out in Buss’s commentary and elsewhere (e.g., Buss 2004; Buss & Duntley 2006; Buss & Shackelford 1997b), Buss’s approach is to list a number of survival and reproductive problems, and to argue that there are specific mental modules designed to solve these problems. Tinbergen (1963) described three other types of explanation in addition to survival value (or function). One was evolution, or phylogenetic history, which is typically applied to the evolution of display characteristics in nonhumans (see Archer 1992b, pp. 149– 75), and in humans, to nonverbal signals (e.g., Andrew 1963; van Hooff 1972). The evolutionary background of the mechanisms underlying aggression, and how they might differ in the two sexes, is particularly important for distinguishing an ethologically based evolutionary approach from the modular approach, and also for addressing issues raised in other commentaries. From an ethological viewpoint, the modular approach seems to have omitted consideration of the process of natural selection. New adaptive mechanisms are built into already-evolved structures, rather than being designed as specific mental modules for new adaptive problems. The neuroendocrine mechanisms underlying aggression and aggressive displays, and the effector organs used in fighting, illustrate this process. Humans still possess the same basic emotions derived from a phylogenetically ancient fight-flight system: more recentlyevolved neural circuitry has been incorporated into older systems rather than forming new and separate structures. Development and causation are the other types of explanation described by Tinbergen (1963), and considerations of the process of evolutionary change imply that the links between these and function are not necessarily straightforward. Any particular adaptive function may be fulfilled by one of several possible mechanisms, and may develop in different ways. Many examples can be found in studies of adaptive behavior in animals, such as kin recognition and mate attraction. The only requirement of the developmental and causal mechanisms underlying adaptive behaviour is that they produce a particular end-product regularly in the environment in which that behaviour evolved. Thus, causal mechanisms are not necessarily mapped on to specific adaptive problems (as in the modular view), 298

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although this does occur in some cases. Perhaps the mechanism closest to this is the ethological concept of the fixedaction pattern, whereby a specific stimulus evokes a specific response (e.g., Lorenz 1971). Mechanisms underlying aggression may range from this sort, as in the case of pain-induced aggression (Archer 1988; 1989– 90), through emotional reactions, which can be seen as filling “the gap between fixed action patterns and impeccable rationality” (Johnson-Laird & Oatley 1992, p. 206), to more specific decision-processes, responsive to local cost-benefit contingencies. The mechanisms underlying human aggression are a complex mixture of these processes, as evidenced by theories that emphasize emotions (Archer 1976; 1988; Baumeister et al. 1996; Berkowitz 1962 2008; Dollard et al. 1939), and those stressing rational goal-directed behavior (Tedeschi & Felson 1994). Aggressive behavior has a very old phylogenetic history, so that more recently evolved mechanisms are built upon, and arise out of, older systems, rather than being created anew for each particular adaptive problem. R4.2. Development

From the previous section, it should be clear that I do not agree that “evolutionary theory predicts the early emergence of sex differences in direct aggression” (Cashdan). Rather, in the target article I stated: “the course of development cannot be precisely specified from an evolutionary explanation” (sect. 2.1.2). Nevertheless, certain possibilities can be ruled out: for example, evolved sex differences in aggression could not be totally reliant on culture. Eagly & Wood comment that I attributed to them the view that “sex difference should start small and increase with age through childhood, coincident with the cumulative influence of socialization.” This was a statement taken from Table 1, summarizing predictions derived from sexual selection and social role theories. In the text, it was elaborated, where I stated that this was a reasonable inference from social learning accounts of sex differences in aggression, which emphasize the cumulative influence of socialization through childhood. Eagly & Wood note that social role accounts have “remained silent” on the issue of age trends in aggression. Yet social role (and “biosocial”) accounts incorporate social learning as one of the mechanisms underlying the transmission of social roles, thus making it reasonable to infer that they are in agreement with the processes described in social learning accounts, in particular the gradual learning over time of aggressive behavior from role models. Tremblay & Coˆte´ make the same point about social learning in their commentary, noting that “Counterintuitively, the frequency of physical aggression declines during periods (middle childhood and adolescence) when exposure to physical aggression in the neighborhood and the media increases dramatically.” As they put it, no social learning or social role theorist has suggested that infants learn to aggress from their parents and subsequently unlearn this when they become exposed to influences from outside the family and from the media. From this perspective, it is difficult to understand why Behme thinks that “it is difficult to see how a theory of sexual selection can explain that the amount of aggressive behaviour decreases steadily

Response/Archer: Sex differences in aggression throughout childhood.” She goes on to argue that “we should expect the highest values of aggression [. . .] at the time when mating occurs.” There is no requirement for the various traits associated with inter-male competition to arise at the same time during development, only that they are all in place by the time of maximum inter-male competition. Behme’s comment again assumes that functional origins and development are necessarily closely linked. It also conflates the assessment of aggression based on frequency of acts (which is greatest at 2– 3 years of age) with their damaging nature (which peaks in young adulthood). It is the effectiveness of physical aggression that is likely to result in success in reproductive-related competition, not how often feeble motor acts occur. As noted by Tremblay et al. (1999), and in subsequent work (e.g., Coˆte´ et al. 2006), the decline in physical aggression with age during childhood comes about through the learning of alternative responses to physical aggression, a process that differs among individuals and between the sexes, and is influenced by a range of maternal characteristics (Tremblay & Coˆte´). Pellegrini poses the question of why there is no early sexual dimorphism in size and strength when there is early dimorphism in behavior. His interesting suggestion is that sex differences in physical activity and locomotor play are developmental precursors for the size and strength differences that result from the actions of testosterone at puberty. Several authors highlight the interactive nature of the development of sex differences in aggression, and note the differential environmental influences on males and females. Tremblay & Coˆte´ emphasize the importance of maternal influences, particularly a number of high risk factors such as early childrearing and smoking during pregnancy – these predict high levels of physical aggression by males. They comment that even though such mothers do not themselves show the high levels of physical aggression more characteristic of males, “they have all the risk factors needed to place their male children on a trajectory of chronic physical aggression.” Their sons will fit the pattern of showing a reproductive strategy characterized by a bias towards mating rather than parental effort (sect. 2.7 in the target article). In a similar vein, the work of Boden and his colleagues showed that an early adverse family environment was more predictive of partner violence for men than for women. Men showed less continuity in their aggression than women did (which, Boden notes, would not be expected from a social role view). R4.3. Causation

Tinbergen’s remaining question, in addition to function, evolution, and development, concerns causation, the immediate internal and external influences on behavior. Some commentators (Cashdan, Finkel & Slotter, and Pound et al.) questioned the inference that there should not be a sex difference in anger, the emotion that underlies aggression, although others (e.g., Campbell) accepted it. The reason given in the target article is that both sexes have reasons for becoming angry but the costs and benefits of the behavior resulting from the anger are different. This would fit the finding (discussed

below) that the sex difference in physical aggression is mediated by risky impulsivity. It would also be consistent with Daly and Wilson’s (1988, pp. 163– 86) emphasis on risky strategies underlying the evolved greater male propensity to violent conflicts. Daly and Wilson stated at the beginning of this chapter: “Men become embroiled in dangerous competitive interactions far more often than do women” (p. 163). I suggested that it is the interactions resulting from anger that are more dangerous in men than in women. Nevertheless, it is possible to see how the motivational mechanism behind angry aggression could have been changed so that men and women differed in the extent to which they become angry. In their “culture of honor” studies, Nisbett and Cohen (1996) found that it was the angry response to certain provoking situations that differentiated people from an honor culture, and those who were not. If men and women differed in the same way, this would produce a sex difference in anger to honorrelated situations, even though general measures of anger might not reveal such a difference. In this respect, the final paragraph of the commentary by Pound et al. is the most pertinent. If it is the state of becoming angry that entails the elevated risk, we should predict a sex difference in the ease of becoming angry in men and women, but only in certain circumstances (e.g., competitive exchanges with members of the same sex). On the other hand, when men perceive physical aggression to have high costs, it is likely that they still experience anger: it is the behavior that is different from when the costs are lower. Applying this to women, the calibration of the level for high costs could simply be set lower. Thus, women’s behavior (but not their initial emotional reaction) would be more inhibited by the costs of physical aggression, as Campbell (1999) suggested. There are pros and cons to both sides of this argument, and while I found the commentary by Pound et al. almost persuasive, I had lingering doubts. Their suggestion provides several interesting avenues for future research. As indicated in section R4.1, causation is a separate issue to function, and in my view it needs to be addressed in a different way than listing adaptive problems and assuming modules in the mind corresponding to each one (Buss). In line with this, I considered possible mediators of the sex difference in aggression, but noted that there were currently no empirical tests of these. Campbell’s commentary describes such a test. In devising a measure of risk, she was careful to include only risks that would have potentially dangerous consequences, as these had been identified as the relevant forms in evolutionary analyses (e.g., Campbell 1999; Daly & Wilson 1988). Controlling for this measure of risk-taking did eliminate the usual sex differences in physical and verbal aggression. Finkel & Slotter suggested that my argument concerning the mediation of sex differences in aggression could be extended with reference to “I3 Theory.” This is an analysis of impelling and inhibiting motivational forces. It involves a binary classification of variables that should be included in any motivational model of aggressive behavior. My article concerned those variables that mediated sex differences in aggression, and therefore would not take into account all the inhibiting and impelling forces controlling aggression. I have two observations on I3 Theory. The first is that it seems to be a recasting of a cost-benefit analysis, BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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References/Archer: Sex differences in aggression which was discussed in the target article, and has been applied to the study of several forms of aggression (Archer et al., submitted; Archer & Southall 2009; Rutter & Hine 2005). The second is that it appears not to be a theory in the sense that specific hypotheses can be generated, but a list of variables that make aggression more or less likely. This may be useful for organizing our thinking of the various influences on forms of aggression, such as partner aggression (Finkel 2007), but it would seem to add little or nothing to how the motivational system underlying aggression is organized. For example, Finkel & Slotter’s penultimate paragraph merely recasts what I (and others) have written about the variability in partner violence – that different balances in the societal power of men and women alter the immediate costbenefit calculus for resorting to physical violence against a partner. In the target article, I stated that the rising levels of testosterone in male adolescents were not associated with an increase in male aggression, as occurs in other species. Elsewhere (Archer 2006b), I argued that the behaviorhormone relationships in humans fit a pattern identified previously by Wingfield et al. (1990) in birds, known as “the challenge hypothesis.” According to this, testosterone rises at puberty, but to moderate levels that support growth and reproductive functioning and behavior, but it does not directly facilitate aggression. Both sexual arousal and challenges involving young males do lead to short-term rises in testosterone levels, and these facilitate competitive behavior, including aggression. Terburg, Peper, Morgan, & van Honk (Terburg et al.) argue that behavioral studies indicate that testosterone is a mediator of aggression; however, the studies they cite are correlational, and there is abundant evidence that aggressive behavior can lead to increased testosterone levels (Archer 2006b; Kemper 1990). Terburg et al.’s commentary goes on to make the important point that interactions between testosterone and cortisol – found in several studies – have been neglected in such analyses: The influence of testosterone appears to be stronger in individuals with low cortisol levels, although in some cases the two hormones increase together (Cohen et al. 1996). Terburg et al. also mention findings of a positive association between aggression and digit ratio (2D:4D), regarded as a marker for prenatal testosterone levels. From this, they suggest that prenatal testosterone may affect the sensitivity to later circulating testosterone (as it does in the classic studies of the organizing effects of perinatal testosterone). Thus, Terburg et al. draw our attention to two specific and testable variables (cortisol and prenatal testosterone) that might moderate the association between testosterone and aggression from puberty onwards.

selection, but which are nonetheless important for a full account of sex differences in aggression. Some of these were referred to in the target article, others were not. Foremost is the theory by Campbell (1999), that women avoid costly encounters to increase their survival chances for rearing offspring. Added to this is the consideration that women do compete for mates, but in less damaging ways than men do. Inter-group conflicts were only mentioned in passing in the target article, but these are clearly of great importance when considering aggression by human males. Adaptations for group conflict are likely to have been built on to those already in place for intra-group conflict. Modern extensions of sexual selection theory extend to post-copulatory competition, notably that between males and females. This was covered in the target article in connection with a game-theory model of the evolution of coercion in animals (sect. 5). I did not include the paternity uncertainty theory of male partner violence, and in my response explained that this was because the evidence from industrialized Western nations on physical aggression between partners did not seem to support its predictions. It nevertheless remains important for considering inter-male aggression during the post-copulatory phase (omitted from the target article), and for considering sexual aggression and subtle forms of mate guarding that are likely to become coercive where restraints on males’ behavior are low. Section R4 provided an opportunity to outline the different approaches taken by evolutionary psychologists grounded in ethological theory and those adopting a modular framework. The ethological approach involves four interconnected explanations of behavior, rather than functions and their mental representations, as in the modular approach. I then used the ethological framework to consider a number of issues concerning development and causation. In particular, learning to decrease physical aggression at an age when there are abundant role models for aggression was discussed in relation to the classic social learning account, which would not seem to predict this. The question of the causal mediating influences for sex differences in aggression raised the issue of why the sexes apparently do not differ in anger. My position in the target article was that the difference resides in how men and women respond to anger, but following a commentary, here in the response I discussed the possibility that there could be differences in reactions to provocation. This is just one example of a number of avenues for future research opened up by the commentaries on my article, and I thank all the commentators for their very interesting and diverse comments.

R5. Conclusions

References

Future research is likely to arise from a widening of the concept and scope of sexual selection. A number of commentaries referred to theoretical extensions of sexual selection theory beyond the two processes originally described by Darwin (1859/1911; 1871/1901). These involved consideration of a number of selection pressures, which may lie outside the classic definition of sexual 300

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doi:10.1017/S0140525X09990938

Numerical representation in the parietal lobes: Abstract or not abstract? Roi Cohen Kadosh Institute of Cognitive Neuroscience and Department of Psychology, University College London, London WC1N 3AR, United Kingdom [email protected] http://www.ucl.ac.uk/neuroscience/Page.php?ID¼12& ResearcherID¼238

Vincent Walsh Institute of Cognitive Neuroscience and Department of Psychology, University College London, London WC1N 3AR, United Kingdom [email protected] http://www.icn.ucl.ac.uk/Research-Groups/Visual-Cognition-Group/ index.php

Abstract: The study of neuronal specialisation in different cognitive and perceptual domains is important for our understanding of the human brain, its typical and atypical development, and the evolutionary precursors of cognition. Central to this understanding is the issue of numerical representation, and the question of whether numbers are represented in an abstract fashion. Here we discuss and challenge the claim that numerical representation is abstract. We discuss the principles of cortical organisation with special reference to number and also discuss methodological and theoretical limitations that apply to numerical cognition and also to the field of cognitive neuroscience in general. We argue that numerical representation is primarily non-abstract and is supported by different neuronal populations residing in the parietal cortex. Keywords: abstract; automaticity; brain; cognition; neuronal specialisation; numbers; parietal lobes; prefrontal cortex; representation

1. Introduction In today’s high tech society, numbers play a central role. We use them to calculate budgets, compare prices, understand food labels, and discuss journal impact factors. Not surprisingly, difficulties in handling numerical information can lead to serious impairments in everyday life (Ansari 2008; Butterworth 1999; 2004; 2005; Cohen Kadosh & Walsh 2007; Parsons & Bynner 2005; Rubinsten & Henik 2009; von Aster & Shalev 2007). Numbers can come in many forms; we can represent the same quantity, say “two” (here a word) as a digit (2), in Roman numerals (II), non-symbolically as on a dice (††), with our fingers, in a temporal series (e.g., a drum beat), or with other words (pair, duo, brace) that carry semantic as well as numerical meaning. The question of how we represent numbers and whether there is a unitary neuronal basis for all forms of numerical representation is therefore important. A full understanding of numerical representation is also important for the correspondence between comparative and developmental studies that use non-symbolic representation and studies in adults that can use symbolic and non-symbolic stimuli. Moreover, insights into the way we represent numbers are proving to be important for educational interventions, for diagnosis, classification, and the design of effective rehabilitation programs for people who suffer from numerical difficulties known as # 2009 Cambridge University Press

0140-525X/09 $40.00

developmental dyscalculia. For example, the way in which some intervention programs are designed in order to help children with dyscalculia (Wilson et al. 2006a; 2006b) is based on the idea of abstract representation. Therefore, it is assumed that training on numerosity will improve the numerical computation with digits. 2. The consensus Over the last ten years a consensus view has emerged that assumes the underlying representation of numerical information to be abstract and to be focussed in the intraparietal sulcus (Dehaene et al. 1998). Here we reassess this abstract representation point of view. By abstract we adopt the previous operational definition (Dehaene et al. 1998, p. 356) that “Adults can be said to rely on an abstract representation of number if their behavior depends only on the size of the numbers involved, not on the specific verbal or non-verbal means of denoting them.” (See also McCloskey, 1992, p. 497, for a similar definition.) Other, more recent studies, support this view and point out that “the intraparietal sulcus (IPS) as an important region for numerical cognition . . . represents number regardless of whether the input notation is symbolic (e.g., number words or symbols) or non-symbolic (e.g., dot patterns) and regardless of whether stimuli are presented visually 313

Cohen Kadosh & Walsh: Numerical representation in the parietal lobes or auditorily” (Libertus et al. 2007, p. 2). Therefore, an operationalization of abstract representation in the present article is that neuronal populations that code numerical quantity are insensitive to the form of input in which the numerical information was presented (e.g., digits, verbal numbers, auditory, numerosity, etc.). In contrast, we define non-abstract representation as neuronal populations that code numerical quantity but are sensitive to the input in which the numbers were presented. Therefore, the neuronal populations that code the magnitude of the digit 7, or the word “SEVEN” will not be identical. However, the expected output for abstract and nonabstract representations is similar. For example, for both representations we know that 7 is larger than 6, and SEVEN is larger than SIX. Nevertheless, we will show here that non-abstract representation can be masked as a function of the response made by subjects and that detecting differences between different notations are optimised by probing automatic processing. Such a difference cannot be explained if the same neuronal population codes numerical quantity independent of the input. There are several ways to define representation (for reviews, see Barsalou 1999; 2003; Markman & Dietrich 2000), but in this target article we define representation only in the general sense that is most common in psychology and cognitive neuroscience. Here representation refers to patterns of activation within the brain that correspond to aspects of the external environment (Johnson & Munakata 2005). We differentiate representation from processing; the latter includes representation, but relates to the sum of pre-representation (e.g., visual identification of the digit) and post-representation components (e.g., working memory, response selection). In the current case numerical representation relates to patterns of

ROI COHEN KADOSH received his PhD from BenGurion University of the Negev in Israel. He is currently a research fellow at University College London. Among his research interests are numerical cognition, parietal lobe functions and their role in numerical and magnitude representation, and the neurocognitive mechanisms of synaesthesia and its possible connections with cross-modal interaction and awareness. His work in the field of numerical cognition focuses on understanding the neural mechanisms and cognitive architectures that are necessary for perceiving, representing, and manipulating information about numbers. To study these topics he uses a variety of neuroscientific techniques – including functional MRI, brain stimulation, and electroencephalography – with normal and clinical populations. VINCENT WALSH is Professor of Human Brain Research at University College London. Among his research interests are higher visual perception, time perception, and numerical cognition. He has forwarded the idea that time, space, and number mechanisms draw on evolutionary and developmentally common resources (“A Theory of Magnitude” in Trends in Cognitive Science, Vol. 7, No. 11, 2003) as a means of explaining the emergence of number in a brain region concerned with sensory motor transformations. Recently, he has begun to work on real scene perception and also the role of sleep in learning and cognition.

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activation that are modulated by the numerical magnitude conveyed by the number. We suggest in this review that the commonly held view of abstract numerical representation needs to be challenged; we present evidence supporting a contrary view, and provide future directions for empirical work in cognitive and developmental neuroscience. 3. Architectures for number processing Models of number processing differ with respect to the issue of whether numbers are abstractly represented. There are many cognitive models in the field of numerical cognition (e.g., Cipolotti & Butterworth 1995; Gallistel & Gelman 1992; Noe¨l & Seron 1993; 1997; Pillon & Pesenti 2001; Schwarz & Ischebeck 2003), but three central models are the most cited and are representative of the key features of different classes of models. McCloskey and colleagues in a series of neuropsychological studies (e.g., Macaruso et al. 1993; McCloskey et al. 1985; Sokol et al. 1991) have shown that a single, abstract representation can provide detailed qualitative and quantitative accounts of the errors made by acalculics (patients with acquired numerical difficulties). These findings led McCloskey (1992) to offer the abstract modular model that is composed of three distinct parts: the comprehension system, the calculation system, and the number production system. The comprehension system converts different notations of numbers (e.g., digit, verbal numbers, roman, etc.) into a common abstract format. The calculation system includes arithmetic facts such as the comparison task and calculation procedure, both of which are also a form of abstract quantity code. The production system produces the output in various notations as requested, such as digits, or spoken numerals. An important assumption in McCloskey’s model is that an abstract internal representation carries out all numerical operations. This implies that all inputs, without exceptions, are converted into a single, modality-independent abstract representation and then are translated into the appropriate form of output. Consequently, the pattern of reaction times (RTs) between digits, verbal numbers, or any other symbolic notation should follow predictions based on abstract coding, because they are translated into one common representation. A general difference among the overall mean RTs might appear because of different processing times of different notation inputs (e.g., digits are responded to more quickly than roman numerals). However, an important prediction that follows from abstract coding is that there should not be RT interactions between the different notations. Rather, the abstract coding model predicts additivity between different numerical notations when one manipulates factors which influence the level of numerical representation. While McCloskey’s model strongly posits abstract representation, Campbell and colleagues (Campbell 1994; Campbell & Clark 1988; Campbell & Epp 2004) have suggested that numbers are not represented abstractly. According to their encoding complex hypothesis, separate modality-specific number codes exist. Therefore, number processing is mediated by modality-specific processes (e.g., visual, digit) and not by an abstract code. Consequently, they predict RT interactions between responses

Cohen Kadosh & Walsh: Numerical representation in the parietal lobes to numbers as a function of notation or stimulus modality. More precisely, they do not predict any additivity between different numerical notations; rather, they predict an interaction between notation and factors that are influenced by the numerical representations. Dehaene (1992) combined features of the abstract modular model and the encoding complex hypothesis and composed the currently most accepted cognitive model: the triple-code model. Similar to the encoding complex hypothesis, this model does not assume a single central number representation. Instead, it assumes that there are three different codes with special and distinct functions for each. The first two codes are modality- and notation-dependent; The Arabic code, which resides in the left and right inferior ventral occipital-temporal areas, is responsible, for example, for multi-digit calculations. Simple calculations, verbal counting, and retrieval of arithmetic facts are executed via a verbal code, which is subserved by the left perisylvian area. However, numerical comparison and number approximation, which access the numerical representation, are performed using the third code, the analogue magnitude code, in which the representation, as in McCloskey’s model (1992), is modalityand notation-independent. Hence, it is possible to find notation-dependent processing for arithmetic operations resulting from non-representation –related processes outside the analogue magnitude code (e.g., verbal code), while the numbers in the equation are represented abstractly by the analogue magnitude code. Therefore, this model, like the abstract modular model, predicts additivity between different numerical notations when one manipulates factors that influence the level of numerical representation. This idea was mentioned in several later works, for example, in Dehaene (1996) where the author writes “the same representation of number magnitudes should be accessed regardless of input number notation” (p. 60). In later works, which marked the transition of the abstract view from a purely psychological concept to a neurally instantiated one, it was stated that the IPS codes the abstract, rather than non-abstract, quantity meaning. For example, after reviewing neuroimaging studies, Dehaene and colleagues concluded that, “Those parametric studies are all consistent with the hypothesis that the HIPS [horizontal IPS] codes the abstract quantity meaning of numbers rather the numerical symbols themselves.” (Dehaene et al. 2003, p. 492). 4. Numbers are abstract The logic behind the idea that numbers are represented in an abstract fashion can be examined in a straightforward way. If numerical representation is abstract, then the representation-related effects caused by one type of notation or modality should be identical for other notations or in other modalities. That is, the effect for each notation or modality should be additive, rather than interacting with the notation. Such effects have been observed for a variety of notations and modalities both at the behavioural (e.g., Barth et al. 2003; Dehaene & Akhavein 1995; Naccache & Dehaene 2001b; Schwarz & Ischebeck 2000) and the neuronal level (e.g., Dehaene 1996; Eger et al. 2003; Libertus et al. 2007; Naccache & Dehaene 2001a; Pinel et al. 2001), thus supporting the idea that

numbers are represented abstractly. The spatial numerical association of response codes (SNARC) effect is a classic example; subjects respond more quickly to small numbers with left-hand key responses than with righthand key responses, and faster to large numbers with the right-hand key than with the left-hand key (e.g., responding to digit 3 will be faster with the left-hand key, whereas responding to digit 8 will be faster with the right-hand key) (Dehaene et al. 1993; Fias & Fischer 2004; Gevers & Lammertyn 2005; for a recent meta-analysis see Wood et al. 2008). The effect is independent of notation or modality (Nuerk et al. 2005; see also our Figure 1a). Similarly, in the numerical distance effect, RT increases as the numerical distance between two numbers decreases (e.g., RT to decide if 8 is larger than 2 is faster than RT to decide if 8 is larger than 6) (Moyer & Landauer 1967). This effect too, by and large, is independent of notation (Dehaene 1996; Dehaene & Akhavein 1995; Naccache & Dehaene 2001b; Schwarz & Ischebeck 2000) (see our Figure 1b). These and other cognitive effects gave support for the triple code model (Dehaene 1992). Extrapolating the idea of abstractness from this cognitive model (Dehaene 1992) to the nervous system implies that within the IPS, the area most associated with numerical representation (see Cohen Kadosh et al. 2008f; Dehaene et al. 2003, for reviews and metaanalyses), the same neural population will be recruited to encode numerical quantity, whatever the format of presentation. Neuroimaging experiments have reported notation- and modality-independent brain activation in the IPS (Eger et al. 2003; Naccache & Dehaene 2001a; Pinel et al. 2001; see also Venkatraman et al. 2005, for evidence of format-independent processing of exact and approximate arithmetic in the IPS) (see our Figure 1c). Together these findings, both at the behavioural and the neuronal level, provide an apparently strong basis for the abstract representation of numbers. However, there are several limitations to this view. 5. Numbers are not abstract Despite the evidence presented in the previous section, the logic behind the assumption that numbers are represented in an abstract fashion is incomplete and suffers both from methodological and theoretical shortcomings. While it is true that different notations/modalities can yield similar behavioural effects, it does not follow that they therefore share a single neuronal representation. It is entirely possible, for example, that similar behavioural effects can be subserved by different brain areas, or neuronal populations in a single brain area, and in different time windows (Cohen Kadosh et al. 2007a; Rumelhart & McClelland 1986). It is also often overlooked that, at the behavioural and neural levels, the assumption that numbers are represented in an abstract fashion is based mainly on null results, that is, on finding no differences between notation or modality and the behavioural or blood oxygenation level dependent (BOLD) variable that correlates with numerical representation. Therefore, the conclusion that numbers are abstract may be due to a lack of statistical power, or the insensitivity of the paradigms used. Indeed, some studies have found differences or a tendency towards a difference between notations BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Figure 1. Effects that underlie the idea that numerical representation is abstract. (A) The SNARC effect for different notations (digits, words, dice) and modalities (visual, auditory). In this experiment the subjects were instructed to decide whether a numerical stimulus is odd or even (i.e., parity judgement) by pressing the right or the left response key (key assignment was counterbalanced within subjects). The slopes that were obtained are independent of format. (B) The Distance effect for digits and words shows the same function independent of notation. In this experiment subjects were asked to decide by a button press whether the displayed number (i.e., the numbers 1 to 9, excluding the number five) is numerically larger or smaller than the standard number five. (C) Brain activation in the IPS (in orange circles) is modulated in similar ways as a function of the numerical distance between the compared digits, independent of the notations that were used (i.e., words or digits). Left IPS appears on the left side, right IPS appears on the right side. In this experiment the subjects decided whether a visually presented number was larger or smaller than a fixed reference number (65) by pressing a button with their right or left hand according to instructions. Adapted from Nuerk et al. (2005), Pinel et al. (2001), and Schwarz and Ischebeck (2000) with permission. A color version of this figure is available online at www.journals.cambridge.org/bbs.

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(e.g., digits, verbal numbers, numerosity, Mandarin numerals) (Campbell & Epp 2004; Dehaene 1996; Dehaene & Akhavein 1995; Droit-Volet et al. 2008; Ganor-Stern & Tzelgov 2008; Koechlin et al. 1999; Reynvoet & Ratinckx 2004) or modalities (i.e., visual or auditory) (Barth et al. 2003), but the implications of most of these results have either been ignored, or alternative explanations have been given that leave the idea of non-abstract representations unchallenged. In addition to the fact that similar behavioural effects can be produced by different mechanisms (Cohen Kadosh et al. 2007a; Rumelhart & McClelland 1986), at the neuronal level, similar brain activations can stem from different neuronal populations that are co-localised within a single imaged voxel (volumetric pixels) and cannot be segregated with conventional neuroimaging techniques (Cohen Kadosh et al. 2007b; Grill-Spector et al. 2006b; Nieder 2004). In other words, in the parietal lobes each voxel that is activated is sampled during the functional magnetic resonance imaging (fMRI) experiment (with a spatial resolution of  3 cubic mm) and contains about 1.25 million neurons (Pakkenberg & Gundersen 1997). Moreover, the neurons in this voxel can fire tens of impulses per second for different functions. However, different functions cannot be detected, as the fMRI signal – which indicates an increase in oxygenated blood bringing energy to active neurons – develops sluggishly, over several seconds. Therefore, observing similar activations at the voxel level for different notations (Pinel et al. 2001) or modalities (Eger et al. 2003), or alternatively, observing similar time courses in event-related potentials (ERP) experiments that lack spatial resolution (Dehaene 1996; Libertus et al. 2007), is not sufficient to indicate abstract representation. This theoretical point is gaining experimental support from single-cell neurophysiology in monkeys. It has been shown, for example, that neurons that are sensitive to numbers, are also sensitive to features that have little to do with magnitude information (Nieder et al. 2006; see also Calabrese 2007). Note that such a finding, although not speaking directly against the idea of abstract numerical representation, challenges the idea that numerical or magnitude representation is modular (Dehaene et al. 1998; McCloskey 1992). Indeed modular representation of any single class of stimulus features of the world does not have a good history. Suggestions that the monkey or human brain contained a colour centre (Lueck et al. 1989; Zeki 1980), a motion centre (Zeki 1974), or a word form area (Cohen et al. 2000; McCandliss et al. 2003) – all good cases for attributes of the external world that one might expect to have a single locus of representation – have been found wanting; and each of these attributes has been found either to be multiply represented for different task demands at almost every level of the visuocognitive system (cf. Orban et al. 1996; Otten & Rugg 2001; Watanabe et al. 1998) or the “centre” has been found to be not specific to the attribute (cf. Merigan 1996; Price & Devlin 2003; Xue & Poldrack 2007). A priori, number information – which is less constrained than simple object features such as colour, form, and motion, and upon which we perform explicit and implicit computations – would seem to be a poorer candidate for a canonical representation. Numerical representation is also modulated by task and automaticity. Various definitions have been attributed to

Cohen Kadosh & Walsh: Numerical representation in the parietal lobes the concept of “automaticity” (e.g., Carr 1992; Hasher & Zacks 1979; Logan 1985; Posner 1978). In the current article, we adopt Tzelgov et al.’s (1996) definition (see also Barge 1992) that a process is automatic if it does not need monitoring to be executed. Most studies that support the idea of an abstract representation are based on subjects carrying out intentional processing of numerical information. However, numbers are also represented automatically (for a review, see Tzelgov & Ganor-Stern 2005). Automatic and intentional processing can lead to very different inferences about the underlying representation (Cohen Kadosh et al. 2008b; 2008g; Tzelgov & Ganor-Stern 2005), and brain activity (Cohen Kadosh et al. 2007a, Lewis & Miall 2003; Orban et al. 1996). Indeed, task-dependency is a fundamental feature of brain representation and has been reported at every level of every perceptual and cognitive domain, including time perception (Lewis & Miall 2003), magnitude processing (Cohen Kadosh et al. 2008c), face processing (Cohen Kadosh et al., in press), and visual processing (Orban et al. 1996). Mental representations can be probed when they are engaged by task demands or when their processing is automatic. The advantage of using automatic processing is that processing and behaviour are unaffected by task demands and intentional strategies (Cohen Kadosh et al. 2008b; 2008g; Tzelgov & GanorStern 2005). This might imply that specific task requirements may induce humans to generate different representations (e.g., shared representation for different notations). Clearly, humans can generate numerical representations according to task requirements (Bachtold et al. 1998; Fischer & Rottmann 2005; Gertner et al. 2009; Hung et al. 2008; Lindemann et al. 2008; Shaki & Fischer 2008; Shaki & Petrusic 2005). For example, Bachtold et al. (1998), in a numerical comparison task of the numbers 1 to 11 (excluding the number 6 which serves as the standard), found that subjects showed a normal SNARC effect when they conceived the numbers as distances on a ruler, which represents small numbers on the left and larger numbers on the right. Importantly, the SNARC effect was reversed (i.e., faster responses to small numbers with right-hand key responses than with left-hand key responses, and faster responses to large numbers with the left-hand key responses than with the right-hand key responses) when the subjects conceived the numbers as hours on a clock face, which presents small numbers on the right side, and large numbers on the left side. Thus, a limit to the abstract representation view we have to face is that observations consistent with shared representations may be true only for specific task conditions in any given experiment. Clearly, then, the evidence that numbers are abstractly represented has several limitations: null results (Cohen Kadosh 2008a; Dehaene 1996; Schwarz & Ischebeck 2000; Shuman & Kanwisher 2004), technical limitations (Ansari 2008; Nieder 2004), and task specificity (Ansari 2007; Ansari et al. 2006a; Bachtold et al. 1998; Cohen Kadosh et al. 2008b; Go¨bel et al. 2004; Van Opstal et al. 2008a; Venkatraman et al. 2005; Wood et al. 2006a). In the next section, we provide evidence that directly challenges the idea that numbers are represented abstractly. The line of experiments we turn to next shows that nonabstract representations exist in a variety of tasks and cultures.

