Animal Groups in Three Dimensions: How Species Aggregate

ANIMAL GROUPS IN THREE DIMENSIONS

ANIMAL GROUPS IN THREE DIMENSIONS Edited by JULIA K. PARRISH WILLIAM M. HAMNER University of Washington

University of California, Los Angeles

CAMBRIDGE UNIVERSITY PRESS

PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE

The Pitt Building, Trumpington Street, Cambridge CB2 1RP, United Kingdom CAMBRIDGE UNIVERSITY PRESS

The Edinburgh Building, Cambridge CB2 2RU, United Kingdom 40 West 20th Street, New York, NY 10011-4211, USA 10 Stamford Road, Oakleigh, Melbourne 3166, Australia © Julia K. Parrish and William M. Hamner 1997 This book is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 1997 Printed in the United States of America Typeset in Times Library of Congress Cataloging-in-Publication Data Animal groups in three dimensions / edited by Julia K. Parrish, William M. Hamner. p. cm. Includes bibliographical references and index. ISBN 0-521-46024-7 (he) 1. Animal societies. 2. Animal societies - Simulation methods. 3. Three-dimensional display systems. I. Parrish, Julia K., 1961-. II. Hamner, William, M. QL775.A535 1997 591.5-dc21 97-25867 CIP A catalog record for this book is available from the British Library. ISBN 0-521-46024-7 hardback

To Akira Okubo

Contents

List of contributors Acknowledgments 1

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Introduction - From individuals to aggregations: Unifying properties, global framework, and the holy grails of congregation Julia K. Parrish, William M. Hamner, and Charles T. Prewitt 1.1 Seeing is believing 1.2 Defining a framework 1.3 Properties of animal congregations 1.4 On adopting new perspectives 1.5 Central themes and "big picture" questions 1.6 Organization - from measurement to models 1.7 What's next? Part one: Imaging and measurement Methods for three-dimensional sensing of animals Jules S. Jaffe 2.1 Introduction 2.2 Existing methods 2.3 Application of three-dimensional measurement techniques to in situ sensing of animal aggregates 2.4 Conclusions Acknowledgments Analytical and digital photogrammetry Jon Osborn 3.1 Introduction 3.2 The geometry and process of image capture 3.3 Stereoscopy 3.4 Tracking

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Contents 3.5 Discussion 3.6 Examples 3.7 Summary Acoustic visualization of three-dimensional animal aggregations in the ocean Charles H. Greene and Peter H. Wiebe 4.1 Introduction 4.2 Acoustic visualization 4.3 Field studies: Hypotheses, methods, and results 4.4 Discussion Acknowledgments Three-dimensional structure and dynamics of bird flocks Frank Heppner 5.1 Introduction 5.2 Line formations 5.3 Cluster formations 5.4 Future directions and problems Acknowledgments Appendix Three-dimensional measurements of swarming mosquitoes: A probabilistic model, measuring system, and example results Terumi Ikawa and Hidehiko Okabe 6.1 Introduction 6.2 Probabilistic model for stereoscopy 6.3 Measuring system for mosquito swarming 6.4 Spatiotemporal features of swarming and the adaptive significance 6.5 Viewing extension of the method Acknowledgments Part two: Analysis Quantitative analysis of animal movements in congregations Peter Turchin 7.1 Introduction 7.2 Analysis of static spatial patterns 7.3 Group dynamics 7.4 Spatiotemporal analysis 7.5 Conclusion Movements of animals in congregations: An Eulerian analysis of bark beetle swarming Peter Turchin and Gregory Simmons 8.1 Introduction

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8.2 Congregation and mass attack in the southern pine beetle 8.3 An approximate relationship between attractive bias and flux 8.4 Field procedure 8.5 Results 8.6 Conclusion Individual decisions, traffic rules, and emergent pattern in schooling fish Julia K. Parrish and Peter Turchin 9.1 Introduction 9.2 Experimental setup: Data collection 9.3 Group-level patterns 9.4 Attraction/repulsion structuring 9.5 Discussion Aggregate behavior in zooplankton: Phototactic swarming in four developmental stages of Coullana canadensis (Copepoda, Harpacticoida) Jeannette Yen and Elizabeth A. Bundock 10.1 Introduction 10.2 Methods 10.3 Results 10.4 Discussion 10.5 Conclusions Acknowledgments Part three: Behavioral ecology and evolution Is the sum of the parts equal to the whole: The conflict between individuality and group membership William M. Hamner and Julia K. Parrish 11.1 Introduction 11.2 Membership and position 11.3 Costs and benefits to the individual 11.4 Group persistence 11.5 Individuality versus "group" behavior 11.6 Cooperation or veiled conflict 11.7 Concluding remarks Inside or outside? Testing evolutionary predictions of positional effects William L Romey 12.1 Introduction 12.2 Where should a flocker be in a group? 12.3 Individual differences in location 12.4 Differences in selection 12.5 Differences in motivation

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12.6 Balancing motivations 12.7 Conclusion Acknowledgments Costs and benefits as a function of group size: Experiments on a swarming mysid Paramesopodopsis rufa Fenton David A. Ritz 13.1 Introduction 13.2 Study animal 13.3 Laboratory conditions 13.4 Food capture success versus group size 13.5 Swarm volume in different feeding conditions 13.6 Food capture versus swarm size in the presence of a threat 13.7 Discussion 13.8 Conclusions Acknowledgments Predicting the three-dimensional structure of animal aggregations from functional considerations: The role of information Lawrence M. Dill, C. S. Holling, and Leigh H. Palmer 14.1 Introduction 14.2 Predicting position 14.3 Testing the predictions 14.4 Null models Acknowledgments Appendix Perspectives on sensory integration systems: Problems, opportunities, and predictions Carl R. Schilt and Kenneth S. Norris 15.1 Introduction 15.2 Sensory integration systems 15.3 Problems and opportunities 15.4 Predictions 15.5 Conclusions Acknowledgments Part four: Models Conceptual and methodological issues in the modeling of biological aggregations Simon A. Levin 16.1 Introduction 16.2 The problem of relevant detail

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16.3 Interacting individuals: From Lagrange to Euler 16.4 Cells to landscapes: From discrete to continuous 16.5 Evolutionary aspects of grouping 16.6 Conclusions Acknowledgments Schooling as a strategy for taxis in a noisy environment Daniel Griinbaum 17.1 Introduction 17.2 Asocial searching: Taxis from directionally varying turning rates 17.3 Simulations of searching with schooling behavior 17.4 A nonspatial deterministic approximation to social taxis 17.5 Discussion Trail following as an adaptable mechanism for popular behavior Leah Edelstein-Keshet 18.1 Introduction 18.2 Trail following in social and cellular systems 18.3 Phenomena stemming from trail following 18.4 Minimal models for trail-following behavior 18.5 Discussion Acknowledgments Metabolic models of fish school behavior - the need for quantitative observations William McFarland and Akira Okubo 19.1 Introduction 19.2 Density in mullet schools 19.3 Mullet school velocity 19.4 Oxygen consumption of swimming mullet 19.5 Modeling oxygen consumption within a mullet school 19.6 Discussion Acknowledgments Symbols Social forces in animal congregations: Interactive, motivational, and sensory aspects Kevin Warburton 20.1 Introduction 20.2 Models of attraction and repulsion 20.3 Sensory modalities mediating the attraction-repulsion system 20.4 Real-life factors mediating attraction and repulsion, and their effects on group cohesion

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20.5 Models of attraction and repulsion which describe the effects of motivational change 20.6 Conclusion Acknowledgments

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References Subject index Taxonomic index

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Contributors

Elizabeth A. Bundock Finch University of Health Sciences/The Chicago Medical School, North Chicago, Illinois 60064, USA. [email protected] Lawrence M. Dill Behavioural Ecology Research Group, Department of Biological Sciences, Simon Fraser University, Burnaby, British Columbia, V5A 1S6, Canada. [email protected] Charles H. Greene Ocean Resources and Ecosystems Program, Corson Hall, Cornell University, Ithaca, New York 14853, USA. [email protected] Daniel Griinbaum Department of Zoology, Box 351800, University of Washington, Seattle, Washington 98195, USA. [email protected] William M. Hamner Department of Biology, University of California, Los Angeles, Box 951606, Los Angeles, California 90095-1606, USA. [email protected] Frank Heppner Zoology Department, University of Rhode Island, Kingston, Rhode Island 02881, USA. C. S. Holling Department of Zoology, University of Florida, Gainesville, Gainesville, Florida 32611, USA. [email protected] Terumi Ikawa Department of Liberal Arts and Sciences, Morioka College, 808 Sunagome, Takizawa-mura, Iwate-gun 020-01 Japan, [email protected] Jules S. Jaffe Marine Physical Lab, Scripps Institution of Oceanography, La Jolla, California 92093-0238, USA. [email protected]

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Leah Edelstein-Keshet Department of Mathematics, University of British Columbia, #121-1984 Mathematics Road, Vancouver, British Columbia, V6T 1Z2, Canada. [email protected] Simon A. Levin Department of Ecology and Evolutionary Biology, Eno Hall, Princeton University, Princeton, New Jersey 08544, USA. [email protected] William McFarland Friday Harbor Laboratories, University of Washington, 620 University Road, Friday Harbor, Washington 98250, USA. Kenneth S. Norris Long Marine Laboratory, Institute of Marine Sciences, University of California, 100 Shaffer Road, Santa Cruz, California 95060, USA. Hidehiko Okabe Research Institute for Polymers and Textiles, Higashi, Tsukuba 305, Japan. [email protected] Akira Okubo

Deceased

Jon Osborn Department of Survey and Spatial Information Science, University of Tasmania at Hobart, GPO Box 252C, Hobart, Tasmania 7001, Australia. [email protected] Leigh H. Palmer Department of Physics, Simon Fraser University, Burnaby, British Columbia, V5A 1S6, Canada, palmer®sfu.ca Julia K. Parrish Department of Zoology, Box 351800, University of Washington, Seattle, Washington 98195, USA. [email protected] Charles T. Prewitt Carnegie Institution of Washington, Geophysical Laboratory, 5251 Broad Branch Road N.W., Washington, D.C. 20015, USA. [email protected] David A. Ritz Department of Zoology, University of Tasmania at Hobart, GPO Box 252C, Hobart, Tasmania 7001, Australia. [email protected] William L. Romey Department of Biology, Kenyon College, Gambler, Ohio 43022-9623, USA. [email protected] Carl R. Schilt 30602, USA.

Institute of Ecology, University of Georgia, Athens, Georgia

Gregory Simmons 92227, USA.

USDA, APHIS, 4151 Highway 86, Brawley, California

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Peter Turchin Department of Ecology and Evolutionary Biology, University of Connecticut, Storrs, Connecticut 06269-3042, USA. [email protected] Kevin Warburton Department of Zoology, The University of Queensland, Brisbane, Queensland 4072, Australia. [email protected] Peter H. Wiebe Biology Department, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543, USA. [email protected] Jeannette Yen Marine Sciences Research Center, State University of New York, Stony Brook, New York 11794-5000, USA. [email protected]

Acknowledgments

Many people helped to make this book possible. Lauren Cowles at Cambridge University Press was a patient, understanding editor. Karen Jensen, Trista Patterson, Johanna Salatas, and Jen Cesca typed, edited, and retyped various manuscripts, as well as sent countless emails, letters, and faxes, and xeroxed, collated, and filed hundreds if not thousands of pages. Every author in this book deserves credit for living through an extended process of book preparation which often involved less-than-tactful editing. Mea culpa (JKP). Every author in this book also served as an anonymous reviewer for at least one other chapter; thanks also to E. J. Buskey and T. J. Pitcher for reviewing. Leah Edelstein Keshet and Simon Levin deserve special thanks for facilitating the inclusion of Chapters 6 and 17, respectively. Chapter 17 is reprinted in large part from an article of the same name in Evolutionary Ecology, and appears by permission of the publishers Chapman & Hall. Nothing would have been possible without the foresight of Larry Clarke at the National Science Foundation, who served as program director for the initial grant, "Three-dimensional analysis and computer modeling of schooling patterns," OCE86-16487, to Bill Hamner and Charlie Prewitt, as well as to our workshop grant, "Workshop - Animal aggregations: Three-dimensional measurement and modeling," OCE91-06924, which allowed us to aggregate in Monterey. Finally, and certainly foremost, we owe a huge and growing debt of gratitude to Peggy Hamner who served as wife, sister, friend, mother, grandmother, colleague, editor, typist, overseer, mediator, and always supreme debutante.

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Introduction - From individuals to aggregations: Unifying properties, global framework, and the holy grails of congregation JULIA K. PARRISH, WILLIAM M. HAMNER, AND CHARLES T. PREWITT

1.1 Seeing is believing An aggregation of anything against a background of sameness captures our eye. Congregations of creatures that routinely swarm and cluster or crowd together capture our imagination and generate new descriptive, often florid, collective terms for groups of living things; descriptors that are species-specific and etymologically precise (see Lipton's "Exaltation of Larks," 1991). A swarm of bees, a host of sparrows, and a smack of jellyfish generate crisp images in our mind's eye, while a cloud of goats, a gaggle of flies, and a pod of parrots only generate confusion. There is no collective term in the English language for this wealth of collective adjectives (Lipton 1991), other than terms of "venery" (from the Latin venari, to hunt game), words that initially described aggregations of game animals, clustered conveniently for the huntsman. Some of these terms denote protean behavioral displays that are visually compulsive. However, when our congregations of creatures are behaviorally coordinated in space and time, synchronously moving and wheeling and twisting before us in three-dimensional space, as in a school of smelt or a flock of phalaropes, they subvert our visual ability to focus on an individual animal and, somehow, suddenly the sum of the parts becomes a cohesive whole. Those of us who are terminally entranced with the three-dimensional, hypnotic beauty of synchronized flocks of birds and schools of fish quite simply cannot be cured. We know there is order within these three-dimensional displays, but it is not immediately obvious how to quantify it. Schools of fish have fascinated evolutionary biologists for many years (Williams 1964) because the individuals in the aggregation do not appear to act selfishly at all; rather they seem to behave and interact as if for the benefit of the school as a whole. Indeed, if the individuals within a school did not look and behave similarly, then one of the primary antipredatory advantages associated with

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schooling, anonymity within the aggregation, could not exist. Odd animals are eaten first; however, this does not necessarily mean the dissolution of group structure as all individuals fight to gain access to the best locations (Krause 1994). Natural selection has produced behavioral patterns which emphasize similarity and uniformity within the group, such that coherence and cohesion are hallmarks of many types of animal congregation. It is this tension between survivorship of the individual within the protection of the school and the constraints imposed by living within a group that poses an evolutionary paradox that still has not been resolved. Collective behavior is illustrative of one of the central philosophical issues of biology in particular and science in general, i.e. the issue of individuality, the dichotomy between the sum of the parts and the whole.

1.2 Defining a framework 1.2.1. The phenomena of aggregation Aggregation is a pervasive phenomenon. At the most basic level, an aggregation is a collection of parts or units which form some coherent, often cohesive, whole. Molecules aggregate to form the basic building blocks of matter and substance as we know them. Inanimate objects of all shapes and sizes aggregate to form the familiar landscape within which we live. Beaches are made of aggregations of sand grains or cobblestones, glaciers are made up of compacted aggregations of snowflakes, planets are aggregated into solar systems, and solar systems are aggregated into galaxies. In many cases, inanimate objects are not only aggregated, but sorted along some set of physical gradients. Adjacent sand grains on a beach are apt to be the same size, having been sorted by the physical force of wave action. But beach material is not all the same size. Thus, a beach contains a gradient of grain sizes instead of a random assemblage of sand, pea gravel, and cobble. Furthermore, the sand on a given beach is likely to be predominantly of a single type. Pink sand beaches in Bermuda are made mostly from coral growing in the adjacent reef, whereas black sand beaches in Hawaii are made from the locally abundant volcanic rock. Both physical sorting and local abundance of source material create nonrandom aggregations which then may be arranged into repetitive patterns. Sand on a dune may be arranged by density and size, but dunes are also repetitively arrayed along a beach. However, aggregation is not only passive sorting. Many objects actively aggregate, such that like materials attract, while foreign materials are repelled. Atoms and molecules are both attracted and repulsed, resulting in cohesion into liquids or solids within which the individual units are held at some minimum distance. Human societies have all adopted the phenomenon of arranged, or ordered, aggregation as basic to living. We build a brick wall one ordered row at a time

From individuals to aggregations instead of in haphazard arrangements. Engineers and architects instruct us about the structural and aesthetic properties of ordered arrangements designed to make our surroundings both functional and pleasing to the eye. Many of us sort silverware by type: knives with knives and forks with forks. Commuters in automobiles follow each other in columns determined by the locations of roads and freeways, attracted to their ultimate destinations, but repelled from each other for fear of having an accident (not always successful). In short, ordered arrangements of like objects surround us comfortably, as a consequence of our actions.

1.2.2 Animate aggregations Most of the aggregation that surrounds us, both inanimate and animate, is arrayed in three dimensions, and some of it contains a fourth dimension, time, as well. Like the physical world, animate aggregations and patterns within them can be the result of sorting by physical forces. Assemblages of plants are often found in discrete locations, not only based on where they can grow, but also on where the seeds were carried (Forcell & Harvey 1988). Wind, water, and animals all distribute seeds nonrandomly (e.g. Becker et al. 1985; Skoglund 1990). Animal aggregations also result from physical sorting. In open water, zooplankton are often found in dense aggregations, associated with localized physical phenomena (e.g. Hamner & Schneider 1986). Animals are not necessarily actively attracted to these aggregations; often they are passively transported there via physical processes. These types of assemblages might be called passive aggregation, although this does not preclude the possibility of the aggregation members acting and interacting once within the group. Within the animate world, aggregations often form around an attractive source, with potential members of the aggregation actively recruited to a specific location. Zooplankton aggregate nightly at the surface of the sea as a result of vertical migration. Clumped patches of any resource, such as food or space, attract animals, especially if the resource is limiting. We refer to these types of aggregations as active aggregations. In these situations the aggregation is apt to disperse if the source of attraction wanes. Once seeds have been consumed, birds no longer visit a feeder. Individuals also may continuously join and leave the aggregation, rather than remain continuous members. Thus, turnover may be high even if the aggregation as a whole remains fairly constant in terms of size, density, shape, or location. Although attraction to a common source may be responsible for the creation of the aggregation, repulsion also plays a crucial role in determining group structure (Okubo 1980). Unmitigated attraction would result in an aggregation so

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dense that the costs to individual members would quickly outweigh the benefits. As density increases, basic resources, such as oxygen in the aquatic environment, are depleted faster than they can be replenished (see McFarland & Okubo Ch. 19). At the same time, waste products are likely to build up faster than they can be advected out of the group. Repulsion may occur on a global level; i.e. individuals are repulsed from an external source (e.g. Payne 1980), creating an open space or vacuole around the repulsion source (e.g. a predator in a fish school; Pitcher & Parrish 1993). Repulsion also occurs on a local level; i.e. regulation of interindividual density (see Parrish & Turchin Ch. 9). The combination of attractive and repulsive forces should thus define the physical attributes of the group as the spacing between many interacting individuals and forms the emergent pattern we see as group structure. In contrast to plants and pebbles, animals have the ability to react rapidly to changes in their environment. While a sand grain or a seed may fall among others of equal size and origin, it does not do so by choice. Many animal aggregations are formed and maintained by the mutual attraction of members. When the source of attraction is the group itself, we define this behavior as congregation (sensu Turchin 1997). Examples of animal congregations abound: flocks of birds, swarms of insects, schools of fish. Congregations can be shaped by internal, i.e. member-derived, forces, by external forces, and by frictional forces (see Warburton Ch. 20; Okubo 1986). The foraging trails of ant colonies may have structure, determined in part by the surfaces they crawl over. However, given a smooth, featureless environment, the ants would still congregate (EdelsteinKeshet Ch. 18,1994; Gordon et al. 1993). Thus the phenomenon of congregation may be structured by the larger environment within which the group resides as well (Gordon 1994). Although a large variety of animals congregate, interactions within the group differ markedly across species (Bertram 1978). Spatially well-defined congregations, such as fish schools, may be composed of individuals with little to no genetic relation to each other (Hilborn 1991), low fidelity to the group (Helfman 1984), and thus no reason for displaying reciprocal altruism. Schooling fish are generally considered "selfish herds" (Hamilton 1971), in that each individual attempts to take the maximum advantage from group living, independent of the fates of neighbors (Pitcher & Parrish 1993). The fact that three-dimensional structure is apparent does not necessarily lead to the conclusion that the individuals within the group interact socially. Rather than active information transfer (i.e. social interaction), information may be transferred passively (sensu Magurran & Higham 1988). For this reason, we refer to these asocial types of congregations as passive. In a. passive congregation (the FSH of Romey Ch. 12), in-

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dividual members are attracted to the group per se, but do not display social behaviors. Many animal congregations, however, are socially developed. Often the individual members are related, sometimes highly so, as in the social insects (see Edelstein-Keshet Ch. 18; Wilson 1975). Unrelated congregation members will often engage in social interactions if group fidelity is high, such that the chance of each individual meeting any of the others is high (Alexander 1974). Social congregations display a variety of interindividual behaviors, necessitating active information transfer. Antennal contact in ants may be used to transfer a variety of information about individual identity or location of resources (Gordon et al. 1993). The rate of contact may also, to some extent, define the structure of the group (see Edelstein-Keshet Ch. 18). Social congregations frequently display a division of labor, such that large tasks unassailable by an individual are accomplished by the group (e.g. hunting in social carnivores - Kruuk 1972, 1975; Packer & Ruttan 1988). The way in which both passive and social congregations transfer information between members about the larger environment which is unsensible by any single individual is the subject of Chapter 15 by Schilt and Norris. Highly social congregations, such as felid or canid packs, or any number of primate groups, may actually display a lack of regularly defined spatial pattern within the group (e.g. Janson 1990), perhaps because of the level of social development. In these cases, constant proximity of neighbors is no longer a requirement for information transfer and the "structure" of the groups is by relatedness and social hierarchy rather than interindividual distance.

1.3 Properties of animal congregations Regardless of species or circumstance, many animal congregations share one or more of the following features. 1. Congregations have edges which are usually very distinct; the change in density from inside to outside is abrupt. This is one operational way to define a group. When a congregation moves or changes shape, the edges remain intact. Thus, individuals are either members or isolates, depending on their location. 2. Many types of animal congregations have fairly uniform densities, particularly when on the move (e.g. herds, flocks, schools). Other types of animal congregations may have a broader distribution of densities most of the time (e.g. midge swarms), yet retain the ability to assemble almost instantaneously into a more uniform mass. Feeding birds often display non-uniform distribu-

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tions around food sources, but if a predator comes into view the flock will take wing as a cohesive, structured unit. 3. Congregations which exist largely as groups of uniform density are often also polarized, with all members facing in the same direction. When a flock of birds is in flight, for instance, it is obvious why this should be so. A bird in the interior of the flock, flying at right angles to the rest, would quite possibly create a significant hazard. However, some animal congregations, notably schooling fish, remain in polarized configurations even at rest. Why this occurs is not known. 4. Within the volume of the group, polarized or not, individuals have the freedom to move with respect to their neighbors. In a resting group this may mean that individuals are constantly shifting positions, even if the position or shape of the congregation as a whole remains static. In moving groups individuals can also re-sort without disturbing the integrity of the group. The ability to shift positions means that individuals can take selfish advantage of momentto-moment circumstances as well as accrue the more general benefit of group membership. 5. Many congregations display coordinated movement patterns of an almost balletic nature. Flocks on the wing appear to turn simultaneously. Fish in schools arc in a fountain-like pattern in response to attack by a predator, completing the move by reaggregating behind the predator. Ant trails branch out in dendritic structures which coalesce back into main paths.

1.4 On adopting new perspectives We live in a three-dimensional medium and we constantly, albeit unconsciously, make thousands of three-dimensional calculations each second. A disproportionately large portion of the human brain is committed to these very functions, yet tiny creatures, like hover flies, make lightning judgments in space and time with hardly any neurological equipment. Even with our stereoscopic, full color, visual abilities we cannot track an individual sardine within a rapidly wheeling school. Perhaps, if we could slow everything down, we would be more effective. So, as scientists, we record the behavior with film or video, and replay the images at slower speed. Again, we are lost. Our films are in two dimensions, and we begin our analysis of three-dimensional behavior at the 0.66% level of confidence. If we film with two or more cameras to capture the third spatial dimension, we then must analytically treat the resulting data set using classical three-dimensional photogrammetric calculations (see Osborn Ch. 3). And then we learn the bad news. Automatic three-dimensional data collection and analysis, for any length of time over several seconds, requires the dedicated attention

From individuals to aggregations of the biggest computers currently on the market. A cloud of gnats obviously does not engage in such time-intensive calculation. There must be simple traffic rules for species' engaging in collective movement. This book is all about animal aggregations in four dimensions, three in space and one in time. It is not confined to just an experimental treatment of the subject. We believe that it will require much more than biology to understand how and why animals do (or do not) congregate in more or less ordered arrangements. Two of us (Parrish and Hamner) experienced the limitations of a purely biological approach, first independently and then together, when we tried to answer questions about how individuals move within groups and how those movements are patterned in space and time. As biologists we found ourselves immersed in a rich literature on why animals aggregate. Hypotheses describing where animals should be in a group, and why they should be there, abound (Alexander 1974; Hamilton 1971; Lazarus 1979; Pitcher et al. 1982b), but the literature on how animals aggregate is much sparser. While we found information on how individuals might match retinal images (Parr 1927), how they might match their speeds (Shaw & Tucker 1965), or how quickly individuals might detect and respond to a stimulus, these papers did not point the way to answering our questions about how these individuals organize themselves in space and time within aggregations. When we pressed these issues, we quickly found ourselves in a technological morass. Following individual animals (or units of anything within a moving aggregation) in space and time turns out to be very difficult. Tracking requires a known frame of reference within which the object moves. If an object moves very fast, the rate at which its position is sampled must also be fast to accurately record changes in speed and direction. For confined objects, such as a fish in a tank, this is relatively easy. However, tracking a fish in the ocean is more difficult, as it is likely to swim away. If a tracking device such as a transponder is attached to a fish, then the receiving array must also move with the fish, and it in turn must be accurately tracked. Quite quickly the limits of technology are reached. Following individual units moving in space and time within a group which also moves is nearly impossible. Even if we did manage to collect the requisite fourdimensional data, analytical tools were not readily available. Distilling fourdimensional data on identified individuals into a form where interesting biological questions can be addressed is a daunting task. We were faced with interesting questions and no way to answer them. So, we did what most of us do when confounded, we found someone with complementary skills to help us solve our problems. Prewitt is a crystallographer, used to thinking about the structure of three-dimensional aggregations and trained in how to detect three-dimensional patterns. In the course of our collaboration we

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subsequently discovered other people working in the general field of threedimensional aggregation, many from perspectives that we had not initially considered. Eventually, we came to the conclusion that examining four-dimensional animal aggregations was a multidisciplinary "field" of its own. Like most individuals within any group, researchers interested in four-dimensional problems generally only have a sense of their own work, and little appreciation of that of their "nearest neighbors." Because intellectual disciplines move forward as new ideas are injected into an existing framework, we decided that it was time to reevaluate the framework for the study of animal aggregations. We convened a group of scientists who work on many different aspects of aggregation, both animate and inanimate. This book is the product of our interactions. Because each of us soon saw our studies in a new perspective (new ways to collect data, new methods of analysis, new phenomena to model, new systems for comparison, new questions to ask), we decided to begin at the beginning and review all aspects of the multidisciplinary study of animal aggregation in space-time. This new field encompasses aspects of animal behavior, ecology, and evolution as well as crystallography, geology, photogrammetry, and mathematics. The thread that ties us together is the how and why of aggregation. Sand grains on a beach and fish in a school share some similar properties. Might models of the former elucidate the latter?

1.5 Central themes and "big picture" questions A defining aspect of any field is the set of questions it attempts to answer. As a multidisciplinary group, we have come up with what we refer to as Big Picture Questions (BPQs) — issues central to the study of animal aggregation (a noninclusive list of which follows). One of the central themes connecting all of these questions deals with the basic conundrum of how a set of selfish individuals can apparently act as a cohesive, coherent whole. What are the costs and benefits of group membership? Are they positionally dependent? What information can, and do, individuals use? Do individuals have a sense of the whole? Is there an optimal group size? The study of animal aggregation can be attempted at several levels. The former questions acknowledge the central importance of the individual member and they attempt to examine the group through the combined action of its members. However, one can also look at the entire group as a unit possessing certain prop-

From individuals to aggregations erties. The second core theme embedded in our BPQs addresses the group as a whole. Why are there discrete boundaries? What is the appropriate scale for assessing pattern? Why should pattern exist in three-dimensional aggregations? Is observed three-dimensional structure no more than would result from optimal packing? The third theme attempts to integrate elements of the individual with those of the group - Essentially, trying to define the whole as some function of the parts. What are the assembly rules? Which properties of the group are epiphenomena and which are functional properties that have been selected for? Can models which predict epiphenomena be used to make predictions about individual behavior? None of the BPQs are easy to answer, and several of them are outside the framework of the scientific method, that is, they do not lend themselves to testable predictions. However, we believe these questions are a starting point from which we will launch our studies. In this book, we attempt to address some of these questions, as well as others which are logical extensions of the few presented here.

1.6 Organization - from measurement to models We have organized this book around four central issues: collecting data, analyzing data, the functional biology of aggregation, and modeling aggregation. Within each section the reader will find several chapters devoted to examples of how to address the issue or define the approach. However, each chapter addresses other issues as well. It is impossible to analyze data without first collecting it. It is useful to have model predictions when examining the functional role of individual position within the group. Rather than read cover-to-cover, we encourage readers to follow their own path through the book as each chapter leads to others within and across sections. Neither group structure, nor individual movement within that structure, can be described, analyzed, or modeled without the ability to collect data in X, Y, Z over time. In this respect, many of us have been limited by technology. It is only recently that off-the-shelf systems with the ability to collect four-dimensional information have become available. Prior to the advent of automated data collection, researchers interested in collecting four-dimensional data sets had to repeatedly digitize hundreds, if not thousands, of points. Methods sections in

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several fish schooling papers from the 1960s and 1970s are full of agonizing descriptions of the number of frames analyzed (e.g. Partridge et al. 1980 hand digitized over 1.2 million points). The endless hours of data collection were enough to turn anyone away. Today technology offers us not only visual options for data collection but also acoustic methods. In concert, these sensory modalities will eventually allow us to examine animal aggregations at the level of the individual, the group, and the habitat. The first section of the book - Imaging and Measurement - reviews the technology and specific methods available to resolve three-dimensional images and track moving points through space-time. Jaffe (Ch. 2) gives a broad overview of three-dimensional technology before focusing in on acoustic techniques. Greene and Wiebe (Ch. 4) give a specific example of data collected via three-dimensional acoustic technology. While Jaffe uses sound to attempt to follow individual plankters (his FTV system), Greene and Wiebe use sound to map plankton aggregation over several kilometer volumes of open ocean. Thus, acoustic technology lends itself to a tremendously broad range of spatial scales. Osborn (Ch. 3) reviews three-dimensional optical methods which rely on the principles of photogrammetry and gives four short examples of photogrammetric analyses in aquatic systems. The final two chapters provide examples of optical collection of three-dimensional data in aerial systems. Heppner (Ch. 5) discusses the development of devices to follow birds in flocks, along with the underlying reasons for flocking. Ikawa and Okabe (Ch. 6) discuss a system for following the movements of swarming mosquitoes. The search for three-dimensional structure or animal architecture has been one the of holy grails of animal aggregation research. Early attempts to detect structure used physical world examples, such as crystals, as a model (Breder 1976). These attempts were largely unsuccessful because the spacings of animals in a school or flock are not as regular as are atoms or molecules in a crystal and perhaps because these investigators did not employ the full range of possibilities for description that exist in the crystallographic literature. We believe that research on animal aggregations should embrace physical models, especially those created from the study of inanimate aggregation. Several authors in this volume, notably in the sections on Analysis and Models, adapt concepts from the physical sciences that can be useful in a more biological context. For example, the concept of diffusion is used by several authors to describe relative movement of aggregations and/or the movement of individuals within those aggregations. Most people think of diffusion as something that occurs when there is a physical or chemical gradient present in a system. McFarland and Okubo (Ch. 19) use advection and diffusion equations to model oxygen depletion as a function of school size. In contrast to much of the existing literature on

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schooling fish, which links schooling with ecological processes such as foraging or predation, these authors suggest that many of the emergent properties of the group (e.g. structure, density, shape) may be dictated by self-imposed physiological constraints. Griinbaum (Ch. 17) models how organisms can detect and aggregate along gradients in a noisy environment. An important aspect of the study of animal aggregation is how one describes relative movement of individuals in schools, flocks, or swarms under varying environmental conditions. Yen and Bundock (Ch. 10), making use of another physically derived concept, measure the fractal dimensions of the trajectories of copepods in two and three dimensions. A fractal dimension by itself is not very useful, but when the dimensions of two or more trajectories are compared, one can conclude that one trajectory is more sinuous than another. This might indicate that individuals making tracks having larger fractal dimensions are more disturbed by the environment than are the others. Analysis of three-dimensional data of aggregating individuals is a relatively new field, emerging as a by-product of our increasing ability to produce threeand four-dimensional data sets. In his introductory chapter to the Analysis section, Turchin (Ch. 7) divided the analysis of animal congregations based on whether data are collected on movement of individuals (Lagrangian) or population fluxes (Eulerian). (This dichotomy is echoed in the introduction to the section on models - Levin Ch. 16.) There are costs and benefits to both approaches. As an illustration, Turchin and Simmons (Ch. 8) adopt a Eulerian approach in the study of pine-bark beetle mass attacks. Rather than attempt to follow thousands of individuals, the evolution and decay of the congregation are tracked by measuring the flux of individuals past set spatial coordinates relative to the attraction source (a Southern pine). For small, moving congregations, following individual trajectories may be more appropriate. Although the Lagrangian approach is fraught with logistical difficulties, it has the advantage of allowing the researcher to analyze behavioral differences between individuals, as well as interactions between congregation members. The final two chapters in this section adopt an individually based approach to analyze the interactions between schooling fish (Parrish & Turchin Ch. 9) and swarming copepods (Yen & Bundock Ch. 10). Whether there is obvious structure or apparently haphazard arrangements of group members, the turnover of individual members through various positions within the aggregation must be mediated by rules governing the flow of traffic, such that both individuality and cohesion are simultaneously maintained. Much like the freeway at rush hour, traffic rules in animal congregations should describe interindividual interactions and predict group-level phenomena at the same time. Several of the chapters in this book deal with ways of describing in-

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terindividual movement, either from real data sets (Turchin & Simmons Ch. 8; Parrish & Turchin Ch. 9, Yen & Bundock Ch. 10), or from models of individualbased interactions (Griinbaum Ch. 17). Physical models and methods of analysis help us discern patterns and provide clues as to how animals might accomplish the monumental task of organizing themselves. However, they do not bear upon the question of why animals organize themselves. Functional considerations, which tend to center on the costs and benefits to the individual, predict a wide range of "optimal" individual actions depending on what selective forces the aggregation is experiencing. Hamner and Parrish set up the dichotomy between the individual and the group within which it exists in the introductory chapter to the section on Behavioral Ecology and Evolution (Ch. 11). If congregations are structured, that does not imply stasis, either of the group as a whole, or of the individuals within it. Group members, having made the basic decision to join and remain in the group, have a variety of positional options open to them. However, the freedom to move within the group is restricted by the positions, or even actions, of other group members. Individual animals simply may not be able to pass by their neighbors. Alternately, they may find it impossible to supersede group members already occupying desirable space. Finally, individuals may find themselves in new positions they did not actively choose to occupy, due to the movement of others around them. This general theme, choices at the level of the individual versus actions at the level of the group, is also addressed by Romey (Ch. 12), who focuses on the question: which positions within the group should individuals choose, and why? The consequences of summed individual actions are addressed by Ritz (Ch. 13) in his examination of the relationship between group size and individual optimality. Traffic rules also provide a way to predict what neighboring individuals will do, given a certain situation, as long as all individuals "play by the rules." Thus, gregarious animals may be paying attention to a much smaller data set than the trajectories of all groupmates within their sensory range. The kinds of information individual group members might use, and the consequences of information transfer across the group, are the subject of chapters by Dill, Holling, and Palmer (Ch. 14) and Schilt and Norris (Ch. 15), respectively. Rules governing individual movement within a congregation, and the emergent properties or "group behaviors" are a subject not easily addressed either experimentally or observationally. The final section of this book explores mathematical approaches to the study of animal aggregation. Modeling is a powerful tool because it allows the freedom to test rules of association by setting assumptions and then determining whether the computer congregations display the attributes of their real-world counterparts. Levin, in his introductory chapter to the Models section (Ch. 16), explores several of the conceptual issues inherent in the

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construction and use of models of aggregation, including scale, emergent pattern, and the interaction between explanatory and actual reality. The remaining chapters explore various rule sets under which aggregation will either evolve (Grunbaum Ch. 17; Edelstein-Keshet Ch. 18; Warburton Ch. 20) or break down (McFarland & Okubo Ch. 19).

1.7 What's next? The strength of this volume, namely that it is a broadly based approach to the study of three-dimensional animal aggregations, is also its drawback in that no subject is covered exhaustively and many topics are untouched. Rather than a final work, this book represents an initial attempt to both define and understand animal aggregations in three-dimensional space and time. We intend it as a springboard for future thought, discussion, and science. Furthermore, we are neophytes. Our measuring devices, our computers, our words, and our graphics may never let us adequately describe the aesthetic beauty of a turning flock of starlings or a school of anchovies exploding away from an oncoming tuna. What we see as apparent simplicity we now know is a complex layering of physiology and behavior, both mechanistically and functionally. It is our sincere belief that an interactive, multidisciplinary approach will take us farther in understanding how and why animals aggregate than merely pursuing a strictly biological investigation. It is also more fun.

Part one Imaging and measurement

2 Methods for three-dimensional sensing of animals JULES S. JAFFE

2.1 Introduction Most animals have the ability to sense their world three-dimensionally. Using visual, pressure-related, and chemical cues, which are filtered through sophisticated neural circuitry and central processing, animals continually measure the distance to and shape of objects in their environment. If the objects are moving, as in an oncoming predator, or fleeing prey, animals automatically track and predict trajectories, allowing both escape and interception. Of course, all of these complex calculations are processed in real time. When we attempt to emulate these feats of three-dimensional perception with scientific instruments and complex computers, we quickly discover that four-dimensional measurement is extremely difficult. This chapter is a general survey of the area of three-dimensional sensing. In recent years, three-dimensional sensing has seen much development, and there is every indication that the current proliferation of computer techniques and capabilities will fuel the continued acceleration of this field. The primary goal of this chapter is to review present methods used to measure the three-dimensional patterns of individuals as well as aggregations of animals in the laboratory and the field. Secondarily, I will comment on the future potential of methods under development. In a very general sense, the requirements for three-dimensional imaging should be examined with respect to the information that one is interested in. However, most applications require measurement in both space and time. For instance, in the area of medical imaging, both static (i.e. anatomical) and dynamic (i.e. physiological) information is necessary to judge individual health. In the case of astronomy, both the position and the trajectory of heavenly bodies are necessary to deduce the dynamic laws by which the solar system evolves.

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In a physical sense, we are interested in measuring the state vector, a function of both position and time of a system. In principle this is everything we need to know. However, many three-dimensional sensing methods assess state variables indirectly, and these data require considerable subsequent interpretation. To reconstruct the necessary three- or four-dimensional data set, inferences must be made by using the physical relationship of the measured property to the ultimate property that one is interested in measuring. For example, when X-rays are used to map the three-dimensional structure of internal organs, a procedure known as computerized tomography (CT), what is actually being measured is the X-ray absorption of electromagnetic radiation through biological tissue, which is proportional to atomic number. With respect to animal aggregations, measurements can be made at several relevant scales. At coarser scales of resolution, one would like to have the capability to measure parameters of an entire animal aggregation, ideally, in both space and time. What is its position, what is its shape, and how do these parameters evolve? In addition, a set of much more detailed questions can be asked regarding individual animals. That is, how do the positions of aggregation members vary over time in both absolute space, as well as relative to each other. However, one need not stop here, because traits of the individual animal, for instance tail beat frequency and amplitude in fish, can be examined for themselves as well as with respect to those of neighboring individuals. A criterion of primary importance to three-dimensional sensing is the degree of spatial resolution, functionally defined by how close together two point objects can be placed without coalescing. Resolution can be specified linearly, e.g. in meters, or more appropriate to three-dimensional systems, in three-dimensional volumetric resolution elements-voxels. These are the three-dimensional analogs of pixels. Adding dimensions quickly increases the complexity of the measurement process. One can easily image the side of a cube containing 1000 elements; however, in three dimensions, the total number of voxels in the image is 109. Three-dimensional imaging thus places severe demands on both processing speed and memory storage. Additional complications often arise because the actual measurement is, in fact, a mathematically transformed attribute of the real three-dimensional object. Suppose that we desire a vector X which consists of 109 elements. What actually is measured is vector Y, related to X via a linear transformation X - H Y. In this case, the matrix H would consist of 109 X 109 elements, beyond the capability of current computers. To overcome this problem, many high-resolution imaging methods (e.g., X-ray, computerized tomography) approximate this space as 1000 sets of 1000 X 1000 matrices, which can be computed quite easily.

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Let us imagine then, that we are interested in examining a state vector, S(X,t), at some number of three-dimensional locations, with some spatial resolution, AX and some temporal resolution, At. The following sections will indicate how this has been done in the past and how some of the emerging techniques will contribute to our knowledge of the three-dimensional structure of animal aggregations in the future.

2.2 Existing methods Existing methods for measuring three-dimensional information can be classified in many different ways. I have grouped available techniques into a somewhat ad hoc classification by similarity of mathematical procedure. Three-dimensional sensing can be appreciated through knowledge of mathematical techniques called inversion procedures. A forward model is used to predict the resultant set of observations of an experiment (the outcome) given prior knowledge of the three-dimensional structure of the object, the collection geometry, and the experimental procedure. By contrast, an inversion procedure computes the three-dimensional structure of an object; the latter is a more difficult problem, partly because knowledge of the forward model is a prerequisite to the inversion. Application of these procedures can be found in such diverse fields as seismology (Menke 1984) and medical imaging (Herman 1979; Kak & Slaney 1987). A journal is now dedicated solely to this class of mathematical analyses (Inverse Problems).

2.2.1 Transmission techniques Let us slice a three-dimensional structure into parallel two-dimensional sections (Fig. 2.1). If the complete structure of each of these parallel sections can be obtained, the entire three-dimensional object can be reconstructed. Transmission techniques achieve this goal by passing natural or artificially created radiation through an object (Fig. 2.1) and projecting a shadow image onto a recording device. The incident radiance distribution of intensity /0, will be attenuated as: (2.1) where the path integral dl is taken over the radiation path through the object and f(r) is the object density resulting in the attenuation of the radiation. In the easiest case, scattering will be small compared to attenuation and radiation will

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o <x> y)

Figure 2.1. Geometry for a transmission tomography experiment.

propagate through the structure in a straight line. Considering only the ith single plane of density/(x, y, zt), by taking the logarithm of the measured intensity and neglecting an additive constant, the received intensity, can be measured as:

• 1f

(2.2)

f(r)dl

(e.flline

Here, the notation (B,i) line signifies that for a general projection, the integrals are computed along a line specified by 6 (view angle) and t (distance along the projection). Fourier transforms of this equation produce: where

= sxcosd

sy sin 9

(2.3)

This is the projection slice theorem, which states that the projection of a twodimensional object can be related to a slice through the structure of the Fourier transform of the object. The entire two-dimensional transform of the object can be obtained by taking different projections (corresponding to the shadows of different views) and then "filling up" Fourier space. Once the entire Fourier space is filled at sufficient density, an inverse Fourier transform (two-dimensional) can be used to obtain all of the two-dimensional slices needed to recreate the threedimensional structure of an object. This latter process is known as tomography.

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In the general case, data are represented by the data vector Y, the collection geometry can be embodied in a transformation matrix H, and the unknown values (i.e. the density values in three-dimensions) are represented by X. The datacollection process can then be approximated by the linear transformation: Y = HX

(2.4)

And the unknown density can be obtained from an inversion procedure: X = H~lY

(2.5)

The matrix for a 10003 voxel image is 10009, but by using the tomographic approximation the problem can be solved as a set of 1000, 10002 images, summarized as: f(r) = F~ ^WF^Pgil))}

where

s = sx cos 0 + sy sin 0

(2.6)

Here, Wis a weighting matrix which takes into consideration some of the redundancy in the Fourier coefficients. F{ represents a one-dimensional Fourier transform, and F2 represents an inverse two-dimensional Fourier transform. Many complex three-dimensional problems can be solved by using simplifications of these matrix structures. The most widely known application of three-dimensional inversion techniques is computerized tomography (CT) (Herman 1979). This technique uses either a parallel or fan beam of X-rays which are projected through a body over a wide range of incidence angles. Starting from the shadow of the object, Pe(t), the data are subjected to a linear inversion procedure, as above, allowing computation of the three-dimensional structure. As is common practice now, threedimensional computer graphics techniques permit these data to be viewed as a composite three-dimensional object, rather than as a set of two-dimensional slices (Fishman et al. 1987). The electron microscope is another example of the use of three-dimensional transmission imaging techniques. Transmission electron tomography can be used at very high resolution to image individual molecules (Henderson et al. 1990) or, even at lower resolution, to image the threedimensional structure of DNA (Olins et al. 1983). Transmission techniques have been used also for sonar imaging. The original idea was to use the attenuation of a sonar beam in a manner similar to computerized X-ray tomography, known as acoustic tomography (Mueller et al. 1979); however, because of unacceptable scattering, resolution was poor, and a more complex method based on travel times was developed. Acoustic diffraction tomography accommodates the fact that sound waves diffract when traveling through tissue. Unfortunately, both of these methods have met with limited practical success, probably due to multiple scattering.

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Deciphering the three-dimensional structure of various biological specimens can also be accomplished with optical microscopy. Serial microscopy (Agard & Sedat 1983) uses the fact that optical microscopes can be set to an extremely narrow depth of field, and thus only one "slice" of a specimen is in focus at a time. Ideally, serial two-dimensional photographs at different depths are inverted to generate three-dimensional structure (Castleman 1979). Unfortunately, data obtained from serial sections is often convolved together in such a way that accurate three-dimensional reconstruction is difficult. A more recent development, confocal microscopy (Wilson 1990), seems to circumvent some of the problems associated with the serial sectioning technique. This method uses a set of camera pinholes to eliminate scattered light (which contains little information about the structure). Procedurally, the system is similar to optical serial sectioning except that a much shorter depth of field is possible. One additional feature of this method is that the resolution of the resultant structures is twice as good as that of a standard microscope. For three-dimensional reconstruction of objects, the short depth of field is invaluable. Many commercial confocal optical imaging systems are in the marketplace today, and a host of biological structures are being explored using this technique. Holographic optical techniques also have recently been used to look at the three-dimensional structure of both natural (zooplankton) and man-made (cavitation nuclei) structures in the ocean. Although several configurations are possible, the technique that seems to be favored consists of photographing an inline or Fraunhoffer hologram. Here, the wave that is scattered by the set of objects is allowed to interfere with the wave that is unscattered and propagated straight through the structure. The interference pattern created between the unscattered and the scattered beam is recorded on high-resolution film. The three-dimensional structure of the object can be reconstructed by using an optical bench which illuminates the recording film with a coherent light beam and then uses a set of lenses to image the resultant pattern. A computer recording can then be made on a plane-by-plane basis to visualize the entire volume, or the two-dimensional images can be viewed directly. A system currently under development (Schulze et al. 1992) will have the capability of observing zooplankton at very high resolution in a volume of approximately 1000 cm3. In some cases, specific optical properties of the object(s) can be used to facilitate three-dimensional imaging. An example is fluorescence imaging, a technique that will allow three-dimensional mapping of phytoplankton via the fluorescence of their chlorophyll-a distribution (Palowitch & Jaffe 1992) (Fig. 2.2). A light stripe beam is projected parallel to the camera plane at a distance and an image of the fluorescence induced in the chlorophyll is recorded by the camera. The illumination stripe is then translated to the next plane and another

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SEQUENTIAL IMAGE PLANES

LIGHT SOURCE Figure 2.2. The system for measuring the three-dimension distribution of chlorophyll-a using fluorescence imaging. Depicted here is an experimental setup that consists of a light source and a camera.

image is collected. This procedure is continued in sequence until a given volume is mapped out. A system of equations can be used to describe the forward model, which can then be inverted to determine the three-dimensional distribution of chlorophyll-a in a way similar to the optical serial microscopy mentioned above. The technique now works for small volumes (1 m3), and the potential exists for imaging larger volumes as well as using other biochemical compounds.

2.2.2 Emission techniques Emission techniques use natural or induced emission of sound or electromagnetic radiation to locate, and in some cases track, objects in three dimensions. In the case of natural emissions, these methods are referred to as passive techniques. For example, radio astronomy images distant celestial bodies, and sound emitted by animals can be used to track them. In active techniques emissions are induced. Examples include stimulating a nucleus into a higher energy state and imaging the electromagnetic wave emitted during decay or attaching a sonar "pinger" to an animal. The most widely known contemporary active emission techniques are used in medical imaging. An array of different imaging techniques all use the emission of energy from inside the structure. In some cases, such as magnetic resonance imaging or MRI, an image is formed by scanning through an activated three-

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dimensional volume. In the other techniques, radionuclides are first ingested and then imaged. In positron emission tomography (PET), a pair of coincident y rays are given off and are then localized by coincidental reception at a ring of detectors. More information on these medical techniques is found in general texts (Kak & Slaney 1987).

2.2.3 Other techniques Two other types of imaging methods which do not really fit into the above scheme but which deserve attention are reflection methods and triangulation methods. Remote sensing, or monostatic reflection methods, represents a class of techniques in which the illumination source and the receiver are close together or even superimposed. A schematic of a simple reflection imaging technique which can be applied to any type of propagation wave is shown in Figure 2.3. In this application one measures the "time of flight" of either light or sound waves of the reflected wave over the target range. Here a pulse of illuminating energy is propagated in the medium at either a single angle with a narrow beam or a multiplicity of angles with a wide beam (Fig. 2.3). A single sensor in the first case, or an array of sensors in the second, is used to judge both the intensity of the reflected radiation and the amount of time (time of flight) it takes for the wave to return. For opaque reflective bodies, only one return pulse per look direction is

©Mfc/SIO

Figure 2.3. A simple reflection imaging system.

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measured. For translucent bodies, radiation is backscattered at all ranges. In both cases, by knowing the time the wave was sent and the speed of radiation in the medium, the reflectivity of the three-dimensional scene as a function of range and direction of return of the wave can be computed. In the case of optical techniques, the extremely fast speed of light (3.0 108 m/sec) creates several advantages and disadvantages. On the one hand, range resolution can be limited, due to the extremely fast digitizing hardware that is needed to record the transient wave. On the other hand, the extreme speed of the light wave can allow many pulses over a very short time period, permitting simpler optics and a much higher scan rate. In the case of sonar techniques, the slower speed of sound (1.5 103 m/sec) permits a much slower digitization rate at the expense of a slower scan speed. Triangulation methods are used primarily in conjunction with optical imaging. The basic idea is that if several views of an object (like stereo pairs) are available, then location in three dimensions can be inferred from a computational procedure which uses "optical disparity," or the difference between the images. In the general case, two views are sufficient; however, several problems usually occur. One of them concerns deciding which points in the final image correspond to others in the second images (the correspondence issue). As the number of objects increases, correspondence becomes an increasing problem. In addition, there is an issue of data sensitivity. Unfortunately, these two problems work against each other. For example, given identical views, the correspondence is, in fact, trivial. However, there is no optical disparity from very different images. On the other hand, given substantial optical disparity from very different views, the accuracy in the reconstruction would be great if similar points could be identified. Osborn (Ch. 3) reviews optical triangulation methods extensively.

2.3 Application of three-dimensional measurement techniques to in situ sensing of animal aggregates Many of the techniques I have described are used primarily to discern the threedimensional structure of a single object (e.g. the internal configuration of organs within a human body) or the three-dimensional spatial relationship between objects (e.g. fluorescence imaging). At present, these technologies have yet to be applied to track an individual, or group of individuals, as they move through space and time. An interesting result of my broad review of these many approaches to three-dimensional mensuration is that almost none of them meet our specific goal of simultaneous good resolution in both time and space. It is also clear that one of the problems in applying the above techniques to sensing individual animals and animal aggregations is the often prohibitive cost. On the

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other hand, surely there are clever ways of using these principles to learn more about animal aggregations.

2.3.1 Optics Optical techniques have unique advantages. The ready availability of either video or film allows lots of information to be stored at quite high rates. For example, in the case of video, most black and white images currently can be approximated by a matrix of grey levels consisting of 360 X 240 elements. Video images are usually recorded at 30 frames/second; if a single element is equal to one byte, aggregated data storage is several megabytes/second. Film also has tremendous storage capability. In the case of 35 mm holographic imaging film, 3000 line pairs/mm can be recorded. Here, the amount of information that can be stored is as high as 109 bytes in a single frame! Optical techniques also have good inherent spatial resolution. Graves (1977) used a slowly sinking camera to attempt to measure the density of fish photographically as the device sank through schools of anchovies. Klimley and Brown (1983) used stereophotography to measure size and spacing of hammerhead sharks and Aoki et al. (1986) did the same with schools of jack mackerel (Trachurus japonicus) and mackerel {Scomber sp.). Graves localized the fish spatially in 3-D by assuming that the animals were all the same size, so that smaller images represented fish that were farther from the camera. A stereophotographic approach avoids this objection, but it is still limited in range by the attenuation of light in seawater and the opacity of fish to light. Partridge et al. (1980) and Cullen et al. (1965) judged the three-dimensional position of fishes in a school via a structured lighting technique that cast shadows of the fish on the side or bottom of the aquarium. By judging the distance between the fish and its shadow, the three-dimensional position of the fish was deduced. This facilitated the studies of many aspects of the behavior of these animals in schools (Partridge 1981). However, this technique is not readily adaptable to the field. Osborn (Ch. 3) provides a detailed discussion of the use of multiple optical images (photogrammetry) to map and track individuals in three dimensions. However, optical techniques cannot look through the bodies of animals that are opaque to light. Ultimately, one cannot see the forest through the trees. When one animal occludes another, the three-dimensional positions of all the animals cannot be determined. In fact, only the outside of an aggregation can be determined in most situations. This has limited the use of optical techniques to situations where the densities of the animals is low or where ranges are short, so that the projection of one animal upon another does not occur.