6. Two = II and 2 does not equal two Given the ubiquity and importance of numbers and the early stage in life at which we learn about them, it is not surprising that, like words, they are eventually overlearned and processed automatically. Automatic numerical processing is an important ability that exists not only in human adults (Cohen Kadosh 2008b; Cohen Kadosh & Henik 2006; Dormal et al. 2006; Fias et al. 2001a; Henik & Tzelgov 1982; Lammertyn et al. 2002; Pavese & Umilta` 1998; Schwarz & Heinze 1998; Schwarz & Ischebeck 2003; Tzelgov et al. 1992; Verguts & Van Opstal 2005), but also in children (Gebuis et al. 2009; Girelli et al. 2000; Mussolin & Noel 2007; Rubinsten et al. 2002; Szucs et al. 2007; Zhou et al. 2007), and animals (Washburn 1994). The automaticity of numerical information processing gives one the opportunity to explore numerical representation per se, independent of one’s strategies (Cohen Kadosh et al. 2008g; GanorStern & Tzelgov 2008; Tzelgov & Ganor-Stern 2005). Automaticity has been explored mainly by using conflict tasks, for example, the size congruity paradigm. Usually, in this paradigm subjects are presented with two digits on the computer screen (one digit in the left visual field, and one digit in the right visual field) and are required to compare the stimuli according to their physical size while ignoring their numerical value (e.g., 2 4), and to press the button that corresponds to the side of the physically larger stimulus (Cohen Kadosh 2008b; Cohen Kadosh & Henik 2006; Gebuis et al. 2009; Girelli et al. 2000; Henik & Tzelgov 1982; Mussolin & Noel 2007; Rubinsten & Henik 2005; 2006; Rubinsten et al. 2002; Schwarz & Heinze 1998; Schwarz & Ischebeck 2003; Szucs et al. 2007; Tzelgov et al. 1992; Verguts & Van Opstal 2005; Zhou et al. 2007). The stimuli can be incongruent (the physically larger digit is numerically smaller; e.g., 2 4), neutral (the stimuli differ only in the relevant dimension; e.g., 2 2), or congruent (the physically larger digit is also numerically larger; e.g., 2 4). A common finding is that incongruent trials, being slower to process than congruent trials (size-congruity effect), as reflected by slower RT, indicate that the numerical information is processed automatically. This paradigm has been employed in behavioural studies and has yielded an interaction between different notations and automatic processing of numerical information (Cohen Kadosh et al. 2008e; Ito & Hatta 2003). For example, Ito and Hatta (2003) found that when participants compared the physical size of Kana scripts – the equivalent of verbal numbers – numerical information was not processed automatically. Therefore, the irrelevant numerical information did not interfere with the relevant physical size judgement. In contrast, when the same participants compared digits or Kanji numbers (ideographic script), a size-congruity effect was observed, thus indicating that the numerical information was processed automatically, and interfered the relevant physical size judgement. Similar results were found and extended by another laboratory (Cohen Kadosh et al. 2008e). A recent study used a simple comparison task in which subjects had to compare the numerical values of digits or verbal numbers while examining the effect of numerical information in trial n – 1 on processing of numerical information in trial n (i.e., sequential effect) (Cohen Kadosh BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Cohen Kadosh & Walsh: Numerical representation in the parietal lobes 2008a). Others conducted a similar analysis on a similar numerical task (Dehaene 1996; Schwarz & Ischebeck 2000) and similar stimuli (Dehaene 1996), and did not find an interaction between notation and the distance effect or differential effects of trial n – 1 on trial n as a function of notation. However, these studies used a long response-to-stimulus-interval (RSI) (.1,500 msec), which is likely to produce expectancy effects (Soetens 1998), whereas automatic processing occurs under short RSI conditions (e.g., 200 msec) (see Neely [1977] for a similar idea for priming tasks). By using a short RSI of 200 msec, and a large number of subjects and trials, three results emerged which support the idea that non-abstract representations of numbers exist: (1) an interaction between notation and numerical distance in reaction time; (2) an interaction between notation, notation repetition, and numerical distance in error rates; and (3) an interaction between notation and the distance between the numerical distance in trial n – 1 and trial n with reaction time as the dependent variable (Cohen Kadosh 2008a). Dehaene and Akhavein (1995) used a same-different task, in which participants were asked to decide via a button press whether two members of a pair of stimuli, which are presented simultaneously, were the same or different. The notations were digit-digit (e.g., 2-2, 2-8), verbal number-verbal number (e.g., TWO-TWO, TWOEIGHT), or a mixed notation (e.g., verbal number-digit; TWO-2, TWO-8). When the subjects compared the similarity of the numbers according to their numerical values, a distance effect independent of notation was observed. In contrast, in physical matching, when the participants compared the numbers according to their perceptual similarity, an interaction between notation and the distance effect was observed with a flat and not significant distance effect for mixed notation. Although the latter finding indicates that numerical representation is non-abstract, because numerical processing should be observed independent of the input (i.e., mixed notation vs. pure notation), Dehaene and Akhavein (1995) argued that numbers, whether digits or verbal, converge towards a common semantic representation. In a recent study, Ganor-Stern and Tzelgov (2008) conducted two experiments: one with a same-different task and another with the size congruity paradigm. The same-different experiment was similar to Dehaene and Akhavein’s (1995) study but with Indian numbers (a different notation for numbers that is used mostly in Arabicspeaking countries) instead of verbal numbers. In the physical comparison task they were not able to replicate the distance effect for digits, Indian numbers, or mixed notation. However, they argued that numbers were still processed automatically by finding what they called the “value interference effect,” that is, processing the numbers’ numerical value impaired participants’ “different” responses to different-notation pairs with the same numerical values (e.g., 8 in digit notation vs. 8 in Indian notation) compared with those with different numerical values (e.g., 8 in digit notation vs. 2 in Indian notation). However, this effect does not indicate semantic processing and it can be attributed to asemantic transcoding (e.g., due to phonological representation). In this case, the digit 8 and the Indian number 8 were recognized as representing the same numbers, even though the numerical 318

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representation was not accessed (see Dehaene & Akhavein 1995, for a discussion on this scenario). Indeed, the lack of distance effect in Ganor-Stern and Tzelgov’s (2008) experiment supports the idea that numerical information did not reach the level of the semantic representation. In another experiment, Ganor-Stern and Tzelgov found that digits, Indian numbers, and mixed-notation (digit and Indian numbers) caused interference to a physical size judgment, as reflected by the size-congruity effect. Again, they argued that this effect indicates abstract representation. However, one should note that the level of the interference interacted with notation, as well as with the numerical distance, thus replicating the findings by Ito and Hatta (2003) and Cohen Kadosh et al. (2008e). This result can be explained not as a result of abstract representation, but simply an interference during response selection, as was shown in several ERP and fMRI studies (Cohen Kadosh et al. 2007c; 2008d; Szu´´cs & Solte´sz 2007; Szu´´cs et al. 2007). Moreover, in another experiment, when subjects were asked to compare pairs of numbers for their numerical value, Ganor-Stern and Tzelgov found that the distance effect was modulated as a function of notation (i.e., interaction between notation and distance effect). Together, these interactions provide results which cannot be explained by assuming an abstract representation – therefore challenging the central idea that numbers are processed in an abstract fashion, as was strongly suggested by the different architectures for numerical cognition (e.g., the abstract modular model [McCloskey 1992] and the triple-code model [Dehaene 1992] discussed earlier). Nevertheless, Ganor-Stern and Tzelgov (2008, p. 430) reached the conclusion that: “different notations are automatically translated into a common representation of magnitude, in line with M. McCloskey’s (1992) abstract representation model.” However, as we have shown, examination of the details of their results does not allow one to conclude that numerical representation is abstract; rather, it seems to strongly support our view that numerical representation is not abstract. In another study (Droit-Volet et al. 2008) 5-year-olds, 8year-olds, and adults participated in a number bisection task in which numbers were presented sequentially to one group of participants or simultaneously to another group of participants. In this task, the subjects are trained to discriminate a “few” standard (e.g., 8 dots) from a “many” standard (e.g., 20 dots). They were then presented with comparison stimuli that contain intermediate values (e.g., 12 dots) or values equal to the standard, while being asked to decide if the comparison stimuli is more similar to the few or many standard. They found that the mode of presentation yielded different Weber-ratios (which indicate the sensitivity to discriminate two numbers). Namely, the Weber-ratio was larger during sequential presentation of numerical quantity compared to simultaneous presentation, and this difference was highly significant for adults and 8-year-old participants, and showed only a trend in the case of 5-year-old children. Importantly, this study, as in the study by Cohen Kadosh (2008a), used a large number of participants (more than 60 participants in each group), and thus increased the statistical power and sensitivity to evidence of non-abstract representation. Other evidence which challenges the existence of abstract numerical representation and supports the

Cohen Kadosh & Walsh: Numerical representation in the parietal lobes existence of non-abstract representations comes from a recent study by Dehaene and colleagues (Dehaene et al. 2008). In their study, subjects from the Mundurucu tribe, an indigenous Amazonian group with a reduced numerical lexicon and little or no formal education, had to indicate the location of a given number (e.g., 6 dots) on a line segment with 1 dot at left and 10 dots at right. The number to be mapped appeared in a random order and in various forms (sets of dots, sequences of tones, spoken Mundurucu words, or spoken Portuguese words). For each number, adults and children pointed to a screen location. The responses for both children and adults were best fitted with a logarithmic curve (i.e., the larger the numbers were, the more closely they were mapped), a response that in the western culture is usually characteristic of young children (Siegler & Booth 2004). In contrast, the responses of adults who have been through a longer educational period were best fitted with a linear curve. Importantly, performance varied significantly with number notation within the more educated group. Responses for Portuguese numerals were best characterized by a linear function, but logarithmic for Mundurucu numerals and dot patterns from 1 to 10. These findings cannot be explained by an abstract representation, as different verbal numbers such as the Portuguese word QUATRO and the Mundurucu word EBADIPDIP donate the same number (FOUR) and should have led to similar mapping of the numbers independent of their notations. Some evidence for non-abstract representations comes from replications of classic effects. For example, a recent study examined the effect of different notations on the SNARC effect (Hung et al. 2008). In this study, the participants were asked to make a parity judgement, similar to the study by Nuerk et al. (2005) that we described earlier (sect. 4, and Fig. 1a). While the numerical information in the study by Nuerk et al. (2005) could appear as digits, German words, auditory German words, or as on a dice, the numerical information in Hung et al. (2008) appeared in three different notations: digits, which appeared horizontally in text, Chinese numerical words in the simple form (e.g., —), and in the complex form (e.g., ), which are presented in vertical text. Hung et al. did find that the SNARC was affected by the numerical notation, as indicated by the interaction between the magnitude category and the responding hand (i.e., the SNARC effect) and notation. This interaction was due to the SNARC effect only for digits. Inspired by previous studies that found the SNARC effect also with vertically aligned manual responses (faster responses to small numbers with bottom-hand key responses than with top-hand key responses, and faster responses to large numbers with the top-hand key than with the bottom-hand key) (Gevers et al. 2006a; Ito & Hatta 2004; Schwarz & Keus 2004), they examined the effect of notation on this vertical SNARC effect. They found a consistent SNARC for the Chinese verbal numbers, but not for the other notations. The results might indicate, as Hung et al. suggested, that the representation of numbers in space is influenced, if not determined, by the dominant reading/writing experience. It is an open question why Nuerk et al. (2005) obtained a null result for the interaction between the SNARC effect and notation. Different subjects, cultures, and stimuli,

might contribute to the discrepancy between the studies. Nevertheless, the current study shows that different notations lead to different mapping of numbers in space. As mapping of numbers in space was shown to take place during the numerical representation (Mapelli et al. 2003; Zorzi et al. 2002), or even later, during the response selection (Gevers et al. 2006b), this result indicates that different notations do not converge into an abstract, singlerepresentation, at least at the level of the numerical representation, and maybe even later. Koechlin et al. (1999) conducted several experiments on priming and subliminal priming. In these experiments the subjects were asked to compare a stimulus (e.g., the number 4) to the number 5, which served as a standard. The numbers could appear as digits, verbal numbers, or numerosity. Although most of the findings by the authors were compatible with the abstract representation view (i.e., they did not find an interaction between distance and notation), the authors also obtained some results that are more in line with the non-abstract representation view. For example, in one experiment they used verbal numbers and digits. Although they did not find an interaction between notation and distance under regular priming, they obtained this interaction under subliminal priming (which might reduce subjective expectancy/strategies). In another experiment, they used numbers in digits or numerosity notations. They found an interaction between notation and quantity priming (reduction in RT as the numerical distance between the prime and target reduced), in both regular and subliminal priming. These results indicate that there are different representations of digits, verbal numbers, and numerosity. Subsequently, Koechlin et al. proposed the existence of separate notation-specific representations of quantity that converge at a post-representational stage of processing. It is important to note that they assumed that these distinct representations are revealed only under a demanding temporal condition (e.g., subliminal priming in which the prime is presented for as little as 66 msec). Nevertheless, this position has been ignored by most researchers in the field in favour of the abstract representation viewpoint. Another effect which shows that numerical representation is not abstract is the compatibility effect (Nuerk et al. 2001; 2004a; 2004b; Wood et al. 2006b). The compatibility effect indicates that when people are comparing two two-digit numbers they are faster to compare the numbers if both the units and decades of a given number are systematically smaller or larger. For example people will be faster to compare the number 42 vs. 57 (4 , 5, and 2 , 7) than 47 vs. 62 (4 , 6, but 7 . 2). This effect seems to be independent of the distance effect (in both examples the distance effect is equal) (Nuerk et al. 2001; 2004b) or response selection (Nuerk et al. 2004a). This effect indicates that the numerical representation is not unitary, even within a single value (Dehaene et al. 1990), but might incorporate additional representations for tens and units. Importantly, the compatibility effect seems to be modulated as a function of notation. That is, the compatibility effect is smaller for verbal numbers than for digits (Nuerk et al. 2002). Further support for the non-abstract view comes from a recent developmental study. Holloway and Ansari (2009) collected the reading and mathematical achievements of BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Cohen Kadosh & Walsh: Numerical representation in the parietal lobes children at the ages of 6 and 8 years. The mathematical examination required the participants to answer as many single-digit addition, subtraction, and multiplication problems as possible within a 3-minute period. The reading skills were tested using a letter –word identification in which the participants needed to correctly read real words aloud to the experimenter, and word attack subtests, which required them to correctly pronounce pseudowords. Holloway and Ansari correlated these scores with the distance effect that was observed when these children compared numbers in digits (symbolic) or squares (nonsymbolic) notations. The abstract representation would predict that the distance effect independent of notation might correlate with mathematical achievement. In contrast, the distance effect was only correlated with mathematical achievement (but not reading achievements) when the numerical notation was in digit form. In contrast, the distance effect when numbers appeared as squares did not predict mathematical achievements. Moreover, they also found an interaction between distance and notation, and a lack of correlation between the distance effect for digits and squares. These results clearly suggest that different developmental trajectories underlie the representation of symbolic and non-symbolic numerical magnitude. However, Holloway and Ansari interpreted these findings as resulting from a better mapping between digits and numerical magnitudes in children with better mathematical achievement, despite the fact that a better mapping of digits to abstract representation can explain overall faster RTs in children with better mathematical achievement, but cannot explain the differences in the distance effect, as the symbolic distance effect occurs at the level of the representation (Dehaene 1996; Schwarz & Ischebeck 2000) or even later, during response selection (Cohen Kadosh et al. 2008b; Link 1990; Van Opstal et al. 2008a; Verguts & Fias 2004), but certainly not earlier. Other differences between different numerical notations have been found when stimuli have been processed automatically. However, in these cases the explanations provided considered only what was consistent with the abstract view. For example, Fias (2001) used the SNARC effect to examine the processing of verbal numbers. A SNARC effect was observed when the participants were asked to make a parity judgement, but was not found when verbal numbers were processed automatically, that is, when the participants were asked to monitor the occurrence of certain phonemes of verbal numbers (i.e., whether there was an /e/ sound in the name of the written verbal number). Notably, in a previous study, the SNARC effect was observed for both parity and phoneme monitoring tasks with digits (Fias et al. 1996). These findings suggest that under unintentional processing, the spatial representation of the two notations might differ. However, Fias (2001) suggested that this difference between digits and verbal numbers was a result of inhibition of the semantic route by the nonsemantic route only in the case of verbal numbers. Other studies also found a dissociation between digits and verbal numbers; however, these studies used naming tasks (Fias et al. 2001b; Ischebeck 2003). Compared to manual tasks, naming tasks are prone to include verbal/ phonological processes, because words are the preferred output format for naming (Dehaene 1992). However, 320

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this explanation cannot account for the differences between different numerical notations in the studies that we described earlier, as they all required a manual response (Cohen Kadosh 2008a; Dehaene & Akhavein 1995; Dehaene et al. 2008; Droit-Volet et al. 2008; Ganor-Stern & Tzelgov 2008; Ito & Hatta 2003). Thus, it might be that the differences between the notations reflect, at least partly, non-abstract representations, rather than solely preferred output format for naming (Dehaene 1992). Neuroimaging studies that have employed the size congruity paradigm using a single notation (Cohen Kadosh et al. 2007c; Kaufmann et al. 2005; Pinel et al. 2004; Tang et al. 2006a) found activity associated with interference between digits and physical size in the IPS (i.e., larger BOLD signal change for an incongruent condition vs. congruent condition). However, when different notations are used (Ansari et al. 2006b; Shuman & Kanwisher 2004) these interference effects are not seen in the IPS, thus supporting the idea of non-abstract representation. Numbers are apprehended automatically and even passively viewing them can activate a sense of magnitude, and therefore modulate neural activation in the IPS (Cantlon et al. 2006; Piazza et al. 2004). This is an important issue because at least one previous study has shown that the activation in the IPS during intentional numerical processing can be due to response selection rather than numerical representation (Go¨bel et al. 2004). This methodological confound may therefore explain IPS activation that is attributed to numerical processing (Eger et al. 2003; Naccache & Dehaene 2001a; Pinel et al. 2001) when similar response selection demands are associated with different types of representation, a proposition that is in line with recent studies (Cohen Kadosh et al. 2008b; Van Opstal et al. 2008a). Eger and colleagues (Eger et al. 2003), for example, used a numerical target detection task to avoid using direct magnitude judgements. In this task, the nine subjects were presented with numbers between 1 and 9 and required to detect, via a button press, the appearance of a target number (e.g., 7). Numbers have been found to activate the IPS independent of modality (visual or auditory presentation). However, this task required the subjects to: 1. Process the numbers intentionally. 2. Look for a target number independent of modality. Given that the numerical representation is flexible and biased by task requirements (e.g., Fischer & Rottmann 2005; Gertner et al. 2009; Shaki & Petrusic 2005) this may lead the subjects to create a modality-independent response set. 3. Prepare a similar response selection for each type of representation: The closer the number is to the target the more likely it will be that the activity associated with response selection is similar across stimulus types (i.e., pressing the button when detecting the target). For example, if the target number is 7 (“SEVEN”), 6 (“SIX”) is numerically closer to 7 than 1 (“ONE”). This idea has been confirmed by behavioural results (Cohen Kadosh et al. 2008b; Van Opstal et al. 2008a). To examine whether numerical representation is abstract and independent of task requirements, two recent studies (Cohen Kadosh et al. 2007b; Piazza et al. 2007) employed passive viewing in a modified adaptation paradigm (Grill-Spector et al. 2006a; Sawamura et al.

Cohen Kadosh & Walsh: Numerical representation in the parietal lobes 2006). Using this paradigm, the repetition of the same stimulus reduces the responsiveness of single neurons in monkeys (Sawamura et al. 2006) and the BOLD signal in humans (Grill-Spector et al. 2006a). In humans, BOLD signal adaptation occurs when the stimulus changes indicate that the neurons are not affected by the stimulus-specific adapting attribute. In contrast, BOLD signal recovery from the state of adaptation implies that different neuronal populations are activated and that these neurons are therefore differentially sensitive to some property of the adaptation and test stimuli. Recently, this paradigm has become popular in fMRI research, particularly because of the claim that it provides improved spatial resolution by revealing sub-voxel effects (GrillSpector et al. 2006a). Therefore, the adaptation paradigm can be used to address some of the limitations discussed earlier, such as spatial resolution, subjects’ strategies, and response selection. In the study by Piazza and colleagues (Piazza et al. 2007), for example, subjects passively viewed dot arrays or digits that varied in numerical value; a quantity presented to induce signal adaptation was followed by a deviation in the quantity to result in signal recovery. The abstract hypothesis suggests that similar adaptation and recovery should occur, irrespective of which combinations of dot arrays and digits were used at the adaptation and test phases. The logic behind this suggestion is that both notations denote the same numerical quantity, and therefore the same neuronal correlate should be sensitive to the numerical quantity, irrespective of its format (Dehaene et al. 1998; 2003). The results, however, challenged the abstract representation: that is,

there was an interaction between notation and recovery in the left and right parietal lobes. Moreover, the abstract representation posits that the recovery of the BOLD signal following the deviant stimuli should be of the same magnitude, again, irrespective of notation. That is, greater recovery should follow large numerical deviation (e.g., the number 50 after constant presentation of quantities between 17 and 19) in comparison to small numerical deviation (e.g., the number 20 after constant presentation of quantities between 17 and 19), and the magnitude of the recovery should not interact with notation. This again was clearly not the case; the left IPS, showed an interaction between notation and recovery that was modulated as a function of numerical distance. Although the authors focused more on the similarity observed in the right IPS between the notations, as indicated by the failure to find a significant interaction between notation, recovery, and numerical distance, the interaction between notation and recovery in both left and right IPS, and particularly the interaction between notation, recovery, and numerical distance in the left IPS (Fig. 2a), lend themselves to an explanation in terms of non-abstract representation. Cohen Kadosh and colleagues (Cohen Kadosh et al. 2007b) presented digits and verbal numbers in pairs. The pair could have an identical quantity (e.g., 8/eight after 8/eight), or a different quantity (e.g., 8/eight after 4/four). Adaptation was identified as the difference in the BOLD signal between pairs that did or did not differ in quantity. The results again indicated a deviation from abstract representation. Namely, the right IPS, but not the left IPS, showed an interaction between adaptation and notation. In

Figure 2. Evidence of non-abstract representations from recent neuroimaging studies. (A) From the left, the recovery effect following the adaptation period for dot arrays and digits due to numerical deviations (Far, Close) was modulated by notation in the left IPS (turquoise circle). (B) The right IPS shows an adaptation effect (different quantity minus same quantity) for digits, but not for words or mixed notation. (Adapted from Cohen Kadosh et al. [2007b] and Piazza et al. [2007] with permission.) A color version of this figure is available online at: www.journals.cambridge.org/bbs. BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Cohen Kadosh & Walsh: Numerical representation in the parietal lobes particular, the adaptation in the right IPS appeared only when a digit preceded a digit (Fig. 2b). The results again challenge the idea that numbers are represented in an abstract fashion, in this case, in the right IPS, and are best explained in terms of non-abstract representation. Thus, two studies, including one that purports to support abstract representation, reveal notation-dependent effects in the two key areas – the right and left IPS – associated with different numerical representations. One might suggest that the lack of interaction between notation and adaptation in the left IPS in Cohen Kadosh et al.’s (2007b) study indicates the existence of an abstract representation. We examined the involvement of the left IPS in abstract representation by using a different technique, transcranial magnetic stimulation (TMS), together with an adaptation paradigm. This innovative combination of TMS and adaptation (termed TMSA) significantly increases the functional resolution and allows one to differentially stimulate distinct but spatially overlapping neural populations within a stimulated region (Silvanto & Muggleton 2008a; Silvanto et al. 2007). The paradigm is based on findings that the effects of TMS are determined by the initial neural activation state, with attributes encoded by the less active/excitable neural populations within the stimulated region being more susceptible to the effects of TMS. Thus, by using adaptation to manipulate neural activation states prior to the application of TMS, one can control which neural populations are stimulated by TMS (for reviews see Silvanto & Muggleton 2008b; Silvanto et al. 2008). In our experiment the subjects were adapted to the digit 7, which repeatedly appeared on the screen for 45 seconds in different locations and fonts. Following this adaptation period, the subjects had to decide in a same-different task whether two numbers, digits, or verbal numbers on the screen are perceptually the same or different, while we stimulated the IPS with TMS during the period of 180, 280, and 380 msec poststimulus presentation – a timing during which numerical representation processes are believed to take place (Cohen Kadosh et al. 2007c; Dehaene 1996; Libertus et al. 2007; Szucs et al. 2007; Turconi et al. 2004). According to the abstract representation view, the participants’ decision time would be affected by the adapted number 7, independent of the numerical notation. In contrast, if separate representations for digits and verbal numbers exist, as the non-abstract representation view predicts, one should expect to find that only the representation for digits was affected. The latter hypothesis was borne out. Only digits were affected by TMS to the left IPS, while words were not affected. Moreover, the TMS effect was most effective when the digit 7 appeared, and was attenuated as numerical proximity decreased. This was not the case for verbal numbers (Fig. 3). In a second experiment, the subjects were adapted to verbal numbers rather than digits. The results were exactly the opposite from the previous experiment, thus completing a double dissociation; TMS to the left IPS was most effective when the adapted verbal number appeared, and was attenuated as numerical proximity decreased. This experiment shows that non-abstract representations for digit and verbal numbers exist also in the left IPS (Cohen Kadosh et al., submitted b). These apparent differences between the neuroimaging findings and the current TMS results are most likely to be rooted in the fact that 322

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TMS and fMRI yield different measures of cause and correlation, respectively (Walsh & Pascual-Leone 2003). 7. Multiple representations of number The fMRA findings in Piazza et al. (2007) and Cohen Kadosh et al. (2007b) and the TMSA results illustrate the idea that improved spatial resolution and automatic processing (or controlling for task-related responses) can uncover non-abstract representations that are otherwise masked. Notably, these studies used different notations, different ranges of numbers, different designs, and different techniques: the generalizability of these findings is therefore likely to be high. Differences in the results between these studies are also apparent. The results in Piazza et al. (2007) indicate that numerical representation for dots and digits is non-abstract in the left IPS, as illustrated by the interaction between notation and recovery (which was also significant for the right IPS) and notation, recovery, and numerical distance. In contrast, the study by Cohen Kadosh et al. (2007b) points towards the opposite conclusion, that is, that numbers in verbal number and digit notations are represented non-abstractly in the right IPS. However, the TMSA results showed that in the left IPS, too, numbers in verbal number and digit notations are non-abstractly represented. It seems clear, then, that non-abstract representation may be a feature of either IPS, and across different notations. However, the parietal lobes in the fMRI studies also showed some pattern that at first sight supports the existence of abstract representation. There are four possibilities for this pattern: 1. Non-abstract and abstract representations coexist. 2. While an interaction between notations is a strong indication of the existence of non-abstract representation, the lack of such interaction does not necessarily indicate the existence of abstract representation, because it is based on an absence of evidence. 3. Piazza et al. (2007) did control for task-related responses, but explicitly asked the subjects to pay attention to the quantity conveyed by the stimuli, and they were informed about the different formats and their approximate values. Moreover, immediately prior to the scanning session, subjects were shown approximately four exemplars of each numerosity (17:20 and 47:50 dots) and informed about their approximate range (20 and 50, respectively) in order to calibrate them to the respective value (Izard & Dehaene 2008). Therefore, one cannot be sure if at least some of the subjects still processed the numbers intentionally (e.g., noting themselves that the number 49 was changed to 18 dots). 4. As originally pointed out by Piazza and colleagues (Piazza et al. 2007; for similar view, see also Tudusciuc & Nieder 2007), to explain the cross-adaptation that they observed, the apparent support for abstract representation within the parietal region might be due to non-abstract numerical representations that are characterised by separate but highly interconnected subassemblies of neurons. Therefore, when notations are mixed, activation of one given population (e.g., digits) would quickly spread to the other population (e.g., dots), thus leading to cross-notation adaptation in the absence of real abstract representation. This idea gains support from findings in the primate brain. For

Cohen Kadosh & Walsh: Numerical representation in the parietal lobes

Figure 3. Non-abstract representations for digits and verbal numbers in the left IPS. In this TMS-adaptation experiment, the subjects were adapted to the digit 7. Top panel: Following this adaptation period the subjects had to decide whether a pair of numbers is perceptually same or different, while TMS was delivered to their IPS. Bottom panel: Adaptation was appreciated by the subtraction of the RT from a baseline condition, in which during the adaptation period the symbol # was presented instead of the digit 7 (i.e., no adaptation for numbers). TMS modulated only digits but not verbal numbers, as indicated by the interaction between notation and distance from the adapted number. This effect was maximal for the adapted digit, and reduced as the numerical distance from the adapted number increased. The straight white line shows the linear trend for the digits (which was significant), while the dotted white line shows the trend for the verbal numbers (which was not significant). A color version of this figure is available online at www.journals.cambridge.org/bbs.

example, based on fMRI studies in humans it was believed that both covert and overt shift of attention are subserved by the same mechanism in the frontal eye fields (FEF) (Corbetta et al. 1998). However, single-neuron recordings in monkeys, which provide better spatial and temporal resolutions, demonstrated that covert and overt shift of attention in the FEF are associated with different neural populations (Sato & Schall 2003), and that these dissociable populations are functionally interconnected (Schafer & Moore 2007).

8. Resolving the resolution problem Single-cell neurophysiology offers better temporal and spatial resolution than human neuroimaging, and several

recent studies have reported neuronal responses to quantity in the monkey brain (Nieder & Miller 2003; Roitman et al. 2007), which resemble the predictions of numericalrelated behavioural effects and computational models (Verguts & Fias 2004). Neuronal populations coding for numbers are highly distributed in the IPS, and also highly overlapping with representations of other magnitudes (for a neuroimaging meta-analysis, see Cohen Kadosh et al. 2008f), therefore making it difficult to disentangle numerical representation from other magnitudes. However, a recent single-cell neurophysiology study provided evidence for the existence of neurons that are specialized for different magnitudes (Tudusciuc & Nieder 2007). Another study that examined whether numerical representation depends on the format of presentation BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Cohen Kadosh & Walsh: Numerical representation in the parietal lobes demonstrated that in the macaque parietal cortex responses to the same quantity are initially formatdependent (Nieder et al. 2006); different neuronal populations discharge to sequential presentation, while others discharge to simultaneous presentation of numerosity. At a later stage during the delay period, these format-dependencies converge to a shared representation of quantity in the parietal cortex. This shared representation may be due to recurrent processing in the prefrontal cortex, which was not examined in the current study, but it showed longer latency and greater activity during the memory-delay period compared to the parietal cortex in a previous study (Nieder & Miller 2004). This suggests that the parietal lobe is equipped with primary non-abstract representations that are later transformed into a shared representation, possibly due to the intentional task requirement. Recently, Diester and Nieder (2007) showed that the neuronal populations for dots and digits in the parietal cortex of monkeys are notation-dependent. After training the monkeys to discriminate dot quantities, the monkeys were trained to associate digits with their corresponding dots (e.g., the digit 2 with two dots). Similar to humans, the behavioural results for digits and dots showed a similar function. However, Diester and Nieder (2007) found that whereas many neurons in the prefrontal cortex (PFC) were activated by digits, dots, or by both digits and dots, neurons in the

parietal cortex were activated primarily for either digits or dots (Fig. 4). Further training may lead to different representations (e.g., further specialisation, or alternatively a convergence towards a shared representation) and awaits further exploration. Of course, this result cannot give us 100% confidence that the basic representation of numbers in the human parietal lobes is non-abstract, because of the comparative question. However, it shows that even after months of training and although digits were explicitly associated with their corresponding dots, it is possible for neurons in the parietal lobes to be non-abstract. This result, together with the behavioural and neuroimaging data in humans (sect. 6), supports the idea that non-abstract representation is the basic representation in the parietal lobes. 9. Prefrontal cortex and number: Operations not representations We have confined our discussion so far to the parietal lobes, while not discussing the PFC. Some might argue that the PFC in the Diester and Nieder (2007) study showed some pattern that might be compatible with the idea of abstract representation (although one should note that the majority of the neurons there showed activation that is in

Figure 4. Non-abstract numerical representations in the monkey’s IPS. Two rhesus monkeys (Macaca mulatta) were trained initially in a delayed match-to-sample protocol to discriminate small numbers of dots (between 1 and 4). Later, over several months they learned to associate visual shapes (the digits 1, 2, 3, and 4) with corresponding numerosities. Finally, both notations appeared in a randomised manner within an experimental session. (A) Behavioural performance for Monkey #1 for dots and shapes. The curves show how often the monkeys judged the first test and sample to be equal. The performance to discriminate dots or shapes between 1 and 4 was quite high and comparable. (B) Lateral view of a monkey brain. The red circle represents the location of recording sites in the parietal lobe. (C) Venn diagram summarising the results in the IPS. Numbers correspond to the numbers of neurons selective for each class. Association neurons indicate neurons that have similar tuning functions for the numerical values in both protocols; Numerosity effect corresponds to neurons that were selective for a particular number; Type effect indicates neurons that were modulated by non-numerical visuospatial properties (e.g., physical size, font). It appears that most of the neurons in the IPS were non-abstract, as they showed selectivity for dots or shape (digits). In contrast, the amount of “abstract” neurons (coding both dots and shapes) was negligible. AS ¼ arcuate sulcus; CS ¼ central sulcus; PS ¼ principal sulcus; STS ¼ superior temporal sulcus; LS ¼ lateral sulcus. (Adapted from Diester and Nieder [2007]. A color version of this figure is available online at www.journals.cambridge.org/bbs.

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Cohen Kadosh & Walsh: Numerical representation in the parietal lobes line with non-abstract representation). In terms of number research, the PFC has received less attention than the parietal cortex, but it is increasingly being seen as important in the field of numerical cognition, which starts mainly from the observation of numerons (neurons which are numbersensitive) in the PFC by Nieder and colleagues (Nieder et al. 2002). There is no doubt that the PFC is involved in numerical processing (for a recent review, see Ansari 2008). However, we argue that the PFC is not involved in numerical representation, at least not in humans. The PFC is important for some numerical operations, but not representations (Duncan 2001; Revkin et al. 2008). The cognitive system is replete with such dissociations of cognitive operations and sensory representations – the hippocampus, while important for reconstructing memories, does not contain the representations of the objects in those memories; the PFC is involved in sequencing behaviours, while not containing the representations of each action in a sequence; the cerebellum is important for skilled use of fingers and motor coordination, but its role may be to support cognitive functions which are implemented by other brain areas (Glickstein 2007; Rosenbaum et al. 2001). There are several other reasons for our emphasis on the parietal cortex. First, in human adults, only the IPS shows numberspecific activation. This does not mean necessarily that this area is solely active in response to the given process. Posner (2003) encapsulates this view in another context in which he refers to activations observed in the same brain area under different task conditions: Although it is not always easy to distinguish between a brain area being specific for a domain or performing a computation that is of particular importance for some domains, either can underlie a form of modularity . . .. Thus these areas and many others that have been described are modules in the sense that they perform specific mental operations . . . sometimes the operations are within a single domain, but sometimes they are more general. (Posner 2003, p. 450)

In line with this idea, parts of the IPS show number-specific activation (Cohen Kadosh et al. 2005; 2008c). This was not found in the case of the PFC, which shows specificity for non-numerical magnitudes rather than numbers (Cohen Kadosh et al. 2005) or joint activation for numbers and other magnitudes (Cohen Kadosh et al. 2008c). Second, the activation in the PFC may reflect other factors than representation including training, working memory, strategy application (Gilbert & Burgess 2008), or changes in response strategy (although some of them are also modulated by the parietal cortex, as was described in sect. 5). For example, neurons in the PFC might respond to dots and digits because there is a similar response strategy for the digit 1 and the dot 1 when comparing them to other stimuli presented. Similarly, Tudusciuc and Nieder (2007) have suggested that the PFC activation might relate to other functions of the PFC (e.g., cognitive control, working memory) that operates on parietal lobe functions (Miller & Cohen 2001). Third, neuropsychological studies have found that neurological damage to the PFC leads to deficits in estimation, not because of representation impairment, but because of impairment at the level of translation from semantic representation to output (Revkin et al. 2008). Fourth, there seems to be a shift from relying on the PFC during numerical processing to the IPS, as age

increases (Ansari & Dhital 2006; Ansari et al. 2005; Cantlon et al. 2006; Kaufmann et al. 2006). This decrease in the reliance on prefrontal regions, and the increase in posterior specialized neuronal circuits, might relate to increased reliability of processes of cognitive control, attention, and working memory with age (Ansari 2008), or might indicate the developmental transition into a stage in which numerical representation becomes more automatic, and therefore involves less PFC resources. Fifth, in contrast to many studies that consistently found that parietal damage leads to acalculia and basic numerical processing deficits (Ashkenazi et al. 2008; Dehaene & Cohen 1997; Delazer & Benke 1997; Delazer et al. 2006; Lemer et al. 2003; Takayama et al. 1994; Van Harskamp & Cipolotti 2001; Van Harskamp et al. 2002; Vuilleumier et al. 2004), there is, at least to our knowledge, a lack of consistent evidence of acalculia resulting from frontal damage. In this respect, we do not refer to secondary acalculia – numerical difficulties due to non-numerical origin, such as working memory problems (Doricchi et al. 2005) – but to a primary acalculia, which is rooted at the level of the numerical representation. Sixth, in monkeys, numerical information is first coded in the parietal lobes, and only later in the prefrontal cortex. This temporal lag is in line with our suggestion that the PFC is involved in numerically-related processes, which might be post-representational (Nieder & Miller 2004). Still, in humans, it is possible that the PFC is involved in numerical representation, rather than operation, during early developmental stages. This idea is gaining support from several neuroimaging studies that found PFC activation in children and infants during numerical tasks (Ansari & Dhital 2006; Cantlon et al. 2006; Izard et al. 2008; Kaufmann et al. 2006). The idea that children activate brain regions that are outside the typical areas activated in adulthood is not unique to the field of numerical cognition, and is observed in other fields. For example, children represent faces in additional cortical areas to the occipitotemporal network: occipital face area (Pitcher et al. 2007), fusiform face area (Kanwisher et al. 1997), and the superior temporal sulcus that are consistently found in adults (Haxby et al. 2000), including the left and right PFC (Gathers et al. 2004; Passarotti et al. 2003). (For a review, see Johnson et al. 2009.) One of the reviewers rightly pointed out that in the recent fMRI study by Piazza et al. (2007), which we discussed in section 6, PFC activation was observed as a function of numerical processing, although the (adult) subjects passively processed the quantity. However, as was described in section 7, in this study Piazza and colleagues draw the attention of the subjects to the different numerical quantities, to the different formats, and to the change that will occur. Future studies should take into account the possibility that the PFC activation, at least for human adults, might not reflect number-specific representation, but other functions that support or utilise numerical representation in the parietal lobes. 10. Abstract after all? Our primary intention in this article has been to question the idea that the default numerical representation is BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Cohen Kadosh & Walsh: Numerical representation in the parietal lobes abstract. We need, however, to account for the evidence that points towards abstraction and against our view. Assuming that abstract representation might after all exist under certain conditions, our contention, following Barsalou (2003), is that it occurs as a consequence of the intentional processing of numbers, which leads to explicit creation of connections between different notationspecific representations. We also contend that this crosstalk between notations occurs on-line on a task-by-task basis, but does not exist off-line. We can do no better than Barsalou’s words: “abstraction is simply a skill that supports goal achievement in a particular situation” (Barsalou 2003, p. 1184). We therefore suggest that when numerical representation is probed automatically (or implicitly), one will be more likely to find evidence for different numerical representations. However, when researchers use an intentional task, they might encourage the subject to modify the default non-abstract representations. Similar examples can be extracted from the mapping of numbers into space. There is good evidence that we map numbers from left to right as numerical value increases. However, under certain conditions one can represent numbers in reverse format, from right to left (Bachtold et al. 1998). Similarly, we argue that humans do not, as a default, represent numbers abstractly, but can adopt strategies that, in response to task configuration and demands, can create real or apparent abstraction. As numerical representation is highly flexible, and not static, what are the neural correlates for such representations? While the IPS shows a consistent modulation for numerical quantity, in different paradigms and labs (Ansari et al. 2006a; 2006b; Castelli et al. 2006; Cohen Kadosh et al. 2005; 2007c; Fias et al. 2003; 2007; Pesenti et al. 2000; Piazza et al. 2004; Tang et al. 2006a; Wood et al. 2006b, for reviews, see Ansari 2008; Brannon 2006; Cantlon et al. 2009; Cohen Kadosh et al. 2008f; Dehaene et al. 2003; Nieder 2005; Walsh 2003), other brain areas outside the IPS also show involvement during numerical processing – for example, the left precentral gyrus (Piazza et al. 2006; Pinel et al. 2004), the right middle temporal gyrus (Cohen Kadosh et al. 2005; Pinel et al. 2001), the right superior temporal sulcus (Cohen Kadosh et al. 2005), the right precentral gyrus (Piazza et al. 2006), the cerebellum (Fias et al. 2003), or the primary visual cortex, and the insula (Piazza et al. 2007). However, aside from the IPS, these areas did not show a consistent activation across studies and tasks. Therefore, the IPS may be the critical part of a distributed and highly interconnected network of regions that gives rise to the representation of numerical magnitude in particular task contexts. In his dual code hypothesis, Paivio (1971; for extensions see Barsalou et al. 2008; Glaser 1992) suggested that semantic knowledge is represented internally by linguistic (verbal) and imagery (pictorial) codes, which involved internal translation between them. Similar to our view on numerical cognition, he proposed that the involvement of each code depends on the task demands. Generally, whereas picture stimuli tend to activate imagery codes, word stimuli are coded initially by the linguistic codes. Paivio further suggested that the dual code of linguistic and imagistic representations might underlie all of cognitive activities. 326

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Our current cognitive neuro-anatomical approach is partly inspired by cognitive processes as described by the dual code theory and its extensions. Similarly, we propose that dual codes are active during numerical representation. Instead of the terminology of linguistic and imagery codes we use the terminology of automatic and intentional codes, respectively. At the first stage, there is an automatic activation of the numerical quantity that is modality- and notation-specific (similar to the linguistic representations in the Language and Situated Simulation model; for a review, see Barsalou et al. 2008) in the IPS. This processing is crude and not as refined (Banks et al. 1976; Cohen Kadosh 2008b; Tzelgov et al. 1992). Later, the representation of numerical information in the IPS can be further refined. This refinement depends on the time of the activation, intentional processing, task demands, and is resource-dependent. The representation at this stage can be transferred to an on-line representation by a few, the majority, or the entire neuronal population in the IPS, which was activated at an earlier point during automatic numerical representation. This transition from automatic to intentional representation can be subserved by the PFC neural circuitry that is malleable, and its activity reflects learned associations and rules (Duncan 2001) (e.g., that 5 and FIVE have the same quantity) (see Fig. 5). Note, that because dot patterns are considered prelinguistic, the terminology of linguistic code cannot be applied here. As for the imagery code, which according to the dual code hypothesis is pictogram, a tentative suggestion is that in the western culture this will be a digit, as it is the most used pictogram for numbers in the western culture.

Figure 5. Automatic (gray) and intentional (black) numerical representations. Automatic numerical always precedes the intentional numerical processing. However, the height, shape, and offset of the two distributions are not fixed, and are context- and task-dependent. The transition from automatic to intentional representation in the IPS can be subserved by the PFC neural circuitry that is malleable, and its activity reflects learned associations and rules (Duncan 2001). Note that this division also mirrors the separation of approximate and exact systems with the former being fast and automatic, and the later slow and intentional. This model is similar to the Language and Situated Simulation model, in which the automatic and intentional representations correspond to linguistic and situated simulation systems (Barsalou et al. 2008).

Cohen Kadosh & Walsh: Numerical representation in the parietal lobes As the occurrence of automatic processing per se, without intentional processing, is rather limited (Perlman & Tzelgov 2006), the height, shape, and offset of the distributions of the automatic and intentional numerical representations that are presented in Figure 5 are not assumed to be fixed, and are context- and taskdependent. For example, in some tasks the intentional processing can be more dominant than the automatic processing. Thus, the two distributions are only examples and can take place in many different forms, and in some conditions without or with minimal intentional processing. This model can explain the different behavioural and neuroimaging results that we reviewed in favour of nonabstract representations (automatic numerical processing), and those that might imply abstract representation (intentional numerical processing). For example, when the intentional representation is more dominant, there is a need for increasing statistical power in order to uncover the non-abstract numerical representation that occurs during the previous stage and is masked by the intentional processing that creates an on-line abstract representation. In addition, when no intentional processing is needed, the detection of non-abstract representation is easier to observe. Furthermore, this model can further explain the distinct and shared representations for general magnitude in the IPS (Cantlon et al. 2009; Cohen Kadosh et al. 2008f; Walsh 2003), which corresponds in the current case also to automatic and intentional, respectively. As one of the reviewers pointed out, our terminology of initial automatic processing that is followed by an intentional and deliberate processing with increased precision can profitably extend the positions in the field of conceptual processing as reviewed by Glaser (1992) and Barsalou et al. (2008). In short, Solomon and Barsalou (2004; see Barsalou et al. 2008, for a review of further studies) suggested that when task conditions allow the usage of shallow processing, participants use a superficial linguistic strategy. However, when a deeper conceptual processing is needed they use simulation (imagery), which occurs after the linguistic code. This interplay between linguistic and simulation codes can be modulated by automatic and intentional processing, respectively. Moreover, our terminology helps explain effects in other domains such as in language comprehension, conceptual processing, social processes, and education (for examples, see Barsalou et al. 2008). For instance, children with developmental dyscalculia might experience difficulties in processing numbers because of deficits in automatic numerical processing (Rubinsten & Henik 2005; 2006). According to the current framework, this problem leads to a greater reliance on intentional processing, which leaves, in turn, less resources for manipulations when they are facing more complicated computation, or when they need to learn more advanced strategies (Butterworth 2004). However, one important distinction between our model and other modifications of the dual-code is that our neuro-anatomical framework includes the IPS, a critical area for numerical cognition. Other fields might depend on other brain areas/networks (e.g., temporal structures during language tasks), but we assume that the information processing, namely, the transition from automatic to intentional processing, is based on similar principles.

11. Future directions The question of specialisation of numerical representation has been relatively neglected, compared to other functions such as face, colour, or object perception (Cohen Kadosh & Johnson 2007). Several possible directions of research can remedy this. 1. Single-cell neurophysiology. Following Diester and Nieder’s (2007) study, it is important to examine how learning affects numerical representation in the parietal lobe. It might be that after longer training, neurons in the parietal lobe will show activation for both digits and dots. However, following the interactive specialisation approach (Cohen Kadosh & Johnson 2007; Johnson 2001; Johnson et al. 2009), we believe that learning will lead to neuronal specialisation, just as observed with magnitude processing (Cohen Kadosh et al. 2008f; Cohen Kadosh & Walsh 2008; Holloway & Ansari 2008). Another direction will be to use automatic and intentional tasks to examine whether the abstract representation in the prefrontal lobes is a function of natural representation or a result of strategies employed according to task requirements. † † Developmental studies. By using habituation paradigms with sequential and simultaneous presentations, it is possible to examine whether infants habituate to the same quantity independent of format. However, one possibility is that the trajectory of numerical representation follows the same principle as other types of magnitude representations (Cohen Kadosh et al. 2008f; Holloway & Ansari 2008), and other brain functions (Cohen Kadosh & Johnson 2007), and follows a trajectory from nonspecific to increasingly specialised representations as a function of learning. III. Automaticity and intentionality. The passive task used in different adaptation paradigms also has some limitations; the experimenter cannot know if some subjects decide to attend to and act on the numbers (Perlman & Tzelgov 2006). Studying numerical representation by using automatic processing (e.g., Stroop-like paradigms) can yield a description of the numerical representation that is not dependent on specific task demands. Adopting this approach of contrasting the automatic and intentional processing of numerical information with different notations will yield a better characterisation of the abstract and non-abstract representations, and the conditions under which each representation is activated. FOUR. Neuroimaging. Combination of techniques with good temporal resolution (magnetoencephalography, ERP) and spatial resolution (fMRI) can shed light on the model that we presented in Figure 5. These techniques will allow the detection of the representations under automatic processing, and the interplay between the representation under automatic and intentional representations in the IPS, and the possible recurrent processing from the PFC, in the case of intentional processing. Aside from fMRI, multivariate pattern recognition, an analysis that uses pattern classification algorithms to decode fMRI activity that is distributed across multiple voxels, can also provides a means to disentangle different neuronal substrates as a function of numerical representation. 5. Neuronal modelling. Not surprisingly, the issue of nonabstract representation has been neglected, possibly because of the salience and convenience of the view that numbers are BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Commentary/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes represented in an abstract fashion. However, a few studies have addressed the issue of abstract representation, at least indirectly. Some of them lead to the conclusion that the properties of numerical representation for dots and digits might not be identical (Verguts & Fias 2004; Verguts et al. 2005). A clear direction for future research in this field is to examine issues such as task-dependent representation, or typical and atypical development of numerical representations as a function of interaction between brain areas (Ansari & Karmiloff-Smith 2002). A great deal is known about the behaviour of numerical systems and we also have good characterisations of the anatomy and functions of key areas to provide constraints on models.

12. Conclusion The idea that numerical representation is not abstract has, in our view, been cast aside too readily. In contrast, the idea that number representation is abstract has become a premature default position that is not as strongly supported by the evidence on which it is based as its predominance may suggest. Here we have provided evidence from behavioural and neuroimaging studies in humans to single-cell neurophysiology in monkeys that cannot be explained by the abstract numerical representation, as they clearly indicate that numerical representation is non-abstract. It is an open question if numerical representation, at least under certain conditions, is abstract at all. We therefore suggest that before sleep-walking into orthodoxy the alternative idea is revitalised and given further consideration. Future studies should take into account the different methodological and theoretical arguments that we have raised in this target article, before concluding that numerical representation is abstract, as well as any other conclusions regarding the commonalities between processes.

ACKNOWLEDGMENTS We would like to thank Kathrin Cohen Kadosh and the reviewers for their helpful suggestions. Roi Cohen Kadosh is supported by a Marie Curie Intra European Fellowship. Vincent Walsh is supported by the Royal Society.

Open Peer Commentary Slippery platform: The role of automatic and intentional processes in testing the effect of notation doi:10.1017/S0140525X09990501 Daniel Algom Department of Psychology, Tel-Aviv University, Ramat-Aviv 69978, Israel. [email protected]

Abstract: The type of processing of numerical dimensions varies greatly and is governed by context. Considering this flexibility in tandem with a

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fuzzy demarcation line between automatic and intentional processes, it is suggested that testing the effect of notation should not be confined to automatic processing, in particular to passive viewing. Recent behavioral data satisfying the authors’ stipulations reveal a considerable, though perhaps not exclusive, core of common abstract processing.

In a clearly written and thought provoking article, Cohen Kadosh & Walsh (CK&W) make three interrelated arguments. First, they claim that the meaning of numerals – numerical magnitude – is activated in an automatic fashion just about whenever a numeral is presented for view. Second, they argue that notation-induced differences in processing can be tapped when one does not impose an intentional task, indeed any task, engaging the presented numerals. Third, they suggest that the best behavioral avenue to uncover the effect of notation is to perform Strooplike conflict studies in which the different notations serve in turn as the target and the to-be-ignored dimensions. The generic view advanced by the authors has merit, but there are difficulties with the arguments. Concerning the first argument, the authors pinpoint the vast experience that humans have with numbers and conclude that, as a result, numbers are over-learned and processed in an automatic fashion. Numbers are certainly ubiquitous in people’s cognitive milieu, but it does not follow that the full arithmetic properties of a number are activated in an obligatory fashion just whenever a number is presented for any purpose. As Stevens noted in his celebrated chapter, a numeral can be “an ink mark on a piece of paper” (Stevens 1951, p. 22); another intellectual giant of quantitative psychology has similarly remarked that numerals can sometimes be mere “scratches on paper” (Guilford 1954, p. 5). Human cognition is a wonderfully adjustable system, flexible enough to treat numerals as mere shapes when that suffices to perform the task (if there is one to perform). This conclusion was reached in a tightly controlled study by Cohen (2009). Cohen presented participants with a single numeral (between 1 and 9) and asked perhaps the simplest possible question: to identify whether the presented numeral was a 5. If numbers automatically activate their magnitude representations, then reaction time should be a function of the distance between 5 and the presented numeral. Instead, magnitude information did not affect the data, only physical shape did. Cohen (2009) concluded that “numerical symbols do not automatically activate quantity representations” (p. 336) and that, in the absence of meaning, the shapes determine the results. Ratinckx et al. (2005) reached similar conclusions with respect to twodigit numerals. Typical markers of automatic activation mentioned by the authors, such as the size congruity effect, are also inconsistent with a sharp dichotomy between automatic and intentional processing. Virtually all studies that demonstrated the effect (of task-irrelevant numerical magnitude on judgments of physical size) used a design that favored the numerical over the physical dimension in the first place. Thus, more values of number than values of physical size were typically presented (indeed, most studies used merely two values for size: large, small). Moreover, the numerals were easier to discriminate from one another than their physical sizes. When these and further contextual biases were removed (Algom et al. 1996; Pansky & Algom 1999; 2002), the size congruity effect evaporated – with the numbers processed as mere shapes. And, when physical size is made the more salient dimension (Fitousi & Algom 2006) the size congruity effect reverses with physical size intruding on number magnitude more than vice versa. Such pliability is inharmonious with (strongly) automatic processing. The absence of automatic activation of (cardinal) numerical magnitude has been shown with respect to another marker of automatic activation, the SNARC effect (Ben-Nathan et al. 2009). Of even more concern, these two putative markers of automatic activation were unrelated for the same numbers with the same observers (Fitousi et al. 2009). The upshot is that (a) automatic and intentional processing do not form a dichotomy, but rather, mark the end-points of a finely

Commentary/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes grained continuum, and that (b) the dominant type processing is under strong contextual control. Consequently, numerical magnitude is not activated in an automatic fashion on an unlimited scale; it is not the default processing option when a numeral is presented for view. When contextual demands do not invite number processing, the presented numerals may well be processed as mere shapes or marks. Therefore, it is not prima facie clear what the recordings in the adaptation paradigms with passive viewing signify. They might not be pure measures of number processing (note: numerals in different notation differ in shape). Alternatively, some features (demand characteristics?) of the experimental situation might have invited/encouraged number processing. Be that as it may, passive viewing seems to be a suboptimal vehicle to test notation-induced differences in processing. CK&W seem to admit this when they mention that the experimenter cannot know what aspect of the stimulus the observers elect to attend. Given the fuzzy demarcation of automatic processing, I do not fully agree with the second claim made by the authors that the effect of notation should be tested via automatic processing. Of course, the authors can retort that, regardless of the generic question of automaticity, the testing can take place in those conditions in which automatic processing has been verified in advance (e.g., a size congruity effect is demonstrated for the stimuli). Note that this stipulation cannot apply with passive viewing. However, I am not convinced that intentional processing is inherently unsuitable for testing the effects of notation. Surely, strategies can bias processing but they do not invariably act to produce a common abstract representation. Thus, Fias (2001) did find a dissociation between a parity judgment task and a phoneme verification task with verbal numbers, even though magnitude information is not needed for performance in both tasks. Damian (2004) demonstrated a task-dependent asymmetry in performance across Arabic and verbal numerals. So, I would not rule out intentional processing as platform for testing the question of notational effects. Concerning the third argument, by a fortuitous coincidence, Ben-Nathan (2009; Ben-Nathan & Algom 2008) performed the experiment recommended by the authors: A pair of numerals appeared on each trial, an Arabic digit and a verbal number, and the participants decided, while timed, whether the number in the target notation was larger or smaller than a standard number. The Stroop effect for each notation was calculated as the difference in performance between congruent and incongruent displays. As the results show (Fig. 1), both Arabic and word performance was affected by the irrelevant number in the alternative notation, although the effect was greater for word. This set of data is not completely decisive, but the Stroop effects recorded for both notations tap a considerable amount of common, hence abstract, processing.

Figure 1 (Algom). The time needed to decide the numerical magnitude (larger or smaller than the standard) as a function of target notation and congruity. [Con: congruent, Incon: incongruent].

ACKNOWLEDGMENT The author thanks Merav Ben-Nathan and Eran Chajut for suggestions and help in preparing this commentary.

Are non-abstract brain representations of number developmentally plausible? doi:10.1017/S0140525X09990021 Daniel Ansari Department of Psychology and Graduate Program in Neuroscience, University of Western Ontario, London, Ontario N6G 2K3, Canada. [email protected] http://psychology.uwo.ca/faculty/ansari_res.htm

Abstract: The theory put forward by Cohen Kadosh & Walsh (CK&W) proposing that semantic representations of numerical magnitude in the parietal cortex are format-specific, does not specify how these representations might be constructed over the course of learning and development. The developmental predictions of the non-abstract theory are discussed and the need for a developmental perspective on the abstract versus non-abstract question highlighted.

In several parts of their target article, Cohen Kadosh & Walsh (CK&W) highlight the importance of taking a developmental perspective in explorations of the brain’s representation of number. However, their article does not provide a model of how non-abstract representation of number in the parietal cortex might arise over developmental time. Since many of the representational formats described by CK&W, such as Arabic numerals and number words, are cultural inventions, their brain representation(s) must be the outcome of a developmental process. In other words, the theory raises the question of why development would involve the construction of a system with multiple format-specific representations of numerical magnitude in the parietal cortex? In this commentary, I explore the notion of non-abstract representations of numerical magnitude from a developmental perspective and contend that currently available theory and evidence suggests that abstract representations of numerical magnitude are a more plausible outcome of development than non-abstract representations. According to several current theoretical proposals (Dehaene 1997; Verguts & Fias 2004), the acquisition of exact, symbolic representations of number requires the interaction between, on the one hand, preverbal systems that have a long evolutionary history and are shared between species and, on the other hand, language-related, symbolic representation of number that are the product of cultural history. Specifically, evidence suggests that infants and nonverbal animals share the ability to discriminate between large, non-symbolic numerosities (such as arrays of dots), and that infants discrimination abilities are, consistent with Weber’s law, ratio dependent (for a review, see Brannon 2006). In addition to this approximate system for the representation of large numbers, infants are thought to have a system for the precise representation of small sets of objects (Feigenson et al. 2004), which is thought to support the ability of children and adults to rapidly (without counting) enumerate small (1– 4) items (frequently called “subitizing”). These early representational systems are thought to play an important role in children’s acquisition of higher-level numerical skills. In particular, recent evidence suggests that infants’ representation of small sets scaffolds their understanding of the meaning of counting (Le Corre & Carey 2007). Subsequent to children’s gaining understanding of the meaning of number words, numerical symbols such as Arabic numerals are learnt and presumably these initially meaningless symbols acquire their meaning by being mapped onto corresponding number words, which are in turn mapped onto preverbal systems for the representation of BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Commentary/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes numerical magnitude. Thus, development is thought to involve the progressive acquisition of the mappings between different external representations of number. Thus, while the processes that are involved in mapping from external to internal representations may differ between stimulus formats, the internal semantic referent does not differ between representation formats. It is this common representation that allows for the translation between formats. This is also the prediction made by Verguts and Fias, who argue that symbolic and non-symbolic representations of numerical magnitude are mapped onto a shared representation of numerical magnitude subserved by the intraparietal cortex via different pathways. Recent empirical work has supported this proposal by showing format-general representation of quantity in the intraparietal sulcus, as well as format-specific activation in other brain regions (Ansari & Holloway 2008; Santes et al., in press). In other words, format-specificity lies in the process of mapping between, on the one hand, different external representations (i.e., number words to Arabic numerals) and, on the other hand, the mapping between external representation and a common, format-general, internal representation of numerical magnitude. This theory is different from the model put forward by CK&W in which the representation of numerical magnitude itself is predicted to be format-specific. Given that development is thought to involve the progressive interconnection between different external representations that refer to a common internal representation of numerical magnitude, it seems more plausible that development involves the progressive specialization of the parietal cortex for formatindependent rather than format-dependent representations of numerical magnitude, while other brain regions might mediate between representations and subserve the association between each external representation and the common, abstract representation of numerical magnitude. Indeed, a recent neuroimaging study (Cantlon et al., in press) provides evidence to suggest that both children and adults exhibit common activation of the inferior parietal cortex during the processing of symbolic and non-symbolic numerical magnitude. However, children additionally activate prefrontal regions, which may mediate the association between different formats. Such data are consistent with the interactive specialization model of functional brain development, in which functional brain specialization is the product of the interaction between multiple brain regions (Johnson 2001). If the proposal by CK&W is indeed correct, then the current models of the development of numerical magnitude representations need to be radically revised. If the semantic representation, for example, of number symbols differs qualitatively from the representation of number words and non-symbolic representations of numerical magnitude, then the development of children’s understanding of these external representations must involve independent developmental trajectories. Specifically, different external representations of numerical magnitude would be expected to acquire their meaning independently of one another, rather than through becoming interconnected. Furthermore, this developmental trajectory would differ between speakers of different languages and second-language acquisition would be predicted to involve the construction of a new parietal representation for the number words in the newly acquired language. What are the neurocognitive processes that allow for the construction of these format-specific semantic representations of numerical magnitude? The implications of such independent representations might be that children cannot use their semantic representation of number words in order to understand the meaning of Arabic numerals. Furthermore, this would have educational repercussions and may lead to less focus on the relationships between different formats of representations in the classroom. Taken together, in its current form, the proposal for nonabstract representations put forward by CK&W does not account for the emergence of non-abstract representations over

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the course of learning and development. Because different formats for the external representation of numerical magnitude are acquired over the course of learning and development, the non-abstract theory must be put to the developmental test.

Numerical abstractness and elementary arithmetic doi:10.1017/S0140525X09990495 Jamie I. D. Campbell and Arron W. S. Metcalfe Department of Psychology, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5A5, Canada. [email protected] [email protected] http://artsandscience.usask.ca/psychology/people/detail.php? bioid¼212

Abstract: Like number representation, basic arithmetic seems to be a natural candidate for abstract instantiation in the brain. To investigate this, researchers have examined effects of numeral format on elementary arithmetic (e.g., 4 þ 5 vs. four þ five). Different numeral formats often recruit distinct processes for arithmetic, reinforcing the conclusion that number processing is not necessarily abstracted away from numeral format.

Cardinal number is an abstract property of a set of elements because it is invariant for all possible kinds of elements or referents. The basic arithmetic operations (i.e., addition, multiplication, subtraction, and division), at least when viewed as formal arithmetical functions, are similarly abstract because the kinds or referents of problem operands are irrelevant. For this reason, both number and arithmetic seem to be natural candidates for abstract instantiation in the brain. Not surprisingly, then, the issue of abstraction has engaged cognitive arithmetic researchers in much the same debate that has occupied research on quantity representation. In the target article, Cohen Kadosh & Walsh (CK&W) have focused on effects of numerical format (e.g., 4 vs. four) in tasks that directly or indirectly tap quantity processing, but they have not discussed in any detail the substantial body of research that has examined effects of numeral format on elementary arithmetic (e.g., 4 þ 5 vs. four þ five). In fact, the prominent models of number processing advocated by Dehaene et al. (1998a) and McCloskey and Macaruso (1995), which assume that different numeral formats activate a common quantity representation, similarly assume that elementary arithmetic is abstracted away from surface form (see also Venkatraman et al. 2005). Alternatively, cognitive processes for arithmetic could vary with format (see Campbell & Epp [2005] for a review of relevant literature). In this alternative view, there are two senses in which elementary arithmetic could be non-abstract. First, calculation performance could be based on discrete, format- and operation-specific processes (McNeil & Warrington 1994). This implies non-abstract representation in the same sense defined in the target article (i.e., different formats recruit distinct neuronal populations). Second, calculation might be based on overlapping representations across formats, but calculation efficiency is format specific. This would occur if problem-encoding processes and calculation processes were interactive rather than strictly additive (Szu´´cs & Cse´pe 2004). As the following paragraphs illustrate, there is evidence that performance of elementary arithmetic by educated adults is non-abstract in both senses. In experimental research examining format effects on elementary calculation, the most common contrast has involved arithmetic problems in Arabic digit format (5 þ 6) versus written word format (five þ six). It is consistently found that performance is much slower and more error prone with written-word operands compared to Arabic digits. Campbell and Epp (2005)

Commentary/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes proposed that relatively poor performance with arithmetic problems in written-word format occurs because number-fact retrieval processes are less efficient with word compared to digit operands. Arithmetic problems are encountered more frequently in digit format (e.g., 2 þ 6, 4  5) than in written number-word format (two þ six, four  five). Consequently, digit problems are more likely to activate a visual retrieval path than would a written-word problem (McNeil & Warrington 1994). Retrieval, given number words, presumably requires phonological recoding of problems so that the proximal retrieval cue is based on auditory-phonological codes. Retrieval with digits, therefore, would be more efficient because it is mediated both by well-established visual and phonological routes, whereas retrieval with number-word format would not provide a direct visual basis for retrieval. The proposal that arithmetic-fact retrieval efficiency is lower with problems in word format than digit format is also supported by the well-replicated finding that non-retrieval strategies (i.e., procedural strategies such as counting or decomposition) are reported more often given word format (six þ seven) than digit format (6 þ 7) (Campbell & Epp 2005). Educated adults report procedural strategies for simple arithmetic up to 50% more with problems in written-word format than digit format (Campbell & Alberts, in press). Format-induced strategy shifts imply that different formats often recruit different neural processes for elementary arithmetic. Indeed, imaging research suggests that retrieval of arithmetic facts is associated with linguistic representations in the left angular gyrus, whereas procedural strategies requiring semantic quantity processing recruit bilateral components of the intraparietal sulcus (Dehaene et al. 2004). As direct retrieval and procedural strategies activate distinct brain regions (see also Dehaene et al. 2003), the effects of format on strategy choice for elementary arithmetic imply that calculation is not generally abstracted away from surface form. Format-related strategy shifts demonstrate that calculation performance sometimes involves discrete, format-specific processes, but calculation also appears to be non-abstract in the second sense mentioned earlier; namely, that format-specific encoding processes or context can interact with calculation processes. One source of evidence for this comes, again, from research examining format effects on simple arithmetic: When procedural strategy trials are removed from analysis and only retrieval trials are analyzed, there remain substantial wordformat costs relative to digit format, and word-format retrieval costs tend to increase with problem difficulty (Campbell et al. 2004; Campbell & Penner-Wilger 2006). This reinforces the conclusion that arithmetic retrieval processes are not abstracted away from surface format. The non-abstractness of elementary arithmetic is demonstrated further by context-dependent activation of arithmetic facts. Bassok et al. (2008) found evidence for obligatory activation of addition facts (4 þ 2 ¼ 6) when problems were primed by word pairs semantically aligned with addition (e.g., tulipsdaisies, which afford addition as a collection of flowers), but not when they were primed by pairs misaligned with addition (hens-radios, records-songs). The automaticity of arithmetic fact retrieval thereby depended on the analogical consistency of the semantic context activated by the prime and the specific arithmetic operation to be performed. This implies that the kinds and referents of problem operands are relevant to cognitive arithmetic, despite being irrelevant to arithmetic as a formal operation. Like the effects of surface form, semantic alignment phenomena demonstrate that cognitive arithmetic is not abstracted away from the conditions of problem encoding. Research on elementary arithmetic thereby aligns with the theoretical perspective represented in the target article, and points toward integrated, multimodal mechanisms in favor of abstract or amodal representations and processes (e.g., Barsalou 2008; Clark & Campbell 1991).

Numerical abstraction: It ain’t broke doi:10.1017/S0140525X09990513 Jessica F. Cantlon, Sara Cordes, Melissa E. Libertus, and Elizabeth M. Brannon Center for Cognitive Neuroscience, Duke University, Durham, NC 27708. [email protected] [email protected] [email protected] [email protected]

Abstract: The dual-code proposal of number representation put forward by Cohen Kadosh & Walsh (CK&W) accounts for only a fraction of the many modes of numerical abstraction. Contrary to their proposal, robust data from human infants and nonhuman animals indicate that abstract numerical representations are psychologically primitive. Additionally, much of the behavioral and neural data cited to support CK&W’s proposal is, in fact, neutral on the issue of numerical abstraction.

Cohen Kadosh & Walsh (CK&W) propose a new dual-code model of numerical representation that posits a psychological and neural distinction between fast, automatic notationdependent representations and slower, intentional notationindependent representations. In their model, notation- and modality-specific (non-abstract) representations are psychologically more primary than abstract representations. We argue that this proposal is limited in its psychological and neurobiological perspective on numerical abstraction, and that the evidence they offer is either neutral on the issue of whether numbers are represented abstractly, or equally compatible with existing models of number representation. A central limitation of CK&W’s proposal is the coarse manner in which it surveys the theoretical landscape of numerical abstraction. At the psychological level, numerical abstraction can refer to notation independence, modality independence, or the representation of number independently of dimensions such as time, space, size, and color. For instance, the capacity to recognize that a group of three elephants is equal in number to a group of three umbrellas, but that both are fewer in number than a series of ten gunshots, is a feat of numerical abstraction. We know from scores of behavioral studies that human infants and nonhuman animals smoothly represent non-symbolic numerical values across modalities and dimensions (e.g., Cantlon & Brannon 2006; Church & Meck 1984; Hauser et al. 2002; Jordan & Brannon 2006; Jordan et al. 2005; 2008; Kobayashi et al. 2005; Nieder et al. 2006; Starkey et al. 1983; Wood & Spelke 2005). Importantly, infants and nonhuman animals exhibit these abstract numerical representations in the absence of symbolic language, and they do so spontaneously. Thus, numerical representations can be abstract in the absence of discrete symbolic representations or explicit task demands. CK&W’s claim that “numerical representation is primarily non-abstract” (target article, Abstract) and that intentional processing is required to achieve notation- and modality-independent representations of numerical values is at odds with the demonstrated existence of this non-symbolic form of numerical abstraction. Abstract non-symbolic numerical representations are important to any theory of numerical representation because they are hypothesized to provide the evolutionary and developmental foundation upon which symbolic numerical representations are psychologically constructed (e.g., Carey 2004; Gallistel & Gelman 2000). In other words, current developmental and evolutionary theories propose that numerical representations are abstract before they are symbolic. Therefore, CK&W’s proposal needs to either (1) provide a theoretical account of the alleged developmental disappearance of automatic numerical abstraction in human children, or (2) make the case that preverbal infants and nonhuman animals spontaneously engage in intentional processing to represent numerical values across modalities and dimensions. BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Commentary/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes A second theoretical limitation of CK&W’s proposal is that their neurobiological definition of numerical abstraction risks reductio ad absurdum. That is, the stipulation that numerical abstraction requires identical responses in identical neurons is potentially impossible to satisfy. Yet, even if it were possible to satisfy that criterion, it is not clear whether it is the appropriate criterion for establishing numerical abstraction. As the authors review, regions of the intraparietal sulcus (IPS) respond during numerical processing across notations, modalities, and dimensions. The mounting evidence that numerical representations across notations, modalities, and dimensions are “distributed but overlapping” in the IPS is neutral on the issue of whether the underlying representations are abstract. Instead, such evidence suggests that different numerical forms invoke both shared and separate neural processes. CK&W’s conclusion that the neurobiological data weigh more heavily in favor of notation-dependent neural processes is therefore merely an assertion at this stage. Other empirical evidence that CK&W cite in favor of their account does not do the theoretical work the authors are asking of it. The authors review both behavioral and neurobiological evidence purportedly revealing notation-specific interactions in numerical tasks. However, many of the notation-specific interactions they review hinge on generic differences in performance level. Specifically, if a single psychological process is involved in judging numerical values from two different numerical notations (e.g., numerical judgments of Arabic numerals and arrays of dots), yet the judgment is easier for one of the two notations (e.g., because the input mode is more rapid, reliable, or fluent), a notation-specific interaction may emerge simply because performance on the easier notation hit ceiling accuracy or floor speed. Such interactions, though cited by CK&W, do not invite the theoretical implications that CK&W draw. Instead, notation- or modality-specific interactions that arise under these circumstances reflect a quantitative difference in performance between notations or modalities. Note that this argument may also apply to neurobiological findings under circumstances in which floor or ceiling response levels are achieved. While bearing this issue in mind, we encourage CK&W to re-evaluate the relevance of the following studies to their argument for notation- and modality-dependent number representations: Dehaene and Akhavein (1995), Droit-Volet et al. (2008), Ganor-Stern and Tzelgov (2008), Hung et al. (2008), and Ito and Hatta (2003). These studies (and likely others) report interactions that do not necessarily support a notation- or modality-dependent account of numerical representation. Importantly, any notation- or modality-dependent interaction that survives inspection for a generic performance effect likely can be accounted for by the two-system view of approximate and exact numerical representation proposed by Dehaene et al. (1999). In the pre-existing two-system proposal, notation-specific interactions may arise from an interplay between the exact and approximate numerical codes. Unfortunately, CK&W have not distinguished the empirical predictions of their dual-code view from the existing two-system view. In short, although we applaud CK&W for highlighting some of the many remaining puzzles about the nature of numerical abstraction in the mind and brain, the solutions they offer do not adequately account for the data. Moreover, the open questions surrounding the cognitive and neural basis of numerical abstraction do not warrant a restructuring of the field of numerical cognition. Robust evidence demonstrates that with or without language, number is represented abstractly – independently of perceptual features, dimensions, modality, and notation. In fact, this is the very definition of “number.”

ACKNOWLEDGMENT We thank Brad Mahon for remarks on this commentary.

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Numerical representations are neither abstract nor automatic doi:10.1017/S0140525X09990549 Dale J. Cohen Department of Psychology, University of North Carolina Wilmington, Wilmington, NC 28403. [email protected]

Abstract: In this commentary, I support and augment Cohen Kadosh & Walsh’s (CK&W’s) argument that numerical representations are not abstract. I briefly review data that support the non-abstract nature of the representation of numbers between zero and one, and I discuss how a failure to test alternative hypotheses has led researchers to erroneously conclude that numerals automatically activate their semantic meaning.

There exists in the numerical cognition literature what I call the triple tautology: that numerical representations are (1) automatically activated, (2) abstract, and (3) analogue. Cohen Kadosh & Walsh (CK&W) present a convincing argument that numerical representations are not abstract. Although CK&W focus on the numerical representation of integers, strong evidence also exists for the non-abstract nature of the numerical representation of quantities between zero and one (Cohen et al. 2002). My colleagues and I have shown that, although most college students understand the correct ordinal relation of numbers expressed in a single numerical format (e.g., decimals), they do not understand the correct ordinal relation of numbers expressed in different formats (e.g., comparing decimals to relative frequencies). If the numerical representation of numbers between zero and one were abstract, the students should have been able to compare the semantic meaning of numbers expressed in different numerical formats once the numbers were converted into the abstract representation. Although researchers may discount this evidence for non-abstract representation of numbers as unique to those between zero and one, CK&W reveal that it is consistent with the evidence for the representation of integers. The crux of CK&W’s argument is that correlations should not be confused for causal mechanisms – no matter how intuitive the causal relations may appear. Below, I describe how the remaining two tautologies (automatic activation and analogue representation) also rely heavily on correlational evidence. It can be argued that Moyer and Landaur (1967) started the modern study of numerical cognition with their discovery of the numerical distance effect. In short, the authors presented two integers side-by-side and asked participants to judge which integer was the larger of the two. The authors found that reaction time (RT) varied as a function of the numerical distance between the two presented integers. The robust nature of the finding, together with its appeal to our intuition about the importance of numerical distance, has made this finding one of the bedrocks of the numerical cognition literature. The numerical distance effect was the foundation of the first tautology of numerical cognition: the analogue nature of the representation. The numerical distance effect is not only the foundation of the first tautology, but it is also a foundation of automaticity. A strong test of the automatic activation hypothesis is a simple task in which participants are to judge whether two numerical symbols are the same or different. In previous versions of this task, researchers dichotomized the stimuli into “close” and “far” groups by choosing numbers that are numerically “close” (e.g., 8 and 9) and numbers that are numerically “far” (e.g., 1 and 9). If semantic meaning is automatically activated, it will interfere with participants’ same/different judgments and evidence for the numerical distance effect should be present in the RT data. Specifically, the time for participants to judge two numerically close numbers as different (i.e., the “close” group) should be longer than the time it takes them to judge two numerically distant numbers as different (i.e., the “far” group). This is

Commentary/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes exactly what researchers found (Dehaene & Akhavein 1995; Ganor-Stern & Tzelgov 2008), and they reasonably concluded that numerical symbols automatically activated their semantic meaning. Researchers should remember that, despite its name, the numerical distance effect is correlational. That is, numerical distance is one of several features that are correlated with the order of the numbers on the number line. Therefore, although numerical distance is correlated with participants’ RTs, it may not be the controlling factor of participants’ RTs. As with all correlational data, there may be a third variable that (1) is correlated with numerical distance and (2) is the true controlling factor of participants’ responses. The first step in determining whether a third variable exists is to test alternative hypotheses. Unfortunately, in numerical cognition research, researchers rarely (if ever) consider plausible alternatives to the numerical distance hypothesis. Recently, I did just that when I tested whether numerical symbols automatically activate their representation. I ran the numerical same/different task with two simple changes: (1) I did not dichotomize the stimuli, and (2) I tested an alternative hypothesis. By not dichotomizing the levels of the independent variable, I reduced the number of plausible alternative hypotheses that could explain the data. The plausible alternative I tested was simple: RT increased as a function of the physical similarity between the two numbers to be distinguished. See Cohen (2009) for the operational definition of the physical similarity function. The data were clear: Physical similarity was the controlling factor in participants’ RTs, not numerical distance. Because the semantic meaning did not interfere with participants’ response, the data demonstrated that integers do not automatically activate their semantic meaning. Because the numerical distance function correlates highly with the physical similarity function (r ¼ .62), researchers may easily confuse the effects of physical similarity for those of numerical distance if they do not actively test both. CK&W benefit the numerical cognition community by reviewing the literature addressing the abstract nature of numerical representations. The authors remind us not to confuse correlations for causal mechanisms. I echo that sentiment and remind readers that the numerical distance effect is, at its essence, simply a correlation. By challenging the tautologies of the field with plausible alternative hypotheses, researchers like Cohen Kadosh & Walsh keep the numerical cognition field moving forward. ACKNOWLEDGMENT This work was supported by NIH grant RO1HD047796.