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2.3.2 Sonar Unlike light, sound will both reflect off of, and pass through, most living tissue. Furthermore, because water conducts sound much farther than the attenuation distance of light in even the clearest oceans, acoustic imaging is a much more flexible tool. For example, acoustic imaging can be used at night, or at depth, where introduced light necessary for optical resolution might alter the behavior of the animals being measured. The use of acoustics in fish stock assessment is not new. Almost all sonar methods can be classified as reflection techniques. Echo sounders have been used in fish detection since the mid 1930s (Sund 1935). Since then, two major approaches to acoustical fish stock assessment have gained prominence: echo counting and echo integration. Echo counting identifies echoes from individual targets, which allows the numerical density of fish to be directly estimated. With a good target strength model (see below), the size distribution of fish within a school can be estimated. However, this technique depends upon the fish being distributed sparsely enough so that individual echoes are distinguishable. Therefore, abundance in large, dense schools will be underestimated. Echo integration, first proposed by Dragesund and Olsen in 1965 (Dragesund & Olsen 1965), relates the total acoustical energy reflected from a school of fish to the amount of biomass it contains. Because it does not require individual echoes, echo integration can be used with higher concentrations of fish than can the echo counting technique. The major drawback is that the relationship between fish size and echo energy must be known before density can be evaluated. This is by no means a simple problem, and has been the focus of research since the development of the technique. In the typical application, the total reflected energy is assumed to be a known linear function of the number of fish. In many cases the dependence of target strength (B) on fish length (L) can be described by the equation (Foote 1983): TS = 20 log L + constant

(2.7)

However, this relationship breaks down when the density of the aggregation substantially attentuates the sound in the observation field. For example, Rottingen (1976) has shown that there are nonlinearities associated with shadowing; fish nearer to the transducer block some of the sound energy so that more distant fish contribute less. Modifications to the linear equation to account for shadowing have been proposed (Foote 1990). Target strength relates the sound level transmitted to a fish to that reflected from it. It is most notably a function of the presence or absence of swim bladder (that is, a contained gaseous medium), although the species under consideration,

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fish size, and even time of day can also affect target strength. Foote determined that 90-95% of the reflected energy from an individual fish is due to the reflection from the swim bladder (MacLennan 1990). Target strengths of Atlantic mackerel (Scomber scombrus) with no swim bladder are about 20 dB lower those of slightly smaller cod (Gadus morhua), which have swim bladders (MacLennan 1990). In addition, MacLennan noted a diurnal variation of about 7 dB in the target strengths of both mackerel and cod. Target strengths have been measured in a variety of ways, including the use of dead fish, live anesthetized fish, caged fish, and finally, free swimming fish, with the last believed to be the most realistic. Two methods of direct in situ measurement have gained prominence in recent years; dual-beam sonar and split-beam sonar. In general, however, both approaches give satisfactory results in terms of the target strengths of individual fish. Interested readers are directed to Ehrenberg (1979). In addition, for a general review of different methods, see Foote (1991). An interesting alternative approach to fish size estimation is to measure the Doppler spread of a narrow-band acoustic signal and relate this to tail beat velocity, which is in turn related to fish length. Holliday (1972, 1974) has also suggested a possible approach to fish identification through the use of wide-band sonar. Because each species has a characteristic size and shape of swim bladder, at a given body length, the frequency content of the reflection from a school of fish will be enhanced at the frequencies corresponding to the resonant frequencies of their swim bladders. Despite the obvious benefits of sonar for oceanographic applications of threedimensional imaging, there has been a paucity of effort to date. In fact, few documents refer to the advantages of using multidimensional arrays for fish assessment. Sonar sensing of the underwater environment is a natural alternative to visual imaging in situations where greater range capability is desired. However, in contrast to light, the speed of sound in water is relatively slow (1500 m/sec), and this prevents several different types of schemes that are feasible in optical imaging from being used with sound. Underwater "high-frequency" sonar imaging has been an area of intense research interest for some time (Sutton 1979). The basic principles upon which almost all of these sonar devices work stem from the relationship between a group of transducers and its sensitivity pattern (Goodman 1986). Assuming that/(jc) represents the object to be imaged and the far field pattern of this object is/(s), the equation relating/(x) and/(s) at the appropriate range can be represented as:

f(s) = exp (ikl) exp| ^5?1 jj f(x) exp[-2m(s-x)/\l} dx^

(2.8)

Methods for three-dimensional sensing

29

The integration is taken over the region of the object/(x). Here / represents the distance from the object to the receiving array and k is the wave number 2ir/l. Note that this relationship can be viewed as a Fourier transformation. The designer of a sonar imaging system must determine how to convert from the Fourier domain to the real space domain in order to obtain an image. One option would be to build a sonar lens; however, adequate sonar lenses are extremely temperature sensitive (Sutton 1979). Alternatively, the relationship can be inverted either by implementing the math electronically or by using software (Goodman 1986). An additional criteria which describes the performance of a sonar imaging system is the range resolution, or accuracy in the judgment of distance. In this case, the resolution or ability to discriminate the distance between two targets in range can be related to the length of the pulse T used to create the image as: I = cT/2

(2.9)

where c is the speed of sound and / is the range-resolving capability of the system. A more sophisticated treatment of this topic takes into account the ability of the imaging apparatus to produce very short bursts of sound. Here, the temporal bandwidth of the transducer (BW) can be related to the shortest temporal pulse that can be created so that T = //BW. That is, the temporal duration of the pulse is the inverse of the bandwidth. This treatment has considered only the simplest type of waveform that can be generated, a gated sinusoid. More sophisticated signal design and its associated processing can result in increased signal to noise ratio (SNR), but the fundamental diffraction-limited and bandwidth-limited resolution can rarely be exceeded. An additional complication occurs in sonar imaging that is not typically present in the light optical case. Because most sonar imaging systems use almost single wavelength sound and most surfaces are rough with respect to this wavelength (1.5 mm @ 1 MHz), the reflection of sound can be considered equivalent to the superposition of a random distribution of time delayed wave forms. This leads to a special kind of multiplicative noise called speckle (Goodman 1986). For fully developed speckle, the SNR is 1. Clearly, this results in very noisy images. Jaffe (1991) has proposed an approximate classification of sonar imaging systems, relative to increasing complexity (Fig. 2.4). In the simplest case, a single transducer is used to obtain an image of continuous backscatter by transmitting sound and then recording the magnitude of the returned wave as a function of time. This is essentially a one-dimensional imaging system. An increase in complexity and also functionality can be obtained by pointing the device in different directions and recording the intensity of the backscattered sound as a function of

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Jules S. Jqffe

SINGLE TRANSDUCER

SINGLE BEAM MECHANICALLY SCANNED VERSION OF (a)

MQ

IMAGJNG

Figure 2.4. A proposed classification for sonar imaging systems. inspector angle, to obtain two-dimensional images. See Greene and Wiebe (Ch. 4) for an interesting three-dimensional application of this technique. A third option, used by a number of commercial systems, is to have a onedimensional array of transmitting and receiving transducers. These systems propagate a beam of sound which is broad in both the horizontal and vertical direction and then resolve the horizontal beam into a number of narrow beams in the horizontal. The image that is formed is essentially a two-dimensional map of backscatter intensity at a given look-angle versus distance. Finally, use of a two-dimensional array can resolve the image into individual beams in both the horizontal and the vertical directions. These systems can create a threedimensional map of backscatter intensity versus direction in both horizontal and vertical direction.

2.3.3 Three-dimensional acoustic imaging Over the last several years we have been developing a three-dimensional underwater imaging system (Fig. 2.5), primarily for tracking zooplankton. The system is composed of two sets of eight "side scan"-like array elements operating at a frequency of 450 kHz which are stacked and pointed in slightly different directions (2 degrees). One set of eight transducers is used as a transmitting array while the other set receives. The system transmits sequentially on all eight transducers in the transmitting array and reflected sound is continuously received, amplified, and digitized on all eight of the receiving transducers. This process continues until all of the transmitting transducers have played their sounds. If

Methods for three-dimensional sensing

31

IMAGING SEQUENCE: Transmit on Row 1 -- Receive on all Columns

I

I

Transmit on Row 8 -- Receive on all Columns

Transmit Channels

(fi)

SYSTEM SPECIFICATIONS: Center frequency (f0): 445 kHz Pulse length (t p ): 40-100 msec Number of beams: 64 Receive Channels (8)

BEAM ORIENTATION:

Number of transmitters and receivers: 16 All elements are identical 2° x 20° Horizontal resolution 2° Vertical resolution 2° Data acquisition rate: 4 frame/sec

©Jaffe/SIO

Figure 2.5. The beam configuration for the FTV system.

one considers the three-dimensional space as a matrix, our system scans the space by transmitting on the rows, one by one, and receiving on all of the columns each time. The pointing angles of the transmit and receive transducers provide the azimuth and bearing resolution, and the time delay of the signals, after transmit, provides the range information. The system's specifications are summarized in Figure 2.5. Figure 2.6 shows the result of tracing a moving object in three dimensions. The approximate dimensions of the figure are 1 m X 1 m X 3 m. Shown inside the rectangle, on the left-hand side of each figure, is a feedback signal which ini-

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Jules S. Jaffe

Figure 2.6. Successive scenes of a test target from an animated film.

tialized each pulse. The test target is shown in the right-hand side of each figure as a solid three-dimensional patch. It is obvious that the object can be visualized as it moves in three dimensions. In the future the system will be deployed on an underwater robot to track individual animals in the water column. We also plan to use it at a fixed depth to quantify the flux of animals as they migrate vertically through the water column on a daily basis. We have also pursued the idea of creating a dual-frequency, dual-resolution imaging system. Because the cost of a sonar system is proportional to the number of independent look directions, it makes sense to maximize the amount of information that can be acquired from a given set of sonar transducers. In some situations a high-resolution image is desirable even though it may be unnecessary to have this high resolution over the entire field of view of the sonar. In fact, a lower resolution image may be suitable over the entire field of view with a highresolution image only in the center of the image. I call this type of imaging system "foveal," in analogy to the basic principle of human vision (Fig. 2.7). The system is designed to assess both the extent of aggregations of fish and characteristics therein, such as interanimal distances. Lower frequencies determine the outline of the school of fish and higher frequencies concurrently obtain interanimal spacings.

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Advanced Concept for Dual Resolution Sonar /} Imaging System

©Jaffc/SIO

Figure 2.7. The proposed foveal sonar imaging system. We are currently developing a prototype of this system by augmenting our existing 450-kHz imaging system with an addition set of transducers at 1.5 MHz. We plan to create a system which has a set of 8 2A degree X 2A degree beams with a concentric field of view (Fig. 2.7). This system could be used to image both the extent of a mass of zooplankton and the individual animals inside. Another possible use of this system is to look at predator-prey interactions between small fish and zooplankton. Because these two classes of animals have very different acoustic target strengths as a function of frequency, it has been difficult to simultaneously image both targets using one frequency. It is possible that a larger version of this system could be used to answer some of the interesting questions posed in this book with respect to movement of individuals and resultant "group" behavior of fish schools. What are the requirements that such a system would have in space and in time? As a modest goal, one can imagine a laboratory type system that has the capability of discerning the three-dimensional positions of an aggregation offish in a tank that is approximately 20 m across (Fig. 2.8). For example, Partridge (1981) analyzed the movement of saithe in a 10-m tank using an optical threedimensional system. Here, fish velocities were always less than 1 m/sec and the interanimal spacings were never less than approximately 2-5 cm. Given this as a starting point the basic system can be designed. Because of the speed of sound propagation (1500 m/sec), it takes approximately 1/15 of a second for the sound to be reflected from the farthest object in a

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Jules S. Jaffe

ELECTRONICS

COMPUTER

TRANSMIT BEAM (60°) ©MCc/SIO

Figure 2.8. The proposed mills crossed array three-dimensional imaging system.

tank of this size. If interanimal spacing is approximately 0.3 m and the top speed of the animals is 1 m/sec, it makes sense to have a system with an angular resolution of approximately 10 cm and a frame rate of at least 10 frames/sec. With the frame rate and the spatial resolution matched, the animals can then be tracked unambiguously. A system with a center frequency at 200 kHz and an aperture of .75 m would certainly fulfill this goal. The resolution of this array would be approximately 10 cm at the full tank width of 10 m. A transmit element of small size (1 \ ) could be used to insonify a cone of width 60 degrees. A crossed array of receivers of 100 elements in the horizontal and 100 elements in the vertical could be used to obtain the necessary resolution in these directions. With a bandwidth of 25 kHz, range resolution would be approximately 3 cm. Crossed arrays are a solution to obtain two-dimensional beams without having fully populated arrays; e.g. this system would have 200 receiving elements instead of 10,000. Systems of this type are known as Mills crossed arrays and have well known trade-offs between side lobe suppression and angular resolution. Other types of array designs such as random or aperiodic arrays are possible, but unconventional. The advantages of this type of acoustical three-dimensional remote sensing system over optical

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35

systems would be that (1) the sonar system could operate in optically opaque environments and (2) occlusion of animals would not be a problem if the animal densities were not too high.

2.4 Conclusions I have reviewed the most common types of three-dimensional imaging systems that exist today. These systems are in routine use and have been used to address a variety of scientific questions from geology to cell biology to animal behavior. Although many variations of these systems exist, they can all be put into a relatively coherent framework via the classification methodology introduced here. The application of these systems with respect to sensing animals or animal aggregations has been addressed. The special area of interest pursued here has been the application of these techniques to sensing animals in the sea. In this context both optical and sonar imaging systems have been reviewed and their relative advantages listed. Several projects, underway in my lab, with the collective goals of obtaining three-dimensional information about the distribution and extent of both phytoplankton and zooplankton in the sea have been discussed.

Acknowledgments The author would like to thank the National Science Foundation for supporting this work under grant OCE 89-143000, the NOAA National Sea Grant College Program, Department of Commerce, under grant number NA89AA-D-SD128, project OE-15 through the California Sea Grant College, and the Office of Naval Research, grant number N0014-89-1419. The author would also like to thank Andrew W. Palowitch and Duncan E. McGehee for contributing to this chapter and Kenneth Foote for reviewing an early version of the manuscript.

Analytical and digital photogrammetry JON OSBORN

3.1 Introduction Photogrammetry is the "art, science, and technology of obtaining reliable quantitative information about physical objects and the environment through the process of recording, measuring and interpreting photographic images and patterns of radiant imagery derived from sensor systems" (Karara 1989). This chapter is an introduction to photogrammetry and its application to biological measurement as it relates to the analysis of an animal's position and motion within a three-dimensional aggregation of similar individuals. The principle analytical methods of measuring three-dimensional coordinates from two photographic images, the geometric basis of stereovision, and three-dimensional visualization are described. Although I concentrate on two-camera systems, the principals can be extended to multistation photogrammetry. I use typical commercial photogrammetric systems and recent applications to illustrate the use of photogrammetry and its costs and complexity. Measurement techniques are centrally important to all of the discussions of three-dimensional animal aggregations in this book. Humans capture images of their surroundings through paired two-dimensional, camera-like eyes, and our brains are able to instantly reconstruct complex images that accurately reflect the three-dimensional world. We make measurements of distance, volume, shape, color, and motion with blinding speed, and we react behaviorally to this incredibly complex array of information with reliability and safety. We take these astonishing feats of visual performance for granted, and it is only when we attempt to recreate simple three-dimensional optical tasks with cameras and computers that we begin to appreciate the actual complexity of three-dimensional optical measurement. Animal aggregations in rapid motion create visual confusion that confounds our ability to track individual animals visually within an aggregation. Cameras and computers can resolve this confusion because cameras record behavioral 36

Analytical and digital photogrammetry

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patterns that can be reviewed repetitively and in slow motion, providing a perceptual luxury that we could otherwise never experience. When movement within the aggregation is reviewed in slow motion, most of the visual confusion disappears. We can then begin to sort out how individual animals react to one another and to individuals of other species, such as when a tuna attacks a school of fish or a falcon a flock of finches.

3.2 The geometry and process of image capture A photograph is a two-dimensional projection of three-dimensional reality, also known as the object space. For a photograph taken with a geometrically perfect camera, every point in three-dimensional object space is imaged through the perspective center of the camera onto a perfectly flat image plane, the photograph. The distance from the perspective center (camera) to the image plane (film) is called the principal distance, and in most respects this is the same as the focal length. For convenience, photogrammetric formulae are normally derived in terms of a positive image, positioned in front of the perspective center (Fig. 3.1). A photograph is not an orthographic projection and it cannot be read linearly like a map. Mathematical representation of a single photograph is normally based on the principle of collinearity. According to collinearity, any point in the object space is connected by a straight line running through the image point on the positive and ending at the perspective center (Fig. 3.1). This condition is expressed by two equations for every such point. The collinearity condition equations can be extended to include parameters which describe additional systematic errors in the image, such as errors caused by disturbance of the light rays passing through object space, distortion of rays within the camera lens, distortions of the recording medium (film or electronic sensor), and errors attributable to the image-measurement process. To reconstruct an object in three dimensions, it must be photographed from at least two positions. Although the collinearity condition is sufficient to calculate the parameters which describe a stereomodel, the mathematical solution may also be based on the principle of coplanarity. That is, for any object point, there is a single plane described by the object point and the two perspective centers, which includes the two image points on each positive (Fig. 3.1). This condition is expressed by one equation for every such object point. The mathematical reconstruction of an object using image coordinates measured on two or more photographs is normally achieved by calculating three distinct orientations: interior (within the cameras), relative (between the cameras), and absolute (between the cameras and the object space). I will describe the rel-

Jon Osborn

38

L2

perspective centres

principal distance

object space

Figure 3.1. Geometry of a stereopair. evant parameters at each scale of orientation, and then discuss how to solve for them. 3.2.1 Interior orientation Interior orientation describes the internal geometry of the camera with reference to four values: principle distance, principal point, lens distortions, and image distortions. The principal point is the intersection of the camera's optical axis at the focal plane, the coordinates of which are expressed relative to either the edge of the image, fiducial marks at the corners of the film, or a grid of reseau marks which are imaged onto the film. Lens distortions can be described by radial and decentering distortion functions. Image distortions, caused by film or sensor distortion, are often irregular and are thus harder to quantify. Cameras are classified according to the accuracy and stability of their interior orientation. Metric cameras are precisely constructed instruments, specifically designed for photogrammetric applications, and they exhibit very low and stable lens distortions. Fiducial marks are used to define the image coordinate system, and film-flattening devices such as a vacuum back are used to minimize film distortion. Metric cameras are manufactured by Wild, Zeiss, Hasselblad, and others. There are no truly

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metric underwater cameras. Semimetric cameras exhibit relatively low and stable lens distortions. They may contain fiducial marks and, rather than a filmflattening device, contain a grid of reseau marks so that film distortions can be modeled. Semimetric cameras are manufactured by Rollei, Leica, Hasselblad, and others. The Camera Alive CAMEL 70 mm and the Photosea 2000 are semimetric underwater cameras. Digital CCD video cameras and electronic still cameras can usually be considered to be semimetric. Nonmetric amateur cameras are not designed for photogrammetry, but they are affordable and they have operational advantages such as low cost. The Nikonos is a nonmetric underwater camera. Nonmetric cameras exhibit high and unstable distortions and do not contain fiducial or reseau marks. In an analytical solution, it is the unreliability of distortions more than their magnitude that is of concern, because systematic errors can easily be modeled. Yet even unreliability can be overcome by making frequent calibrations (i.e. for each photograph taken). For most biological applications, the type of camera to be used depends more on project considerations, such as cost, portability, and object space control, rather than on accuracy. Various calibration techniques are used to determine a camera's interior orientation parameters. Laboratory methods (collimators and goniometers) are used for large-format aerial mapping cameras, but these are used only occasionally for metric terrestrial cameras, and they are usually not appropriate for semimetric or nonmetric cameras. Calibration ranges are three-dimensional arrays of targets with known geometric orientations and distances (control points). The known object space coordinates of the targets and their measured image space (photo) coordinates are used to solve for the interior orientation parameters contained in the modified collinearity condition equations. At least fifteen control points are normally required (e.g. Fig. 3.2). Because the position of the cameras (particularly the camera-object distance) and the principal distance are usually both unknown and are highly correlated in the solution, it is imperative that the control points are noncoplanar and that there must be as much depth as possible. An alternative approach is analytical plumb-line calibration (Brown 1971; Fryer & Brown 1986) in which a series of known straight lines are photographed. This method is based on the fact that, for a distortion-free lens, each straight line in object space should appear as a straight line on the image. Therefore, measured departures from collinearity can be attributed to lens distortion. A disadvantage is that the principal distance and the coordinates of the principal point cannot normally be determined using this method. A convenient method of obtaining photographs for a plumb-line calibration is to photograph a series of straight lines, rotate the camera by 90 degrees and then rephotograph. Typically, fifty points along each of approximately ten plumb lines are observed (Fryer 1992).

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Figure 3.2. A control frame for underwater calibrations.

On-the-job calibration is used with nonmetric cameras. The technique is the same as calibration ranges except that the control points must surround the object to be measured, and must be used to calibrate the camera for each and every photograph. Although this overcomes the limitations of unstable interior orientation, on-the-job calibration has obvious disadvantages when measuring animal aggregations, namely the inconvenience of requiring some sort of control frame as well as its probable effects on animal behavior. If nonmetric cameras are used with only periodic calibrations, measurement error becomes a consideration. Self-calibration is a more sophisticated method of camera calibration (Shih 1989). Like on-the-job calibration, self-calibration requires a large number of well-defined targets on or surrounding the object. However, the targets do not need to be coordinated. Self-calibration techniques are used in very high-accuracy industrial applications of convergent close-range photogrammetry and are of limited general application. When using semimetric and nonmetric cameras, calibration range or on-the-job calibration techniques are normally the most appropriate solution in close-range biological applications.

Analytical and digital photogrammetry

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3.2.2 Relative orientation Once the camera has been calibrated, the geometric relationship between cameras, or relative orientation, must be measured. Relative orientation is a function of the position and the angular orientation of one camera relative to the other. Relative orientation parameters are usually solved for analytically by comparing the positions of image points that appear in each photograph. Either the coplanarity or collinearity condition can be used to solve for the position and orientation of the two cameras in an arbitrary coordinate system. Direct measurement of the orientation and position of the cameras is usually not sufficient to determine relative orientation because it is difficult to physically locate the perspective center. Once interior and relative orientation have been achieved, it is possible to measure three-dimensional coordinates. This allows the creation of a three-dimensional optical or mathematical model. However, there is still no absolute scale of measurement or orientation with respect to the three-dimensional object space.

3.2.3 Absolute orientation Absolute orientation relates the cameras and the three-dimensional model to an object space coordinate system. By using points of known geometrical orientation (control points) in the field of view of the cameras, absolute orientation parameters can be easily solved for analytically. For in situ observations, the absolute orientation defines the scale of the stereomodel and relates the fixed camera geometry to the vertical and, if necessary, to absolute position and azimuth (e.g. a north point). There are two common methods of calculating absolute orientation parameters. If the coplanarity condition equations have been used to determine a relative orientation, then coordinates of object points, measured in the model space, can be transformed into an absolute coordinate system with the use of a three-dimensional similarity transformation. A minimum of three object space control points must appear in the stereomodel so that it can be related to the object space coordinate system. Alternatively, the collinearity condition equations can be used to calculate the absolute orientation of each camera without going through the intermediate model space calculations. Once the interior, relative, and absolute orientations of a stereopair are known, image coordinates of image points appearing in both photographs can be measured and used to calculate corresponding object space coordinates. The mathe-

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matical model and computational procedures used to solve for the orientation parameters and object space coordinates vary considerably. Some, such as the Direct Linear Transformation (DLT) (Abdel-Aziz & Karara 1971; Marzan & Karara 1975; Walton 1994), can provide a more direct solution than the procedure described above and are very suitable for many close-range biological applications. Increasing accuracy, of course, requires increasing rigor and greater complexity. McGlone (1989) and Walton (1994) discuss alternative algorithms.

3.3 Stereoscopy One of the most common approaches to photogrammetry is stereoscopy, where two cameras are mounted with their optical axes nearly parallel. Although this is not a necessary condition for photogrammetry, it is useful if one wishes to view the target as a three-dimensional stereoscopic image. The stereoscopic approach does offer some real advantages, including reliable visual correlation of corresponding images, increased measuring speed, and improved photointerpretation, the last leading to more reliable identification and increased accuracy if the image quality is poor. Close-mounted parallel cameras are also simpler to handle than cameras mounted along orthogonal axes. The geometric basis of stereovision is illustrated in Figure 3.3. The essential requirement for three-dimensional visualization is that the two corresponding image points and the observer's eyes lie in the same optical plane, the epipolar plane. If the observer's left eye observes only the left image and the right eye observes only the right image, changes in parallax (or apparent displacement between the corresponding image points) are interpreted by the brain as height changes in the perceived stereomodel. A variety of techniques is used to ensure optical separation. The simplest example is the stereoscope, in which optical overlap of the two eyes is physically inhibited. Nearly all high-accuracy analytical stereoscopic systems use separate optical trains. Anaglyphic systems use filters of complimentary colors, usually one red and one cyan, to produce separate optical trains. The observer wears glasses with left and right filters that correspond to the filters through which the left and right photographs have been projected. This is a cheap and simple solution; however, it does preclude the use of color film and results in a significant amount of light loss. Anaglyphic systems have been implemented in some threedimensional computer displays. Polarized light systems use the same principal as anaglyphies except that polarizing filters are used instead of color filters. The advantages are that color film can be viewed and light loss is minimal. One of the

Analytical and digital photogrammetry

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model space

Figure 3.3. The geometric basis of stereovision. most versatile stereoviewing systems currently available is based on the polarized projection system. Using a high-resolution graphics monitor, interlaced images are projected through a synchronized liquid crystal shutter so that differently polarized images are consecutively presented to the viewer. The viewer wears appropriately polarized glasses to view the stereomodel. Stereo-image alternation systems use synchronized mechanical shutters to alternately obscure the projected image and interrupt the observer's line of sight for the left and then the right eye. Graphics monitors based on this approach are available, with the left and right images updated on a graphics screen synchronized with LCD shutters on the left and right side of the viewers' glasses. Although there are several techniques for viewing the stereomodel, none of these alone allows for data collection (e.g. intra-object distance). Analytical data reduction of film images is accomplished by the use of comparators or analytical stereoplotters (see Petrie 1990 for a general review). Comparators are used to measure the image coordinates of targets; they do not necessarily perform any further processing of the measured coordinates. Monocomparators measure only

Jon Osborn

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i i

T Plotter

X

LH photo

RH photo

y Computer x y

X,Y »

Data file X.Y.Z

II11 Ml 11II

Illllflllll

left Y

right X

Figure 3.4. Schematic illustration of a stereocomparator (adapted from Petrie 1990). one image whereas stereocomparators (Fig. 3.4) allow corresponding images to be measured while the observer views a stereomodel. However, the observer must continually adjust the position of the left and right images because stereocomparators do not automatically maintain the stereomodel. The real advantage of stereocomparators is that by viewing a stereomodel, the observer can ensure that corresponding left and right images of every target are correctly correlated. Reliable correlation of target coordinates measured on a monocomparator, depending on the number and distribution of targets, can be a very difficult task. On the other hand, stereocomparators are generally unsuitable for highly convergent photography because they cannot accommodate the image rotations required to maintain the epipolar geometry necessary for viewing a stereomodel. Image coordinates measured on a comparator can be used to calculate the true coordinates (object space). For many biological applications, where only a relatively small number of measurements have to be made and where feedback mechanisms for contour tracing are not required, stereocomparators are an attractive data-reduction system (Fig. 3.4). Unlike comparators, analytical stereoplotters automatically maintain the stereomodel (Fig. 3.5). Once the model is set up, three-dimensional object space coordinates are inputted directly into the computer, the left and right image coordinates are calculated, and the images (or measuring marks) are then shifted accordingly. Analytical stereoplotters are used almost exclusively for analytical aerial mapping because of the requirements of contour plotting and the need to drive the measuring mark to predefined object space coordinates. A wide range of analytical stereoplotters is available (Karara 1989). A number of these run

Analytical and digital photogrammetry

PX,

py

px |

j py

45

software & orientation data

• -1 I

t f

to. X,Y

Plotter

Computer RH photo

LH photo

Data file X.Y.Z optics I

X

Y

Z

Figure 3.5. Schematic illustration of a fully analytical stereoplotter (adapted from Petrie 1990).

software specifically designed for close-range photogrammetry and appropriate for biological applications.

3.3.1 Digital imagery All of the techniques noted above exploit film-based image analysis techniques. However, images can also be captured digitally, that is, projected through a lens directly onto a pixel array at the back of the camera. The advantages of capturing an image digitally include high temporal resolution, three-dimensional visualization of dynamic processes, digital enhancement of the image, and real-time measurement. In addition, digital photogrammetry offers the possibility of automatic target recognition and tracking. Until recent years, photogrammetry has not made use of digital cameras to extract spatial information, although these techniques are widely used in remote sensing (see Jaffe Ch. 2). In part, this is because photographic emulsions had a much higher resolution and provided greater accuracy than did digital images, metric digital cameras simply were not available, and real-time visualization and measurement were not normally required. Furthermore, storage and manipulation of digital images demanded expensive computers. All of these problems are being resolved. Real-time visualization and measurement are required for a growing number of close-range applications, particularly in robotics, industrial quality assurance, and a wide variety of medical and

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biological applications. High-resolution metric digital cameras are becoming available. In the past twenty years, commercially available arrays have increased from 100 100 pixels to over 3000 2000. High-definition television is certain to increase the availability of cameras containing high-resolution sensors. Accurate and reliable target recognition and correlation techniques are being used in military, industrial, and medical applications, although it is these aspects that remain the greatest impediment to fully automatic digital photogrammetry. Digital photogrammetry requires solid-state digital cameras, of which the charge coupled device (CCD) is a well-known example. These still contain both geometric and radiometric errors, although all indications are that their geometric reliability is currently at least as high as that of semimetric film cameras. Geometric errors result from a variety of sources, including lens distortion, nonperpendicularity of the image plane and the camera's optical axis, the limited spatial resolution of the pixel array, differing pixel spacing in the x and y directions of the pixel array, and distortions resulting from the analog-to-digital conversions from a CCD video array either directly to the computer or via tape. Although commonly referred to as digital cameras, CCD area array video cameras essentially rely on analog processes. The charge builds up in the array elements and is transferred from the array as an analog signal. The image is usually stored on tape as an analog signal and later converted to a digital image for analysis (A/D conversion) using a. frame grabber. To properly digitize an image, the image source (camera or tape player) and the framegrabber must be synchronized. If video cameras are used, most of the errors result from synchronization differences. Beyer (1990, 1992, 1993) describes radiometric and geometric accuracy of digital cameras and framegrabbers. Most framegrabbers rely on a line synchronization process called phase locked loop (PLL) genlocking to control the sampling rate of the video signal. This can lead to significant errors across each line of the digital image and between lines of the image, usually referred to as line-jitter. Line-jitter can be avoided by running the camera and the framegrabber on the same clock, a process known as pixel synchronous frame grabbing. Unfortunately, many cameras and framegrabbers cannot be driven by an external clock, and only provide for PLL genlocking. Digital video cameras and still video cameras, on the other hand, use internal pixel synchronous framegrabbing and output a digital image free of line-jitter. When a tape player is the framegrabber's image source, there are additional sources of error, the most significant being caused by the instability of the synchronization pulses contained in the video signal. To capture images reliably from a tape it may be necessary to play the signal through a time base corrector,

Analytical and digital photogrammetry

Al

which normally collects either a full frame or a field of the output image and reestablishes reliable synchronization (e.g. Inoue 1986). Recent advances in computer technology allow the observer to view digitized images in reconstructed three-dimensional image space (i.e. the stereomodel). Digital Photogrammetric Workstations (DPWSs) permit real-time threedimensional visualization. By using a floating cursor superimposed on the screen, the observer can measure three-dimensional object space coordinates from the image model. Basic image processing routines can be used to enhance the images while viewing in real time. More sophisticated image restoration and enhancement techniques can also be used. The recent availability of DPWSs is a consequence of the dramatic increase in affordable and sufficiently powerful computers. An important additional possibility offered by a digital photogrammetric approach is automation. Two aspects of this process, target recognition and target correlation (see Fig. 3.6), essentially the only "human" activities on a modern analytical plotter, deserve particular comment. To automatically extract threedimensional data it is necessary to recognize and correlate features in one image with corresponding features in the matching image. There are essentially two approaches: grey-level-based and feature-based matching. Algorithmic aspects of image matching that are primarily concerned with speed - such as employing image pyramids (e.g. Ackerman & Hahn 1991; Schenk et al. 1990); extensions to standard algorithms such as applying geometric constraints (e.g. Griin & Baltsavias 1987; Wrobel & Weisensee 1987), or window shaping (e.g. Norvelle 1992); as well as the more esoteric matching algorithms such as relational matching, Fourier domain methods, and Al methods (e.g. Shapiro & Haralick 1987; Lemmens 1988; Greenfeld 1991; Gopfert 1980) - are outside the scope of this discussion. For a description of these techniques see reviews by Dowman et al. (1992), Lemmens (1988), or Weisensee and Wrobel (1991). Grey-level-based matching, also known as area- or signal-based matching, relies directly and exclusively on the image signal. The two most commonly employed grey-level-based matching methods are cross-correlation matching and least squares matching. In cross-correlation methods a smaller target array is systematically shifted across a larger search array. The target array may be either an "ideal" target the observer wishes to identify or an actual subsample from one of the digitized images. The result of this process is an array of discrete correlation coefficients from which a most likely position of the match can be interpolated. The mathematical basis of cross-correlation matching and some different correlation coefficients are reported by Duda and Hart (1973), Haggren and Haajanen (1990), Gopfert (1980), Lemmens (1988), Trinder et al. (1990) and Pilgrim (1992). Although relatively simple, cross-correlation approaches have

48

Jon Oshorn camera 1

camera 2

Image Acquisition

Enhancement

Function selection

Segmentation

Image

Extraction

Recognition

Characteristics

Sub-pixel point location

Correlation

Photogrammetric solution

Orientation parameters & object space control

3D object space coordinates

Figure 3.6. Processing steps for real-time measurement (adapted from El-Hakim 1986; Karara 1989).

some disadvantages (Dowman 1984; Trinder et al. 1990; Mitchell 1991; Pilgrim 1992). Cross-correlation is computationally expensive, especially if subpixel matching is attempted. Furthermore, it does not adapt to geometric distortions (e.g. from scale differences and rotations) in each image, nor does it adapt to radiometric differences (e.g. from illumination effects and shadows) or image differences (e.g. from occlusions). Finally, cross-correlation does not provide reliable feedback on the accuracy of the match. Thus, although cross-correlation techniques can be useful approximate methods, they are unsuitable for highprecision matching.

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Least squares matching techniques are appropriate when high-precision matching is needed (see for example Ackermann 1984; Lemmens 1988; Trinder et al. 1990; Rosenholm 1987; Mitchell 1991; or Pilgrim 1992). In this technique, the grey level of each pixel in a defined subset of one digitized image (a window) is related to the grey level of a corresponding pixel in a window from the second image, via some functional model that incorporates both geometric and radiometric differences in the images. Matching is achieved by minimizing the sum of the squared residuals of the grey-level values. The least squares approach has several advantages (Trinder et al. 1990; Mitchell 1991; Weisensee & Wrobel 1991; Pilgrim 1992). The technique is computationally efficient because a pixelby-pixel search of the target array over the entire search array is not required. Other advantages include the potential for incorporation of error detection, such as data snooping, as well as the fact that the model provides data on the quality of the match. Feature- or attribute-based matching (Forstner 1986), which relies on extracting information about the structure and attributes of images, is a suitable technique for low-accuracy applications or as a precursor to a least squares area based match (e.g. Chen et al. 1990). The information extracted might include numerical descriptors (contrast, length, or area), topological descriptors (connectedness), or symbolic descriptors (shape classification). Operators are used to detect specific features, for instance edges, in the image resulting from object shape, color, or shadows. Once specific features have been recognized, they are matched to corresponding features in the other image on the basis of their attributes (Trinder et al. 1990). Information extraction is normally referred to as segmentation. Although there are many different approaches, three categories (Pilgrim 1992) are illustrative: When only a few regions of interest exist in an image, thresholding can be used to divide the image into scenes by separating targets from the background on the basis of brightness (i.e. grey level). Image thresholding prior to target detection is commonly applied in real-time photogrammetry (e.g. Grun 1988; Haggren 1986; Wong & Ho 1986). Portions of the image with similar attributes, such as a similar statistical distribution of grey levels, can be isolated as discrete regions for matching. Finally, image analysis techniques such as edge or point detectors can be used to isolate specific features in the image. Feature-based matching has several advantages (Forstner 1986; Trinder et al. 1990; Pilgrim 1992). It is more versatile and generally faster than either the cross-correlation or least square method and has a greater range of convergence than least square techniques. Its disadvantages (Trinder et al. 1990; Weisensee & Wrobel 1991; Schenk & Toth 1992) are that accuracy is limited to approximately

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the pixel size of the data, estimation of matching accuracy is more difficult, and implementation is more difficult than least squares (area) based matching. Much of the current research in object recognition and matching relies on defining targets in terms of generalized geometric objects, such as lines, planes, and cylinders. While this is appropriate for industrial applications such as quality assurance for manufactured parts, these methods are less well suited to biological tasks where animals move and their shape changes as a function of animal distance and orientation with respect to the cameras. Aloimonos and Rosenfeld (1991) note, " . . . it seems unlikely that such techniques can handle object recognition in natural three-dimensional scenes, or can deal with scenes that deal with a large number of possible objects." Image correlation often exploits the epipolar geometry illustrated in Figure 3.3. The coordinates of a target in one image and the known exterior orientation parameters are used to define the epipolar plane and thus the epipolar line along which the second image of the same target must lie. Correlation along that line leads to a most likely solution for the position of the corresponding target (e.g. Konecny & Pape 1981). However, correlating targets in an animal aggregation can be considerably more complicated than more common mapping tasks, because the targets are clustered in three dimensions. Ambiguities arise when more than one animal lies along an epipolar line, or when two animals cross paths. In these situations, three-dimensional coordinates can be resolved only by using three images rather than two or by relying on humans to edit the model. Errors such as an ambiguity lead to outliers, a common problem in photogrammetry. If the image is of a predictable surface, as in most photogrammetric mapping, then outlier detection is not particularly difficult. For a structure such as an animal aggregation where there is essentially no a priori knowledge of the structure's dimensions, outlier detection can be extremely difficult. If a small number of undetected outliers cannot be tolerated in the model for which the data are being collected, then unsupervised image recognition and measurement routines should not be used.

3.4 Tracking Once a target has been reliably identified and its coordinates measured in each image, its three-dimensional position can be calculated. The remaining task is to track the object in space and time. The complexity of this task is truly formidable. Success depends upon individual animal parameters (e.g. speed and path complexity), group level parameters (e.g. number and density of animals and the frequency of occlusions), and technical parameters (e.g. spatial accuracy of the measurements and the image sampling rate). It is difficult to generalize about

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the probable success of motion tracking techniques applied to animal aggregations as most of these problems noted above have yet to be resolved. Some preliminary attempts at tracking are described below in this chapter and in Chapter 9 by Parrish and Turchin. Readers interested in photogrammetric threedimensional tracking systems are referred to Haggren and Leikas (1987), Walton (1990, 1994), Mostafavi (1990), Turner et al. (1991, 1992), Axelsson (1992a, 1992b), Grim (1992), and Dowman et al. (1992).

3.5. Discussion Accurate and reliable fully automated target recognition, correlation, and tracking is still in the developmental stage. Although accuracy requirements may not be particularly high for biological applications, recognition issues are more complicated than for physical systems, and identifying outliers caused by incorrect correlation can be quite difficult. Most commercial automatic recognition systems rely on feature recognition for binary images (e.g. a high-contrast edge recognized as black against white). Therefore, image recognition of aggregating ants filmed against a high-contrast background is relatively simple. But automatic identification of every fish in a school (e.g. Fig.3.7), let alone recognition of the head and tail of each individual, becomes a problem of considerable

Figure 3.7. Schooling fish.

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difficulty. In my experience, obtaining images of sufficient quality to allow human recognition and correlation is one of the greatest difficulties in photogrammetric analysis of animal aggregations, and automatic recognition is far more challenging. Tracking trajectories of individual animals in dense or spatially complex aggregations still requires the use of the human mind's exceptional image-recognition and correlation powers. Photogrammetric systems that allow three-dimensional visualization of video images can be powerful tools for animal behaviorists. The advent of fully automated three-dimensional tracking systems will allow biologists to address a wide range of questions (see Ch. 11 by Hamner & Parrish) that they have only begun to address.

3.6 Examples Photogrammetric techniques have been used by various researchers to study animal aggregations, particularly fish schools (Aoki & Inagaki 1988; Aoki et al. 1986; Cullen et al. 1965; Dill et al. 1981; Graves 1977; Hasegawa & Tsuboi 1981; Hellawell et al. 1974; Hunter 1966; Koltes 1984; O'Brien et al. 1986; Partridge et al. 1980; Pitcher 1975; Symons 1971a; Van Long & Aoyama 1985; Van Long et al. 1985). Although several of these references describe approaches that are different from the methods described in this chapter - for example, the cameras may be configured orthogonally, or mirrors are used to provide the second view - the geometry and data reduction are essentially identical. Rigorous photogrammetric treatment of the images (e.g. O'Brien et al. 1986) is not the norm. Most solutions simplify the mathematics and make assumptions about the physical model. For example, it is commonly assumed that images can be measured from paper prints without allowing for errors introduced during enlargement and or for the dimensional instability of photographic paper. It is also assumed that images can be measured with calipers rather than a comparator, that refraction can be ignored, that nonmetric cameras remain stable, that cameras can be fixed in position reliably for constant relative and absolute orientations, and that camera positions and orientations can be known accurately from physical measurement rather than analytical determination using object space control points. It is reasonable to make these assumptions, provided that the resultant errors in object space coordinates are properly understood. O'Brien et al. (1986), however, note that several researchers quote accuracies inconsistent with their experimental techniques. The following examples illustrate four different photogrammetric solutions. These examples demonstrate that off-the-shelf technology, particularly nonmetric cameras or CCD video cameras, can be used to make reliable and useful

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three-dimensional measurements. The first two examples are described in greater detail in O'Brien et al. (1986) and Osborn et al. (1991), the third is courtesy of Ritz (per. comm.), and the fourth is taken from Hamner and Hamner (1993).

3.6.1 Laboratory analysis of macroplankton This example demonstrates that rigorous photogrammetric techniques can be used without expensive equipment (except a rented monocomparator). The only added complexity is the mathematical treatment of the measured image coordinates. For this analysis a flume tank was constructed to study the schooling behavior of planktonic shrimp (Fig. 3.8). Two nonmetric 35-mm film cameras (Pentax MEF) were mounted on a frame approximately 75 cm above the water level of the tank. A glass tray of known thickness and refractive index was floated on the water surface. The glass improved the image quality of the photographs by eliminating surface irregularities. The tray supported a photogrammetric control frame containing twenty-two control points, of known distance and geometric orientation. Stereo images of the control frame were used to solve for the interior, relative, and absolute orientation of the two cameras. The image coordinates of one eye of each shrimp were measured with a monocomparator. Because the shrimp and the cameras were in different media, the refractive effects of the water-glass and glass-air interfaces had to be taken into account. The relationship between the true and apparent position of an animal is illustrated in Figure 3.9. The ray-tracing technique used in this project requires that the refractive index of each medium be measured to calculate the direction vectors of each ray. After calculating the coordinates of the point of intersection of these rays with the planes defined by the media interfaces, the coordinates of the intersection of the two rays at the object point (i.e. the shrimp eye) could be

cameras

n

control frame

re-circulating system Figure 3.8. Section view of the flume tank (adapted from O'Brien et al. 1986).

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Jon Osborn camera 1

camera 2

air

glass apparent position

"">-

water

true position

Figure 3.9. Refraction of light rays through the three media environment (adapted from O'Brien et al. 1986). found. The mean positional error of this system was less than 0.5 mm and the mean error in calculated distances between individuals was less than 0.25 mm.

3.6.2. In situ fish stock assessment Biologists at New Zealand's Ministry of Agriculture and Fisheries, Fisheries Research Centre (NZFRC), use acoustic methods to estimate the total stock biomass of deep water fish such as orange roughy (Hoplostethus atlanticus). The three-dimensional extent of aggregations is determined from repeated ship transects and the density of the aggregation is estimated from reflected signals. Target strength for a particular acoustic frequency depends on the species and size of the fish, body orientation with respect to the acoustic device, and school packing. In order to groundtruth the acoustic data set, the minimum photogrammetric information needed was verification of fish species and an independent estimate of school density. To further refine the estimates produced by acoustic methods and to calibrate the acoustic system, information was required about the vertical distribution of the target species and the size, orientation, and packing arrangement of individuals within the aggregation. The NZFRC uses two Lobsiger DS 3000 cameras, equipped with 28-mm Nikkor underwater lenses mounted behind a flat acrylic port, each with a reseau grid in the focal plane. Camera separations can be set at 250 mm, 500 mm, or 700 mm. A control frame (Fig. 3.2) is photographed before and after each cruise and is carried on the vessel during the cruise in case the cameras are disturbed at sea. The control frame contains about sixty control points, which have been coordinated to submillimeter accuracy using traditional survey techniques. The control frame photography is used to cal-

Analytical and digital photogrammetry

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0.1Q. Std.Dev. (m)

Z orthogonal to camera base X & Y orthogonal to Z

0.05_

'4 '6 Distance from cameras (m)

T

8

10

Figure 3.10. Accuracy of the NZFRC system (with cameras separated by 0.7 m).

culate the interior, relative, and one component (scale) of the absolute orientation of the two cameras. On both calibration photographs, image coordinates of the control points and the corner reseaus are measured using a stereocomparator. Many different software packages are available to calculate orientation parameters from the measured photocoordinates, some of which are in the public domain (e.g. Karara 1989). In this project a formulation of the collinearity condition equations known as the Direct Linear Transformation (DLT) (Abdel-Aziz & Karara 1971; Marzan & Karara 1975) and the University of New Brunswick Analytical Self Calibration Program (UNBASC1) (Moniwa 1976) are being used to obtain initial and then rigorous solutions for the orientation parameters. Distortions due to the flat camera port are treated as an additional lens distortion and modeled accordingly. This is significantly simpler than the ray-tracing techniques needed in the previous example. Both an ADAM Technology MPS-2 analytical stereoplotter and a Zeiss stereocomparator are used to measure and reduce the data on the photographs containing fish. A typical stereomodel containing some fifteen fish takes about twenty minutes to set up and measure. The estimated accuracy of the NZFRC system is illustrated in Figure 3.10. Note the rapid deterioration in the Z coordinate (parallel to the camera's optical axes) compared with the X and Y coordinates. This illustrates the importance of defining requirements of the photogrammetric solution before choosing cameras, deciding on calibration procedures, and designing the stereocamera geometry.

3.6.3 Measuring mysid aggregations The project was designed to investigate the costs and benefits of aggregation (see Ritz Ch. 13 for an extended discussion of the behavioral ecology of this research). Approximately 100 mysids were placed in each of two identical glass

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tanks, one with an adequate food ration and the other with an insufficient ration. Characteristics of the aggregations, such as volume and density, and properties of the individuals, such as swimming speed, were monitored. This project illustrates the simplicity of some photogrammetric solutions. Because accuracy requirements were relatively low, a single CCD video camera in conjunction with a mirror was used to generate two images of the tank (Fig. 3.11; see Pitcher 1973, 1975 for other applications of this solution). The mirror was positioned at 45 degrees above the tank, creating a second orthogonal image. The camera was approximately 5 m from the tank but a zoom lens was used so that the mirror and the tank filled the field of view. The camera was placed this far from the tank to minimize both the refraction at the water-glass-air interfaces and the difference in scale between animals moving at a maximum and minimum distance from the camera. The images were grabbed from the S-VHS videotape and loaded into an image-processing system. After contrast enhancement, the images were scaled, using three axes marked on the tank. Frame advancement was manual. Calculating the three-dimensional position of animals was very simple because one image contained the scaled X and Y object space coordinates and the other image contained the scaled Y and Z coordinates. The common Y coordinate was used to correlate the two images. Although not used in this project, if the aggregation size and/or density is high, a third orthogonal image can be introduced to reduce the possibility of an ambiguous solution. To improve accuracy, simple empirical corrections can be formulated by measuring test grids within the tank. For this system, mean and R.M.S. errors on calibration targets were X: 0.2 ± 1 . 0 mm; Y: 0.0 ± 0.9 mm; Z: 0.0 ± 0.6 mm. A single-camera approach has the advantage that image correlation is simplified. However, placing both images on a single frame does reduce the resolution of each image, an important issue because current video technology already has significantly lower resolution than film.

plan view

section view

image

tank

Figure 3.11. Single camera mysid tank.

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3.6.4 Three-dimensional tracking with EV3D Behavioral studies in open water must deal with three-dimensional movements of animals. To quantify in situ swimming behavior, a submersible-mounted dual camera video system was developed (Fig. 3.12; Hamner & Hamner 1993). "Offthe-shelf" monochrome video cameras with fixed-focus lenses and wide-angle adapters were permanently mounted in custom housings at the empirically determined distance behind the dome port at which refractive distortions at the water-port interface (see Fig. 3.9) were physically eliminated (Walton 1988). Separation of the cameras was maximized to improve accuracy of measurements made along the horizontal axis perpendicular to the plane of the two cameras, and the cameras were angled toward each other so that the two fields of view intersected approximately 2 m in front of the submersible, within the volume of water illuminated by the submersible's lights.

camera

camera

SUBMERSIBLE video # 2 camera control box VCR #1

[microphone) VCR audio#l

audio # 2

video #1 time code generator

#2

video # 2 time code video # 1

monitor

7

Figure 3.12. Schematic of 3-D video system on the submersible Johnson Sea-Link. The two cameras are mounted outside the submersible, on either side of the sphere, and are linked by cable to the video equipment inside the sphere (see text).

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Camera power and focus were remotely controlled from inside the submersible through a pressure-resistant cable that also transmitted video signals from each camera to a separate video cassette recorder. Prior to data collection the two cameras were calibrated in situ by holding a cuboidal frame with eight control points motionless in front of the cameras with the submersible's claw and recording the grid with both cameras (Fig. 3.13). The calibration frame filled approximately 3/4 of each camera's field of view. After the frame was recorded for several minutes at depth, the manipulator arm on the submersible moved it out of view, allowing behavioral sequences to be recorded. As the scene was recorded, a time-code signal laid down simultaneously on one audio track of each VCR synchronized the two videotapes for subsequent identification of corresponding frames. Later, on work tapes dubbed from these originals, the auditory time code was transformed into a visual code, with the minute, second, and frame number (at 30 fps) imprinted on every frame. Images on the two synchronized videotapes were automatically tracked through time and in three-dimensional space with an "Expert Vision 3-D Tracking System (EV3D)" created and sold by the Motion Analysis Corporation. From known distances between targets on the calibration frame, the EV3D determines relative and absolute orientation X, Y, and Z axes of the volume viewed by both cameras. The outline of each digitized image is reduced to a centroid. The soft-

camera •#•! (port) 5 (0,71,0)

camera #-2 (starboard) 5 (0,71,0)

(71,71,0)

6

1 (0,0,0)

Figure 3.13. The digitized calibration grid in port and starboard views. White cubes at the eight corners were used as targets. One cube was poorly illuminated and its video image could not be digitized. Known spatial coordinates for each target established the x, y, and z axes for subsequent three-dimensional measurements. Any one target could be selected as the origin and the remaining targets were then identified in relation to that target.

Analytical and digital photogrammetry

camera #1 (port)

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camera # 2 (starboard)

Figure 3.14. The two-dimensional paths of a sergestid shrimp and a fish recorded by port and starboard cameras. Because of the camera angles, the sergestid appears to lobstertail at two different angles and the two apparent paths of the fish are diametrically opposed. Only when the x,y coordinates in both views were combined to calculate positions in three-dimensional space could the true paths of either animal be determined.

ware automatically recognizes each set of image points and calculates the threedimensional coordinates of each centroid through time. A set of algorithms is then available to calculate speed, direction of travel, etc. Behavioral sequences for swimming fish and planktonic invertebrates at about 900-m depth were successfully collected with the research submersible Johnson Sea-Link. In one example sequence, each of the two video cameras recorded two-dimensional centroid paths of a sergestid shrimp and an unidentified fish as they swam in front of the submersible (Fig. 3.14). The sergestid swam into view from the port side above the fish, which entered the cameras' view from the starboard side. Review of the original video suggests that at least one of the sergestid's long, trailing antennae touched the fish, startling both animals into changing course and speed. Three-dimensional analysis of the approximate 1.5 sec interaction indicates that the sergestid increased its speed from 12 cm/sec to a maximum value of 140 cm/sec in response to the fish, while changing course.

3.7 Summary Photogrammetry offers critical advantages over traditional measurement techniques for biological applications, particularly in three-dimensional environments. The mathematics of photogrammetry are relatively straightforward, particularly when applied to simple stereophotography, but it does require careful

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analysis and modeling of systematic geometric errors and random measurement errors. A wide range of metric, semimetric, nonmetric, film, and digital cameras are available. The choice of camera depends largely on logistical considerations such as the trade-off between additional object space control against the cost and restrictive limitations of metric cameras. The introduction of solid-state digital cameras offers great possibilities for real-time visualization and near real-time measurement, although automatic real-time measurement of digital images is currently possible only if the targets are very well defined. The enormous potential of real-time measurement in industrial, medical, and military applications is certain to ensure significant advances in the near future. To track the trajectories of individual animals in a dense or complicated aggregation, it is still, and for some time will remain, necessary to use the human mind's exceptional image recognition and correlation powers. Consequently, photogrammetric systems that allow three-dimensional visualization of video images are likely to be particularly useful to researchers studying animal behavior. Recently some impressive methods of visualizing stereomodels have become available. Affordable off-the-shelf technology can be used to make reliable three-dimensional measurements and, in some cases, to track individuals, but it is critical that the system be properly designed and that full consideration be given to the effect of propagating systematic and random errors.

r

~i LONGITUDE

127.93 32.57

127.63

LATITUDE

32.31 INTEGRATED VOLUME BACKSCATTERING

HHB < 2.01 x E-6

1 > 6.33 x E-6

Plate 4.1 Plate 4.1. Cruise track of the star survey pattern. Color bar corresponds to values of mean acoustic backscatter averaged over 30-sec report intervals and integrated from 10 to 120 m. Bathymetric contours of Fieberling Guyot from 500 to 1500 m are shown in the figure as well as a rectangle encompassing the area mapped in plate 4.2.

Plate 4.2. Map of depth-integrated acoustic backscatter in the waters overlying and surrounding the summit of Fieberling Guyot. The irregularly spaced survey data presented in plate 4.1 were interpolated, using a point Kriging algorithm (Isacks & Srivastava 1989), to produce a regularly spaced, two-dimensional grid of values for mapping. Bathymetric contours of Fieberling Guyot from 500 m to 1500 m are shown in the figure.

Plate 4.3. Three-dimensional visualization of acoustic backscatter in the waters overlying and surrounding the summit of Fieberling Guyot. In this case, the survey data were divided into 22 5-m depth strata and interpolated, using punctual Kriging, to produce a regularly spaced, three-dimensional grid of values for volume rendering and visualization. Bathymetric contours of Fieberling Guyot from 500 to 1500 m are projected on the lowest horizontal plane shown in the figure.

r

~i 127.87 35.52

LONGITUDE

LATITUDE

32.38 INTEGRATED VOLUME BACKSCATTERING

< 2.01 x E-6

Plate 4.2

Is. le. 11.

Plate 4.3

> 6.33 x E-6

127.70

Acoustic visualization of three-dimensional animal aggregations in the ocean CHARLES H. GREENE AND PETER H. WIEBE

4.1 Introduction Pelagic animals exist in a three-dimensional fluid medium and are continuously subjected to the physical processes of advection and turbulent mixing. Despite the tendencies of turbulence to mix and homogenize scalar properties in the ocean, most distributions of pelagic animals exhibit patchiness over a wide range of spatial and temporal scales (Haury et al. 1978; Powell 1989; Steele 1991; Levin et al. 1993). Since many pelagic animals are active swimmers, it is perhaps not surprising that the power spectra of their spatial distributions deviate, at least on smaller scales, from those of passive scalar properties such as sea surface temperature and chlorophyll fluorescence (Levin 1990). The patchiness of pelagic animal distributions results from the interaction between physical processes at work on the fluid and animal aggregation responses to biotic and abiotic cues in their fluid environment (Omori & Hamner 1982; Mackas et al. 1985; Hamner 1988; Greene et al. 1994). This interaction between physics and biology is both complex and fascinating; its study will demand new methods in oceanography and ethology which are more sophisticated than those brought to bear on the subject in the past. Three fundamental problems complicate efforts to study patchiness and animal aggregations in the oceanic environment. First, the ocean presents humans with a relatively hostile environment within which to work. Second, the ocean is largely opaque to light and other forms of electromagnetic radiation. Third, the distributions of pelagic animals are highly dynamic, continuously changing in both space and time. All three of these problems make it difficult to observe or sample pelagic animal distributions without confounding spatial and temporal patterns. In combination, these problems necessitate the development of novel approaches for visualizing the distributions of pelagic animals in the ocean environment (Greene et al. 1994).

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4.2 Acoustic visualization Underwater acoustics have provided an arsenal of powerful tools for scientists interested in remotely sensing the ocean's interior (Clay & Medwin 1977). Unlike electromagnetic radiation, which is rapidly absorbed and scattered by seawater and the small particles suspended within it, low- to high-frequency (<200 kHz) sound is able to penetrate the ocean to much greater depths and ranges. Thus, surface-deployed acoustic instruments using low- to high-frequency sound offer the potential to circumvent two of the three problems described earlier. The use of low- to high-frequency sound as a remote-sensing tool does not come without certain trade-offs. These frequencies are adequate for remotely detecting aggregations of small animals, such as zooplankton and micronekton, and large individual animals, such as fish, but they are inadequate for studies that require the detection of small individual animals (Clay & Medwin 1977). For these smaller organisms, very-high to ultra-high-frequency (>200 kHz) sound is typically required. Unfortunately, these much higher acoustic frequencies are absorbed more rapidly in seawater, and their value in remote sensing is correspondingly diminished. For applications requiring the detection of small individual animals, the reader is referred to the review article by Greene and Wiebe (1990). Since the focus of this volume is on three-dimensional animal aggregations, we will introduce here new methods recently developed for visualizing zooplankton and micronekton distributions in three dimensions using high-frequency sound. These methods, which we refer to as acoustic visualization, have proven to be effective in characterizing the distributions of zooplankton and micronekton on scales ranging from meters to tens of kilometers (Greene et al. 1994). In the section that follows, we will present results from a field study conducted at sea during October 1990. The results from this study provide a useful example for discussing the power and present limitations of acoustic visualization in the three-dimensional analysis of animal aggregations in the ocean.

4.3 Field studies: Hypotheses, methods, and results The field study described below was conducted as part of the Office of Naval Research's Accelerated Research Initiative on Flow Over Abrupt Topography. This research initiative was designed to explore the physical and biological oceanographic consequences of abrupt topographic features occurring in the open ocean. Fieberling Guyot (32.5 degrees N, 127.7 degrees W), a relatively isolated

Acoustic visualization of three-dimensional aggregations seamount in the eastern Pacific, was chosen as the primary study site for field investigations. The minimum summit depth of this seamount is 435 m. The main objective of our investigation was to determine whether or not abrupt topographic features, such as submarine banks, seamounts, and guyots, generate characteristic bioacoustical signatures in the open ocean. For example, one such bioacoustical signature might correspond to the gaps devoid of vertically migrating zooplankton and micronekton which have been hypothesized to form over abrupt topography (Isaacs & Schwartzlose 1965; Genin et al. 1994; Greene et al. 1994). These gaps arise from interactions between the topography and a combination of physical and biological processes including advection, vertical migration, and predation. Specifically, the following sequence of events was hypothesized to occur at Fieberling Guyot. During the evening, vertically migrating zooplankton and micronekton from deep waters surrounding the seamount's summit ascend to near-surface waters. Since fewer animals ascend from waters directly overlying the seamount's summit, a gap in the distribution of zooplankton and micronekton is formed. In the presence of surface currents, this gap would be advected downstream throughout the night. The following morning, the animals descend back to deep water, except for those trapped by the seamount's summit. During the day, some of the trapped animals may escape by migrating horizontally or by being swept by currents off the summit to where they can descend back to deep water. Many of the remainder are consumed by predators resident to the seamount. In either case, the topography impedes the replenishment of deep-water zooplankton and micronekton by day, thereby setting the stage for gap formation the following evening. During October 1990, an acoustic survey was conducted aboard the RV Atlantis II to search for a bioacoustical signature of the hypothetical gap overlying Fieberling Guyot (Plate 4.1). Since this gap is hypothesized to be a nighttime feature, we collected survey data only between 21:00 hr and 05:00 hr. Due to the large areal extent of Fieberling's summit, the survey required two nights to complete. On each night, acoustic data were collected with a BioSonics 120-kHz echo sounder as the ship steamed a four-pointed star pattern. The second night's star pattern was designed to have each point of the star offset by approximately 45 degrees from the previous night's pattern. The Global Positioning System (GPS) satellites provided accurate navigational data for each night's cruise track. The conventional method for analyzing an acoustic data set of the type we collected would involve individually analyzing each section corresponding to each transect line comprising the two stars. This, in fact, should be done, and Nero and Magnuson (1989) provide an excellent description of some of the statistical techniques available for such analyses. Although statistical analyses of the indi-

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vidual sections can provide insights into some of the physical and biological processes at work during the survey, they fail to provide an overview of the entire area surveyed. Our first attempt at visualizing the area is presented in Plate 4.2. Here, the acoustic backscatter integrated from 10 to 120 m has been mapped for only the portion of the total survey area where the spatial coverage of data appeared adequate. Since the star survey patterns did not produce regularly spaced data, kriging (see caption to Plate 4.2) was used to grid the depthintegrated acoustic data prior to mapping. Despite logistical constraints in the survey's design and implementation, most of the seamount's summit and adjacent surrounding waters received coverage we deemed adequate for our mapping and visualization procedures. The map of depth-integrated acoustic backscatter is reasonably consistent with the gap hypothesis, but certainly does not provide indisputable evidence by itself. In general, depth-integrated acoustic backscatter in the surface waters overlying Fieberling's summit was found to be low relative to most of the surrounding waters. This was the result we were looking for, but whether one chooses to view it as convincing evidence for a gap or not is debatable. Therefore, to improve our view, we created a three-dimensional visualization of acoustic backscatter throughout the entire volume of water being examined (Plate 4.3). This involved kriging the acoustic backscatter data from each 5-m depth stratum individually (from 10 m to 120 m), and then combining them all to generate a three-dimensional data grid. An IBM Power Visualization System (PVS), running IBM's Data Explorer software, was used to visualize these volume-rendered data. The new and improved view had immediate consequences on our interpretation of this large and complex data set. In particular, two features captured our attention immediately. First, there appeared to be a fairly distinctive gap in the sound-scattering layer overlying the seamount. Although a lack of better survey coverage on Fieberling's western flank makes our case less complete than we would have desired, the evidence for a gap overlying the seamount's summit is clearly more convincing in this visualization than in Plate 4.2. The second feature immediately obvious in Plate 4.3 is the presence of discrete, soundscattering aggregations on the seamount's upstream and downstream flanks. These aggregations can be associated with the two hot spots on the map of depth-integrated acoustic backscatter (Plate 4.2). The hot spots arose, not from local increases in the backscatter intensity of the 30- to 60-m-deep sound scattering layer, but rather from the appearance of deeper aggregations of animals. Unfortunately, the full vertical extent of these deeper aggregations could not be determined from our acoustic data. Also, we were unable to determine from conventional net sampling the identity of sound scatterers comprising these

Acoustic visualization of three-dimensional aggregations

65

deeper aggregations. They may correspond to predators resident to the flanks of the seamount, such as lophogastrid mysids and sternoptychid fish, which are demersal by day and enter the water column to feed on zooplankton at night. This phenomenon has been described for other seamounts (Boehlert & Genin 1987) and seems like a reasonable hypothesis to explain our observations. Other hypotheses could explain these findings equally well and resolution of the issue will require further investigation.

4.4 Discussion One of the fundamental goals of ecology is to understand the processes regulating the distributional patterns of organisms in space and time. This goal has been particularly elusive in the oceanic environment since we rarely have an opportunity to watch pelagic organisms directly, and even when we do, they rarely stay in one place long enough for us to characterize their distributions on scales greater than meters to tens of meters (fine scales - Haury et al. 1978). Sampling with water bottles and nets has proven useful for certain applications, but issues associated with spatial coverage, spatial resolution, and sample processing time pose severe constraints on what we can learn from such methods (Greene 1990). For these reasons and others, we have turned to acoustic methods for studying the distributions of pelagic animals in the ocean (Greene & Wiebe 1990). Acoustic visualization represents the next logical step in the evolution of acoustic remote-sensing methods. Two-dimensional sections of acoustic transect data have been studied qualitatively and quantitatively for many years. The subject of interest, however, is the three-dimensional distribution of pelagic animals in a volume of ocean. As we have shown, with the powerful computing hardware and software currently available, it is feasible to extrapolate two-dimensional sections of acoustic transect data and create three-dimensional composite visualizations. These visualizations have proven extremely valuable in the search for patterns in the distributions of pelagic animals, but they must be interpreted carefully and with proper attention to methodological limitations. The most exciting part about generating an acoustic visualization like Plate 4.3 comes in the recognition that it is feasible to characterize the distributions of zooplankton and micronekton in a relatively large volume of ocean over a relatively short period of time. It must be recognized, however, that our acoustic surveying capabilities at present are limited, and these limitations impose important constraints on what we can interpret from such acoustic visualizations. The field study just described exceeded the spatial and temporal limits of what one might call a truly synoptic survey of animal distributions in the waters overlying and surrounding Fieberling Guyot. Given the local advective regime (as

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Charles H. Greene and Peter H. Wiebe

indicated by satellite-tracked drifters: Haury & Genin pers. comm.), the volume of water surveyed the first night would have moved several kilometers prior to the second night. Furthermore, the animals would have undergone one complete diel vertical migration cycle between the beginning and the end of the two-night survey. Thus, it was clearly inappropriate to interpret Plate 4.3 as a snapshot visualization of the nighttime distribution of zooplankton and micronekton over Fieberling Guyot. Instead, we interpret this figure as a composite visualization from the two-night acoustic survey. A composite visualization, we argue, that helps reveal the locations of recurring or persistent bioacoustical signatures specifically associated with seamount-related processes. Recurring or persistent bioacoustical signatures might be expected to arise when animal behavior is of comparable importance to physical advection in determining zooplankton and micronekton distributions. The two phenomena proposed earlier, the hypothetical gap overlying the seamount's summit and the midwater aggregations of predators overlying the seamount's flanks, both result from behavioral mechanisms that separate animal trajectories from the streamlines of the local flow regime (Mackas et al. 1985). Both phenomena should generate characteristic bioacoustical signatures, a negative signature associated with the gap and positive signatures associated with the aggregations. Although there was circumstantial evidence for these phenomena, our inability to draw more definitive conclusions about their existence and origin points toward another limitation of acoustic visualization. Relying as it does on acoustic backscatter data, acoustic visualization methods must be supplemented by other methods to determine the identities of the sound-scattering animals. In this regard, acoustic and satellite remote-sensing methods share comparable limitations. Acoustic backscatter data are as difficult to relate to the taxonomic composition of zooplankton and micronekton as ocean-color data are to relate to the taxonomic composition of phytoplankton. Despite this limitation, acoustic visualization can provide an unprecedented, relatively large-scale overview of pelagic animal distributions in the ocean. As such, it has the potential to revolutionize the way ocean scientists study the ecology of pelagic animals in much the same way that satellite remote sensing has revolutionized the study of oceanic phytoplankton ecology.

Acknowledgments We would like to thank the officers and crew of the RV Atlantis II as well as members of the scientific party that assisted us with our data collection at sea. Eli Meir and Hugh Caffey provided considerable help in the analysis of acoustic data; their help is gratefully acknowledged. Bruce Land provided the brains be-

Acoustic visualization of three-dimensional aggregations

67

hind the mouse during visualizations using the IBM Power Visualization System (PVS); his expertise is greatly appreciated. Finally, thanks are extended to Bill Hamner and Julia Parrish for allowing us to participate in the workshop leading to this volume. Our research was supported by the Office of Naval Research and Department of Defense University Research Initiative. Access to the IBM PVS was provided by the Cornell Theory Center, a center supported jointly by Cornell University, International Business Machines, the National Science Foundation, and the state of New York. This is contribution number 9 of the Bioacoustical Oceanography Applications and Theory Center.

Three-dimensional structure and dynamics of bird flocks FRANK HEPPNER

5.1 Introduction Of all coordinated groups of moving vertebrates, birds are at the same time the easiest to observe and perhaps the most difficult to study. While fish can be brought into a laboratory for study, and many mammals move in a two-dimensional plane, a single bird in an organized flock can move through six degrees of freedom at velocities up to 150 km/hr. Present three-dimensional analysis techniques generally demand either fixed camera or detector positions, so free-flying flocks must either be induced to fly in the field of the cameras, or the cameras must be placed in locations where there is a reasonable probability that adventitious flocks will move through the field. Perhaps because it has been so difficult to obtain data from free-flying natural flocks, there is now a current of imaginative speculation, and lively controversy, in the literature on flock structure and internal dynamics. Birds can fly in disorganized groups, such as gulls orbiting over a landfill, or organized groups, such as the Vs of waterfowl (Fig. 5.1a). To the evolutionist, behaviorist, or ecologist, any group is of interest, but I will primarily consider only the organized groups. Heppner (1974) defined organized groups of flying birds as characterized by coordination in one or more of the following flight parameters: turning, spacing, timing of takeoff and landing, and individual flight speed and direction. The term used for such organized groups was "flight flock," but for consistency in this volume, the term "congregation" will be used herein. Two general questions have driven the examination of bird congregations. The first, usually expressed while observing a skein of geese flying overhead, is, "Why do they fly in this precise alignment?" The second is prompted by the sight of perhaps 5000 European Starlings, Sturnus vulgaris, turning and wheeling over a roost. "How do they manage to achieve such coordination and polarity?" The first question is usually asked in reference to relatively large birds, like waterfowl, flying in line formations (Heppner 1974; Fig. 5.1a): groups of birds 68

69

Three-dimensional structure of bird flocks

•T- . '

.

(a)

Figure 5.1. (a) A V-formation of Canada Geese (i.e. line formation). Notice, in this oblique two-dimensional view, the difficulty of determining distance between birds and angular relationships between birds, (b) A cluster formation of mixed blackbirds.

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flying in a single line, or joined single lines. Typically, such formations are approximately two-dimensional, the birds all lying in an X-Y plane parallel to the ground. The "how" question is customarily asked about relatively large flocks of small birds, like sandpipers, flying in cluster formations (Fig. 5.1b): flocks characterized by development in the third dimension, and rapid, apparently synchronous turns. Attempts at analysis of structure and dynamics in these two major classes of organized flight formations have been driven both by the characteristics of the formations and the types of questions that have been asked. In the line formations, the functional significance (i.e. why) of the groupings has been of cardinal interest; therefore data have been sought on the values of parameters that might be supportive of hypotheses concerning costs and benefits to the individual. Because these formations have characteristically been interpreted as twodimensional, structural analysis, although challenging due to the ephemeral nature of flocks, has not required true three-dimensional analysis techniques. In contrast, it is the synchronous and coordinated turning of the cluster flocks that has drawn the greatest interest. Questions such as, "Is there a leader in such groups?" or "If there is no leader, how is coordination achieved?" have spurred the structural analyses. However, because these formations occupy a threedimensional volume, the formidable technical challenges involved have produced few field studies to date. In this chapter, I will explore how progress in the study of both line and cluster flocks has proceeded in stepwise fashion, sometimes being stimulated by a new technique, at other times prompted by a testable (as opposed to speculative) idea.

5.2 Line formations 5.2.1 Theoretical considerations Speculation and unsupported conclusions about the function of apparent structure in line formations have a long history. Rackham (1933) translated Pliny's authoritative observation in the first century A.D. that geese "travel in a pointed formation like fast galleys, so cleaving the air more easily than if they drove at it with a straight front; while in the rear the flight stretches out in a gradually widening wedge, and presents a broad surface to the drive of a following breeze." Two thousand years later, Franzisket (1951) posited that close-formation flight provided an area of turbulence-free air. In contrast, Hochbaum (1955), attempting to explain why waterfowl fly in staggered formation, hypothesized that it was to "avoid the slipstream of rough air produced by the movement of its companions." Hunters often offer the folk suggestion that birds in these formations might be "drafting," like auto or bicycle racers do: tucking in behind the vehicle

Three-dimensional structure of bird

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ahead to reduce air resistance. Geyr von Schweppenburg (1952) suggested that a phase relationship in wing beating might be important in the aerodynamics of flight in line formations. Nachtigall (1970) found such a relationship in geese, but von Berger (1972) and Gould (1972) did not. Hainsworth (1988) did not see phase synchrony in pelicans. If the wings of each bird in a flock are regarded as independent oscillators, there will be some periods of time in which significant numbers of the flock will be in temporary synchrony, and this may have been what Nachtigall observed. Non-aerodynamic hypotheses also have been offered for line formation flight. One of the most compelling suggestions stated that structured formations facilitate the collection of information by and from flock mates (see Dill, Holling & Palmer, Ch. 14 for a discussion of this possibility in fish schools). Hamilton (1967) suggested that a stagger formation allowed communication between individuals. Forbush et al. (1912) and Bent (1925) suggested that staggered flight permitted a clear field of vision to the front, while at the same time allowing a leader to fly at the head of the formation. Heppner (1974), Molodovsky (1979), and Heppner et al. (1985) all offered the possibility that V or echelon flight lines might be the result of the optical characteristics of the birds' eyes. Until 1970, students of line formations could only offer streams of hypotheses about function, because there was no suggestion about what parameter(s) might be useful to measure to test those hypotheses. However, Lissaman and Shollenberger (1970) published a seminal, but enigmatic, paper that suggested the function of the V-formation was to enable each bird in line to recapture energy lost by the wingtip vortex produced by the preceding bird. According to their hypothesis, birds abreast in line, flying tip-to-tip, should have a range approximately 70% greater than a lone bird. Distance between wingtips was inversely proportional to maximal energy recapture. In other words, the closer neighbors are, the higher the potential energy savings. Based on Munk's (1933) stagger-wing theory from aircraft aerodynamics, they predicted that the "optimal" V-formation formation (Fig. 5.2) was achieved at a tip spacing equal to 1/4 of the wingspan. However, the Lissaman and Shollenberger (1970) paper was vague; it presented neither the theoretical equations nor sample calculations illustrating their predicted energy savings. Furthermore, there were some major deviations from biological reality. For instance, flapping flight (as opposed to gliding aircraft flight) was not considered. May (1979), in a brief review of flight formation, suggested that Lissaman and Shollenberger's (1970) calculations predict an optimal V angle for saving energy of roughly 120 degrees. Hummel (1973, 1983) also felt that significant power savings were possible by V-formation flight and presented the calculations he used to arrive at this conclusion. He argued that the power reduction for a V-formation flock as a whole

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Frank Heppner

Figure 5.2. An optimal V-formation (Lissaman & Shollenberger 1970). was strongly dependent on the lateral distance between wingtips, whereas energy savings for individuals in a flock could be affected by longitudinal distances between wingtips. Haffner (1977) attempted to replicate Lissaman and Shollenberger's predicted energy savings also using Munk's stagger theorem, and only obtained a calculated 22% potential energy saving for formation flight. When Haffner then modified the calculation using Cone's (1968) flapping wing theory, the potential maximum energy saving dropped to 12%. Several investigators seized this possibility of a testable hypothesis: determine the geometry of a flock and the distance between the birds, and then the tip-vortex hypothesis could be tested. There was now incentive to develop analytic techniques for the spatial structure of line formations.

5.2.2 Data collection If a photograph of a level V-formation of geese was taken when the birds were directly over the camera position (or if the camera was directly over the birds), there would be little problem in determining either the geometric relationship of the birds in the formation or the distances between two birds. A known distance, say bill-to-tail length, could be used to establish a distance scale. However, the number of times line-flying birds fly directly over an observer in the field is sufficiently small to tax the patience of the most dedicated researcher. Heppner (1978) made a fruitless attempt to fly a radio-controlled, camera-equipped model airplane directly over goose flocks, but the geese were faster than the aircraft. If a photograph is taken at an oblique angle to an oncoming or departing Vformation (Fig. 5.3), perspective will change both the angle between the legs of the V and the distances between birds. Gould and Heppner (1974) published the first technique for determining the angular relationship and distances between Canada Geese, Branta canadensis, flying in a V. Their technique employed a single cine camera and assumed that (1) the birds were flying in a level plane, (2)

Three-dimensional structure of bird flocks

APPARENT

73

/

TRUE

Figure 5.3. Overhead view, looking down at a camera mounted on a tripod, tracking a Vformation that maintains a constant angle between the legs during its passage. The apparent angle of the V, as seen through the viewfinder and recorded on the film, changes as the birds approach their nearest point to the camera and then depart. At the point of closest approach, the apparent angle is at a minimum, and a line drawn between the camera position and the head of the formation at closest approach describes a right angle with theflightpath. This angular relationship is then used for projective geometry to calculate the true angle (from Gould & Heppner 1974). the flight path was a straight line, and (3) the shape of the formation did not substantially change in the few seconds needed for filming. The key observation for this technique (Fig. 5.4) was that when the formation was at its closest point to the camera position, the apparent angle of the legs of the V on the film was at a minimum, while the angle of the optical axis of the camera above the horizon was at a maximum. By marking the angular elevation of the camera at this point of closest approach, it was possible to use projective geometry (Slaby 1966) to obtain the true angle of the formation and the distances between birds. In the five formations they measured, the true V angle was 34.2 ± 6.4 degrees, and the distance between the centers of the birds was 4.1 ± 0.8 m. O'Malley and Evans (1982) used this technique to measure the angle of the Vformation in White Pelican, Pelecanus erythrorhynchos, flocks, and found a mean angle of 69.4 ± 4.5 degrees. They noted that the range of their values was

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Frank Heppner HORIZON

Figure 5.4. Relationship of camera position to flight path, apparent angle in the viewfinder, and camera elevation in a V-formation. This relationship forms the basis for the projective technique used to calculate true angle and distance between birds. (From Gould & Heppner 1974).

large (24-122 degrees) and did not seem to follow a pattern in flight direction, formation type, or flight size. Hainsworth (1988) filmed echelon formations of Brown Pelicans, Pelecanus occidentalis, that flew directly overhead, then in a straight line away from the camera. A known distance, the outstretched wingspread of a pelican, was used as a scale to determine wingtip-to-wingtip spacing which ranged from —171 cm (overlap) to +183 cm. Williams et al. (1976) used a mobile, modified small boat radar called an "ornithar" to determine the angle between the legs of a V-formation of Canada Geese. The portable radar technique offered smaller distortion due to perspective than optical methods, approximately 3 degrees maximum, but individual birds were not resolvable. V angles ranged from 38 to 124 degrees. Interestingly, there was greater variance among formations than within the same formation over time. In 1975, Heppner, using Gould and Heppner's (1974) optical method, and Williams et al. (1976), using their radar method, both measured the same formations at the same time at Iroquois National Wildlife Refuge in New York. Two formations met the requirements for measurement for both techniques, i.e. they

Three-dimensional structure of bird

flocks

75

were large enough for radar and well-organized enough at the apex for optical measurements. Both methods yielded essentially identical results (Williams et al. 1976). Although it has not yet been used for looking at flocks, a technique developed by Pennycuick (1982), and described in detail by Tucker (1988, 1995), offers potential for following flight paths of individual birds. It makes use of a device called an "ornithodolite," an optical range finder with a 1-m base mounted on a panoramic head that electrically records elevation and azimuth, with the range indicated by the range finder. In this way, a continuous record of a bird's threedimensional flight path was obtained. Error in the system increased with distance of the bird from the instrument. At a range of 1 km the true position of the bird is somewhere within a 10 m3 "volume of uncertainty." Tucker (1991) used this technique to follow the flight paths of landing vultures. One could, presumably, use a modification of this technique for tracking individual birds in a flock, but one would need either one ornithodolite for each bird, or a combination of ornithodolites and some accessory system for tracking the flock, such as the portable radar or optical techniques already described. Tracking radars (as opposed to planned-position indicator radars, like the familiar airport screen) have been used to follow individual birds. There is no technical reason why the technology that has been developed to track multiple targets for military purposes could not be used for bird flocks. However, as Vaughn (1985) pointed out in his excellent review of birds and insects as radar targets, high cost and limited accessibility to high-precision radar tracking devices have reduced the number of active radar ornithologists to a handful. However, there are several excellent studies on tracking of individual birds from the 1970s (DeMong & Emlen 1978; Emlen 1974; Vaughn 1974) that indicated the potential of the technique. If there is such a thing as a key paper in line formation flight in birds, it is probably Lissaman and Shollenberger (1970). They proposed, for the first time, a testable hypothesis about flock formation. Although the Lissaman and Shollenberger paper has had a powerful effect on stimulating thought and action, there has never been a direct experimental test of the aerodynamic assumptions in the paper. Haffner's (1977) unpublished study of Budgerigars, Melopsittacus undulatus, flying in a wind tunnel with smoke plumes suggested that the tip vortex in flapping flight was interrupted during the wingstroke cycle. Both Rayner et al. (1986) and Spedding (1987) found that tip vortices behind flying animals moved both vertically and horizontally during the wingstroke, making precise positioning relative to neighbors less advantageous. Most investigators of the structure of the V-formation have found wide variation in spacing and angular positions (Hainsworth 1988; O'Malley & Evans 1982), but have interpreted this variation

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Frank Heppner

as a failure of birds to maximize energy savings, rather than rejecting Lissaman and Shollenberger's (1970) energy-saving model.

5.3 Cluster formations 5.3.7 Function and synchrony The phenomenon of coordinated flight has been known since the ancients. The redoubtable Pliny (Rackham 1933) noted that "It is a peculiarity of the starling kind that they fly in flocks and wheel round in a sort of circular ball, all making towards the center of the flock." Selous (1931) organized many years of anecdotal observations of cluster flocks and framed the basic question, "There does not appear to be an identifiable leader in such groups, so how do these birds coordinate their movements?" Selous's speculative hypothesis was "thought-transference," and he viewed a coordinated flock as a kind of group mind. Selous was handicapped by lack of a conceptual model that would permit the formation of testable hypotheses and an almost total lack of quantitative information. On the other hand, Heppner and Haffner (1974) presumed that there had to be a leader in such flocks, and then proceeded to demonstrate the formidable obstacles to visual or acoustic communication between such a putative leader and its followers. Synchrony, or apparent synchrony, in the turning movements of cluster flocks has drawn much attention. Observers describe a "flash" that passes, wave fashion, through the flock, and conclude from this that the turn is initiated in one part of the flock and then spreads. Gerard (1943) observed that birds that were pacing his car at 35 mph turned within 5 msec of each other. Unfortunately, like many early studies, the details were vague; we do not know what kind of birds were involved, nor how the determination was made. Potts (1984), Davis (1980), and Heppner and Haffner (1974) describe waves of turning in European Starlings, suggesting the existence of some originating point for the turn, or a possible follow-the-leader model. Heppner and Haffner (1974) expressed the time lag between the initiation of a turn by a leader on one side of a spherical flock, and a subsequent turn by a follower taking his cue to turn by the sight of the leader turning, as a function of the reaction time of individual birds, and the diameter and density of the flock. Potts (1984) suggested a "chorus-line hypothesis" to explain a rapid wave of turning in cluster flocks. In this hypothesis, turning birds respond not to turning neighbors, but to more distant birds. In other words, they anticipate the approaching wave of motion. However, there is a possibility that observers who have seen a wave of turning may, in fact, have seen instead an artifact of the way that a stationary observer perceives the turn. Birds, like fish, do not reflect light uniformly over their bodies. Starlings have semireflective feathers, and the shorebirds reported in other

Three-dimensional structure of bird flocks

11

Figure 5.5. How simultaneous turns might give the impression of a "flash," or wave of turning. In a denseflockof Dunlin, birds turning catch the light off their bodies, creating a wave of white that passes through the flock. (Photograph by Betty Orians.)

studies are also differentially colored. If a ground observer was watching a group of birds that were turning simultaneously, the "flash" might appear first in one portion of the flock, then give the impression of moving through the flock as the flock's position in three-dimensional space changed relative to the observer and light source (Fig. 5.5). Davis (1975) investigated another apparent simultaneity in take-off of a flock of pigeons. Using "actor" and "observer" pairs, the "actor" was induced to take off with a mild shock. Observers departed within .5 msec, unless the "actor" displayed some preflight intention movements before the shock, in which case its flight tended to be ignored.

5.3.2 Analysis Major and Dill (1977) provided the first determination of the three-dimensional structure of freely flying bird flocks: European Starlings and sandpiper-like Dunlin, Calidris alpina. In this and a later paper (Major & Dill 1978), they used a

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Frank Heppner

stereoscopic technique that employed two synchronized still cameras mounted on a rigid, 5 m bar. Although they were able to determine interbird distances, there was not enough information to determine flight paths of individual birds. Major and Dill concluded that the internal organization of the cluster flocks they studied strongly resembled that of minnow schools (Pitcher 1973); that is, nearest neighbors tended to be behind and perhaps below a reference fish. Dunlin had a tighter, more compact flock structure than Starlings, somewhat surprising because the Dunlin had flight speeds approximately two to three times faster than the Starlings. One might rather expect that at higher flight speeds, more distance between birds would be desirable for collision avoidance. Pomeroy (1983) and Pomeroy and Heppner (1992) described a technique for plotting the three-dimensional locations and flight paths of individual pigeons in flocks of twelve to twenty birds using two orthogonally placed synchronized 35-mm still cameras focused on a common point (Fig. 5.6. See Appendix for a description of their method). Although their method of data reduction involved making photographic prints and measuring locations with calipers, the basic technique could be easily modified to use video and a digitizer or video framegrabber. Being able to plot flight paths over time allowed a more detailed examination of the dynamic structure of cluster flocks. Pomeroy and Heppner (1992) found that birds regularly shifted position within the flock (Fig. 5.7). Birds in front ended up toward the back, and birds on the left ended up on the right at the completion of a turn. This rotation of position was a consequence of the birds flying in similar-radius paths, rather than parallel paths during the turn, suggesting that no individual bird was the "leader." The possibility still exists that there might be a kind of rotating positional leadership although there is no evidence for such a mechanism at this time. Pomeroy (1983) suggested that flocking birds are more easily able to transit through the interstices between neighbors than fish can move between individuals in a school. In most of Pomeroy's trial flocks, nearest neighbor distances decreased during a turn. Progress in the analysis of cluster flocks was slow, not so much for a lack of analytical tools, but (until recently) the lack of a conceptual alternate to a leadership model to produce coordinated movements. Presman (1970) was committed to a leader model, but refined Selous's (1931) "thought transference" model to a more sophisticated model in which electromagnetic fields produced by either the brain or neuromuscular system of the leader would be instantaneously transmitted to other members of the flock, there to act either on the follower's brain or directly on the follower's neuromuscular system. The flock would then become a kind of "superindividual." Neither of these hypotheses had any experimental

Three-dimensional structure of bird flocks

79

Negative from Camera A

X

Figure 5.6. Nonstereo determination of three-dimensional location of individual birds. Two cameras. A and B, are aimed at, and equidistant from a common point, S, that represents the center of a sphere of radius, CS, that represents the maximum volume in which a bird's location may be determined. Point T is the projection of the bird's position in three-dimensional space (from Pomeroy & Heppner 1992). support and stretched biological communication to or perhaps beyond the limit, but there was then no biologically plausible nonleader model available either. Although it is traditional to think of the internal architecture of cluster flocks in terms of potential adaptive significance, there are difficulties presented by some generally accepted suggestions for the adaptive advantage of tight, highly coordinated, and polarized flocks. For example, if coordinated flocking is of advantage against predation by hawks (Tinbergen 1951), why then do European Starlings turn and wheel in highly coordinated fashion for a half-hour to fortyfive minutes above a roost before retiring for the night, exposing themselves to what would appear to be an unnecessary risk of predation? Wynne-Edwards

Frank Heppner

80


.in l|. #l * °

-16.0 -16.0

Timel

Time 5 (b)

Figure 5.7. (A) Two-dimensional projections of each individual numbered pigeon in a flock at 650 msec intervals. Birds rotate their positions in the flock during the turn. (B) Demonstration of how flight on paths of equal arc will result in position shift within the flock (from Pomeroy & Heppner 1992).

Three-dimensional structure of bird

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(1962) suggested that these movements served to inform individuals how big their population size had grown, but it is hard to see why it would take almost an hour of flight a day to serve this purpose. Because of these problems, by the early 1980s, publication about cluster flocks had almost dried up, with the exception of Davis's (1980) and Potts's (1984) descriptive accounts of turning. As more has been learned about the behavior of complex dynamic systems, however the possibility arises that behaviors that are enigmatic in adaptive terms may in fact be interpreted as emergent properties that are the outcome of more fundamental physical or mathematical properties of the system itself. By the mid-1980s, it appears that a Zeitgeist was at large, because working independently, and approaching the subject from very different disciplines, three investigators raised the possibility of a nonleader, nonadaptive (at least directly) model that could account for the coordinated movements of flocks. Okubo (1986) published a theoretical paper suggesting that coordination in flocks might be achieved by the application of the mathematics of nonlinear dynamics. Heppner (1987) suggested that flocking might be an emergent property arising out of simple rules of movement followed by individuals in the flock. Reynolds (1987) and Heppner and Grenander (1990), working independently, developed computer flock simulations in which the flock was a self-organized structure. Both models used the basic principles of attraction and repulsion to direct the movements of individuals. Heppner and Grenander's (1990) simulation was based on a stochastic differential driven by a Poisson process with associated random variables equations.

(5-D vj(t)=du.(t),

i=l,2,

...,n

where uft) = (x.(f),v .(0) is the location of bird number / at time t. The equation incorporated the following assumptions and variables: A. Attraction toward a central place. The model was based on the behavior of starlings, whose most highly coordinated flocks appear near an attraction such as a roost, or feeding area. Therefore F home expresses a tendency toward an attraction. As a bird draws closer to the perimeter of the attraction, it is more strongly attracted until it crosses the perimeter, at which time the influence of the attraction drops to zero. This relationship was expressed for the zth component.

= -«,(0/ home ( uft));

i = 1, 2,. . ., „

(5.2)

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Frank Heppner

where u. is the vector from the homing zone to bird i, / home is a scalar valued function, and t0 is the minimum radius of a circular attraction area. B. Velocity regulation. If individual birds in a flock tend to have the same velocity, the chance of overrunning, or being overrun, is minimized. However, an individual bird might depart from the mean velocity of its neighbors to avoid collision with a neighbor intersecting its flight path, or its velocity might be affected by physical factors such as gusts of wind. After such perturbations, it was assumed that individuals would return to a "preferred" velocity. In nature this would be determined by the collective behavior of the flock, but in the model it could be varied by the experimenter. The velocity control term was expressed as ^

I

v

d

J

(5-3)

where v0 is the preferred velocity. C. Interaction between birds. The spacing that individuals might choose to maintain between themselves and neighbors might be influenced by collision-avoidance requirements, communication, aerodynamic considerations, and predator avoidance to name a few. The model assumed that individuals would integrate the spatial requirements of these factors and arrive at a preferred distance to neighbors. Birds closer than the preferred distance would be repelled in proportion to their proximity to neighbors. Birds above, but close to, the preferred distance would be strongly attracted to a neighbor. However, this attraction would decrease with increasing distance, eventually dropping to zero. The later provision allows the flock to split into two or more subflocks - a phenomenon often seen in nature. If dr (t) means the vector difference from individual / toy, dtj(t) = u.(t) — uft) the ith component will be: (5-4)

The interaction dies out if the interindividual distance dr > dr D. Random impact. The fourth term dP(t) was originally included with the idea of more closely simulating a natural environment in which wind gusts, distractions from moving objects on the ground, and predators might randomly perturb the flight paths of in-

Three-dimensional structure of bird

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83

dividuals. In practice, without the inclusion of this term, it was not possible to produce a coordinated, polarized simulated flock, an interesting observation in terms of both the dynamics of the model system and the transitions between coordinated and uncoordinated flocks in nature. The random impact term was modeled by an n-dimensional, time-homogeneous Poisson process with stochastically independent components. The ith component of dP(t) was zero unless t happened to be an event of the ith component of the Poisson process. In the latter case, dP(t) equals a random three-vector with uniformly distributed components, with a scalar parameter controlling the magnitude of the random vector. Heppner and Grenander's (1990) model produced polarized flocks that would either orbit an external attraction and demonstrate the rotation of individual position seen in Pomeroy and Heppner's (1992) natural pigeon flocks, or escape the influence of the attraction and fly a straight flight path indefinitely, depending on the values attached to the variables in the model, such as preferred spacing. The model would not, however, produce the spontaneous coordinated turns seen in natural flocks. Heppner and Pakula (unpublished) prepared a computer simulation of a type of natural flock behavior that resembles, in basic character, a simultaneous, or near-simultaneous, departure from a wire or field, and thus bears resemblance to a coordinated, or near-synchronous turn. In this behavior, flocks of blackbirds will descend to a field and forage. From time to time, individual birds will "pop up" spontaneously to a height of a few meters above the ground (Heppner & Haffner 1974). Occasionally, a bird will depart the area after "popping up," but more typically will settle back to the ground. From time to time, small groups will pop up and leave, but after a variable interval, the entire flock will appear to rise up simultaneously and move to a new foraging area. In Heppner and Pakula's two-dimensional model, an individual bird is represented by a graphic "bird" that can move freely on a Y axis line above the X axis ground surface. At the beginning of the demonstration, birds are spaced equidistantly along the ground surface. Each bird is a member of a cohort of birds that are within a defined lateral distance from a bird in question. The cohorts overlap. At the beginning of a run, individual birds pop up randomly in space and time. The mean interval between pop-ups can be varied by the experimenter. When a bird pops up, it rises to a height on the screen where it can "see" the other birds in its cohort. If no other birds in its cohort are in the air, or if the number of other birds in its cohort who have also spontaneously popped up and are airborne are below a preset threshold, the popped-up bird will slowly descend back to the ground. If, however, the threshold number is exceeded, the bird will depart the area by flying vertically off the screen.

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Frank Heppner

Decision Height;

c.

D.

E. .^^f^*

4~9f^.

Figure 5.8. Demonstration of a "pop-up" model. (A) All birds are on the ground. (B) One bird randomly flies above the decision height, detects no other birds, and (C) returns to ground as two other birds which happen to be next to each other in the same cohort randomly "pop up" above the decision height, but seeing no other birds, (D) return to ground as three birds which happen to be in the same cohort randomly "pop up," and seeing a threshold number of their cohort above the decision height, (E) fly away, as other birds on the ground see a cohort depart and depart themselves.

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Birds on the ground will ignore popped-up birds in the cohort, unless the number of birds in the air exceeds a threshold, in which case all of the birds in the cohort will rise simultaneously and depart the area. Birds not in the cohort in question will ignore the behavior of birds in other cohorts, unless the number of cohorts in the air exceeds a preset threshold, in which case all birds in the flock rise up and depart the area (Fig. 5.8). By manipulating the thresholds, it is possible to produce qualitatively a behavior that resembles natural flocks; individuals pop up at random, usually dropping back to the ground, small groups rise up and leave without affecting the flock as a whole, and after a period of time, the balance of the flock rises up almost simultaneously and departs. A similar mechanism might be employed to produce coordinated turns in a flock. In natural flocks, individuals and small groups are constantly turning away from the flock as a whole. Sometimes they return, other times they do not. Individual birds might have a threshold for being influenced by neighboring turners; if only a few neighbors turn at random, they will be ignored, but if a greaterthan-threshold number turns, the individual will follow the turners. In this case, coordinated turns, like the formation and cohesion of the flock itself, might be driven by a stochastic process.

5.4 Future directions and problems Low-tech, inexpensive techniques now exist for determining the two- and threedimensional structure of bird flocks, but they require so much time for manual data reduction that few people would now be willing to employ them. High-tech, expensive methods exist that would solve the data-reduction problem, possibly even permitting real-time three-dimensional analysis, but there remains the problem that essentially killed wide use of radar ornithology - cost and availability. The perfect three-dimensional analysis technique does not currently exist for bird flocks, but if it did, it would have the following properties: 1. Portability. Whether using stereo (e.g. Major & Dill 1977), or orthogonal (e.g. Pomeroy 1983) techniques, present optical methods require a relatively fixed volume of space within which the birds can fly. This greatly reduces the usefulness for the analysis of wild flocks. Ideally, one should be able to set up and take down a recording device in ten minutes or so, to take advantage of blackbird or shorebird flocks whose appearance is unpredictable. 2. Auto-correspondence. To date, three-dimensional analysis methods require images from at least two matching viewpoints. A technique that would permit

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rapid, automatic, and accurate correspondence of the images would be very valuable. 3. Low initial cost and data-acquisition cost. Most footage obtained of wild animals in the field is worthless for one reason or another, so many feet of film or tape must be exposed. Cine film is very expensive now, but offers excellent resolution, and true slow motion. Videotape is very cheap, but has only a fraction of the resolution of 16-mm film, and with consumer camcorders, does not permit true slow motion. Perhaps more important than the development of a faster, cheaper, and better analytical technique is resolving the question of what to measure with this technique (see discussion by Dill et al. Ch. 14). What parameters should be measured to address questions of leadership, synchrony, internal structure, and driving mechanism? How do you define a "turn"? Is it when more than a certain fraction of the birds depart from the mean flight path of all birds by a given angular amount? Is the interval between turns significant in some way? To use an ornithological metaphor, there is a chicken-and-egg problem here. Without knowing what the technique has the capacity to measure, it is difficult to set the task for the technique, and without the technique, it is difficult to know what questions can be addressed with it. Ultimately it will be desirable to "truth-test" the models and simulations that have been made. It is all well and good to prepare a stunning and realistic computer simulation of a flock, but how do you know real birds are using a similar algorithm? To test this, it will be necessary to measure parameters in both the simulation and the real flock, and with some appropriate statistical test, compare them. At this stage in the development of the field, it is not clear what the key parameters should be, so perhaps a shotgun approach might be in order, in which every parameter that can be measured by a technique (such as interbird distances) is measured in both simulations and flocks, to see which offer promise for identifying characteristic flock properties of particular bird species. Model-makers still have much to learn from their models. Heppner and Grenander (1990) noted that the values of the parameters in their model that produced flocking behavior were arrived at serendipitously, and the choice of a Poisson-based force rather than a Gaussian one to drive the model was fortuitous rather than deliberate. In essence, the model worked, but it was not altogether clear why. Attraction-repulsion models (Warburton & Lazarus 1991) may be useful in investigating flock formation. Studying the properties of a flocking model at a screen may permit avian investigators to have the same facility in testing hypotheses as, for example, students of schooling have had in looking at fish in a tank.

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In summary, the three major immediate tasks that must be addressed in the analysis of the structure and dynamics of bird flocks are (1) the development of an inexpensive, portable device for determining three-dimensional space positions of free-flying individuals over time, and whose data can be reduced directly by computer; (2) the determination of what parameters to measure in either a real flock or a model, or both, that will speak directly to questions of leadership, synchrony, initiation of turning and takeoff, internal structure, and coordinating mechanism; and (3) a complete and thorough analysis of the properties of existing simulations to determine what factors influence the formation and movements of simulated flocks.

Acknowledgments I thank Susan Crider, who did most of the yeoman work in the library, and C. R. Shoop, J. G. T. Anderson, and W. L. Romey, who read early drafts of this manuscript and offered helpful suggestions. J. Parrish did a wonderful job of reducing the manuscript by 20% without causing either hurt or outrage.

Appendix Absolute position. Information derived from the two photographic prints was first used to establish where in three-dimensional space each bird in the flock was located each time photographic samples were taken. A Cartesian-coordinate system was defined for this point-in-space analysis. The X- and 7-axes of the system were perpendicular and crossed at the point of intersection of the optical axes of the two 35-mm cameras. The XF-plane was parallel with the ground. The Z-axis, or vertical axis, of the system was defined as perpendicular to the XF-plane. The elevation (Zaxis) and the bird's displacement along the horizontal grid system (Xy-plane) were the real-space coordinates of the bird. Real-space coordinates were calculated for each bird in the flock for every point in time at which the flock was photographed. For the computer program developed to determine the positions of a bird, the horizontal and vertical deviations of a bird's image from the center of a negative were used as the basis for all calculations (Fig. 5.6). The position of a bird on a negative from camera A can be used to locate that bird along a line originating and extending from point T (the optical center of the lens) to point G at infinity. The bird could be anywhere along line TG. Line TG is

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Frank Heppner

determined as follows: The horizontal displacement (distance Dx) of the image of the bird's head from the center of the negative is measured to yield the length of side QR in triangle QRT. Side RToi the triangle is the focal length of the camera lens when focused at infinity (58 mm). Angle B in right triangle QRT can be expressed as tan-' (QR/RT). Triangles QRT and MET are corresponding right triangles, such that angle S, in triangle MET is equal to angle B in triangle QRT. Angle B{ in triangle MET defines the horizontal displacement of line TG on the Y axis. With this information only, the bird could be in quadrant I or II. The same process is used with data from camera B to locate the bird along line CD. The intersection of lines TG and CD defines point F, which will be the position of the bird in three-dimensional space. It now becomes necessary to determine the X-, Y-, and Z-coordinates of point F. In the example shown in Figure 5.6, the photograph from camera B shows that the bird is left of the center line (Z-axis). In the view taken from camera A, the bird is also left of the Z-axis, placing it in quadrant II of the XY plane. Lines FE (Z-coordinate), ME (F-coordinate), and MS (X-coordinate) must now be determined. Triangle TEC in the XF-plane connects the optical center of the lens of camera A (point T), and of camera B (point C), with point E, which is the projection of point F onto the XT-plane. Side TC of triangle TEC, the distance between the cameras, is a measured distance. Angle t (given by LBX + 45°), angle c (given by A5° — /LF, which is the angular deviation of CD from the Y axis as determined from photographs taken by camera B), and angle e (given by 1 8 0 ° - \ L t + Lc]) are all known. All internal angles and side TC of triangle TEC are now known. Thus, side TE can be determined as TE = [(TC) sin (Z.c)]/sin (Le)

(5.5)

The position of the bird along the F-axis (side ME of right triangle MET) is given by (TE) sin (^B,). The elevation of point F above the AY-plane can be calculated by determining the length of side EF of right triangle TEE Side TE and angle (f) of the triangle are known. Distance EF, the elevation of point F, can be expressed as [cos ()] (TE). The displacement of the bird along the X-axis (side MS) is determined as follows. The distance from the optical center of the lens of camera A to point S is constant (TS = 60.80 m). Side TM of right triangle MET can be calculated as TM = (M£)[tan (LBX)]

(5.6)

In this example, where the bird is in quadrant II, distance TM must be subtracted from 60.80 to yield MS.

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The X, Y, and Z Cartesian coordinates of all birds in the flock were determined for every time at which photographic samples of the flock were taken. Coordinate positions of each possible pairing of birds were used to calculate distances between flock members using the formula D = [(XR - XN)2 + (YR - YNy + (ZR - ZN)2]05

(5.7)

Subscripts 7? and N in the formula refer to the reference (/?) and neighbor (AO birds. Each bird in the flock was analyzed in turn as the reference bird for every time at which the flock was photographed. Distances between each reference bird and all other birds in the block were calculated to yield a series of values for first-nearest neighbor, second-nearest neighbor, through Mh-nearest neighbor. Data for each of the neighbor-distance categories, and the associated mean values, were plotted over time to represent graphically the structure of the flock (Pomeroy & Heppner 1992).

6 Three-dimensional measurements of swarming mosquitoes: A probabilistic model, measuring system, and example results TERUMI IKAWA AND HIDEHIKO OKABE

6.1 Introduction Aggregations in flight such as mating swarms and group migration are widespread phenomena in the insects. However, due to the difficulties of threedimensional measurement, many questions about insect aggregation, such as the process of group formation, identification of spatial structure within a group, or aspects of individual behavior such as spacing or mutual interference, remain unanswered. Using instruments available at the time, various methods have been developed for three-dimensional measurements of animal aggregations (for insect swarms: Okubo et al. 1981, Shinn & Long 1986; for fish schools: Cullen et al. 1965, Pitcher 1973, 1975; for bird flocks: Gould & Heppner 1974, Major & Dill 1978). In our methods, still or video cameras are used to record the positions of objects simultaneously from different perspectives. The principles of stereoscopy are then used to reconstruct the full three-dimensional positions of the objects based on sets of two-dimensional images. In conventional stereoscopic methods, there are two problems which make three-dimensional measurements difficult. One is the camera calibration problem: precise adjustment of the cameras or other apparatus is essential for minimizing distortion in the images. The other is the correspondence or matching problem: matching the points in each image that correspond to the same object is difficult. Manual matching is an exhausting and unreliable process. Automatic matching is preferable, but so far there have been few algorithms or theories for such methods. Moreover, even if matching is done automatically, there are no effective methods of ensuring accuracy. To overcome these problems, we have constructed a probabilistic model and computer programs for automatic matching and reconstruction of the threedimensional position of objects and then applied these methods to the design of a portable photographic system originally designed for measuring mosquito

90

Three-dimensional measurements of swarming mosquitoes swarms in the field (Ikawa et al. 1994). Precise adjustment of apparatus is not a prerequisite and the process of matching is automated. Our method has the advantages of flexibility in experimental application as well as efficiency in data processing. It is applicable to three-dimensional measurements of various kinds of animal aggregations both in the laboratory and in the field. In this chapter, we describe the main features of the probabilistic matching technique, show how it is applied to reconstructing three-dimensional positions, and discuss the actual measuring system used in the field. We also present example data that illustrate spatial and temporal features of mosquito swarming in Culex pipiens pallens Coquillett.

6.2 Probabilistic model for stereoscopy The two main principles, on which most systems of noncontacting measurement of three-dimensional position are based, are trigonometric stereoscopy and range detection with the delay of signal propagation. In a stereoscopic system, the essential and difficult problem is to identify, in each view, the object (point, edge, etc.) which corresponds to the identical real object in space. Most methods for solving this problem can be classified into the following three categories: 1. When objects can be distinguished on the basis of features such as shape, color, or size, similar objects in both views can be readily matched (Herman et al. 1984; Cavanagh 1987; Tatsumi 1987). 2. If two identical cameras are juxtaposed horizontally and their optical axes are parallel, the projected images of a point should have the same vertical coordinates in both views. Conversely, two points having almost the same vertical coordinates are likely to match. This method can be generalized to arbitrary settings of two cameras and is called the "epipolar plane constraint method" (Ohta&Kanadel985). 3. Additional views obtained by supplemental cameras can decrease erroneous matchings (Ito & Ishii 1986; Morita 1989; Randall et al. 1990). For a more general survey of three-dimensional measurement and related methods, the readers are referred to Chapter 3 by Osborn in this volume. In determining the position of a point from two views, we face the problem of redundancy in that although there are four numbers obtained (two pairs of plane coordinates of the image of the point), only three numbers are required for the calculation of the spatial coordinates of the real point. Because it is impossible to eliminate errors in actual measurement of the plane coordinates, the coordinates calculated by each choice of three of the four numbers never coincide and some

91

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Terumi Ikawa and Hidehiko Okabe

kind of average is usually adopted (Rogers & Adams 1976; Yakimovsky & Cunningham 1978). Finally, to evaluate the precision of the obtained coordinates, some estimate for the expected error should be given. Although some studies have focused on this problem (McVey & Lee 1982; Verri & Torre 1986; Blostein & Huang 1987; Mohan et al. 1989), most of the practical work for stereoscopic range measurement give only empirical data for errors. Our method treats these problems of redundancy by means of Bayesian inference. This is basically the epipolar plane constraint method. However, based on the probabilistic model, our criterion to reject false matching has a precise meaning. Although our consideration here is limited to the measurement of independent points in space, this approach can be extended to the matching of more complicated objects and to a larger variety of situations of stereoscopic measurement.

6.2.1 Binocular system For simplicity, consider the case of two cameras, yielding a pair of images, each photographed from a different direction (a binocular system). Each photograph is simply a planar projection of real three-dimensional objects. Given six reference points whose three-dimensional coordinates are known, the projection matrix can be estimated using the projected positions of these points on a given photograph (Sutherland 1974). For example, a mosquito at true position x has images a , and a 2 on two photographs W{ and W2 (Fig. 6.1). Using the coordinates a ( and the projection matrix, one can determine the equation of the line /. from the camera's projection center C, to a,-. In the practical case, there is error associated with each of our measurements, so that the lines l{ and l2 may fail to intersect. They may pass close to x, but will be separated by some small distance d. If we consider many images, such as a swarm of mosquitoes, there will be many such lines, and the problem of correctly matching pairs of lines arises. Define <5, to be the (small) angular error associated with the reconstructed lines: i.e. the angle between /; and the true direction of x from the camera's projection center C.. We assume that the distribution of error angles follows an isotropic two-dimensional normal distribution with predetermined standard deviation 17,. Then the error would be constant all along a circular cone with vertex at C.. (This surface represents an isoprobability surface for the normal distribution.) However, if the standard deviation is small, and the "matching" lines pass sufficiently close to one another (i.e. d is small), then the cone can be approximated by a cylinder as shown in Figure 6.2. Without loss of generality, we can

Three-dimensional measurements of swarming mosquitoes

93

Figure 6.1. Scheme of binocular stereoscopy illustrating potential error in the coordinates of an observed image. (Modified from Ikawa et al. 1994)

take the coordinate system as Figure 6.2, and the relative probability p that a point at x is observed as on l{ and l2 is expressed as follows, where <x, = \TtC\ 17,, for i = l and 2, respectively.

p(x,y,z) =

1

1

2TTCT+

2TT(T\

(6.1) (x sin 6 - y cos df + (z +

1 4T72O-1V^

Integrating equation (6.1) all over the space, we obtain the probability H(lv l2) that the pair of lines /, and l2 corresponds to the same point somewhere in the three-dimensional space; i.e. that the lines lx and l2 are a correct pair as follows: ,/2) = \ pdv =

1

2(o-2 + o-\)

al)\sin d\

(6.2)

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Terumi Ikawa and Hidehiko Okabe

(x,y,z)

W

Figure 6.2. Close-up view of the true object position (x) and the lines of projection /, and Z2 from two cameras. Due to error, the lines fail to meet at*. Using cylinder approximation of the distribution function of the observation error, we can calculate the most probable location of x. (Modified from Ikawa et al. 1994) Now, for each a , in Wp we pair a a f in W2 that gives the highest probability of matching H(lv I*). Then, the estimate of the position x (i.e. the most probable position of JC) is given by x* =

o,o,-

cr,

cr, a\

(6.3)

The point JC* has the property that it divides the line segment TXT2 into segments in the ratio o-2:a2 N o te that the probability H(lvl2) and the most probable location x* are determined by 6, d, and cr = I^CJT/^, which themselves are all directly calculated from the equations of lx and l2 or from the coordinates of a, and a 2 ,without the coordinate transformation indicated by Figure 6.2. 6.2.2 Trinocular system In some cases, a pair of lines that actually correspond to two distinct points in space may lead to a high value of H, resulting in an erroneous matching. The third camera helps to decrease this kind of mismatching in the following manner.

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Table 6.1. Precision of the estimated three-dimensional coordinates

Axis

Mean absolute error (mm)

Standard deviation of error (mm)

Number of observations

x y z

3.1 4.4 1.9

4.1 5.2 3.0

54 54 54

Modified from Ikawa et al. 1994. First, for each lx in one photograph W{, we look for a second line l2 in W2 for which H(lv l2) is greater than some threshold Hmin. Then, we examine whether there is a line /3 in the third photograph W3 which passes near the point estimated from the pair (/,, / 2 ). If no such line is found, i.e. there is no point W3 that would correspond to such a line, we discard the pair (/,, l2). If no point in W2 clears the check above, we can presume that lx has no matching in W2.

6.2.3 Precision in estimation and errors in matching The preceding discussion can be extended to the analytical evaluation of the precision of estimated three-dimensional coordinates and the evaluation of the probability that an erroneous matching occurs in a binocular system or a system with more cameras. Omitting mathematical details, we illustrate the method on an actual test of the precision of measured coordinates and on the estimation of mismatching probability for concrete examples. To investigate the precision of our method, we photographed points with known spatial coordinates. To do so, we used a square frame of steel rods of size 1.2 m. Threads marked off with equally spaced small beads were stretched across the frame, and the structure was photographed repeatedly from different perspectives, and using different camera positions. Actual errors in the bead positions were within 3 mm. The positions of the bead images and the images of the six vertices of the frame were digitized from each photograph. After calculating the projection matrix, the three-dimensional positions of the beads were determined. Table 6.1 demonstrates the mean absolute errors with standard deviations for the X, Y, and Z axes. These errors agreed with the analytically estimated errors and, more importantly, were small enough for biologically accurate three-dimensional measurement of mosquito swarming. The maximum number of points that can be correctly matched depends on several factors, including the way that the images are distributed on the photograph as well as on the resolution of the digitizer. The resolution of image-

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entering devices ranges between —1/200 (TV camera outputting NTSC signal) and ~ 1/700 (photograph + digitizer or image scanner, or 'high vision' quality TV camera). Correspondingly, the number of points which can be matched within error probability 0.01 ranges between —2 and —7 for the binocular system and between —35 and —130 for the trinocular system, provided that the distribution of objects is not too much concentrated.

6.3 Measuring system for mosquito swarming One of the initial motivations for this research was to determine whether it is possible to measure the three-dimensional position of flying insects in the field. Encouraged by the result of the preparatory experiment, we conducted field experiments to measure the swarming behavior of Culex pipiens pallens Coquillett in Tokyo, Japan. In the field, our apparatus was made up of the following units: three motor driven 35-mm cameras (Nikon F3) with zoom lens (28-80 mm), a xenon lighting unit (Nikon SB6), a portable reference unit, and a 1.2 m X 1.2 m black cloth, which served as an artificial marker to attract mosquitoes (Fig. 6.3). The reference unit (crossed bars in Fig. 6.3), which gave us six points (one on each vertex) with known coordinates, was placed in the center of the experimental site. The light source was placed under the reference unit and the three cameras were placed in a triangular arrangement around the reference unit. The distance between the reference unit and each camera was approximately 3.5 m. Cameras were attached to low tripods and positioned so as to cover more than 3 m X 3 m X 3 m o f space above the cloth. High-sensitivity film (Konica 6x3200 Professional) was used. Cameras were synchronized by an electric signal, and a delay unit was inserted before the flash to ensure that it fired only after the shutters of all three cameras were open. Flash exposures reduced mosquito images to shining points on the photographs (Fig. 6.4). Mosquitoes swarm in the dark, and if exposed to continuous light, they leave the swarming site. However, momentary illumination by flash unit appeared not to affect swarming behavior. The swarm we measured was always contained in the visual field of cameras. The same hardware and software as that of the preliminary experiment were used for the input, computation, and display of the reference and object points. Figure 6.5 shows the images of swarming mosquitoes reconstructed by threedimensional computer graphics. By repetitive firing of the flash we could even measure the speed and acceleration (Fig. 6.6; reconstructed images of a flying mosquito are in Fig. 6.7). To obtain a more complete record of the process of swarming, we are developing a stereoscopic video analyzing system where the pursuit of the object points over time-sequential video frames is linked with the matching of points among synchronous views.

Three-dimensional measurements of swarming mosquitoes

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Camera 3 Camera 1

Figure 6.3. The system for the three-dimensional measurement. A reference unit and a flash unit were placed next to a black cloth used as a swarm marker. The six tips of the reference unit served as reference points. The shutters of cameras 1, 2, 3 were released by an electric signal. All the cameras were illuminated with the flash unit, which was regulated by a synchronization unit.