The case for a notation-independent representation of number doi:10.1017/S0140525X09990033 Stanislas Dehaene Inserm-CEA Cognitive Neuroimaging Unit, NeuroSpin Center, CEA/SAC/ DSV/I2BM, Baˆt 145, Point Courrier 156, F-91191 Gif/Yvette, France. [email protected] http://www.unicog.org

Abstract: Cohen Kadosh & Walsh (CK&W) neglect the solid empirical evidence for a convergence of notation-specific representations onto a shared representation of numerical magnitude. Subliminal priming reveals cross-notation and cross-modality effects, contrary to CK&W’s prediction that automatic activation is modality and notation-specific. Notation effects may, however, emerge in the precision, speed, automaticity, and means by which the central magnitude representation is accessed.

Cohen Kadosh & Walsh (CK&W) revive a twenty-year-old proposal in numerical cognition, according to which our capacity for abstract mathematical thought results from a complex interaction of multiple concrete notation-specific codes (Campbell & Clark 1988). Their conclusions, unfortunately, result from discarding of solid empirical evidence supporting a convergence of notation-specific representations onto a shared representation of numerical magnitude, in favor of weak evidence for notation effects. Thus, their article consists in a catalogue of findings in which any difference or interaction involving number notation is taken as strong support for the notation-specific view. In this commentary, I first return to the evidence for notation-independent representations, then discuss interesting reasons why notation occasionally influences brain and behavior. Evidence for notation-independent number processing. CK&W cite, but do not seem to draw conclusions from, the many functional magnetic resonance imaging (fMRI) studies that have observed shared fMRI activations across different notations for numbers. Most important, are studies showing cross-notation fMRI adaptation, because they cannot be dismissed as just showing activation overlap, or as resulting from artifacts of response selection (Jacob & Nieder 2009; Naccache & Dehaene 2001a; Piazza et al. 2007). As an example, extending earlier work by Piazza et al. (2007), Jacob and Nieder (2009) recently demonstrated that after adaptation to a fraction expressed with Arabic numerals (e.g., 1/2), anterior intraparietal sulcus (IPS) shows a distance-dependent transfer of adaptation to number words (e.g., half). As a second example, Figure 1 replots the data in Naccache and Dehaene (2001a), showing that IPS activation is reduced whenever the same numerical quantity is repeated, regardless of whether notation is changed (Arabic digits vs. number words). Note that in this experiment, the first presentation of the number was subliminal, and yet the results showed clear cross-notation convergence. In general, it is surprising that CK&W do not cite the extensive behavioral literature on subliminal priming demonstrating clear notation-independent effects (e.g., Dehaene et al. 1998b; Reynvoet & Brysbaert 2004; Reynvoet et al. 2002). Even cross-modal subliminal priming was recently demonstrated, from a subliminal Arabic numeral to a conscious spoken numeral (Kouider & Dehaene, in press). These effects argue directly against CK&W’s proposal that when numerical representations are probed implicitly, convergence across notations does not occur. Equally impressive are electrophysiological studies showing that some single neurons, particularly in prefrontal cortex, respond identically to symbolic and various non-symbolic displays of number, with the same exact tuning curve across the interval of numbers tested (Diester & Nieder 2007; Nieder et al. 2006). Astonishingly, CK&W dismiss these beautiful data with the claim that the animals are using a “similar response strategy,” for example, for digit 1 and dot 1 compared to other numbers – not acknowledging the fact that their interpretation would require as many putative strategies as there are numbers! Returning to fMRI, another method that is likely to play a strong role in the coming years is multivariate decoding, which probes fMRI activation for the presence of decodable patterns and their generalization to novel experimental conditions. Using this technique, with Evelyn Eger (Eger et al., submitted), we recently demonstrated that human IPS signals can be used to decode which number a participant is temporarily holding in mind. When trained with Arabic numerals, the IPS decoder generalizes to dot patterns, indicating the presence of an underlying notation-independent neuronal population. Likewise, with Andre´ Knops (Knops et al. 2009), we found that a classifier trained with posterior IPS activation during left versus right saccades could spontaneously generalize to a classification of subtraction versus addition trials, whether these calculations were performed with non-symbolic sets of dots or with symbolic Arabic numerals. BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Figure 1 (Dehaene). Evidence for cross-notation subliminal priming and access to a shared representation of Arabic and verbal numerals. Naccache and Dehaene (2001a) presented a subliminal prime prior to each target number in a number comparison task. Using whole-brain fMRI, repetition suppression was observed only in bilateral intraparietal cortex: Trials in which the primes and targets corresponded to the same quantity yielded reduced activation compared to trials in which the quantities differed. Response times were also accelerated by subliminal repetition. In both fMRI and behavior, it made no difference whether the prime and the targets appeared in the same or different notations. Reynvoet et al. (2002) later expanded this work by showing that the amount of priming in response times varies continuously as a function of the numerical distance between the prime and target. The concept of “abstract representation” is never defined by CK&W, and here the Knops et al. (in press) findings point to an important theoretical point: A representation may be shared across numerical notations, and yet rely on a spatial, non “abstract” format of representation. Knops et al. show that the putative human homolog of monkey area LIP, a retinotopic region involved in attention and eye movement, is partially coopted for symbolic and non-symbolic arithmetic on the number line – a clear instance of “cortical recycling” of a sensorimotor area for a more abstract mathematical use (Dehaene & Cohen 2007). Interesting reasons why number notation occasionally influences brain and behavior. If numbers presented in various nota-

tions contact unified representations of magnitude and space, then why are significant notation effects occasionally observed? Several explanations can be proposed, none of them requiring a hasty dismissal of notation-independent representations. 1. Numerical precision. Neural network simulations suggest that the introduction of symbolic representation can lead to a refined precision of the tuning curves for number (Verguts & Fias 2004). Importantly, according to this view, the same neurons remain responsive to both symbolic and non-symbolic presentations – only their accuracy changes. Mathematical developments of this theory (Dehaene 2007) suggest that it has

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the potential to explain many of the known effects of education to symbols on mental arithmetic, including the linearization of number-space mappings (Dehaene et al. 2008; Siegler & Opfer 2003), the improved accuracy with which Arabic numerals can be compared or combined into calculations, and the spontaneous competence of young children when symbols are first introduced (Gilmore et al. 2007) – an effect hard to explain without assuming cross-notation convergence. 2. Speed and automaticity. There is no reason to expect all number notations to be equally fast and automatic in accessing the shared magnitude representation. On the contrary, identification is slower for number words than for Arabic numerals. In number comparison, interactions between the distance effect and the verbal versus Arabic notation of the targets can be attributed to a word-length effect unique to written words (Dehaene 1996). Education and over-training also play a role – as children get older, increasingly automatic effects of numerical magnitude are seen, particularly with Arabic numerals (Girelli et al. 2000). These notation effects occur at a perceptual or transcoding level and are largely irrelevant to the existence of a shared central representation for number. 3. Neural machinery for transcoding. In the course of converting from a notation-specific neural code to a numerical magnitude code, it is likely that the brain requires special neural

Commentary/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes machinery, possibly including neurons that are attuned to both quantity and notation. Indeed, in parietal cortex, neurons with a joint sensitivity to multiple parameters (e.g., eye position and retinal location) are frequently recorded and are thought to play a compulsory role in transcoding to and from pure representations of each parameter (Pouget et al. 2002). Similarly, neurons simultaneously tuned to both numerical magnitude and notation (e.g., simultaneous dots vs. serial flashes [Nieder et al. 2006]; or dots versus Arabic symbols [Diester & Nieder 2007]) may play a key role in accessing a common magnitude representation via different routes. Identifying the numerosity of a set of dots may require special neural machinery for summing size-invariant representations of object locations (Dehaene & Changeux 1993), potentially explaining both the existence of neurons monotonically tuned to non-symbolic numerosity in area LIP (Roitman et al. 2007) and the specific form of behavioral priming observed with dots compared to Arabic numerals (Roggeman et al. 2007). Conclusion. Considerable evidence points to a notation-independent representation of number in the monkey and human IPS. It would, however, be wrong to think of this representation as a “module.” First, it does not involve a dedicated area, but only a fraction of IPS neurons, highly distributed in the IPS, and intermingled with other representations of extent, time, location, and other continuous parameters (Pinel et al. 2004; Tudusciuc & Nieder, 2007). Second, it is not “encapsulated,” but communicates broadly with other areas, thus allowing humans to attach arbitrary spoken and written symbols to it. Because it acquires its “abstract” character, in large part, through education to number symbols, it is not surprising that notation effects are occasionally seen. Such effects should not divert from the incontrovertible fact that arithmetic, like much of mathematics, consists in the manipulation of internal conceptual representations that abstract away from the specific format of input.

Concrete magnitudes: From numbers to time doi:10.1017/S0140525X09990045 Christine M. Falter,a Valdas Noreika,b Julian Kiverstein,c and Bruno Mo¨lderd a Department of Psychiatry, University of Oxford, Warneford Hospital, Oxford OX3 7JX, United Kingdom; bCentre for Cognitive Neuroscience, Department of Psychology, University of Turku, Turku 20014, Finland; cDepartment of Philosophy, School of Philosophy, Psychology and Language Sciences, University of Edinburgh, Edinburgh EH8 9AD, Scotland, United Kingdom; d Department of Philosophy, Institute of Philosophy and Semiotics, University of Tartu, Tartu 51003, Estonia. [email protected] http://www.alice-dsl.net/subjective.time/index.html [email protected] [email protected] [email protected] http://moelder.wordpress.com

Abstract: Cohen Kadosh & Walsh (CK&W) present convincing evidence indicating the existence of notation-specific numerical representations in parietal cortex. We suggest that the same conclusions can be drawn for a particular type of numerical representation: the representation of time. Notation-dependent representations need not be limited to number but may also be extended to other magnitude-related contents processed in parietal cortex (Walsh 2003).

Number (Piazza et al. 2004) as well as time (Rao et al. 2001) have been found to be represented in the intraparietal sulci (IPS). The mode of their representation – abstract or not abstract – is put into question by evidence uncovered by Cohen Kadosh & Walsh (CK&W). The authors define abstract representation as the insensitivity of neuronal populations coding numerical quantity to the notation in which the numerical quantity was presented. CK&W elegantly show in their careful scrutiny of

existing studies that this property cannot be attributed to all representations of number. We suggest that their conclusion may be extended to representations of time. We will refer to representations that are notation-specific as concrete representations. We will argue that primary neuronal representations of time (which we speculate may also be found in IPS) could be concrete. CK&W take as their measure of concreteness, the interaction of variations in behavioural data or neuronal activation with different numerical notations. We will show that comparable interactions are found in behavioural performance relating to notation- and modality-specific representations of time. First, we describe some studies that suggest that the representations of number we use to tell the time from clocks are concrete. Second, we will discuss studies that suggest that duration perception may also be concrete. In a study of clock reading behaviour in children, Friedman and Laycock (1989) found an interaction effect. They asked 6- to 11-year-old children to detect the time displayed in pictures of analog and digital clocks. The success at reading the time from analog displays systematically varied with presented time, but this was not the case for digital displays. The independent variation in performance supports a view of representations of clock time as concrete. Clock time also seems to be represented concretely in adults. Goolkasian and Park (1980) also found an interaction of notations with presented time. They asked subjects to compare clock times presented as words, with a second clock time presented either in analog or digital notation. There was an effect of the angular distance between the two times if the second stimulus was a clock face as compared to a digital display. This corroborates the finding by Friedman and Laycock (1989) in children and shows that concrete representations of clock time do not disappear during development. Support for concrete representations of clock time also comes from repetition priming tasks. In a study by Meeuwissen et al. (2004), participants had to name the time from analog clocks, followed by naming the time from a digital clock. Although there was no obvious repetition priming effect with respect to the hour, there was a facilitation present for naming the minutes. If subjects used an abstract representation to name the hour, we would expect to find a priming effect. The absence of such a priming effect suggests that the representations used in naming the hour are concrete. The authors interpreted this finding as evidence that we use different strategies to determine the hour, depending on whether we are using an analog clock or a digital display. Since determining the hour is the first stage in telling the time, we conclude that at this first stage, concrete representations of clock time are employed. Meeuwissen and colleagues showed that once the hour is known, determining the distance in minutes from the hour (e.g., 5 minutes before or after an hour) relies on the same operation for both display formats. This two-stage account of the processing of clock time is consistent with the model CK&W advance concerning the possibility of transformation of primary concrete numerical representations in parietal areas into a common format depending on task demands. Representations of clock time seem to exert notation-dependent effects on behaviour. We propose that comparable interaction effects can also be found for duration perception, suggesting that the brain may represent temporal intervals concretely. Smith et al. (2007) employed a duration bisection procedure to examine interval timing of two different temporal ranges, 100–500 msec and 1 – 5 sec, in patients with Parkinson’s disease and healthy controls. The authors found a significant interaction between the temporal ranges and modality (visual vs. auditory). Both patients and controls overestimated visual short durations and underestimated visual long durations, but this effect was not observed in the case of auditory durations. This pattern in performance suggests that duration perception is modality-specific, hence concrete. BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Commentary/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes Further support for this conclusion comes from the following auditory duration judgment task (Wearden et al. 2007). Participants were presented with a standard stimulus and a comparison stimulus consisting of filled or unfilled auditory durations, and they had to judge if the two stimuli had the same duration or different durations. There were four conditions, filled following unfilled (UF) durations, unfilled following filled (FU), filled following filled (FF), and unfilled following unfilled (UU) durations. The temporal generalisation gradients (i.e., functions plotting the proportion of “same duration” answers over duration differences between standard and comparison stimuli) showed slightly but significantly different shapes for FF trials compared to UU trials and markedly different shapes between FU and UF trials (see Fig. 1). These findings suggest that different notations of auditory stimuli can take distinct processing forms in the brain, providing additional support for the claim that durations are represented concretely. In conclusion, the reported evidence suggests that not only number, but also time can be represented concretely in the

brain. This shared characteristic is in line with the idea of a general magnitude system, which codes time, space, and quantity (Walsh 2003). Both CK&W’s and our evidence strongly suggest that a general magnitude system could code different forms of magnitude using concrete representations. ACKNOWLEDGMENTS The authors were supported by the Volkswagen Foundation (grant I/82 894). In addition, C. Falter was supported by a German Research Council (DFG) fellowship, V. Noreika by the Academy of Finland (project 8110957), J. Kiverstein by an AHRC grant (AH/E511139/1), and B. Mo¨lder by an Estonian Science Foundation grant (ETF7163).

Brain neural activity patterns yielding numbers are operators, not representations doi:10.1017/S0140525X09990057 Walter J. Freemana and Robert Kozmab a Department of Molecular and Cell Biology, University of California at Berkeley, Berkeley, CA 94720-3206; bDepartment of Mathematics, University of Memphis, Memphis, TN 38152-3240. [email protected] [email protected]

Abstract: We contrapose computational models using representations of numbers in parietal cortical activity patterns (abstract or not) with dynamic models, whereby prefrontal cortex (PFC) orchestrates neural operators. The neural operators under PFC control are activity patterns that mobilize synaptic matrices formed by learning into textured oscillations we observe through the electroencephalogram from the scalp (EEG) and the electrocorticogram from the cortical surface (ECoG). We postulate that specialized operators produce symbolic representations existing only outside of brains.

Figure 1 (Falter et al.). Temporal generalisation gradients (mean proportion of “same duration” responses plotted against duration differences between standard and probe stimuli) for comparing filled and unfilled auditory durations. Upper panel: Comparison of filled durations (black circles) versus comparison of unfilled durations (white circles). Lower panel: Filled standards followed by unfilled probes (black circles) versus unfilled standards followed by filled probes (white circles). (Figure from Wearden et al. 2007.)

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Cohen Kadosh & Walsh (CK&W) define representations as: “patterns of activation within the brain that correspond to aspects of the external environment” (sect. 2, para. 2). They “differentiate representation from processing” that includes “pre-representation (e.g., visual identification of the digit) and post-representation components (e.g., working memory, response selection)” (sect. 2, para. 2). Thereby, CK&W “argue that the PFC [prefrontal cortex] is not involved in numerical representation, at least not in humans. The PFC is important for some numerical operations, but not representations” (sect. 9, emphasis theirs). Figure 5 reflects their view that numerical representations depend on environmental cues that are “coded” initially in “linguistic and imagistic representations.” The neural populations in the parietal area provide early “automatic numerical representation,” which later transitions to “intentional representation subserved by the PFC neural circuitry.” The authors’ distinction between abstract versus non-abstract depends on their restriction of “early representation” to the firings of populations of parietal neurons that are induced or evoked by sensory inputs, and that are revealed by single neuron recordings and areas of functional magnetic imaging (fMRI) activation, while excluding “operations” performed on those populations by the PFC or other parts of the brain. We share CK&W’s views that the direct route to understanding how brains do numbers is by study of activity patterns of the neural populations in question. On experimental grounds, we do not accept their hypothesis that the patterns can be detected by microscopic units, because the numbers of neurons observed by present methods are too few, or by macroscopic fMRI images, because the time scales are too slow. We believe that the patterns will be found, if ever, in mesoscopic brain waves (EEG, EcoG, and the magnetoencephalogram from magnetic sensors fixed around the head [MEG]), which provide the requisite temporal and spatial resolutions (Freeman et al. 2009).

Commentary/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes On theoretical grounds, we do not agree that the patterns are representations, because the mesoscopic wave patterns, which we have observed to accompany sensation and perception of invariant conditioned stimuli, lack invariance; the patterns change with variations in context and experience. We hypothesize that our observed patterns are mesoscopic operators in the form of synchronized neural oscillations in the beta and gamma ranges, which map the connection patterns in cortical synaptic networks shaped by learning into spatiotemporal patterns of amplitude modulations. We see the concept of representations as a carry-over from Cartesian dualism, which presupposes the primacy of stimuli as determinants of percepts. No, the primary determinants are memories. Certainly the firings of neurons, when they are appropriately averaged with respect to time and place of repetitive stimulus onset, manifest the presentations of receptor input into cortex, which differ across trials. Sensory-driven and motor-related microscopic activity reported by the authors in the parietal lobes is consistent with the consequences of lesions in the right parietal lobe, first described by Gerstmann (1958): the syndrome of inability to distinguish left from right (disorientation); difficulty in writing (dysgraphia); difficulty with arithmetic (dyscalculia); and inability to name the digits (finger agnosia). The syndrome suggests that skills in elementary arithmetic are closely tied to intentional actions involving use of the hands in symbolic communication that preceded the emergence in evolution of numerical skills (Freeman 2009). These data support the authors’ opposition to abstract representation, but the units are too close to the tactical sensorimotor operations of counting and too far from the conceptual strategic operations of arithmetic. In our view, perception begins with intention and not with sensation. The capacities to foresee a goal, to plan action to achieve it, and to predict the sensory consequences of the action in mammals clearly involve the PFC in the prior structuring of the wave operators in recall of experience. We believe that all species construct neural operators that direct the body in the action-perception cycle (Merleau-Ponty 1942/1963). What distinguishes humans is the capacity to construct hypothetical meta-operators that combine and reshape the ordinary wave packets that we share with other mammals and make symbols. These representations are in, on (e.g., tattoos), or outside the body, serving social planning and communication. It is easy to suppose that brains work the way computers do, but the metaphor fails. The mathematician John von Neumann wrote: Thus the outward forms of our mathematics are not absolutely relevant from the point of view of evaluating what the mathematical or logical language truly used by the central nervous system is. . . . It is characterized by less logical and arithmetical depth than what we are normally used to. . . . Whatever the system is, it cannot fail to differ considerably from what we consciously and explicitly consider as mathematics. (von Neumann 1958, pp. 81–82)

It is likely that the hypothetical symbol-making operators provide the substrate for both words and numbers. How they differ from the ordinary operators is not known. We think that they are not local operators of the kind postulated by CK&W; instead, they are carried by the patterns of activity that cover wide regions in intermittent spatially coherent oscillations (Kozma & Freeman 2008), which are seen in EEG (Freeman et al. 2003; Pockett et al. 2009; Ruiz et al. in press), ECoG (Freeman et al. 2003), and MEG (Bassett et al. 2008). The human brain capacity for this meta-organization can be ascribed to evolution of the most recent enlargements that sculpt the temporal and frontal fossae in hominid endocasts. The added cortices should not be conceived of as loci for storage of numerical representations, but as facilitators of global organization of meta-operators. The eminent neuropsychiatrist and neuropathologist Paul Yakovlev (1962) described human brains as unique in having

areas of cerebral cortex without direct connections to and from the basal ganglia. He speculated that these areas might provide the neural insulation from environmental vicissitudes that is necessary for abstract thought. These areas have not to our knowledge been otherwise identified. We postulate that a marker for them might be the lack of identifying cytoarchitecture that characterizes some neocortical areas having so many seemingly identical neurons that their nuclei appear as grains of dust; hence the venerable anatomical term koniocortex (Freeman 2009).

Automatic numerical processing is based on an abstract representation doi:10.1017/S0140525X09990781 Dana Ganor-Stern Behavioral Science Program, Achva Academic College, M. P. Shikmim, Israel 79800. [email protected]

Abstract: The goal of the present commentary is to show that past results on automatic numerical processing in different notations are consistent with the idea of an abstract numerical representation. This is done by reviewing the relevant studies and giving alternative explanations to the ones proposed in the target article.

As indicated by Cohen Kadosh & Walsh (CK&W), looking at automatic processing provides an informative insight into the nature of the underlying numerical representations that are relatively uncontaminated by task-dependent strategies. Automatic numerical processing was explored in past research using two main paradigms. The first was the size congruency paradigm, showing that automatic numerical processing takes place when participants intentionally compare the physical sizes of numerical stimuli. Of particular relevance are recent works by Cohen Kadosh et al. (2008e) and Ganor-Stern and Tzelgov (2008), which examined automatic processing of numerical magnitude for digits and number words, and for numbers in Arabic and Indian notations. The second paradigm was the SNARC effect, showing automatic magnitude processing and mapping of magnitude to space when participants perform a variety of tasks that do not require magnitude processing. Relevant for the present context are works that looked at the SNARC effect for digits and number words (e.g., Fias et al. 1996; Nuerk et al. 2005). The target article authors’ conclusion from past studies is that the representation underlying automatic processing is notationspecific. This conclusion is mainly based on the fact that the evidence for automatic numerical processing was not identical for the different notations. In this commentary, I suggest that a notation-specific representation does not necessarily follow from the empirical findings, and I propose alternative explanations for the patterns of findings reviewed in detail in the target article. First, CK&W have cited a series of studies showing more robust evidence for automatic processing of digits than of number words, and have interpreted this pattern of results as supporting the idea of notation-specific representation. It should be noted, however, that automatic processing is heavily influenced by skill level. People are not equally skilled with extracting numerical information from different notations, but rather, they are more skilled in extracting such information from digits than from number words. As a consequence, automatic numerical processing of number words might be more limited than that of digits. Hence, it might take longer time to occur (Cohen Kadosh et al. 2008e), it might not take place when a verbal task is performed (Fias et al. 2001a), or under BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Commentary/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes some conditions, it might not occur at all (Ito & Hatta 2003). Thus, it is possible that there is a common underlying abstract representation, but it could be that it takes longer to access it from a number word compared to a digit. In some cases the processing of the relevant dimension is fast enough so that the relatively slow process of accessing the abstract numerical representation from the number word does not interfere with it. Second, CK&W have based their argument for a notationspecific representation underlying automatic processing on the fact that the size congruency effect took a slightly different form for the different notations (Cohen Kadosh et al. 2008e; Ganor-Stern & Tzelgov 2008). The problem with the argument is that this effect reflects the interaction between the processing of the relevant and irrelevant dimensions, and a difference in this interference effect between notations might stem from the relevant physical size dimension and not from the irrelevant numerical one. Therefore, this should not be seen as evidence for a notation-specific underlying representation. For example, in Dehaene and Akhavein’s (1995) study, the absence of a distance effect in the physical same-difference task for pairs composed of a digit and a number word may very well be due to the fact that such pairs are so physically dissimilar – which makes the decision faster and, as a consequence, too short to be affected by the processing of the irrelevant dimension. Indeed, our recent study that used two numerical notations (Arabic and Indian) was able to show evidence for automatic numerical processing when the numbers were presented in different numerical notations (Ganor-Stern & Tzelgov 2008). The debate over the interpretation of Ganor-Stern and Tzelgov (2008) or Cohen Kadosh et al. (2008e) seems to be a case of which half of the glass you are looking at. In my opinion, the fact that incongruency between numerical and physical sizes affected performance in the physical task, even in mixed-notation pairs, seems to be especially strong evidence for the idea of an abstract representation (Ganor-Stern & Tzelgov 2008). More support is provided by studies reporting a size congruency effect not only for numbers but also for number words (Ansari et al. 2006b; Cohen Kadosh et al. 2008e). CK&W, in contrast, seem to focus on the empty half of the glass and to spotlight the differences in the pattern of results for the different notations. As explained earlier, some of these differences might be a product of other factors and are not informative as to the nature of the underlying numerical representation; and some may even be accidental. More generally, it seems that the authors set the criterion that any non-additive difference between the numerical processing of the different notations is evidence for a notation-specific representation. This criterion might be too lenient, as not all differences are theoretically relevant for the issue in question. As explained earlier, some of the differences are due to skill level, some are due to the nature of the relevant dimension, and some are truly accidental. In the debate over the issue of abstract/non-abstract representation, attention should be given only to such differences that are either theoretically interpretable or at least that are replicable across studies. Finally, one of the main points made by the target article is the importance of studying automatic processing in addition to intentional processing. Behavioral studies indeed provided evidence for dissociable patterns of results in the two modes of processing (Ganor-Stern et al. 2007; Tzelgov et al. 2009). Unfortunately, brain-imaging studies that looked at intentional and automatic numerical processes did not report such a dissociation in terms of different electrophysiological activity, or areas being active when the two modes of processing were taking place (Ansari et al. 2006b; Cohen Kadosh et al. 2007c). Future neuropsychological research should attempt to dissociate these two types of processes in terms of the underlying brain activation.

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Expertise in symbol-referent mapping doi:10.1017/S0140525X09990793 Roland H. Grabner Institute for Behavioral Sciences, Swiss Federal Institute of Technology (ETH) Zurich, CH-8092 Zurich, Switzerland. [email protected] http://www.ifvll.ethz.ch/index_EN

Abstract: Much evidence cited by Cohen Kadosh & Walsh (CK&W) in support of their notation-specific representation hypothesis is based on tasks requiring automatic number processing. Several of these findings can be alternatively explained by differential expertise in mapping numerical symbols onto semantic magnitude representations. The importance of considering symbol-referent mapping expertise in theories on numerical representations is highlighted.

The target article by Cohen Kadosh & Walsh (CK&W) can be considered as very timely in light of increasing evidence suggesting a strong impact of input format on numerical information processing (e.g., Campbell 1994). One explanation for such findings is CK&W’s proposal that different neuronal networks represent numerical quantity depending on the notation. The authors do not only distinguish between non-symbolic (e.g., dot patterns) and symbolic formats, but also suggest separate representations for different symbol systems (e.g., Arabic digits vs. number words). In their dual-stage model, they argue that the (initial) automatic processing of numerical information relies on these non-abstract, notationspecific representations, whereas (later) intentional processing could lead to the creation of connections between them and give rise to result patterns congruent with the abstract-representation view. Therefore, a large part of the findings reported in favor of their hypothesis comes from studies requiring automatic number processing, which should be “unaffected by task demands and intentional strategies” (sect. 5, para. 3). A critical issue that was not considered by CK&W is the role of expertise in processing different numerical notations. This primarily holds true for number symbols, which, in contrast to non-symbolic representations, have an arbitrary relationship to the numerical magnitude to which they refer (Peirce 1955). Over development, we learn to map these cultural symbols onto semantic magnitude information (cf. Ansari 2008) and attain different levels of expertise for different notations. For instance, we are generally more proficient in the numerical processing of Arabic digits compared to number words, since the former are the standard visual notation for quantity processing and calculation. The more expertise we have acquired for a specific type of numerical symbol, the more likely its presentation leads to an automatic activation of the underlying semantic magnitude representation. A similar account was put forward by Campbell and colleagues in their encoding-complex hypothesis: “task-specific retrieval processes will be more efficient when numerical stimuli appear in a familiar, well-practiced format, relative to the retrieval processes activated by an unfamiliar surface form” (Campbell & Epp 2004, p. 231). If differences in symbol-referent mapping expertise are not considered in tasks drawing on automatic number processing, notation-related effects are not conclusive with regard to the question of non-abstract representations. This point should be illustrated by briefly reviewing some behavioral key findings reported in the target article. CK&W cited two studies in which interactions between notation and automatic number processing were observed in the size-congruity paradigm (Cohen Kadosh et al. 2008e; Ito & Hatta 2004). These studies revealed that numerical information from number words did not interfere with physical size comparison, whereas such an interference emerged for Arabic digits, indicating that “numerical information was not processed automatically” (sect. 6, para. 1). However, if the semantic representation was not automatically accessed by the number words, presumably due to less symbol-referent mapping expertise for verbal numbers, this result cannot be interpreted as evidence for notation-specific representations. Fias and colleagues

Commentary/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes investigated the well-established SNARC effect using Arabic digits (Fias et al. 1996) and verbal numbers (Fias 2001). Automatic number processing was probed by requiring participants to monitor the occurrence of certain phonemes in the numbers; in the intentional number-processing task parity judgments were required. The latter task elicited SNARC effects for both, Arabic digits and number words. In the phoneme-monitoring task, however, a SNARC effect was only observed for Arabic digits, not for number words. A lack of expertise in mapping number words to semantic magnitude representations can again explain the absence of a SNARC effect in the phoneme-monitoring task. Also, the reported results from the priming study by Koechlin et al. (1999) can be interpreted in a similar vein. Participants were presented a prime number before they had to compare a numerical stimulus to a standard. They observed notation-related effects only when the prime number was subliminally presented (for 66 msec). Specifically, a quantity priming effect (i.e., shorter response times in the number comparison task with decreasing numerical distance between prime and target) emerged for Arabic digits but not for verbal numbers. Koechlin and colleagues discussed these findings in terms of notation-specific representations under demanding temporal conditions, which may converge at a later stage of processing. However, it also appears plausible that the number words were not presented long enough to sufficiently activate the underlying semantic quantity representation. Taken together, notation-related differences in symbol-referent mapping expertise, which result in differential activation of the underlying semantic magnitude representation, can explain the reviewed findings without the need for assuming notation-specific representations. Symbol-referent mapping expertise may also loom large in understanding individual differences in mathematical competence. Recent studies suggest that little expertise or even deficits in processing numerical symbols are related to poor mathematical performance. Rousselle and Noe¨l (2007), for example, reported that children with developmental dyscalculia displayed similar performance as matched controls in a non-symbolic magnitude comparison task, whereas they performed more poorly in the symbolic task version. Holloway and Ansari (2009) investigated typically developing children and found that only the symbolic, but not the non-symbolic, distance effect predicted later mathematical achievement (but see also Halberda et al. 2008). The point raised in this commentary is compatible with both the abstract and the non-abstract view of numerical representation in the brain. We may learn to map numerical symbols onto a unitary abstract representation (Dehaene et al. 2003), or we may develop separate representations for these symbols as is proposed by CK&W. At present, our knowledge about the neurocognitive processes involved in the acquisition of symbol processing expertise is very limited. Recent neuroimaging studies revealing developmental (e.g., Ansari et al. 2005) and training-related (e.g., Diester & Nieder 2007) activation changes during basic number processing, however, suggest a high degree of plasticity in neuronal networks coding numerical quantity. Whether evidence for abstract or nonabstract representations is found could thus partly depend on the acquired level of expertise in numerical symbol-referent mapping.

Abstract after all? Abstraction through inhibition in children and adults doi:10.1017/S0140525X0999080X Olivier Houde´ University Paris Descartes, Institut Universitaire de France, CI-NAPS, UMR 6232, CNRS and CEA, Sorbonne, 75005 Paris, France. [email protected] http://olivier.houde.free.fr/

Abstract: I challenge two points in Cohen Kadosh & Walsh’s (CK & W) argument: First, the definition of abstraction is too restricted; second,

the distinction between representations and operations is too clearcut. For example, taking Jean Piaget’s “conservation of number task,” I propose that another way to avoid orthodoxy in the field of numerical cognition is to consider inhibition as an alternative idea of abstraction.

I wish to challenge two points in Cohen Kadosh & Walsh’s (CK&W) argument: First, the definition of abstraction is too restricted; second, the authors’ distinction between representations and operations is too clear-cut. I challenge their argument from the viewpoint of cognitive developmental psychology, using a famous experimental design by Jean Piaget as an example: the “conservation of number task” (Piaget 1952; 1984). CK&W discuss the abstraction of number representations only in relationship to the form of the input in which the numerical information was presented; namely, specific verbal or nonverbal means of denoting numbers (following Dehaene’s definition). In doing so, they miss directly discussing the question of cognitive abstraction of number representations in relation to space per se. However, numbers in the human brain – particularly in the parietal lobes – also must be abstracted from space. This question is especially relevant in developmental studies on number conservation. Remember that, in the conservation-of-number task (Piaget 1952; 1984), when shown two rows containing the same number of objects, but of different lengths (after the objects in one of the rows have been spread apart), the child has to determine whether the two rows have the same number of objects. Up to the age of 7 years, children erroneously respond that there are more objects in the longer row, reflecting the use of the misleading visuospatial “length-equals-number” strategy that they fail to inhibit (Houde´ 1997; 2000; Houde´ & Guichart 2001). Moreover, adult brains don’t fully overcome this spatial bias; hence, they require an executive prefrontal network to overcome it (Daurignac et al. 2006; Leroux et al. 2006; 2009). Even if, as stated by CK&W, number representations are primarily non-abstract and are supported by different neuronal populations residing in the parietal cortex, the activation of number representations may nevertheless require that individuals inhibit irrelevant visuospatial cues. In my mind, this executive process corresponds to an abstraction process from space (or perception of space) to numbers. The authors suggest, however, that such intentional prefrontal processes (executive functions, cognitive control, selective attention, and so on) are “important for some numerical operations, but not representations” (sect. 9, para. 1, emphasis theirs). I disagree. During cognitive development (Houde´ 2000), as well as in the dynamic large-scale-network cognition which characterizes adult brains (Fuster 2003), logico-mathematical operations and representations are not so easily dissociable. The Piagetian concept of number conservation is a good example. It is both a numerical operation and a numerical representation, that is, the child’s or adult’s ability to represent or “keep in mind” (conserve) numbers independently of any irrelevant visuospatial cues (e.g., the unequal lengths of the two rows in Piaget’s task). This number representation requires “at its heart” an inhibitory operation. Brain imaging (fMRI) results from our laboratory have clearly shown that this number-conservation ability is sustained, both by posterior (especially the bilateral intraparietal sulcus [IPS] and superior parietal gyrus), anterior-cingulate-cortex (ACC), and prefrontal activations (Leroux et al. 2009). Other examples of this kind of abstraction process are available in the literature on the neural foundations of logical and mathematical cognition (Houde´ & Tzourio-Mazoyer 2003). In the field of deductive reasoning, it has been shown that, after error-inhibition training, a clear activation of the cerebral activation pattern occurred, which shifted from the posterior part of the brain when individuals relied on an erroneous visuospatial strategy to the prefrontal part when they accessed abstract logic (Houde´ 2008; Houde´ et al. 2000; see also Prado & Noveck 2007). In conclusion, I think that another way to avoid current orthodoxy in the field of numerical cognition is to consider, beyond the BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Commentary/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes question of input notations, an alternative idea of abstraction; that is, abstraction through inhibition in children and adults.

A developmental model of number representation doi:10.1017/S0140525X09990069 Karin Kuciana and Liane Kaufmannb a MR-Center, University Children’s Hospital Zurich, CH-8032 Zurich, Switzerland; bDepartment of Psychology, University of Salzburg, A-5020 Salzburg, Austria. [email protected] [email protected]

Abstract: We delineate a developmental model of number representations. Notably, developmental dyscalculia (DD) is rarely associated with an all-or-none deficit in numerosity processing as would be expected if assuming abstract number representations. Finally, we suggest that the “generalist genes” view might be a plausible – though thus far speculative – explanatory framework for our model of how number representations develop.