6.4 Spatiotemporal features of swarming and the adaptive significance The term swarm refers to the aggregation of small animals in motion. Frequently, it refers in particular to insects such as groups of honeybees emigrating from a hive, large bodies of migratory locusts, or mating swarms found in several insect orders. In a mating swarm, adults of both sexes aggregate in one area and copulate, usually in flight. In mosquitoes, as with other dipteran insects, swarming behavior is often associated with mating. Many species swarm at dawn and/or dusk over specific objects such as trees, animals, or corn shoots. These objects are called "swarm markers" or "landmarks" and appear to serve no function other than acting as a signal for aggregation. Mosquito swarms are usually monospecific and in many cases, only males are found in swarms. Females

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Terumi Ikawa and Hidehiko Okabe

Figure 6.4. Swarming mosquitoes (shining points) photographed with a flash unit and the reference unit (cross-shaped bar).

Figure 6.5. Reconstructed images of swarming mosquitoes by three-dimensional computer graphics. The crossed bar is the reference unit.

Three-dimensional measurements of swarming mosquitoes

A flying mosquito.

Interval; 88.3 msec Figure 6.6. A trace of a flying mosquito photographed by repeating flash.

Computer graphic images of reconstructed positions Figure 6.7. Reconstructed image of the trace of a flying mosquito.

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Terumi Ikawa and Hidehiko Okabe

0

10 20 30 Time after Swarm Initiation ( min)

40

50

Figure 6.8. The number of mosquitoes in the swarm during the swarming period.

B

'X

* *

•

• * * •

+

4

*

E

D A

*

* *

*** * 4-

• *

* * *

F

4 *

*+

+

-

4>

*

4

*

* •

A

I

Figure 6.9. Projections of the spatial positions of swarming mosquitoes onto the ground. The size of each panel is 300 cm X 300 cm.

Three-dimensional measurements of swarming mosquitoes

101

often visit swarming sites, where they are eventually caught by a male, mate, and then leave the swarming site with their mates (Downes 1969). Figure 6.8 shows how the number of mosquitoes fluctuated throughout the swarming period. This fluctuation may be better observed by examining the x,y coordinates of mosquitoes (i.e. the projections of spatial positions of swarming mosquitoes onto the ground; Fig. 6.9). Panels A, B, and C on Figure 6.9 were taken at intervals of several seconds, when the mosquitoes crowded into the swarming site. Later, mosquitoes dispersed rapidly (Panels D, E, and F). This suggests that mosquitoes did not remain at a single swarming site, but repeatedly entered and left the sites. Figure 6.10 shows the distribution of nearest-neighbor distances in one swarm. Although mosquitoes clustered tightly at times (as evidenced by the peaks at small nearest-neighbor distances), the fluid structure of the swarm was just as likely to dissolve (traces with no tall peaks or with peaks at higher nearest-neighbor distances). In fact, this was due to changing numbers of mosquitoes in the swarm. There was a negative correlation between the number of individuals and nearest-neighbor distance, suggesting that the swarming space did not change significantly with mosquito numbers.

15

Figure 6.10. A distribution of the distances between nearest neighbors throughout the swarming period. The time intervals between series shown are about 5 min.

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In a separate publication, we describe the details of principal component analysis and how it can be applied to describing the overall shape of the mosquito swarm. Using this method, we showed that the swarms we observed resembled ellipsoids with axes in proportion roughly 50 : 30 : 20 and that this shape was roughly constant over the time period of observation. This suggests that there was little change in the region in which swarming took place. The swarm height above the marker was between 50 cm and 100 cm throughout the swarming period (Fig. 6.11). Height, time of swarming, and marker characteristics seem to be species specific. For example, some sibling species swarm simultaneously above the same marker; however, the swarms are monospecific because they form at different heights (Downes 1969). Such species-specific variations in swarm behavior may serve to ensure the species isolation. Within the swarm, we could also trace the path of individual mosquitoes. However, because our flashlight power was limited, we could follow only very short trajectories. For nine paths traced, mosquito speed varied between 24 cm/sec and 156 cm/sec with a mean of 81 cm/sec. Thus, individuals within the swarm boundaries move across a broad range of speeds. Our results lead us to conclude that, although mosquitoes act as relatively independent entities, moving quickly in and out of the swarm, the shape, size, and height of a swarm are fairly constant throughout the swarming period. Thus,

15

Figure 6.11. A distribution of the heights of the mosquitoes from the swarm marker throughout the swarming period. The time intervals between series shown are about 5 min.

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individual mosquitoes may swarm primarily with reference to a marker and their behavior may be influenced by the presence of other individuals only as a secondary effect. Gibson (1985), however, has shown with the two-dimensional analysis of Culex pipiens quinquefasciatus that although mosquitoes change flight speed or flight path in the presence of conspecifics, the swarm area itself does not change. Note the distinction between mosquito swarms and herds, flocks, or schools in which interactions between individuals are a dominant effect, as shown in many chapters of this book. Are there any adaptive advantages in spatial and temporal features of mosquito swarming? Swarming behavior gives mosquitoes opportunities for mating. However, this behavior has a cost, because swarms attract many predators (Downes 1969). Therefore, it may be quite important for mosquitoes to increase the efficiency of finding mates and to keep the swarming period short so as to reduce the risk of predation. Constancy of swarm shape, size, and height may serve not only to promote species isolation, but also to increase the efficiency of finding mates. Male mosquitoes locate potential mates by the distinct sound of the female wing beat. Because this sound is low amplitude, clustering about the marker increases the likelihood that males are within hearing distance of the females. Frequent migration from one swarm station to another results in several advantages. First, by visiting a number of markers, males may find a better swarming site where they can find more females. Second, mosquitoes may find mates while flying between sites as well as at the swarming site. The combined strategy of searching for mates in and between swarms may serve to increase the total encounter rate of males with females.

6.5 Viewing extension of the method The methods and measuring system described in this chapter have a number of advantages over previous techniques: (1) The equipment needed is inexpensive and readily available commercially. (2) The system is portable and compact, and so can be easily transported and used in the field. (3) The precision of placement of camera and reference unit is not a limiting factor in the measurement. Thus, the apparatus can be used for a variety of field experiments. (4) The procedures are automated once the positions of images and reference points on the photograph are entered into the computer. (5) Calculation times are short, even on a personal computer. (6) A three-dimensional graphics program (also developed here) displays the reconstructed images easily on the personal computer. This flexibility and portability make our method applicable to three-dimensional measurement for many kinds of swarms and groups of animals in the field or in the laboratory.

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Automatic tracking of the three-dimensional movement of each member of a group recorded in movie films or video tapes is a goal of our work. Given a proper kinetic model of the movement of an individual, one could consider two different approaches to reconstruct three-dimensional movement. First, we could track the two-dimensional movement in each view in advance and match the obtained time sequences of two-dimensional positions by our method. Alternatively, we could calculate the three-dimensional coordinates of the objects by stereoscopy and only then track the three-dimensional movement. In the first approach, tracking two-dimensional movement is difficult because there are many apparent collisions among individuals: lacking information about movement in the perpendicular direction, the kinetic model is incomplete. On the other hand, in the second approach, solving the matching problem can be troublesome when the density of individuals is high. To address these problems, we propose a third approach in which the tracking and matching are done simultaneously. We are now developing a computer vision system to realize this approach for the analysis of swarming mosquitoes.

Acknowledgments We are most grateful to Dr. L. Keshet, who encouraged us, read the manuscript at various stages, and provided invaluable comments. We thank Dr. T. Ikeshoji and Dr. H. Akami, to whom we owe the motivation of this study. We are indebted to Mr. E. Masuda and other staff of the Nikon service center for technical advice and to Dr. A. Matsuzaki and the staff of the Tanashi Experimental Farm for allowing us to conduct experiments on site and for their help and kind interest. Finally, we express special thanks to the late Dr. A. Okubo for helpful discussions.

Part two Analysis

Quantitative analysis of animal movements in congregations PETER TURCHIN

7.1 Introduction Most animals spend part or all of their life in groups (Pulliam and Caraco 1984). Gregarious behavior can strongly affect individual fitness, as well as spatiotemporal dynamics of populations (Allee 1931; Hamilton 1971; Thornhill & Alcock 1983; Taylor 1986; Part IV of this book). Quantitative analyses of gregarious movement behaviors, however, are rare (Turchin 1989a). In population ecology, for example, most theoretical analyses assume a contagious, or clumped distribution of organisms (often summarized by a single number, e.g. the variance to mean ratio), without attempting to examine behavioral mechanisms by which organisms clump together. This bias is partly due to the intrinsic difficulty of studying movement, and partly to our limited understanding of how individuals interact within aggregations. It is often difficult to collect data on the spacing and movements of individuals in aggregations, especially in large three-dimensional aggregations such as bird flocks, fish schools, and insect swarms. Recent advances in instrumentation (reviewed in Part I) are beginning to address this problem. However, even when data are available, innovative methods of analysis are needed to test hypotheses about how aggregations are formed, and to build dynamical models of aggregation structure. Movement by organisms is most generally defined as a change in an organism's spatial position over time. Thus, by its nature, the process of movement involves two scales - a temporal and a spatial. Because the description of spatial position typically involves two or three coordinates, a description and an analysis of movement has to be multidimensional (3-D for most terrestrial organisms, and 4-D for aquatic, aerial, arboreal, etc., organisms). A primary conceptual difficulty of analyzing animal movement, thus, is the necessity of dealing with multidimensional data and models. This difficulty caused most population ecol-

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ogists to avoid studying movement, concentrating instead on one-dimensional processes of birth, death, and population interactions that can be studied at a point in space, or integrated over a spatial area. To give an example of this avoidance reaction, the "ecologist's bible" (Southwood 1978) devotes only 15 pages out of more than 500 to methods for quantifying movement. Active aggregation (using the definition of Parrish, Hamner, & Prewitt, Ch. 1) is any movement process that results in a nonuniform spatial distribution of organisms. It could result from organisms responding to a wide variety of stimuli, including avoidance of inimical physical conditions and attraction to patchily distributed resources (food, mates, shelter, etc.). The analysis of aggregation presents even greater difficulties than other kinds of movement, because it involves spatially varying movement rates. Yet, until quite recently, the overwhelming majority of quantitative studies of ecological movement employed models with spatially invariant coefficients, such as the simple diffusion (Turchin 1989b). A subset of active aggregation is what I have termed congregation (Turchin 1997): aggregation as a result of behavioral responses of organisms to conspecifics (congregate is to gather together, as opposed to aggregate, which is to gather at some locality). Congregating organisms may respond directly to neighbors or to defined groups of conspecifics using visual and acoustic stimuli, or indirectly to cues such as pheromones and to population density cues, e.g. feeding damage on a host plant. Modeling and analyzing congregation presents even greater conceptual difficulties than aggregation or movement in general. This is because congregation involves a positive feedback between movements of two neighbors, or between individual movement and population density. Eulerian models of congregation can be formulated as nonlinear diffusion problems which pose a number of mathematical challenges (Turchin 1989a; Lewis 1994). Lagrangian models of individual behavior with congregation quickly lead to highly instable, chaotic kinematics. The preceding paragraphs with their litany of difficulties may give the reader an impression that the quantitative analysis of congregation is so difficult that it is practically impossible. This is not, however, the message that I intend to convey. Rather, I would argue that we need a clear understanding of difficulties involved, so that we can design analytical approaches to this difficult, but ultimately tractable and potentially very rewarding problem. In this introductory chapter, I will briefly review various approaches that have been developed for studying congregation. I begin with two broad groups of methods that attempt to reduce the dimensionality of the problem, by concentrating either on the spatial or on the temporal aspect of it, and then turn to full spatiotemporal methodologies.

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7.2 Analysis of static spatial patterns Analysis of spatial patterns has received a lot of attention from plant ecologists, because the majority of plants do not move (or rather, only pollen and seeds can move). Although most animals are not sedentary, their spatial distribution at any given point in time can also be quantified by similar methods. A number of quantitative measures of the degree of clumping or clustering have been developed (for a review see Pielou 1977). If organisms are distributed in discrete units of habitat patches, such as herbivorous insects feeding on host plants, then their statistical distribution can be characterized by such statistics as the variance/ mean ratio, the negative binomial parameter, Lloyd's indices of mean crowding and patchiness, and so on (see Pielou 1977). Organisms distributed in a continuous space can be sampled by means of imposing an arbitrary spatial discretization, e.g. by placing quadrats and counting the number of individuals in them. The same aggregation indices as mentioned above can be then applied to such counts. Although calculating various aggregation indices is straightforward, interpreting them is not. The size of sampling quadrats will often have a great influence on the numerical value of an aggregation index. Changes in mean density between two samples are typically confounded with changes in aggregation as measured by an index. By focusing only on the number (or density) of organisms in a discrete unit of habitat or in a quadrat, an aggregation index ignores potential spatial autocorrelation with neighboring units (quadrats). Thus, aggregation indices ignore not only the temporal component in the data, but also most of the spatial one! As a result, while many papers reporting aggregation indices have been published, little insight has been gained into the dynamical process of aggregation. My subjective impression is that the number of papers reporting an aggregation index for spatial data has declined over the last decade, which hopefully reflects a shift to more sophisticated methods of spatial analysis. Analysis of nearest-neighbor distances (NND) has a greater potential for yielding insights into potential causes of aggregation or, at least, for testing specific hypotheses. For example, Kennedy and Crawley (1967) used an NND analysis to demonstrate what they called a "spaced-out gregariousness" in a sycamore aphid: there is a minimum separation between aphids that is maintained by their habit of vigorous kicking at too close neighbors, and at the same time these aphids form recognizable congregations. Another example of NND analysis is found in Parrish and Turchin (Ch. 9). More generally, spatial positions of individuals within congregations may be modeled as a spatial point process (Diggle 1983). Andersen (1992) provides a recent example of an ecological application of this methodology.

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An alternative to analyzing animal positions in space is to "smear" individuals, and analyze their spatial density distribution. Traditional methods for analyzing variation in spatial density are spatial autocorrelation (Sokal & Oden 1978) and spectral (Platt & Denman 1975) analyses. As a result of an increased current interest in landscape ecology and in analysis of large-scale spatial patterns, ecologists have become interested in adapting geostatistics methodology to their problems. For an overview of statistical methods in landscape ecology see Turner etal. (1991). Although we have apparently progressed beyond aggregation indices in the field of statistical spatial ecology, much work still remains. We still do not know how to make inferences about potential mechanisms that have produced the observed spatial pattern from a description of the pattern itself (Levin 1992). Moreover, methods that focus exclusively on the spatial pattern ignore the dynamical features of the pattern evolution. By throwing out a large component (the temporal dimension) of data, we decrease the statistical power of our methodology to distinguish between rival mechanistic hypotheses.

7.3 Group dynamics While the methods briefly reviewed above focus exclusively on the spatial dimension of the data, an opposite approach is to focus exclusively on the temporal dynamics of congregations, or groups. The dynamical variable of interest is the group size. For example, Cohen (1971) developed models for a stochastic growth/decline of "casual groups," which continuously lose some individuals, while being joined by others. Many such models are reviewed by Okubo (1986:43-54). Okubo (1986) gives a number of applications of these models to data by comparing the observed and predicted frequency distributions of group sizes, including zooplankton patches, fish schools, and mammalian herds. Of particular interest is his fitting of a dynamical model of bark beetle congregation to the field data on the cumulative number of bark beetles attracted to a massattacked host tree (Okubo 1986:64-66).

7.4 Spatiotemporal analysis The most conceptually difficult, but potentially most rewarding are multidimensional (spatiotemporal) analytical techniques. These techniques can be classified into two broad groups. The Lagrangian approach is centered on the individual. Individual movement is characterized by a position, a velocity, and an acceleration (the latter includes turning). The velocity and acceleration can be influenced by spatial coordinates of the organism (environmental influences). By contrast, the Eulerian approach is centered on a point in space. The spatial point is char-

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acterized by densities and population fluxes of moving organisms. These two approaches are reflected in models used to represent animal movements: random walks and individual-based simulations (Lagrangian) or diffusion models (Eulerian). Which of the approaches is used will be determined in part by the types of questions one wants to ask of the system, and partly by the kinds of data one can collect. Following individuals through space and time can provide very detailed information about movement, and is the preferred approach where it is possible (Turchin et al. 1991; Turchin 1997). Detailed understanding of individual movements can be translated into an understanding of population redistribution (e.g. Patlak 1953; Othmer et al. 1988; Turchin 1989b, 1991, 1997; Grunbaum 1994), but the converse is generally not possible. Most Lagrangian approaches, especially in the terrestrial systems, have employed a random walk framework. In this framework, paths of organisms are broken into a series of discrete "moves," which are characterized by one temporal coordinate, move duration, and two (three if movement is in 3-D space) spatial coordinates, move length, and direction (or, sometimes, turning angle). The random walk framework with various elaborations, e.g. correlated random walk, has proved to be a very fruitful approach to modeling and analyzing animal movements, including a number of applications to congregation (e.g., Alt 1980; Turchin 1989a; Lewis 1994; Grunbaum Ch. 17). The random walk framework is especially appropriate to analyzing movements of organisms that make periodic stops, such as a butterfly that moves from one host plant to the next (Kareiva & Shigesada 1983). Animals that move continuously present a difficulty. While their paths can be broken into arbitrary moves at some regular time intervals (Kareiva & Shigesada 1983), this leads to certain problems at the analysis stage (see Turchin et al. 1991). Perhaps a more natural way of modeling continuously moving organisms is based on breaking animal movement into a series of discrete accelerations, rather than discrete moves. This kinematic approach has been used by Okubo and Chiang (1974), Okubo et al. (1977), and will be more fully discussed in Parrish and Turchin (Ch. 9). In recent years a novel approach based on calculating fractal dimensions of observed trajectories has become popular. An example of application of this approach to data on copepod swarming will be discussed by Yen and Bundock (Ch. 10). The estimated fractal dimension of a pathway can be used as a measure of trajectory complexity: "sinuosity" or "tortuosity." In addition to using it as a phenomenological measure of trajectory complexity, some authors have proposed that the fractal dimension can be used to extrapolate movement patterns of organisms across spatial scales (e.g. Wiens et al. 1995). This latter approach may not be valid, since a strict self-similarity is a necessary condition for such an

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extrapolation, yet self-similarity is rarely tested for in fractal analyses of individual paths (Turchin 1996). While individual-based Lagrangian approaches are more mechanistic and provide more detailed information about movement, it is not always possible to follow individuals, because they could be too minute, move too fast, or enter regions inaccessible to human observers or opaque to their recording equipment. In addition, studies based on following individuals are typically limited in spatial extent, temporal duration, and the number of organisms for which trajectories can be obtained. When for some reason it is impractical to follow individuals, one has to resort to observing spatial and temporal changes in their population density. The Eulerian approach, however, should not be considered a poor cousin of the Lagrangian one. It is perfectly adequate, and may even be preferable, in situations where one aims to understand and quantify populationlevel redistribution processes and their consequences for population dynamics and species interactions. Most typically the data for an Eulerian investigation of movement is obtained by some variation of mass-marking and recapturing organisms. The essential purpose is to quantify the temporal change in the spatial distribution of population density. At the analysis stage, the data are fitted to a variety of models, most frequently formulated as partial differential equations, although other mathematical frameworks can also be used (e.g. making either space, time, or both discrete variables). Good references to diffusion models and their uses in modeling and analyzing population redistribution can be found in books by Okubo (1980), Edelstein-Keshet (1988), and Turchin (1997). Although Eulerian models are typically fitted to spatial distribution of organism density or numbers, sometimes we have more information which can be used in sharpening the analysis insights. For example, in Chapter 8 Simmons and I analyze both the spatial densities and population fluxes of swarming bark beetles.

7.5 Conclusion My main exhortation here is that we should not limit ourselves to analyzing only one aspect of the data. In the past, too many analyses focused exclusively on static spatial patterns and ignored the temporal or dynamic component. Full spatiotemporal analysis is conceptually difficult. Construction of explicit models, or better, a set of rival models, to guide the analysis is usually unavoidable. Yet the dramatic increases in computer power and in the quantity and quality of data that we can now collect leave us no excuses for employing outdated, limited techniques of analysis.

8 Movements of animals in congregations: An Eulerian analysis of bark beetle swarming PETER TURCHIN AND GREGORY SIMMONS

8.1 Introduction The mechanisms determining three-dimensional dynamics in animal congregations are behavioral, and thus it is appropriate that the approaches covered in this book are focused primarily on individuals. This chapter breaks out of this mold, because we use a population-level, Eulerian approach (see Ch. 7 by Turchin). A focus on populations, rather than individuals, was forced upon us by the characteristics of our empirical system - the congregation of southern pine beetles around mass-attacked host trees. In fact, in our first (unsuccessful) attempts at quantifying beetle movements in the vicinity of attractive foci, we tried to use an individual-based approach. However, we were not able to consistently follow flying beetles. A certain proportion of beetles flew upwards, out of sight. Even when they remained low, beetles were easily lost against the forest background because they are very small (about 3 mm in length), are dark colored, and fly fast, following erratic paths. In our second approach, we shifted our focus from the behavior of individuals to the dynamics of groups. Because the Eulerian approach does not keep track of individuals, one cannot directly measure parameters of individual behavior. However, by using behavioral observations and making certain assumptions, we can construct a model of population redistribution, which in turn can be used to interpret population-level data, as well as to make inferences about individual behavior. In this chapter we describe an example of how an Eulerian approach can be usefully employed for measuring certain quantitative features of congregating behavior, in particular, the attractive bias exhibited by flying beetles toward the source of congregation pheromones. The organization of this chapter is as follows. We begin by giving a brief description of the biological features of the empirical system. Next, we develop a simple model relating individual parameters of beetle behavior to their popula-

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tion-level characteristics - beetle densities and fluxes. In the section after that we describe the specific methods we used to measure fluxes of beetle density at various spatial points, which allowed us to estimate the attractive bias. We conclude with some final remarks on using an Eulerian approach in the analysis of movement behavior.

8.2 Congregation and mass attack in the southern pine beetle The southern pine beetle, Dendroctonus frontalis, is a native predator of pines in the southern United States. It is an aggressive bark beetle, that is, it generally needs to kill a host tree in order to complete development in it. Pines, however, possess defenses against bark beetle attack - the oleoresin system (Lorio 1986). An attack by a single female (the pioneering sex in this beetle) or by a small group of females is unlikely to succeed on a healthy pine, because resin flow from wounds will prevent beetles from penetrating inside the tree bark and excavating galleries in the inner bark for egg laying. In response, the southern pine beetle has evolved a remarkable strategy to overcome tree defenses. As pioneering beetles bore into the tree bark, they begin emitting a mix of volatile compounds, of which the most important is frontalin (Payne 1980). The mixture of beetle-produced and host volatiles attracts other beetles. A positive feedback loop is established: As more beetles (primarily females) bore into the tree, they release more pheromone, attracting additional beetles. As beetles congregate on the tree, they literally drain it of its resin resources, nullifying the tree's ability to defend itself (Hodges et al. 1979). It may take 2000-4000 beetles to overcome defenses of a healthy pine tree (Goyer & Hayes 1991). This phenomenon is known as mass attack. As the mass attack progresses, and the larval resource - inner bark of the tree - starts to fill up, beetles (primarily males) begin releasing repelling pheromone, which eventually inhibits congregation at the tree (Payne 1980). Although the southern pine beetle is the most serious insect pest of the southern pines, quantitative information on its dispersal and congregation is lacking. Over the past few years one of us (Turchin) has been involved in research aimed at constructing a model for understanding and predicting spatial population dynamics of this beetle (see Turchin & Thoeny 1993). Because mass attack of host trees plays such an important role in the beetle's biology, it is clear that quantitative understanding and measurement of southern pine beetle congregation is critical for our ability to predict its spatial dynamics. These considerations motivated a field study of beetle attraction to mass-attacked trees that was conducted in Summer-Fall 1991 (full details of this study will be reported elsewhere).

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The basic premise of the study was that beetles flying in the vicinity of a massattacked tree use chemical (pheromones and host volatiles) and visual (vertical shape of tree bole) cues to bias their movements toward the tree (Gara & Coster 1968). This bias results in congregation, which in turn fuels mass attack. The attractive bias is assumed to be a function of the distance and direction from the tree to the flying beetle. This bias is modified by the total number of beetles already boring into the tree. At the beginning of mass attack, the strength of the bias should increase with the number of attacking beetles, since more beetles are congregating on the tree, releasing more frontalin. As the tree begins to fill up, the bias should decrease in strength, possibly even becoming negative (repulsion).

8.3 An approximate relationship between attractive bias and flux Consider movement of a beetle in the vicinity of a congregation focus, a massattacked tree. Behavioral observations suggest that the spatial scale of movement A (the spatial step or the mean free path) is about 1 m. We will model the movement process of beetles as a random walk occurring within a threedimensional lattice of 1 m3 cells, biased toward the attraction focus. At any given point in time, the magnitude of the bias is a function of direction and distance from the focus, that is, there is an "attraction field" centered on, but not necessarily symmetrical around, the focus. The attraction field will change with time as a result of shifts in the wind direction and the number of beetles already attacking the focal tree (there are many other factors that could potentially influence the attractive field, but we will ignore them in order to keep the model simple). Without loss of generality, let us orient the x-axis so that it would pass through the current position of a beetle and the attraction focus. Let R be the probability per unit of time that the beetle will hop one cell toward the attractive focus (say, to the right), and L the probability of moving one step away from the focus (e.g. to the left). Let the sum of these two probabilities be the motility: fi = R + L. Thus, 1 — IJL is the probability that no displacement with respect to focus will occur during the time interval (either the organism did not leave the 1-m cube, or it moved laterally with respect to the focus). We define the attractive bias (/3) as the difference between the probabilities of going toward focus versus going away, given that some displacement with respect to focus has occurred: /3 = (R - L) ix. The attractive bias can vary from 1 (perfect attraction) to - 1 (perfect repulsion), and j3 = 0 implies random movement with respect to the attractive focus. Our goal is to translate the random-walk parameters, in particular the attractive bias, into quantities that can be measured at the population level with exper-

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iments using groups of beetles, rather than individuals. A continuum model such as the diffusion equation may help us to interpret population-level data. We know that a biased random walk can be approximated with a diffusion equation (Okubo 1980; Turchin 1989b). If u — u (x,t) is defined as the density of swarming beetles at position x at time t, then it obeys the following partial differential equation: du

A2 d2

Ad

(8.1)

This equation can be rewritten in terms of the flux (/). Flux with respect to the attractive focus at point x: J , is the difference between the number of organisms passing through a unit (1 m2) surface at x going toward the attractive focus, and the number going in the opposite direction, per unit of time (Fig. 8.1). The diffusion equation in terms of flux is: - = - - / , dt

dx

(8-2)

x

Thus, the flux Jx is related to the behavioral parameters m and b as follows: (8.3)

*X ATTRACTIVE FOCUS

Figure 8.1. Flux in relation to the attractive focus, Jx, is defined as the net flow of beetles through a i m 2 surface toward the focus.

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The flux has two components. The first term on the right side is the directional component: It is the product of the local density of swarming insects, u, and the difference in the probability of going toward versus away from the attractive source (yu,j8). The second term on the right side is the random component of flux. It indicates that as a result of random movements, net flow of organisms will be down the population density gradient. Because the density of organisms tends to increase toward the center of the swarm, the random component of flux will work against the directed component. Equation (8.3) suggests that we may be able to estimate the attractive component of flux, and thus /3, by subtracting the random component of flux from the total flux. Let us return to the random-walk formulation and derive an explicit relationship between the attractive bias /3 and the quantities that we can observe experimentally. Suppose we put a sticky screen at the boundary between two neighboring cells, with one side facing the attractive focus, and the other side facing the opposite way (Fig. 8.1). Beetles attempting to move from the cell on the left to the cell on the right will hit the screen and stick to its side facing away from the focus (Fig. 8.1). The rate (numbers per unit time) at which beetles hit the screen on its away-facing side, Jx, is the product of the density of beetles in the cell on the left multiplied by the probability of each beetle moving right per unit time: x

= ux - \,t Rx -

\,t

(8.4)

Similarly, we can write that the rate at which beetles hit the screen side facing toward the focus is j ; = ux + \,t

Lx + {,t

(8 5)

Expanding these relationships in a Taylor series, we obtain J+ = ux-\,t

Rx-{,t

= uR

(uR) + • • •

(8.6)

2 dx Jx =ux

+ \,t

Lx + [,t

=uL + - — I ox

The difference between these two rates is the flux, which is approximately

j, = J; - ,;

**-U-~

K* + «] - ft- - ~

0»>

(8 . 8)

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Note that this expression is simply equation (8.3) where all quantities have been expressed in units of A and T. Let us now consider the total number of beetles hitting both sides of the screen. Like Jx, Sx is affected by the population density gradient. However, random-walk simulations indicated that the magnitude of this effect is slight, and in order to simplify the relationships we have chosen to ignore it. Thus, very approximately Sx = /+ + J~

u(R + L) = IJLU

(8.9)

Both Jx and Sx are instantaneous rates of flows through a unit area, while the data are collected at discrete time intervals, in this case once a day (see next section). Thus, the observed numbers (numbers captured on a sticky screen during T = 24 hr) are actually time integrals of / and 5^: T

jx =

Jxdt

(8.10)

o T

sx=

Sxdt

(8.11)

o T

Integrating both sides of equation (8.8), substituting sx in place of /xudt, and solving for /3 we obtain °

p = L + LW^iA sx

2

(812)

dx

We have assumed that (3 changes slowly compared to T, and that this change can be neglected (this is not a bad assumption since T equals one day, while complete course of mass attack took several weeks to develop). Note that a naive estimator of the bias jS would bejx/sx: the difference between numbers of beetles crossing a unit area toward versus away from the focus, scaled by the total number of beetles crossing in any direction. Although this quantity resembles the definition of /3, it would yield a biased estimate, because of a net flow of beetles down the gradient of population density, resulting from the random component in their movements. The second term on the right side of equation (8.12) corrects for this flux component.

8.4 Field procedure A loblolly pine (Pinus taeda) was selected as the focal tree for mass attack. At each of 6 distances from the focal tree (1.5, 4, 7.5, 12.5, 20, and 30 m) in each of

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the four cardinal directions we placed a 1-m 1-m hardware cloth screen. These screens were placed at 5 m above the ground (we have also placed screens at other heights, but here we will concentrate on the data from the 5-m screens). The screens were made sticky by spreading tanglefoot (viscous semiliquid material used to capture insects or protect trees from pests) on them, and then spraying the tanglefoot with a pesticide (otherwise, beetles were able to walk off the screens). The attack was initiated by baiting the focal tree with the synthetic pheromone frontalin, as well as turpentine to simulate host volatiles. As soon as mass attack was underway, the artificial volatiles were removed, allowing the attack to proceed naturally. The course of mass attack on the focal tree was monitored by smoothing with a drawing knife 16 square areas of bark (each 1 dm2 in area) and counting entrance holes of boring beetles in each area every day. The smoothed areas were located in pairs (on East and West sides of the trunk), with a pair at 2, 3, 4 , . . ., 9 m above the ground. Throughout the course of mass attack, all beetles captured on sticky screens were counted and removed once per day. We recorded how many beetles were caught on each side of the sticky screen (facing toward and away from the focal tree). The data reported here are based on three focal trees that were studied in August-October 1991. The course of mass attack was relatively slow during this period, varying from two to four weeks between different replicates.

8.5 Results A typical example of data is shown in Figure 8.2. Numbers are summed over a period of four days, because this provides a less noisy picture of the population fluxes around the attack focus (but still constitutes a short segment of the course of mass attack, so that the strength of attraction did not change very much). The width of the boxes indicates the magnitude of flows towards (filled)/away (open) from the focal tree. Figure 8.2 illustrates two features of the beetle swarm around the attacked tree. First, the population density of flying beetles, as indicated by the total number of beetles captured on both sides of the sticky panel (sx), increases drastically near the focal tree (Fig. 8.3). Distance from the attractive focus (x) explained 70% of variance in total captures, as indicated by a linear regression of ln(sx + 1) on In x. This result is not surprising, since congregation should result in population concentration around attractive foci. A more striking feature of the data is that the relative flux jx/sx exhibits a nonlinear relationship with the distance to the attractive focus: jx/sx is low close to the tree or far away from the tree, and highest at intermediate distances

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1

X

wind

ll

fl f

Figure 8.2. The spatial structure of the beetle swarm around replicate tree 4 during the period of 29 Sept.-2 Oct. 1991. X indicates the focus of congregation (a mass-attacked pine tree). Filled boxes indicate travel toward the focus. Open boxes indicate travel away from the focus. Boxes show how many beetles hit the 1-m2 sticky screen going toward/away from the tree. The width of the box indicates the actual number of beetles captured.

(Fig. 8.4a). This raises the following question: is the decrease in relative flux near the focus a result of decreased attraction there, or is it due to undirected flow of beetles down the population density gradient? We can answer this question by estimating the attractive bias and plotting it as a function of distance to the focus. The attractive bias was estimated from the data using the equation (8.12), assuming a linear relationship between sx and In x. If a and b are the regression intercept and the slope respectively, then the equation (8.12) becomes (8.13)

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5 10 15 20 25 30 DISTANCE, m Figure 8.3. Average population densities, as measured by s^ the sum of beetles captured on both sides of each screen, as a function of distance to the focus tree. Attack stages: early, middle, and late correspond to the time periods during which 0-25%, 25-75%, and 75-100% of attacks occurred.

Peter Turchin and Gregory Simmons

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DISTANCE FROM FOCUS, m -1J Figure 8.4. Comparison between a) the relative flux, jjsx, (averaged over all replicates) (b)functions of distance from the focus. to b) the estimated attractive bias, j3{x); both (the intercept a reflects the average density of swarming beetles, and does not affect the estimate of /3). The basic data unit for estimating attractive bias was the number of beetles collected at a given trap during a given interval of time. The difference between the number of beetles caught on either side of the trap is j i k t , where i and k code, respectively, for the distance and direction from the focus to the trap, and t indexes time period. Analogously, sjkt is the total number of beetles caught on both sides of the trap. Capturing no beetles at a trap provides no indications about the bias at this point and time. Thus, traps with sikt - 0 were dropped out of the data set. To obtain an estimate of the slope, we regressed In s!kt on In x while keeping k and t constant. The slope estimate bkt was thus different for each combination of direction and time period, because the relationship

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between s and x varied from day to day (as attack progressed, the population density gradient got steeper), and also depended on the direction from the focal tree and current wind direction. In formal terms, an estimate of the attractive bias for each trap which caught beetles during each time period was (8.14) s

i ikt

Plotting average attractive bias against distance from the focus (Fig. 8.4b), we see that, unlike relative flux (Fig. 8.4a), attractive bias does not decrease in magnitude near the attractive focus. This observation suggests that low relative flux near the tree does not reflect low attractive bias at these distances, but instead is due to an increased influence of the undirected flux component. The density gradient of flying beetles, and thus the magnitude of the undirected component, is steepest near the tree (see Fig. 8.3). Sometimes, the undirected component can even overpower the attractive bias. For example, the 1.5-m traps situated upwind of the focus tended to exhibit inverse (outward) fluxes of beetles (e.g. the nearest trap to the NE of the focus in Fig. 8.2). To investigate the factors influencing attractive bias, we performed multiple regressions of )3.fa on the distance from the focus to the trap, x., the cosine of the angle between the wind direction and the direction from the focus to the trap, ckl, and the number of attacking beetles per unit area of bark on the focal tree, At. We tested the linear effects of these three independent variables, the quadratic terms, and all pairwise interaction terms. Both xi and xf terms were significant (F, 364 = 10.96, p < 0.001; and F, 363 = 8.64, p < 0.005), suggesting that the relationship between the attractive bias and distance from the attractive focus is nonlinear (this conclusion is confirmed by Fig. 8.4b). Interestingly, the relationship between the attractive bias and At was highly nonlinear: Neither At nor A2t terms were significant by themselves, but they were significant when included into the model jointly (F 2361 = 3.78,/? < 0.025). Wind direction was also influential: Including the three terms, Ckl,Cjt and the interaction term CktAt doubled the percent of variance explained by regression and was highly significant (F 3241 = 4.57, p < 0.005). As expected, attractive bias toward the attacked tree was stronger in the downwind, compared to the upwind, direction. The other two interaction terms did not significantly better the regression. The coefficient of determination (R2) of the model that included all significant terms was low at 0.13. This is not surprising, however, since many traps captured just a few or even one beetle. Thus, the estimate of the relative flux for a trap that captured only one beetle is either 1 or - 1 , which introduces a lot of variability in the /3 estimates.

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8.6 Conclusion The analysis of this data set indicates that the flux approach can provide more information about the behavior of congregating organisms than an approach based on measuring population density near an attractive focus. Measuring population density indicated only that beetles were swarming densely around the attractive focus, suggesting that there was an active congregation at the attacked pine tree. Analysis of population fluxes, on the other hand, provided more details about the southern pine beetle congregation. Most importantly, beetles were actively biasing their movements toward the attacked trees, as indicated by positive /3 at distances of up to 12.5 m. However, there was also a significant undirected (random) element in beetle movement, as evidenced by negative fluxes (away from the focus) just upwind of the tree where the population density gradient was very steep but the attractive bias was weak. The significant effect of wind direction on congregative bias supports the hypothesis that congregation is, at least partly, mediated by airborne chemicals such as congregating pheromones and plant volatiles. The number of beetles attacking the focal tree had a highly nonlinear effect on the attractiveness of the tree to beetles. During the early stages of attack, beetles were drawn to the tree from distances of up to 7.5 m (Fig. 8.5 - early), and the average attractive bias at these distances was about 0.45. During the middle stages of attack the spatial extent of the attractive field increased to at least 12.5 m (Fig. 8.5 - middle), and the average attraction went up to 0.53. Such an increased attraction was most probably due to greater numbers of beetles boring into the tree, whose activity elevated concentration of the congregative pheromone. However, during the late stage of attack, when the tree began to fill up, the average attractive bias decreased to 0.41 (Fig. 8.5 -late), probably as a result of elevated concentration of repelling volatiles.

8.6.1 General implications for individual-based versus population-based approaches The Lagrangian and Eulerian points of view are distinct but related approaches to studying movements of congregating animals. The Lagrangian approach has an a priori advantage, since the complete knowledge of individual behaviors, in principle, allows one to deduce all the population-level patterns. However, by making assumptions and building models one can also deduce individual-based parameters from population data, as this chapter demonstrated. Moreover, the Lagrangian approach will sometimes be an overkill in ecological applications. When all we need to know is the influence of movement on spatial population

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dynamics of organisms, it is an easier and a more direct approach to simply measure the population redistribution parameters, rather than first quantify individual movements and then make an extra step of translating these data into population-level quantities. To summarize, the choice of an approach will depend on many factors, e.g. what kinds of questions are of importance, what kinds of data we can collect. Sometimes, the most powerful approach is to collect the data at both levels (e.g., Turchin 1991).

Individual decisions, traffic rules, and emergent pattern in schooling fish JULIA K. PARRISH AND PETER TURCHIN

9.1 Introduction Schools of fish are one of the most studied and best known of all animal congregations (see Pitcher & Parrish 1993). Over 25% of the world's fish school throughout their lives, and over 50% school as juveniles (Shaw 1978). Behavioral and evolutionary studies of schooling fish have indicated that group membership is more advantageous than a solitary existence. Group members may incur a lower risk of predation (Turner & Pitcher 1986; Magurran 1990; Romey Ch. 12), have greater access to food resources (Street & Hart 1985; Ryer & Olla 1992), and expend less energy swimming (Zuyev & Belyayev 1970; Weihs 1973, 1975). Regardless of the reason, most studies assume that membership in a stable congregation is beneficial to the individual. This positive cost to benefit ratio is then used as an argument for both the evolution (Hamilton 1971; Mangel 1990) and maintenance (Parrish 1992) of aggregative behavior in fish. However, as with the study of congregation in general, mechanistic approaches to the study of fish schooling have lagged behind functional approaches. While we may have a good idea why fish congregate, we know relatively little about how fish congregate, let alone form polarized schools of synchronously responding individuals. Traditionally, schools have been defined by a polarized orientation of the individuals, regardless of whether the school itself is moving or stationary (see Pitcher & Parrish 1993). Thus it is easy to imagine a congregation of fish slipping into, and out of, a schooling configuration, while still maintaining the same group boundaries, volume, shape, and even relative position of the individual members. For instance, a school will often form when the group moves from one location to another; however, should a patch of food be encountered, the polarized configuration may break down as each individual begins to feed independently. Therefore, while the literature often refers to schooling species, this does

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not necessarily imply that these fish are constantly confined to a polarized configuration, but rather have the ability to adopt such an orientation should the circumstances warrant it. Attempts to find structure within animal aggregations have often used a static, time-independent approach (but see Okubo 1986), such as the analysis of the distribution of nearest-neighbor distances from a set of still images, irrespective of how identified individuals are moving within the group (Partridge 1980; Campbell 1990). At its extreme, this approach becomes a search for defined structure (e.g. Symons 1971a, b; Partridge et al. 1983), or even a theoretical attempt to constrain school structure to rigidly predefined arrangements (e.g. the crystalline-lattice structure - Breder 1976). Yet animal aggregations are dynamic entities where individual elements within the group are constantly moving with respect to each other. One of the most striking examples of this fluidity are fish schools, which can continuously change volume, shape, density, and direction, yet maintain a coherent, even patterned, structure to the human eye. The apparent visual simplicity of a fish school or a bird flock is belied by the fact that individuals can constantly re-assort without loss of group-level structure. Mechanistically, the group-level properties, such as the discreteness of boundaries and the apparent ability of the group to respond as a unit, are a result of a set of decisions made by each individual about where to go and where to stay (see also Potts 1984; Adler & Gordon 1992; Pitcher & Parrish 1993). In general, movement decisions of an individual group member can be viewed as a balance of forces (Okubo 1980), in particular a set of attractions to, and repulsions from, various sources or foci (for specific applications see Mullen 1989; Heppner & Grenander 1990). The important biological question then becomes: what are the foci of attraction and repulsion from the point of view of an individual group member? Individuals may be attracted to "external" sources, such as concentrations of prey (beetles - Turchin & Simmons Ch. 8; fish - Mullen 1989), or "internal" sources, namely each other (Warburton & Lazarus 1991). Once the sources are identified, the next question is whether the strength of these forces can maintain the congregation (not all kinds of attraction will necessarily lead to congregation formation; see Turchin 1989b). Finally, if attraction sources are stable and the balance of attraction/repulsion leads to group formation and maintenance, can these forces be used to explain the observed structure? Documenting association between individuals in a three-dimensional animal aggregation and a focal point (e.g. aggregation center, specified individual, etc.) requires knowledge of the path taken by identified individuals relative to the path taken by the focus. Therefore, individual positions must be resolved in space (X, Y, Z) and plotted through time to obtain trajectories as well as more

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specific information about the component of movement (both direction and acceleration) relative to the focus. Once relative movement with respect to the focus has been assessed for all individuals in the group, commonalities in movement pattern, perhaps resulting in group-level architecture, should emerge. Relatively few studies have examined how individuals within a school of fish interact, and how these interactions sum to produce the school as we know it. Aoki (1984) recorded the spatial positions of identified individuals, but limited the school to eight fish, constrained to a planar configuration. Knowledge of individual-based interactions has been technologically hard to obtain, because it requires four-dimensional spatiotemporal information on all individuals (three dimensions for position, and one dimension for time). Thus, many studies collect a series of three-dimensional static images, which lack the temporal component or the reference to identified individuals or both (Graves 1977; Partridge et al. 1980; Koltes 1984). Such studies, therefore, cannot provide direct answers to the questions we have raised above. Partridge (1981) obtained four-dimensional information on a school of saithe constrained to swim within a lighted area. Although individuals were identified, fish frequently swam into and out of the camera view, such that continuous path records were impossible to calculate. However, recent advances in technology (see Osborn Ch. 3; Jaffe Ch. 2) have allowed for automated collection of four-dimensional data on identified individuals, albeit for short periods of time. The other stumbling block has been a lack of analytical tools with which to properly examine four-dimensional data (see Partridge 1981). There are two major approaches to quantifying movements of organisms. Movement of many individuals past fixed locations can be assessed through time, or identified individuals can be followed. The first approach is useful if the group size and/or spatial dimensions preclude the second approach. Turchin (Ch. 7) explores the uses of both approaches and provides an example of the former. Our analysis of fish schools adopts the latter method, based on the point of view centered on the moving individual. Individual movement is characterized by velocity and acceleration, which can be influenced by the position of the organism relative to other objects in its environment. The magnitude and the direction of acceleration can be used to formulate hypotheses about cues that individuals use to stay within the group. In this chapter we demonstrate how the individually based approach can be used to identify potential focal points of attraction/repulsion with a data set on the positions of all individuals within congregations of fish, as they move through three-dimensional space and time. Once biologically relevant foci have been identified, our goal is a quantitative description of the rules of individual movement based on the balance of attractive and repulsive forces. Furthermore,

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we interpret these rules in the context of functional considerations, that is, the selective advantages which may govern the maintenance and evolution of individual movement decisions (see Warburton Ch. 20).

9.2 Experimental setup: Data collection Juvenile blacksmith, Chromis punctipinnis, are temperate, nearshore, upperwatercolumn planktivores, feeding in loose, nonpolarized groups of tens to hundreds of fish. When threatened by predators, either aquatic or aerial, the group coalesces into a tight, polarized school which quickly moves away from the oncoming threat, usually into nearby kelp or rock-reef. Thus, while not an obligatory schooling species, these fish are obviously gregarious at all times and are capable of assuming a packed, ordered arrangement on occasion. Observations of fish behaviors took place at the Catalina Marine Science Center on Catalina Island, California during 1989. A captive population was obtained by netting fish near the laboratory dock. The experimental setup consisted of a still-water Plexiglas tank (1 m3), placed in the middle of a white, featureless room. Thus, fish in the tank had no moving objects to react to (apart from each other). Three SVHS video cameras were placed 7.8 m from the center point of the tank, along each of three orthogonal axes. Thus, the camera views overlapped in all dimensions twice (i.e. X, Y; Y, Z; X, Z). The cameras were connected to three Panasonic video tape decks (VCRs) wired to start and stop simultaneously, and recording at 30 frames/sec. As the videos recorded, a timecode stamp was laid down on each video, so that each frame possessed a date and minute:second:frame code. In this way, frames from all cameras could be matched in time. For each experiment, the tank was filled with filtered seawater, and 5, 10, or 15 individuals were chosen from the captive population and placed in the experimental tank for a one-hour acclimatization period. After the initial transfer, the fish were totally secluded, as all subsequent manipulations were remotely controlled from an adjacent room. The VCRs were set to record for half an hour. After the recording session finished, the fish were removed and replaced in the wild, several hundred meters away from the original capture location to minimize the chance of recapture. Altogether, nine replicates of each fish congregation size (5, 10, and 15) were taped. Small segments of each taping were randomly chosen for analysis. Information from these segments was automatically digitized in 10-sec clips (300 frames) by an automatic framegrabber (Motion Analysis VP310) connected to a Sun Microsystems 3/110 workstation. Therefore, for each sequence, 900 frames (i.e. 300 from each of three cameras) were processed to obtain three-dimensional

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information. Details of the digitization and three-dimensional data collection are provided elsewhere (Osborn Ch. 3). Briefly, the timecode stamp on each frame allowed individual frames from each camera to be readily identified. Rather than digitize the entire image, the VP310 records only the position of pixels along lines (edges) of sufficiently high contrast. For example, a dark fish against a light background would be digitized as an outline. Reducing a complex image to a set of perimeters allows for a much larger number of frames to be digitized, at the expense of detailed information about individuals (e.g. fin movement, color pattern, etc.). When all views had been digitized, each clip was trimmed so that the start and stop frame of the sequence were identical among the views. To streamline the computational process, every other frame was deleted from each view, so that the effective recording speed became 15 frames/sec. The three-dimensional coordinates of the centroid of each fish were then calculated by the Motion Analysis EV3D program. Centroids were defined as the average X and Y positions of the set of pixels defining the perimeter of each fish, for each frame. The final centroid position (X, Y, Z) was resolved across the three camera views by matching redundant axes (i.e. X, Y; Y, Z;X,Z). Calculated centroids were within .5 cm of the true center of the fish. Error was a by-product of the fact that fish shape (and thus two-dimensional center point) differed between camera views. Within the EV3D program, all fish were assigned an identifying number (1 through AO at the beginning of each 10-sec clip. The program then kept track of each individual by plotting its trajectory and forecasting the most likely volume within which to search for the next point. Mis-assignments were corrected by the program operator and occurred with regularity only at higher school sizes (i.e. >10 fish). The final data sets contained an X, Y, Z coordinate for each individual fish, located in the approximate center of the fish, for every second frame, over a 10-sec interval, for each school.

9.2.1. Analytical approach Our analytical approach was two pronged. First, we attempted to discover whether the relative positions of fish in a given school were structured to any degree (i.e. nonrandom). We defined the presence of structure by testing the spatial associations between nearest neighbors, as well as between all pairwise combinations of known fish (e.g. fish 1 and fish 5; fish 3 and fish 7, etc.) against an expectation of random positions throughout the tank, as well as against random positions within a smaller volume constrained by the separation between individuals.

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After finding nonrandom associations between fish, we explored the data set for potential attraction/repulsion foci which might lead to the observed structures. The basic premise of this analytical approach was that fish react to changes in the positions of other members of the school by changing either the direction or the speed (or both) of their movement; in other words, they will accelerate. Acceleration is the time derivative, or temporal rate of change in the fish velocity, and the second time derivative of the spatial position, X. Because fish positions were measured at discrete time intervals, we use the discrete version of the second derivative: (9.1) where At is the acceleration at time t, Xt is the spatial position at time t, and T is the time interval between successive observations (Fig. 9.1). Like Xt, At is a three-dimensional vector. The discrete acceleration measured according to the above formula is a finitetime approximation of the instantaneous acceleration. Thus, the time interval T

Figure 9.1. Diagrammatic representation of the component of an individual fish's discrete acceleration, Af projected onto the direction toward the attraction focus. If the proportion is positive, the fish is accelerating toward the focus. A negative value indicates thefishis accelerating away from the focus.

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should not be too long, or the approximation will be too coarse-grained. However, if the time interval is too small, then the opposite problem of redundance is encountered. For example, when a fish perceives that it is too close to a neighbor, it will turn (accelerate) away. If the data are collected too frequently, then the acceleration of the fish will occupy several time frames, and discrete acceleration calculated during consecutive frames will not be independent. Indeed, we observed that there were positive serial correlations between discrete accelerations when calculated at time intervals of 1/15 of a second. In other words, the data set is oversampled, and subsequent data points are somewhat redundant (see also Partridge 1981). To overcome this problem, we increased the time interval until the autocorrelation between successive accelerations disappeared. This occurred at T = 0.2 sec, which we subsequently used in our analyses. We are primarily interested in the behavioral response of the fish to some "congregation focus," which could be a neighbor, a group of neighbors, or the entire school. Accordingly, we started with the simplest subset - an individual's nearest neighbor - and then incremented the subset by adding the next nearest neighbor, and so on, until the focus eventually became synonymous with the entire school. For each subset of neighbors (NN1 through the school), we defined the potential focus as the centroid of all relevant fish positions. Then, for each fish, we calculated the projection of its acceleration vector on the direction toward the potential focus of attraction (Fig. 9.1). If this projection is positive, then the fish is accelerating toward the focus; if negative, then the fish is accelerating away from it. Our analysis focused on this component of acceleration in the direction of a focus. 9.3 Group-level patterns In the absence of any disturbance, juvenile blacksmith explored the limits of the tank, both as singletons and as a group. Individuals frequently left the main congregation, and then later rejoined it. Although undisturbed fish did not display any polarized or otherwise recognizably regular configuration, they did appear to be clumped together nonrandomly. When tested against a random arrangement of positions within the volume of the tank, real fish were significantly more clumped than their random counterparts (Student Mests, P < 0.001 for all school sizes; Fig. 9.2a). However, this comparison is somewhat artificial in that blacksmith were originally chosen because they aggregate. Therefore, the data sets (real and random) were constrained by excluding stragglers, defined as those individuals greater than 18 cm (approximately 3 body lengths) from any other fish. The exclusion of stragglers had several effects: First, sample sizes (the number of nearest-neighbor distances (NND) calculated) were lower in both

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random positions real positions

15 School Size Figure 9.2. The mean and standard deviation of the distance between each fish and its nearest neighbor (nearest-neighbor distance, NND in cm) for randomly derived positions (black) and real fish positions (white). Numbers above each bar are sample sizes (= the number of NNDs calculated per time sequence). Asterisks indicate significant differences. (A) All fish in the tank included. (B) Stragglers, defined as those fish greater than 18 cm (3 body lengths) away from any other fish, eliminated from the data sets.

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data sets, albeit dramatically in the random position data set (Fig. 9.2a, b). Second, with the effect of these stragglers removed, the remaining fish were more closely associated, although the real schools were tighter (Student f-tests, P < 0.001 for 10- and 15-fish school sizes; Fig. 9.2b). There was no apparent difference between random and real schools at the 5-fish school size; however, this is quite probably due to the extremely small sample size of the random school (6 NND < 18 cm out of a possible 240). Finally, fish in real schools appeared to maintain more constancy in their nearest neighbor associations (Fig. 9.2b). If the congregations had been rigid, distances between identified pairs would have varied little, resulting in a small measure of deviation around each mean distance, regardless of its absolute size (i.e. whether the fish pair were nearest neighbors or far apart). Conversely, if the fish had been swimming randomly with respect to each other, any measure of deviation around the mean distance between identified pairs would have been high, because of the total lack of linkage between pairs of fish. We would expect real fish to fall somewhere between these two extremes. Obviously, linkages between fish pairs are not rigid, but perhaps elastic. The degree of elasticity may depend on the species and the situation. Although the blacksmith did remain clumped within the boundaries of the tank, they did not maintain any degree of fixed architecture with respect to each other (Fig. 9.3). The range and the shape of the distribution of these pairwise

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Standard Deviation of Pairwise Distances Between All Individuals (cm) Figure 9.3. Box-and-whisker plots (vertical bar-mean, box - standard deviation, horizontal line - range) of the standard deviations of all paired distances between all identified individuals in all schools of each size (5, 10, and 15) respectively. For example, within a single 10-sec video clip, the distance between fish 1 and fish 2 is recorded for every frame (= 150 frames). Then a mean and standard deviation are calculated for each pair. The range and shape of the distribution indicates something about how much individuals move with respect to each other.

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deviations is large and unimodal, respectively, indicating that these fish varied between the two extremes. While some fish pairs may have remained more or less equidistant (low standard deviation), other fish pairs ranged widely in interfish distance. Therefore, while fish are not randomly distributed about the tank, they are also far from forming any type of rigid association. Constantly changing the distance between individuals is not necessarily synonymous with a total lack of three-dimensional structure. It may simply mean that associations between unique pairs of individuals are constantly forming and breaking as the fish move past each other, regardless of degree of regularity of interfish spacing. Across all school sizes, blacksmith maintained a fairly regular distance between themselves and their nearest neighbors, regardless of the identity of that individual (approximately 11 cm, or 2 body lengths; Fig. 9.4). Thus, in the absence of any external structuring force, such as predation or food, the fish nevertheless appeared to congregate and maintain a set average distance between adjacent individuals, even though the identity of nearest-neighbor pairs was constantly changing.

9.4 Attraction/repulsion structuring Maintenance of the congregation, in the absence of external forcing factors, implies that the sources of attraction/repulsion are the fish themselves. How many of their neighbors do fish pay attention to? Fish could be attracted to all school members equally, or they could respond to some subset of the school. Further-

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more, any particular focus could be either attractive, repulsive, or neutral, depending on the distance separating it from the fish. We explored this issue by examining the influence of a range of foci on fish movement. Foci ranged from an individual's nearest neighbor to the centroid of the school. We regressed the component of each individual's acceleration in the direction of the focus on the distance between the focus and the individual. Distance had to enter the model, because the degree of attraction varies with distance to that focus (see below). This procedure was iterated for all fish in the tank. The influence of the focus on individual movements was quantified by the coefficient of determination of the regression (R2). Our first observation was that the proportion of variance explained by the distance to the focus (for all subsets) was quite low (Fig. 9.5). This means that individual fish move quite freely with respect to their neighbors, rather than having to constantly accelerate to adjust their position with respect to the positions of other school members. Second, and more interestingly, the highest R2 values tended to be on the extremes of the continuum (Fig. 9.5). In other words, indi-

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Figure 9.5. The relationship between the correlation of a fish's acceleration in the direction of the focus and the distance to that focus (R2), and the number of neighbors in the focus. Foci ranged from the next nearest neighbor (NN{), to the next two nearest neighbors (AW, + NN2),. . . , to all neighbors (i.e. the school centroid). A high R2 value would indicate that individual fish movements were highly responsive to movement changes of the focus.