Challenging “dogmas” in cognitive neuroscience is important for the advancement of our professional development. Therefore, we highly appreciate Cohen Kadosh & Walsh’s (CK&W’s) target article, which attempts to challenge the widely held belief that the neural representation of numerosity may be abstract rather than non-abstract. According to “neural constructivism,” the representational features of the human neo-cortex are strongly modulated by a dynamic interaction between neural growth mechanisms and environmentally derived neural activity (Quartz & Sejnowski 1997; see also Fisher [2006] for discussion of the gene – environment interdependency). Hence, a closer look at the development of the brain, and in particular, at the development of neural representations of numerosity, will shed further light on the question of whether numbers are represented in an abstract or non-abstract manner. The primary aim of this commentary is to provide more recent developmental data revealing that number representations in children are not stable, but rather, undergo a developmental shift from distinct (non-abstract) to shared (abstract) representations. Beyond behavioral data, we attempt to apply a functional geneticist view as an explanatory framework for the complex data reported thus far. As outlined rather briefly by CK&W, the findings of the few developmental studies that were dedicated to examining notation-dependent effects on number processing in children largely support the authors’ notion that children’s number representations are likely to be non-abstract (Holloway & Ansari 2009). Maybe even more interesting is the finding that 3-year-olds’ abilities to compare non-symbolic number sets seem to rely on perceptual cues if the ambiguity between (discrete) numerical and (continuous) non-numerical stimulus properties is overwhelming (Rousselle et al. 2004). The latter results clearly speak against the notion of an abstract number representation. A similar conclusion has been drawn by Butterworth (2005), who argues that “if put into conflict . . . continuous quantity seems a more powerful cue” (p. 5; see also Mix et al. 2002). Five-year-old children are able to compare and add large sets of elements presented in different non-symbolic modalities (dot arrays, tone sequences) (Barth et al. 2005). Importantly, the authors’ report a significant interaction between the presentation format and the ratio of the two sets to be compared, being characterized by a steeper ratio-dependent decline in crossmodal performance. If one assumes an abstract representation of numbers, no performance differences within and across modalities should have been observed. Likewise, children’s mapping between non-symbolic and symbolic number representations

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becomes more refined with age, which is contrary to expectation if one assumes abstract number representations (Mundy & Gilmore 2009). Findings of dissociations between different notations are not restricted to typically developing children; dyscalculic children also are reported to exhibit impaired performance when comparing symbolic Arabic digits, but not when comparing non-symbolic object sets (Rousselle & Noe¨l 2007). With respect to developmental dyscalculia (DD) the distinction between automatic and intentional performance is an important one. Empirical evidence, supporting the authors’ claim that automatic number processing might be a more powerful tool to assess differential number processing skills, comes from a single-case study of DD (Kaufmann et al. 2004). Results are incompatible with the notion of abstract number representation, as they revealed that number-processing deficiencies predominantly emerged upon automatic, but much less upon intentional number processing. A further interesting issue in this case study was the finding of operation-specific effects in fact retrieval (addition and subtraction facts being relatively preserved, while multiplication facts were severely impaired; Kaufmann 2002). In our view, operation-specific effects (which have been frequently reported in the patient literature, e.g., Pesenti & van der Linden 1994) – like effects of notation – are not in line with an abstract view, but rather, are strongly suggestive of the existence of distinct number representations. Finally, we suggest that the “generalist genes” theory may provide a plausible – though thus far, speculative – explanatory framework for the view that number representations undergo a gradual developmental change (Kovas & Plomin 2006). In particular, concepts of polygenicity (many genes affect one trait/ one cognitive domain) and pleiotropy (one gene affects many traits/cognitive domains) are not only apt to explain the frequently observed comorbidity between DD and other learning disabilities such as dyslexia or attention disorders, but may also provide a useful theoretical framework for the assumption that number representations become shared (abstract) with more experience/practice, which is inevitably accompanied by a more fine-tuned gene – environment interdependency (Fisher 2006; Kovas & Plomin 2006). In sum, developmental findings challenge the existence of an abstract number representation. However, in our view, notation-specific effects are not necessarily indicative for the existence of non-abstract number representations, especially when it comes to developmental studies. The observed interactions between different input modalities could also be a result of deficient mapping between symbolic and non-symbolic representations in children with and without DD. We assume that developmental progress goes along with higher overlap of brain activation between, as well as across, different numerical input modalities. Previously, we found no activation differences between approximate and exact calculation in school children (Kucian et al. 2008). These results, rather, point to a mutual neuronal network for both tasks. However, one has to keep in mind that both tasks have been presented symbolically, differing solely in demands. Taken together, we suggest that brain activation patterns for different numerical tasks are partly overlapping and that some brain regions are dependent on notation/input modality. Moreover, activation patterns get influenced by task demands such as automatic or intentional number processing. If a core region for number processing exists, it is plausible that this region consists of highly interconnected neurons for different numerical inputs and that activation of one neuronal population quickly spreads to other populations, leading to cross-notational activation, as proposed by CK&W. With development and higher numerical proficiency, these cross-notational activations might increase, reflecting automatization processes. There is probably a gradual difference in definition between non-abstract and abstract representation of numerosity with respect to both the strength of connections and to coactivations of different neuronal

Commentary/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes

Figure 1 (Kucian & Kaufmann). Our developmental model of number representation proposes an increased overlap of representations across different number notations with advanced expertise, and, furthermore, implies a gradual shifting from nonabstract to abstract representations of numerosity. populations. If, for instance, the connection is extremely tight and both neuronal populations get activated simultaneously independent of inputs, one could label it as an abstract numerical representation, although this representation is built up by distinct neuronal populations. Upon summarizing the above-mentioned findings, we propose the following developmental model (Fig. 1) of how number representations might be formed:

Symbols in numbers: From numerals to magnitude information doi:10.1017/S0140525X09990550 Oliver Lindemann, Shirley-Ann Rueschemeyer, and Harold Bekkering Donders Institute for Brain, Cognition, and Behaviour, Radboud University Nijmegen, 6500 HE Nijmegen, The Netherlands. [email protected] [email protected] [email protected]

Abstract: A dual-code model of number processing needs to take into account the difference between a number symbol and its meaning. The transition of automatic non-abstract number representations into intentional abstract representations could be conceptualized as a translation of perceptual asemantic representations of numerals into semantic representations of the associated magnitude information. The controversy about the nature of number representations should be thus related to theories on embodied grounding of symbols.

The review of Cohen Kadosh & Walsh (CK&W) in the target article demonstrates that numerical representations are modulated by task demands. The authors propose the existence of two cognitive codes for numbers, that is, (1) an automatic nonabstract representation, which is notation and modality dependent, and (2) an intentional abstract representation, which is notation and modality independent. We agree with this hypothesis. However, we think that a dual-code model of number representation needs to take into account further aspects about the differences in the nature of the two representations and should theoretically distinguish between an asemantic representation of the symbolic stimulus (e.g., Arabic numeral) and the representation of its associated meaning (e.g., magnitude information). The controversy about abstract magnitude representation in the parietal lobes relates, therefore, directly to the ongoing debate about symbol grounding. Interestingly, CK&W’s model of number processing seems to be inspired by the recently suggested Language and Situated Simulation (LASS) theory of Barsalou et al. (2008) and their

proposal of dual codes in embodied representations of conceptual knowledge. Indeed, both models hold that automatic and intentional stimulus processing results in different types of cognitive representations and assume that a deeper deliberate processing is central to the semantic representation of abstract concepts. We believe that both notions provide an interesting framework that contributes directly to the question of whether magnitude representations are abstract or non-abstract. However, we want to point out some substantial theoretical differences between the current model of number processing and dualcode models on conceptual knowledge in psycholinguistic research. First, most dual-code models of semantic processing view the faster emerging automatic representation as an asemantic stimulus coding that does not go beyond a perceptual, linguistic, or phonological representation of the presented word or number symbol (see, e.g., Barsalou et al. 2008; Mahon & Caramazza 2008). The target article shows that effects of magnitude processing are modulated by the notation of the number symbol if and only if the task does not require any semantic processing of the numerical magnitude information. Taking a closer look at studies on automatic processing that provide evidence in favor of non-abstract number representations, it becomes clear that effects of number meaning are smaller or even nonexistent if the number stimulus is perceptually more complex (e.g., number words vs. digits: Cohen Kadosh 2008a; or Japanese Kanji numbers vs. Kana numbers: Ito & Hata 2003) or printed in an unfamiliar notation (e.g., Indian vs. Arabic digits: GanorStern & Tzelgov 2008). Moreover, CK&W argue that because automatic processing is unaffected by intentional strategies, indirect number tasks provide an unbiased inside look into the nature of the representation of numerical magnitude information. However, an alternative reason for the presence of notation-dependent effects in these tasks might be that automatic processing of number words and unfamiliar symbols is likely to be restricted to a superficial stimulus coding without activation of the underlying numerical magnitude information. We consequently assume, in line with dual-code models of conceptual knowledge (Barsalou et al. 2008), that under conditions of automatic processing, complex and unfamiliar number symbols will be merely transcoded and represented asemantically in a perceptual, linguistic, or phonological format. It is therefore questionable whether the automatic non-abstract number representation proposed by CK&W can be understood as a semantic representation of numerical magnitude information. Alternatively, the transition from an automatic to an intentional numerical representation might be better conceptualized by different levels of semantic processing and the translation of a perceptual representation of the number symbol into a semantic representation of the associated magnitude. Second, a central aspect of the LASS theory of Barsalou et al. (2008) is the assumption that abstract symbols such as words and numbers become meaningful only when they are somehow mapped to concrete bodily experiences (the so-called embodied cognition hypothesis; for reviews see, e.g., Fischer & Zwaan 2008). Following this view, intentional number processing consists of an activation of correlated information in brain areas that originally evolved to process non-symbolic stimuli, that is, perceptual and motor areas. This embodied mechanism of conceptual knowledge representation has been described as perceptual and motor resonance (Rueschemeyer et al., in press a) and represents a bidirectional coupling of semantic representations with processes of action planning and motor control. Interestingly, empirical evidence for such a sensorimotor grounding of symbol meaning has not only been reported by studies on word processing (Glenberg & Kaschak 2002; Lindemann et al. 2006; Rueschemeyer et al., in press b; Zwaan & Taylor 2006), but has also been recently shown for the processing of Arabic digits in numerical tasks (Andres et al. 2004; Fischer 2008; Lindemann et al. 2007). One might therefore speculate that the abstraction BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Commentary/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes of number meaning consists of an association between the numerical information and magnitude-related motor codes – an assumption that is in line with the idea that magnitude representations for numbers and actions share common cognitive codes within a generalized system for size and quantity (Walsh 2003). Since the notion of embodied cognition is one of the most controversially debated hypotheses of recent psycholinguistic dual-code models of conceptual processing, the principle of motor resonance should also be addressed in the context of number processing models. In conclusion, we think that the idea of an action-based number semantics might provide new insights into the nature of numerical magnitude representations, and might thereby fruitfully contribute to future theoretical developments in mathematical cognition research.

Inactivation and adaptation of number neurons doi:10.1017/S0140525X09990070 J. Patrick Mayo Department of Neuroscience, Center for the Neural Basis of Cognition, Center for Neuroscience at the University of Pittsburgh, University of Pittsburgh, Pittsburgh, PA 15260. [email protected]

Abstract: Single-neuron recordings may help resolve the issue of abstract number representation in the parietal lobes. Two manipulations in particular – reversible inactivation and adaptation of apparent numerosity – could provide important insights into the causal influence of “numeron” activity. Taken together, these tests can significantly advance our understanding of number processing in the brain.

Cohen Kadosh & Walsh (CK&W) present a comprehensive argument against the abstract representation of numbers in the parietal lobes. Their discussion focuses on behavioral and neuroimaging studies, which comprise the bulk of the numerosity literature. But, as CK&W point out, these techniques do not provide the sampling resolution necessary to definitively answer the question of abstract number representation. In contrast, single-neuron electrophysiology provides high spatial and temporal resolution, allowing researchers to monitor the activity of individual neurons in real time. This technique is therefore the most promising avenue for addressing the issue of abstract number representation. In this commentary, I present two single-neuron experimental manipulations that, to my knowledge, have not been used in studies of number-sensitive neurons. These manipulations could help move single-cell studies beyond simple correlation to a more causal understanding of the neuronal basis of number processing. First, temporary pharmaceutical inactivation (Li et al. 1999; Wardak et al. 2002) of number-sensitive patches of parietal cortex can be used to test the usefulness of reported number representations. Although it would be a challenge to demonstrate that all number neurons were inactivated in the parietal lobe, a large portion of neurons can be reliably “switched off” and reactivated over time. Accordingly, animals should show severely diminished performance on number-related tasks during inactivation if numerons truly support their ability to accurately process numerosity. Following the lead of the tasks reviewed in the target article, number-related task performance would have to be assessed across different number formats. The existence of abstract number representations predicts comparable decreases in performance regardless of number format when compared to pre-inactivation measurements. Temporary inactivation is therefore one way in which our understanding of number representations can progress beyond correlational evidence.

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If abstract number neurons exist, then they presumably underlie our ability to perceive and process various numbers. Thus, to tease apart the influence of number neurons on perception, it would be useful to have a situation in which perceived numerosity can be manipulated independently of displayed numerosity. Fortunately, such a psychophysical “trick” has been recently discovered (Burr & Ross 2008; see also Durgin 2008). The second manipulation involves the “apparent numerosity adaptation” paradigm (Burr & Ross 2008). In this task, subjects fixate a center target while two patches consisting of many stationary stimuli are presented, one to the left and one to the right of fixation. Immediately after an extended period of adaptation, test patches are then presented in the same two locations and subjects are asked to make a numerical judgment, usually in the form of a two-alternative forced choice task (e.g., “Which patch contains more items, left or right?”). Burr and Ross (2008) showed that adapting to a large number of stimuli decreases subsequent numerosity judgments, while adapting to a small number of stimuli produces artificially increased numerosity judgments. The numerical perception of the subjects can therefore be manipulated in a controlled manner based on the number of stimuli in the adapting patch. For single-neuron recordings, this task could be passively presented to animal subjects. Better yet, animals could be trained to make “more” or “less” judgments when the two test patches are presented after adaptation. We can then ask how number neurons in parietal cortex respond over time in the adaptation task (i.e., during and after adaptation). For example, if a neuron with a preferred numerosity of 20 (Nieder & Merten 2007) is isolated and the animal is adapted with a patch of 100 stimuli, will the subsequent test presentation of 20 stimuli cause the neuron to fire maximally, consistent with the veridical presented number? Or, alternatively, will the neuron’s response shift towards the adapted numerosity, in line with the subject’s percept? Again, different formats of number stimuli can also be used for adaptation and testing (Diester & Nieder, in press). Following the labeled-line coding hypothesis (Nieder & Merten 2007), numeron selectivity should be predictably manipulated by low- and high-numerosity adaptation across formats. A series of systematic adaptation-and-test conditions on the same neuron would help elucidate the functional role of number neurons, and shed light on the issues of automaticity and intentionality raised by CK&W. A combination of the two manipulations may prove to be the most fruitful. Changes in task performance during inactivation – both in the standard delayed-match-to-sample task (typically used by Nieder and colleagues) and the adaptation task proposed above – can be used to assess the function of number neurons in numerosity judgments. This investigation could be extended to putative number-sensitive neurons in prefrontal cortex (PFC). This extension would help disambiguate the role of parietal and prefrontal number neurons, as well as allow for the testing of CK&W’s hypothesis that PFC plays a “post-representational” role in relation to number processing in the parietal lobes. These two manipulations are, to be sure, not complete experiments. But they are based on established techniques in the field that are well within our current capabilities. The onus to carry out these experiments is on proponents of abstract number representation because, as CK&W highlight, there are currently too many issues of interpretation to conclude in favor of abstractness. Regardless, for both sides of the issue, a straightforward manipulation of the responses of single neurons seems to be the most definitive method for uncovering the abstractness of number representations in the parietal lobes. ACKNOWLEDGMENTS This research was supported by the Alfred P. Sloan foundation and NIH R01-EY017592 to Dr. Marc A. Sommer, and a Mellon Fellowship from the University of Pittsburgh to J. Patrick Mayo.

Commentary/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes

Non-abstractness as mental simulation in the representation of number doi:10.1017/S0140525X09990811 Andriy Myachykov,a Wouter P. A. Platenburg,b and Martin H. Fischera a School of Psychology, University of Dundee, Dundee, DD1 4HN, Scotland, United Kingdom; bDepartment of Psychology, Erasmus University Rotterdam, Rotterdam, 3000DR, The Netherlands. [email protected] http://www.dundee.ac.uk/psychology/people/research/amyachykov/ index.htm [email protected] [email protected] http://www.dundee.ac.uk/psychology/people/academics/mhfischer/ index.htm

Abstract: Abstraction is instrumental for our understanding of how numbers are cognitively represented. We propose that the notion of abstraction becomes testable from within the framework of simulated cognition. We describe mental simulation as embodied, grounded, and situated cognition, and report evidence for number representation at each of these levels of abstraction.

Whether the human mind computes numerical information by creating uniform abstract representations of magnitude or by making reference to distinct modality- and notation-specific representations is an important theoretical question. Similarly to Cohen Kadosh & Walsh (CK&W), we favor the latter view, but we also propose the notion of “simulation” to further clarify the quality of such representations. Ambiguity in defining “abstractness” leads to attribution of several features (e.g., automaticity, implicitness/explicitness, and generalizing power) to number representations without explaining how they are related hierarchically and functionally. Without this elaboration, specific predictions and implications for non-abstract theories of numerical cognition may also remain ambiguous. The simulation theory of cognition (e.g., Barsalou et al. 2008) avoids such ambiguities. Simulation in this view is “the re-enactment of perceptual, motor and introspective states acquired during experience with the world, body and mind” (Barsalou 2008, p. 618). We agree with the idea that simulation is the principle diagnostic feature of non-abstractness and propose a further distinction between grounded, embodied, and situated conceptual simulations. The resulting hierarchy helps to clarify the empirically testable implications of this view for human cognition in general and explain the wide range of features specific to numerical representations. In the following, we first describe this hierarchy and then provide empirical support. A cognitive representation is grounded when its structure reflects the properties of the Euclidean world. This is the most fundamental aspect of non-abstract representations. Next, a cognitive representation can be embodied if it is bound by the experiential (e.g., perceptual or motor) constraints imposed by the human organism. Not all cognitive representations are embodied (e.g., some dreams). Finally, a cognitive representation can be situated when it is sensitive to the context in which it is generated. The experimental study of number processing provides ample evidence for a simulation view of numerical cognition. Specifically, we think that the spatial biases known to accompany number processing (SNARC effect; see Figure 1 of the target article) systematically highlight the features of non-abstract number representation. Grounding, for example, is revealed in the association of larger numbers with upward positions and smaller numbers with downward positions (Schwarz & Keus 2004; see also Fischer & Campens 2008). The embodiment of number processing is evident from effects of finger counting habits on adult number processing (Fischer 2008) and from the spontaneous modulation of grasp aperture by task-irrelevant number magnitudes (Andres et al. 2008). Finally, situatedness

Figure 1 (Myachykov et al.). Participants with a typical SNARC (left side of the graph) tend to have a weaker size congruity effect (SiCE). This suggests a conflict between attention to physical and semantic aspects of numbers. of numerical cognition is indicated by the range-dependence of the SNARC effect that shows that we take into account (or simulate) the current relative meaning of numbers (see Fischer 2006, for evidence and discussion). CK&W correctly point out that such context-dependence is especially evident in the cognitive representation of negative numbers (Fischer 2003; Fischer & Rottmann 2005). Understanding non-abstract representations as cognitive simulations along the dimensions of grounding, embodiment, and situatedness provides a theoretical platform for real-life number representation. The proposed hierarchy of features of number representation allows us to interpret observed effects within an interconnected model. A recent study of both SNARC and size congruity effect (SiCE; see sect. 6 of the target article) illustrates how features of nonabstract number representation interact. In a speeded binary classification task, 18 participants indicated whether single digits were more or less than 5. Digits 1, 4, 6, and 9 were randomly shown in either 12- or 60-point font size. In addition to the typical SNARC ( p , .01) and SiCE ( p , .01) effects, we found a positive correlation between the two (p , .05; see our Fig. 1): Participants with a strong SiCE tend to have a weaker SNARC. This interaction between SiCE and SNARC indicates that features of number representation compete for the same cognitive resource. One possible interpretation of this novel result from the perspective of cognitive simulation theory is that attending to irrelevant physical attributes of digits grounds their cognitive representation. This may, in turn, prevent their embodiment by inhibiting their mapping onto space. Further studies of the task-dependence of number simulation will clarify to which extent SiCE and SNARC can be situated (Platenburg et al., in preparation). A re-analysis of recently published data supports the view that number representations can be simulated on-line. In a pointing task (Pinhas & Fischer 2008), adults located the results of addition or subtraction problems on a visually presented line with flankers 0 and 10 on a touch screen. They located the same number more rightward during addition (e.g., 4 þ 2) than during subtraction (e.g., 8 – 2). This suggests a simulation of addition as rightward movement along a mental number line and a simulation of subtraction as leftward movement. A congruency effect in pointing times supports this interpretation and shows that our task evoked grounded, embodied, and even situated number representations. We next tested the prediction of CK&W’s processing model that non-abstract effects are more prevalent for fast compared to slow responses. To do this, we split each participant’s response times in the zero problems (e.g., 4 þ 0, 4 – 0) along the mean of their distribution into fast and slow responses. The spatial simulation effect was significant for fast responses, t(13) ¼ 2.66, p , .02, but not for slow responses, t(13) ¼ 1.65, p . .12. This result supports CK&W’s proposal (see their Fig. 5) that automatic number processing precedes intentional processing. It is worth noting that this outcome BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Commentary/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes is actually in conflict with Barsalou et al.’s (2008) suggestion that situated simulations always follow abstract (language-based) representations.

Numbers and numerosities: Absence of abstract neural realization doesn’t mean non-abstraction doi:10.1017/S0140525X09990082 Rafael E. Nu´n˜ez Department of Cognitive Science, University of California, San Diego, La Jolla, CA 92093-0515. [email protected] http://www.cogsci.ucsd.edu/  nunez/web/index.html

Abstract: The neural realization of number in abstract form is implausible, but from this it doesn’t follow that numbers are not abstract. Clear definitions of abstraction are needed so they can be applied homogenously to numerical and non-numerical cognition. To achieve a better understanding of the neural substrate of abstraction, productive cognition – not just comprehension and perception – must be investigated.

Cohen Kadosh & Walsh (CK&W) provide a compelling argument for challenging the currently accepted view – intuitively appealing and convenient – that the nature of numerical representation is inherently abstract. They lucidly explain why it is implausible that number has a single specific representation center given that classic cases for external world attributes such as color and motion lack a single locus of representation. In reviewing relevant behavioral, neuroimaging, and single-neuron (monkey) studies, they convincingly show that, despite the fact that many reports appear to support the abstract representation view, the evidence is incomplete and presents serious methodological and theoretical problems (e.g., null results, paradigm insensitivity, task specificity factors). Indeed, the data seem to support the opposite view. However, contrary to what the authors’ defend, from this it doesn’t follow that “numbers are not abstract” (sect. 5’s title). The authors’ definition and usage of crucial concepts such as “abstraction,” “representation,” and “number,” lacks conceptual clarity and creates unnecessary confusion and discontinuities with the understanding of other realms of cognition. Here, I only address the first one – abstraction. CK&W provide a narrow and confusing characterization of abstraction. First, they adopt a behavioral definition (sect. 2, para. 1) that applies exclusively to numbers (and, as an extension, they operationalize the notion of abstract representation in terms of neuronal populations’ insensitiveness to the form and notation of the input in which numerical information is presented). This operational definition of abstraction is specific but unnecessarily restrictive, making its extension to other non-numerical areas of cognition hard, if not impossible. How are we to relate the authors’ arguments with other, presumably supra-modal conceptual domains? Second, the authors’ terms “abstract” and “nonabstract” as defined in the narrow domain of neural sensitiveness, become unfortunate misnomers that generate confusion. The only hint the authors give of the nature of (not specifically numerical) abstraction, is a reference to Barsalou (sect. 10, para. 1): “abstraction is a skill that supports goal achievement in particular situations” (Barsalou 2003, p. 1184). But, this is vague and incomplete. That work deals with concepts that refer to entities or state of affairs “about the world” (e.g., chair), where even the abstract concept of truth is analyzed in that manner (p. 1185). What can then be said about the passage from the abstracted cardinal numbers to, say, transfinite or infinitesimal numbers (i.e., actual infinity), cases in which there is no fact about the world that corresponds to the concept (Nu´n˜ez

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2006; in press; Lakoff & Nu´n˜ez 2000)? We do need the term “abstraction” in order to correctly handle such concepts. And we do need the authors’ arguments to clearly address the fact that neuronal populations are sensitive to form of input. What is required is a fruitful theoretical proposal of supra-modal entity processing (e.g., numbers) that is able to encompass the authors’ arguments while leaving room for fruitful distinctions between abstract and non-abstract concepts in a way that is clearly extendable, without discontinuities, to other forms of everyday and mathematical abstraction. In addressing abstraction, CK&W make a distinction between automatic and intentional processing (of numerical information with different notations). By automatic, they mean a process that does not need monitoring to be executed (sect. 5, para. 3). They argue that by adopting such a distinction, we can yield a better characterization of abstract and non-abstract representations (sect. 11, para. 4). And they go on to build a parallel between this distinction and Barsalou’s linguistic and situated simulation (imagery) systems. But, again, this is narrow and problematic. The authors’ arguments are mainly concerned with the side of cognition that deals with perception and comprehension. When we look at the productive side of cognition we can see that the automatic/intentional (and linguistic/imagery) distinction can be really troublesome. Consider a person who, during an everyday conversation, says, “that was way back in my childhood,” and while doing so points with her thumb backwards over the shoulder. Such speech-gesture coproduction (1) is not monitored (McNeill 1992) and, therefore, is “automatic,” and (2) it is inherently abstract because the uttered word “back” and the backwards pointing don’t refer to anything in the real world, but to the past, which is metaphorically conceived as being spatially behind ego (Nu´n˜ez 1999; Nu´n˜ez & Sweetser 2006). Moreover, this fast spontaneous speech-gesture coproduction is, both, linguistic and imagery-driven. When trying to understand the productive side of cognition involving abstract concepts (numbers included) and their neural instantiations, the authors’ distinctions break down. More conceptual clarity is needed. But, looking at the productive side of cognition can actually be quite supportive of the CK&W’s claims. For instance, the authors argue that “it is entirely possible that similar behavioural effects can be subserved by different areas, or neuronal populations in a single brain area” (sect. 5, para. 1). Regarding our space-time mapping example, it is known that humans can spontaneously conceptualize temporal events as being spatial locations along the sagittal axis, with events in the future as being in front of ego and events in the past as being behind. And, neurally, this can be instantiated through the recruitment of neural populations in the ventral intra-parietal area (VIP) and the polysensory zone (PZ), among others (Nu´n˜ez et al. 2007). However, the linguistic and spontaneous gestural production of the Aymara of the Andes shows a striking counterexample: They conceive future events as being behind them and past events as being in front of them (Nu´n˜ez & Sweetser 2006; AAAS 2006). These two forms of spatial conceptions of time are internally consistent but mutually inconsistent, having, presumably, different neural realization. Similarly, numbers and arithmetic can be realized conceptually through different metaphorical mappings such as object collection and motion along a path (Lakoff & Nu´n˜ez 2000). These distinct mappings can have different neural instantiations while supporting the same inferential organization (e.g., in both cases “two plus three is five.”) Both conceptions characterize a cascade of isomorphic entailments, which are presumably, as the authors claim, subserved by different neural populations in the brain.

ACKNOWLEDGMENT I am grateful to Kensy Cooperrider and Srinivas Narayanan for comments on an earlier draft. Preparation of this commentary was facilitated by a Fellowship at the Wissenschaftskolleg zu Berlin (Institute for Advanced Study, Berlin).

Commentary/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes

The discussion of methodological limitations in number representation studies is incomplete doi:10.1017/S0140525X09990823 Guy A. Orban Laboratorium voor Neuro- en Psycho-fysiologie, Katholieke Universiteit Leuven Medical School, 3000 Leuven, Belgium. [email protected]

Abstract: Cohen Kadosh & Walsh (CK&W) discuss the limitations of the behavioral, imaging, and single-cell studies related to number representation in human parietal cortex. The limitations of the imaging studies are grossly underestimated, particularly those using adaptation paradigms, and the problem of establishing a link between single-cell studies and imaging is not even addressed. Monkey functional magnetic resonance imaging (fMRI), however, provides a solution to these problems.

Cohen Kadosh & Walsh (CK&W) correctly point out that assessing technical limitations is critical in weighing the evidence favoring one or the other of the opposing views, abstract or non-abstract, about numerical representation in parietal cortex (PC). On at least three counts, they have overlooked relevant limitations. CK&W state that: “Single-cell neurophysiology offers better temporal and spatial resolution than human neuroimaging” (sect. 8, para. 1). While strictly true, this seems to imply that the two techniques are measuring the same variable. This is of course untrue: The functional magnetic resonance imaging (fMRI) measures a haemodynamic response, not neuronal activity. Contrary to what has been conveniently assumed, the relationship between these two variables is far from resolved and depends upon the experimental conditions: while the link might be relatively direct in passive sensory stimulation, this is not the case when using task paradigms (Sirotin & Das 2009). The statement also ignores the whole issue of homology between the human and monkey brain, which we have only begun to resolve with the advent of monkey fMRI (Orban et al. 2004). Two facts are particularly relevant here. The surface area of the cortical sheet is ten times larger in humans than in the monkey (Van Essen 2004), which implies that human cortex includes two to five times more functional areas than its monkey counterpart. On the other hand, the relationship of these areas with cortical sulci having identical labels can differ between the species, as the human MT/V5 complex illustrates. In human parietal cortex, the regions corresponding to the lateral bank of monkey intraparietal sulcus (IPS) are located in the medial bank of human IPS, especially on the posterior side (Grefkes & Fink 2005). This implies that the homologue of monkey ventral intraparietal (VIP) area, where Nieder records his numerically selective neurons (Diester & Nieder 2007), is not actually located in the human IPS! CK&W present the results of fMRI adaptation experiments as one of the main indications for a non-abstract representation in PC. They neglect the evidence that adaptation differs between time scales and between cortical areas (Krekelberg et al. 2006; Verhoef et al. 2008). More seriously, they failed to see the implications of the Sawamura et al. (2006) study, which they did quote in their review. Briefly, Sawamura et al. showed that inferotemporal (IT) neurons which respond equally well to two stimuli, say, images of a pig and of a hammer, will adapt when the two identical images follow one another, either two pigs or two hammers, but not, or much less, when the hammer follows the pig or the reverse. Thus, adaptation overestimates neuronal response selectivity and functional magnetic resonance adaptation (fMRA) cannot be used to derive neuronal tuning widths, as in Piazza et al. (2004). The results also imply that at these high levels adaptation occurs not at the cell soma level, but somewhere earlier, either in the dendritic tree or in the inputs. The use of adaptation to prove a non-abstract representation actually implies adaptation at the soma. If this assumption

does not hold, the predictions for the abstract and non-abstract case become identical. Exactly the same argument can be made for the combination of adaptation with transcranial magnetic stimulation (TMS), presented by CK&W as their second main argument for non-abstract representation. If adaptation does not involve the cell soma, both hypotheses predict that the parietal neurons will be equally active, and hence, that TMS will have the same effect, opposite to what has been assumed. This dramatic example shows that it is of utmost importance that assumptions made in interpreting fMRI data, be tested. This also holds for the multivoxel technique. The final evidence for non-abstract representation are the Nieder single-cell data (Diester & Nieder 2007), but here CK&W neglect the limitations that the experimental model imposes upon these results. To be sure, the monkey is the best model that we have experimental access to, but it is not perfect, as there is ample evidence for differences in brain size (Van Essen 2004) and cognitive competences (Penn et al. 2008) between the two species. Hence, what applies to the monkey may not necessarily hold for the human. It is conceivable that the non-abstract representation in the monkey is supplemented in humans by abstract representations, say, in the evolutionarily new areas of the parietal cortex. Does this mean, then, that the evidence for an abstract representation is solid? This is not the case either. As CK&W correctly pointed out, even it had been demonstrated that different numerical notations activated the same voxels in PC, this need not imply that the representation is carried by a single neuronal population. It is important to notice that even this demonstration is unconvincing thus far, given the extensive smoothing and averaging across subjects that is typical of most fMRI studies (Georgieva et al. 2009). Unfortunately, the authors in their discussions of future directions completely overlooked the studies that provide a solution to the problems outlined here: fMRI in the awake monkey (Vanduffel et al. 2001). In fact, it replaces a direct comparison between human fMRI and single-cell studies in monkeys, which involves two unknowns, with two comparisons, each of which involves only a single unknown that can be resolved (Orban 2002). The comparison between single-cells and MR signals in the monkey allows one not only to address the relationship between neuronal activity and MR signals (Logothetis et al. 2001; Sirotin & Das 2009), but equally important, to understand the relationship between MR procedure and neuronal selectivity. This procedure can take a variety of forms: it may be a slow adaptation procedure (Nelissen et al. 2006), or a test, based on a comparison of response levels under different conditions (Georgieva et al. 2009). On the other hand, a comparison of fMRI in humans and monkeys allows the homology question to be addressed, when multiple properties of several neighboring regions are compared (Durand et al. 2009). The integration of single-cell studies and human functional imaging using awake monkey fMRI creates a brilliant future for cognitive neuroscience and lies at the heart of translational research in cognitive neurology.

Abstract or not abstract? Well, it depends . . . doi:10.1017/S0140525X09991063 Alison Pease, Alan Smaill, and Markus Guhe School of Informatics, University of Edinburgh, Edinburgh EH8 9AB, Scotland, United Kingdom. [email protected] [email protected] [email protected]

Abstract: The target article by Cohen Kadosh & Walsh (CK&W) raises questions as to the precise nature of the notion of abstractness that is intended. We note that there are various uses of the term, and also BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Commentary/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes more generally in mathematics, and suggest that abstractness is not an allor-nothing property as the authors suggest. An alternative possibility raised by the analysis of numerical representation into automatic and intentional codes is suggested.

We support Cohen Kadosh & Walsh’s (CK&W) well-argued warning against sliding into the dogma of assuming a uniform abstract representation of number in the intraparietal sulcus, regardless of modality of input or purpose of the task. This question is especially pertinent now, given the last three decades of research into visual reasoning in mathematics and the recent application of work in embodied cognition to mathematics representation and reasoning. Our interest is from a cognitive science and philosophical, as opposed to a neuroscientific, perspective. In general, we find the notion of abstraction in the field to be not well-defined. In the article, we are given an initial operational definition from Dehaene, where the presence of an abstract representation, the “behavior depends only on the size of the numbers involved, not on the specific verbal or non-verbal means of denoting them” (Dehaene et al. 1998a, p. 356). But towards the end of the article (sect. 10, para. 1), CK&W cite approvingly Barsalou’s comment that “abstraction is simply a skill that supports goal achievement” (Barsalou 2003, p. 1184). Is this in fact consistent with the earlier operational definition? Barsalou’s own characterisations in Barsalou (2005) of the use of the term abstract include a sense in which perception is in itself typically abstract, inasmuch as it involves categorical judgements out of the “confusion of experience.” As this addresses the central issue of the target article, a clearer account of what is at stake here is required. We do not think that the binary distinction between abstract and not abstract is the right way to conceptualise the problem. In identifying the digit 2 over a range of typefaces, or ignoring the colour of a number of dots in the visual field, it is natural to consider that there is abstraction from the token that is physically present. Certainly the mathematical notion of abstraction allows many levels of abstraction, and we believe that mathematical cognition in general is built in part on some version of arithmetical representations. (This notion of abstraction is also referred to in Barsalou [2005], allowing that there is a question of the degree of abstractness in this case.) CK&W’s analysis in terms of automatic and intentional codes is clearer, and seems potentially of greater explanatory power than deciding on the question of abstractness. Here we note the comments on this topic in Wilson (2002), on the apparent paradox that in more elaborate tasks, the more automated approach actually allows finer control of the activity than do more “controlled” strategies. The suggestion is that the automation builds up internal representations, thereby providing a more efficient way to deal with some of the regularities of the problem at hand. Thus, with practice in arithmetical calculation, more persistent representations will be formed, and on this view these may well be more abstract. The distinction between automatic and intentional processing raises the question of how automatic compares to the so-called innate arithmetic of Lakoff and Nu´n˜ez (2000). A series of screen experiments on babies (not mentioned by CK&W) suggest that babies are born with basic addition and subtraction skills on small numbers, and indeed appear to recognise sameness of number when objects are replaced with an identical number of different objects (Simon et al. 1995). Presumably, the processing here is automatic, but we are curious as to how these results fit with the authors’ account of numerical representation. Lakoff and Nu´n˜ez (2000) emphasise the metaphorical process in mathematical development. They identify four “grounding metaphors” for arithmetic (metaphors in which the source domain is a familiar, environmentally grounded domain) that all abstract into a common target domain. These metaphors are all principally visual. The sense of abstraction here is close to

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the sense in which the term is used in informatics generally, where structure common to some data or mathematical entities can be reasoned about while ignoring properties that differ from instance to instance. Similarly, multi-modal representations of mathematics such as diagrammatic or algebraic reasoning are assumed to abstract to a common domain. It may therefore be relevant to consider work on the cognitive status of metaphor processes. In Lakoff (2008), it is claimed that mirror neurons are multimodal, that is, the same mirror neurons fire whether we imagine, or perform/perceive certain actions. The neural theory is based on the premise that if we see two domains simultaneously enough times, then connections between the nodes that process the domains are strengthened and we build a strong association. It is not clear to us if there is substantial disagreement between Lakoff’s views, as applied to arithmetic, and the views of CK&W. The target article naturally does not address the issue, of interest to us, of how arithmetical judgements that quantify over all numbers are represented (e.g., associativity of addition). This can be expected to relate to the representation of particular numbers, but remains, as far as we know, an open question. ACKNOWLEDGMENT Thanks to the Philosophy, Psychology, and Informatics Reading Group (PPIG) seminar in Edinburgh for helpful discussion on these topics.

Common mistakes about numerical representations doi:10.1017/S0140525X09990835 Mauro Pesenti and Michael Andres Unite´ de Neurosciences Cognitives, De´partement de Psychologie, Universite´ Catholique de Louvain, 1348 Louvain-la-Neuve, Belgium. [email protected] http://www.nesc.ucl.ac.be/mp/pesentiHomepage.htm [email protected] http://www.nesc.ucl.ac.be/recherche/projects/number.htm

Abstract: Cohen Kadosh & Walsh (CK&W) argue that recent findings challenge the hypothesis of abstract numerical representations. Here we show that because, like many other authors in the field, they rely on inaccurate definitions of abstract and non-abstract representations, CK&W fail to provide compelling evidence against the abstract view.

Whereas number magnitude was initially assumed to be represented abstractly as a function of powers of ten (McCloskey et al. 1985), an analog representation figuring numerical magnitudes by overlapping activations on an oriented and compressed mental line was later proposed (Dehaene 1992). These views have often been mixed ill-advisedly, and it is now common to read that the parietal cortex hosts “an abstract numerical representation taking the form of an oriented number line” (e.g., Cohen Kadosh et al. 2005; Dehaene et al. 1998a). This, however, is a double nonsense: by definition, analog representations cannot be abstract; by essence, abstract representations cannot be oriented or compressed. This conceptual drift from an analog to an abstract number line occurred because many authors in the field used loose definitions of abstract/analog representations leading to several profound mistakes. Abstract representations capture the ideational content of knowledge irrespective of the original input modality. Being languageindependent, they are formalized in a propositional code specifying the meaning of assertions, thanks to a logical system called the predicate calculus; importantly, being amodal (i.e., not tied to any modality), they possess no isomorphic properties influencing performance (Anderson & Bower 1973; Pylyshyn 1973). In contrast, analog representations share with the reality they represent a

Commentary/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes first- or second-order isomorphism and are displayed on mental media preserving physical properties (e.g., spatial distances for visuo-spatial representations; Kosslyn et al. 1978). Because the processes acting on analog representations are sensitive to these properties, they can be traced in behavioral performance. Using criteria from seminal papers in cognitive (neuro)psychology, we highlight three important mistakes compromising CK&W’s argumentation. A first mistake consists in attributing the properties of the content of a representation (representation of [object/concept X with properties P]) to its format ([representation of object/ concept X] with properties P; Pylyshyn 1978; 1981). Format and content being independent, content properties can be represented in modality-neutral and modality-specific formats (Caramazza et al. 1990). Stating that a numerical representation is abstract if behavioral effects depend only on magnitude is thus erroneous. Contrary to what CK&W write, McCloskey’s semantic representation was not abstract because of its quantitative content, but because of its propositional format. Dehaene’s magnitude representation on an analog medium provides the a contrario argument. Another common mistake concerns the inferences drawn from the (in)dependence between semantic representations and the various modalities/notations of access. Although abstract representations are amodal, a representation accessed through several modalities/notations is not necessarily abstract. Number semantics could be accessed from and give rise to similar effects in verbal, Arabic, or non-symbolic inputs while being non-abstract (e.g., Dehaene’s analog representation). Conversely, modality/notation-specific effects do not necessarily sign non-abstract representations, because abstract representations could be accessed differently by modality-specific presemantic systems (Riddoch et al. 1988). By simply defining non-abstract representations as “sensitive to input modalities” (see sect. 2, para. 1), CK&W fail to provide a constraining framework. For example, finding that, after habituation, magnitude processing in one notation becomes more vulnerable to virtual lesions of the parietal cortex than in other notations, does not contradict the abstract view, as habituation could have modified the connectivity between notation-specific systems and abstract representations prior to the lesion. Trying to consider representations and processes separately constitutes CK&W’s third mistake: Whatever their format, representations cannot be conceived as mental entities distinct from the processes acting upon them (Anderson 1976; Palmer 1978), and processes are totally determined by the format of the representations upon which they act (Shepard & Podgorny 1978). Therefore, any proposal of non-abstract representations must come along with a set of compatible processes clearly specified both at the functional and anatomical levels. To properly assess the format of numerical representations, we make the following recommendations. First, a data type (a way of organizing information in memory; Simon 1978), and the primitive operations that can be performed on it, must be specified and supported by unambiguous behavioral effects. Rightward biases on the number line in neglect patients (Zorzi et al. 2002) is an instance of how intrinsic properties of representations may show through behavioral effects, but other frequently cited effects are not: The distance effect can be accounted by various types of representations (e.g., abstract semantic labels: Banks 1977; distributed representations: Verguts & Fias 2004), the congruity effect by a power-of-10-based propositional representation, and the SNARC effect by associations with abstract codes (Gevers et al. 2006c). Second, activations must be demonstrated in brain areas whose general cognitive role and pattern of activity are compatible with the assumed type of representation. For example, non-abstract representations tied to space predict numerical processes isomorphic to spatial orientation, with overlapping activations of number and space processing areas. Finally, a lesional approach must demonstrate that these areas are necessary to perform correctly the tasks relying on this

representation. Indeed, non-abstract representations could simply be automatic by-products of mental activity and not its medium. CK&W’s suggestion to rely on Stroop-like interference to infer the nature of numerical representations is thus irrelevant, because automaticity does not guarantee that the activated representation is functionally required. The format of representations in memory is a major question in cognitive neurosciences. It was at the heart of the first architectures of numerical cognition, and CK&W should be commended for drawing our attention again to this critical but messy issue. Assessing the existence of abstract representations is a tricky if not impossible enterprise, because it boils down to demonstrating the absence of effects (e.g., of modality). Efforts should therefore rather be expended on testing possible candidates for non-abstract representations. However, although we believe that non-abstract numerical representations may have a true functional role, we think that the definitions and evidence provided by CK&W do not allow them to infer that numerical representations are non-abstract. We recommend using terms like “abstract/analog,” “(a)modal,” “supramodal,” or “modality(in)dependent,” and so forth, with great care, because each of these conveys a specific meaning. Far from being a rhetorical question, this issue has strong theoretical and empirical implications. It is now time to overcome mistakes that hamper research on numerical representations and their relationship with the functioning of the human brain. ACKNOWLEDGMENTS Michael Andres is a post-doctoral researcher and Mauro Pesenti is a research associate at the National Fund for Scientific Research (Belgium).

Numerical representation, math skills, memory, and decision-making doi:10.1017/S0140525X09990847 Ellen Petersa and Alan Castelb a Decision Research, Eugene, Oregon 97401; bDepartment of Psychology, University of California, Los Angeles, Los Angeles, CA 90095-1563. [email protected] http://www.decisionresearch.org/About/People/peters.html [email protected] http://castel.bol.ucla.edu

Abstract: The consideration of deliberate versus automatic processing of numeric representations is important to math education, memory for numbers, and decision-making. In this commentary, we address the possible roles for numeric representations in such higher-level cognitive processes. Current evidence is consistent with important roles for both automatic and deliberative processing of the representations.

The consideration of deliberate versus automatic processing of numeric representations is important to both math education and decision-making. Numeric information is ubiquitous in the decisions that we make, and thus numeric representation may play an important role. Basic number skills have only recently received attention in the decision literature. Numeracy, defined as the ability to process mathematical and probabilistic concepts, for example, has been shown to reduce susceptibility to framing effects and improve judgment accuracy (Peters et al. 2006). However, the effects of numeric representations in decisions have been largely ignored with two recent exceptions (Furlong & Opfer 2009; Peters et al. 2008). These lines of research raise important questions concerning relations between numeric representations, math skills, and the use of numeric information in decisions. This commentary adds to the Cohen Kadosh & BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Commentary/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes Walsh (CK&W) viewpoint by addressing the possible roles of automatic and deliberate processing of numeric representations in higher-level cognitive processing. Numeric representations and math skills. Peters et al. (2008) tested a large sample of healthy younger and older adults (mean age ¼ 20 and 70 years, respectively) using a distanceeffect reaction-time task with Arabic integers and dots (“Is the quantity shown bigger or smaller than 5?”), among other notations. In a reanalysis of the younger-adult data including only these two notations, the size of the distance effect varied by notation, with more precise representations (smaller distance effects) for Arabic integers than dots, supporting CK&W’s point that numeric representations are not necessarily abstract. CK&W claim further support from findings that the distance effect with integers relates to math achievement, but the distance effect with dots does not. However, in the reanalysis of Peters et al.’s data, more precise numeric representations for both Arabic integers and dots were associated with higher numeracy scores. Halberda et al. (2008) demonstrated a similar positive relationship between 14-year-old children’s performance on a task that used only numerosities (dots) and their math ability back to kindergarten. The question remains whether this association is based on automatic or deliberate processing of the representations. An age comparison may be illuminating because of the shift that occurs in reliance on more deliberative to more automatic processes from younger to older adulthood across a variety of domains. If the relation between numeracy and numeric representations is based on more automatic processes, then this correlation should increase, as older adults tend to rely relatively more on automatic processes (see Peters et al. 2007 for a review); if it is based on more deliberative processes, one might expect a decreased correlation. In Peters et al.’s (2008) original data, the distance effect was less associated with numeracy for older than younger adults (r ¼ .06, p ¼ .64 and r ¼ .41, p , .001, respectively). These data best support deliberate processes underlying numeracy’s association with numeric representations. In addition, Castel (2007) found that older adults who were accountants and bookkeepers demonstrated memory ability remarkably similar to younger adults for arbitrary numbers, but not for arbitrary non-numeric information (where the usual age declines in memory were found). In another study, older adults were exceptionally good at remembering grocery-store prices, but not arbitrary prices (Castel 2005). Such data could support a more precise abstract representation for these individuals (who have more experience with numbers in general or grocery prices in particular) that is carried into later life. However, in combination with Peters et al.’s data, these findings are also consistent with motivated selectivity in deliberative processing (Hess 2000), with some numeric information (or all numbers for some individuals) being particularly important and valued. Numeric representations and decision-making. In accord with CK&W’s notion of a deliberate level of numeric representations, decision-makers are thought to use numeric information intentionally and deliberatively (e.g., stock-market indicators, mortgage rates, and grocery bills). Because human decisionmaking likely derives in part from the same mechanisms evolved by other animals in response to risky natural environments, intuitive representations of symbolic numbers should relate to how individuals respond to numeric information in decision-making. Peters et al. (2008) developed and tested hypotheses relating an individual-difference measure of the size of the distance effect to decision-making. They hypothesized that individuals with more precise representations would weight proportional differences between numeric attributes in choice more than individuals with less precise representations. In addition, a larger proportional difference should result in a bigger difference between individuals than a smaller proportional difference.

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Results of two decision studies in Peters et al. (2008) supported these hypotheses. In the first study, individuals with more precise representations (compared to those with less precise representations) were more likely to choose larger prizes received later than smaller, immediate prizes, particularly with a larger proportional difference between the two monetary outcomes. In a second study, they were more likely to choose a normatively worse option that saved a greater proportion of lives at risk (but a smaller number of lives) compared to those with less precise representations. Importantly, these findings were more consistent with the abstract-representation view, because the results of both studies held after controlling for numeracy and various measures of intelligence associated with prefrontal activity. The precision of number representations appears to underlie: (a) perceived differences between numbers, (b) the extent to which proportional differences are weighed in decisions, and, ultimately, (c) the valuation of decision options. Human decision processes involving numbers important to health and financial matters may be rooted in elementary, biological processes shared with other species, and which depend on an automatic representation of numerical information across notations. It is critical to better understand number representation in the context of how individuals use numbers. The CK&W article forces us to consider whether the role of these representations in higher-order cognitive processing emerges from a shared representation across notations resulting more from prefrontal activity or whether their role results from an abstract representation. The current results are most consistent with numeracy being related to the former shared representation and decisionmaking being associated with the latter automatic processing of the representations. Human decision-making, however, often involves prefrontal activity (Rangel et al. 2008), and further consideration of numeric representations being some combination of abstract and deliberate may converge with and ultimately explain some findings in the neuroanatomy of decision-making. It remains plausible that a shared deliberate representation (that is separate from what is associated with numeracy) could explain Peters et al.’s findings. A better understanding of the automatic versus deliberate nature of these representations’ influences on decision-making will illuminate the important contribution of numeric representations on everyday decisions and should ultimately lead to improvements in decision aids.

What is an (abstract) neural representation of quantity? doi:10.1017/S0140525X0999104X Manuela Piazzaa and Veronique Izardb a Center for Mind Brain Sciences, University of Trento, 38068 Rovereto (TN) Italy; bDepartment of Psychology, Harvard University, Cambridge, MA 02138. [email protected] [email protected]

Abstract: We argue that Cohen Kadosh & Walsh’s (CK&W’s) definitions of neural coding and of abstract representations are overly shallow, influenced by classical cognitive psychology views of modularity and seriality of information processing, and incompatible with the current knowledge on principles of neural coding. As they stand, the proposed dichotomies are not very useful heuristic tools to guide our research towards a better understanding of the neural computations underlying the processing of numerical quantity in the parietal cortex.

According to Cohen Kadosh & Walsh (CK&W) a neural representation of quantity is abstract if “neuronal populations that code numerical quantity are insensitive to the form of input in which the numerical information was presented” (sect. 2, para. 1). This

Commentary/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes definition is extremely shallow; it does not state at what level the hypothesized neural code takes place; and it fails in taking into account that different attributes of stimuli may be coded by separate yet interconnected brain areas, by separate yet interconnected neuronal populations within the same brain area, or by exactly the same neuronal populations, yet with different tuning schemes (deCharms & Zador 2000). Indeed, in the specific case of the comparison between symbolic and non-symbolic numerical processing, we have proposed that our observation might be compatible with a common quantity code instantiated in the firing of a common set of parietal neurons with different tuning schemes for different input formats (finer tuning schemes for symbolic and broader tuning schemes for non-symbolic stimuli), as also predicted by a powerful computational model of number processing (Dehaene 2007; Piazza et al. 2007; Verguts & Fias 2004). On CK&W’s view, how should such quantity code be defined – as abstract or non-abstract? At what level(s) does abstractness need to be present for a given representation to be qualified as abstract? What if there are neural populations within parietal cortex that encode the quantity aspect of each notation separately, but that these populations are so deeply interconnected that the spread of the activation is automatic and the resulting larger scale population code appears as invariant to modality? In this case, the abstractness of the coding would almost literally be in the connections. Would this mean that the emerging population code is non-abstract? Despite the absolute centrality of these issues, this discussion is not even approached, and the existence of different possible levels of neural coding are not even considered. To us, this reflects an extremely naı¨ve approach to a question (on what is a neural code) that is central and highly debated in the current neuroscientific literature. As a result, the dichotomy between abstractness versus non-abstractness seems like a very weak heuristic tool for our ability to answer the most meaningful issue, which is to unveil the computational principles underlying processing of numerical quantity in parietal cortex. We also feel uncomfortable with the more general definition of neural representations in this target article. CK&W define their view of neural representations in extremely vague terms (“patterns of activation within the brain,” sect. 2, para. 2), but in the rest of the article their operational definition of neural representations appears to be grounded on implicit views inspired by the classical cognitive psychology notion of module (Fodor 1983). Despite overtly criticizing the idea of neural module, CK&W actually embrace two important aspects of the classical definition of module: encapsulation (which here implies seriality of information processing), and domain selectivity. The assumption of encapsulation and seriality is evident in CK&W’s strict use of the additive factor method, for which the presence of statistical interactions between quantity-related effects and notation effects is taken as evidence in favor of notation-specific quantity representations. In light of our most recent knowledge of fine brain structure and function, encapsulation and seriality are extremely difficult to maintain. It is a known fact that different and also distant brain regions are massively bidirectionally interconnected and work in parallel (Felleman & Van Essen 1991). Not surprisingly, models that do take into account some degree of parallel processing show that interactions between factors can occur even if the factors affect completely separate processing stages (McClelland 1979; Rumelhart & McClelland 1986). This can happen, for example, if one factor affects one aspect of the information processing (say, the rate of evidence accumulation), and the other factor affects another aspect (say, the decision threshold). More refined data analysis taking into account precise response distributions and testing alternative (and more neurally plausible) models are therefore necessary before driving conclusions on the basis of scattered reports of (often weak) statistical interactions between factors. Second, CK&W implicitly link abstractness to domainselectivity. Thus, the fact that brain regions or individual neurons

that are modulated by numerical quantity may also be modulated by other quantity- as well as non-quantity-related parameters, like physical length (Tudusciuc & Nieder 2007), color (Shuman & Kanwisher 2004), or motion direction (Nieder et al. 2006), is taken as undermining the possibility of an abstract representation of quantity. We disagree with this view. In the first place, selectivity might be a property that arises at some level of neural coding that is not yet probed by most current methods of investigation (but see Tudusciuc & Nieder 2007). For example, in the case of numerical quantity, it is possible that numerical quantity-selective representations do exist, but emerge only as the averaged population activity of numerical quantity-sensitive, but not selective neurons. This would be the case, if, for example, some neurons respond both to number and length, others to both number and motion direction, and others to both length and motion direction (Nieder et al. 2006; Pinel et al. 2004; Shuman & Kanwisher 2004; Tudusciuc & Nieder 2007). Under this scenario, at the population level the codes for number, length, and motion direction would be distinct, but neither the single neuron spiking activity nor the functional magnetic resonance imaging (fMRI) signal averaging across all three populations would reveal such selectivity. In this respect, multi-unit recording allowing population coding properties to be more clearly unveiled, and multivoxel pattern analysis of the fMRI signal, capitalizing on very small variations in domain specialization across voxels, might reveal population codes which are indeed selective (Kamitani & Tong 2005; Tudusciuc & Nieder 2007). Alternatively, because of massive local connectivity, functional selectivity may only be revealed by taking into account long-range connections between distant brain regions. In either case, the issues of selectivity and of abstractness are two orthogonal ones. In conclusion, we think that reasoning in terms of ill-defined dichotomies (selectivity vs. non-selectivity, abstractness vs. non-abstractness) may induce unnecessary over-simplifications and is very unlikely to bring us towards a deeper understanding in this domain.

Abstract or not? Insights from priming doi:10.1017/S0140525X09990859 Bert Reynvoet and Karolien Notebaert Laboratory of Experimental Psychology, University of Leuven, 3000 Leuven, Belgium. [email protected] [email protected] http://ppw.kuleuven.be/labexppsy/newSite/

Abstract: Cohen Kadosh & Walsh (CK&W) argue that numerical representation is primarily non-abstract. However, in their target article they failed to consider recent behavioral priming experiments. These priming experiments provide evidence for an abstract numerical representation under automatic conditions.

Recently, there has been a growing consensus favoring an abstract representation of numerical magnitude. According to Cohen Kadosh & Walsh (CK&W), this assumption might be premature, and they raise the alternative possibility that the default numerical representation is not abstract, but rather, dependent on notational input. CK&W argue that we will be more likely to observe evidence for a non-abstract representation under automatic processing conditions. We applaud the idea of examining numerical representations under conditions of automatic processing, because then number processing is less affected by intentional strategies. However, based on research using the priming paradigm, the conclusion of CK&W is not supported. The priming paradigm is a very popular method to investigate underlying representations under BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Commentary/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes highly automatic conditions. In a typical number priming paradigm, participants have to react on a target number that is preceded by a prime number while the numerical distance between both is systematically varied. Interestingly, when the numerical distance between prime and target is small (e.g., “1” preceded by “2”), the target is processed faster than when the primetarget distance is large (e.g., “1” preceded by “9”) – that is, the priming distance effect. This effect was first shown by Den Heyer and Briant (1986) and later replicated under more automatic conditions using short stimulus onset asynchronies between prime and target and visual masking in order to eliminate strategic prime use (e.g., Reynvoet & Brysbaert 1999). Certain priming studies manipulated the notation of prime and target: Prime and target were either presented in the same notation (e.g., prime “6” – target “7”) or in different notations (e.g., prime “six” – target “7”). Originally, Koechlin et al. (1999) observed an interaction between notational change and distance priming: no distance priming effect was observed when prime and target were presented in different notations. This led to the proposal of notation dependent representations of quantity in line with the proposal of CK&W. However, the same group of researchers did observe cross-notation distance priming later on (Naccache & Dehaene 2001b), and they argued that the interaction effect obtained previously was a “spurious effect” and that “cross-notation priming is the norm rather than the exception” (Naccache & Dehaene 2001b, pp. 234–35). We ourselves (Reynvoet & Brysbaert 2004; Reynvoet et al. 2002) confirmed this observation of cross-notation priming in which magnitude processing was highly automatic (i.e., short stimulus-onset asynchronies between prime and target). Furthermore, we also extended this finding by showing cross-notation priming under conditions in which the target had to be named, which implies that the numerical magnitude was completely irrelevant for the task. In addition, we also demonstrated cross-notation priming under conditions in which the formation of intentional links between different notation-dependent representations is discouraged. In a first study, the targets were always presented in the same notation, while the preceding primes, invisible to the subjects, were presented in different notations. Still, a distance priming effect was observed when notation changed (Van Opstal et al. 2005a). In a second study, investigating the lexico-semantic system of trilingual speakers, we found distance priming when masked English number word primes (e.g., “three”) were presented before a tobe-named Dutch (e.g., “twee”) or French (e.g., “deux”) number word target (Duyck et al. 2008). This cross-notation and crosslanguage priming provide convincing evidence for an abstract numerical representation under automatic conditions. If behavioral priming supports the idea of an abstract numerical representation, how can we account for the interactions between number notations and magnitude-related effects observed using other paradigms reviewed by CK&W? It should be noted that many of the observed interactions are due to the (near) absence of the magnitude-related effects in particular conditions (e.g., Dehaene & Akhavein 1995; Fias 2001; Hung et al. 2008; Ito & Hatta 2004). These null results may be caused, for example, by differences in the strength of the associations between an input notation and the corresponding magnitude and/or spatial representations (see also Brysbaert 2005). Because of these notation-dependent associations, it could be that a magnitude-related effect is not observed for a particular notation, which results in an interaction when combined with other notations in an omnibus analysis. We believe that a better way to address the issue of notation-dependent representations is to look for positive results, and that is exactly what we did in our cross-notational priming experiments, where we found evidence for cross-notation priming in many experiments, even under highly automatic conditions. In sum, much of the evidence in favor of a notation-dependent magnitude representation is based on a null effect in a particular condition. We reviewed a series of experiments using cross-

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notational priming that were based on the presence of an effect, that is, cross-notational distance priming. These results are in favor of an abstract magnitude representation and should be dealt with in any theory on numerical processing. ACKNOWLEDGMENTS This work was supported by grant G.0415.06 from the Flemish Fund for Scientific Research and grant P5/04 from the IUAP Program of the Belgian Federal Government.

Symbolic, numeric, and magnitude representations in the parietal cortex doi:10.1017/S0140525X09990860 Miriam Rosenberg-Lee,a Jessica M. Tsang,b and Vinod Menona,c,d a Department of Psychiatry and Behavioral Sciences, Stanford University School of Medicine, Stanford, CA 94305; bStanford University School of Education, AAA Lab, Stanford, CA 94305-2055; cProgram in Neuroscience, Stanford University School of Medicine, Stanford, CA 94305; dSymbolic Systems Program, Stanford University, Stanford, CA 94305. [email protected] [email protected] [email protected]

Abstract: We concur with Cohen Kadosh & Walsh (CK&W) that representation of numbers in the parietal cortex is format dependent. In addition, we suggest that all formats do not automatically, and equally, access analog magnitude representation in the intraparietal sulcus (IPS). Understanding how development, learning, and context lead to differential access of analog magnitude representation is a key question for future research.

We agree with Cohen Kadosh & Walsh’s (CK&W’s) central contention that representation of number in the parietal lobes is format dependent. The authors should be commended for presenting the clearest discussion yet of this topic, and for revisiting and reinterpreting findings from older studies. It is indeed surprising how many investigators have abandoned their own results only to reiterate staid theories. In this context, one is reminded of Ioannidis (2005): “[F]or many current scientific fields, claimed research findings may often be simply accurate measures of the prevailing bias” (p. 0696). By explicitly pointing out research biases extant in the literature, CK&W present the field with an opportunity to consider new interpretations and formulate more targeted research questions. CK&W frame their review in terms of abstract number representations in the parietal cortex, as is the norm in the field. However, a more appropriate question is: How do various symbolic systems exploit magnitude-processing capacities of the intraparietal sulcus (IPS) and under what conditions? CK&W do not address exactly why, or how, numerical formats differ in the degree to which they evoke effects consistent with an analog magnitude representation. By focusing on the absence of transfer of magnitude information across formats, the authors appear to have overlooked more fundamental differences between formats that have roots in experience and development. Given that numerical symbols are cultural artifacts that are learned over time, we believe that not all formats will necessarily access analog-magnitude representations equally, and, in general, the degree to which a format has access to this representation depends on past exposure and current task context. The findings reported by Cohen Kadosh et al. (2007b) in a twotrial adaptation paradigm are consistent with our view. This study found that presenting the same digit twice produced less activity in the right IPS compared to sequential presentation of two different digits. When the two numbers were presented in different formats (digit and number word), there were no differences

Commentary/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes in activity for same or different quantities, consistent with a format-dependent view. However, there was also no difference between same and different quantities when both numbers were presented as number words. This result is inconsistent with the view that number words are automatically represented as magnitudes in the IPS, a central assumption of both the abstract and non-abstract views. One intriguing result from Cohen Kadosh and colleagues’ (2007b) study is that although number words did not show numerosity-related adaptation, they did produce robust activity in the IPS, comparable to the level observed for digits. This suggests that the IPS can encode number words in a nonmagnitude-dependent manner. Strong evidence for notationdependent activity in the IPS also comes from neurophysiological studies: Diester and Nieder (2007) found that monkeys who had learned to pair digits with dots activated distinct neuronal populations for each format. However, some of the digit-selective neurons did not demonstrate graded tuning curves; instead they fired only for a specific digit (Diester, personal communication). These non-magnitude representations are potential precursors to the development of automatic analog magnitude representations. Consistent with this proposal were results from a training study by Lyons and Ansari (2009) in which participants learned a pairing of arbitrary symbols with approximate magnitudes. Although the IPS was active both early and late in training, and distance effects grew more pronounced with experience, only late in training did activity in the IPS correlate with individual differences in the size of the distance effect. Our view is also consistent with existing behavioral data, including those cited by CK&W. For example, among Japanese participants, digits and Kanji numbers, but not Kana scripts, showed interference from numerical magnitude on a font size discrimination task (Ito & Hatta 2004). Like number words, Kana scripts may not evoke an automatic analog magnitude representation. This is possibly because Kanji numbers elicit magnitude representations in their visual form more so than Kana scripts (Kanji number symbols begin with one, two, and three (horizontal) lines and have closer ideographic connection to numerosities than do Kana script). In this case, differential degrees of magnitude representation could be due to limited experience with Kana scripts in the context of number processing. Context can influence magnitude representations, even within formats. For example, adults in the Mundurucu tribe produce behavior consistent with a compressed analog magnitude (i.e., logarithmic) for dot displays. Within verbal number words, Mundurucu words evoked logarithmic representations, whereas Portuguese words evoked linear representations (Dehaene et al. 2008). Grade-school-aged children have both linear and logarithmic representations on the same stimuli depending on whether they were in a 0– 100 range or a 0 – 1000 range (Siegler & Opfer 2003). How these behaviors are represented in the brain is currently unknown, but we suggest that this involves more than the IPS – they are likely to depend on the context-dependent interaction of the IPS with the ventral visual stream and the prefrontal cortex (Wu et al. in press). How can we disambiguate the view that different neuronal populations encode different formats with the same magnitudebased organization, from the idea that different populations have dissimilar analog-magnitude representations that are contextand experience-dependent? Longitudinal developmental research and learning paradigms, such as Lyons and Ansari (2009), could go a long way towards clarifying such questions. CK&W note that null effects have been over-interpreted as evidence of notation dependence – many studies may, in fact, have been grossly underpowered to detect notation-specific effects. Increasing sample sizes, particularly in imaging studies, would be a simple way to increase detection and improve interpretability and generalizability of research findings. Finally, feature selection and classification algorithms, which search for consistent patterns of activation between conditions, could potentially uncover differences

between formats that would not be manifest in differences in overall levels of activation (Ryali & Menon 2009). ACKNOWLEDGMENT We thank Dr. Lucina Uddin for useful discussion.

Abstract representations of number: What interactions with number form do not prove and priming effects do doi:10.1017/S0140525X09990872 Seppe Santens, Wim Fias, and Tom Verguts Department of Experimental Psychology, Ghent University, B-9000 Ghent, Belgium. [email protected] http://users.ugent.be/  ssantens/ [email protected] http://expsy.ugent.be [email protected] http://users.ugent.be/  tverguts/

Abstract: We challenge the arguments of Cohen Kadosh & Walsh (CK&W) on two grounds. First, interactions between number form (e.g., notation, format, modality) and an experimental factor do not show that the notations/formats/modalities are processed separately. Second, we discuss evidence that numbers are coded abstractly, also when not required by task demands and processed unintentionally, thus challenging the authors’ dual-code account

A crucial part of Cohen Kadosh & Walsh’s (CK&W) argument against abstract representations concerns the fact that different effects (e.g., distance, SNARC, compatibility effects) are often not quantitatively the same for different number forms like notation (e.g., Arabic vs. verbal), format (e.g., symbolic vs. nonsymbolic), and modality (e.g., visual vs. auditory modality). For concreteness, we will here focus on the distance effect. The authors note that distance between two numbers in a comparison task interacts with notation: Cohen Kadosh (2008a), for example, reports that the distance effect is larger for numbers in Arabic notation than in verbal notation (notation – distance interaction). However, the fact that a common abstract coding system is accessed by different notations does not mean that the representation of these notations should be exactly equal. In a neural system, obtaining exactly the same representations for different notations would be possible only if the input pathways to the common coding system for the different notations are exactly the same, which is clearly impossible. If there is a common coding system, but some divergence between the input pathways to it, the activation pattern on the common system will be (at least slightly) different for different notations, and any effects downstream from the common representation will be influenced. This also holds when number formats are different, in particular when comparing symbolic (Arabic, verbal) with non-symbolic (collections of objects) number formats. Computational modeling has suggested that there is a common abstract coding system for symbolic and non-symbolic formats (Dehaene & Changeux 1993; Verguts & Fias 2004), but that the input pathways for the two formats are different, with one format (non-symbolic number) being much more noisy and passing via an extra representational processing stage (Santens et al., in press). Because of this extra stage, there can again be different behavioral signatures for the two formats (e.g., format –distance interaction; Roggeman et al. 2007), even when they eventually converge on a common coding system. Finally, given that different modalities are processed by different sensory input systems, a similar argument holds for modality – distance interactions. Having argued that the evidence against an abstract coding system of number is not convincing, we now turn to some positive evidence in favor of such a system. CK&W argue that it may exist, but only in limited circumstances, in particular when participants BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Commentary/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes are required as part of the task demands to treat different number notations (or formats, or modalities) as similar, or when they (for whatever reason) intentionally choose to treat different notations as similar. To evaluate this claim, we look at number priming studies in which (1) prime and target numbers are presented in different notations (so numbers in the prime notation are not included in the task demands); and (2) it is explicitly demonstrated that primes are not consciously processed (so it is excluded that participants would intentionally create a cross-notation number system). In such studies, we can then check whether there is a cross-notation prime-target distance effect, which is commonly regarded as evidence for access of prime and target to a common semantic coding system (e.g., Reynvoet et al. 2002). At least two studies fulfill both criteria. Both studies used a number comparison task with a fixed standard for comparison. Reynvoet and Ratinckx (2004) used Arabic and verbal primes, but Arabic target numbers only, so verbal numbers were not included in the task demands. In their Experiment 2b, primes were shown to be not consciously perceived, so participants could not have intentionally included verbal numbers in their number set. When prime and target were both presented in the left hemifield (right hemisphere), there was no cross-notation priming effect; however, the effect was present in the right hemifield (left hemisphere). Hence, at least in the left hemisphere, there seems to be a common coding system, even when it is not required by task demands and outside participants’ intentions. Second, in the study of Van Opstal et al. (2005a), primes were presented in both notations (verbal and Arabic), and targets were presented in one notation only (either verbal or Arabic, varied across participants), so participants were again performing the comparison task on one notation only. Primes were demonstrated to be unconscious, so they were also aware of one notation only. A prime-target distance effect was present in this case (reported in Van Opstal et al. 2005b). Further detailed analysis of this effect showed a significant cross-notation prime-target distance effect when primes were Arabic and targets were verbal (F(1, 21) ¼ 8.59, p , .01). The prime-target distance effect was not significant when primes were verbal and targets were Arabic (F(1, 21) ¼ 1.64, p ¼ .21), perhaps because verbal stimuli less easily survive visual masking (cf. Reynvoet & Ratinckx 2004). Whatever the reason, these priming studies demonstrate cross-notational, semantic priming even under circumstances in which participants do not consciously perceive the prime notation during the whole experiment. To sum up, interactions of an experimental factor like distance with notation, format, and modality are not informative with respect to the existence of an abstract coding system; cross-notation priming effects are, and they demonstrate that such a system exists. ACKNOWLEDGMENTS We thank Filip Van Opstal for executing the analysis reported here. This commentary was supported by grant P6/29 from the Interuniversity Attraction Poles program of the Belgian federal government

Beyond format-specificity: Is analogue magnitude really the core abstract feature of the cultural number representation? doi:10.1017/S0140525X09990884 De´nes Szu´´cs, Fruzsina Solte´sz, and Usha Goswami Centre for Neuroscience in Education, University of Cambridge, Cambridge CB2 8PQ, United Kingdom. [email protected] http://www.educ.cam.ac.uk/people/staff/szucs/ [email protected] [email protected] http://www.educ.cam.ac.uk/people/staff/goswami/

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Abstract: The issue of abstractness raises two distinct questions. First, is there a format-independent magnitude representation? Second, does analogue magnitude really play a crucial role in the development of human mathematics? We suggest that neither developmental nor cultural studies support this notion. The field needs to redefine the properties of the core number representation as used in human arithmetic.

Can magnitude really be considered the core abstract defining feature of numbers as cultural products? We argue here that developmental and other evidence is against this notion. We agree with Cohen-Kadosh & Walsh (CK&W) that numerical representation is primarily not format-independent. However, we propose that a clear distinction must be made between an evolutionarily grounded sense of approximate magnitude (Dehaene 1997) and a different, culturally acquired, abstract number concept. We propose that what the field requires are criteria to define the abstractness of the number representations as used by humans in mathematics. In support of CK&W, data of our own suggest that numerical coding is dependent on surface format. Szu´´cs and Cse´pe (2004) presented two numbers (N1 and N2) using consecutive visual presentation. Participants were asked to add the numbers and to decide whether or not the proposed sum was correct. N1 could be presented as an Arabic digit or as a visual word, or acoustically as a heard number word. N2 was always an Arabic digit. The modality of N1 had a systematic effect on the amplitude of event-related brain potentials measured at N2. These data suggest that N1 was not translated into a common abstract number representation. Rather, N1 was retrieved from modality-specific stores when needed. Alternatively, both abstract and modality-specific stores may be involved in coding numbers. Similarly, the functional magnetic resonance imaging (fMRI) evidence to date does not necessarily provide clear evidence for a core common magnitude representation. Current imaging studies may map the comparison process rather than overlapping representations. For example, the most frequently used marker of the putative magnitude representation is the numerical distance effect. Phenomenologically similar distance effects with various stimulus materials do not in themselves imply a single underlying neural representation. Specifically, Pinel et al. (2004) have shown that comparing numbers and physical size results in overlapping distance effects in terms of brain activity. Hence, they assume a shared representation for numerical and physical magnitude. But it may be the processes operating on these representations that overlap in terms of brain activity. Number magnitude and physical size may be represented in non-overlapping brain areas, with overlapping brain areas involved in the process of size comparison rather than the representation of abstract magnitude. Indeed, fMRI distance effects are rarely constrained to the intraparietal sulcus (Szu´´cs et al. 2007). Hence, a single abstract representation is difficult to define in terms of a simple anatomical hypothesis. As CK&W note, neural adaptation studies do not provide unambiguous evidence either. Neural adaptation studies supporting an abstract magnitude representation are based on repetition priming and do not require participants to carry out comparisons. This research design excludes confounds related to comparative activity. However, a problem inherent to adaptation paradigms still remains. As Naccache and Dehaene (2001a, p. 967) state, this is a “general problem of potential strategical or attentional changes elicited by the awareness of repetition.” Hence, “ideally experimental designs based on the priming method should prevent subjects from becoming aware of the presence of repeated versus non-repeated trials” (p. 967). In other words, in number adaptation paradigms participants may direct attention to the numerical dimension, even if they are instructed not to. Hence, adaptation results will be confounded by simple change detection effects. Such confounds are especially likely when participants are instructed explicitly to

Commentary/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes “pay attention to the quantity conveyed by the stimuli” (Piazza et al. 2007, p. 303) or when symbolic numbers are used (Cohen Kadosh et al. 2007b). A published exception is the study of Naccache and Dehaene (2001a), which used symbolic stimuli and combined the adaptation paradigm with masked priming, so that participants were not aware of any stimulus repetitions. However, this result to date remains unreplicated. Developmentally, it is important to ask whether a sense of magnitude is actually important in order to carry out successful arithmetic. So far, developmental studies have demonstrated that magnitude comparison performance does not correlate with early arithmetic skills beyond 3– 4 years of age (Brannon & Van de Walle 2001; Mix 1999; Mix et al. 1996; Rousselle et al. 2004). This raises the possibility that magnitude discrimination skills do not play a crucial role in the development of the cultural number concept. For example, Halberda et al. (2008, p. 666) claimed that magnitude comparison skill in ninth grade “retrospectively predicted” symbolic maths performance. Hence, they concluded that the magnitude representation “may have a causal role in determining individual maths achievement.” However, this inference is problematic, as magnitude comparison was measured at age 14, whereas arithmetic performance was measured between ages 5 and 11. Hence, it is equally possible that better mathematics skills caused better magnitude performance. This conclusion is actually supported by the data from Amazonian Indians. These data showed that Indians have marginally worse magnitude discrimination skills than adults educated in Europe (Pica et al. 2004). It seems unlikely that Amazonian Indians are worse in symbolic maths than Europeans because their number sense is genetically limited. A more plausible explanation would be that Europeans’ number discrimination skills are better because they are educated. In fact, if we assumed that there was no difference between Indians and Europeans (given that the difference was marginal), the conclusion would again be that number discrimination skills have no relationship to mathematical skills (as the latter would be expected to be better in educated Europeans). Therefore, both methodogical and theoretical problems surround the notion of an abstract number representation. Furthermore, a distinction may be needed between an evolutionarily grounded approximate sense of magnitude (Dehaene 1997), whether abstract or not, and a distinct, culturally acquired abstract number concept. CK&W cite Barsalou (2003), “abstraction is simply a skill that supports goal achievement in particular situations” (p. 1184). Given that the goal of mathematics education is to teach children an abstract number concept, the real question would seem to be whether this putative abstract core number representation bears any relation at all to the analogue magnitude representation. ACKNOWLEDGMENTS De´nes Szu´´cs was supported by the Hungarian Research Fund (T049345). Fruzsina Solte´sz and Usha Goswami were supported by the ANALOGY project (NEST program, contract 29088) funded by the European Comission.