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viduals appear to be paying most attention to their nearest neighbor, as well as to the school as a whole unit. Intermediate numbers of neighbors seem to be less important. In the 10- and 15-fish schools, the relationship reaches a plateau at some large number of neighbors, albeit 3 or 4 fish shy of the entire school. This may be because during all tapings, individuals were constantly leaving the group such that the congregation as a cohesive unit would usually have contained less than the total number of fish in the tank. Thus, perception of the congregation as a focus appeared to exclude straggling individuals. Because the larger-group foci undoubtedly contained stragglers, the calculated centroid was not necessarily representative of the exact center of the aggregation. However, single points did not contribute much weight to the centroid, especially as group size increased (i.e. foci > 10 fish). Although individuals appear to pay more attention to their nearest neighbors, and to the congregation as a whole, the strength and direction of response to both foci change as the distance from the focus increases (Fig. 9.6). At close range, nearest neighbors are always avoided, as evidenced by the strongly negative acceleration component at distances less than approximately 10 cm, regardless of congregation size (Fig. 9.6). Interestingly, the strength of this close-range negative response appears to increase with increasing school size. One possible ATTRACTION 5 Fish 2.0

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Figure 9.6. The relationship between the fish's acceleration component in the direction of the focus, and the distance to that focus, for two foci of interest: the nearest neighbor (open symbols) and the school centroid (closed symbols). Positive values indicate acceleration toward the focus, while negative values indicate acceleration away from the focus (i.e. repulsion).

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explanation for this pattern is that in larger schools a larger proportion of individuals will find themselves in the interior. (This is because the volume, or number of interior positions, increases with the cube root, but the surface area, or number of peripheral positions, increases only with the square.) The movements of such fish will be more restricted, because they are surrounded by congregation members on all sides, and will thus find themselves frequently accelerating to avoid collisions. As NND increases, the direction of acceleration changes to positive, and the strength of the response increases (Fig. 9.6). When separated by 40 or more cm, individuals are greatly attracted to their nearest neighbors, regardless of school size. We believe this is a straggler response. If the nearest individual is 40 cm (6-7 body lengths) away, the fish is likely to be well outside the congregation, and the nearest neighbor is most probably the nearest fish on the school periphery. A fish aiming to rejoin the congregation will strongly accelerate toward both the nearest neighbor and the school centroid, as both lay in the same general direction. Attraction toward the school centroid is always positive and gradually increases in strength as the distance to the centroid increases (Fig. 9.6). At small distances to the centroid, an individual may be in the interior of the congregation, especially at the largest group size (i.e. 15 fish). Interior fish may not have either the ability or the need to accurately assess the location of the centroid. It is only necessary for them to maintain their position via nearest-neighbor interactions. As the individual gets farther from the centroid, it should find itself on the periphery of the group. Edge fish should be able to readily assess the direction of the school centroid, as one side will have neighbors, and the other side will not. Finally, at very large distances from the school centroid, the individual will be entirely outside the group. Stragglers within sight of the school will easily be able to distinguish the direction of the centroid because the school is now visible as a cohesive unit. In this study, limited tank size and clear water effectively prevented individuals from leaving sight of the school. However, under natural conditions, attraction to the centroid will eventually become zero as the distance approaches infinity.

9.5 Discussion 9.5.1 Conceptual issues One of the most impressive features of animal congregations is the apparent ability of the group to respond fluidly, as a cohesive, coordinated whole. In practical terms, this group-level phenomenon effectively protects individual mem-

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bers because stragglers or aberrantly behaving individuals are easily sighted, and thus become the focus of predatory attention (Major 1978; Landeau & Terborgh 1986; Parrish 1989). When watching a school of anchovies move apart to let a larger fish through, or a flock of starlings turn en masse, it is easy to forget that these group responses are actually the result of a set of individual movement decisions of each group member. How do they do it? The difference between disorder and order is that the latter is structured. That is, there are rules governing the relationships between individual elements. When the elements move, there are effectively traffic rules which, when taken as a whole, dictate the pattern of movement. Within a school of fish, or a flock of birds, traffic rules must govern, not only an individual's movement with respect to its static environment (e.g. immobile obstacles), but also an individual's movement with respect to adjacent moving individuals. Thus, all fish in a school will move to avoid an oncoming predator, but they must also move to avoid each other. Any set of traffic rules governing three-dimensional movement of individuals in a congregation must have several attributes. First, rules must dictate congregation structure, but still allow for individual freedom. That is, individuals must always be able to move freely within the confines of the group, as well as in and out of the group proper. Second, when applied, the rules should explain grouplevel phenomena, such as the cohesiveness of the congregation, the formation and maintenance of edges, and the internal structure of the group. Third, the rules must be straightforward and few in number. The penalty for incorrect decision ranges from lost opportunity for short-term reward, such as food or shelter, to loss of life (e.g. Major 1978; Morgan & Godin 1985; Parrish 1989). Complexity requires attention. If an individual fish must constantly assess and reassess its movement decisions in light of a constantly changing surround of neighbors, attention to other things, such as predators and food, might suffer. In this study, congregating blacksmith maintained a loose structure by apparently monitoring interfish distances between neighbors. However, although the average NND was similar across school size indicating that NND is a property of the fish, there was a large amount of variation (±1/2 body length). In addition, adherence to a set NND was not accomplished via pairwise interactions of specific individuals, for instance one fish following another (leader-follower pairs), or two fish moving in tandem (i.e. Fig. 9.3). Thus, individuals may be using the observed NND as a statistical guideline, rather than a more rigid optimum. This is important, because it allows individuals to move freely within the group, while still maintaining group structure on average. The blacksmith appeared to maintain a set NND with a simple set of rules governing the speed and direction of their movements with respect to other con-

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gregation members. The first rule might be to "pay attention to the nearest neighbor." Accelerate away if the NND is below a threshold (in this case, approximately 10 cm), and accelerate toward as the NND increases. In general, this rule should keep school members from running into each other, but also keep the group from dissolving. Obviously, individuals did choose to move away from their nearest neighbor (i.e. Fig. 9.3), and often from the congregation as well. Thus, paying attention to the nearest neighbor is an important rule regulating congregation structure and ease of interindividual interaction, but is not so rigid as to deny individuals the freedom to leave the group, if only momentarily. The second rule may be to pay attention to the group as a unit and accelerate toward the centroid as the distance to this focus becomes large. In this study we were unable to distinguish between acceleration toward the nearest neighbor and acceleration toward the school centroid, as both foci lay in the same direction as the individual became ever distant from the group. However, this rule would bring individuals that have chosen to leave the congregation back into the group. Although untestable in this study, the relative strength of a nearest neighbor as a focus, relative to the school centroid as a focus, could easily be tested by allowing individuals divorced from the school the choice between a single close neighbor and a larger, more distant group. Hager and Helfman (1991) found that individual fathead minnows, Pimephales promelas, when allowed to choose between joining equidistant groups of different sizes, had a significantly higher preference for groups over singletons. However, when forced to choose between two nonsingleton groups, the test fish responded equivocally, indicating that attraction to the school is not necessarily a straightforward function of group size, once the group is larger than one. Given the amount of individual freedom, with respect to their movement, that the blacksmith showed in this study, the school centroid attraction rule may act as a failsafe preventing congregation disintegration. If an individual remains within the confines of the group, this rule is not important because the centroid may not be discernible at close range, and the nearest-neighbor rule will achieve the same end. The interaction between these two rules allows the simultaneous maintenance of the congregation as a unit and freedom of individual movement. In theory, as the structure of the NND rule increases (i.e. the R2 value in Fig. 9.4 increases), three-dimensional structure within the group should emerge until individuals lose all of their freedom of movement and the congregation assumes a crystalline structure. This could be a facultative response, for instance when the congregation assumes a polarized orientation in response to predatory attack. Conversely, it could be a more inherent property of the fish, for instance the difference between resting schools of blacksmith (this study) and the ordered,

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polarized arrangements of resting flat-iron herring schools, Harengula thrissina (Parrish et al. 1989).

9.5.2 Functional considerations The ability to ask complex questions about the movements of individuals through space and time, especially with reference to membership in a group, has been compromised in the past by both technical and analytical constraints. This study presents automated three-dimensional data-collection techniques, combined with a simple, effective analytical approach for the study of threedimensional aggregations. The use of trajectory information could easily be applied, not only to other species of fish, but to any animal forming stable congregations (both two- and three-dimensional). Using the Lagrangian approach, three-dimensional coordinates can be converted into meaningful information about how individuals move with respect to each other. However, this analytical approach is useful only if a three-dimensional data set has been collected on identified individuals. In this study, the EV3D system (Motion Analysis) was used to collect spatial data on all individuals within a small school, over brief periods of time. These data are extremely useful for the analysis of static pattern (i.e. single-frame analysis), but also for a more complex analysis of individual movements with respect to neighboring individuals, as we have attempted in this chapter. Thus, with data such as these, we may be able to describe more completely the structural aspects of three-dimensional animal aggregations, as well as the apparent rules governing moment-to-moment movement decisions that gregarious animals must make. However, one must be cautious about overuse of these data. At present the data-collection system is limited to small groups (i.e. 15 fish as a maximum) and short periods of time (i.e. 10-sec intervals). Increasing either variable vastly increases the amount of time and effort required to obtain accurate information. Unfortunately, many of the questions of interest in the study of animal congregations are more appropriately asked on a longer time scale, relevant to the biology of the animal in question. For instance, a cost/benefit analysis may predict a set of optimal locations within the school, depending on moment-to-moment external influences, such as food or attack by predators (see Romey Ch. 12). The next logical question is whether some individuals are able to maintain these positions to the exclusion of other congregation members, and how this competitive process might be achieved in light of traffic rules such as the ones we have described in this study. While it may be possible to test whether predicted opti-

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mal locations act as a focus of attraction to school members, this question should be asked over longer (i.e. not 10 sec) periods of time, and also with a larger group size, such that discrete positions (e.g. peripheral, interior, leading edge) exist. Thus, while current technology has definitely allowed us to begin to tease apart mechanistic rules of three-dimensional animal aggregation (i.e. the hows of gregarious behavior), behavioral and evolutionary aspects (the whys) still await further advances.

10 Aggregate behavior in zooplankton: Phototactic swarming in four developmental stages of Coullana canadensis (Copepoda, Harpacticoida) JEANNETTE YEN AND ELIZABETH A. BUNDOCK

10.1 Introduction 10.1.1 Zooplankton swarming Uneven distributions of zooplankton, where concentrations can be two to three orders of magnitude greater than the average abundance, have been well documented (Ambler et al. 1991; Omori & Hamner 1982; Ueda et al. 1983; Wishner et al. 1988). Such aggregations have been considered mandatory for the survival of plankton that need to feed at high food concentrations to meet their metabolic costs (Davis et al. 1991; Lasker 1975). In attempting to quantify zooplankton patchiness, researchers have surveyed patch size and density on a broad scale (Haury & Wiebe 1982; Wiebe et al. 1985) and examined the causes of patch formation and maintenance against the forces of mixing (Okubo & Anderson 1984). Within patches, research has focused on genetic relatedness (Bucklin 1991) and physiological limitation (fish - McFarland & Okubo Ch. 19; krillMorin et al. 1989). However, a measure of zooplankton patchiness has challenged oceanographers for years (Hamner 1988). Average densities generally underestimate local densities because conventional sampling methods, such as net sampling, can pass through several swarms (Omori & Hamner 1982). This has led to the development of new methods for assessing the true abundance and distribution of zooplankton, including SCUBA, submersibles, video-imaging, acoustics, and optical counters (Alldredge et al. 1984; Schultze et al. 1992; Smith et al. 1992; Greene & Wiebe Ch. 4). Even with these newer techniques, it is difficult to monitor patch characteristics and dynamics because patches occur over a wide range of scales (Dickey 1990; Haury et al. 1978). There appears to be no single model of aggregation, in part because structuring factors are related to the scale of the patch: The broad scale is dominated by physics, the intermediate scale by group behavior, and the fine scale by individual responses (S. Levin, comment).

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10.1.2 Mechanism and cues Zooplankton aggregation appears to be influenced by a variety of factors. Plankters can be passively concentrated or actively motivated. Passive aggregations can be produced by physical features of water motion, like eddies, fronts, shear layers, or Langmuir cells (Haury et al. 1978; Okubo 1984) which can restrict dispersion by currents. However, shear layers also can stimulate an active avoidance response (Haury et al. 1980; Yen & Fields 1992). Some zooplankton actively change their swimming behavior in response to food patches or odors (attractants - Hamner & Hamner 1977; Katona 1973; Poulet & Ouellet 1982; or deterrents - Folt & Goldman 1981), e.g. they swim shorter reaches and turn more frequently inside favorable patches compared to their behavior outside of patches (Price 1989; Tiselius et al. 1993; Williamson 1981). Others actively respond to light gradients (horizontal migrators follow certain angular light distributions - Siebeck 1969; Ringelberg 1969) or point sources (swarms form in light shafts - Ambler et al. 1991), or avoid water of certain temperatures or salinities (Wishner et al. 1988). Each cue (e.g. light, odors, fluid motion) has a range of attributes, varying in time and space, such as 1. spectral quality or directionality of polarized light, 2. composition, age, or cohesiveness of chemical metabolites, 3. intensity (speed) and direction of water movement. The signals must be discerned above the ambient noise of the aquatic environment. These are the external variables which lead the zooplankter to the swarm. Internally, variations in receptor sensitivities and physiological state of the organism will modulate their response to each cue, affecting whether they will join and stay in a swarm or leave it. Such cues change random-walk movement patterns into directed swimming paths (see Romey Ch. 12 for a discussion on whirligig beetle movement). Phototaxis is a directional response to a light stimulus (Forward 1976). Given a defined light source, positively phototactic animals will be attracted and aggregations will form. For instance, Ambler et al. (1991) documented phototactic swarm formation of copepods to light shafts within mangrove prop roots. Although they note that light may be the proximal cue for swarm formation, predator avoidance is invoked as the ultimate cue. Light shafts are formed in between the shadows cast by interlacing prop roots. Thus, those copepods orienting to the light cue aggregated within the protection of the roots and away from open-water predatory fish. While phototaxis may be a proximal cue leading to copepod aggregation, swarm members must derive some ultimate benefits,

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such as predator mediation or enhanced frequency of mating encounters (Hebert et al. 1980), in order for swarms to persist (see Hammer & Parrish Ch. 11). Copepods are small (1-10 mm) crustaceans often found in large aggregations (1—10s of meters). Although a detailed study of swarming behavior in copepods is needed, this has yet to be done principally because of both logistical and analytical limitations. Fish schools are easy to detect and observe relative to copepod swarms. We still cannot stroll through the ocean as we do through forests to see midge swarms, although this is becoming more possible with the use of submersibles or remotely operated vehicles (ROV) equipped with cameras. Repeated sampling of patches is difficult since patches often do not occur in a reliable location and zooplankton can be easily disturbed. It has been difficult to monitor situations where we can evaluate quantitatively the individual-based dynamics of aggregative behavior. Furthermore, copepod movement patterns do not appear to be coordinated at the group level. Rather than forming regular arrays, such as those exhibited by polarized schools of fish, individual plankters move apparently haphazardly through the swarm. Instead of attempting to perform in situ studies of zooplankton swarms, we now present results from a laboratory-induced copepod swarm. Thus, we can stimulate swarming behavior at a specified location by the phototactic response to a point source of light. When the light source is placed at the focal point of two videocameras oriented at right angles to each other, we can reconstruct the three-dimensional spatial locations in time (x, y, z, t) of the swarmers from the two right-angle views. With such a laboratory-controlled situation, we can examine how copepods interact in close proximity to each other - as in a natural swarm. We began with analyses of the characteristics and kinematics of swarming: rate of aggregation and dispersion, patch size and density, trajectories, velocity of individuals, swimming patterns. Other behavioral patterns that presently are being examined include orientation, posture, and turning frequency.

10.2 Methods Coullana canadensis is a harpacticoid copepod that is planktonic as a larva and epibenthic as an adult (Lonsdale & Levinton 1985). Each of four stages were separated from cultures of a population collected in Maine, that had been maintained in the laboratory for several generations. Stages were delimited by size: early nauplii (EN) 0.10-0.14 mm, late nauplii (LN) 0.16-0.26 mm, copepodids (COP) 0.28-0.60 mm, and adults (AD) 0.64-0.86 mm. Because nauplii are naturally found in the water column, they were used to examine swarm characteris-

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tics. All stages were used in a behavioral analysis of locomotory patterns mechanically responsible for swarm formation and maintenance. Prior to each experiment, selected copepods of each size/stage category were taken from the cultures and kept in filtered seawater for less than 12 h at room temperature (approximately 20°C). The copepods then were transferred to a small glass tank (5 cm3) filled with approximately 100 ml of filtered seawater. A 2-mm-diameter fiber optics light source suspended 3 cm off the bottom of the tank was used as the attractant stimulus. After a dark-acclimation period of 30 min, the copepods were subjected to a 10-min period of illumination followed by a 4-min period of darkness. Each stage was videotaped twice, on separate days, using different individuals. The density of animals in the tank, and thus available for patch formation, was either 50 or 200. The size of the swarm was smaller (< 5 mm in diameter) than the width of the tank (5 cm in width). Swarm visualization By duplicating the laser-illuminated videoimaging techniques of Strickler (1985), we developed a system to observe zooplankton swarms in three dimensions and record their behavior (Yen & Fields 1992). Two videocameras (Pulnix TM745 B/W high-resolution cameras), oriented at right angles to each other, were focused on the fiber optics light source positioned in the center of the square glass tank of seawater with copepods (Fig. 10.1). A HeNe laser light source, following a modified Schlieren optical light path, provided the illumination for the cameras; animals did not appear to be sensitive to this wavelength (632 nm) of light. Each camera recorded the activity within an area (10 mm X 15 mm) surrounding the light source on VHS-format tape at 30 frames/sec, magnifying the image 20 times. The magnification was adjusted so that as much of the swarm as possible was within the fields of view. Quantitative analysis The number of individuals that could be counted was limited by the camera's field of view and swarm size. At a density of 200 animals, copepods between the light and the camera but not within the focal plane appeared as double images. If the entire swarm was not in focus, many blurred images would appear on the screen. Because neither of these artifacts happened with a tank density of 50 animals, we assumed that the entire swarm was seen, even though swarm size was always less than 100% of the animals present in the tank. To estimate swarm size, the maximum number of copepods seen during a one-second interval (i.e. over 30 frames) was recorded every 5 sec during the first minute, every 10 sec during the second minute, and every 30 sec until the light was turned off. Select-

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Cl

Figure 10.1. Diagram of optical pathway (Fig. 3 from Strickler 1985) and experimental setup (Fig. 5 from Strickler 1985) used to observe copepod swarms forming in the center of the vessel. Our setup is fixed frame and differs from the movable one shown here.

ing the maximum number within a one-second interval took the constant exchange of animals in and out of the swarm into account.

Patch characteristics Patch dimensions and the percentage of available population in the swarm were examined for two densities of early nauplii: 50 and 200. Because the swarm appeared symmetric in both right-angle views, we analyzed patch characteristics from the two-dimensional projection of a single camera. After the swarm formed, the positions of the nauplii were digitized from a series of 20 frames. Concentric circles with centers at the light were placed over the plot. The density

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of animals (#/vol) within a column below the light source at different distances from the light source was used to obtain an estimate of patch size. To obtain three-dimensional (x, y, z) coordinates with multiple two-dimensional projections of a swarm, it was necessary to match individuals viewed in one projection with individuals in the companion projection (see Osborn Ch. 3; Fig. 10.2). Initial analysis began with an examination of the two orthogonal views without knowing which individual on one scene corresponded to the same individual in the other view. By mapping the trajectories of each nauplius and determining their coordinates, the movements in the x, z plane could be compared to movements in the y, z plane. Individuals can be identified by matching the temporal and spatial sequence of movements in the z-axis. Three-dimensional data were used to estimate modal nearest-neighbor distance (NND) within the swarms (Leising & Yen, submitted). Swarm formation models The curve describing the rate of aggregation was modeled by logistic versus saturation curves. A good fit to the logistic curve would indicate that the rate of aggregation is enhanced by the presence of other swarming individuals, implying that mutual communication was accelerating the rate of aggregation (Okubo & Anderson 1984). The equation for the logistic model is: NQKert

~(N0-K)

(10.1)

where N is the number of individuals, No is the initial swarm size, here designated as 1, and K is the maximum number in the swarm. The variable r describes the rate of approach to the maximum. Swarm formation also can be modeled with the saturation curve where individuals are attracted independently to the swarm marker (Okubo & Anderson 1984). Therefore, in this model, swarm formation is not dependent on mutual communication. The saturation curve is expressed by the equation: N = K(\-eb<)

(10.2)

where N is the number of individuals within the swarm, K is the maximum number in the swarm or swarm size, and b describes the rate of approach to the maximum. Without communication, swarming members may orient themselves only to the attractant. On the other hand, interacting swarm members may show some attraction or orientation to other members as well as the attractant, and may alter their swimming patterns accordingly. The data were fit to the curves using the software package SigmaPlot which estimates the curve's parameters through multiple iterations. The maximum

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number aggregated around the light was determined from the SigmaPlot fit of the saturation model to data from 0 to 600 sec for the naupliar stages and from 0 to 60 sec for the copepodid and adult stages. The time needed for 90% of the maximum in the swarm to aggregate (T90a ) was determined by solving the derived equation of the saturation model for 90% of the maximum value. Although swarm size differed for each stage, the number of copepods available to swarm was kept constant at 50 individuals. The data from 600 sec (light off) to 840 sec was fit to a second-order polynomial, and the time until 90% of the maximum number in the swarm was dispersed (T9Odis) also was determined by solving the derived equation. These time measures, T90agg and T90dis, help quantify attractive versus repulsive forces. Fractal analysis of trajectories A fractal dimension (D), first introduced by Mandelbrot (1977, 1983), was applied by Dicke and Burrough (1988) and Sugihara and May (1990) to describe the complexity of a trajectory, where D represents a measure of roughness or irregularity. Dicke and Burrough (1988) used the estimated D value as a quantitative discriminator to compare tortuosity of various insect trails. Here we estimate D to describe trajectories taken by individual zooplankters. D values are

Figure 10.2. Hypothetical distribution of 4 nauplii (XK) beneath a light source, portrayed in an x,z and y,z projection (designed by David M. Fields). Patterns on body show identity of nauplii, permitting matching. Distances (s,, s2) are shown between matched nauplii in two projections.

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N=6

N = 22

N=39

Figure 10.3. Superimposition of squares of smaller and smaller side lengths (/?) used to estimate the fractal dimension of a trajectory taken by a late nauplius of Coullana canadensis as it approached a point light source. N is the number of squares that the trajectory intersected.

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compared across different stages as well as at different times in the evolution and maintenance of a swarm. Paired trajectories were mapped out for each 90 degree view and analyzed individually by the "dividers" method of varying step size (Dicke & Burrough 1988; Sugihara & May 1990). Acetate tracings were taken of the paths off a 30-cm videomonitor. The path was divided into two sectors corresponding to (1) directed swimming to the light and (2) swarming behavior under the light. A single square (4.6 cm X 4.6 cm) was positioned so as to enclose as much of the trajectory as possible under the light (i.e. within the swarm) versus the path taken to the light. The square was subdivided four times to provide the values of R (length of side; R = 2., 1.15, 0.575, and 0.288 cm, respectively) and N (number of squares that a trajectory intersected; Fig. 10.3). The fractal dimension (D) was computed as the slope of In R vs. In N. A /-test (Sokal & Rohlf 1981) was performed to ascertain differences in mean values. In a twodimensional view, fractal dimensions can range from 1.0 (straight line) to 2.0 (maximum tortuosity).

10.3 Results All stages of Coullana canadensis were attracted to the light. Copepods showed directed swimming, resulting in a clumped distribution centered around the light. Soon after the light was illuminated, many animals came into the field of view surrounding the light. When the light was extinguished, the copepods resumed a more random-walk pattern of movement resulting in an even redistribution throughout the tank. Different developmental stages showed different dynamics of patch formation (Fig. 10.4). Swarms of late nauplii were denser (53% of the number in the tank) than those formed by the early nauplii (24%). Although copepodids and adults initially were attracted to the light, after 2 min of illumination no more than 20% of the copepodids and 10% of the adults remained up in the water column. The two models used to describe the rate of swarm formation, the logistic and saturation curves, fit the empirical data equally well for the naupliar stages (Fig. 10.5; Table 10.1). The rate of aggregation during the exponential phase of swarm formation, compared as T90a , was significantly shorter for the late nauplii (39 ± 7 . 1 sec, n — 2) than the earlier nauplii (84 ± 25.4 sec, n = 2). However, there was no significant difference in the swarm dispersal time (T90dis). Analyses of the multiple exposures (Fig. 10.6A,B) of the swarms during the plateau phase showed that the shape of the swarm appeared conical below the light source. In the 50-individual treatment, a swarm of 12 nauplii formed. Swarm density declined exponentially away from the source (—0.32, r2 = 0.956). The border enclosing 95% of the swarm was 3.7 mm. In the 200-individual treat-

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Figure 10.4. Aggregation of four developmental stages of Coullana canadensis around a 2-mm-diameter fiber optics light source. Each panel shows the number of animals gathering at the light source over time (seconds) for early nauplii (A), later nauplii (B), early copepodids (C), and adults (D). The light was illuminated at 0 sec (open symbols) and extinguished at 600 sec (closed symbols). Trials (I squares, II triangles), separated by 3-7 days, represent two responses to the same light source for a different group of each stage. The total number of animals within 100-ml tank was 50.

100

200

Time (s) Figure 10.5. Rate of aggregation as modeled by the logistic (S-shaped curve) and saturation (smooth rise) equations when 50 nauplii Coullana canadensis were added to the tank and were available for patch formation. Parameters for the best fit curves to these models are listed in Table 10.1.

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Table 10.1. Parameters describing the best-fit of the saturation and logistic equations modeling the aggregation dynamics of two developmental stages of Coullana canadensis: early nauplii (EN) and late nauplii (LN); n = sample size Logistic

Saturation Stage (n) EN EN EN LN LN

(50) (50) (200) (50) (50)

K

b

res

K

r

res

10.30 5.82 59.93 26.36 14.98

0.018 0.033 0.017 0.046 0.039

35.235 67.490 131.792 74.644 61.702

9.86 5.91 56.82 25.62 14.60

0.055 0.063 0.090 0.175 0.127

41.986 65.787 172.712 75.159 60.372

ment, a 64-member swarm formed (-0.28; r2 = 0.916; 95% at 4.5 mm). The patch size/density analysis showed that nearest-neighbor distance (NND) varied with distance from the light source as well as with swarm population size. Preliminary estimates of nearest-neighbor distances of an 18-member swarm showed that there was approximately a 1-2 body length separation between swarming nauplii. Modal values for center-to-center distances were 0.517, 0.625, and 0.603 mm (Leising and Yen submitted). All developmental stages of C. canadensis showed directed swimming, indicating positive phototaxis. For all stages, the fractal dimension for the path taken to the light was nearly straight (Fig. 10.7; Table 10.2). Both copepodids and adults swarm toward the light in an undulating fashion. However, upon reaching it, these stages would stop swimming and sink. In contrast, when the nauplii were within 2 mm of the light, the spiral became tighter and the net displacement decreased (Fig. 10.7). Within the swarm, the mean fractal dimension of the early and late naupliar paths was significantly higher than that for the copepodid and adult stages (an 11% difference, P < 0.02; Fig. 10.8, Table 10.2). The higher fractal dimension indicates nauplii were moving around and exploring their swarm volume more completely than either copepodids or adults. Adults rest longer between swimming bouts and consequently sink farther from the light due to their high sinking speed. Sinking speeds were well correlated with T90dis, showing that high sinking rates limited swarm formation (Fig. 10.9). Because sinking speed was a function of increasing body length (i.e. age), sinking effectively removed older stages from the area around the light source. Instead of aggregating near the light source like the nauplii, these stages appeared to accumulate within the area on the bottom lit by the cone of light emanating from the light source.

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Distance (mm)

Figure 10.6. Multiple exposures (20 frames) of two-dimensional projections of spatial distribution of Coullana canadensis swarms around a fiberoptics light source when 50 early nauplii (A) and 200 early nauplii (B) were available for patch formation. The radii of the concentric circles around the 12-member swarm in A were 1.0, 1.8, 2.8, 3.7, and 5.6 mm. The radii of the concentric circles around the 64-member swarm in B were 1.2, 2.0, 3.1, 4.2, and 6.3 mm. The decline in the number of animals, enumerated in the column under the light source, with distance from the light source is depicted below each swarm illustration. (C) The relationship between distance from the light source vs. the areal density of swarms of two different sizes within a column below the light source.

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B

Figure 10.7. Typical two-dimensional trajectories of the developmental stages of Coullana canadensis when attracted to the light source (box drawn above paths). Both perpendicular views (x,z: left side view and y,x: right side view) are shown for (A) early nauplii, (B) late nauplii, (C) early copepodids, and (D) adults.

10.4 Discussion 10.4.1 Zooplankton swarms While aggregative behavior has been well studied in larger aquatic organisms (fish, krill) and terrestrial animals (mammals, birds, insects), little is known about how copepods form aggregations or how they maintain aggregations against the tendency of spreading by random motion or the dispersive energy of mixing in the ocean. Furthermore, we have little quantitative knowledge of the cues leading to aggregation, or of the purpose of these aggregations once formed. The existence of patchiness in zooplankton distributions were once inferred, when the metabolic needs of fish larvae could not be reconciled to the too-low average concentration of their prey in the sea. Laboratory-based behavioral observations also inferred the occurrence of patches in nature because zooplankters entering a created "patch" increased their turning rate, a behavior

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Table 10.2. Fractal dimension (D ± 95% confidence interval, n = number of replicates) of trajectories taken by four developmental stages of Coullana canadensis [early nauplii (EN), late nauplii (LN), copepodids (COP), and adults (AD)] in response to illumination of a 2-mm point source of light. Da and Db are the fractal dimensions of the trajectories from paired orthogonal two-dimensional projections. Ds are the dimensions for animals swimming under the light within the swarm, while D are the dimensions for animals swimming on the path toward the light when first illuminated. Stage

EN

LN

D

D

b

1.515 1.759 1.427 1.561 1.552 1.469 1.417 1.262

1.426

1.317 1.231 1.426 1.426 1.380 1.274 1.270

.426

P

1.182 1.154

1.459 .473 .310 1.416 1.400 1.455

1.209 1.241 1.459 ±0.063 (15)

COP AD

1.158 1.370

1.420 .325

1.011 1.349 + 0.054(10)

1.066 1.174 + 0.091 (8)

which would tend to keep them in a patch. We now know that zooplankton swarming occurs across a variety of temporal and spatial scales. At smaller scales, fist-sized, ephemeral clouds of Acartia form in eddies behind coral heads (Omori & Hamner 1982) or are found milling around shafts of light (Ambler et al. 1991). In contrast, zooplankton can also form extensive layers existing at depth (Alldredge et al. 1984) or migrating as deep-scattering layers (Greene et al. 1991). When swarms were documented by visual or acoustic observations, or chemical probes, the degree of variance in plankton abundance was extremely high relative to the statistical average. These high concentrations were real (Greene & Wiebe Ch. 4) and it is to these larger signals, greater than the noise, that the zooplankton were responding. Here we present a study where we are beginning to examine, not the statistical average concentration per volume, but the aggregated patchy distribution of zooplankton embodied as swarms. Copepod swarm formation, artificially stimulated in a laboratory setting, permits quantitative analyses of swarm mechanics at both the individual and group level. Temporal analyses showed the evolution and decay of the swarm in

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z c

- 1 In R

Figure 10.8. Fractal dimensions (D) were determined for each two-dimensional trajectory by relating N, the number of boxes crossed by the path, and R, the length of the side of the box. The slope (fractal dimension D) of In N vs. In R for paths under the light of the early nauplii (x; Fig. 10.7A) and adults (0; Fig. 10.7D) was 1.515 and 1.380, respectively. Fractal analysis of the path to the light in Figure 10.7A and D gave dimensions of 1.182 for the early nauplii (closed triangles) and 1.011 for adults (open boxes).

response to the presence of a light source. Light could easily be replaced by another modality, such as a chemical attractant. Thus, the laboratory-based situation can be used to characterize the dynamics of the lifetime of an aggregated swarm in the face of naturally occurring attractive or dispersive forces. An understanding of patch dynamics in small-scale situations such as ours may provide a link from observations of individual zooplankter behavior to the larger patterns observed in open-water zooplankton populations.

10.4.2 Trajectory analysis A useful way to quantify the shape of a trajectory is by determining its fractal dimension (Dicke & Burrough 1988; Sugihara & May 1990). When fractal values from paired, two-dimensional projections of the same event are equal, the three-dimensional value can be estimated as the two-dimensional value plus one. Fractal dimensions close to 3 describe trajectories that use the entire threedimensional space. Fractal dimensions close to 2 describe paths that remain within a plane. For example, ants explore flat surfaces and have fractal dimensions close to 2. The three-dimensional fractal value of approximately 2.5 for the nauplii in a swarm is suitable for a pelagic larva balancing full utilization of its

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m/s

2.0

E

1. 5 -

1 1.0 Q.

nki

CO O) c

(0

0.5 -

0.0 200 H

"sr 150 H E H

§ 100 H a) Q.

b

50 -

0.0

0.2

0.4

0.6

0.8

1.0

Body Length (mm) Figure 10.9. Relationship between the (a) time until 90% dispersion (T90dis) and (b) sinking speed vs. body length of the four developmental stages of Coullana canadensis. The mean ± standard deviations are plotted.

three-dimensional space with crowding by swarm mates. The lower fractal dimension of path trajectories during swarm formation indicates that plankters must change their behavioral responses as they approach external attractants (e.g. light source), sense increasing swarm density, or both. Fractal analysis can provide a measure to compare paths taken by unpolarized animals or paths taken during the different phases (evolution, maintenance, decay) of swarming. Although swarming may seem to be uncoordinated at the interindividual level

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(i.e. high variance in nearest-neighbor distances), the use of fractal analysis can reveal how individual, and individualized, path shapes contribute to the maintenance of the swarm as a whole.

10.4.3 Communication Once in a swarm, do zooplankton communicate with each other? Communication does not appear to occur by a rapid means of signal transmission, such as visual or sound transmission, because in zooplankton the sense of sight is not acute (Eloffson 1966) and acoustical detection has not been adequately documented (Schroder 1960). Hence, it is unlikely that aggregation can impart protection from predators for zooplankton by more rapid detection and visually mediated response at the level of the group. There must be other, stronger benefits that led to swarm formation in zooplankton, such as facilitation of mating (Brandl & Fernando 1971; Hebert et al. 1980; Gendron 1992) or foraging (Hamner et al. 1983; Kils 1993). Kils (1993) demonstrated how water is moved within swarms of swimming tintinnids (a process known as bioconvection), where surface water, containing concentrated interfacial material, can be entrained to deeper layers while nutrient-rich deeper water can be mixed toward the surface. Besides promoting water mixing, which exposes plankters to more food, bioconvection in a still region of no pycnocline and little turbulence can enhance encounter rate with food particles. If communication occurs via chemical or mechanical cues which are more slowly transmitted along paths of fluid flow, how do zooplankton respond to each other within a swarm? Rheotactically, krill sense and follow the wake of their school mates (Hamner et al. 1983). The movements of krill schools appear amoeboid, indicating this type of transmission is rather slow (Hamner et al. 1983). Sex pheromones excreted by swarmers present in high numerical abundance within a limited volume may reach threshold concentrations within a swarm, triggering mating. Chemicals exuded from the food or by-products of the foragers' ingestion process can be excreted within a small volume so that concentrations reach thresholds that release behavioral responses such as increased turning frequency or more directed swimming. The ratio of exudates (attractants) to metabolites (deterrents) may determine attraction or dispersion. However, it is important to note that the time needed to observe these responses to chemical cues or fluid mechanical signals is much greater than that needed to see a fish school scatter from a shark or a bird flock swerve around a tree. In this study, swarm formation by nauplii fit both the logistic and the saturation models equally well. Therefore, any degree of communication between

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swarming individuals could not be discerned mathematically. It is unclear to what degree each nauplius responded individually to the light versus the increased presence of neighbors, as both processes lead to swarm formation.

10.4.4 Orientation and arrangement In fish schools, polarity exists, and there may be set nearest-neighbor distances given certain circumstances. At the level of the group, there is cohesion and edges. In contrast, zooplankton within swarms show seemingly chaotic movement and have no readily apparent orientation or predictable trajectory. Individuals in a plankton swarm are at random angles to one another. No polarity exists and the distance between individuals may be highly variable. Nevertheless, at the level of the group, one can still observe some of the same resultant properties as fish schools display (e.g. cohesion and edges). What mechanisms or cues allow individual plankters to form a recognizable unit observed as a swarm? It is unlikely that visual perception of swarm mates is a strong orientational cue since few copepods have image-forming eyes. The only copepods that appear to form aggregates that exhibit coordinated movements between individuals, similar to true schooling, are copepods that have lenses in front of their photoreceptor (Labidocera pavo - Ueda et al. 1983); yet these lenses are not attached to focusing muscles nor is there any evidence of an image-forming retina within the photoreceptor. The general lack of imageforming visual perception of swarming copepods may preclude an ability to orient to each other with linearly symmetrical spacing patterns, or to respond with quick cross-school synchrony (Hamner et al. 1983). It is entirely likely that swarming cues in zooplankton are nonvisual. We know relatively little about the spatial distribution of chemical or fluid mechanical cues within a swarm. These patterns are difficult to visualize and to document in time and space and, hence, are not familiar. For an animal that has no eyes and is chemoreceptive, orientation may be along trails of high chemical concentration (Hamner & Hamner 1977; Poulet & Ouellet 1982). Mechanoreceptive plankters may align along gradients of minimum shear (Yen & Fields 1992) or minimum change in pressure. Local orientation in zooplankton may be along streamlines generated in the flow field surrounding swimming or feeding neighbors. Neither chemical trails nor turbulence follow necessarily regular spatial patterns in three-dimensional space that would result in zooplankter orientation with the familiar spacing of bird flocks or fish schools. Thus, the spatial distribution and movement patterns exhibited by swarming zooplankton may reflect the threedimensional spatial distribution of the signals in the sea which they sense.

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10.4.5 Spacing and perceptive field The definition of interindividual distance, and thus the density of the patch, may be related to an individual's maximum perceptive distance. Vision, chemoreception, and mechanoreception each have different perspective ranges for copepods, making them variously important at different spatial scales and reaction times. Nearest neighbors may be separated by the span of the appropriate sensor. For example, individuals may remain separated from each other by a distance determined by the sensitivity of a mechanoreceptor and the intensity of a hydrodynamic signal emanating from a neighbor (Leising & Yen, ms.). The threedimensional pattern of signal transmission also will influence the paths and positions taken by members within the swarm. Individual plankters, unable to sense beyond the limits of their perceptive range, could be coordinated in a loose form of sensory integration (see Schilt & Norris Ch. 15, for an extended discussion of the sensory integration phenomenon), each sensing and responding to their closest neighbor. Few measurements of these gradients have been taken along with the orientation by the animals.

10.5 Conclusions For small organisms like zooplankton dispersed in a huge ocean, it is fortunate that aggregations form - so that predators can find their prey and reproductively mature plankters can find their mates. Zooplankton, considered at the mercy of ocean currents, indeed can execute directed movements of their own. Such movements include attack lunges, escape flights, and mate tracking. These individual moves give evidence that zooplankton are not passive, but rather are active - responding to signals transmitted through the fluid medium, the sea. Even though we certainly need a greater understanding of the attractive cues that elicit group responses from zooplankton populations and how such forces maintain the swarm in spite of constant dispersive action, it is documented clearly that zooplankton swarms exist and show many of the properties of vertebrate congregations. Here we presented a means to begin a quantitative analysis of swarming behavior: swarm size, path structure, rates of evolution and decay of aggregations. Future research, nesting the 3-D flow visualization optical design within an in situ sonified volume, could provide the data for ground-truthing acoustic images. Overlaying maps of 3-D paths taken by acoustic images of swarm members onto dynamic fluid structures can verify our consideration that the zooplankton tracks can reveal aspects of the structure of fluids at small temporal and spatial scales.

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Acknowledgments We would like to thank Julia Parrish and Bill Hamner for organizing the 3-D aggregation meeting at Monterey Bay Aquarium, for putting this book together, and for insightful criticism of this chapter. We would like to thank Akira Okubo for his enthusiasm and expert guidance in many aspects of this study. We would like to thank David M. Fields for statistical and technical assistance, Andrew W. Leising for contributing his unpublished estimates of NND, and Darcy Lonsdale for providing cultures of C. canadensis. J. Yen would like to thank Claudia Mills for the opportunity to participate in Pisces IV dives in Saanich Inlet, Canada, where she saw that copepods did swarm in dense patches and layers. We thank the Ward Meville Foundation for providing a summer undergraduate student fellowship to E. A. Bundock. This research also was supported by the Office of Naval Research contract N-00014-92-J-1690 and National Science Foundation grant OCE-8917167 and OCE-9314934 to J. Yen. This is Contribution No. 1050 from the Marine Sciences Research Center at the State University of New York at Stony Brook.

Part three Behavioral ecology and evolution

11 Is the sum of the parts equal to the whole: The conflict between individuality and group membership WILLIAM M. HAMNER AND JULIA K. PARRISH

The schools swam, marshaled and patrolled. They turned as a unit and dived as a unit. In their millions they followed a pattern minute as to direction and depth and speed. There must be some fallacy in our thinking of these fish as individuals. Their functions in the school are in some as yet unknown way as controlled as though the school were one unit. We cannot conceive of this intricacy until we are able to think of the school as an animal itself, reacting with all its cells to stimuli which perhaps might not influence one fish at all. And this larger animal, the school, seems to have a nature and drive and ends of its own. It is more than and different from the sum of its units. (Steinbeck & Ricketts 1941)

11.1 Introduction Aggregation behavior can be found in almost every animal taxa, from the rudimentary assemblages of planktonic larvae reacting to photo- or geokineses to the highly developed social orders of terrestrial mammals. Somewhere in the middle of this cline lie the dense aggregations of birds, insects, and fish - perhaps directed by individually based attractions/repulsions to extraneous source material, as well as by the development of simple social order. Visually, these groups may appear, at least superficially, similar. They are dense, structured congregations with distinct edges, often moving as a group from place to place. It is tempting to imagine that the forces regulating the evolution and maintenance of these congregations were/are similar as well. However, practically, we know that species are subject to very different selective pressures. This section focuses on the broad question: Why do animals form dense, often three-dimensional, aggregations? Within that question there exists an ethological, as well as a historical, framework. Tinbergen (1963), after Huxley, outlined four approaches ethologists take when studying the behavior of animals in the context of their environment: causation, survival value, evolution, and ontogeny. With respect to gregarious behavior these approaches might be posited as: What

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is the proximal cause explaining gregarious behavior? What is the survival value, or ultimate benefit, of grouping? How is grouping behavior learned during ontogeny? How has grouping behavior evolved during phylogeny? Historically, these questions referenced the behavior more than the individual. Earlier work, summarized and reviewed by Keenleyside (1995b), Radakov (1973), and Shaw (1970, 1978) saw the most visible of the three-dimensional animal aggregations, namely schools of fish and flocks of birds, as egalitarian assemblages of essentially equal individuals. Classically, all individuals in a school were considered to be identical in every aspect of morphology and behavior (Breder 1959; Shaw 1978). Research was characterized by its focus on emergent attributes of the congregation as a whole, such as size, shape, density, packing geometry, movement synchrony in space and time, and the sensory stimuli involved with maintaining station in the group (Shaw 1970, 1978). A set of identical individuals all contributing to the well-being of the group led to a group selectionist paradigm (Shaw 1978). However, the individual has replaced the group as the proper unit of selection, and Tinbergen's four questions must now be answered with respect to group members. Assuming that selfish individuals are the currency of selection, and individuals in a stable three-dimensional animal aggregation are not necessarily, even usually, related to each other or even faithful to the group (Helfman 1984), membership must be individually advantageous because it exists. This admittedly tautological statement brings us to a restatement of the multidimensional "Why?" How is an individual's fitness maximized by maintaining membership in a group? The answer to this question has implicated four basic causal factors, contributing to proximate, as well as ultimate, individual benefit: reproduction, energetic expenditure, food, and predation. 11.2 Membership and position Many types of aggregations are, in fact, for the purpose of mating. Midge swarms, krill schools, and the migratory schools of many fish concentrate the sexes so that either individuals can pair off (insects) or mass spawning can occur (fish). Reproductive aggregations may also allow individual members to assess the sexual receptivity of other members so that the synchrony necessary for mass spawning can be maximized. Either way, absence is at least equal to not reproducing and may be equal to effective mortality in those species which only reproduce once. Larger groups mean more choices of mates and may mean more mates, in the case of mass spawners. While there is an obvious benefit to group membership, at least during the reproductive season, this still does not explain persistent animal aggregations such as bird flocks and fish schools.

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Maintaining membership in a group would be advantageous if it conferred some benefit not available to lone individuals. Following the lead of Hamilton (1971), there has been a search for selective forces favoring group membership. Several researchers have suggested that membership in schools or flocks provide individuals with an energy savings relative to swimming or flying solo. Hydro/aerodynamic theory has provided testable hypotheses concerning the position of individuals relative to their immediate neighbors for maximal energy savings (Breder 1965; Lissaman & Schollenberger 1970; Weihs 1975; see also Heppner Ch. 5). There is also an array of hypotheses concerning the effects of membership, as well as position within the group, with respect to the acquisition of food. Although groups have been hypothesized to find food faster in a patchy environment (Pitcher et al. 1982a; Clark & Mangel 1984; Giraldeau 1984), there is also the obvious element of competition between members once a patch has been located (Eggers 1976; Ekman 1987). However, the vast majority of theoretical work regarding the potential benefits to the individual of maintaining group membership are based on the broad premise that aggregation mitigates predatory pressure on the individual. Two of the most cited hypotheses are the effects of dilution and confusion (Bertram 1978; Pitcher & Parrish 1993). As the group increases in size, the dilution hypothesis states that anything affecting the group will be shared by a larger number of individuals, each experiencing a smaller "piece of the pie." Assuming predatory pressure, measured as attacks per unit time, either remains constant or at least does not increase in 1 : 1 correspondence to group membership, the "average" member of a prey aggregation should receive fewer attacks per unit time and thus be safer. Threedimensional animal aggregations are clearly, among other things, behavioral adaptations designed to confuse the optical ability of vertebrate predators to focus on an individual within the group long enough to effect its capture (but see Parrish 1992). The combination of safety in numbers and selection against odd individuals and thus for uniformity in morphology and behavior to that of one's neighbors, creates large, dense aggregations of seemingly identical individuals, all of which are safer than any conspecific outside of the group.

11.3 Costs and benefits to the individual In general, there are two basic ways in which an individual can benefit from group membership. Passive benefit is accrued simply by being a member of a group. Classically, we have calculated these benefits (e.g. more food, dilution, confusion, reproduction) as one over the number of group members (i.e. the average benefit or the average cost). Active benefits, on the other hand, are accrued by individuals as a consequence of decisions they make (Parrish 1992). Al-

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though we are inherently aware of the fact that there must be differences between individuals in order for selection to effect evolution, much of behavioral ecology has been oriented toward optimal or average behavior (see discussion in Magurran 1993). This has been especially true of aggregating animals (e.g. Shaw 1970). . . . almost no attention has been paid to adaptive individual differences between [group members] because of the common misconception that [group members] . . . share the same background and needs. (Romey Ch. 12) Yet one of the most important decisions a group member can make is where to be, that is, the specific location within the group (Krause 1994). Positional effects within the group, with respect to predation, food, and energetic expenditure, are discussed in detail by Romey (Ch. 12). Romey suggests that it should be possible to construct "danger isopleths" with respect to individual location within the confines of the group. The logical extension of this is the construction of survival or fitness isopleths, given a range of varying environmental constraints. We should be able to predict, at least grossly, which positions are favorable and thus desirable. These predictions can then be tested by determining whether individuals within the group attempt to change positions as the external constraints, and thus the fitness isopleths, are changed. Whether individuals are successful at "capturing" and maintaining station in "optimal" positions will be a consequence of their internal state or motivation (Romey Ch. 12), their competitive ability (e.g. Milinski 1988), and their inherent individuality (sensu Magurran 1993).

11.4 Group persistence If we assume that membership is more beneficial than isolation, at least ultimately, then that explains the formation of aggregations. However, this is not to say that individual members do not experience proximal costs outweighing benefits. If group members only experienced passive benefits or were not able to change positions within the confines of the group, this would translate into group dissolution because at some combination of selective forces, every location within the group would be disadvantageous. However, individuals, even while maintaining group membership, do retain some (at least pseudo-independent) decision-making capabilities. Therefore, a single group member incurring costs while all others benefit should be able to maneuver itself into a more beneficial position, to the detriment of some other group member. Jakobsen and Johnsen (1988b) have shown that individual Bosmina adjust their positions in the group as a function of predatory threat. For this, we can make a prediction that if the

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proximal cost/benefit ratio swings negative for the majority of the group, group structure should break down. If the majority of the individuals are experiencing costs, then no amount of rearrangement will change the "group level" cost/ benefit ratio to positive, and individuals should leave. In the presence of predators, individuals may do well to remain within the confines of the group (Bertram 1978; Pitcher & Parrish 1993). While some positions will undoubtedly confer a greater benefit upon their occupants, all positions are preferable to becoming a straggler (e.g. Hamilton 1971; Morgan & Godin 1985). However, aggregations experience other forces, like hunger. If a school of planktivores finds a patch of food, then those individuals in the vanguard will eat while the next rows back should receive less. If the patch is small and the school is large, then the majority of the school will not eat (i.e. incur relative costs). Thus, under these conditions, school structure should break down as each individual competes with former neighbors for food. Should a piscivore swim by, the costs of competition are outweighed by the benefits of membership in a coherent group (life-dinner principle sensu Dawkins & Krebs 1979, see also Morgan 1988; Abrahams & Dill 1989). The unifying framework is survival and fitness (Mangel 1990), terms that incorporate the realities of a constantly shifting environment. Is a flock of migrating birds the same as a swarm of mating midges the same as a school of herring? Functionally, no. We can measure differences in group duration, dimensionality, architecture, "purpose," and proximal environmental constraints. However, all individuals should respond to the cost/benefit threshold, regardless of the selective forces in operation. In reality, three-dimensional animal aggregations are flexible entities, undergoing constant transformations in and out of close, structured architectures (Schilt & Norris Ch. 15). It is important to remember that group dissolution is not synonymous with total abandonment of a gregarious lifestyle. Schooling planktivores often disband at night (when they feed) only to re-aggregate the next morning (when they become visible to the diurnal predators - Hobson 1965; Parrish 1993). Where is the cost/benefit threshold? At the level of the individual, risks versus benefits must be time averaged in some way such that individuals balance their ability to take advantage of position changes with the social chaos resulting from all individuals constantly changing position to better their short-term gain. This is the relationship between how much proximal risk is accepted for a promise of ultimate gain. At the level of the group, the negative/positive threshold should be set by number of individuals experiencing costs longer than the individual time lag allows. Group-level thresholds should set a maximum size, given a known range of environmental parameters such as predator pressure and food availability. Individuals in the group do not need to know the size of the group, but sim-

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ply whether they are able to find a beneficial position. The relationship between optimal and maximum group size is addressed by Ritz in Chapter 13.

11.5 Individuality versus "group" behavior In order to survive, all individuals need to detect incoming signals from the environment, interpret those signals, and decide what to do about them. In novel situations, such as a school of fish faced with an unknown predator, individuals may grossly overreact, possibly until more information (i.e. more signals) can be obtained and properly deciphered (Parrish 1993). Conversely, individuals may not react at all (with the possible consequence of death), presumably because the incoming "signal" is not detected, or interpreted as meaning predator (Magurran & Seghers 1990). In an aggregation, these duties are shared. That is, all individuals still detect-interpret-decide, but now a multitude of potential information is available from other group members. This has the advantage of minimizing missed detection and incorrect interpretations through averaging (see Schilt & Norris Ch. 15; Grunbaum Ch. 17). By becoming an interacting array of sensors and effectors animals in . . . aggregations . . . are able to gather more information about the world than would be possible for a lone individual. (Schilt & Norris Ch. 15) Group members can do without direct detection of an incoming signal because they can receive necessary information from their neighbors. But now, individuals need to monitor both their immediate surroundings (i.e. neighbors) as well as the larger environment. For instance, if a school of anchovies is attacked by a passing tuna, anchovies in the path of the oncoming predator need to respond to the position and trajectory of the tuna as well as to what their neighbors, who are also presumably escaping, are doing. Dill, Holling, and Palmer (Ch. 14) propose that structure in three-dimensional groups may be a result of individuals optimizing their position relative to neighbors in order to gather information. The architecture and degree of "noise" in a group will be a function of how information is transferred. Dill et al. (Ch. 14) propose three potential visual signals fish receive from their neighbors: angular velocity, loom, and time to collision. However, it is also probable that signals are transferred nonvisually (e.g. chemosensory, auditory, mechanical, etc.). Switching from one sensory modality to another may necessitate rearrangement of nearest-neighbor geometry, which would effectively change the architecture of the group as a whole (see Hobson 1978; Abrahams & Colgan 1985). If we know something about signal type and decay, we should be able to make predictions about group structure (Dill et al. Ch. 14).

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The next problem the aggregation faces is one of decision. Individuals will interpret information and respond to it whether they are in a group or not. However, in a group, non-uniform decision making can be at least costly and at most deadly. An individual which decides to go right when neighbors go left may risk running into a neighbor. For airborne animals, collision can be fatal (Cuthill & Guilford 1990). For aquatic aggregations, running into a neighbor may create a localized disturbance, of which predators may take advantage (Pitcher & Wyche 1983). What is important, at the level of the selfish individual, is that both the group member making the incorrect decision, and its immediate neighbors, are penalized, even though the latter may be acting in general consensus with the group. Although it seems likely that incorrect decisions would be made, we rarely see breakdowns in the structure of three-dimensional animal aggregations. Pelagic schools move with a collective synchrony that is visually mesmerizing. Flocks on the wing negotiate around obstacles en masse. How do they all know what to do? Restated in a broader context, this is the same question we came to earlier: How does the seemingly egalitarian behavior of the group benefit group members as selfish individuals? Here is the apparent paradox of many three-dimensional animal aggregations. Individuals must be selfish according to our current evolutionary paradigm, and yet as group members they respond as a collective whole. In fact, there need not be a discrepancy between the individual and the collective. In every case the individuals in the group will benefit by maintaining the cohesion of the group as a whole through time. (Dill et al. Ch. 14) The same selective pressure that results in morphological uniformity should result in de facto consensus in response, the appearance of which is coherence and coordination (Parrish 1992).

11.6 Cooperation or veiled conflict In this chapter, we have developed a paradigm of the stable, coordinated aggregation of selfish individuals, at least 50% of which are experiencing a net gain over that of a loner. In order for this scenario to work, there must be several necessary conditions. 1. There must be a cost for not staying, as well as for not cooperating. If the benefits for cooperation are too small, or nonexistent, then group structure should break down continually. Fish evolving in a predator-free environment school less well than do conspecifics facing the threat of predation both ontogenetically and phylogenetically (Seghers 1974; Liley & Seghers 1975).

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2. Individuals in the group must be able to glean information from fellow members. Whether information is passed actively or passively (Pitcher & Parrish 1993), there must be a set of understood signals. These may be visual, auditory, chemical, and/or tactile (e.g. lateral line sensations), or some combination. If the price of misinterpretation is high, then "understanding" a signal and responding to it correctly is selected for. This means it is also necessary that one's neighbors "understand" because misinterpretation of a signal by any individual can make its neighbors vulnerable by close physical association. 3. If individuals are not familiar with each other such that one member can predict what another one will do based on individual knowledge (unlikely in large three-dimensional aggregations), then there must be a set of rules governing response. An analogous situation is freeway traffic. We survive the drive to our destination, not because we are personally familiar with all other drivers as individuals, but because we understand the traffic rules. Drivers who do not know or who do not choose to obey the rules are dangerous. When viewed from afar, the traffic pattern of automobiles on the freeway appears beautifully orchestrated, as if all of the vehicles are being driven by drivers concerned only with the safety of others. But what appears from afar as courteous concern is in reality an exercise in survival tactics, with trajectories projected into future time and space, and with a special flair for breaking the rules whenever it is even remotely advantageous as long as we do not have an accident or get caught. 4. There must be an opportunity for payback. If the cost/benefit ratios are not evenly distributed in group space, and are unpredictable from one time point to the next, then individuals on the "short end" of the stick should mutiny or all individuals should continuously cycle through all positions as have-nots supplant haves.

11.7 Concluding remarks Much of the work on three-dimensional animal aggregation has been descriptive (Pitcher & Parrish 1993; Krause 1994; Heppner Ch. 5). This is a product of the historical framework of ethology, the lack of testable hypotheses concerning the behavior of individuals within a group under a given set of constraints, and a lag in technology. The chapters in this section attempt to integrate observation with experimental approaches in order to formulate testable hypotheses about the structure of three-dimensional animal aggregations, based on the behavior of individual group members. Functionally, this can be accomplished because the

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maintenance/dissolution of the group can be reduced to predicting at what point the majority of the group will experience relative costs, and the structure of intact aggregations can be reduced to predicting at what locations within the group individuals will maximize individual benefit, and at what location relative to neighbors individuals will be able to gather the most information.

12 Inside or outside? Testing evolutionary predictions of positional effects WILLIAM L. ROMEY

The schooling phenomenon presents the student of animal behavior with a paradox. On the one hand, schooling is superficially a simple phenomenon and would seem to lend itself readily to quantification and casual analysis. On the other hand, there has been a notable lack of success in relating schooling to general biological principles, and there are no really convincing ethological, ecological, or evolutionary explanations. There is no vital function to which it seems to make an efficient contribution, and it can not be immediately assigned to reproductive, defensive, or any other category of adaptive behavior. (Williams 1964: 351)

12.1 Introduction During the three decades since the above statement was made a great deal of theoretical and empirical work has established a number of plausible functions for animal grouping. These functions typically relate to feeding efficiency or predator avoidance. Such generalizations may allow us to see overall patterns and generate hypotheses which can be tested experimentally. However, by considering the selection pressures on groups in general, there is the danger of missing some of the details. Instead, the relative advantages and disadvantages of group membership may vary in different parts of the group (Bertram 1978). For example, although individuals at the edge of a group may be more likely to be preyed upon than those at the center, they may also be more likely to obtain food. The costs and benefits to an organism as a function of location within the group has rarely been assessed. I hope to convince the reader that groups are not homogeneous units, and that different selective pressures operating in different locations within a group lead to position preferences by its members. Furthermore, by focusing on individuals and differences between group members (see Magurran 1993), we may study the function of grouping more effectively.

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Because researchers have traditionally had difficulty generalizing and structuring their observations on grouping, many definitions of social groups have been created to fit each particular case. I wish to define and discuss a subset of the more general term congregation as defined by the editors of this book. I shall hereafter call this subset an FSH (for flocks, swarms/schools, and herds). In the continuum of grouping types, FSH are more structured than active aggregations, in which each member's movement is independent, and below social congregations, which may be structured by age and sex and within which cooperation may be displayed (Fig. 12.1). Thus, FSH is a type of passive congregation (see Parrish, Hamner, & Prewitt Ch. 1). I shall also refer to a single member of such a group as a "flocker" whether it is a bird or not. Behavioral ecologists might break the study of FSH into three major questions: (1) Does grouping serve a function? (2) What are the constraints on grouping? and (3) Are there differences between individuals? Several chapters in this

Congregation terms used in chapter

FSH -

characteristics

examples

Social

bats in caves, butterflies at puddles

- mutually gregarious - unrestricted group entry and exit - limited individual recognition

herring, tuna, minnows starlings, ladybird beetles whirligig beetles, krill, midges

Q. O O

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Group/Aggregation

- incidental associations - not gregarious - attracted to common resource

2

I - mutually gregarious - restricted group entry and exit - individual recognition - communication - cooperation - age/sex structured

- primate troops - wolf packs - eusocial insects - whales and dolphins - mating groups

Figure 12.1. The grouping continuum from less to more complex, from left to right. This figure serves as a guide to the terminology used in this chapter. Although individuals spend most of their time in one type of grouping, a number of factors, such as mating, may lead individuals into higher or lower grouping classifications. For example, butterflies which are normally solitary will form complex age and sex structured mating groups during the mating season.

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book deal with the adaptive value of schooling (Hamner & Parrish Ch. 11) or possible constraints such as the sensory modality of flockers (Griinbaum Ch. 17; Edelstein-Keshet Ch. 18). This chapter focuses primarily on the third question. How do differences between individuals and differences in selection pressure influence positional preferences within a group? Magurran (1993) summarized five areas where individual differences in behavior are well documented: mating, habitat use, dominance hierarchies, foraging, and predator avoidance. Yet almost no attention has been paid to adaptive individual differences between flockers. There is a common misconception that each flocker in a group shares the same background and needs (Keenleyside 1979; Magurran 1993). Magurran (1993) suggests that as schooling tendency increases, the degree of individual differences is expected to decrease. However, as individuals are packed closer to one another, there may be a greater need to structure FSH according to individual motivations such as hunger. A primary limit to the study of FSH is that it is often difficult to identify individuals in a group. Therefore, the first hurdle to be overcome is a methodological one. Recent advances in three-dimensional tracking (Jaffe Ch. 2; Osborn Ch. 3; Parrish & Turchin Ch. 9) should aid the task of studying individual differences between group members.

12.2 Where should a flocker be in a group? 12.2.1 Evolutionary predictions based on external selection pressures The adaptionist stance, that an organism and its behavior are a reflection of its current environment (given some developmental limitations) is often the best starting place for biological studies such as these because this view provides testable hypotheses (Krebs & Davies 1981). Most of the evolutionary predictions elaborated in this chapter arise from adaptionist thinking, which assumes that most behaviors and other phenotypes are adaptive, having been fine-tuned over evolutionary time to maximize fitness (evolutionary fitness = the contribution to future generations) (Maynard-Smith 1978). However, it must be noted that other starting points in explaining causation may also be taken and that the nonadaptive hypotheses must be falsified if we are to rigorously accept adaptive hypotheses (Gould & Lewontin 1979). There are a number of commonly cited, and debated, explanations for why animals congregate (e.g. Pulliam & Caraco 1984; Bertram 1978; Hobson 1978; Pitcher & Parrish 1993). Many of these hypotheses carry implicit predictions about the location within the group where an individual can best accrue the associated benefit. I will briefly describe those hypotheses in which there appears to

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Hypothesis

Food Dispersion

Homeostasis

Location Best - Worst Center-Edge

Locomotion Efficiency Feeding Efficiency

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Back -- Front random

Front-- Back Edge - Center

clumped

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Pred. Avoidance Increased Conspicuousness

Center - Edge

Predator Swamping

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Increased Vigilance

random clumped

Selfish Herd

Center - Edge Edge -- Center Densest - Least Dense

Confusion Effect

Random -- Still

Oddity Effect

Near similar Near dissimilar phenotypes - phenotypes

Figure 12.2. Summary table of predictions for optimal locations within an FSH group according to various hypotheses. See text for discussion of each effect, examples and references.

be some inequality as a function of location, and then rank the different locations in the group based on each hypothesis (Fig. 12.2). Pitcher and Parrish (1993) give a more complete review of the overall explanations for many of these hypotheses, with regard to fish.

12.2.2 Homeostasis In most instances the center of the FSH would be most advantageous for maintaining homeostasis. In many homeothermic species such as birds and bison, there is a thermoregulatory advantage to grouping in cold weather. This advantage is probably less important for poikilotherms but may still be important to some insects who have warmed up during the day and want to maintain their heat into the night (e.g. bees). Insects may also group in order to reduce water loss (Frielander 1965; Lockwood & Story 1986), especially in ladybug beetles which overwinter together (Greenslade 1963; Thiele 1977; Lee 1980; Copp 1983). It has also been shown that intertidal invertebrates reduce water loss by grouping. In these situations, maximal benefit is achieved by centrally located members at the expense of those individuals on the edge (Fig. 12.2).

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12.2.3 Locomotion Flockers moving in the same direction (i.e. polarized flocks and schools) have long been thought to benefit from the reduced drag incurred by "drafting": i.e. flockers in the middle or back of the group would expend less energy than those on the vanguard (fish - Weihs 1973; 1975; bird flock structure - Heppner Ch. 5). This belief may stem from the group-level observation that there appears to be a distinct and regular architecture to moving fish. In other words, all individuals are precisely located with respect to their immediate neighbors. To date, empirical studies have not found that flockers are able to take advantage of this effect (Gould & Heppner 1974; Partridge & Pitcher 1979). Both the theoretical and empirical treatment of position-related energetic benefits need to be further explored. For instance, it has not been shown whether there is truly no difference in energetic expenditure by flockers in the front versus the back. This could perhaps be addressed by remotely monitoring the metabolic rate of different individuals within the group as a function of their position.

12.2.4 Foraging It should not be forgotten that one of the most important ^advantages of grouping is increased competition for food. This is because grouping increases the number of organisms eating the same patch of food, which decreases the probability that the average individual will either find food or acquire a given ratio (see Ritz Ch. 13). However, feeding efficiency is also one of the most commonly cited advantages of forming FSH. Some hypotheses predict that organisms should group in order to efficiently utilize dispersed resources (e.g. Cody 1971). Other hypotheses predict that organisms should group in order to take advantage of clumped resources that are difficult to find (Brown 1986). In either situation, it is important to ask what is the best location within an FSH. Hypotheses related to foraging vary more in their predictions of optimal location in the group than do any of the other postulated FSH functions. Some of these theories suggest that group cooperation may play a role in the development of truly social congregations, as opposed to FSH. Some species seemingly gather for the purpose of displacing territory holders from a feeding ground ("Gang Theory" - Barlow 1974; Altmann 1956). The preferred location for an individual may be at the rear of the group so that flockers can avoid injury if the territory holder defends its position. The whole group gains equally from gaining access to the resource, while only the lead individuals incur the potential cost of being attacked by the territory holder.

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If food is distributed in patches and is difficult to find, then staying in an FSH will increase the probability of detecting and profiting from the food discoveries of others (Brown 1986). This applies equally to FSH that are moving forward and to those that are static. Pitcher and Magurran (1983) found that fish in groups find food more quickly than loners. They hypothesized that changes in the behavior of the discoverers transmitted information (either overtly - active information transfer, or inadvertently - passive information transfer) to other nearby flockers. There may be some minor advantages for flockers at the leading edge of such groups because individuals can enjoy some amount of uninterrupted feeding time before the rest of the group discovers the food source. When resources are randomly distributed and relatively nonrenewable, or renewal time is slow, it pays organisms to reduce the probability of returning to the same location. This "clear-cutting" technique involves extracting as much as possible from a particular area and not returning to that area until much later. The group trajectories and return times of some foraging flocks have been found to closely mimic the path predicted by optimality models employing clearcutting strategies and reduced return times (e.g. Cody 1971). In this case, the best location within a group would be the leading edge and sides. Occasionally, especially in heterogeneous environments, food resources may be concealed or cryptic such that flockers on the leading edge pass into a patch without discovering the prey. This effect has been noted for insectivorous bird flocks (Morse 1970). Here, the combined effect is greater than the sum of the individual effects with regard to disturbing, and thus discovering, the prey. The best location for individuals to take advantage of this effect is toward the trailing edge of an FSH.

12.2.5 Antipredation Many researchers consider predator avoidance to be the primary function explaining the initial formation of FSH (Barnard & Thompson 1985; Vulinec 1990). Certainly the greatest percentage of adaptive hypotheses for grouping have centered around defensive strategies. Defense against predation, whether group-oriented or not, can happen at several time points along the predator-prey interaction. There are a number of behavioral steps that many predators go through before consuming prey. For example, Neill and Cullen (1974) described the following sequence of steps for a predatory pike attacking schooling prey: contact-orient-stalk-attack-capture. Although some species have developed adaptations for interrupting one of these steps, grouping often provides advantages at more than one stage.

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Grouping in many species of insects has been explained as a "secondary" defense system which reinforces a primary morphological or chemical defense (Sillen-Tullberg 1988; Vulinec 1990). Aposematism usually occurs as warning coloration (e.g. distasteful insects often develop bright colors so that predators will learn to avoid them). However, instead of evolving bright coloration, selection may have favored gregariousness. Grouping may be considered an aposematic characteristic which warns predators. In fact, many aposematically colored insects also group to form a supernormal stimulus. It has been suggested that whirligig beetles congregate in order to warn predators about their primary defense: gyrinidal, a nasty-tasting exudate (Heinrich & Vogt 1980). Riffle bugs also seem to group to advertise their unpalatability (Bronmark et al. 1984). A bad-tasting organism without aposematic coloration might use grouping as a type of "facultative aposematism" so that it could be alone at other times (e.g. during mating territoriality). For a group whose main function is to warn predators of distastefulness, the best location would be anywhere but the very edge, where naive predators might occasionally attack. Vigilance Lack (1954) first suggested the "many-eyes" hypothesis as an advantage for individuals joining a group. This hypothesis assumes that the predator relies on surprise and that once a predator is detected, flockers will have a better chance of evading it. There are actually two advantages to the "many-eyes" hypothesis. First, by becoming alerted early to an approaching predator, there is more time for evasive action. Earlier action on the part of the most vulnerable prey may also warn other flockers in time for them to effect an escape. Indeed, the reaction wave passing through a tightly packed group of prey is transmitted much more quickly than the speed of the approaching predator (Foster & Treherne 1980). Whether flockers respond, once the predator has been detected, is another question (see Seghers 1974; Caro 1989). The second advantage applies only to species where vigilance and feeding are mutually exclusive. Birds, for example, maintain a higher feeding rate while in groups because the vigilance time of any individual decreases as a function of increasing group size (for review see Elgar 1989). Vigilance time may vary as a function of distance in from the edge. This is because edge flockers are more vulnerable and also have an unimpeded view. If food is clumped, there would initially be a disproportionate advantage to being in the center because the flocker would spend relatively less time looking for predators and could feasibly get

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more food. However, food may quickly become depleted, especially if the FSH is static, leading to increased competitive interactions (Caraco 1979). Therefore, if the food is dispersed, there may be an advantage to being on the periphery, where competition is lower and the chance of intercepting new patches is high, even though predator exposure may also be high.

The confusion effect This hypothesis predicts that oncoming predators will be unable to select a single individual within the confines of a homogeneous group of interweaving individuals, forcing the predator to hesitate or even abort an attack. Therefore, a flocker should not have a preferred location within a group as much as it has a preferred pattern of movement. As soon as the flocker's behavior becomes predictable, the predator has a greater chance of catching it. The related Oddity Effect (Landeau & Terborgh 1986) predicts that the minority phenotype in a mixed-species FSH should stay with like flockers. Here, oddity can refer to morphology/coloration (e.g. Hobson 1978; Landeau & Terborgh 1986) as well as movement/behavior (e.g. Major 1978). In the former, it might be more important to facilitate the confusion effect rather than to follow the dictates which other adaptive positioning hypotheses might argue. However, Wolf (1985) demonstrated that odd individuals may stay at the edge of groups in order to escape more easily, once a predator has detected the group.

Predator swamping Assuming a predator will eat grouped prey until satiated, if the FSH is large enough the majority will be left alone. This is essentially the same as the "Dilution Effect" (Bertram 1978). Traditionally, the center of the group is thought of as the best location because predators attack flockers on the edge first. On the other hand, if the predators are attacking the region of highest density, such as a turtle nest site or a swarm of Daphnia (Milinski 1977a), then the center of the group may be the worst location. In short, we need to consider the prospect that different predators prefer to attack groups in different locations. The best place for an anchovy to avoid an attacking tuna may differ from the best location to avoid an attacking pelican. If there is time to assess what type of predator is attacking, then an anchovy's behavioral response should be flexible: i.e. it will depend on the type of predator. However, if there is little time for the anchovy to respond, then natural selection may have favored a fixed response in anchovies to take the position which is safest overall.

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Hamilton (1971) predicted that an organism will minimize the "domain of danger" around itself by ducking between neighbors whenever possible. An assumption which underlies this theory is that an organism responds to local density optima rather than an absolute knowledge of where the center or edge of the group exists. The best position, therefore, is not necessarily the geometric center of a group, but the localized center of density. Flockers with exposed flanks, either because they are on the edge or in an interior gap or vacuole, sustain the highest risk. This may lead to an uneven distribution of flockers within the FSH, and at the extreme, the formation of several separate FSHs (see Hamilton 1971). Vine (1971) finds similar theoretical results even when the predator attacks only from the edge of a group (vs. the predator being allowed to appear anywhere such as in Hamilton's model).

12.3 Individual differences in location Several early studies concluded that flockers were randomly dispersed throughout FSH. For example, Radakov (1973) found that all fish have an equal probability of being on the periphery or within a group when a predator approaches. However, several recent studies have found evidence for position preferences within FSH. Jakobsen and Johnsen (1988a) present indirect evidence that the largest individuals in a swarm of waterfleas, Bosmina, are the first to get to the center of the group when threatened (because they are faster swimmers). Several recent studies of schooling fish have also demonstrated individual differences in position preference. Healey and Prieston (1973) demonstrated individual preferences in position among 12 schooling sockeye salmon. Each fish was marked and photographed many times over several days, and the rank order of each fish from front to back was determined. Using Principle Component Analysis, they determined that different fish maintained different positions within the group. Partridge (1978) found individual position preferences in one small school of five saithe. And Pitcher et al. (1982b) also concluded, on the basis of Principal Component Analysis, that individual preferences existed in their study of ten mackerel. Interestingly, these differences seemed to disappear when the school was under attack, perhaps because individuals were exhibiting protean displays (Humphries & Driver 1967) which lead to random positions within the group. Unfortunately, none of the above studies adequately addressed the question of why there were nonrandom distributions within groups.

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12.4 Differences in selection Krebs and Davies (1981) describe three causes for individual differences in behavior: (1) a variable environment, (2) phenotypic differences, and (3) the behavior of others. It is important to examine all three of these causes when evaluating selective forces relevant to grouping. Differences in the environment within groups (e.g. temperature or the probability of food acquisition or predation) can be important selective forces which may lead to heritable behaviors within a group. McFarland and Moss (1967) found that there was a decrease in oxygen at the center of large schools of striped mullet, Mugil cephalus (see also McFarland & Okubo Ch. 19). Differences in size, sex, and color of individuals may also account for different optimum positions within a group. Lastly, the best behavior to pursue at a particular time depends on the behavior of others. This is especially true when considering groups, in which all behaviors are dependent and thus measured in relation to the position/behavior of others. Although most adaptionist models assume that predators preferentially attack prey located alone or on the outside of FSH, few studies have actually assessed this (except see: Milinski 1977a,b; Jakobsen & Johnsen 1988a). In some cases, fish at the center of the group may be at greater risk because they become the stragglers as the group breaks up (Parrish 1989). Ideally, it should be possible to obtain enough data to determine "danger isopleths" within a group so that we could test where choosy flockers (those most likely to exercise their preference) position themselves based on past predation pressure. To determine which areas of the group are generally more advantageous for foraging, individual rates of food intake must be measured as a function of food distribution. It is also important to estimate the total amount of food eaten, as opposed to simple foraging attempts, which may not give a good indication of food consumed (Keys & Dugatkin 1990). Major and Dill (1978) found that the front of the school is the best place to be to get the most food in predatory groups. Krause et al. (1992) also reported that fish in the front of a school obtained more food than those in the rear. Similarly, Keys and Dugatkin (1990) reported that starlings at the edge of a feeding flock obtained more food than those at the center.

12.5 Differences in motivation "Causation does not indicate adaptiveness and functional analysis does not reveal causation" (Colgan 1986). In showing adaptation, as when proving a case in court of law, it is not enough to establish that the individual was at the scene of

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the crime and had the means, it is important to establish the motive. When applied to positional benefits within an FSH this caveat might be summarized as: even if difference in position and selective pressures within a group have been demonstrated, one has not conclusively demonstrated a function. Positional differences within a group may be due to lack of mobility within the group, or nonadaptive reasons, such as activity levels. Romey (1996) showed that individuals who moved faster than others, but otherwise followed the same movement rules, might, in a simulation model, end up at the edge of a group, much as a faster electron ends up in the outer orbital of an atom. So the rule of thumb for a hungry individual may not actually be to move to the edge per se, but to simply raise its activity level. Hunger, fear, aggression, and sex account for most of the immediate motivations of an organism (Colgan 1986). Although the level and specific response to each of these factors is either learned or "programmed" by natural selection, the current state is dependent on immediate history.

12.5.1 Differences in hunger Differences in hunger may be the single greatest force promoting individual differences in position within a group. There are two primary methods for testing how hunger affects positional preference: (1) short-term satiation levels can be manipulated by experimental feeding, or measured indirectly (e.g. cropdistention in birds, or fullness of the gut in fish), and (2) long-term satiation levels (e.g. lipid storage or overall measures of body condition) can be assessed. There is already some evidence that hunger-level affects the overall spacing of some groups. Hunter (1966) found that schools of juvenile jack mackerel grouped more tightly after feeding. Morgan (1988) also found a relationship between hunger (as well as shoal size and predator presence) and group spacing in bluntnose minnows. Robinson and Pitcher (1989a, b) also found such a relationship in schools of herring. Romey (1993) and Krause et al. (1992) are some of the first to explicitly address the effect of hunger on location within groups. When half of the whirligig beetles in a group of 20 were kept hungry, they maintained positions significantly farther from the center of the group than the well-fed beetles (Romey 1995). These differences in position disappeared within 24 hours of feeding both groups equally. It was also confirmed that beetles at the outside of the group consistently discovered floating food before individuals near the center of the group. Krause et al. (1992) showed that hungry roach, Rutilus rutilus, are at the front of schools more often than satiated individuals.

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12.5.2 Differences in fear Predation is arguably the major cause for the initial formation of many types of FSH, but may be less responsible for the individual differences which then develop. If flockers mostly stay within a FSH then there will be little difference in the average exposure time to the predator. However, there are certainly different risks associated with different positions within the group. It is this perception of risk of attack that I define as "fear." Differences in phenotype may lead to differences in fear, which may lead to different optimum positions within a group. Alternatively, differences in exposure to predators, or experience, may also result in positional preference as flockers learn to associate location, predator type, and risk. Naive individuals might be expected to be less "choosy" or even risk prone (e.g. Magurran & Seghers 1991). Krause (1993) found that the minnows alerted to danger by Schreckstoff relocated to positions nearer to schoolmates. Schreckstoff is a pheromone released by fish in the minnow order (Ostariophysii) when specific epidermal cells are broken. Other fish in the school are sensitive to its smell and take evasive measures when they sense it. In some cases the minnows group more tightly or leave the group altogether and take shelter elsewhere.

12.5.3 Differences in aggressiveness Aggression can structure groups through dominance hierarchies or through the defense of a particularly advantageous location within a group. In regard to my original definition of FSH, species with a high degree of intragroup aggressiveness would not be considered true FSH congregations, but would instead fall under the rubric of social congregations. Dominant individuals may obtain positions with the best food, least risk, and most access to mates. Satiated whirligig beetles are more aggressive within the group than are hungry beetles (Romey & Rossman 1995). In those groups where there is no clear hierarchy, those individuals that have the highest motivation level at a particular moment may obtain the desired position. Some individuals may not be able to occupy optimal positions, or even enter a group, due to weakness or other inability. Kenward (1978) found out that loner wood pigeons were more likely to be successfully attacked than those in groups, and that the loners were by themselves because they were in poor physical condition. Flockers in poor physical condition may be in the least beneficial location within an FSH. If the center of the group is the best location to avoid predators, then one would expect the strongest individuals to push their way to the center of the group when the group was under attack (e.g. Jakobsen &

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Johnsen 1988a). An exception to this occurs when there is kinship and/or cooperation among the group, for example in groups of bison where the stronger individuals remain on the outside to protect their relatives on the inside.

12.5.4 Experimental manipulation of motives in whirligig beetles Whirligig beetles, Dineutes, are a useful study organism to test some of the predictions that have been raised in this chapter. They are useful because they: (1) exist in two-dimensional groups at the surface of the water, (2) can be easily marked and video-taped from above (Fig. 12.3), and (3) are amenable to experimental manipulation in the laboratory. Individual beetles are not distributed randomly within groups; their position has to do with individual motivations, as well as size and sex (Romey 1993). The relevant selection pressures as a function of location seem to be: (1) a variety of potential predators with different attack preferences, and (2) unequal probability of finding food because beetles on the edge will encounter insect prey, trapped at the surface of the water, first. The effect of hunger, fear, aggression, and sex on positional preference within groups was studied in a series of controlled laboratory and field experiments (Romey 1993). The positions of marked individuals within the group were measured following manipulation of fear and hunger levels. To avoid being consumed by fish, whirligig beetles release gyrinidal, a noxious defensive chemical (Benfield 1972). Individuals that have recently released gyrinidal must perceive a higher probability of predation (i.e. have more fear) because they are left with a lesser supply of chemical defenses against future predators. Therefore, tracking the movements of "fearful" individuals should indicate which positions within the group represent "safety." Fear levels were manipulated by experimentally changing the level of gyrinidal. This involved "squeezing" the whirligigs with tweezers and then comparing them to a control group which was also handled, but not squeezed. Both groups, the squeezed and the control, were marked with different colors and then observed. Subsequent observations showed that there were no significant differences in group position based on differences in the level of defensive chemical, corroborating the observation that fish predators were equally as likely to attack the center of the group as the edge (Romey 1993). Direct studies are underway by the author to determine if fish attacks are equally likely at the edge and center. It would be interesting to note the effect of age on position within the group, since the gyrinidal-producing gland of younger individuals is less well developed (Romey 1993). Sih (1980) has found that some smaller/younger water striders have a greater risk of predation and will choose the location which is safest.

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Figure 12.3. Upper panel: Marking whirligigs allow individuals to be tracked. Lower panel: Whirligigs are videotaped and transferred to computer screen to obtain coordinates.

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N = 11

Inside

Outside

100

Females Males N = 20

N = 17

1001

in

o o

B

m O)

c 3

Inside

Outside

Figure 12.4. Effect of satiation and sex on the position of beetles within a group for 24 beetles in six tanks.

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As predicted, individual differences in hunger-levels were significantly correlated with positional preference. However, rather than all hungry individuals moving to the edge, there was a complicating sex by hunger interaction, even though experiments were carried out in the nonmating season. Experimentally fed females were more likely to be at the center of the group than experimentally fed males (Fig. 12.4). The trend for males was confirmed for measures of longterm satiation (i.e. relative lipid levels per beetle). Males on the periphery had significantly more lipids than those at the center (Romey 1993). It appeared that while female beetles were following the motivation-based predictions, male behavior may have been modified by aggressive encounters. One of the main motivational underpinnings of positional differences within whirligig beetle congregations appears to be aggression. Central males were the smallest; larger beetles remained on the outside of the group. There was a significant correlation between the size of the beetle, measured as length of elytra, and distance from the center of the group. Large males were able to dominate smaller conspecifics and maintain favorable locations.

12.6 Balancing motivations Both the proximate and ultimate fitness of an organism depends on simultaneously balancing a number of factors such as feeding, predator avoidance, and mate selection (Sih 1980; Godin 1986; Dill & Ydenberg 1987; Gilliam & Fraser 1987). The optimal position to avoid predation may be in the center of a group (assuming most predators attack the edge), although the edge might be the optimal location in which to find food. Theoretically, a flocker's position within an FSH should reflect the best balance of these sometimes contradictory motivations. Individuals trying to optimize their fitness would have to strike a dynamic balance between center and edge (Fig. 12.5). The relative importance of each of the adaptive hypotheses mapped out at the beginning of this chapter will vary with the environment (both biotic and abiotic), genes, and motivational level of a flocker. Individuals may also make temporal rather than spatial compromises when balancing selection forces. For example, FSH may tighten during the day when predation is most likely, and then break into looser feeding groups during the night when predation pressure is reduced. The limits of optimality theory should also be remembered, and one should consider the following points when trying to understand why individuals are in different parts of the group: (1) the cognitive requirements of ideal strategies, (2) the relative efficiency of alternative approximations (rules of thumb), and (3) the importance of stochastic factors relative to determinist movements by individuals.

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considering only feeding on dispersed prey v>

I considering only predator avoidance center

edge

center

edge

considering only idator avoidance

considering only feeding on clumped fo>

center

edge

center

edge

Figure 12.5. Several optimization curves for maximizing single factors and their summed curves to the right. Flockers feeding on dispersed food do best to feed on the outside of a group. When feeding on clumped food, flockers do best to feed at the center. Increasing hunger would increase the utility of feeding and the entire feeding curve would be raised. Note that in the upper panel the optimum position depends on the state of the flocker, whereas in the lower panel all members of the FSH compete for the same area, the center. For a similar model see Bertram (1978: 73).

It should be possible to rank each of the above factors in terms of their relative importance to fitness: a "weighted average" of the costs and benefits that could be used to predict the optimal location in a group for an individual of a particular species in a given environment (Fig. 12.5). For example, the energy savings gained in adopting a position to take advantage of drafting might not be as important as keeping a position that enables you to detect and evade predators. In theory, individual fitness is determined by the average of many minute-byminute fitness consequences over a lifetime of choices. However, this reduction-

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ist level of detail should not be necessary (and possibly not relevant to the individual flocker) for an assessment of the adaptive value of individual positions.

12.6.1 En vironmental fluctuations There are many important physical factors structuring FSH (e.g. time of day, season, and temperature). However, most of these abiotic factors affect all of the flockers in a group similarly and do not greatly affect our predictions of how individuals should balance conflicting positional preferences within a group except through their interaction with other motivations such as hunger and fear. One of the most important biotic factors influencing an individual's decisions is the distribution of food. When food is clumped and abundant, the center of the group is the best place for feeding and avoiding predators, whereas when food is distributed evenly, there is a tension between optimal foraging location and the optimum location for avoiding predators. If an individual is on the brink of starvation, it may favor a position which maximizes feeding, even if it also maximizes the chance of predator encounters (e.g. Sih 1980; Gilliam & Fraser 1987). If there is a single optimum location, this should select for increasing competition leading to smaller group sizes, increased aggression, and perhaps even the development of dominance hierarchies. On the other hand, in an environment with dispersed food or small patches relative to FSH size, there may be a natural sorting of individuals between the outside and inside of a group due to differences in food obtained during the previous foraging period. This would lead to larger group sizes, lowered aggression, and a decreased occurrence of dominance hierarchies. As mentioned before, resource renewability is also an important factor in structuring the degree of group sociality.

12.6.2 Genes and chance Differences in phenotype arising from discrete genotypes may have a strong impact on motivation and how flockers balance conflicting demands. Most of these phenotypic differences relate to the relative ability to compete within groups. But differences in ability to utilize a food source are also important (Fig. 12.6). A larger flocker, whether due to genes or previous luck at finding food, has several advantages. For one, it may be less susceptible to predation because of its size. It may also be the winner in aggressive interactions with other members of the group and therefore get priority access to its preferred locations within the FSH. Although flocker behavior usually lends itself to FSH cohesion and thus may be constrained, even canalized to some degree, there is not reason to assume a

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optimize feeding optimize predator avoidance optimize mating

Behavior which balances the optimization rules

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Figure 12.6. A flocker will try to simultaneously balance many factors which affect fitness, such as feeding, mating, and predator avoidance. How it balances these factors depends on its previous experience (hunger and fright), physical environment (temperature, season), and the density of other organisms near it.

priori all flockers are equal. Magurran (1993) has pointed out that differences between individuals should be the rule, not the exception. Alternative strategies between different individuals have been shown to lead to similar fitness levels in non-FSH systems (Gross 1982), and there is every reason to believe that this would also hold true for different strategies within an FSH. Individuality within FSH may take on more subtle aspects, as overt differences in morphology or behavior might attract the attention of predators. Smaller individuals often remain at the center of groups regardless of hunger (Healey & Prieston 1973; Sih 1980). Healey and Prieston (1973) showed that the fish at the edge of a group were most often medium-sized. Their explanation for this was that the outside fish were trying to keep a preferred distance to other fish. However, the explanation for why they preferred a different spacing was not tested. Their data might be explained in terms of balancing the costs and benefits of hunger and fear. The largest fish could be most forceful and take the center. The smallest fish might also choose a non-edge position as well, because of their relatively high predation risk. This leaves the medium-sized fish at the edge, who need food to reach breeding size and are big enough to protect themselves. It is the questions of functional distribution that need to be tested in future FSH studies.

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12.7 Conclusions During the last 20 years a great number of hypotheses have arisen for why animals congregate. A number of theoretical studies for the function of grouping (i.e. Hamilton 1971; Eshel 1978; Rubenstein 1978) spurred the field studies of the 1980s (Bertram 1980; Partridge 1980; Elgar & Catterall 1981; Thompson & Barnard 1983). In this chapter I have made a number of predictions for how a constantly changing environment might interact with individual differences between group members to influence the evolution of preferred locations within groups. I have then described a few of the studies which have tested these predictions, and have suggested some future directions for studying the internal structuring of groups. Hopefully the understanding of dynamics within groups can benefit from the incorporation of the following key questions: (1) What are the differences in selection pressures in different parts of the group? (2) How does an individual's past history and genetic makeup alter how it balances the costs and benefits of conflicting selection pressures in choosing, or being relegated, to a particular location within a group?

Acknowledgments Many thanks to J. Parrish, K. Warburton, W. Hamner, and the behavior/evolution group at Binghamton University (especially A. Clark, T. DeWitt, B. Robinson, J. Shepherd, S. Wilcox, D. S. Wilson, and J. Yoshimura), whose comments and discussion helped refine the ideas in this manuscript.

13 Costs and benefits as a function of group size: Experiments on a swarming mysid, Paramesopodopsis rufa Fenton DAVID A. RITZ

13.1 Introduction Congregation is a common behavioral trait among pelagic crustaceans. The benefits of such swarming behavior are generally assumed to be the same as those proposed for fish schools, i.e. protection from predators, improvement in feeding and foraging efficiency, efficiency in energy expenditure, and reproductive facilitation (Wilson 1975; Miller & Hampton 1990; Ritz 1991). Several studies have indicated that planktonic aggregations serve reproductive functions (gelatinous zooplankton - Hamner & Jennsen 1974; Hernroth & Grondahl 1985a,b; euphausiids - Hanamura et al. 1989). It is much less clear whether congregating also confers more long-term benefits, such as antipredation or foraging, or whether one is traded off against the other (i.e. life before dinner principle). Rigorous testing of the costs and benefits of congregative behavior in aquatic invertebrates has lagged a long way behind that for fish. The reason is partly due to the relatively new realization that the larger so-called planktonic animals are not the passive particles they had formerly been believed to be (Omori & Hamner 1982; Hamner 1985, 1988; Ritz 1991, 1994). For example, many undertake extensive diel vertical migrations that serve to protect themselves from predators in surface waters. Also many have evolved a range of active escape responses which are manifested when a predator attacks (Ohman 1988; see below). Several authors have reported that congregations persist despite turbulent water conditions and predatory attacks (e.g. Wittmann 1977; Kawamura 1974; Modlin 1990). Recent work suggests close parallels between congregations of aquatic crustaceans and fish schools in terms of internal structure (O'Brien 1989), and possibly also of function (O'Brien 1988; Ritz 1991, 1994). Congregations of micronektonic crustaceans display an array of responses aimed at facilitating escape from predators that rival those offish in their complexity (O'Brien & Ritz 194

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1988; Ritz 1991). Swarms and schools of crustaceans display a graded response to predatory threat, the level elicited depending on proximity of the predator and imminence of the attack. At the primary level when the congregation first detects the predator, the immediate response is for the group to condense, polarize, and swim away at increased speed. If this action is ineffective at reducing the threat, a secondary level of coordinated escape techniques is activated. Congregations may split and reform in such a way that confusion of the predator is enhanced. One such tactic is flash expansion in which individuals accelerate away from the center of the school and out of the path of the attacker. In the case of mysids and euphausiids this may involve coordinated tail-flipping by those individuals closest to the point of attack. As a last resort, in the tertiary level response, an uncoordinated vigorous tail-flipping leads to a breakdown of group cohesion. Thus only when all else fails is group structure sacrificed. In a laboratory evaluation of costs and benefits of aggregative behavior in terms of feeding rates in two species of copepods from Lake Tahoe, Folt (1987) concluded that although aggregation was a cost, a benefit was gained in terms of avoiding predation. However, this conclusion does not take into account a number of complicating factors. First, food resources in the field are rarely homogeneously distributed as they usually are in laboratory containers. Second, aggregations probably find food patches more quickly, and feed on them more effectively, than do individuals. Average levels of food concentration probably have little meaning for congregations of micronektonic crustaceans which are capable of rapidly locating high-density food patches and remaining within them until they have been grazed down to unprofitable levels (Price 1989). Waterfleas have been shown to be capable of assessing gradients in food concentration and distributing themselves in accordance with patch profitabilities when food is limiting (Jakobsen & Johnsen 1987). Third, individuals in larger aggregations can afford to allocate more time to feeding and less to vigilance than those in smaller ones (e.g. Lazarus 1979; Godin et al. 1988). Fourth, aggregation size might be adjusted to maximize food capture by group members consistent with minimizing predation risk. If groups are viewed as collections of selfish individuals each attempting to maximize its own share of the resources (Pulliam & Caraco 1984), then it is necessary to focus on per capita costs and benefits to understand the dynamics of congregations. The interaction between two major pressures, e.g. the need to feed and the need to stay alive, and the behavioral outcome when these needs are in conflict have been well studied in vertebrate aggregations (e.g. Milinski & Heller 1978; Pitcher et al. 1988; Helfman 1989). In the case of aquatic invertebrates, the majority of studies on the conflicting requirements of feeding and antipredation have been directed towards diel vertical migration of zooplankton (e.g. Gliwicz

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1986). However, Sih (1980) demonstrated that invertebrate foragers can adaptively balance the demands of the need to feed efficiently and the need to avoid predation when these two factors conflicted. There are few experimental investigations on the influence of swarming behavior in aquatic invertebrates on feeding and antipredation costs and benefits to individual swarm members (Treherne & Foster 1980; Folt 1987; Jakobsen & Johnsen 1988b). In particular, the effect of group size on feeding success of individual swarm members has not been studied. New experiments described here test predictions about feeding success in aggregations of mysids of different sizes under conditions of threat and no threat. Recent work on animal aggregation, and group size in particular, suggests that group size cannot be predicted on a purely optimization basis (Krebs & Davies 1984; Clark & Mangel 1986; Giraldeau 1988). In other words, the evolutionarily stable size is not necessarily one in which average fitness among group members is maximized. Group size is rather the resultant of individual decisions to leave or join. Presumably each individual experiences slightly different levels of external forces (e.g. predation and food abundance) as well as internal motivating factors (e.g. hunger and fear - see Romey Ch. 12 for a more in-depth discussion of both internal and external selective pressures). As Pulliam and Caraco (1984) state, hypotheses suggesting relationships between group size and ecological variables are best tested by investigating costs and benefits to individual group members. Extreme patchiness, or unpredictability, in distribution of food resources should select for large groups, partly due to the benefit of reduced search time for group members versus loners (Pulliam & Caraco 1984). If patches are ephemeral, the benefits of foraging in groups will increase as a function of patch size relative to patch persistence and individual capacity (Clark & Mangel 1986). At the same time, group size should increase as predator encounter frequency increases, due to a variety of antipredator functions of prey aggregation (Bertram 1978; Pitcher & Parrish 1993). This latter expectation is supported by the results of Pitcher et al. (1983), who showed that the median elective group size increased substantially when minnow prey encountered a predator. Individual schoolers appear to be sensitive to group size and make joining decisions based on apparent threat of predation (Hager & Helfman 1991). The same appears to be true in birds (e.g. Caraco 1979). No similar experiments have been conducted on invertebrate congregations. However, Daly and Macaulay (1991) suggested that response to variation in food abundance and predation pressure could account for seasonal differences in shoal size of Antarctic krill. The immense size attained by swarms of Euphausia superba (Miller & Hampton 1989) may thus be a reflection of extremes in patchiness of food and predation pressure.

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Thus the present study was designed to investigate three major questions: 1. Is there a demonstrable "optimal" group size in mysids? 2. How does the optimum change with overall food availability? 3. Is there a group size trade-off between foraging and antipredation? The relationship between group size, individual fitness, and the selective forces of food distribution and predation has been the focus of several theoretical reviews (e.g. Clark & Mangel 1986; Giraldeau 1988). Both of these papers explore various model parameters affecting individual fitness and review published "case studies" of group foraging. However, none of these studies use invertebrates, although there are a number of swarming crustaceans and insects. In this chapter I present some results of group foraging studies in mysids, swarming crustaceans. The experiments were designed to explore the concept of optimal group size relative to both foraging and antipredation. Results from these experiments will be considered in the broader context of costs and benefits to individuals in animal aggregations.

13.2 Study animal The mysid used in these experiments, Paramesopodopsis rufa, occurs commonly in conspicuous swarms (it is a bright orange-red) in shallow nearshore habitats, at approximately 1-5 m depth, on the north, east, and south coasts of Tasmania (Fenton 1985, 1992). By the term swarm I mean an integrated group with clearly defined margins in which members maintain an even spacing from neighbors but are not polarized. Swarms varying from fist-sized spheres to cigar or ribbon shapes occupying several cubic meters (O'Brien 1988b) occur year round in these shallow habitats. Swarm integrity has been recorded at very low light intensities, and there is some evidence that it is maintained in the dark (O'Brien 1987). Although individual size varies considerably within groups, stage of maturity tends to be consistent, e.g. there is segregation between congregations of juveniles and of adults (O'Brien 1987). O'Brien (1988b) reported that in calm conditions swarms of mysids could be found occupying the same position for more than a week, though Wittman's (1977) observations suggest this could be much longer. He found swarms in the same positions over periods exceeding a year. By staining and releasing individuals, he found that congregations were apparently more site-faithful than individual mysids. Swarms of P. rufa characteristically occupy areas immediately above and between fronds of macroalgae and above clear sand patches between clumps of algae. Maximum individual size is about 14 mm. Examination of stomach fullness and contents

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suggest that this mysid is a diurnal carnivore (Fenton 1992; Metillo & Ritz 1993); the most common items found in the gut are crustacean fragments.

13.3 Laboratory conditions In the laboratory, in still water conditions with only gentle aeration, the mysids formed coherent swarms which usually contained all individuals. Group size, ranging from 30 to 500, had no effect on swarming tendency. It was rare to find mysids separated from their nearest neighbor by more than 3-4 body lengths except after disturbance by the fish predator (Australian salmon, Arripis trutta). To simulate patchiness, powdered food (measured as a constant proportion of the biomass of mysids in the tank) was divided into 6 equal portions, each delivered at 5-min intervals. Although each food aliquot spread quickly over the surface of the experimental tank, individual particles absorbed water and sank to the bottom unpredictably, creating both temporal and spatial patchiness. The amount of food captured by members of each swarm was measured after 1-2 hr, by dissecting out and weighing dried stomachs from at least 30 individuals. Average weight of stomachs dissected from mysids starved for 24 hr subtracted from these gave actual quantity of food. Preliminary experiments had shown that a subsample of 30 stomachs give an acceptable reflection of average food capture. Experimental duration was fixed at 30 min so as not to exceed gut passage time.

13.4 Food capture success versus group size Giraldeau (1988) proposed a model to explain individual fitness as a function of group size (Fig. 13.1). When group size is small, additions to the group will cause gross per capita benefits to increase at a decreasing rate, while feeding requirements (costs) increase linearly. This is because larger groups should find food faster in a patchy environment (the "many-eyes" hypothesis - e.g. Pitcher et al. 1982a). Net benefit per individual reaches a maximum at some intermediate group size: the optimum size («*). At this point, the benefits of many eyes equals the costs of many mouths. After this, any further increase in group size results in declining net benefit to the individual. If food capture success is used as a dimension of fitness, then aggregation might be expected to lead to increased efficiency of foraging and feeding up to the point at which increasing competition for available resources begins to reduce the per capita share, and ultimately individual fitness. I selected to test this model empirically because the implicit assumptions apply to a wide range of animal congregations. Giraldeau's model (1988) would predict that food capture per unit time per individual should increase as mysid swarm size increases, and then decrease

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"many eyes = many mouths"

too many mouths

Net benefit

\

n*

Group size Figure 13.1. Model of the hypothetical relationship between net benefit per individual and group size, n* is the optimum group size at which net benefit is maximized (modified after Giraldeau 1988).

again as swarm size continues to increase. In this set of experiments, groups of 30, 50, 100, 150, and 200 mysids were introduced into an experimental tank and fed at the rate of either 5% or 25% biomass. After 30 min, food captured by a subsample of 30 individuals was measured. At both levels of food density the shape of the relationship between swarm size and food capture approximated that in Giraldeau's model (Fig. 13.2). When fed at 5% biomass, individual capture success was low but did change as a function of group size (ANOVA, F — 2.75, df = 4/35, p < 0.05; Fig. 13.2). At the higher food density (25%), capture success was markedly higher for all swarm sizes, and there was a highly significant effect of group size on individual capture success (ANOVA, F = 6.47, df = 4/40, p< 0.0005). Under laboratory conditions, it appears that there is an optimal swarm size according to the predictions of Giraldeau's model (1988). When food was plentiful, individuals in intermediate-sized swarms captured more food than those in smaller or larger ones. At the smallest group size (30 individuals) foraging efficiency may have been affected by search time. Although the absolute amount of food per individual was constant, relative patchiness increased as a function of decreasing swarm size, because tank size remained constant. In essence, swarms of 30 mysids may not have had "enough eyes." Interference competition may have decreased individual foraging efficiency in the largest swarms. (Note, however, that the possibility that ingestion rate increased up to a maximum as a func-

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Swarm size Figure 13.2. Relationship between food capture success, expressed as mean dry weight of food in mg per 10 stomachs and swarm size at two feeding regimes: (A) 5% biomass; (B) 25% biomass. Trend linesfittedby eye. Vertical bars represent standard error. tion of swarm size after which it remained constant [as in Krebs 1974] cannot be discounted since the decrease in capture success by swarm size 200 was not strongly significant.) The presence of more neighbors, as a function of patch profitability, may modify an animal's "choosiness" in favor of maximizing intake (Clark & Mangel 1986). When food was plentiful (e.g. 25% of biomass)

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the distribution of intake may reflect straightforward costs and benefits of group size (i.e., Fig. 13.1). However, when food was scarce (e.g. 5% of biomass), increased competition in medium-sized groups would lead to higher intake in the short term (in essence, a scramble for resources), shifting the peak intake rate to the right (Fig. 13.2). Although there is strong evidence that social groups forage more successfully than solitary individuals (e.g. Pitcher et al. 1982a), it has not often been established that actual food capture success is enhanced (Ranta & Kaitala 1991). These results demonstrate for the first time differential food capture success in different sized aggregations of aquatic invertebrates.

13.5 Swarm volume in different feeding conditions We noticed that after feeding, mysid swarms tended to rapidly become more compact. There is experimental evidence that satiation affects group density in fish (Hunter 1966; Robinson & Pitcher 1989a,b). It may be that this represents a trade-off between maximizing interindividual spacing for foraging versus antipredation. To quantify this response, different numbers of mysids were introduced to an experimental tank and fed at the rate of either 5% or 25% of biomass arbitrarily selected to represent low food or adequate food conditions. Volume of the swarm could readily be estimated by reference to a 5 cm X 5 cm grid on the side of the tank and a similar grid on top of the tank, both of which were simultaneously visible to the observer by means of a 45 degree mirror. Swarm volume was recorded every 5 min during the experiment. In every case, when fed at 25% biomass, swarm volume decreased, on average by 48%; however, when fed at 5% biomass, swarm volume increased, on average by 33% (Fig. 13.3). This would seem to indicate that swarms fed at low food densities did not satiate, even at the small group size. Therefore, group density reflected hunger level as the overriding motivation. At higher food densities, individuals apparently became satiated, and group density may reflect antipredation as the principal motivator. To test whether swarms feeding at 25% biomass were satiated, food capture by individuals of a swarm of 100 fed at 25% biomass was compared to that of one fed 5 times this amount. There was no significant difference (Mest, t = 0.266, df = 19, p > 0.05). Dispersal of aggregated individuals in low food conditions has been reported by several authors (fish - Keenleyside 1955a; Hunter 1966; Robinson & Pitcher 1989a; waterfteas - Jakobsen & Johnsen 1988b). Mysid swarms are also reported to become more diffuse and to sink closer to the substrate at night (Wittman 1977), though this may be a response to relaxation of predation pressure. The fact that swarms become more diffuse when food resources are limit-

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Swarm expanded 50

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Swarm contracted Feeding regime:

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Figure 13.3. Changes in swarm volume under two feeding regimes, i.e. 5% and 25% biomass. Swarm volume change is expressed as initial/final. Numbers above the histograms, i.e. 50, 100, 150, 200, are swarm sizes. ing, as the present results show, may herald an eventual split if conditions do not improve. This may also be the reason why swarms fed at 5% biomass showed only a weak effect of group size on capture success.

13.6 Food capture versus swarm size in the presence of a threat Although individuals in smaller groups should achieve satiation more quickly than those in large swarms, when a predator threatens, the per capita risk in small swarms is high relative to individuals in larger groups. Thus, there is a conflict in predictions of optimal group size: foraging for limited resources would tend to push the optimality curve (Fig. 13.1) to the left, while antipredation pressure would push it to the right. Therefore, if food is scarce or patchy, individuals may gain protection by congregating when there is a predatory threat, at a cost of capturing less food. However, because the risk of predation is spread across more members in larger groups, individuals in large swarms may continue to forage in the presence of a predator. To examine the relationship between foraging rate, predator threat, and group size, food intake of 100- and 500-member mysid swarms in the presence of a fish predator was assessed. The predator was introduced into the experimental tank

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and allowed to acclimatize for 12 hr. After 2 hr the tank was divided into two compartments with a temporary partition and the mysid swarm was introduced into the unoccupied compartment 10 min before the experiment started. At the start of the experiment, food was added at 25% of the biomass of the larger swarm, at intervals in the manner described above. Control experiments were carried out in the same way except no fish was present in the tank. Both predator presence and swarm size exerted a highly significant effect on food capture (2-way ANOVA, F = 29.64, 73.84, p < 0.0005, df = 1/32; Fig. 13.4). Both of these effects were driven by changes in food intake of small swarms as a function of predator presence. In the presence of the fish, capture success decreased significantly in small swarms (Student Neuman-Keuls, q = 4.39, p < 0.05). Dinner was traded off for life. By contrast, average food capture by mysids in large swarms was not affected by predator presence, but remained virtually constant across the treatment. This may be a reflection of lowered individual risk such that hunger became the most important selective force determining individual behavior. It is interesting that individuals in large swarms were able to capture more food relative to small swarm members. This may be a function of increased scramble competition (i.e. decreased choosiness) in a relatively more patchy environment (i.e. food was 25% biomass of the 500-member swarm for all trials). Compare, for instance, the intake rate of 30-member swarms fed at 25% biomass with 150-member swarms fed at 5% biomass (Fig. 13.2). Alternatively it may be that large-swarm individuals can afford to allocate more time

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to feeding (Magurran & Pitcher 1983). My own unpublished observations show that mysids in smaller congregations swim straighter paths than those in larger ones. The more sinuous paths of the latter presumably reflect attempts to maximize food capture whereas straight paths may reflect a greater alertness to danger.

13.7 Discussion There is good reason to suppose that optimal group sizes do not normally exist in nature (Sibly 1983; Clark & Mangel 1984; Pulliam & Caraco 1984; Clark & Mangel 1986). Most workers have found that in field situations groups are larger than predicted (although most studies have been on mammals or birds; see review in Clark & Mangel 1986). This can be explained on the basis that optimally sized groups are unstable because they will attract individuals from other suboptimal group sizes (i.e. groups < «*). This argument depends on certain assumptions of the "ideal free" model proposed by Fretwell and Lucas (1970), namely that individuals are of equal competitive ability, and that each is free to choose to feed where it can maximize its individual fitness. In practice, these assumptions are probably often violated; nonetheless the ideal free concept seems to be robust for a wide variety of situations where animals in groups are competing for limited resources (Milinski & Parker 1991). Both Clark and Mangel (1986) and Giraldeau (1988) concluded that groups in nature will not be optimal but instead will be of a size that will not attract solitary individuals: the stable group size ("n(max)"; Fig. 13.5). As groups form,

Fitness

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Group size Figure 13.5. Model of the hypothetical relationship between fitness function and group size, n* is the optimal group size; n(max) is the stable group size (modified after Giraldeau 1988).

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each member can increase its fitness by aggregating with conspecifics up to some optimal group size, n*. Although n* provides maximum fitness for members, the group will continue to attract recruits until it reaches "n(max)" because of the discrepancy between the fitness of loners versus group members. Paradoxically, this implies that members would end up in a group where each individual has no more fitness than that of solitary individuals. However, there are several ways in which group size could be kept from reaching "«(max)," e.g. predatory attack or unpredictable fluctuations in physical parameters. For mysids, a battery of fish predators, as well as excessive wave action or localized turbulence, probably act to break up large swarms. Social means by which groups can be kept from reaching "ra(max)" (i.e. dominance - Giraldeau 1988) are presumably not relevant to mysid aggregations, or other passive congregations. Clark and Mangel (1986) suggested several potential forage parameters affecting not only optimal group size, but also the shape of the fitness curve, including: competition, communication, learning, satiation, and patch persistence. Results from this study indicate that "optimal" group size, measured as maximal per capita food intake, shifts in a nonintuitive direction as a probable function of food availability and scramble competition. The interindividual interactions producing group-level effects have yet to be extensively explored in foraging fish schools or mysid swarms. There is no doubt that predation risk decreases as aggregation size increases (see reviews in Bertram 1978; Magurran 1990), with the obvious exception of a predator with the ability to eat all members. Thus it follows that food capture should be traded off against safety. If so, one would predict that aggregation size in these animals would be in a constant state of flux and that elective size at any particular time would be dependent inter alia on food availability and level of threat. Arguments about maximizing individual fitness and selfish behavior seem to beg the question of whether animals are able to assess the size of their own and other groups. Fish display some ability to differentiate group size, although demonstrated preferences for large groups weaken as absolute group size increases and the size differential between groups decreases (e.g. Hager & Helfman 1991). Although this may occur within social groups of higher vertebrates, it seems unlikely within large swarms of mysids. However, adjustments in group size of this kind can be explained simply on the basis of individuals either capturing an adequate ration or not. Swarming waterfleas have been shown to readily and rapidly distribute themselves in a food gradient according to the available resources (Jakobsen & Johnsen 1987). Romey (Ch. 12) has suggested that individuals need not have a sense of the whole to make adjustments apparent at the level of the group; rather, individuals may simply adjust their activity (or mean velocity) levels. This phenomenon of individual-based behav-

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ior that can lead to group-level response is also explored mathematically by Griinbaum (Ch. 17). Notwithstanding the above, it is possible that even mysids could assess group size by the frequency with which they encounter the margins. This could be one reason why margins are often very clearly defined. The fact that stragglers are readily picked off by predators is obviously another. The need to monitor group size could be acute for small groups separated from a larger congregation. In the field, these small subgroups invariably rejoin the larger congregation if this can be readily located (unpubl. obs.). If monitoring group size is of adaptive significance, this could explain why individuals make frequent excursions throughout the extent of the swarm and are not restricted to a particular region (unpubl. obs.). Alternatively, it could be that mysid congregations continue to attract new recruits until disrupted by topography, predators, turbulence, or other factor(s) and that individuals have no sense of size. Regular excursions through the swarm could be a means of resolving the conflicting requirements of feeding, safety, and mating, in a similar way to that suggested for dipteran swarms by Hamilton (1971).

13.8 Conclusions Much of the theoretical framework for analysis of social interactions within animal groups has been developed from work on vertebrates, chiefly mammals, birds, and fish. Invertebrates, particularly aquatic ones, have been neglected in comparison (see Ritz 1994 for a recent review). The above series of simple experiments demonstrate that social invertebrates can provide valuable data for developing and extending group foraging models. There are very good reasons to expand the study of aquatic invertebrate congregations as models for understanding costs and benefits of social group interactions. They display many of the characteristic group reactions offish (O'Brien & Ritz 1988; Ritz 1991) but in several key respects are much easier to study: being generally smaller they have shorter generation times and less demanding husbandry techniques, they are usually much easier to catch in large numbers, and they are ubiquitous in aquatic habitats (Ritz, 1994).

Acknowledgments I would like to express my gratitude to Sophie Creet and Andrew Sharman for assistance with these experiments. Thanks are due also to Jon Osborn for advice on analysis of video films. Funding was provided through a grant from the Australian Research Council.