In search of non-abstract representation of numbers: Maybe on the right track, but still not there doi:10.1017/S0140525X09990896 Joseph Tzelgova,b and Michal Pinhasb a Department of Psychology, Achva Academic College, M. P. Shikmim, 79800, Israel; bDepartment of Psychology, Ben-Gurion University of the Negev, BeerSheva, 84105, Israel. [email protected] [email protected] http://bgu.ac.il/tzelgov/

Abstract: We agree that the default numerical representation is best accessed by probing automatic processing. The locus of this representation is apparently at the horizontal intraparietal sulcus (HIPS), the convergence zone of magnitude information. The parietal lobes are the right place to look for non-abstract representation of magnitude, yet the proof for that is still to be found.

Cohen Kadosh & Walsh (CK&W) focus on the mental representation of numbers. They do not state it explicitly, but it is clear from their argument that they are interested in the default internal representation of an external stimulus that corresponds to a specific magnitude. It should be distinguished from “working representations” generated to perform specific tasks. This default representation symbolizes magnitude as stored in semantic memory and is sometimes described in terms of the “mental number line” (e.g., Restle 1970). The authors suggest that the locus of this representation is in the parietal lobes and propose that it is best probed by automatic processing of numerical information. The authors review the existing data and conclude that it does not allow a conclusion in favor of an abstract representation of numerical information. As an alternative, they propose that numerical processing starts with non-abstract representation (coded by different neuronal populations for different categories/modalities of inputs) in the parietal lobes, which is automatic in the sense of not being affected by task requirements. Abstract representations may emerge later in the prefrontal cortex (PFC) as a result of the task requirements. Whatever the representation of numerical information in the brain is, it codes the relevant features of the mental number line, such as the increased discriminability between magnitudes farther away from each other, known as the distance effect, and, for a given intra-pair distance, better discrimination for pairs of small numbers, known as the size effect (e.g., Moyer & Landauer 1967). The size congruity effect (SiCE) is frequently used as a marker of automatic processing of numerical information (e.g., Tzelgov & Ganor-Stern 2005). It refers to shorter latencies of physical size decisions when the presented physically larger number is also numerically larger (congruent condition, e.g., 5 3) than when it is numerically smaller (incongruent condition, e.g., 3 5). The SiCE increases with the intra-pair numerical distance (e.g., Tzelgov et al. 2000), and is larger for numerically smaller pairs (Cohen Kadosh et al. 2008g, but see Van Opstal et al. 2008; Verguts & Van Opstal 2008; Verguts et al. 2005). Thus, conceiving magnitudes means activating the mental number line and mapping the specific magnitudes on it. We do not believe that representation of magnitudes in general, and numbers in particular, can be reduced to the neural activation of specific populations of neurons. Another definition of the representation of magnitudes would be in terms of the relevant neural circuit activated when information in a given domain (e.g., numerical) is processed. Dehaene et al. (2003) pointed out that the horizontal intraparietal sulcus (HIPS) is activated by numbers independently of their notation, and proposed it as the neuronal locus of the mental number line. Thus, while specific populations of neurons are the locus of activation of feature detectors for different kinds of stimuli corresponding to magnitudes, it seems to us that the HIPS is a possible candidate for the convergence zone (Damasio 1989) for magnitude information. It follows that even if different populations of neurons fire for different kinds of inputs, magnitude is represented once the HIPS is activated. In this sense, the network resulting from the convergence of the stimulus-specific neuron populations, corresponding to various kinds of quantities and numbers in various notations, whose activation converge in the HIPS, generates what Barsalou (1999; 2005) calls a simulator. It simulates the “mental number line,” and while it may be based on perceptual symbols (Barsalou 1999), it summarizes the magnitudes specifically coded by the various populations of neurons. In this sense, while the automatically probed numerical representations may be non-abstract in the sense of being based on the firing of different population of neurons, they are BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Commentary/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes “abstract” in the sense of summarizing the different inputs by the HIPS. Although, according to CK&W, the existing data do not allow for a clear conclusion in favor of an abstract representation, they do not support the opposite conclusion, either. Only numbers that are stored in memory as part of the mental number line can be automatically activated, that is, retrieved from memory without intentional effort (Logan 1988; Perruchet & Vinter 2002). According to findings from our lab, the set of numbers included on the mental number line is quite limited. It seems that the mental number line represents only singledigit positive integers, that is, it does not include two-digit numbers (Ganor-Stern et al. 2007), negative numbers (Tzelgov et al. 2009), or fractions (Kallai & Tzelgov, in press). Thus, the single-digit positive integers may be considered as the “primitives” of numerical cognition, and are automatically accessed (or “retrieved from memory”). The representations of numbers that are not part of the mental number line are generated on-line, when needed, by intentional operations. They are generated as part of “working representations,” as a result of intentionally applying task-relevant operations on the “primitives” included on the mental number line. The prefrontal cortex is apparently active in this process, as it is in additional operations that involve numbers, such as arithmetic (Ansari 2008). Therefore, neural activity in the prefrontal cortex reflects the working representations heavily loaded by the task requirements. Thus, while we agree with CK&W that probing automatic processing should provide the answer to the question of whether the representation of numerical information is abstract, we emphasize that this should be done by analyzing the numbers that are members of the mental number line. The data that one can accumulate according to these criteria, at this point are not strong enough for the rejection of a hypothesis of abstract representation of numerical information.

Numerical representations: Abstract or supramodal? Some may be spatial doi:10.1017/S0140525X09990902 Giuseppe Vallara,b and Luisa Girellic a Universita` degli Studi di Milano-Bicocca, Dipartimento di Psicologia, Edificio U6, 20126 Milan, Italy; bNeuropsychological Laboratory, IRCCS Istituto Auxologico Italiano, 20122 Milan, Italy; cUniversita` degli Studi di Milano-Bicocca, Dipartimento di Psicologia, Edificio U9, 20126 Milan, Italy. [email protected] http://www.psicologia.unimib.it/03_persone/ scheda_personale.php?personId¼92 [email protected] http://www.psicologia.unimib.it/03_persone/ scheda_personale.php?personId¼62

Abstract: The target article undermines the existence of a shared unitary numerical format, illustrating a variety of representations. The “abstract”/ “not-abstract” dichotomy does not capture their specific features. These representations are “supramodal” with respect to the sensory modality of the stimulus, and independent of its specific notation, with a main role of spatial codes, both related and unrelated to the mental number line.

In their article Cohen Kadosh & Walsh (CK&W) review an extensive psychological and cognitive neuroscience literature, with the aim of showing that, contrary to the dominant view put forward by McCloskey (1992) and Dehaene et al. (1998a), numeric representations are primarily not abstract. The process of abstraction of numbers has a long story (Schmandt-Besserat 1999), starting circa 8000 B.C . from a one-to-one correspondence between three-dimensional tokens (e.g., an ovoid) and units (e.g., a jar of oil), and finally developing, through successive stages, into the current “abstract” numerical representation, which is

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discussed by CK&W. What CK&W mean by “abstract” is that the relevant representation conveys information only related to the size of the numbers involved, independent of the particular number notation (symbolic: number words or Arabic digits; non-symbolic: e.g., dot patterns), and of the sensory modality of presentation of the stimuli (auditory, visual, somatosensory) (Libertus et al. 2007). Over and above its semantic nature, the specific format of such an “abstract” numerical representation has been regarded as primarily propositional by McCloskey (1992), while Dehaene et al. (1998a) have emphasized its spatial characteristics. CK&W’s review, more than focusing on what is promised by their title (“Numerical Representation: Abstract or not Abstract?”), presents evidence drawn from a variety of experimental paradigms to the effect that, under specific experimental conditions and task requirements, different numerical representations may be generated. The conclusion here is that “multiple” representations versus a “single” or “shared” numerical representation exist in the brain. More specifically, CK&W suggest that a shared numerical representation does not exist as default, but may result by connecting on-line multiple representations only when intentional processing of numbers occurs. This shared versus multiple numerical representation distinction, however, speaks little as to the abstract/non-abstract dichotomy, unless the relevant representational formats are specified. In particular, as CK&W note, it is generally assumed that the occurrence of a behavioral effect, as for example the SNARC effect, across different notations (Nuerk et al. 2005), speaks in favor of a unique numerical “abstract” representation. The fact that the SNARC effect is independent of notation or modality may well suggest that it comes from the activation of a unique “supramodal” representation – but this says little about its abstractness. For example, in the experiments by Ba¨chtold et al. (1998), the observation that the SNARC effect is preserved when numbers are conceived as distances on a “ruler,” but reversed when they are conceived as hours on a “clock-face,” suggests the existence of distinct numerical representations. These results indicate that the involved representation is primarily “spatial,” rather than “abstract,” as shown by the observation of a SNARC (“ruler” condition), and of a reversed-SNARC (“clock-face” condition) effect, as well as flexible enough to be modulated by the experimental instructions (i.e., ruler, mental number linerelated, vs. clock-face). Accordingly, Ba¨chtold et al. (1998) discuss their results in terms of spatial stimulus-response factors, which may be conceived as analogical processes, rather than with reference to “abstract” versus “non-abstract” codes. Other studies suggest the existence of “supramodal,” “nonabstract” numeric representations, independent of the mental number line, and affecting spatial processes. De Hevia et al. (2006), using a manual line bisection paradigm, found that neurologically unimpaired participants displace the subjective midpoint of lines and of unfilled spaces, flanked by two different Arabic numbers (e.g., 2 – 9, 9—2) towards the larger digit, independent of its left-sided or right-sided position. This effect is not modulated by numerical distance, making unlikely an interpretation in terms of mapping onto a mental number line. These findings may be accounted for by the hypothesis of a “cognitive illusion,” largely independent of the allocation of attentional resources, whereby visually presented larger digits are associated with an expansion of the closer portion of space, be it a segment or an empty space. This “position of the larger number” effect reflects the processing of relative numerical magnitude, since the bisection of horizontal strings composed by larger or smaller digits (i.e., absolute numerical magnitude) does not modulate bisection according to a mental number line effect, namely, with leftward/rightward errors associated with smaller/larger numbers, as found by Fischer (2001). In a later study, de Hevia et al. (2008) extended these findings that larger numbers are associated with an expansion of spatial extent, using a task whereby participants were required to reproduce

Commentary/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes the perceived length of an empty space, delimited by pairs of smaller/larger digits. De Hevia and Spelke (2009) have recently replicated and extended these findings, using not only pairs of visual digits flanking a line, but also non-symbolic visual displays, for example, with nine smaller circles denoting a larger numerical magnitude, and two larger circles a smaller magnitude. With nonsymbolic displays, adult participants, young school (7-years-old), and preschool (5-years-old) children show a line bisection bias towards the larger numerical magnitude. With symbolic cues (digits), the deviation towards the side of the larger digit is present in adult participants, but not in 7-year-old children. Taken together, these findings suggest the existence of a “supramodal” (i.e., independent of the particular format of the stimulus) representation of numerical magnitude – unrelated to the mental number line – which modulates spatial representations. With reference to the operational definition adopted by CK&W, this representation is “abstract,” being accessed by different notations. We would however qualify this representation – present as early as in 5-year-old children – as “supramodal” or, more precisely, “notation-independent,” and closely related to, or possibly overlapping with, spatial representations. In conclusion, CK&W’s review is definitely successful in showing that multiple numerical representations exist. The empirical data we have briefly reviewed here, however, indicate that the “abstract”/“not-abstract” dichotomy is too general to capture the variety of possible supramodal numerical representations, to which spatial codes provide a main format.

Do infants count like scientists? doi:10.1017/S0140525X09991038 Andreas Wiefel,a Sabina Pauen,b and Michael Dueckc a

Clinic for Child and Adolescent Psychiatry, Charite´-Universita¨tsmedizin Berlin, D-13353 Berlin, Germany; bDepartment for Developmental Psychology, University of Heidelberg, D-69117 Heidelberg, Germany; cDepartment for Anaesthesiology and Operative Intensive Care, University of Cologne, D-50937 Ko¨ln, Germany. [email protected] http://kjp.charite.de/patienten/baby_und_kleinkindsprechstunde/ [email protected] http://www.sabina-pauen.de [email protected] http://cms.uk-koeln.de/anaesthesiologie/content/index_ger.html

Abstract: We discuss methodological problems and present our own empirical data on calculation tasks in toddlers. We propose to develop enriching theoretical models concerning quantity representations, based on empirical findings from developmental psychology. A revitalization of the debate is worthy, because it is reminiscent of the philosophical dispute on universal entities in scholasticism and Plato’s theory of ideal numbers.

Cohen Kadosh & Walsh (CK&W) brilliantly discuss methodological and theoretical limitations of neurophysiological evidence supporting the claim that numerical representation is abstract. However, this reasoning can also be applied to their own arguments: 1. Finding no difference in BOLD signal intensity in functional magnetic resonance imaging (fMRI) studies between different modalities (“null result”) may be due to a lack of statistical power. However, even by increasing the statistical power (i.e., increasing the number of subjects, or the intensity of the paradigm, respectively), thus potentially resulting in a significant difference in BOLD signal between different forms of input, would not necessarily imply a relevant notation-dependent cortical output (Logothetis 2008). 2. Single-cell neurophysiology does not solve the problem of reduced spatial resolution of fMRI experiments, because only a small portion of neurons in a specific brain region can be explored using this technique.

3. Although single-cell physiology is used in clinical settings (e.g., Engel et al. 2005), single-cell experiments are not yet applicable to humans. Thus, this method cannot yield direct evidence of a non-abstract numerical representation in the human brain. 4. The fact that CK&W address single neurons as abstract or non-abstract neurons is questionable. First, any understanding of abstract representations as neuronal populations that are insensitive to the form of input does not imply the existence of abstract neurons. Second, how do the authors classify a mental representation localized in a specific brain region, including abstract and non-abstract neurons that are highly co-located? Despite these methodological concerns, we share the authors’ doubts that an abstract number representation exists in the human brain. According to recent developmental approaches, preverbal infants, as well as monkeys, have two different systems for representing quantitative information: one system for small numbers of objects that can be tracked over space and time, and one system that represents large, approximate numerosities (Spelke 2000). Both systems are independent of verbal information processing and apply to different sensory modalities, stimuli, and task contexts. In that sense, one could say that they are abstract. But this is not the type of abstract representation that CK&W talk about. The authors focus on an adult number concept. In order to communicate about number representations in an adult-like way, young children must learn to (a) abstract the general meaning of number words as representations for quantities, (b) say number words in the correct sequence, (c) identify number symbols, and (d) associate words as well as digits with exact quantities. To form some sense of a number scale, they also need experience in bringing exact quantities in a linear order. Children who have already acquired basic counting skills cannot yet solve mathematical equations, but are able to solve the same problems using less abstract representational formats. This can be illustrated by data from our own laboratory (Pauen, in preparation). A study with 138 4–5-year-olds tested performance on simple addition problems involving small numbers (x , 10). Four different task formats were presented: (1) Real objects: Children were shown two groups of objects and were asked, “How many marbles are there together?” (2) Object words: No object was presented, but children were asked the same kind of question as before, combining object and number words, for example, “How many are one banana and five bananas together?” (3) Number words only: For example, “How many are three and three together?” As revealed by our Figure 1, performance systematically varied with task format. Performance was highest when real objects were presented, lower for questions combining object and number words, and very low when only number words were involved. These findings illustrate that number operations strongly depend upon how numerosities are presented at preschool age. With the beginning of elementary school training, task format gradually loses importance and children learn to flexibly shift from one format to another. Based on developmental research, one can conclude that there is no such thing as an innate abstract representation for exact numbers in terms of their representation format (words, digits, quantities). The cognitive subsystems involved in processing different types of numerical information seem to be distinct at the beginning. They become gradually associated as a result of repeated exposure to simultaneous presentation of different representation formats (e.g., number words combined with specific object quantities and/or digits). In summary, we argue that two distinct innate systems representing small numbers of objects and large quantities may exist, and that they are not tied to any verbal or visual symbols of numbers (Spelke 2000). Hence, they are abstract in a different sense than that defined by CK&W. A more elaborate representation of exact numbers evolves by forming associations between exact quantities and symbolic systems identifying digits and numbers during preschool years. BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Response/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes Abstract: The commentators have raised many pertinent points that allow us to refine and clarify our view. We classify our response comments into seven sections: automaticity; developmental and educational questions; priming; multiple representations or multiple access(?); terminology; methodological advances; and simulated cognition and numerical cognition. We conclude that the default numerical representations are not abstract.

Figure 1 (Wiefel et al.). Mean number of correct answers for two simple addition problems presented in three different task formats (real objects, object words, number words).

Based on this conclusion, we think that the work of CK&W could be extended by taking into account a developmental (ontogenetic) perspective. Could it be useful to combine the authors’ theoretical approach with the knowledge about the emergence of representation in infancy? This might mean that a representation of quantities is more basic than a representation of exact numbers. Fonagy and Target (2003) claim that we need “something more” than knowledge about cognitive-behavioral pathways for understanding representations/mentalization in general. This could be a key to understanding why neuroimaging alone does not reveal how numbers/quantities are represented in the human mind. May the results from paradigms of preferential looking in the newborn and early infancy period (infants love “A” more than “B”; e.g., Meltzoff 1990) represent the pre-existence of abstract quantities? Could this be reminiscent of the philosophical dispute on universal entities in scholasticism (“universalia sunt ante res”)? This question is associated with Plato’s theory on the existence of ideal numbers. The Renaissance of this in Neo-Platonism contributes to the current scientific debate. It could be enriched by further trans-disciplinary research between neuroscientists, developmental psychologists, clinical practitioners, and philosophers.

Authors’ Response Non-abstract numerical representations in the IPS: Further support, challenges, and clarifications doi:10.1017/S0140525X09990987 Roi Cohen Kadosh and Vincent Walsh Institute of Cognitive Neuroscience and Department of Psychology, University College London, 17 Queen Square, London WC1N 3AR, United Kingdom. [email protected] http://www.ucl.ac.uk/neuroscience/ Page.php?ID¼12&ResearcherID¼238 [email protected]# http://www.icn.ucl.ac.uk/Research-Groups/Visual-Cognition-Group/ index.php

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So, do we represent numbers non-abstractly? We appreciate the tone and the quality of the commentaries on our target article in general. The commentators provided us with a mixed view: Only 7 commentators defend the abstract view, 11 commentators are agnostic and their arguments tend toward the non-abstract representations or abstract representation, and 10 commentators support the idea that numerical representations are non-abstract. Clearly, our view has facilitated an important debate. In this response, we integrate the different positions, explain why some of the arguments against the nonabstract view are invalid (mainly based on clarifications of arguments that we provided in the target article), and conclude that the default representations of numbers are non-abstract. R1. Automaticity Algom raised important concerns, and contentious topics. Before dealing with his main points, we would like to point out several places in his commentary where our perspective was extended to places that we did not state in our article. It might be that we were not clear enough on these topics in our article, and for some of the readers these misinterpretations might be minor, but we would like to state them for the sake of theoretical clarity. We neither said nor believe that numerical magnitude is processed automatically whenever a numeral is presented for view. This is a very strong definition of automaticity, and Algom and others have shown that such a definition of automaticity does not hold. We also did not state that Stroop-like tasks are the best behavioural tasks to reveal the effect of notation on numerical magnitude. We do believe that there are some advantages for using this paradigm (and also some disadvantages). Cohen and Algom describe findings by Cohen (2009), in which the physical shape, rather than the numerical magnitude, was processed. There is no reason to be surprised by this result. If the physical shape is more salient than the numerical magnitude, it will mask the effects of the numerical magnitude. We expect that the reverse will be obtained if the numerical magnitude is made more salient using the same paradigm. The other point that Algom mentioned is one raised some years ago, researched extensively, and we believe, refuted. Algom states that, virtually all studies that demonstrated the effect (of task-irrelevant numerical magnitude on judgments of physical size [i.e., size congruity effect]) used a design that favored the numerical over the physical dimension in the first place. Thus, more values of number than values of physical size were typically presented (indeed, most studies used merely two values for size: large, small) [termed variability]. Moreover, the numerals were easier to discriminate from one another than their physical sizes [termed discriminability]. (Our explanations added to Algom’s in square brackets.)

Response/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes These are potential problems that Algom has raised previously (Algom et al. 1996; Pansky & Algom 1999; 2002), and that were ignored by some researchers, including us (Cohen Kadosh et al. 2007d; Girelli et al. 2000; Henik & Tzelgov 1982; Rubinsten et al. 2002; Tzelgov et al. 1992). However, recently we examined whether the factors discriminability and variability affected the size congruity effect. We found that modulating these factors does not affect the size congruity effect, even when they are completely biased toward the other dimensions in discriminability or variability, and the size congruity, in contrast to Algom’s arguments, does not disappear (Cohen Kadosh et al. 2008e). Furthermore, a careful examination of Algom and colleagues’ previous studies reveals that the size congruity effect disappears when only two numbers are being presented (Pansky & Algom 1999). This limited amount of stimuli increased the chance for response repetition, thus creating a confound. Cohen Kadosh, Gevers, and Notebaert (submitted a) examined this issue, and found that the size congruity effect disappears when the response sequence of the irrelevant, rather than the relevant dimension, is repeated. In light of the issues that we raised here, we disagree with Algom’s theoretical perspective. Variability and discriminability play little role in the appearance of the size congruity effect, and other factors, such as response repetition (or processing speed; Cohen Kadosh et al. 2008e) that were confounded with variability and discriminability in some experiments, might diminish the size congruity effect. Our view of automaticity, however, is compatible with Algom. We agree with Algom that automatic processing and intentional processing are not dichotomous, but are end-points of a fine-grained continuum, and that numerical magnitude is not activated in an automatic fashion on an unlimited scale (see also, Schwarz & Ischebeck 2003; Tzelgov & Ganor-Stern 2005). Algom’s concern from the adaptation paradigm is partly justified (as we mentioned in sect. 11). Namely, he suggests that some features of the experimental situation might encourage numerical processing, and this is totally compatible with our claims in the target article, as we suggested that the specific instructions by the experimenters might lead to different patterns of activation (see also, Piazza et al. 2007). In addition, other non-numerical factors should be controlled, as was done in other studies (Ansari et al. 2006a; Cantlon et al. 2006; Cohen Kadosh et al. 2007b), and preferably the level of activation in the parietal lobes should be modulated by numerical quantity factors (e.g., numerical deviation from the adapted quantity; Ansari et al. 2006a; Piazza et al. 2004; 2007). However, stating that a passive viewing task is a suboptimal tool to explore neuronal specialization is overstating the case. Passive viewing is just another task, and one should not use a single approach to characterize how cognitive processes are operationalized, and how the brain is organized. This seems to be a general problem that many commentators such as Orban; Wiefel, Pauen, & Dueck (Wiefel et al.); Mayo; and Freeman & Kozma have criticized (e.g., paradigm/technique x is not suitable) or praised (e.g., paradigm/technique y is the solution) (see sect. R6). However, we believe that integration and variety of different paradigms/techniques is the right approach to pursue, and our theory in the target article is not based on a single given paradigm/technique.

Other commentators are not convinced that intentional processing is inherently unsuitable for testing the effect of notations. We are puzzled by this position, as we showed that several studies (Cohen Kadosh 2008a; Dehaene et al. 2008; Droit-Volet et al. 2008; Ganor-Stern & Tzelgov 2008; Holloway & Ansari, 2009) used intentional numerical processing and still obtained different numerical quantity effects for different notations. To be accurate, we argued that non-intentional tasks are more sensitive to differences in the representations for different notations, and this is also reflected in our model (see target article, Fig. 5). Algom also provides some experimental evidence that allegedly supports the existence of an abstract representation. However, in the discussed task, both Arabic digits and verbal numbers are presented, and the task is an intentional comparison task. We cannot understand how such a design can overcome the limitations that we mentioned in our review. Moreover, the effect of the Arabic digits on verbal numbers processing was approximately twice as large as the effect of verbal numbers on Arabic digits, although the processing time for Arabic digits and verbal numbers seems to be equal. This finding is not completely in line with the abstract view, and actually is in line with the idea of multiple numerical representations, and our model. Finally, some authors consider parity a suitable measure for non-magnitude processing, for example, in priming tasks. Tzelgov and Ganor-Stern (2005) noted that the level of triggering (i.e., activation of the irrelevant dimension, in this case magnitude, provided by the experimental task) by numerical parity task is high. This is due to the fact that both dimensions are numerical and require semantic access to numerical information. Therefore, the processing of the relevant parity dimension can trigger the processing of the irrelevant magnitude dimension. This notion of triggering is also important to priming studies that are cited in the priming section. Cohen argues that numerical representations are neither abstract nor automatic. We agree with the first part of the statement and, to some degree, also with the second part. Numerical representation is not always automatic (see our reply to Algom). Different tasks will lead to different degrees of automaticity. This relates to the notion of triggering that we mentioned in the previous paragraph. The comment made by Cohen that numerical distance is one of several features that are correlated with the order of the numbers on the number line, and that researchers rarely (if ever) consider plausible alternatives to the numerical distance hypothesis is true (for similar views see Cohen Kadosh et al. 2008b; Van Opstal et al. 2008a). For example, the numerical distance effect might be affected by linguistic frequency (Cohen Kadosh et al. 2009; Landauer & Dumais 1997). However, some studies were able to limit the number of other factors that might affect the numerical distance effect (Lyons & Ansari 2009; Tzelgov et al. 2000; Van Opstal et al. 2008b), and still observed the distance effect. We believe that numerical information can be processed automatically, but further processing is required for it to affect performance (Cohen Kadosh et al. 2008e). The results by Cohen (2009) are important, and should be examined with other paradigms, and also under conditions in which the physical shape is harder to process. BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Response/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes Ganor-Stern raises important points to consider when one finds differences between notations under automatic processing, before concluding that numerical representation is not abstract. We agree with part of her comments, and considered them in previous works. For example, Cohen Kadosh et al. (2008e) found that the processing of verbal numbers differs from digits not only quantitatively, but also qualitatively. In addition, at least in size congruity tasks, slower access to abstract representation (see also Grabner and Santens, Fias, & Verguts [Santens et al.]) should have led to larger size congruity effects with the slower processed notation when it is the relevant dimension, and smaller size congruity effect when it is the irrelevant dimension (Schwarz & Ischebeck 2003), but these patterns of results were not obtained (Cohen Kadosh et al. 2008e; Ito & Hatta 2003). Therefore, speed of access to the representation cannot (fully) explain the interaction between notation and congruity. Ganor-Stern mentions that finding a size congruity for the mixed notations, as in Ganor-Stern and Tzelgov (2008), is evidence for an abstract representation. This might be the case, but a more likely explanation, in our view, is that each notation activated a separate representation and the conflict arose at the response level. This response-related explanation for the size congruity effect has support from recent studies that examined the source of the size congruity effect (Cohen Kadosh et al. 2007c; 2008d; Szu´´cs & Solte´sz 2007; Szucs et al. 2007; Szu´´cs et al., in press) (see also our remarks in response to Algom). Even the argument that the size congruity effect is obtained not only for digits, but also for verbal numbers (although the effect is qualitatively and quantitatively different), does not indicate that numbers are represented abstractly, as size congruity is obtained also for nonnumerical dimensions, for example, animals’ names (Rubinsten & Henik 2002); but it will be odd to claim that animal names shared an abstract representation with digits. This type of argument demonstrates our view that similar behavioural results do not indicate shared representation. Even if one assumes that some of the parameters that Ganor-Stern mentioned are correct, it is not apparent why she concludes that automatic numerical processing is based on an abstract representation. We nevertheless agree with Ganor-Stern that not any nonadditive difference between numerical processing of the different notations is evidence for a notation-specific representation, and the differences should be theoretically relevant to the issue in question. The results that we reviewed in Section 6 of the target article are in line with this view. Nu´n˜ez gave some examples from the productive side of cognition. We think that more research on the issue of the productive side in numerical cognition is required, and thank Nu´n˜ez for pointing out this issue. We nevertheless think that some of the examples might not be suitable for examining automatic processing. The reason, in our view, is that they do not fit with the view of automaticity, that is, they are all task-relevant, and therefore are monitored (e.g., are parts of the conversation, and therefore deliberative; Dulany 1996). Tzelgov & Pinhas suggest that although different populations of neurons are sensitive to difference numerical representations, at the level of brain area (horizontal 358

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IPS) numerical representation is abstract. We do not agree with this definition. The question is one of (spatial) resolution, and the better it is, the better one will be able to discriminate between different representations or other processes. For example, looking at Tel-Aviv and Jerusalem on a map with a scale of 1 : 30,000,000 cm one will not find any difference in the location of these cities; however, at a scale of 1 : 10,000,000 cm the differences between these cities are apparent. One would not conclude that at the more crude scale these cities are the same. The same logic can be applied when one needs to detect differences in the human brain. Another issue, as Tzelgov & Pinhas rightly pointed out, is that single-digit positive integers may be considered as the “primitives” of numerical cognition and are automatically accessed. However, the same is also true for non-symbolic numbers (Gebuis et al. 2009; Roggeman et al. 2007), and for verbal numbers (Cohen Kadosh et al. 2008e; Dehaene & Akhavein 1995).

R2. Developmental and educational questions The commentators raise very important issues about the construction of numerical representation over the course of learning and development. We are grateful for these comments, as they make the discussion much fuller and complete, and we dealt in our review mainly with adults and less with infants and children. Ansari suggests that abstract representations of numerical magnitude are a more plausible outcome of development than non-abstract representations. He claims that, “while the processes that are involved in mapping from external to internal representations may differ between stimulus formats, the internal semantic referent does not differ between representation formats.” We agree with the first part of his claim, but could not understand what is the evidence for the last part, that is, that the internal semantic referent does not differ between representation formats. Ansari further suggests that format-specificity lies in the process of mapping between different external representations, and the mapping between external representation and internal numerical representation. However, this suggestion is invalid given the experimental evidence that we provided mainly in section 6. The differences are not only in general processing speed, and the parameters that reflect the numerical representation differ quantitatively and even qualitatively both for symbolic and non-symbolic numbers. Ansari also discusses the developmental trajectory for format-independent representation, which Kucian & Kaufmann extend and for which they provide a theoretical framework that hypothesises the creation of increased format-independent representation from format-dependent representation. Kucian & Kaufmann and Ansari might be right, and further research is needed, but we suggest that: (1) this format-independent representation is partly due to maturation of the prefrontal cortex, and (2) that it is a working representation and not the default representation (and therefore it needs a mature prefrontal cortex). The results from children and monkeys (Cantlon et al., in press; Diester &

Response/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes Nieder 2007), which have a less developed prefrontal cortex (Striedter 2005; Tsujimoto 2008), support this idea. Another possibility that the commentators did not mention is that infants might have initial shared representation for numbers, but with learning, and interaction with the environment, there is a neuronal specialisation in the brain that leads to multiple numerical representations. This idea is feasible (Johnson 2001), and has been shown in other domains (Cohen Kadosh & Johnson 2007). For example, children do not show cortical specialisation for face processing and other non-facial objects. However, as a function of development and interaction with the environment, their brain becomes tuned to different categories (Johnson et al. 2009). We see no reason why numbers, which depend much more on education, and are acquired later in life, will not follow a similar trajectory of neuronal specialisation. (See also the comment by Szu´´cs, Solte´sz, & Goswami [Szu´´cs et al.].) Ansari also bases his suggestions on the recent study by Cantlon and colleagues (Cantlon et al., in press), however, this functional magnetic resonance imaging (fMRI) study involved an intentional comparison task, and therefore has the limitations that we mentioned in section 5. Moreover, the discussed study focused only on what is shared between symbolic and non-symbolic numbers, and neglected the important question of the differences between the notations, and whether children show more evidence of the existence of non-abstract representations than adults. However, as this study suffers from the limitations that we discussed in section 5 (e.g., the insertion of response selection to the experimental task, spatial resolution), we are not sure if it is the most optimal study to shed light on this question. An important point Ansari mentions is that, “If the proposal by CK&W is indeed correct, then the current models of the development of numerical magnitude representations need to be radically revised,” and that “children cannot use their semantic representation of number words in order to begin understanding the meaning of Arabic digits.” Therefore, this may have educational repercussions and lead to less focus on the relationships between different formats of representations in the classroom. However, cognitive psychologists have shown that humans are able to learn artificial digits to a high level of expertise, and show numerical effects, even without any connection to numerical information, symbolic or nonsymbolic (Tzelgov et al. 2000). This might suggest that it is not necessary to map one numerical notation to another in order to have intact numerical understanding. Moreover, it might be that this mapping is even maladaptive. For example, children with visuospatial impairments might suffer from mapping digits to numerosity, or children with dyslexia might have similar problems if required to understand digits by mapping them to verbal numbers. At this stage, our discussion is purely theoretical, but a better understanding might be able to shed light on the connection between visuospatial impairment and dyscalculia (Rourke 1993), as well as dyslexia and dyscalculia (Rubinsten & Henik 2009). Cantlon, Cordes, Libertus, & Brannon (Cantlon et al.) (see also Nu´n˜ez) argue that the stipulation that numerical abstraction requires identical responses in identical neurons is potentially impossible to satisfy. We find this statement paradoxical, since Cantlon and colleagues

stated recently that, “different quantitative dimensions can be represented by generic magnitude-coding neurons” (Cantlon et al. 2009, p. 89). For other nonnumerical features in the ventral stream, it is also possible (e.g., Sawamura et al. 2006). Cantlon et al. argue that even if it is possible to satisfy this criterion (see Diester & Nieder [2007] for fulfilling this criterion for numerical representation in the prefrontal cortex), it is not clear whether it is the appropriate criterion for establishing numerical abstraction. We would like to thank Houde´ for his suggestion that the initial numerical representation is not abstract, and that abstract numerical representation is gained through inhibition processes. This leads to support for our suggestion that abstraction is created intentionally, but does not exist as a default representation, or, in Tzelgov & Pinhas’s terminology, it is a “working representation.” The involvement of inhibitory operations is subserved by prefrontal cortex maturation (Tsujimoto 2008; Wood et al., in press), and therefore, the involvement of prefrontal cortex in creating an abstract representation is also in line with our dual-code model. Houde´ provides important evidence that children up to the age of 7 years confuse the layout of the display with the numerical estimation. Kucian & Kaufmann provide another example from 3-year-old children, who seem to rely on perceptual cues if the ambiguity between numerical and non-numerical stimulus properties is overwhelming (Rousselle et al. 2004; cf. Hurewitz et al. 2006, for evidence with adults; but see Gebuis et al. 2009). Wiefel et al. present data on calculation tasks in toddlers showing that number operations strongly depend upon how numerosities are presented at preschool age. Elementary school education teaches the children to flexibly shift between the different numerical notations. Future studies should examine whether this shift is due to maturation of the prefrontal cortex, expertise, and education. However, these results, as well as others that were mentioned in this section, are in contrast to Cantlon et al.’s argument against the existence of non-abstract representations in early developmental stages. We would like to thank Peters & Castel for highlighting the influence of the nature of numerical representation, whether intentional or automatic, on decision-making. Indeed, this will generate a new area of research that will elucidate the significance of numerical representation in everyday decisions. Another important comment is that, to have a better understanding of numerical representations, researchers need to examine this question in connection with individual use of numbers. Will high expertise with numbers be associated with non-abstract representation, or vice versa? We believe that this question will be of interest for cognitive psychologists and developmental psychologists. Rosenberg-Lee, Tsang, & Menon (RosenbergLee et al.) highlight the scenario in which various numerical notations exploit magnitude-processing capacities in the IPS to different degrees. More specifically they suggest, based on behavioural, neuroimaging, and single-cell neurophysiology studies, that at a first stage, different numerical notations are encoded in the IPS in a non- magnitude-dependent fashion. As a function of experience these non-magnitude representations become involved in automatic analogue magnitude BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Response/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes representations. This is a powerful prediction, and as suggested by Rosenberg-Lee et al., future studies that will use learning paradigms and longitudinal developmental research will shed light on this developmental hypothesis. One interesting question is how different hemispheres are influenced by these developmental trajectories. Why, in Cohen Kadosh et al. (2007b), did the right IPS not show adaptation for verbal numbers (which is in line with Rosenberg-Lee et al.’s suggestion), while the left IPS did show an adaptation? Szu´´cs et al. emphasize the educational perspective in numerical cognition. They make a clear distinction between an evolutionarily grounded sense of magnitude and a culturally acquired abstract number concept. They further suggest that developmental and cultural studies do not support the idea of format-independent numerical representation. They also raise another issue that is of high importance: whether numerical representation causes better math skills, and vice versa, or whether there is any correlation between these two abilities at all. We believe that further studies are needed to examine this issue, which at the moment shows more support for the connection between numerical abilities and math skills (Booth & Siegler 2008; Rubinsten & Henik 2009) In contrast to the nativist approach that is dominant in the field of numerical cognition, Kucian & Kaufmann base their discussion on “neural constructivism” – which suggests that the representational features in the human neocortex are dynamic and influenced by interactions between neural growth mechanisms and environmentally derived neural activity. This view is also in line with the suggestions made by Szu´´cs et al. We are more sympathetic to this approach; numerical skills that are heavily influenced by education and environment (e.g., Hung et al. 2008; Tang et al. 2006b) will probably be modified as a function of development and training. After Kucian & Kaufmann provided evidence for non-abstract numerical representations from studies that include children with typical and atypical development, they presented a model that describes the overlap between different numerical representations as a function of age, experience, and schooling. We found this model stimulating, and it emphasizes the dichotomy in the field of development on numerical representation: Kucian & Kaufmann, Wiefel et al., Ansari, and Houde´ suggest that the numerical representation at early developmental stages is non-abstract, whereas Cantlon et al. suggest that the numerical representation de novo is abstract. On the whole, it seems that commentators from the field of developmental psychology/neuroscience did not reach a consensus, but most of the commentators supported the existence of non-abstract representations. One should note that the computational model by Verguts and Fias (2004) assumes abstract representation by training digits and non-symbolic numbers together (thus also biases the model from the beginning toward abstract representation). In light of the comments in this section, it seems that this model should examine different methods for learning and development of numerical representations. In sum, we are happy to trigger such a scientific disagreement and hope that future studies will shed further light on this issue. 360