14 Predicting the three-dimensional structure of animal aggregations from functional considerations: The role of information LAWRENCE M. DILL, C. S. HOLLING, AND LEIGH H. PALMER

14.1 Introduction A great deal of attention has been devoted to measuring the three-dimensional structure of such animal aggregations as fish and invertebrate schools and bird flocks. Several ingenious techniques, including the shadow method (Dambach 1963; Cullen et al. 1965; Partridge 1980,1981; Partridge et al. 1980), split-frame photography (Cullen et al. 1965; Pitcher 1973, 1975; Healey & Prieston 1973), stereo photography (Symons 1971a, b; Major & Dill 1978; Dill et al. 1981; Hasegawa & Tsuboi 1981; Hasegawa 1982; Klimley & Brown 1983; Koltes 1984; Aoki et al. 1986; O'Brien et al. 1986; O'Brien 1989) and others, have been devised for this purpose. Jaffe (Ch. 2) and Osborn (Ch. 3) detail many of the current methods of three-dimensional data collection. These techniques can generate a large amount of data, sometimes more than one has the time or computing capacity to analyze properly. Partly for this reason, it seems essential to formulate an hypothesis about aggregation structure before collecting the data. Without an a priori hypothesis, one can wander aimlessly through the database, trying out one transformation after another, seeking evidence of structural pattern. With perseverance and luck, something may emerge, but it will be a descriptive analysis of pattern, and no generality may be implied. It is therefore surprising that, in contrast to the many detailed descriptive studies of aggregation structure which have been conducted, very little attention has been given to developing theoretical models of spacing behavior within groups. Such theory is needed to predict structural detail such as the preferred nearestneighbor distance, bearing, and elevation. Without it, we are severely limited in our ability to make sense of all the data which do exist. To be sure, there are lots of mathematical models of aggregations (e.g. Okubo et al. 1977; Okubo 1986; Reynolds 1987; Huth & Wissel 1992). These mostly model the forces of attrac-

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tion and repulsion in relation to the relative position of neighbors, and often are little more than attempts to invent ad hoc systems of equations to mimic the behavior of actual aggregations; biological realism is frequently lacking in these models. To take one example, there is usually no biological rationale given for the inverse square attraction law on which many such models are based, beyond the rather irrelevant analogy to mechanics. There have been only a few attempts to erect and test hypotheses about spatial positioning using functional arguments, i.e. to make predictions from a priori hypotheses concerning what individual animals are trying to achieve by arranging themselves in a structured fashion. One idea that appears in the literature is that fish (and birds) ought to take up positions which minimize energy expenditure per distance traveled (for fish-Breder 1965; Weihs 1973; for birdsLissaman & Shollenberger 1970). These arguments, based on hydrodynamic or aerodynamic principles, predict that animals will assume positions which allow them to take advantage of vortices produced by the animals ahead of them. However, this approach has not been particularly successful at predicting the structural features of real schools (Partridge & Pitcher 1979) or flocks (Badgerow & Hainsworth 1981; Hainsworth 1987). Badgerow (1988) attempted to predict position in Canada goose (Branta canadensis) formations based on the facilitation of visual communication among the birds. According to this hypothesis, facilitating visual communication among members "permits the most advantageous use of the combined orientation experience of the flock" and "communication of orientation experience may be best at a specific angle between birds." Thus, this argument, like the one we will develop here, predicts that the bearing angle from birds to their nearest neighbors will be constant, which was true of some flocks analyzed (Badgerow 1988), but not the majority. However, because the Badgerow hypothesis is not more explicit about what is actually being optimized by the birds, it cannot make quantitative predictions about angular relationships of animals in groups. The purpose of the present chapter is to consider some variants of this hypothesis in more detail, to demonstrate how one can make theoretical predictions against which data on aggregation (or congregation) structure can be tested. It is important to begin by considering the objective of the individual animals who make up a flock, school, or swarm. Such congregations exist for a variety of reasons related to foraging, reproduction, and predator defense, but in every case the individuals in the group should benefit by maintaining the cohesion of the group as a whole through time. This will be especially true in the case of the coordinated movements in a group under attack by a predator (e.g. Radakov 1973; Nursall 1973; Pitcher & Wyche 1983; Hall et al. 1986; Potts 1984; O'Brien 1987), when it will be important for individuals to stay close together,

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and thus to move together. It will therefore be extremely important for individuals to have good information about changes in the behavior (e.g. heading, speed) of their neighbors, so as to react quickly to maintain their relative positions and the integrity of the group as a whole. Thus, assuming that maintaining relative position with minimal disruption (and without collisions) is an objective of each individual, we propose that there exist optimal positions for detecting changes in a neighbor's behavior. We will first illustrate how to make predictions concerning such positions, and then discuss how to test them against particular null models. It is not our purpose to convince the reader that we can accurately predict the positions of individuals in any particular flock, school, or herd (although this may be possible in some special circumstances), but rather to suggest the procedure as a somewhat novel approach to the study of aggregation structure.

14.2 Predicting position The predicted optimal position of an individual relative to its nearest neighbor depends entirely upon the signal which one imagines that individual to be monitoring, and here one is limited only by one's imagination. Even making the assumption that the signal is a visual one, there are still many possibilities. However, three seem most likely, and we will consider these in turn. The first signal candidate is simply the angular velocity (Cl) of some point on the neighbor's body (say the tip of its nose or beak) across the observer's field of view, i.e. across the retina. The importance of this particular signal is suggested by Hunter's (1969) data showing that the latency of response of jack mackerel (Trachurus symmetricus) to a sudden increase in the speed of a neighbor (caused by a remotely applied electrical shock) depends on the angular velocity of the stimulus (see Fig. 2 from Hunter 1969). The angular velocity resulting from a turn of angle 9 by the leader fish can be specified as: O = (vfsin2 /3 - vLsin /3 sin(/3 - 0))/xQ,

(14.1)

where vL = leader speed vF = follower speed 8 = angular deviation between leader and follower headings /3 = bearing angle of leader relative to follower xQ = horizontal distance separating the parallel courses of the leader and the follower (= path width)

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Figure 14.1 shows the geometric conventions used throughout this analysis, illustrating them with two neighboring fish in a school. Note that angular velocity can also be thought of as dB/dt. Equation (14.1), and the others to follow, are derived in the Appendix. The second signal candidate is the rate of change of the solid angle (a) subtended by the neighbor. This signal, referred to as loom (A), is known to be important in other contexts, such as predator avoidance by small fish (Dill 1974). For simplicity, imagine that the solid angle of interest is that subtended by the leader's eye. This can be specified as: a = E sin(j8 - 0)/D2

(14.2)

where E = cross-sectional area of the eye of the leader D = the distance separating the two fish (eye-to-eye)

Then loom = da/dt, and it can be shown (see Appendix) that: E loom = —r sin3 B{ vjsin B cos(fl — 6) + 2 cos B cos 8 sin(/3 — 6)] - 3vL sin(j8 - 6) cos(/3 - 6)}

(14.3)

Figure 14.1. Overhead view of a pair offish, illustrating the geometric conventions used throughout the chapter. Symbols are defined in the text. Thefishare assumed to be traveling along parallel paths until the leadfishturns (by angle 6) and/or accelerates (to VL).

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Our third and last signal candidate is tau (T), believed by some (e.g. Lee & Reddish 1981; Lee & Young 1985) to be used by many animals when timing interceptive actions or avoiding contact with objects. It is the optical specification of the time to collision, at least when the leader's eye cross-sectional area (E) is small relative to the distance between leader and follower (D), and it is geometrically equivalent to 2a/(da/dt). Now consider the simple situation illustrated in Figure 14.1, which is the one we have in mind throughout all that follows: we ask at what bearing angle (j8) one fish (the follower) should position itself behind a leader, so as to be maximally sensitive to any changes in the leader's speed and heading. We make several simplifying assumptions: (1) the school is two-dimensional, i.e. the two fish are swimming on the same plane; (2) each fish in the school (regardless of the school's size) monitors the behavior of only one neighbor, the nearest one ahead, and there is no ambiguity about who this is; (3) the follower monitors some relatively small, discrete part of the leader's body; and (4) the path width (the minimum distance between neighbors; x0) is fixed, probably at a value which allows sufficient time for path correction if the leader changes its heading (this could also be subject to optimization in a more complete treatment). These assumptions are all necessary for mathematical tractability, but could be relaxed without loss of generality. The procedure for calculating the follower's optimal angular position can best be illustrated for angular velocity. We imagine that the follower fish is monitoring angular velocity and ask at which position relative to the leader there will be maximal sensitivity to any change in the leader's speed. To solve for this optimal angular position (/3o t ), we first differentiate angular velocity with respect to vL; this result (dO,/dvL) is designated "Sensitivity." We then look at the limiting case when the fish are swimming along parallel courses (60 = 0) with equal speed (vF = vL). The resulting equation for Sensitivity is then itself differentiated with respect to the angular position of the follower (i.e. 3(Sensitivity)/d/3). Setting this last derivative to zero, and solving for /3, gives the desired result, i.e. /3 o ,. To find the position maximizing sensitivity to changes in leader heading (when the follower is monitoring angular velocity), this procedure is repeated for dCl/dO. Both calculations are then repeated for loom and tau, the latter with a slight variation (see Appendix). The six results of this procedure are shown graphically in Figure 14.2b and summarized in Table 14.1. Notice that the only signal which predicts a single position maximally sensitive to both the heading and the speed of the leader is tau, and that the peaks of these two functions are very sharp (Fig. 14.2b, bottom panel); moving away from a bearing angle of approximately 35 degrees reduces sensitivity drastically. Loom predicts a diagonal position only if the leader's speed is the behavioral

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60

8

90 bearing (degrees)

ca

~0

fcaUI'T

*.

CO

60 bearing (degrees)

c

S

9 = 5°

CO

i

vL = 1.05 vF

bearing (degrees) 60

1°

90

(a) Figure 14.2. (a) The influence of small changes of leader heading (5°) and speed (5%) on the value of three visual cues that might be monitored by a follower, plotted against the angular position of the leader relative to the follower (bearing, j8; see Fig. 14.1). The three cues are (reading from the top): angular velocity (fi), loom (A), and tau (T).

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Predicting three-dimensional structure

a c

60

90 bearing (degrees)

bearing (degrees) 60

90

60

90 bearing (degrees)

(b) Figure 14.2. (cont.) (b) The sensitivity of the three potential cues monitored by a follower to changes in the behavior of the leader (either speed, vL, or heading, 6), plotted against the angular location of the follower (/3). Maxima (minima) indicate optimal angular locations for monitoring changes in that particular behavioral parameter, using that particular cue. The six values of /3o t are shown in Table 14.1.

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Table 14.1. The bearings ()3o t ; degrees) that maximize the follower's sensitivity to changes in either leader speed (vL) or heading (6), for three different signals from the leader that the follower could choose to monitor Bearing which maximizes sensitivity to Signal

Speed

Heading

Angular velocity Loom Tau

90.0 63.4 35.3

45.0 90.0 35.3

parameter of most interest to the follower, and angular velocity only if the leader's heading is most important.

14.3 Testing the predictions The next step is to test these predictions by comparing them to the frequency distributions of bearing angles observed in real animal aggregations. Since tau seemed to be the most promising candidate, we asked whether there was any tendency for bearing angle in real aggregations to cluster around 35 degrees. Given the simplifying assumptions of our model, there are two sorts of aggregations which seem most appropriate for testing this prediction: geese (Branta canadensis) and pelicans (Pelicanus erythrorhynchos) in V-formations and echelons, and bluefin tuna (Thunnus thynnus) at the outer edges of "parabolic" schools (Partridge et al. 1983). These aggregations are essentially two-dimensional, each individual has only one forward neighbor, and the preferred position is clearly not 90 degrees. For V-formation in birds, the best estimate of the interbird angle (/3) is 1/2 the V-angle (Fig. 14.3). Three studies provide sufficient data to allow a comparison with our prediction of 35 degrees (Table 14.2); the fit is excellent for two of the data sets. For tuna on the outer arms of parabolas (which are approximately linear), /3 is about 20-50 degrees (Partridge et al. 1983), again supporting the prediction. The agreement of data and prediction are intriguing, but this is not our main concern. Our objective is to present an approach to the aggregation structure problem, not necessarily to provide the answer; our models are intended to be heuristic rather than predictive. To refine these models, and to reduce the number of simplifying assumptions, it will be necessary to examine a number of other sensory modalities and potential stimuli and to generalize the ideas to three dimensions. It will also be necessary to allow individuals to integrate information

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Table 14.2. Estimates of interbird bearing in two-dimensional flocks (sample size, n, in parentheses). If birds choose a position to most sensitively monitor tau (time-to-collision), /? would be 35 degrees. Note that the single failure has the smallest n. Species

)3 estimate

Source

Canada geese Canada geese White pelicans

36 degrees (54) 17 degrees (5) 35 degrees (45)

Williams etal. (1976) Gould and Heppner (1974) O'Malley and Evans (1982)

Figure 14.3. The relationship between the V-angle of a flock, and the interbird bearing angle (j3), assuming a symmetrical V-formation.

from several neighbors simultaneously, and perhaps to have unobstructed views of their surroundings (e.g. to scan for predators). Finally, we should include the potential for the follower to actually use the information monitored in order to alter its own speed or direction to avoid collision, since the ability to do so will also vary with relative angular position, owing to time lags in the follower's response. Extending the analysis in this way will provide a set of hypotheses which can be tested against the rich empirical database already available.

14.4 Null Models To rigorously test the predictions of the sort of models derived here will also require an appropriate null model against which to compare the data. This is

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rarely done in the aggregation literature, with the exception of Partridge et al. (1980), who compared data obtained from fish schools to those derived from an imaginary school composed of the same number of points randomly assigned to positions in the same volume. Because the two patterns were different, they concluded that their schools had structure of some sort. This represents a maximally random null model, which assumes absolutely no structure to the aggregation. However, it is possible to imagine other, more complex null models which incorporate some constraints on fish position (e.g. a minimum free volume around each fish, but no preferred angular position), and this may be a more biologically realistic sort of null model against which to test the type of predictions about structural characteristics which concern us here. It is of considerable interest that null models of this sort can produce apparently regular angular structure purely as an artifact. Clearly, this will make testing any predictions a nontrivial task. We can illustrate this point with the following very simple null model for twodimensional aggregations. This model assumes only that individuals maintain a constant headway (path width) from their neighbor, i.e. a fish is allowed to be anywhere on one of two parallel lines to the side of its neighbor, but nowhere else (Fig. 14.4a). This is the sort of simple rule of thumb animals might use to reduce the chance of collision. The consequences of this very simple rule are structural regularities very similar to those reported for real schools and flocks. First, the distance to the nearest neighbor (NND) will be shortest at a bearing angle of 90 degrees and will increase as we move away from that bearing (Fig. 14.4a,b). Second, the probability of having a nearest neighbor will be lowest in the sector centered at 90 degrees and will increase as we move away from that bearing, because a constant angular bin size subtends an increasing length of the line (and is thus more likely to contain a neighbor) (Fig. 14.4a). However, when bearing is either very large or very small, the distance (D) to any neighbor in that angular position becomes so great that it will be more likely that some other fish will be the reference fish's nearest neighbor. Therefore, the proportion of nearest neighbors at these extreme angles will decrease, producing a bimodal distribution of frequency of nearest neighbors at different bearings (Fig. 14.4c). Similar patterns have been reported in real schools (e.g., Partridge 1980; Aoki et al. 1986). Patterns emerge if simple rules are applied in three-dimensional space as well, but these are somewhat harder to visualize intuitively, particularly since the angular position of a fish relative to its neighbor must be specified by both bearing and elevation. Consequently, we built a simulation model in which neighbors are positioned at random on a tube, elliptical in cross section (like an idealized fish), centered on the reference fish; the model basically assumes that fish maintain a constant path width from the closest point on their neighbor. We placed 250

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a

Distance to Nearest Neighbour

90° Bearing

Proportion of Nearest Neighbours

90° Bearing Figure 14.4. The two-dimensional null model and the apparent structural features which it produces, (a) The model assumes that fish maintain a constant path width (x0) from their neighbor; (b) resulting relationship between nearest-neighbor distance (NND) and bearing angle (j8); (c) resulting frequency distribution of nearest neighbors at different bearings.

Dill, Hotting, and Palmer

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neighbors on the tube at random, one at a time, measured the resulting relative distance to the reference fish, bearing and elevation of each one, and plotted the relationships between them (Fig. 14.5). One need only compare the simulation results to the data of Partridge et al. (1980) on saithe (Pollachius virens) to see the rather striking similarities (Fig. 14.6). We conclude from this that, as desirable as it may be to do so, it will often be very difficult to test functional hypotheses about aggregation structure, particularly when simple null models can make the same predictions. The problem will be exacerbated if animals are simultaneously monitoring several signals and continuously shifting their angular positions in order to do so. It is critically important, therefore, that we make our functional hypotheses and our null hypotheses as explicit as possible. Only in that way can we hope to develop an understanding of the sensory and functional basis of aggregation structure. Perhaps it is appropriate in a volume dealing with aggregations, and with methods for studying them, to end on a note of caution. We anticipate that there

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180

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Figure 14.5. Results of the three-dimensional simulation model, which assumes that fish position themselves on a tube, elliptical in cross section, centered on their neighbor, (a) Nearest neighbor distance (NND) vs. elevation; (b) NND vs. bearing; (c) frequency distribution of NN elevation; (d) frequency distribution of NN bearing.

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Predicting three-dimensional structure

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Figure 14.6. Data on school structure of the saithe (Pollachius virens), redrawn from Partridge et al. (1980). Arrangement of panels identical to Figure 14.5.

will be instances in which even the best possible level of resolution in data obtained with the most advanced techniques available may be insufficient to distinguish alternative hypotheses. Knowing this in advance could save precious research funds and resources. In other words, we should know exactly what we are looking for (and what we could possibly learn) before we go out into nature to study these aggregation patterns that so intrigue us.

Acknowledgments We thank Ken Lertzman for assistance with the simulation modeling and Marc Mangel for a discussion which helped pull us from a logical morass. LMD was supported by NSERC Canada Grant A6869.

Appendix We derive below simple mathematical relations which describe some of the visual cues seen by a "follower" fish (or bird) who observes a sudden change in

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Dill, Holling, and Palmer

the velocity of a "leader" fish in the school (or flock). We confine our attention to a model consisting of a planar school which we will take to be horizontal. Suppose that leader and follower fish initially swim with equal speeds vF along parallel paths separated by a distance xQ. The follower fish trails the leader by a distance y0 as shown in Figure 14.1. Imagine that the leader makes a sudden alteration of velocity to a new speed vL and/or a new heading 0. We shall refer to this as "the velocity change." The position (x,y) of the leader relative to the follower for time t afterward is given by the expressions x = x0 + vLt sin 9 y = y0 + O L cos e-

vF)t

From Figure 14.1 we see that the bearing, (3, of the leader with respect to the follower, is given by x x, + v,t sin 6 b = arctan - = arctan — y y0 + (VL c o s 0 ~ VF)1 The leader is initially stationary in the field of view of the follower. Immediately after the velocity change, the leader's bearing varies with angular velocity i l given by _ dp _ vF sin2 /3 - vL sin j3 sin(/3 - 8) ~ dt~

x0

It is interesting to note that there are combinations of the parameters for which fl vanishes. Thus, for example, for an initial bearing of (3 = 45 deg, a turning away by 8 - 5 deg, accompanied by a speed increase of 10% by the leader, would be perceived by the follower as producing no change in /3. The perceived angular velocity would be zero. The same would be true if the leader were to alter course toward the follower (6 < 0) while simultaneously slowing. In this case for a bearing of /3 = 45 deg, a turn toward the follower by 8 = —6 deg accompanied by a speed decrease of 9% would be perceived by the follower as producing no resultant angular velocity. It is thus the case that the follower would be insensitive to some velocity changes signaled by the leader's angular velocity alone within what seems like a reasonable range of values. We now examine the question of optimal sensitivity. At what relative bearing is the follower most sensitive to velocity changes of the leader, given angular velocity as the visual cue? We imagine that the follower adjusts its position along a track parallel to the leader's (at a distance x0) in such a manner that the angular velocity perceived is a maximum for the above velocity change.

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First, we will consider a change in heading of the leader by 6 with no change in speed (vL = vF). Under this circumstance ft is simply fte = -^ [sin p - sin(/3 - 0)]sin /3 x0 which has its maximum at j8 = 45 deg + \d, exemplified in Figure 14.2a for a change in heading of 5 degrees. There is a maximum angular velocity (equivalent to a maximum change in angular velocity, since CtQ — 0) resulting from a small change in heading at a leader bearing near /3 = 45 deg. The limiting case (for vanishingly small heading change) is the sensitivity to heading change

where the partial derivative is evaluated for the initial values of 6 = 0 and vL — vF. Sensitivity to heading change has a maximum value at (5 = 45 deg (Fig. 14.2b). Next we consider the case for which the leader's heading is maintained (d = 0), but its speed changes to vvv In this case, shown in Figure 14.2a for an increase of v L by5%,

The maximum angular velocity (= change in angular velocity) occurs at a bearing of fi = 90 deg in this case (Fig. 14.2a). The corresponding sensitivity to speed change also has a maximum at /3 = 90 deg (Fig. 14.2b) and is given by

aO_ _ dvLL

2 sin2j3 x00

where the partial derivative is evaluated as before, for 6 = 0 and vLL = vrr A follower fish using angular velocity to monitor changes in the leader's behavior might well take up a compromise position at a bearing somewhat greater than 45 degrees, in order to be sensitive to velocity changes of both types, since sensitivity to speed change is fully half as great at 45 degrees as it is at 90 degrees (Fig. 14.2b). As noted before, however, these two types of changes can offset one another, in some cases exactly. A second visual cue available to the follower is the loom (A) caused by a change in leader velocity. Loom is the time rate of change of the solid angle sub-

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tended by the leader (or some part of the leader) with respect to the follower. Loom depends sensitively upon the orientation of the object used as a cue with respect to the direction of motion. We will consider the eye of the leader nearer to the follower to be that object in the treatment which follows, and we will model it as a disc of area E lying in the plane determined by the vertical and the leader's direction of motion. The solid angle subtended by the leader's eye, a, with respect to the follower is a—

E sin(/3 - 0) x2 + y2

E sin(j8 - 0) (*o + vLt sin 0)2 + (y0 + (vL cos 0 - vF)tf

This expression, and those we derive using it, are valid only if B > 0, since the nearer eye is only visible to the follower in that circumstance. We adopt the approach used before in treating angular velocity and substitute a constant final leader velocity approximation. The resulting loom we calculate is the rather complicated expression da E A = — = — sin3 jSfv^sin B cos(/3 - 0) + 2 cos B cos 9 sin(/3 - 9)] at x0 — 3vL sin()8 — 0)cos(/3 - 0)} If the speed remains constant, the loom associated with the leader moving at a new heading 0 is Fv Afl = — / sin3 /3[sin B cos(fi - 0) + 2 cos B cos 0 sin(6 - 0) x0 - 3 sin(/3 - 0) cos(/3 - 0)] This expression represents only the loom perceived after the initial abrupt change in solid angle attending the sudden change in heading of the leader. In Figure 14.2a we show the dependence of Afl on bearing for a change in heading of the leader by 0 = 5 deg with no change in speed (vL = vF). Similarly, the loom resulting from a change in leader speed with no change in heading is Av =

3£ 4 r (yL - vF)sm B cos B x0

We plot this function also in Figure 14.2a, for a speed increase of 5%. The corresponding sensitivities of loom to changes in heading and speed are , , dA EvF — = —T- sin 8(1 - 3 sin B) 39

XQ

Predicting three-dimensional structure

223

and dA 3£ . 4 — = — 5 - sin B cos B dv, xi where the partial derivatives are evaluated for 0 = 0 and vL = vF The maximum sensitivity of loom to change in heading in the interval 0 < B < 90 deg occurs at B = 90 deg, and the maximum sensitivity to change in speed occurs at a bearing of B = 63.4 deg, as shown in Figure 14.2b. The last cue we shall examine is the trickiest and requires some development. We first define the relative loom (A), which is the loom divided by the solid angle subtended by the observed object. If two objects moving at constant velocities are on a collision course, it can easily be demonstrated that, in the limit of small solid angle, the time remaining before collision is equal to twice the reciprocal of the relative loom, commonly called tau (T) in the literature. Tau has the dimension of time. We will have use for A as well in our discussion. A I da d A= —= = — In a

a

T=

T

a dt

=

dt

A

Adopting the model we have used above, we calculate T for the two kinds of velocity changes. Using the subtended solid angle and loom values we calculated before, we find relative loom values corresponding to those changes A. = —- = — [sin2 B cot(/3 - 0) + 2 sin B cos B cos 0 - 3 sin B cos(/3 - 0)] ax and A , = _3(v^Lv£)s. a x

Q

Corresponding to these we have

and

We plot Te and TV in Figure 14.2a for the same simple cases as before, namely 0 = 5 deg and constant speed, and a speed increase of 5% with constant heading.

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The sensitivities of T to changes in 9 and v cannot be defined as partial derivatives in the simple manner we adopted for angular velocity and loom. If we evaluate the partial derivatives at 9 = 0 and vL = vF, we find that both sensitivities are infinite. The reason for this is that time to collision itself is infinite when two individuals are on parallel courses, regardless of their speeds. This is quite different from the situation for the angular velocity and loom cues, both of which have an initial value of zero if two individuals have equal velocity. In the case of tau, we must evaluate our derivatives for a small angle 9 = A0 « 1 rather than for 9 = 0. This is not unreasonable, since the headings of the two fish will seldom be perfectly identical, given the sinuous movement of both. Using this method we calculate, to the most significant power in A0, dT

2jCn

1

d9

vF 1 - 3 sin 2 /3

and dT dv,

=

6*Q sin B cos B vl (1 - 3 sin2 B)2

2

Both these sensitivities have infinite values at a bearing corresponding to a zero denominator: 1 - 3 sin^ 0 = 0 The solution to this equation occurs at f3 - 35.26° (Fig. 14.2b). If alternate sensitivities are calculated, by first setting 9 = 0 and then finding the functions of the dominant term for a small speed change, Av, we find the maximum sensitivity values at completely different bearings. However, these are biologically meaningless, since tau is infinite when 9 = 0, and is insensitive to changes in speed, as noted above.

15 Perspectives on sensory integration systems: Problems, opportunities, and predictions CARL R. SCHILT AND KENNETH S. NORRIS

It is more pleasant to present great ideas than to engage in painstaking collection of data. Tjeerd van Andel

15.1 Introduction There is something captivating about large groups of animals moving swiftly and synchronously. A flock of pigeons wheeling over a city park or a silvery cloud of anchovies at the Monterey Bay Aquarium is fascinating and beautiful to people far removed from those of us who study and think critically about animal aggregations and schools. Although scientists have been interested in animal group dynamics for many years, these phenomena have proved difficult to manage quantitatively. Until recently, much that was written about school structure and function was of necessity based on the analysis of very small groups or upon rather subjective or rational arguments. A pertinent example of the latter is Hamilton's 1971 model for animal aggregation, the "Selfish Herd." This results from a progression of logic that predicts that individuals will seek the interior of a group because they are safer there than they would be at the edge. Given his assumptions, the frogs in Hamilton's thought experiment hop into groups and thereby improve their odds. At least one of those frogs will lose due to its lack of nearby neighbors. The "selfish herd" has rightly been an important part of thinking about predators and schooling prey for two decades. But models must be tested against nature and the naturalists among us know that there's more to it than jockeying for the inside track. Among the city pigeons, recognizable individuals change relative positions frequently and move throughout the flock. And now Parrish (1989) has done experiments that indicate

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that the center may be more risky than the edges, at least sometimes. The modeler, the naturalist, and the experimenter each have a role. The aggregating creatures that brought us together are diverse. One way or another we include fanciers of arthropods, cnidarians, and vertebrates both higher and lower. Some of us watch boids (Reynolds 1987) and their allies. We include the evolution and development of intelligence, both animal and machine. Our understanding of the systems that we each study is likely to be a very eclectic endeavor. Only very recently have tools become available that make practical the acquisition and analysis of the trajectories of several to many individuals within a group (see Jaffe Ch. 2; Osborn Ch. 3). New tools mean new ways of asking, and therefore new questions are formed. Toward that end we present some organizing thoughts.

15.2 Sensory integration systems Although there are advanced social congregations which exhibit cooperative foraging and hunting, we suspect that most congregations are an adaptive response to predation in open environments. "Open" here means without structures that allow opportunity of concealment. The scale of openness is important. A meadow may be open for deer but not for beetles. To persist in open environments animals must have other methods than concealment for avoiding predators, at least in daylight (see Hamner 1985 for aquatic examples). Some openspace animals are cryptic or toxic or huge, and therefore they can escape predators. Or they can clump. Simply clumping can reduce risk of predation, at least briefly, by requiring search time of predators, by swamping predators with prey, and by confusing predators when they attempt to attack. That is all well reviewed in Hobson (1978), Pitcher and Parrish (1993), Inman and Krebs (1987), and Romey (Ch. 12). So far there need be nothing social. Animals can congregate at food patches, dark places, watering holes, or sometimes just near objects. Fish of many species assemble at flotsam and fish aggregation devices (FADs). The advantages for predator avoidance mentioned above accrue whether the group is social or not. Groups that are the result of individuals maintaining proximity to each other rather than to some environmental feature have been called "shoals" (Pitcher 1983, 1986), "asocial aggregations" (Norris & Schilt 1988), or "congregations" (this volume). It may sometimes be difficult to tell a social group from an asocial one and some groups may have characteristics of both. There may be a progression or oscillation from one state to another.

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A group of animals all facing the same direction is said to be "polarized." Of course stationary groups may be polarized. Gulls resting on a beach all face into the wind. But we are primarily concerned with groups that move. If animals are to stay together in a three-dimensional fluid medium such as open air or water then they must move on paths that on average over time are parallel. If the paths were not on average similar over time, regardless of how they differed instantaneously, the individuals would separate. This is true of any moving group, even including those in which the paths approach randomness, such as insect swarms (e.g. Okubo & Chiang 1974), in which individual variation in rate of travel helps to maintain cohesion. But if the group is to be very mobile or maintain a regular internal structure, then the paths must more closely approach being instantaneously parallel. If the paths approach being instantaneously parallel, then individual speeds must be similar or individuals will separate. The more mobile and the more structured the group, the more similar speeds and directions of members should be. To stay together in a fluid environment individuals must pay attention to each other (see Dill, Holling, & Palmer Ch. 14). Both actual and simulated schoolers need means to assay the bearing and speed of at least one to several schoolmates. How many neighbors are monitored may depend upon processing limits of individuals, limits of environmental signal propagation (such as water clarity for vision), or upon information-processing architectures within the school. Schooling animals have systems of stimulus and response to facilitate mutual monitoring and station keeping. Such stimuli include body markings that sometimes change with changing environmental and social conditions (Hobson 1968, 1978; Katzir 1981; Guthrie 1986) and may provide reference points for schoolmates. Some schooling and flocking species have bold patterns of contrasting color or value that may make position and changes in body, fin, and wing orientation visible to schoolmates (Norris et al. 1992). Special senses involved in mutual monitoring, especially in three-dimensional aquatic congregations, are not limited to vision, but include acoustic and hydrodynamic systems (Partridge & Pitcher 1980; Hawkins 1986; Coombs et al. 1989). In fact, we should consider all sensory integration systems at least potentially multimodal (see Bullock 1989), lest our higher primate visual bias blind us to other possibilities. For example, flocks of shorebirds (Davis 1980; Potts 1984) may well rely mostly on vision to coordinate their group movements. Dunlin have laterally placed eyes and markings on wings and bodies that probably help mediate their maneuvers. The individual birds may well look down the "chorus line" at the oncoming wave of turning and extrapolate to time their own individual turn, as Potts (1984) suggested. But flock turns also produce a sound (not unlike a

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deck of cards being shuffled) that one can hear propagate across the flock. They might as easily be listening for the oncoming turn as well as watching for it. Known modalities by which creatures pass information range from diffusion of cyclic AMP pulses across aggregating groups of slime mold amoebae (Konijn et al. 1967; Malchow et al. 1978), touching of spines in sea urchins (Pearse & Arch 1969), vision in arthropods, squid, fish, birds, and mammals, and the "distant touch" or Fernstastinn (Dijkgraaf 1963, 1989) of the mechanosensory lateral line (Coombs et al. 1989) of fishes. There are others. Of course living in a group involves costs, including competition for resources such as food and oxygen (see McFarland & Okubo Ch. 19) and the possibility that a large group can often be detected from a greater distance than can an individual. Individual freedom of movement, for example to pursue prey or to avoid predators, may be reduced. Animals in groups must contend with metabolic wastes and possible pathogens and parasites from schoolmates (Moss & McFarland 1970; Geraci & St. Aubin 1979). In large congregations, schoolmates can obscure an individual's view of the world in at least some directions (Abrahams & Colgan 1985). An animal might not see (or hear or smell or feel) a predator or a food source because schoolmates obscure its vision or create noise (turbulence for example) that hides more necessary information. The world can be a noisy place where relevant signals may become swamped (see Griinbaum Ch. 17). On the other hand, an animal that judiciously monitors its schoolmates may be as well or better off than one with an unobstructed view of an attacking predator. By becoming an interacting array of sensors and effectors, animals in polarized schools, and perhaps to a lesser extent nonpolarized aggregators or congregators, are able to gather more information about the world than would be possible for a lone individual. This is so for at least two reasons: First, more sets of eyes (or ears or noses or other sensing systems) can monitor a larger volume than one set can. There is a considerable body of literature that associates larger group size with reduced individual vigilance and increased individual time devoted to feeding or other activities. Examples from fishes include Godin and Morgan (1985), Pitcher (1979), Pitcher and Magurran (1983), Magurran et al. (1985), Magurran and Higham (1988), Street et al. (1984), and Ryer and Olla (1991). Elgar (1989) has provided a recent critical review of similar studies from birds and mammals. Second, groups are also better monitors of the environment because of spatial summation (Norris et al. 1992). Like a nerve cell in which more distal inputs are weighted less than those nearer the decision making "trigger zone" of the neuron (Kandel & Schwartz 1985), an individual can weigh the alarm of the other members in its group by their proximity. Individual error either by oversight or overreaction can be damped by the group.

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Once individuals begin relying on observation of schoolmates to determine their subsequent behavior, the stage is set for an emergent level of organization. Mutually monitoring and responding groups of individuals may be able to constantly process information from a variety of simultaneous and sequential stimuli from many directions (see Balchen 1979) and effect appropriate coordinated responses. We think that these very coordinated groups have the capacity to respond in a coherent way to a sum of the signals passing throughout them. We have presented a model (Norris & Schilt 1988) for the evolution and functioning of integrated animal groups or congregations sensu Parrish, Hamner, and Prewitt (Ch. 1) that we call the "Sensory Integration System" (or SIS). Briefly, we propose to explain the evolution of group function in animal aggregations of one type, usually called "schools" in fish (Pitcher 1983, 1986) but including many kinds of coordinated animal groups. The fundamental tenets of sensory integration systems are: 1. transduction of environmental stimuli external to the group via the sensory capacities of many individuals; 2. propagation of resulting social signals across the group, possibly with attenuation or amplification or other signal conditioning; 3. coordinated group response based on a summation of these social signals from various sources in various directions at any moment. Although there have been some measurements of social signals across groups (Radakov 1972; Potts 1984) and the idea that a group is greater than the sum of its parts is certainly not new, there is no body of experimental work that demonstrates that animal groups operate as information-processing systems the way we think that they do. Here we hope to present a rational structure for experiments to establish the existence of, and to explore the constraints inherent in, sensory integration systems. The sensory integration system is a verbal model intended to describe a group information reception and processing system that we expect to exist in many but not all group-dwelling animals. Although individual cognition may be helpful, it may not be a necessary prerequisite. In sensory integration systems, individuals receive, process, and respond to stimuli from the environment. Their responses may influence (change) near neighbors, which may in turn influence still others. The signal thereby generated may die out or may, by propagation and summation, change the greater group's behavior. Group members may also generate social signals (i.e. internally derived) that propagate through the group. We use the word "integration" in the sense of combining or blending into a unified response. The functional result of such a process is that the individuals in the group can respond in a coordinated manner to stimuli to which many or most of them have no direct access. A school

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member can, given information from many schoolmates, give a very refined response not possible for a lone animal. It is this capacity to acquire, process, and act upon multiple stimuli as a unit that makes it possible for otherwise very vulnerable animals to persist in a world with no place to hide.

15.2.1 The social medium or anchovy ex machina Any physical signal, such as a sound or light, is subject to attenuation over the distance that it travels. The rate of signal attenuation is set by the environment and signal type (Hopkins 1988). For example, sound decay depends upon the sound frequency, the impedance of the medium, and the boundary conditions. Visual signals attenuate depending on medium opacity and available light. Unlike physical signals, social signals need not diminish. Once a signal from the outside is transduced into any of these multi-animal processing systems, it may be either amplified or attenuated by the system. Because the signal must go only from individual to individual (or at most over a few individuals; see Partridge & Pitcher 1980; Potts 1984), the physical environment does not necessarily impose a transmission loss on a social signal across a social medium. For a signal to travel beyond its physical propagation limits, it must be transduced into a social medium. An alarm call, for example, can alert all members of a bird flock virtually simultaneously. Twenty starlings may take off because they all see the same predator or hear the same alarm call but the vast clouds of birds that erupt from disturbed roost sites more likely responded to a signal across a living social medium. As long as the signal gets to the next individual (or few individuals) it need not attenuate at all. Theoretically, at least, a school of fish could set its own sensitivity and signal gain (Schilt 1991). The social signal could travel all the way across the school, regardless of school size. Sensitivity (threshold to produce an intraschool signal) may be high and gain (attenuation across the school) may be low when predators are near (such as at twilight and dawn; see Helfman 1986; Pitcher & Turner 1986). Reduced sensitivity and gain might allow rest and attention to other behavior patterns when the threat of predation is less immediate.

15.2.2 The message and the medium One can see pulses of change in speed and direction traveling across schools of fish, flocks of birds, and other integrated animal groups. The American ichthyologist Breder (1959) first described "waves of excitation" across fish schools. The Russian Radakov (1972) made further observations and some measurements of these disturbances that he said exhibited some of the properties of physical

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waves in that they attenuated, potentiated, and even reflected off tank walls and seemed to cancel each other when they met in midschool. Although some measurements of information pulses have been made from animal groups (for example Radakov 1972; Potts 1984), the problems of data capture and analysis have delayed exploration of the nature of group information transmission. Just knowing what to measure is a challenge, but measures of magnitude, velocity, acceleration, and attenuation of these behavioral waves are needed. Related work with more accessible systems, such as propagated physical, chemical (Field & Burger 1985; Zaikin & Zhabotinsky 1970), and biochemical (Lechleiter et al. 1991) reactions, aggregation and group movement in slime molds and myxobacteria (Devreotes et al. 1983; Dworkin & Kaiser 1985), developmental processes such as mitotic waves (Parisi et al. 1981), physiologic processes such as peristalsis and cardiac control, and ecological phenomena such as epidemic spread may have paved the way for us (Epstein 1991; Winfree 1980; Zykov 1984). Sensory integration systems appear to be members of a large class of phenomena in which discrete pulses of change propagate through a medium. The nature of the sensory integration system is biophysical, and specifically sociobiological. Any measurable change in a medium over time and distance has, at least, a velocity and acceleration of the progress of that change. If we can develop a measure of amplitude of that change, then we can measure potentiation and attenuation. And change in amplitude over time is a waveform and waveforms can be compared directly or by frequency and phase analyses. How does one measure amplitude of a behavioral wave? That depends upon the nature of the change in the medium that defines the wave. In an acoustic medium, sound produces both elastic and viscous disturbances (Kalmijn 1988, 1989) and one makes different measurements of pressure and flow. Perhaps in a social medium (say a school of fish), there are analogs. Both physical (acoustic) and social media have component members (water molecules and fish) that have preferred mutual orientations and preferred nearest-neighbor distances. Water molecules keep station by hydrogen bonds; fish use sensory and motor systems. The physical (water) and social (fish school) media can compress, rebound, and flow in response to disturbance. There may be an amplitude of compression and rebound among school members analogous to sound pressure (measured by change in nearest-neighbor distance) as well as translational changes analogous to viscous flow (measured by change in individuals' speeds and directions). The nature of the mechanical disturbance and its propagation in an acoustic medium depend upon characteristics of the medium, especially density and elasticity. Water is a stiff medium and air is a soft medium. Similarly, a social medium (the school) also has characteristics that might govern propagation char-

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acteristics. Rigid fidelity to some preferred nearest-neighbor distance should produce a stiffer school compared to one that tolerates more variance in nearestneighbor distance (Fig. 15.1). A stiffer school, like a stiffer acoustic medium, would propagate signals more efficiently. A looser school would dampen the signal. Such a change can be expected to occur within the pelagic dolphin social medium from a spread configuration in which diverse social patterns may emerge to a tightened configuration in times of danger (Norris et al. 1994). The preferred nearest-neighbor distance (or "schooling distance"; Norris et al. 1992) is likely to be that distance at which individuals can monitor each other's

B

t

D Figure 15.1. (A) A loosely packed condition with relatively high variance in individual speed, bearing, and nearest-neighbor distances (NNDs). A moderately stiff social medium. (B) A more confused condition such as a school meeting an obstacle or another school (Pitcher & Wyche 1983) or in the process of school formation. Higher variances in individual bearing, speed, and NNDs. A moderately soft social medium. (C) An aggregation with a very high variance in individual speed, bearing, and NNDs. A very soft social medium. (D) A tightly packed and highly integrated condition, with low variance in individual bearing, speed, and NNDs. A very stiff social medium.

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positions, orientations, and signals with most precision and least reaction time (see Dill, Holling, & Palmer Ch. 14 for a discussion of likely signals). Like other aspects of the sensory integration system, the fidelity to schooling distance (here analogous to elasticity) could be varied facultatively, such as when schools tighten ranks when predators attack. Is the amplitude of the social disturbance, however measured, greater for a large stimulus than for a smaller one? Does a more sudden approach of a looming Peregrine falcon produce a larger disturbance in a wheeling pigeon flock? Does a denser plankton patch attract more anchovies? Once appropriate parameters of the information wave (or pulse) are devised and can be measured, then we can investigate the relationships among stimulus, signal, and medium in sensory integration systems. What about the information content of the message? We know that animals can extract information about the source of a signal through a physical medium. A large body of research, reviewed in Buwalda (1981) and Fay (1988), indicates that a fish can assay source position from an acoustic disturbance. The behavioral wave may also transmit clues about its source. If there is a consistent relationship between the source of the social signal and the nature of that signal, then an individual within the school might be able to collect a variety of information about the source from signal characteristics. We have presented sensory integration systems as a grade of social organization that has evolved independently many times in many taxa. In flocks of birds, schools of fish, squid and krill, and herds of mammals, these social systems have in common shared surveillance of the environment, mutual monitoring among group members, and integrated response to multidimensional transductions of both environmental and social stimuli. We consider predation in open environments to be of paramount importance in the evolution of sensory integration systems. This notion is neither unreasonable nor new. However, Barrette (1988) points out that while open environments certainly allow schools to exist and move about freely, that does not in itself mean that predation is causing aggregation and schooling. The point is well taken. Environmental complexity imposes constraints on animal groupings and a very complex environment is not conducive to large integrated animal groups which require freedom of movement. Perhaps these groups tend to occur in open spaces because that is where they can function. Although mitigation of predation is certainly important, it is by no means all sensory integration systems can do; certainly they can also function as coordinated feeding groups. Cooperative hunting and prey herding by fish (Schmitt & Strand 1982; Partridge et al. 1983), hawks (Bednarz 1988), pelicans (McMahon & Evans 1991), social carnivores (Lamprecht 1981; Gittleman 1989), and dolphins (Wiirsig & Wiirsig 1980; Conner & Norris 1982) are examples of preda-

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cious sensory integration systems. Reproduction and migration are certainly also reasons for aggregating and some aspects (spawning or learning migration routes) require behavioral integration.

15.3 Problems and opportunities The study of animal behavior is especially challenging because behavior is often an integrated response to a complex situation. Dealing with groups of animals rather than individuals does nothing to simplify this problem. Furthermore, groups in nature are usually moving, making individual tracking difficult or impossible. Finally, environmental parameters such as light level or current or wind may be constantly and unpredictably changing. With the same group in the laboratory it is possible to stay near, to watch, and to record for further analysis what the animals do. But a captive group is liable to be very different than it would be outside. The laboratory is sure to profoundly influence the individual and thus the social behavior we observe there. Of course the group in the lab also has much in common with its counterpart on the outside. We have learned, and will learn a great deal more, about nature from laboratory observations. In fact the very artifacts that we introduce may turn out to be valuable tools for discovering what matters to sensory integration systems and how they operate. What might at first appear to be demons may prove to be muses.

15.3.1 The effects of context Group size If there is a minimum cell size or minimum number of individuals required for a sensory integration system to operate, then animals in groups of that size or smaller may behave very differently than will members of larger groups. Aside from the issue of minimum school size (above), there may be preferred group size (Hager & Helfman 1991; Ritz Ch. 13) and there may be a maximum size over which a group ceases to be an operational unit of a sensory integration system. Unlike maximum congregation size, upper size thresholds of a sensory integration system may be higher in animals that are cooperatively searching for food. Individuals may make decisions about joining or leaving a "basic school unit" without a resultant group-level fragmentation. Although some schooling animals from very large groups (fish come to mind) seem to be relatively homogeneous, there may be intraschool architectures of individuals or subgroups (see review in Pitcher & Parrish 1993).

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Environment size and shape Those of us that move fish around and keep them in tanks know that fish behave differently depending upon what the tank is like. There may be predictable volumetric relationships to be investigated, such as the relationships between tank size, group size, and polarization (Fig. 15.2). If there is a volumetric threshold for polarizing in a given kind of animal (e.g. species or age), that threshold may be necessarily higher for a larger group. Tank shape may also influence group behavior. Round tanks with a circulating current encourage polarization, thereby reducing damage by collision in obligate schooling species such as anchovies. Tanks with corners may encourage aggregation by stopping individuals in the same place but may discourage polarization by forcing abrupt changes of direc-

Figure 15.2. (A) Fish [i.e. blueback herring (Alosa aestivalis)] collect in corners of a square tank but swim in a continuous mill in a similar-sized round tank. (B) Fish [i.e. striped bass (Morone saxatilis)] swim in a polarized school in a large-diameter tank but are not polarized in a smaller tank of about the same depth. (C) A few fish [i.e. northern anchovies (Engraulis mordax)] do not polarize and remain near walls, while more individuals polarize and mill in a similar tank.

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tion. Tanks with different dimensions but the same volumes may produce different behavior patterns. Ontogeny (life history) Different aged animals of the same species may have different sensory, locomotory, or other capacities, such that they will respond to stimuli differently (Kingsford & Tricklebank 1991). They may eat different things, have different energy constraints, live in different places, and face different suites of predators. Experience early in life may also affect development (Huntingford 1986). Separating the effects of ontogeny and experience on group formation and function may be necessary. Whether the animals being observed are in nature, are wild caught captives, or are raised in captivity may be important factors in interpreting their behavior. Hunger Just as humans may get anxious or irritable if their blood sugar level is low, schools and the individuals comprising them may behave differently when they are hungry. Cellular slime mold amoebae (Dictyostelium discoideum) begin their aggregation sequence when they exhaust their food supply and can be induced to disaggregate on a replenished microbial lawn (Bonner 1967). Hunger may induce more individual (less coordinated) behavior in some animal groups (Morgan 1988; Robinson & Pitcher 1989a) but in animals that rely on the sensory integration system process for feeding, such as anchovies, this may not be the case. Proximity of cover In a heterogeneous environment, cover for prey may also be cover for predators (LaGory 1987; Potts 1983). In some situations nearby cover may cause shorebirds to increase vigilance (Metcalfe 1984). Leger and Nelson (1982) found sandpipers nearer to cover than to the source of an alarm call were more likely to fly when the call was given than were individuals nearer the source of the call. Proximity of cover and its effect on group formation, structure, and response to predators and other disturbances bears further investigation. Experiments with different cover types varying, for example, the size of possible refuges made available (as in Johnson & Stein 1979; Johnson 1993; Walthers et al. 1991) might help determine the cues that some animals may use to decide to school. Light and diurnality Vision is often the most important sensory modality for hunting, feeding, and detecting predators. In many cases behavior and even appearance of animals is linked to diel changes in light level (Hobson et al. 1981). For our experiments

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with real animals, light level and quality are sure to be important variables to measure and control. However, we must also consider that in dark or opaque environments (e.g. the deep sea, murky water, or fog) vision may be aided or replaced by other senses.

15.3.2 Problems of scale The animal groups that we study operate on temporal and spatial scales that sometimes are not conducive to our investigations. The sudden turn or flash expansion that confuses predators confuses us too. For many kinds of animals, time resolution of hundredths or thousandths of a second may be needed to resolve who went where in a coordinated turn. But with fast enough cameras we should be able to capture the data that we need, and the analytical problems are being resolved. Spatial scale may be more difficult. Interactions within a fairly small group are manageable but some of the phenomena we need to investigate may not be visible or may not even occur on a small scale. Just as tank size has a profound effect on sound signal propagation (Harris & van Bergeijk 1962; Parvelescu 1967; Hawkins 1986), the size of an experimental enclosure may affect the propagated social disturbance (Radakov's "waves of excitation"). A social signal may need space to be generated, to propagate, or even to be observed. An example from grammar school physics may serve as illustration of the latter. A Ping-Pong table is completely covered with mouse traps, all set to snap. On each trap is perched two Ping-Pong balls. One more ball tossed onto the table starts a chain reaction that is used as a model for nuclear fission. Ping-Pong balls fly everywhere and those that hit unsprung traps contribute to the disturbance. The directions the balls take appear to be random. But what if, rather than just a Ping-Pong table, the demonstration covered an entire football field. An observer in the press box would see a rather organized phenomenon. In fact there would be a "wave of excitation" that would spread away from the original disturbance. We don't mean that a field full of Ping-Pong balls hitting mouse traps is very much like a sensory integration system. The point is, what you see may depend upon the scale at which you look and some sensory integration phenomena may happen (or at least may be best observed) on a rather large scale. Estes (1967) described a wave of stotting (vertical jumping in place) spreading across the widely spaced individual gazelles on an African plain. Recently Pomeroy and Heppner (1992) presented the analysis of a pigeon flock that they tracked through a 1000 m2 stadium. The larger the scale the more difficult the experimental design, data capture, and data analysis become. If we have to look at 300 fish (for example) instead of

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30, then we and our computers have our work cut out for us. We might try marking a small subset and sampling the group at intervals. However, we will surely need a large group to learn about "wave" propagation, attenuation, reflection, and interference. In many cases these integrated three-dimensional systems are made up of literally innumerable individuals and occupy tremendous, constantly moving volumes. Settling for less than appropriate scale and dimensionality for our research is sure to leave us, like the blind men who examined the elephant, with contradictions and misunderstandings. Unfortunately, huge mobile groups in three dimensions (all over time, of course) create considerable trouble for both data capture and analysis. We would like to submit that there is much yet to be learned from the exploration of two-dimensional and approximately twodimensional systems.

15.4 Predictions So far we have presented a verbal model to describe the transmission of social signals through a congregation, and how congregations might be structured to facilitate and extend that function. However, a verbal model is only as good as the predictions it makes. Accordingly, we lay out a few simple predictions resulting from our thoughts on sensory integration systems. Some of our predictions are more testable than others, although we have tried to provide insight into how field and laboratory work might elucidate elements of sensory integration systems. One way to investigate the relationship between environmental forces and behavior is to compare group structure and processes between schools of closely related animals from different ecological regimes. For example, Gliwicz (1986) compared diurnal vertical migration patterns among conspecific copepods (Cyclops abyssorum) from Polish lakes that have had no planktivorous fish predators for millennia with those from lakes that had planktivorous fishes introduced decades ago and those that have always had such predators. Copepods from lakes with longer predation histories migrate deeper than do those from lakes with recent predator introduction, and those that have not had fish predation pressure for millennia do not migrate at all. The inference that planktivory is the cause of vertical migration is supported. A similar research strategy could help elucidate the evolution of sensory integration systems:

15.4.1 Prediction 1: Sensory integration systems will exhibit homogeneity of appearance and behavior among group members Predator confusion works well only if there are many similar prey. Prey that are different with regard to color (see Ohguchi 1981; Landeau & Terborgh 1986),

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behavior (Hobson 1963) or size (Theodorakis 1989) are more likely to be attacked and killed. Thus, many congregating species are impressively monomorphic (dolphins - Norris et al. 1992; fish-Parrish 1989). Similarity among group members involves behavior as well as appearance. Acting differently from one's schoolmates draws predator attention as much as or more than being a different size or color. But there is a more fundamentally important reason for invariant behavior in schooling animals. We expect sensory integration systems to be made up of modular components (individuals or basic school units) that are for the most part interchangeable. It may be useful to think of them as similar to components of a biological (Bullock & Horridge 1965; Thorpe et al. 1975; Ali 1986; Mackie 1986; Mackie et al. 1988; Hooper & Moulins 1989) or electronic (Caudil & Butler 1987; Rumelhart & McClelland 1986) neural net. We expect animals in advanced sensory integration systems, at least when under attack, to be relatively rule-bound in their behavior. Immediate predation threat will tip the balance between the benefits of individuality and improved sensitivity, speed, and efficiency in group process. A sensory integration system, in order to transduce, propagate, and respond to information usefully must be internally consistent. A novel response from a member would have the effect of disrupting overall group processing to the potential detriment of itself as well as neighboring members.

15.4.2 Prediction 2: Sensory integration systems will resist habituation Groups of animals in open environments are seldom far from predators. Sensory integration systems involved in predator surveillance and avoidance have to respond quickly and unambiguously again and again. In other words, a sensory integration system must quickly reset itself so that it is available for new stimuli. Furthermore, its reactivity must not diminish with repeated stimulation, unless the information gained in the present interaction mediates response in the future (e.g. reassessment of the level of risk a novel predator represents). Isolating a stimulus that not only excites a sensory integration system (initiates a turn, for example) but does so again and again would give us an experimental probe for further examination of information processing in animal groups. If physical decay of the stimulus is very abrupt, as are water velocities for example, then we may be able to develop a stimulus that will directly stimulate only the edge of the school, thereby removing ambiguity as to whether interior animals are responding to the initial stimulus or signals internal to the sensory integration system. We expect that individuals and groups of animals that are dependent on sensory integration systems will not quickly habituate to stimuli that mediate their

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sensory integration systems. Likely stimuli for habituation experiments with schooling species are as varied as the sensory modalities that make up sensory integration systems including mechanical, acoustic, chemical, lateral line, electrical, and visual stimuli.

15.4.3 Prediction 3: Sensory integration systems will tolerate fluidity of group composition and structure To some degree even the most static of animal groups change, at least to the extent that animals recruit or die. In open environments, it is reasonable to expect that schools, herds, and flocks will constantly rearrange themselves or be rearranged by environmental discontinuities, predator attacks, and/or behavior patterns such as feeding or mating. Low group fidelity is known for some groups that are likely to form sensory integration systems (sanderlings - Meyers 1983; urchins - Pearse & Arch 1969; tuna-Hilborn 1991); however, others may have high group fidelity (tits-Eckman 1979; sheep - Arnold & Pahl 1974; quail - Bailey & Baker 1982). Fidelity, like many other behavioral traits, can be variable (yellow perch - Helfman 1984). Because sensory information systems are made up of units acting in concert (whether units are individuals or subgroups), unit identity, and thus fidelity to a specific group, is not as important as learning or knowing how to respond to and process transmitted signals.

15.4.4 Prediction 4: Sensory integration systems will exhibit some degree of regularity in spacing Fish schools have been described as resembling a crystal lattice structure (Breder 1976). Certainly there is a degree of regularity to the spacing and orientation among group members, but real animal groups all vary as to spacing and position over time (see Parrish & Turchin Ch. 9; Dill et al. Ch. 14). Just how regular are the architectures of real animal groups? How regularity varies with environmental and social variables as well as propagation characteristics of social signals might be especially instructive. Some characteristics of school geometry are determined by sensory constraints. Whether a group depends primarily upon vision or hydrodynamic flows (such as those that fish produce by swimming and that the hair cells of their lateral lines transduce) may determine such regularity and preferred schooling distances and positions. Perhaps by experimentally disabling various sensory systems as in Pitcher et al. (1976) or by introducing turbidity or turbulence we could begin to understand the connections between sensory modality and group structure.

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New ways of observing animals, such as the use of infrared light (Blaxter & Batty 1985) and high-speed and high-resolution video and photography, may help us investigate the effects of environmental changes in group structure and sensory integration. Digitizing systems that allow capture and analysis of the paths and rates of individuals are becoming more amenable to the questions we are asking (see Osborn Ch. 3).

15.4.5 Prediction 5: There will be a minimum size below which sensory integration systems break down We suggest that the most advanced sensory integration systems (including pelagic dolphins, some bird flocks, and species of schooling pelagic fish) are likely to have architectures that are (or become under predation threat) relatively regular matrices of animals with relatively little flexibility in regard to interindividual distances and orientations. We expect lower limits on group size and dimensions below which integration will break down. If there is a minimum cell size or "Basic School Unit" (Norris et al. 1992) and that lower constraint is violated, then one would expect a profound change in behavior of both individuals and groups. Phenomena such as "Isolation Syndrome" (Gomez-Laplaza & Morgan 1986) and the "Delius Stress Syndrome" (Delius 1970; Norris et al. 1992) may be common to many obligate schoolers. Minimum cell constraints may also affect the minimum constriction through which a school will flow. Field experiments with wild dolphin schools (Norris & Dohl 1980) indicate that such may be the case with those animals.

15.4.6 Prediction 6: Sensory integration systems will actively process information in the absence of external stimulation. This maintenance signaling may take the form of rhythmic sounds or movements The "pep rallies" of hunting dogs (Estes & Goddard 1967) and "zig-zag swimming" of Hawaiian spinner dolphins (Norris et al. 1985) are thought to be synchronization mechanisms preparatory to coordinated hunting. But some animals may have to maintain synchrony at all times or most of the time. Anchovies are a good mouthful for a wide array of predators. They are much smaller and therefore absolutely slower than their predators. Maintaining a state of "readiness" is a necessary reality. How might they keep their sensory integration systems engaged and operating during lulls in external stimulation? In fish and dolphins at least, individual motion is directly related to oscillating body motions (especially tailbeat amplitude and frequency), and fish have a hydrodynamic sensing system for just that sort of stimulus. Body movements

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and trajectory are directly related. Therefore it is reasonable to suspect tailbeat as a candidate signal for maintaining mutual awareness and synchrony. Of course swimming motions also change mutual orientations and nearest-neighbor distances. Resulting changes in subtended retinal arc, revealed or hidden markings or flashes from neighbor's sides, could also provide visual maintenance signals. More urgent signals may somehow overlie the tailbeat carrier signal. For static sensory integration systems, such as resting fish schools, subtle combinations of tail and median fin pulses will not only keep fish stationary but may send the necessary hydrodynamic signals for sensory integration system maintenance. Regardless of sensory modalities and mechanisms involved, we predict that there will be a rhythmic cadence of signals, often related to locomotory movements, that keeps the mutual monitoring system engaged and operating.