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R3. Multiple representations or multiple access? Grabner emphasizes the importance of considering symbol-referent mapping expertise in theories of numerical representation. We agree with his suggestion, and believe that such an approach can provide better understanding of learning, education, and development, and in addition, provide knowledge on how the different representations can be created and modified as a function of symbol-referent mapping. We would like to stress that, in our case, the differences between numerical representations cannot stem from differences in the access to the numerical representation. In this scenario, one would find differences in the overall processing time and/or accuracy, but not different numerical representation-related effects for different notations (e.g., different Weber-ratio: Droit-Volet et al. 2008; mapping of number into space: Dehaene et al. 2008; distance effect: Cohen Kadosh et al. 2008e; Ganor-Stern & Tzelgov 2008; Holloway & Ansari 2009), or size congruity effect (e.g., different facilitation, interference, and differences between incongruent and congruent conditions: Cohen Kadosh et al. 2008e; Ganor-Stern & Tzelgov 2008; Ito & Hatta 2003). Moreover, in some cases, even when the differences in the processing time between the different notations is taken into account, this cannot explain the differential effects for different notations (e.g., Cohen Kadosh et al. 2008e). Lastly, the difference in symbolreferent mapping expertise cannot explain why, in brain imaging studies, left or right IPS is notation-sensitive, while the contralateral IPS does not reach significance (Cohen Kadosh et al. 2007b; Piazza et al. 2007). Another argument by Cantlon et al. is that the observed interactions are due to some ceiling or floor effects for one dimension but not the other. This might apply to a small fraction of the studies that we presented (e.g., Dehaene & Akhavein 1995), but cannot explain other results. The interactions between different formats and factors that originate from the mental number line include different Weber-ratios for different modalities (Droit-Volet et al. 2008), different mappings of different numerical formats on a physical line (Dehaene et al. 2008), or correlations between math abilities and performance in one numerical format, but not another format. These are all instances of evidence of non-abstract representations that are not due to floor or ceiling effects. The same holds also for the neurobiological evidence that we provided, and especially the case of double dissociation (sect. 6). Furthermore, the argument that the classification by Dehaene et al. (1999) for approximate and exact can explain our results, is not accurate. Although, we agree that there is overlap between our model and the approximate –exact numerical codes, which we originally mentioned in section 10, our model has more explanatory power. For example, our model presents a continuum rather than a binary classification to approximate and exact systems that are subserved by different brain areas. In addition, our model explains the classification between different symbolic notations, and not only between symbolic and non-symbolic notations. Dehaene’s rebuttal of the non-abstract view dismisses some of the data that we provided – which found differences between a variety of numerical formats in different

Response/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes paradigms, labs, and techniques – by calling them “weak evidence.” Dehaene’s description of the data from behavioural, neuroimaging, transcranial magnetic stimulation (TMS), and single-cell neurophysiology that showed evidence for multiple numerical representations as “occasional” also avoids serious discussion. Dehaene states that our review of findings (which he terms a “catalogue”) of difference or interaction involving number notations in support for the notation-specific view is wrong. However, looking at previous studies by Dehaene on this question shows that he bases his argument toward the abstract view by not finding differences between notation, or an interaction (Dehaene 1996; Dehaene & Akhavein 1995; Dehaene et al. 1998a; 2003). Dehaene also discusses the single-cell neurophysiology results from the prefrontal cortex, while not considering the results in the IPS that were observed in the same study (Diester & Nieder 2007). We are said to dismiss these results. However, we focus in our target article on the IPS, the key area for numerical cognition, which is highlighted by Dehaene in many papers (Dehaene et al. 1998a; 2003; 2004). It may be that Dehaene is revising his position, and now suggests that numerical abstraction is in the prefrontal cortex, rather than the parietal cortex. However, before this conclusion can be reached one has to take into account that these data were: (1) obtained after explicit training of associating digits with numerosity (e.g., 1 is one dot), and (2) in intentional task. Both of these factors might have contributed to the results that were obtained in the prefrontal cortex, as we discussed in the target article. Dehaene also gives some new unpublished data from his lab (i.e., Eger et al., submitted). It is clear from his description that the task was intentional, and we stressed in our article the limitations of using such tasks. On the other hand, it is unclear if response selection was required in this study, and moreover, the IPS decoder is still limited to the voxel level; and therefore Dehaene ignores our comment that not finding a difference between the notations does not imply that there is an abstract representation: absence of evidence is not evidence of absence; a single demonstration of a dissociation is more compelling than a failure to find evidence of segregation. Nevertheless, if one would like to seriously consider these results as indicative of abstract representation, there are two further analyses that we suggest Eger, Dehaene, and colleagues conduct: First, to show also that when trained with dots, the IPS decoder generalised to digits. Second, to examine the existence of segregation in the multivoxels pattern by using multivariate pattern analysis. Accordingly, in a recent fMR-adaptation paradigm in which subjects processed the colour of the stimuli, we found that that the numerical representation for digits and dots is subserved by overlapping multiple representations that are format-dependent (Cohen Kadosh et al. 2008a). One of the analyses that support such a view is a multivariate pattern analysis. If we are right, and indeed the task that Dehaene reported is intentional, this provides strong support for the model that we presented in section 10. Other evidence is offered showing that the classifier trained with the posterior IPS activation during saccades could be generalised to a classification of subtraction versus additional trials independent of the notation (digits, or dots) (Knops et al., in press). Reading this

work reveals that the activation that Dehaene mentions was found in the bilateral posterior superior parietal lobule (PSPL), an area that according to him and others is outside the classical areas that are involved in numerical representation per se (Cohen Kadosh et al. 2008f; Dehaene et al. 2003). Moreover, in previous works Dehaene and others considered the PSPL as involved in attention, orienting in space, and attentional selection, rather than numerical representation per se (Dehaene et al. 2003). Surprisingly, the horizontal IPS (hIPS) that has been found to be involved in numerical representation in meta-analyses by us (Cohen Kadosh et al. 2008f) and by Dehaene and colleagues (Dehaene et al. 2003), did not show a shared decoding for numerostity and digits. This point supports the idea that the shared coding for numerosity and digits did not occur at the level of the representation. We found Dehaene’s contention that the PSPL is a “cortical recycling” of a sensorimotor area for a more abstract mathematical use puzzling. This is a new argument that does not appear to be consistent with his previous position that the horizontal segment of the IPS (hIPS) is the area that is involved in abstract numerical representation and calculation (Dehaene et al. 2003; 2004), and the putative area for the cortical recycling seems to fall out of the PSPL (see Figure 2 in Dehaene & Cohen 2007). Indeed, in a meta-analysis the hIPS was found by Dehaene et al. (2003) to be involved in abstract mathematical use. As Dehaene puts it: “Those parametric studies are all consistent with the hypothesis that the HIPS codes the abstract quantity meaning of numbers rather the numerical symbols themselves” (p. 492). In a more recent meta-analysis of numerical cognition (Cohen Kadosh et al. 2008f) we found that the middle IPS is involved in numerical representation. In a comprehensive review of the literature, Dehaene identified the PSPL as “being involved in attention orienting in space, can also contribute to attentional selection on other mental dimensions that are analogous to space, such as time, space, or number” (Dehaene et al. 2003, p. 498). The differences in the coordinates of the PSPL and hIPS are too large to be ignored (more than 2 cm on the anterior to posterior axis) (hIPS: x ¼ 41, y ¼ 247, z ¼ 48 [Dehaene et al. 2003]; mIPS: x ¼ 37, y ¼ 246, z ¼ 42 [Cohen Kadosh et al. 2008f]), and PSPL: x ¼ 32, y ¼ 268, z ¼ 46 [Sereno et al. 2001). Moreover, the behavioural part (Knops et al. 2009) of the cited work is based on several important differences between symbolic and non-symbolic notations that are in line with Campbell & Metcalfe’s view. This part was not considered by Dehaene. Dehaene ignores other results that are not in line with the abstract view. For example, he claims that notation effects “occasionally” affect performance because of numerical precision. Numerical imprecision is observed with non-symbolic numbers (Izard & Dehaene 2008). However, this cannot explain the differential effects between symbolic notations (Arabic digits, Indian digits, Kana, Kanji, verbal numbers in different language), which others, including Dehaene, have observed (see sect. 6 of the target article). Another invalid argument is that the effects – for example, between digits and verbal numbers – are due to speed of processing and perception, or occur at the transcoding level. However, these factors were taken into account in previous studies (e.g., Cohen BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Response/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes Kadosh et al. 2008e), and again some effects that we mentioned cannot be explained by these factors (e.g., Cohen Kadosh et al. 2007b; Dehaene et al. 2008; Droit-Volet et al. 2008; Holloway & Ansari 2009). It is ironic that this comment is made by Dehaene, who based the abstract numerical theory partly on null differences between digits and verbal numbers (Dehaene 1996; Dehaene & Akhavein 1995). If the effects in the studies that we mentioned are due to speed of processing, or are perceptual, or occur at the transcoding level, then his earlier results should have being interpreted as evidence toward the nonabstract view. Dehaene concludes that considerable evidence points to a notation-independent representation in the monkey IPS. We ask which evidence? The only evidence is for notationdependent representation in the monkey IPS (Diester & Nieder 2007; see section 8 of the target article and Fig. 4). We agree with Dehaene that the IPS in humans and monkeys is not a module for representation, and it includes highly distributed neurons in the IPS that are intermingled with other representations of time, space, and other continuous dimensions, including numbers as proposed by Walsh (Walsh 2003), and has been tested and confirmed later by others (Cohen Kadosh et al. 2005; Pinel et al. 2004; Tudusciuc & Nieder 2007; for a review and meta-analysis, see Cohen Kadosh et al. 2008f). We do not see any reason why the principles of these distributed magnitude neurons should not be extended also for different numerical notations. Santens et al. suggest that the differences between notations in behavioural and neuroimaing studies can occur because of some divergence between the input pathways to this common representation. One should notice that the model by Verguts and Fias (2004) does not include any different pathways for different symbolic numbers, but only differentiates between symbolic and non-symbolic numbers. Moreover, none of the models (including Verguts & Fias 2004) can explain the interaction between effects that stem from numerical representation and different symbols for numbers. Therefore, we do not see any support for Santens et al.’s suggestions, even from their own studies (Santens et al., in press) and model (Verguts & Fias 2004). Some commentators argued that the effects we discussed might occur prior to the level of numerical quantity representation. Therefore, some clarification is needed. We did not intend to challenge the idea that number words and digits are processed differently at the perceptual stage – and it would be wrong to do so, since there are many studies that showed this difference in processing, including Dehaene (1996) and Schwarz and Ischebeck (2000). Therefore, we did not base our conclusions on the overall difference in reaction times (RTs) between number words and digits, which stems also from differences at the perceptual stage. Rather, the crucial point is the interaction between notation and effects that are post-perceptual and stem from the level of the numerical representation or even later. For example, many studies have shown that the distance effect is independent of the perceptual stage since it takes place at a post-perceptual stage, whether at the level of numerical representation (e.g., Barth et al. 2003; Cohen Kadosh et al. 2007c; Dehaene 1996; Pinel et al. 2001; Schwarz & Ischebeck 2000) or response selection (Cohen Kadosh et al. 2008b; Link 1990; Van Opstal et al. 2008a; 362

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Verguts & Fias 2004). Note that in the case of an interaction between distance effect and notation, it does not matter whether the locus of the distance effect is at the level of numerical representation or response selection, because response selection follows the level of the numerical representation. All studies that examined the differences between notations involved different visual displays for their notations, and there were differences in the overall RTs. However, the distance effect is the key effect for examining the question of abstract numerical representation because it taps post-perceptual stages (as reflected by event-related potential (ERP) (e.g., Dehaene 1996; Libertus et al. 2007; Pinel et al. 2001), fMRI (e.g., Eger et al. 2003; Pinel et al. 2001), and behavioural results, which have been shown specifically and convincingly by the sequential paradigm (Cohen Kadosh 2008a; Schwarz & Ischebeck 2000). Another piece of evidence is that in ERP studies, the number of letters (but not the distance effect) modulates the N1 component (perceptual component) (Dehaene 1996). However, the distance effect affects only later postperceptual components (P300: Cohen Kadosh et al. 2007c; Schwarz & Heinze1998; P2p: Dehaene 1996). In addition, we are not familiar with any findings in the neuroimaging literature (or any other method) that have shown modulation of the perceptual areas by numerical distance and notation when words and digits were used (e.g., Pinel et al. 2001). Falter, Noreika, Kiverstein, & Mo¨lder (Falter et al.) support the non-abstract view for numerical representation, and extend it to other domains such as time. They show that not only numbers are represented nonabstractly, but also other representations that involve the IPS, such as time. In our view, this idea should generate further experiments that will examine the representation of time, similar to our suggestions for numbers. Campbell & Metcalfe support our theoretical view, and extend it to basic arithmetic. They provide evidence that basic arithmetic is not abstract in two ways. First, it is based on discrete, format- and operation-specific processes. Second, calculation efficiency is format-specific. Our view is very close, and indeed, Campbell was one of the few who has supported the idea of non-abstract numerical representation in the last 20 years (Campbell 1994; Campbell & Clark 1988; Campbell & Epp 2004; 2005). Moreover, our view that strategies might play a role in numerical representation is similar to his view that arithmetic is affected by subjective strategies. We believe that future studies should examine the issue of strategies on numerical representations, as it will clarify why some labs reveal non-abstract representations while others do not find any differences between the different formats. We need to take into account what exactly the researcher tells the subject. This has been shown to affect the results in some studies that reported these instructions (Piazza et al. 2004; 2007). R4. Priming Part of the evidence that Dehaene, Reynvoet & Notebaert, and Santens et al. focus on is subliminal priming. Surprisingly, they all ignore the good evidence that subliminal priming can originate at the level of response (for behavioural evidence, see Kiesel et al. 2007; Kunde et al. 2003; 2005; for fMRI and ERP

Response/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes evidence, see Dehaene et al. 1998b). More surprising is that Dehaene uses the cross-notation subliminal priming data from Naccache and Dehaene (2001a) in his commentary (see Dehaene’s Fig. 1) to argue that digits and verbal numbers have a shared representation. However, these data are based on the same data in earlier work by Dehaene et al. (1998b). In this work, Dehaene et al. showed that an unconscious prime (digit or verbal number) is processed up to the response level (see Figs. 3 & 5 in Dehaene et al. 1998b). Therefore, the results by Naccache and Dehaene (2001a) can be explained perfectly by response selection rather than shared numerical representation, which is in line with other behavioural evidence in the field of subliminal priming (Kiesel et al. 2007; Kunde et al. 2003; 2005). Therefore, both digits and verbal numbers were processed up to the response level, a result that is in line with the non-abstract view (e.g., the digit 1 activated response by the left hand and the verbal number NINE activated response by the right hand), and can explain the subliminal priming effect (Kiesel et al. 2007; Kunde et al. 2003; 2005). Support for our view also comes from another study that used functional connectivity analysis. It was shown that the IPS and the frontal eye field, that are involved in response selection, are also coactivated with the motor cortex, when numerical magnitude is processed up to the response level (Cohen Kadosh et al. 2008d). Therefore the activation in the IPS in Naccache and Dehaene (2001a) and the motor cortex activation in Dehaene et al. (1998b) that were observed in the same data, can be argued to be functionally connected and involved in response selection, rather than shared representation. Another issue is that some of the results from the cited subliminal priming studies actually support the nonabstract view, for example, by suggesting a preferred format to which the different numbers are mapped (e.g., digit; Noe¨l & Seron 1993). Unfortunately, alternative explanations are given to explain these effects that are not compatible with the abstract view, rather than mentioning the additional support for the non-abstract view (see, e.g., Santens et al.). Reynvoet & Notebaert also raised the issue that some of the evidence in favor of a notation dependent magnitude representation is based on a null effect in a particular condition. It is true that in some results a null effect was observed for one notation and not for another, but this is only a small fraction of the data, and other studies show that the numerical representation depends on the notation both qualitatively and/or quantitatively (e.g., Cohen Kadosh et al. 2007b; Cohen Kadosh et al. 2008e; Dehaene et al. 2008; Droit-Volet et al. 2008; Ganor-Stern & Tzelgov 2008; Holloway & Ansari 2009; Nuerk et al. 2002; Piazza et al. 2007). The researchers who are working on priming suggested that subliminal priming is automatic. However, they would need to take into account the view that the priming distance effect is not evidence for automatic processing, but rather of incidental processing (Tzelgov & Ganor-Stern 2005). R5. Terminology Several commentators raised the issue of the definition of abstract. We based our review on a previous and

well-accepted definition in the field of numerical cognition, and we are grateful for their contributions that will provide us with a better definition for the abstract representation. Nu´n˜ez criticizes our characterization of abstraction. He mentioned that this definition is specific and unnecessarily restrictive, thus making the extension to other nonnumerical areas of cognition hard. We are sympathetic to this concern, but see no reason why the terminology of abstract in the field of numerical cognition cannot be applied to other domains. It is interesting to note that numbers as a concept do not clearly fall into abstract or concrete categories. For example, chair is more concrete than truth but 2 does not fall clearly into one of these categories, and can vary among these dichotomies. Pease, Smaill, & Guhe (Pease et al.) also comment on the definition of abstraction in the field. We agree with their view that a binary distinction between abstract and non-abstract is not the optimal way to conceptualise the problem, and our model reflects this view. Pease et al. suggest also that multi-modal representations of mathematics, such as diagrammatic or algebraic reasoning, are assumed to abstract to a common domain. We do not agree with this claim, and several researchers argued that the deeper knowledge of experts facilitates the ability to integrate the different representational formats (Ainsworth et al. 2002; Kozma et al. 2000; Tabachneck et al. 1994) (see Peters & Castel, for some support with this view in numerical cognition). This idea is similar to the one made by Lakoff (2008) that Pease et al. cite, and is similar to our suggestion, that the numerical representation is composed from multiple representations, and that a strong association can be created between them by the subject as a working representation. Piazza & Izard raise many questions that will be of interest for future studies. We agree with them that abstract representation has become the default theory of the mathematical brain; indeed the need for our target article is partly predicated on the fact that it has become an unhealthily unquestioned default. However, in contrast to their claim, we do not offer a dichotomy (see Fig. 5), and our focus on non-abstract representations was done in order to shake the foundations of the prevailing orthodoxy, which leading researchers have ignored to some degree (Piazza & Dehaene 2004; Piazza et al. 2007; Pica et al. 2004). In contrast to Piazza & Izard’s claims, we also do not view numerical representation as a module, and we stated in our review our divergence from such a view (see sect. 5). Neuronal populations that code numerical quantity can be modality-sensitive, but they can still be sensitive to other non-numerical features. As for the issue of serial processing: albeit that there is ample evidence that supports the idea that numbers are processed serially (Blankenberger & Vorberg 1997; Dehaene 1996; Schwarz & Ischebeck 2000), the interaction between modality and numerical effects, such as the distance effect, does not depend only on serial processing, because the additive factor method analysis is also valid in most of the cases of cascade processing (Sanders 1998). It is worrying that researchers in the field of numerical cognition, such as Piazza & Izard and Santens et al., consider interactions between modality and the representation-related effects as an indication of abstract BEHAVIORAL AND BRAIN SCIENCES (2009) 32:3/4

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Response/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes representation. We have explained in this section, and in section R3, why this view is wrong. Nevertheless, these commentators’ view is a new view, but a risky one. If additive or interactive effects indicate abstract representation, the abstract view is immune to falsification – the death knell for any scientific idea. We like very much the idea of selectivity of neurons to numbers and other features, a view that is partly in line with previous works by us (Cohen Kadosh et al. 2008f; Walsh 2003). Piazza & Izard gave an example of how when one examines single neuron spiking activity or the fMRI signal, some neurons that respond both to number and length, or number and motion, or length and motion, will not show selectivity when averaged across populations. Extrapolating their idea, the same can also hold when one examines dots and digits, digits and verbal numbers, and dots and verbal numbers. Given that all the studies so far were confined to only two modalities, the chance that abstract representation was concluded mistakenly is increased. Vallar & Girelli pointed out that the dichotomy between abstract and non-abstract is too general to capture the variety of possible supramodal numerical representations. We agree with their argument, and would like to stress that our view is not that there is a dichotomy between abstract and non-abstract, but that both are endpoints of a continuum, and may interact with spatial codes. However, we believe that spatial codes do not affect different numerical notations to the same extent (see Dehaene et al. 2008, for support for our view), and therefore, that spatial codes are notation-dependent. Pesenti & Andres raise very important points as to the definitions of abstract and non-abstract representations that are used by many authors in the field, including us. These definitions prevail also in the current issue (e.g., our target article review, the commentaries by Dehaene, Cantlon et al., etc.). Some of Pesenti & Andres’ comments are thought-provoking, such as that analog representations cannot be abstract. We are grateful for their comments, and agree that the researchers in the field of numerical cognition need to use more accurate definitions. However, we believe that their commentary raises more concerns for the existence of abstract representation. It seems that differential effects at the semantic level as a function of notation (e.g., Dehaene et al. 2008; Diester & Nieder 2007; Droit-Volet et al. 2008; Tudusciuc & Nieder 2007) cannot be compatible with abstract representation, whereas results that support the existence of shared representation do not necessarily indicate abstract numerical representation. Nevertheless, even if one abandons the definition of abstract/non-abstract representations and adopts instead the idea of shared/multiple representations, or alternatively, modality-(in)dependence, the weight of evidence seems to support the existence of multiple representations (or modality-dependence). R6. Methodological advances Freeman & Kozma, Mayo, and Orban offer several suggestions to advance our understanding of numerical cognition in humans and nonhuman primates. Freeman & Kozma suggest that aside from single-cell neurophysiology, and fMRI, additional techniques such as 364

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electroencephalography (EEG) or magnetoencephalography (MEG) are required to examine the nature of numerical representations, and that these techniques will enable one to uncover the involvement of wide regions in intermittent spatially coherent oscillations. We entirely agree with their suggestions and mentioned some of them toward the end of our article. Mayo suggests two manipulations in single-neuron recording: reversible inactivation and adaptation of apparent numerosity. We agree that these new manipulations, which to date have not been used in this context, will be of help and can provide a causal understanding of the neuronal basis of numerical processing. It is worth asking, however, whether in principal this could be established in neurons in the rat brain that responded to numerosity, or by using TMS adaptation techniques in humans. Orban suggests that monkey fMRI provides a solution to the limitations of neuroimaging studies that we raised (which, according to him, we grossly underestimated). He correctly mentions the study by Sirotin and Das (2009) – which appeared after our target article had been accepted – to stress the idea that, compared to intentional tasks, passive tasks (e.g., adaptation paradigm) provided a better link between the haemodynamic response and neuronal activity. Indeed, adaptation paradigms have some limitations, but this is clearly a better tool to explore the theoretical question at hand, as also implied by Orban. Orban further mentions the important study by Sawamura et al. (2006) (also cited in our review), which shows that cross-format adaptation (e.g., adaptation for two consecutive trials for pigs, or hammers, vs. pig follows a hammer or vice versa) overestimates neuronal response selectivity. This point should be taken into account when the conclusions toward abstract/nonabstract are based on the level of cross-notational adaptation. After mentioning several possible methodological problems, Orban suggests the use of fMRI in the awake monkey as the solution to the theoretical question. We would suggest a note of caution in using monkeys as a model for human numerical cognition. Human numerical cognition cannot be studied independently of language (Carey 2004; see also Ansari). We must also take into account the large hemispheric asymmetries in different numerical functions, as well as deal with the human tendency to represent numbers spatially. Monkeys do not speak, do not show our pronounced lateralisation, do not represent numbers from left to right, or right to left, as far as we know, and they do not learn about numbers and quantity in the same way as humans. Technical muscle may therefore not be the answer to these conceptual questions.

R7. Simulated cognition and numerical cognition Lindemann, Rueschemeyer, & Bekkering (Lindemann et al.) provide a new point of view on numerical cognition, by suggesting an action-based number semantics to provide new insights into the way that we represent numerical magnitude. They suggest that abstract representation might emerge from association between the numerical information and action. We agree with this view, which is in line with Walsh (2003), and is in

References/Cohen Kadosh & Walsh: Numerical representation in the parietal lobes accordance with our suggestion in the target article (i.e., abstraction requires intention). Similarly, Myachykov, Platenburg, & Fischer (Myachykov et al.) extend our theory to the simulated cognition framework. We appreciate their innovative thinking, which suggests that understanding nonabstract representations within the framework of simulated cognition provides a theoretical platform for real-life numerical representation. Their view provides a hierarchy of features of numerical representation, which includes embodied, grounded, and situated cognition, and can explain effects in the field of numerical cognition, and provide support for some of the effects that we discussed and for our theoretical view. Furthermore, Myachykov, et al. provide the first independent experimental data to examine our dual-code model (sect. 10).

R8. Conclusions We are grateful to the commentators for their valuable comments that helped us to refine and clarify our theoretical perspective. We have shown that even if one takes into account factors that might affect numerical representation, numerical representation is primarily non-abstract. Many questions were raised by the commentators and we are sure that new questions will come from this interaction. It is now time to return to the lab and generate new data on the ways that humans represent numbers.

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If you are not a BBS Associate and wish to enquire about joining, please see the instructions for associate membership at http://www.editorialmanager.com/bbs/account/BBS_ifc.pdf Once the Commentary stage of the process has begun, the author can no longer alter the article, but can respond formally to all commentaries accepted for publication. The target article, commentaries, and authors' responses then co-appear in BBS. (Note: Continuing Commentary submissions are no longer being accepted.) Criteria for acceptance: To be eligible for publication, a paper should not only meet the standards of a journal such as Psychological Review or the International Review of Neurobiology in terms of conceptual rigor, empirical grounding, and clarity of style, but the author should also offer an explicit 500 word rationale for soliciting Commentary, and a list of suggested commentators (complete with e-mail addresses). A BBS target article an be: (i) the report and discussion of empirical research that the author judges to have broader scope and implications than might be more appropriately reported in a specialty journal; (ii) an unusually significant theoretical article that formally models or systematizes a body of research; or (iii) a novel interpretation, synthesis, or critique of existing experimental or theoretical work. Occasionally, articles dealing with social or philosophical aspects of the behavioral and brain sciences will be considered. The service of Open Peer Commentary will be primarily devoted to original unpublished manuscripts written specifically for BBS treatment. However, a recently published book whose contents meet the standards outlined above spontaneously and multiply nominated by the BBS Associateship may also be eligible for Commentary. In such a BBS Multiple Book Review, a comprehensive, article-length précis by the author is published together with the commentaries and the author's response. In special cases, Commentary will also be extended to a position paper or an already published article that deals with particularly influential or controversial research or that has itself proven to be especially important or controversial. In normal cases however, BBS submissions may not be already published (either in part or whole) or be under consideration for publication elsewhere and submission of an article is considered expressly to imply this. Multiple book reviews and previously published articles appear by invitation only. Self-nominations cannot be considered, neither can non-spontaneous (i.e. author elicited) nominations. However, the BBS Associateship and professional readership of BBS are encouraged to nominate current topics, books and authors for Commentary; e-mail [email protected] In all the categories described, the decisive consideration for eligibility will be the desirability of Commentary for the submitted material. Controversiality simpliciter is not a sufficient criterion for soliciting Commentary: a paper may be controversial simply because it is wrong or weak. Nor is the mere presence of interdisciplinary aspects sufficient: general cybernetic and "organismic" disquisitions are not appropriate for BBS. Some appropriate rationales for seeking Open Peer Commentary would be that: (1) the material bears in a significant way on some current controversial issues in behavioral and brain sciences; (2) its findings substantively contradict some well-established aspects of current research and theory; (3) it criticizes the findings, practices, or principles of an accepted or influential line of work; (4) it unifies a substantial amount of disparate research; (5) it has important cross-disciplinary ramifications; (6) it introduces an innovative methodology or formalism for broader consideration; (7) it meaningfully integrates a body of brain and behavioral data; (8) it places a hitherto dissociated area of research into an evolutionary or ecological perspective; etc. In order to assure communication with potential commentators (and readers) from other BBS specialty areas, all technical terminology must be clearly defined or simplified, and specialized concepts must be fully described. In case of doubt of appropriateness for BBS Commentary, authors should submit a detailed target article proposal using the new BBS Editorial Manager site at http://www.editorialmanager.com/bbs/. After evaluating the proposal, the Editors will encourage or discourage formal target article submission. A note on commentaries: The purpose of the Open Peer Commentary service is to provide a concentrated constructive interaction between author and commentators on a topic judged to be of broad significance to the biobehavioral science community. Commentators should provide substantive criticism, interpretation, and elaboration as well as any pertinent complementary or supplementary material, such as illustrations; all original data will be refereed in order to assure the archival validity of BBS commentaries. Commentaries and articles should be free of hyperbole and remarks ad hominem. Please refer to and follow exactly the BBS Instructions for Commentators at http://www.editorialmanager.com/bbs/account/BBS_ifc.pdf before submitting your invited commentary. Style and format for target articles: Target Articles must not exceed 14,000 words (and should ordinarily be considerably shorter); commentaries should not exceed

1,000 words, excluding references. Spelling, capitalization, and punctuation should be consistent within each article and commentary and should follow the style recommended in the latest edition of A Manual of Style, The University of Chicago Press. It is advisable to examine a recent issue of BBS as a model. Target articles should be submitted in MSWord format to the new Editorial Manager site at http://www.editorialmanager.com/bbs/. Figures should appear in the body of the text, not at the end of the paper, and should also be supplied as separate TIFF, EPS, JPEG, or GIF files. However, if your article is accepted, TIFF or EPS format will be requested for publication since printing requires resolutions of at least 1100dpi. (Please note that costs for color figure reproduction will be passed along to the author. Color printing is expensive, and authors are encouraged to find alternative methods for presentation of their argument.) Once accepted, a Call for Commentators will be sent to thousands of BBS Associates and readers. The Call letter includes a link to the pre-copyedited final draft archived publicly for potential commentators. The copyedited final draft will only be posted for the invited commentators. Please make sure your target article file has ALL of the following in this order: Four Separate Word Counts (for the abstract, main text, references, and entire text – total + addresses etc.), an Indexable Title, Full Name(s), Institutional Address(es), E-mail Address(es) and Homepage URL(s) for all authors (where available), Short Abstract (100 words), Long Abstract (250 words), 5–10 Keywords (in alphabetical order), approx. 12,000 word Main Text (with paragraphs separated by full blank lines, not tab indents), and Alphabetical Reference List. Target article authors must also provide numbered headings and subheadings to facilitate cross-reference by commentators. Tables and figures (i.e., photographs, graphs, charts, or other artwork) should be numbered consecutively, and should appear in its appropriate location. Every table should have a title; every figure, a caption. Endnotes and appendices should be grouped together at the end of the paper and should ideally be locally linked to in the text to facilitate the reader (and of course the referee’s task). Acknowledgements should be placed at the end of the paper. The short abstract will appear by way of an advertisement, one issue in advance of the publication issue. The long abstract will be circulated to referees and then potential commentators should the paper be accepted, and will appear with the printed article. BBS’s rigorous timetable constraints (requiring the coordination of target articles, commentaries and author’s responses within the publishing queue) make it extremely difficult for us to process follow-up drafts of your submission. Please make sure that the paper you submit is the carefully checked final draft to which you wish the referees to address. Please also ensure that your submission has been proof-read by a native English speaker before submission. This, of course, greatly improves its chances at the refereeing stage. References: Bibliographic citations in the text must include the author’s last name and the date of publication and may include page references. Complete bibliographic information for each citation should be included in the list of references. Please also include and link to the WWW URL for any paper for which it exists. Examples of correct styles are: Brown (1973); (Brown 1973); Brown 1973; 1978); (Brown 1973; Jones 1976); (Brown & Jones 1978); (Brown et al. 1978). References should be in alphabetical order in the style of the following examples. Do not abbreviate journal titles: Freeman, W. J. (1958) Distribution in time and space of prepyriform electrical activity. Journal of Neurophysiology 2:644–66. http://cogprints.soton.ac.uk/abs/ neuro/199806009 Dennet, D. C. (1991) Two contrasts: Folk craft versus folk science and belief versus opinion. In: The future of folk psychology: Intentionality and cognitive science, ed. J. D. Greenwood, pp. 26–7. Cambridge University Press. http:// cogprints.soton.ac.uk/abs/phil/199804005 Bateson, P.P.G. & Hinde, R.A., eds. (1978) Growing points in ethology. Cambridge University Press. Editing: The publishers reserve the right to edit and proof all articles and commentaries accepted for publication. Authors of target articles will be given the opportunity o review the copy-edited manuscript and page proofs. Commentators will be asked to review copy-editing only when changes have been substantial; commentators will not see proofs. Both authors and commentators should notify the editorial office of all corrections within 48 hours or approval will be assumed. Author response to commentaries: All invited commentaries received before the deadline are only accessible to the Authors and Editors. Please note that no commentary is officially accepted until the Editor in charge has formally reviewed it and notified both the authors and the Editorial Administrator. Please refer to and follow exactly the BBS Commentary Response Instructions at http://www.editorialmanager.com/ bbs/account/BBS_ifc.pdf before submitting your response. Authors of target articles receive 50 offprints of the entire treatment, and can purchase additional copies. Commentators will also be given an opportunity to purchase offprints of the entire treatment.

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Offprints of the following forthcoming BBS treatments can be purchased for educational purposes if they are ordered well in advance. For ordering information, please write to Journals Department, Cambridge University Press, 32 Avenue of the Americas, New York, NY 10013-2473.

Does sexual selection explain human sex differences in aggression? John Archer

Numerical representation in the parietal lobes: Abstract or not abstract? Roi Cohen Kadosh and Vincent Walsh

To appear in Volume 32, Number 5 (2009)

A sociorelational framework of sex differences in the expression of emotion

Behavioral and Brain Sciences

In this issue

Jacob Miguel Vigil, University of North Florida

With commentary from F Basso & O Oullier; D Buss; AH Fischer; JMB Fugate, H Gouzoules & LF Barrett; S Goldstein Ferber; CE Izard, KJ Finlon & SR Grossman; NP Li & D Balliet; V LoBue & JS DeLoache; GA Lozano; M Lyons; G Madison; RR Provine; JE Swain; A Todorov; S Vazire, LP Naumann, PJ Rentfrow & SD Gosling; N Vermeulen; A Wiefel & R Schepker; V Zayas, JA Tabak, G Günaydýn & JM Robertson

Nicholas Evans, Australian National University, and Stephen C. Levinson, Max Planck Institute for Psycholinguistics Talk of linguistic universals has given cognitive scientists the impression that languages are all built to a common pattern. In fact, there are vanishingly few universals of language in the direct sense that all languages exhibit them. Instead, linguistic diversity is the crucial datum for cognitive science: we are the only species with a communication system that is fundamentally variable at all levels. Recognizing the true extent of structural diversity in human language opens up exciting new research directions for cognitive scientists.

With commentary from MC Baker; EL Bavin; I Berent; AC Catania; MH Christiansen & N Chater; W Croft; R Freidin; AE Goldberg; D Harbour; M Haspelmath; D Margoliash & HC Nusbaum; B McMurray & E Wasserman; B Merker; A Nevins; DC Penn, KJ Holyoak & DJ Povinelli; D Pesetsky; S Pinker & R Jackendoff; GK Pullum & BC Scholz; L Rizzi; P Smolensky & E Dupoux; M Tallerman; M Tomasello; H Waterfall & S Edelman Among the articles to appear in forthcoming issues of BBS:

Volume 32, Number 3/4

The myth of language universals: Language diversity and its importance for cognitive science

June/August 2009

Despite extensive empirical demonstrations of sex differences in expressed emotion, no critical examination and account of their evolution and development yet exists. There is a consistent difference in the typical social setting in which each sex has functioned and evolved; that is, the predominance of male philopatry in past and present human societies. I argue that, because of the requirements of sex-typical social settings, emotional systems that differentially project and assess perceived capacity will be favored in males contrasted with those related to perceived trustworthiness in females. A sociorelational framework to account for the advertisement and perception of these basic social predispositions in conjunction with situational factors is described.

J. M. Vigil, “A sociorelational framework of sex differences in the expression of emotion” http://www.bbsonline.org/Preprints/Vigil-02212008/Referees N. Evans & S. C. Levinson, “The myth of language universals: Language diversity and its importance for cognitive science” http://www.bbsonline.org/Preprints/Evans-08042008/Referees R. T. McKay & D. C. Dennett, “The Evolution of Misbelief” http://www.bbsonline.org/Preprints/McKay-08262008/Referees

Pages 249–374

Cambridge Journals Online For further information about this journal please go to the journal website at: journals.cambridge.org/bbs

An International journal of current research and theory with open peer commentary Volume 32 | Issue 3/4 | June/August 2009 | ISSN: 0140-525X