15.4.7 Prediction 7: Although there is much convergence in the evolution of sensory integration systems among diverse taxa, phylogenetic differences will be evident Some kinds of animals are more dependent on the group than others, each having a unique set of energetic, reproductive, and other constraints. For example, both anchovies and pelagic dolphins are dependent on their schools for protection, but anchovies are filter-feeding spawners that live most of their lives in closely coordinated and relatively homogeneous groups while dolphin schools are much more loosely structured groups that permit mammalian social patterns. Mammal herds, whether on land or at sea, must allow for mammalian processes. Some adults are encumbered by young calves. The social system must allow for courtship and competition, birthing and care of young, group defense, and sometimes hierarchies and kin groups. Sensory integration systems, which call for uniformity and order, must coexist with other aspects of animal life. Groups with more complex and stratified social patterns must not only make room in the school for those patterns, but may often use the structure of the congregation to further them. Therefore, mammals and some birds, at least, are likely to present more variance in individual, and perhaps group, behavior than are more homogeneous, size-segregated congregations. The place of individual cognition across the spectrum of sensory integration systems has yet to be worked out. In some cases, such as the repeated turning of anchovies to low-frequency impulse sounds (Norris & Schilt 1988; Schilt 1991), individual response may be reflexive. Certainly animals with high cognitive capacity, including ourselves, may sometimes also respond reflexively. Some of the events which sensory integration systems mediate, such as attack avoidance responses, may not allow time for cognitive processing. On the other hand,

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cooperative hunting (Bednarz 1988; Conner & Norris 1982; Estes & Goddard 1967; Lamprecht 1981; McMahon & Evans 1991; Partridge et al. 1983; Schmitt & Strand 1982; Wursig & Wiirsig 1980) and predator inspection (Pitcher et al. 1986), which may allow or require more flexibility and decision making, may well involve higher cognitive processes.

15.5 Conclusions We are fortunate to be working at a time when methods and tools are becoming available that will let us explore some of the ideas we have presented here. We are doubly fortunate to have colleagues with the diverse backgrounds and talents that are required to address these issues. Among us we can bring to bear the skills, methods, and points of view that we will need to understand these fascinating systems. The mathematical-modeling and information-processing issues that we have suggested here will have a long wait indeed if they are left to us of the field glasses and snorkel set. Aside from the inherent beauty and charm of these animal groups, there are a number of opportunities for practical applications of sensory integration research. Understanding the systems that govern group movements can lead to systems for directing group movements. For example, there may be contributions to the design of industrial water forebays and intake systems to direct schools of fish away from turbines or to cause them to move along escape routes. Fishing gear and techniques might be improved to increase catch efficiency or reduce bycatch through escapement of nontarget species and sizes. The stress of school disruption, for example, may increase the kill of dolphins in the pelagic tuna seine fisheries of the eastern tropical Pacific Ocean (Norris et al. 1978). Understanding the relationship between environmental structure and predation can assist in habitat enhancement. Changes in prey vulnerability with ontogeny in different habitat types could help inform fishery management decisions. Fish aggregation devices (FADs) might be improved. Understanding the lower limits of size of the functioning school ("the basic school unit") might assist curators of schooling animals for either research or display. Architectures made up of individuals and subgroups within schools and the processing characteristics that they produce might be of interest to information scientists. There are many other potential applications. But the grand scale of the diversity of these phenomena is an especially seductive enticement. Swarms of mycobacteria move across the microscopic landscape and stream toward food patches (Dworkin & Kaiser 1973). How does that compare (in structure, function, mechanism, and evolution) to coordinated anchovy feeding? Shimkets and Kaiser (1982) describe "ripples" of "rhythmi-

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cally advancing waves of cells" that "arise spontaneously during the aggregation of Myxococcus xanthus," a bacterium. Do these waves contain sensory integration system elements similar to Radakov's waves in fish schools? We present these ideas in the hope that some of them will serve as points of departure for the formulation of hypotheses, design of experiments, and interpretation of results in our exploration of sensory integration systems. Toward that end we commend us all to the painstaking collection of data.

Acknowledgments The authors would like to thank the original conveners of the meeting that precipitated this book for the opportunity to contribute. The manuscript was greatly improved by comments from Drs. Ted Cranford and Lori Wickham, two anonymous reviewers, and editing by Dr. Julia Parrish.

Part four Models

16 Conceptual and methodological issues in the modeling of biological aggregations SIMON A. LEVIN

16.1 Introduction In the past two decades, there has been a growing recognition in ecology of the problem of scale. This generalization is especially true in the study of schooling, herding, and swarming, in which there is an inherent duality in scale between individual behavior and group and population level dynamics. Steele and others (Steele 1978; Haury et al. 1978; Levin 1992) have pointed out that our measurements and perceptions of pattern are conditioned by the perspectives we impose through our scales of description. At any scale of resolution, we average dynamics that take place on faster scales; the strategy is analogous to that used by other organisms in their evolutionary responses to variability. Indeed, it is clear that not every fine-scale detail is relevant to understanding phenomena on broader scales and that inclusion of unnecessary detail only obfuscates understanding of the mechanisms underlying patterns of interest. The central problem is to determine how information is transferred across scales and exactly what detail at fine scales is necessary and sufficient for understanding pattern on averaged scales. The problem of how information is transferred across scales cannot be addressed without modeling. In relating behaviors on one scale to those on others, one is often dealing with processes operating on radically different time scales, in which much of the detail on faster or finer scales must be irrelevant to those on slower or broader scales. Because decisions about what one can ignore require a quantitative evaluation of the manifestation of processes across scales, a quantitative approach is both unavoidable and powerful. One class of problems in which the quantitative approach has been dramatically successful is when behavior on broader scales can be understood in terms of the aggregate statistical behavior of individual units, as in the dynamics of three-dimensional aggregations. The earliest triumphs of this approach were in statistical mechanics, in which one sought to explain the laws of thermodynam-

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ics in terms of mechanical principles. The German physicist Rudolf Clausius, who invented the word "entropy" (the portion of a closed system's thermal energy that cannot be converted into mechanical work), James Clerk Maxwell, Ludwig Boltzmann, and Josiah Willard Gibbs developed the subject of statistical mechanics and thereby revolutionized the study of thermodynamics as well as creating a fertile area for mathematical investigation. Numerous efforts in ecology have attempted to capitalize on the success of the statistical mechanical approach in ecology. Early work (Kerner 1959; Goel et al. 1971) built heavily on the notion of Gibbs ensembles, but did not relate population dynamics to the behaviors of individuals and was not robust to modifications of the crucial assumption of conservative trophic interactions. The not surprising result has been that the initial considerable interest in this effort soon peaked, and it is difficult to find even the seminal papers mentioned in any ecology book, theoretical or otherwise, today. In contrast, less formal statistical approaches to the movement of individuals, tied heavily to measurable attributes of individual behavior (Skellam 1951), have inspired numerous empirical and theoretical investigations. It is the latter body of research which is the starting point for the discussions in this chapter. The approach of Skellam, and indeed of others before him (Fisher 1937; Kolmogorov et al. 1937), was to demonstrate that many of the broad features of population spatial distributions (in particular, the rates of movements of invading fronts) could be understood in terms of two macroscopic descriptors of individual behavior, the intrinsic rate of natural increase and the variance (diffusion coefficient) of individual movements, even when those movements are assumed to be random, in analogy with Brownian motion. There is nothing in this approach that suggests that individual movements are random. Indeed, that question raises serious philosophical issues regarding even the meaning of randomness. Though individuals clearly use information about their environments in making movement decisions, if that information is known only probabilistically by the modeler or by the organism, then describing it in probabilistic terms (albeit with correlations) is the only sensible option. Furthermore, the goal of modeling is not to recreate every detail, but rather to separate signal from noise. Therefore, the objective is to demonstrate how much detail regarding individual movements is essential to explaining the observed patterns; if those patterns can be explained in terms of only a few macroscopic parameters relating to individual dynamics, then we have learned a great deal about how information is transferred across scales. Two caveats must be made. First of all, the demonstration that observed patterns can be explained in terms of a few simple rules does not mean that those rules provide the only admissible explanation; alternative competing hypotheses

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(consider science and religion) may serve equally well as explanations for patterns, and the resolution as to which should be accepted must rely on empirical tests as well as matters of taste. Thus, the interplay between theory and experiment enters at two points: in the description of pattern, which stimulates and informs the models, and in the experimental testing of hypotheses, which is informed by the model results and subsequently informs a new generation of models. It is also the case that no explanation is likely to prevail at every scale of investigation. For example, diffusive models of the spread of organisms, chemicals, or heat work extremely well at locations close to a source, and poorly at large distances. A similar scale dependence of explanation must be expected as a general rule and may argue for multiple models appropriate for multiple scales.

16.2 The problem of relevant detail The problem of relevant detail (Levin 1991), which must concern both modelers formulating mathematical descriptions and empiricists attempting to characterize complex phenomena, is a thorny one. Too much detail introduces problems of estimation and complex dynamics, problems that may disappear when broader scales of aggregation are used (Ludwig & Walters 1985). On the other hand, too little detail may miss relevant interactions, whether in population structure (Levin 1981) or community structure (Bolker et al. 1995), or in spatial detail (Levin 1992). The amount of detail needed for any particular application poses a research topic of deep importance, and the exploration of this issue leads naturally to attempts to explain the dynamics of aggregates in terms of the behavior of individuals. Perhaps the best case for this approach is in the study of the dynamics of spatially distributed populations. The problems of interest include the spread of invading organisms, discussed earlier; the nonuniform distribution of organisms along environmental gradients and the consequences for the coexistence of species in fluctuating environments; and the aggregation of individuals into groups, the focus of this chapter. These are, indeed, simply separate manifestations of the same problem and yield to similar avenues of attack. The usual approach is to begin from a description in which each individual's position is traced over time, or from a lattice in which the number of individuals in a given cell is followed. These two approaches, the first termed Lagrangian and the second Eulerian, are complementary, in the sense that they are in theory derivable from one another. In both, individuals are important; but whereas individuals are followed in the Lagrangian approach, individual identities have been lost in the Eulerian formulation. In either case, it is useful to let time steps and spatial steps shrink to zero and to derive a continuum description, based on the

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usual equation of diffusion and advection. The approach is a simpler version of the classical approach to fluid dynamics, in which the Eulerian description is embodied in the Navier-Stokes equations. The diffusion of individuals is a simpler problem than the fluid dynamical one and leads naturally to the densitydependent extensions of the next section. The advantages of the continuum approach are those of ease of analysis and elimination of arbitrary spatial discretization; the disadvantages include especially the fact that the integrity of individuals must be compromised. By dealing in infinitesimal individuals per unit volume, one achieves tractability but may alter conclusions in important ways. It is possible in some cases to proceed to continuum limits in ways that compensate for this, but the limiting process may be a delicate and difficult one (Durrett & Levin 1994). Some processes are inherently discrete, whether in space, time, or state; others are continuous. In the first case, the continuum limits must be viewed as approximations; in the second, the situation is reversed. This must guide our view as to the interpretation of the continuum limit, as well as the details of how that limit is to be taken. Indeed, similar issues underlie the alternative approaches (the Ito and Stratonovich calculi) for continuum descriptions of stochastic processes (see for example Ricciardi 1977).

16.3 Interacting individuals: From Lagrange to Euler The classical statistical mechanical approaches to movement deal with ensembles of individuals that do not interact with one another. When individuals interact and those interactions influence movement decisions, the problem is a more difficult one. The problem of schooling or swarming is the prototypical example and has captured the attention of biologists and social scientists alike. As Griinbaum and Okubo have shown (Grunbaum & Okubo 1994; Griinbaum Ch. 17), following the general formulation of Sakai (1973; Suzuki & Sakai 1973; Okubo 1986), one can still begin from a Lagrangian approach, writing a Newtonian description for the acceleration of an individual in terms of the forces acting upon it; these include both external forces, e.g. those due to turbulence and water movements, and internally determined ones, including chemotactic forces (internal responses to external gradients) and those governing an individual's responses to the positions, densities, or velocities of other individuals. Approaches such as this are relevant, for example, to models for the distribution of krill (Levin et al. 1989), whose broad-scale patterns are probably determined by physical forces and fine-scale patterns by orientation to other individuals. The mathematics becomes much more difficult in these circumstances, but it is in theory possible to move from individuals to aggregates, and from discrete space

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to continuous; the advantages are ones of increased understanding of mechanisms and increased analytical power. Griinbaum (1992; 1994) discusses applications of this approach for marine organisms, deriving as a continuum limit a partial differential integral equation, rather than simply the usual partial differential equation of diffusion theory. The reason for the difference is that in the usual theory, individuals respond only to their infinitesimal surroundings, whereas in Griinbaum's model individuals make decisions in terms of sample averages over a neighborhood. Neighborhood size is, in this case, a parameter that is not reducible to an infinitesimal limit. Indeed, in a number of applications it is of considerable interest to explore how the behavior of the system depends on the neighborhood size relevant to decisions or interactions. This problem is of interest not only to modelers and field ecologists, but also to evolutionary biologists. Why do individuals sample (or forage or disperse or lie dormant) over the spatial or temporal scales that they do (e.g., Cohen & Levin 1991)? What are the fitness costs and benefits? These are issues of deep evolutionary content and rich areas for theory. The use of local cues may take a number of forms. Most simply, individuals may respond directly to physical cues, such as the distribution of chemicals. Models of chemotaxis have an honored place in the theoretical literature (Keller & Segel 1971) as examples where sophisticated mathematical models have helped in the understanding of biological phenomena. Griinbaum (Ch. 17) explores the notion that schooling behavior can facilitate the detection of chemical gradients by individuals, through information sharing, while EdelsteinKeshet (Ch. 18) explores trail-following and its consequences for grouping. The obvious complementarity of these approaches demonstrates the complementarity of the underlying biological issues. Beyond physical cues, individuals may respond directly to other individuals, rather than simply to the clues that they leave of their activities. Such direct information is essential to the approaches of Griinbaum, Gueron, Levin, and Rubenstein discussed earlier, but often are difficult to measure. Warburton (Ch. 20) discusses how the interactions of individuals with each other, and the dynamics of groups, are affected by the motivational states of individuals in relation to both internal and external factors. Information of the type they discuss is a rare commodity, invaluable to the modeler, and a key point of interaction between modeler and empiricist.

16.4 Cells to landscapes: From discrete to continuous As discussed earlier, proceeding to continuum limits is a potentially powerful analytical advance, but not always easily achieved. In the case of Griinbaum's

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work, key assumptions must be made that local stimuli approximate a Poisson distribution, and careful analysis is needed to derive the appropriate macroscopic parameters that facilitate the transition to the population level. The problem is perhaps even more difficult when one is proceeding from grid-based approaches to continuum limits: Even when movement is random, the continuum description differs quantitatively and qualitatively from what would be achieved by simply appending diffusion terms to the mean field dynamics. Durrett and Levin (1994) compare the behavior of mean field models (that is, models in which space is ignored and it is assumed that every individual has equal interaction with every other individual) with behaviors of three classes of models that extend the mean field approach to a spatial context: reactiondiffusion equations formed by simply appending diffusion terms to mean field descriptions; metapopulation models, in which interactions are localized but space is not explicit; and interacting-particle models, in which space is explicit and interactions are confined to appropriate neighborhoods. Each approach embodies certain biological assumptions as to what is important; each has unique dynamic features. For example, the reaction-diffusion and interactingparticle approaches incorporate detailed information about spatial relationships of all individuals; the metapopulation approach (known as island models in population genetics) recognizes that localized interactions are important, but assumes that individuals are organized into demes that interact closely with other individuals in the deme, but less so with other demes. Both the interacting-particle approach and the metapopulation approach maintain finite neighborhood size for interactions, recognize individuals as discrete entities, and allow easily for the examination of stochastic effects; in each of these assumptions, they differ from the reaction-diffusion models. The differences in observed dynamics are best considered through examination of particular cases; these are discussed in Durrett and Levin (1994). A case of particular interest involves an interaction between a fugitive species and a superior competitor; the fugitive has an advantage in colonizing newly available space, but is ultimately outcompeted by the superior competitor; the competitive species, in an environment populated only with its own kind, finds resources so depleted that it ultimately goes extinct. In the mean field description, the system of interacting species simply goes extinct; in the reaction— diffusion formulation, the behavior is the same. However, when interactions are localized and individuals are treated as discrete units, as in the other two approaches, long-term coexistence is possible because isolated clusters of fugitive individuals are able to maintain themselves against invasion long enough to permit recolonization of other areas. Extinction does occur locally; but in the classic sense of patch dynamics (e.g. Levin & Paine 1974) this simply creates

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the opportunity for the fugitive to persist globally by exploiting the local variability. This behavior benefits both species, which are able to coexist regionally when they could not locally (see also Levin 1974). Fascinating evolutionary questions are raised by this example and are discussed somewhat in the next section. The central difficulty is that persistence is a population level phenomenon, whereas selection is acting primarily at the level of genes and coalitions of genes termed individuals. It is a challenge of long standing in evolutionary biology to understand group level properties in terms of selection operating at individual levels, and without appeal to group level selection exception where such influences can be demonstrated clearly, as in many parasite host systems (see, for example, Levin 1983). For the system discussed earlier, involving the fugitive species, it is again possible to derive an appropriate continuum limit as cell size becomes infinitesimal; and again, an assumption that on some scales distributions are Poisson proves critical. In this case, the limiting equations take the form of a diffusion-reaction system with reaction terms quite different from those that define the original system. Neighborhood size is a crucial parameter, and the results demonstrate the importance of grouping to the persistence of species. Obviously, there are evolutionary implications, though population persistence must be understood as a manifestation of selection pressure operating at the level of individuals, not groups.

16.5 Evolutionary aspects of grouping Investigation of the evolutionary aspects of grouping can also shed light on the cues that individuals use to aggregate. As the previous example shows, random movement coupled with population interactions that exaggerate inhomogeneities can result in nonuniform distributions of individuals; this is also well known for other systems, for example the classic Turing model of activator (prey) and inhibitor (predator) with differential movement rates (Turing 1952; Levin 1974; Segel & Jackson 1972; Levin & Segel 1976). Selection operates on rates of movements of individuals, facilitating the search for resources or the averaging of uncertainty; and such selection clearly can affect the potential for persistence of species, even though species persistence is not the currency of natural selection. Under other circumstances, there are clear benefits to individuals to be in groups; these include improved resource acquisition, predator defense, and mating success. Under such circumstances, selection can act on the individuals' responses to each other, but there is clear conflict between what is best for the individual wanting to join a group and what is best for the group that the individ-

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ual wishes to join. For example, if there is an optimal group size in terms of what is best for each individual in the group, then a group close to that optimum should seek to exclude others, while solitary individuals should still seek to join (Rubenstein 1978; Giraldeau & Gillis 1985; Levin 1994). How the trade-off will be resolved will depend on a variety of details, including whether the size of the group can be assessed by individuals and whether members of the group can recognize other members; these conditions should be satisfied most easily when group sizes are small and groups maintain coherence. On the other hand, when group sizes are large, group size itself is unlikely to be the critical variable; measures such as density or distance to nearest neighbor must be substituted. The consequence should be that in the latter situation, groups will have no clear definition, and patterns of patchiness will be apparent across a continuum of scales of space and time. In this case, we should expect that large aggregations are really ill-delineated hierarchies of groups within groups within groups, and that only statistical features of spatial distributions have relevance at the broad scales. The fundamental evolutionary issue, then, is to determine which aspects of grouping have selective importance and which are epiphenomena, manifestations of pressures and processes being played out on other scales. Is the aggregation per se an important unit, or simply the result of behaviors selected for their importance at more local levels? What is the scale of selection? Do the front patterns and herd geometries often observed have importance in their global detail, or only in local features? This is complicated of course by the fact that some aspects (such as the responses to neighbors) may have been historically important in the shaping of adaptive syndromes, whereas others (herd geometry) may well have selective importance despite their evolutionary origins as epiphenomena. McFarland and Okubo (Ch. 19) demonstrate that individual oxygen consumption will reduce the environmental oxygen experienced by other school members. This is a classic situation in which what is good for an individual does not translate easily into what is good for the group. How will these conflicts be resolved evolutionarily? McFarland and Okubo, using a three-dimensional advection-diffusion-reaction model, quantify the trade-offs and set the stage for examination of the evolutionary aspects. Most of the modeling reported in this book examines ecological processes and interactions, but modeling offers a powerful avenue to the examination of evolutionary processes as well. One can, for example, consider in models the competition among different strategies for dealing with spatial relations - different levels of averaging, different ranking of cues, different foraging strategies, etc. - and examine the selective elimination or coexistence of multiple strate-

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gies. For problems of grouping, this is almost virgin territory and promises to be an exciting and productive area of research in the next decade. Nearest neighbor or density rules underlie the approach of Griinbaum discussed earlier, as well as those of Gueron and Levin (1995) and of Gueron et al. (1996). In the latter, aggregation patterns of terrestrial vertebrates ranging from single files to wave-like fronts are explained in terms of local rules of interaction, in which individuals adjust their velocities based on assessments of their positions relative to those of their neighbors; the local rules include movements toward others when individuals are isolated, and movements away from them when they are crowded. By modifying the strengths of these simple rules, one can produce an array of patterns mimicking those seen in nature (Scott 1988; Sinclair 1977; Gueron et al. 1996). Under some conditions homogeneous groups can be maintained, but under others these break apart; in the latter case, attention focuses on the group size distribution and to relating observed distributions to rules of fusion and fission of groups (Gueron & Levin 1995). Another approach to the problem of the geometry of the herd is through analogy with viscous fingering (the interface between fluids of different viscosities, Langer 1989); preliminary research has been done by a variety of authors, but this represents work in progress.

16.6 Conclusions The problem of animal grouping poses fascinating challenges regarding the ability to understand aggregation patterns in terms of forces, external and internal, acting upon individuals. From a mathematical point of view, the problems include those of the duality between Lagrangian and Eulerian descriptions, and the appropriate ways to take limits of lattice-based models. Individual behaviors, even undirected ones, can lead to patterns of grouping; these can have consequences for persistence and coexistence, as well as evolutionary implications. The interplay between evolution and ecology can be especially informative in terms of the cues that individuals use to aggregate. The range of problems worth investigating is wide, and the likely payoffs substantial. Modeling provides us with a way to connect phenomena across scales, to study phenomena on inaccessible scales, to explore hypotheses and identify critical interactions, and to isolate which details on one scale are relevant to phenomena observed on others. It is a powerful tool for connecting empirical information at broad and fine scales, as well as a bridge not only between theoreticians and empiricists but also between population biologists and ecosystem scientists.

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The approach emphasized here is one of using individual-based models, which can be related to measurable behaviors of individuals in response to physical and biological cues, to explain patterns that can best be described by remotely sensed visual or acoustic information about patterns. The framework provides an effective way to explain observed patterns, but also a powerful device for understanding evolutionary processes.

Acknowledgments I gratefully acknowledge the support of the Office of Naval Research through its University Research Initiative Program grant number ONR-UR1P-N00014-92J-1527 to Woods Hole Oceanographic Institution. I am also pleased to acknowledge helpful comments by Dan Griinbaum on an earlier version of this paper.

17 Schooling as a strategy for taxis in a noisy environment DANIEL GRUNBAUM

17.1 Introduction One of the most basic problems confronting aquatic organisms is locating favorable regions within their fluid environment that contain appropriate levels of resources such as food, oxygen, and sunlight. Because limiting resources typically have "patchy" distributions in which concentrations may vary by orders of magnitude, success or failure in finding favorable areas often has an enormous impact on growth rates and reproductive success. To locate resource concentrations, many aquatic organisms display tactic behaviors, in which they orient with respect to local variations in chemical stimuli or other environmental properties. Taxes may be based on a variety of cues, including temperature, salinity, chemical constituents such as odorant plumes, and population density of small organisms such as phytoplankton. These material fluid properties are dispersed in the aquatic environment in a non-uniform and irregular way, through the combined effects of molecular diffusion, turbulent transport, and density stratification (Atema 1988). Through these processes, cues for taxis may take on a convoluted, three-dimensional structure, with fluctuations in concentration at both large and small length scales (Nihoul 1981; Monin & Ozmidov 1985). Aquatic organisms attempting to use local variations in material properties to locate patches of resource concentrations thus frequently face a formidable task. Here, I propose that schooling behaviors improve the tactic capabilities of school members and enable them to climb faint and noisy gradients which they would otherwise be unable to follow. A large literature exists on the evolutionary benefits and costs of social aggregative behavior. Social behavior is thought in many cases to confer protection from predation and to enable unsuccessful foragers to exploit resources discovered by fellow group members, while subjecting group members to intensified intragroup competition (Clark & Dukas 1994). The positive interaction of

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social and tactic responses hypothesized here provides an additional mechanism by which sociality could be an evolutionarily favorable strategy. Schools are groups of aquatic animals which are maintained by social interactions and which display synchrony of orientation and movement (Pitcher 1983, 1986). Schooling is thought to result from two principal behavioral components: (a) tendencies to move toward neighbors when isolated (and away from them when too close) so that the group retains a characteristic level of compactness (see Parrish & Turchin Ch. 9); and (b) tendencies to align orientation with those of neighbors, so that nearby animals have similar directions of travel and the group as a whole exhibits a directional polarity. These same behaviors underlie formation of polarized social groups in terrestrial animals, such as avian flocks (Heppner & Grenander 1990; Kshatriya & Blake 1992), mammalian herds (Sinclair 1977; Prins 1989; Gueron & Levin 1995), and swarms of insects such as migratory locusts (Kennedy 1951; Waloff 1972; Baker et al. 1984). The most conspicuous effect of attraction and alignment is to maintain the school as a cohesive and orderly unit. However, if school members are simultaneously attempting to climb resource gradients, these social interactions have the additional effect of propagating the results of individual tactic responses throughout the group. The theoretical results in this chapter suggest that, because of this information propagation, even simple schooling behaviors might improve animals' ability to climb noisy gradients. In this chapter, I focus on schooling in aquatic animals, and particularly on phytoplankton as a distributed resource. However, although I do not examine them specifically, the modeling approaches and the basic results apply more generally to other environmental properties (such as temperature), to other causes of population movement (such as migration), and to other socially aggregating species which form polarized groups (such as flocks, herds, and swarms).

17.1.1 Phytoplankton distributions and taxis Phytoplankton density is a well-studied example of an ecologically important resource which takes on patchy distributions under the influence of advective processes in the aquatic environment. As measured by concentration of chlorophyll, fluorescence, or rates of primary production, phytoplankton distributions are generally found to have significant spatio-temporal variation at both a "micro"-scale (i.e. <10 m and <10 hr) and at much larger scales (Powell 1989). Oceanographic sampling (with micro-scale variation removed by averaging) has shown that phytoplankton densities commonly vary horizontally by an order of magnitude or more at "macro" spatio-temporal scales of >10 km and >10 days (in, for instance, the Southern Ocean: Witek et al. 1981; Weber et al. 1986; the

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Baltic Sea: Schultz et al. 1989; the North Atlantic: Pattiaratchi et al. 1989). Vertical distributions can vary on similar time scales from concentrated layers a few meters in thickness to almost uniform dispersion throughout the mixed layer (>100m). The importance of micro-scale patches of phytoplankton and tactic behaviors to locate them were investigated theoretically by Davis et al. (1991), who also examined the role of turbulence in dispersing patches and increasing encounter rates of consumer and prey. Using realistic movement and growth models for copepods and larval fish, Davis et al. estimated that individuals can move to local peaks within the micro-scale distribution of food abundance over the course of a few hours and that such movements can increase growth rates of copepods and larval fish substantially. Fluctuations at larger scales probably have equally important ecological consequences for pelagic fish such as herrings (Clupeidae) and anchovies (Engraulidae), and for large crustacean zooplankton such as Antarctic krill, Euphausia superba, which are principle consumers of phytoplankton. However, relatively little is known about the tactic capabilities of these filter-feeders and the extent to which they are able to take advantage of large-scale variations in phytoplankton density. For example, Antarctic krill and related species are known from aquarium studies to respond accurately to local phytoplankton gradients and to use them to seek out micro-scale phytoplankton patches several centimeters to several meters across (Hamner et al. 1983; Price 1989; Strand & Hamner 1990). Krill, swimming at speeds in the range of 10-20 cm/sec (Kils 1981; Hamner 1984), would theoretically be able to move to 10 km-scale phytoplankton concentrations in a day or so, long before other physical and biotic factors could disperse them. Yet biomass of Antarctic krill is found to have variable, often very low, degrees of association with phytoplankton concentrations (Witek et al. 1981; Weber et al. 1986; Levin et al. 1989; Daly & Macaulay 1991; see also Rose & Legget 1990). Large differences in gut fullness observed between krill from different schools in the same area (Priddle et al. 1990) also suggest that some schools had difficulty finding food even when phytoplankton concentrations were present. These observations suggest that nektonic phytoplankton consumers face strong evolutionary pressures to improve their tactic abilities.

17.1.2 Bacterial chemotaxis Difficulties in taking advantage of phytoplankton concentration fluctuations at a 10 km scales may stem from the fact that, even when fluctuations are substantial, the large spatial scale means that the average concentration gradient is extremely shallow. A forager thus encounters an exceedingly faint and noisy

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signal as it seeks to climb phytoplankton concentration gradients at these larger scales. Under these circumstances, the search of a nektonic filter-feeder for large-scale concentrations of phytoplankton is analogous to the behavior of a bacterium performing chemotaxis. The essence of the analogy is that, while higher animals have much more sophisticated sensory and cognitive capacities, the scale at which they sample their environment is too small to accurately identify the true gradient. Bacteria using chemotaxis usually do not directly sense the direction of the gradient. Instead, they perform random walks in which they change direction more often or by a greater amount if conditions are deteriorating than if they are improving (Keller & Segel 1971; Alt 1980; Tranquillo 1990). Thus, on average, individuals spend more time moving in favorable directions than unfavorable ones. Although the path of an individual is stochastic and may be very complicated, analysis of the probabilities of transition from one orientation to another often results in simple expressions for the average rate of tactic movement resulting from a particular tactic algorithm (Keller & Segel 1971; Okubo 1986; Othmer et al. 1988, Edelstein-Keshet 1988; Murray 1989). A bacterial analogy has been applied to a variety of behaviors in more complex organisms, such as spatially varying diffusion rates due to foraging behaviors or food-handling in copepods and larval fish (Davis et al. 1991), migration patterns in tuna (Mullen 1989), and restricted area searching in ladybugs (Kareiva & Odell 1987) and seabirds (Veit et al. 1993,1995). The analogy provides for these higher animals a quantitative prediction of distribution patterns and abilities to locate resources at large space and time scales, based on measurable characteristics of small-scale movements.

17.1.3 Social taxis In this chapter, I present theoretical evidence that even the simplest of interactions between social and tactic behaviors, i.e. a superposition of these two types of behavior, confers enhanced capacity for taxis. I do not consider more sophisticated (and possibly more effective) social tactic algorithms, in which explicit information about the environment at remote points is actively or passively transmitted between individuals, or in which individual algorithms (such as slowing down when in relatively high concentrations) cause the group to function as a single sensing unit (Kils 1986; described in Pitcher & Parrish 1993; see Schilt & Norris Ch. 15). I lay the groundwork for testing the impact of social behavior on searching success in the next section by analyzing a simple, asocial bacterial-type taxis algorithm in which small-scale variation of the resource is implicitly included in

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the "random" component of the tactic random walk, and the large-scale variation is represented locally by a constant, uniform gradient of the attractant. With the results of this analysis as a null model, I introduce in Section 17.3 a simulation in which individuals display schooling behaviors in addition to taxis and show that up-gradient motion can be increased by the addition of this social behavior. In Section 17.4,1 present a deterministic nonspatial model of the schooling behavior, applicable within large schools in which most individuals have a large number of neighbors. Finally, in Section 17.5,1 discuss possible evolutionary implications of these results for foraging dynamics of social animals and empirical tests of the social taxis mechanism.

17.2 Asocial searching: Taxis from directionally varying turning rates An animal that cannot directly sense favorable regions must locate them through some sort of trial-and-error process of probing in various directions and modifying course depending on the results. For example, suppose that individuals, searching on a plane surface and moving at unit speed, change their direction randomly at discrete time intervals of At. Suppose further that the individuals are in an environment where the average concentration increases uniformly in the positive x-axis, but where small-scale noise causes the animals sometimes to perceive that concentration is increasing when actually it is decreasing, or vice versa. Then, the directionally varying rate of turning might be described by (17.1) where A0 is the angular change in a time interval At, 6 is the angle with respect to the concentration gradient (the x-axis), and A0O and A6X specify the turn rate at various orientations (Fig. 17.1). rQ and r, are randomly chosen at each step to be either — 1 or 1, so that an individual turns with equal probability to the left or right. The A0O component represents the small-scale "noise" - it causes individuals to make random turns at the same rate, regardless of their heading. The A0j component, on the other hand, varies with orientation and represents the largescale "signal." It is proportional to the rate at which conditions are getting worse, i.e. it is low when the individual is headed up-gradient and high when it is headed down-gradient. A searcher does a random walk in the range of possible heading directions {—IT to TT), but on average it climbs the gradient because it turns away from "wrong" headings faster than from "right" headings. Taxes of this type have been analyzed thoroughly (Alt 1980; Okubo 1980, 1986; Othmer et al. 1988), making them convenient searching behaviors with

262

Figure 17.1. "Bacterial" chemotaxis by directionally variable "step" size in the change of heading angle. Shown are two heading directions, a nearly up-gradient orientation (6a) and a nearly down-gradient orientation (6b), where the concentration of an attracting substance increases in the positive x-direction. An individual changes heading in either direction, right or left, with equal probability (in this example, the increment of da is to the right, or negative-6 direction, and that of 6b is to the left, or positive-6 direction). However, increments in angular orientation are smaller if the individual is oriented upgradient (A0a) and larger if orientation is down-gradient (A0fc). Thus, on average, an individual spends more time moving in up-gradient than down-gradient directions, resulting in up-gradient taxis.

which to compare social to asocial individuals. The long-term behavior of these individuals can be expressed concisely by taking the diffusion limit of the random walk in 6. The present case is a "repulsive" random walk, in which the probability of moving depends only on conditions at the point of departure (see Okubo 1986, for a discussion of diffusion limits and repulsive and attractive random walks). The probability density of orientation angles, p(8,t), evolves according to

Schooling as a strategy for taxis

- p(0,f) - —^ (D(0) p(0,O), f p(0',O dff = 1 dt dtr J_v

263

(17.2)

where D(0) is a directionally varying diffusivity. Equation (17.2) is periodic, i.e. p(0) = p(0 + 2TT), D(ff) = D(6 + 2TT), etc. p(0,O represents the probability at time t that an individual is heading in the direction 0 or, equivalently, the fraction of a large population of individuals with that orientation. The diffusivity has a constant and a directionally varying component, D,

(17.3)

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where d = D{/Do is the relative diffusivity (Davis et al. 1991), a measure of the relative strength of the tactic signal and noise. Small d means that the gradient is heavily obscured by small-scale noise; large d means that the gradient is distinct. The average up-gradient velocity of an individual, as a fraction of individual's forward speed, is U(d) =

,

(17.6)

Equations (17.5) and (17.6) summarize the effectiveness of the bacterial taxis algorithm. Thus when the signal dominates the noise (d » 1), individuals virtually always orient correctly and progress directly up-gradient at nearly full speed (Fig. 17.2). When the noise predominates (d « 1), the angular distribution of individuals is nearly uniform, and the up-gradient velocity is near zero. In a range of intermediate values of d (0.3 £ d < 3), there is measurable but slow movement up-gradient. The question I will address in the next two sections is: can individuals in this intermediate signal-to-noise range with slow gradient-

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climbing rates improve their tactic ability by adopting a social behavior, i.e. schooling?

17.3 Simulations of searching with schooling behavior To investigate the gradient-climbing abilities of schooling searchers, I use a simplified model of schooling behavior. This model omits some of the subtleties of schooling models from the literature, but captures the essentials for evaluating the effect of schooling on taxis (Grtinbaum & Okubo 1994). The key attributes of these models are: (a) a decreasing probability of detection or responsiveness to neighbors at large separation distances; (b) a social response that includes some sort of switch from attractive to repulsive interactions with neighbors, mediated by either separation distance or local density of animals; and (c) a tendency to align with neighbors (Inagaki et al. 1976; Aoki 1982; Matuda & Sannomiya 1980, 1985; Huth & Wissel 1990, 1992; Warburton & Lazarus 1991; Griinbaum 1994). The rules in these simulations are as follows: At each time step, an individual counts the number of "detectable" neighbors (i.e. those within a detection radius, here normalized to 1); individuals more than a unit distance away are ignored (Fig. 17.3). If the number of neighbors is within an acceptable range then the individual doesn't respond to them. On the other hand, if the number is outside that range, the individual turns by a small amount, A03, to the left or right according to whether it has too many or too few of them and which side has more neighbors. In addition, at each time step, each individual randomly chooses one of its visible neighbors and turns by a small amount, A04, toward that neighbor's heading. Over many time steps, the individual tends to align with the average heading of its nearby neighbors. These behaviors can be made independent of step size by expressing them as a = A03/A/, the rate of turning toward and away from neighbors, and /3 = A04/Af, the rate of turning to align with neighbors. The parameters a and /3 can also be usefully thought of in terms of r=— ^ (17.7) a + p the radius of the tightest circle that an individual can make under the combined influence of the two social behaviors. The size of this radius, relative to other characteristic lengths such as the detection range, determines in part the group properties of the school. In addition to this social behavior, individuals retain the same tactic behavior as in Section 17.2. The results of simulations based on these rules show that schooling individuals, on average, move more directly in an up-gradient direction than social

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Figure 17.3. Schematic of schooling behavior. In the simplified schooling algorithm, each individual reacts to neighbors within a unit distance, shown here as a shaded circle. Also shown is r, the radius of the tightest turn that can result from social behavior. If this radius is smaller than the reaction distance (r « 1), then individuals can turn tightly to remain close to neighbors; if it exceeds the reaction distance (r » 1), individuals are not capable of turns tight enough to stay near a neighbor.

searchers with the same tactic parameters. Figure 17.4 shows the distribution of individuals in simulations of social and social taxis in a periodic domain (i.e. animals crossing the right boundary reenter the left boundary, etc.). The taxis parameters, Do = 0.3 and Dx = 0.6, are within the range of relative diffusivity (d = 2) for which up-gradient motion due to bacterial taxis alone is relatively inefficient (U = 0.268, from (17.6)). As predicted by (17.5), asocial taxis results in a broad distribution of orientations, with a peak in the up-gradient (positive xaxis) direction but with a large fraction of individuals moving the wrong way at any given time (Fig. 17.5a). By comparison, schooling individuals tend to align with one another, forming a group with a tightened angular distribution. There is stochasticity in the average velocity of both asocial and social searchers (Fig. 17.5b). On average, however, schooling individuals move up-gradient faster and more directly than asocial ones. These simulation results demonstrate that it is theoretically possible to devise tactic search strategies using social behaviors that are superior to asocial algo-

Schooling as a strategy for taxis

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(b) Figure 17.4. Simulations of social and asocial chemotaxis, at t = 100, N = 64. (a) positions of individuals for the asocial, "bacterial" chemotaxis algorithm; (b) individual positions for the "social" chemotaxis algorithm. The gradient is uniform and increases to the right. Initially, individuals are randomly distributed within a unit square, with random orientations. Boundary conditions are periodic (i.e. individuals moving off the domain reappear at the opposite boundary and do not perceive a discontinuity in concentration gradient at the boundary). Parameters are DQ = 0.3, D, = 0.6, a = 6.0, and )3 = 6.0. Individuals seek to have between 56 and 63 nearby neighbors.

Daniel Griinbaum

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rithms. That is, one of the advantages of schooling is that it potentially allows more successful search strategies under "noisy" environmental conditions, where variations on the micro-scales at which animals sense their environment obscure the macro-scale gradients between ecologically favorable and unfavorable regions.

17.3.1 Effects of school size How large a group is required to obtain this benefit, and are there diminishing returns at larger group sizes? For the current simulations, the group need not consist of very many individuals to provide its members with a searching advantage - as shown in Figure 17.6, schools with a few as eight members do substantially better on average than isolated individuals. The simulations summarized in this plot suggest that tactic efficiency increases with group size until roughly 64 individuals, and that further increases in size have a much smaller effect on upgradient velocity.

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Another effect of increasing group size is to decrease the variation in searching success between individuals. Isolated searchers vary considerably in their rates of up-gradient travel: a few are very successful, but some end up downgradient of their initial position. This range of variation falls quite rapidly with group size, the difference between 10th and 90th percentile searchers falling by a factor of almost four between asocial searchers and those traveling in groups of 32. School-size effects must depend to some extent on the tactic and schooling algorithms, as well as the choices of parameters. However, underlying social taxes are the statistics of pooling outcomes of independent decisions, so the numerical dependence on school size may operate in a similar manner for many comparable behavioral schemes. For example, it seems reasonable to expect that, in many alternative schooling and tactic algorithms, decisions made collectively by fewer than 10 individuals would show some improvement over the aso-

Schooling as a strategy for taxis

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cial case but also retain much of the variability. Similarly, in most scenarios, group statistics probably vary only slowly with group size once it reaches sizes of 50-100. As suggested by Figure 17.6, when group size becomes large, the behavior of model schools change in character. With numerous individuals, stochasticity in the behavior of each member has a relatively weaker effect on group motion. The behavior of the group as a whole becomes more consistent and predictable, for longer time periods. It is possible to take advantage of this change of character to formulate a deterministic model of the effect of schooling behavior on taxis in large dense groups. The next section deals with such a deterministic approximation to the simulations of Section 17.3.

17.4 A nonspatial, deterministic approximation to social taxis I consider now a school of large size and high density and assume that the school is strongly cohesive, i.e. the group always remains together (as was the case in the simulations of Section 17.3). Most members are then able to interact with numerous other members and almost always see among their neighbors a large and representative sample of the angular distributions in their part of the group. Furthermore, if the school is large, the grouping tendency rarely provokes turning responses in a typical member, since most of the members are not near edges, where density changes rapidly. Angular distributions in large, dense, cohesive schools thus lose their sensitivity to the exact relative positions of members and become less stochastic, compared with those in smaller, less dense, less cohesive schools. This is the rationale for formulating a deterministic nonspatial equation for the probability density of orientation angle, p(8,t), for social individuals performing taxis with an alignment tendency. Drawing on the diffusion limits of Section 17.2 and calculating the average rates of alignment to neighbors under the schooling algorithms in Section 17.3, the changes of the distribution of orientation angles over time can be written as 3 dt (17.8)

- )8— (p(0,O |J

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In (17.8), the first right-hand-side term corresponds to the tactic behavior from (17.2), and the second describes the alignment behavior. The expression in the square brackets represents an individual's equal probability of choosing any one

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Schooling as a strategy for taxis

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Alignment Rate, P

Figure 17.8. Average up-gradient velocity, U, under the "perfect vision" scenario as a function of the rate of alignment, ft. Velocity initially increases rapidly with /3, then saturates and approaches the maximal value (U = 1) asymptotically.

of its neighbors at a given time; j3 is the rate of turning toward neighbors' headings. Related equations have been suggested to model spatial animal aggregations (Kawasaki 1978; Alt 1985; Pfistner & Alt 1990; Grunbaum 1994). Equation (17.8) is a nonlinear partial integro-differential equation. It cannot in general be solved analytically, but useful approximate solutions are possible. Furthermore, it is much faster to solve numerically for large populations than the full simulations described in Section 17.3, and so it is a useful way of encapsulating the effects of alignment behavior on taxis in large groups. Solutions of (17.8) are consistent with the simulations in Section 17.3: aligning with neighbors is an effective strategy for climbing a noisy gradient under conditions where simple taxis is ineffectual (Fig. 17.7). Starting from an initially uniform distribution of orientation angles, increasing rate of alignment with neighbors (/3) results in more rapid convergence about the up-gradient direction and progressively tighter equilibrium angular distributions. Interestingly, for these dense aggregations, even relatively weak alignment tendencies (0.25 ^ /3 ^ 1) result in significantly higher up-gradient velocities (Fig. 17.8). This compares to the relatively strong alignment, j8&6, that was necessary in the simulations (Section 17.3) to produce coherent schooling behavior. As expected from the discussion above, these calculations predict a relatively tighter angular distribution for a given alignment tendency in large, dense groups than was observed in the simulations in Section 17.3.

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17.4.1 Optimal alignment rates How strong should alignment rates be? The calculations have so far considered only an initially uniform angular distribution and constant tactic signal. In a more realistic environment, where concentration of the resource varies in time and space, the direction of the large-scale gradient might change as the searcher swims along. To climb gradients effectively under these circumstances, searchers need the ability to adjust and correct heading direction. In such cases, excessive attention to what neighbors are doing may prolong an erroneous "consensus" direction. An example of group response to changing gradient direction shows that there can be a cost to strong alignment tendency. In this example, the gradient is initially pointed in the negative j-direction (Fig. 17.9). After an initial period of 5 time units, during which the school orients perpendicularly to the x-axis, the gradient reverts to the usual x-direction orientation. The school must then adjust to its new surroundings by shifting to climb the new gradient. This example shows that alignment works against course adjustment: The stronger the tendency to align, the slower is the group's reorientation to the new gradient direction. This is apparently due to a nonlinear interaction between alignment and taxis: asymmetries in the angular distribution during the transition create a net alignment flux away from the gradient direction. Thus, individuals that pay too much attention to neighbors, and allow alignment to overwhelm their tactic tendencies, may travel rapidly and persistently in the wrong direction.

17.5 Discussion Simple, asocial types of taxis such as those employed by bacteria are effective because, over time, the displacement of an individual reflects the outcomes of many movement decisions. "Right" decisions (e.g. turning toward the up-gradient direction) are more likely than "wrong" decisions, but both occur at significant frequencies. The idea of averaging is thus central to understanding the long-term movements of an individual or the density flux of a population. Social aggregative behaviors have the potential to enhance taxis by providing an additional mechanism for averaging movement decisions: if averaging decisions among a large group of individuals at one instant can substitute in part for averaging many decisions by a single individual over space and time, then each member of the group may arrive at the "right" decision more quickly and with greater accuracy than it would in isolation.

277

Schooling as a strategy for taxis

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Time, t (b) Figure 17.9. Response to changing gradient directions under the "perfect vision" scenario for social searching (/3 = 0) and three choices of the alignment parameter /3. These calculations are the same as those in Figure 17.7, except that the gradient is along the y-axis (6 = - if) for the time interval 0 s i < 5 , and reverts to the usual orientation (0 = 0) thereafter, (a) Transient angular distributions at t = 20, showing lower degrees of adjustment to the new gradient direction for stronger alignment tendencies, (b) Average up-gradient velocity, U, as a function of time. Although the equilibrium velocity is highest for the strongly aligning case, strong alignment also prevents a group from rapidly correcting course when the gradient direction changes. In this particular scenario (gradient changes after 15 time units), an intermediate alignment tendency (/3 1) appears to result in the highest upgradient motion.

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The models developed in this chapter suggest that animals attempting to climb faint and noisy environmental gradients by taxis may improve their searching ability by participating in such a collective searching process. This positive interaction of taxis and schooling contrasts with that of mutual attraction through a diffusing secondary substance, which has been found to inhibit upgradient motion (Ezoe et al. 1994). While asocial searchers have a broad range of orientation angles, the alignment component of schooling behavior tends to shrink the angular distribution within a school, so that individuals move more directly up-gradient. The collective "decision" is statistically more likely to correctly identify a noisy or faint environmental gradient: In the models, even relatively small groups of schooling individuals (N £ 8) have a larger average upgradient velocity than social searchers. The models also suggest that there is a trade-off in strengthening tendencies to align with neighbors: Strong alignment produces tight angular distributions, but increases the time needed to adjust course when the direction of the gradient changes. A reasonable balance seems to be achieved when individuals take roughly the same time to coalesce into a polarized group as they do to orient to the gradient in asocial taxis.

17.5.1 Evolutionary benefits of schooling Social taxis is potentially effective in animals whose resources vary substantially over large length scales and for whom movements over these scales are possible. Examples of social taxis might be found among pelagic consumers of phytoplankton and small zooplankton such as herrings and anchovies, which form large, tightly organized schools (Royce 1972). Antarctic krill, the dominant grazer in the Southern Ocean, also form schools when searching for phytoplankton concentrations (Hamner 1984; O'Brien 1989; Miller & Hampton 1989). Interestingly, krill have been reported to school until a food patch has been discovered, whereupon they disperse to feed, consistent with a searching function for schooling. The apparent effectiveness of schooling as a strategy for taxis suggests that these schooling animals may be better able to climb obscure largescale gradients than they would were they asocial. Interactive effects of taxis and sociality may affect the evolutionary value of larger groups both directly, by improving foraging ability with group size, and indirectly, by constraining alignment rates. The implications of social behavior for taxis fit into a large body of theory and observations on the advantages and disadvantages of group foraging in aquatic animals (Pitcher 1986; Parrish 1992; Pitcher & Parrish 1993). That work has established the importance of foraging benefits as an evolutionary benefit of schooling behavior and provided details about processes underlying school func-

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tion such as information transfer between members of foraging groups (Pitcher et al. 1982a; Ryer and Olla 1991; see also the discussion of sensory integration systems in Ch. 15 by Schilt & Norris). Many of the foraging benefits thought to accrue from shoaling in general and schooling in particular are related to the risk of predation. For example, shoaling may result in a perceived reduction in the need for vigilance while foraging in groups, taking advantage of the so-called many eyes effect in which any group member may detect a predator in time to foil an attack (Wolf 1987; Domenici & Batty 1994). Larger group size in bluntnose minnows is associated with both fewer attacks by a predator, smallmouth bass, and with increased foraging rates by shoal members (Morgan & Colgan 1987). Other possible predation-related benefits of group foraging include overcoming confusion (Smith & Warburton 1992) and overcoming territorial defenses (Foster 1987). An example where sociality directly affects foraging strategy is forage area copying, in which unsuccessful fish move to the vicinity of neighbors that are observed to be foraging successfully (Pitcher et al. 1982a; Pitcher & Parrish 1993; Ranta & Kaitala 1991). Pitcher and House (1987) interpreted area copying in goldfish as the result of a two-stage decision process: (1) a decision to stay put or move depending on whether feeding rate is high or low; and (2) a decision to join neighbors or not based upon whether or not further solitary searching is successful. Similar group dynamics have been observed in foraging seabirds (Porter & Sealy 1982; Haney et al. 1992). A form of area copying, synchrokinesis, has been proposed to have a role in the migration of herring (Kils 1986; described in Pitcher & Parrish 1993). Synchrokinesis depends upon the school having a relatively large spatial extent: part of a migrating school encounters an especially favorable or unfavorable area. The response of that section of the school is propagated throughout the school by alignment and grouping behaviors, with the result that the school as a whole is more effective at route-finding than isolated individuals. Forage area copying and synchrokinesis are distinct from social taxis in that an individual discovers and reacts to an environmental feature or resource, and fellow group members exploit that discovery. In social taxis, no individual need ever have greater knowledge about the environment than any other - social taxis is essentially bound up in the statistics of pooling the outcomes of many unreliable decisions. Synchrokinesis and social taxis are complementary mechanisms and may be expected to co-occur in migrating and gradient-climbing schools. Besides increasing the average rate of gradient-climbing, another effect of social behavior on taxis is to reduce the "spread" or variance of searching success among individuals. For example, in the comparisons of taxis among groups of various sizes, the most successful individuals were in the asocial simulation,

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even though as a fraction of the entire population they were vanishingly small. This suggests that the effectiveness of a social tactic strategy for a particular organism may depend in part on whether its reproductive rate is small or large on the time scale of foraging movements between resource concentrations. For organisms limited by resources but which otherwise are capable of explosive reproductive rates (macroscopic examples may include gelatinous plankters such as cnidarians, ctenophores, and salps) an alternative strategy is to disperse offspring as widely as possible. In such a species, the ultimate population level within the resource concentration is not necessarily proportional to the number of searchers which enter it, because rapid population growth rate within favorable areas can make up for the small fraction of individuals which find them. If, on the other hand, reproduction does not occur on the time scale of foraging movements, then the benefit to an individual may be roughly proportional to the amount of time spent within resource patches. In this case, a searching strategy which on the average is more effective at climbing gradients is superior, even if it eliminates the extremely fortunate individuals which move in the right direction by chance. Thus one would predict that, phylogenetic constraints aside, social taxis would be advantageous only in species that live a relatively long time and reproduce slowly compared to the variations they experience in their environments.

17.5.2 Experimental tests of social taxis Group olfactory dynamics similar to social taxis were studied experimentally in foraging zebrafish by Steele et al. (1991). They monitored movements between regions of an aquarium with differing levels of a food odorant (L-alanine). At concentrations near the detection threshold, Steele et al. found ambiguous results: Groups of four zebrafish were more responsive to faint odors than both smaller and larger groups. The next most responsive were isolated fish. Steele et al. speculated that these results arise from competing effects, such as the greater probability of including exceptionally sensitive individuals and increased avoidance behavior due to confinement in a small space with larger group size. One of the merits of the mechanistically based models I have outlined is that they identify two clear directions for experiments. First, they predict that the ability to follow an odor gradient with noise changes as a function of group size (Fig. 17.6). If one can manipulate the size of a school, but hold the environment constant (such as in large aquaria or flow chambers), one can test this prediction. Of course, schools may increase their up-gradient velocity for reasons other than the mechanisms identified by the models I have discussed. However, the models are sufficiently explicit in connecting changes in effectiveness of schooling to

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the amount of noise in the gradient signal that one could design experiments to rule out "getting the right prediction for the wrong reason." Specifically, by changing turbulence, or by directly inputting misleading odor patches, one can manipulate signal-to-noise ratio in an experimental setup. Second, the models predict that the differences among histograms as a function of group size for social schoolers will diminish as the signal-to-noise ratio increases. Even without estimating all the parameters in the models I have examined, an experimental program that crossed manipulations of group size with signal-to-noise ratios could provide compelling evidence for the processes identified by the social taxis models developed in this chapter.

18 Trail following as an adaptable mechanism for popular behavior LEAH EDELSTEIN-KESHET

18.1 Introduction There are numerous examples of animal groupings (aggregations) which form as emergent patterns derived from individually based behaviors in situations where each individual has a limited knowledge of the group as a whole. This type of collective behavior occurs in fish schools, in swarms of insects and krill, as well as in large herds and flocks, and is particularly prevalent in situations where individuals have limited intelligence. To offset the lack of global knowledge, gregarious organisms have evolved individually based mechanisms for maintaining group cohesion. Other chapters have focused on mechanisms through which aggregation members communicate (see Ch. 15 by Schilt & Norris on sensory integration systems). It is also clear that less cognitive organisms must use a variety of different signals to assess their position with respect to their neighbors, if not within the group as a whole (see, for example, Ch. 14 by Dill, Holling, & Palmer, on visual and angular information). In social insects such as ants, individuals communicate and transfer information in many ways, including chemical signals and following chemical trails. This chapter presents an examination of the phenomenon of collective behavior using an example taken from the world of ants. Although many of the ideas in this chapter are written in terms of ant behavior, they apply more generally to examples from other social organisms (see Watmough & Camazine 1995; Watmough 1996). Social insects use trail marking and following to coordinate group response. Without necessarily having a sense of the whole, individuals can form a variety of aggregation patterns by following fairly simple algorithms and relying on a limited number of sensory inputs. In ants, trail following can serve one of several functions: exploration, migration, foraging, or defense. Each function dictates different social groupings and movement patterns resulting in different spatial arrangements. For example, exploration requires a diffuse low-density

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Swarm of the army ants, Eciton Hamatum. From W. F. Kirby (1898), Marvels of Ant Life. S. W. Partridge.

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coverage of a broad area, whereas migration demands a direct pattern of movement from one site to another. Although ants travel along surfaces, they move between two- and three-dimensional space. When exploring the canopy of a tree, the geometry of the branches imposes a three-dimensional pattern to the set of trails taken as a whole. In a flatter environment, the structure of trails will tend toward two-dimensionality even though the branching pattern may be similar. Thus, the nature of the trails varies across environmental conditions as a function of colony behavior, as well as between different species (see Moffett 1986 for a popular review). Ant swarms provide a clear example of aggregations in which individuals do not have a sense of the whole and do not follow instructions from a leader or an organizer. By following elementary algorithms at the individual level, the population becomes coordinated. In this sense, a direction is selected, the density of traffic is regulated, and migration occurs in a cohesive way (see also Ch. 17 by Griinbaum). Relatively small changes in the behavior of individuals marking and/or following trails can lead to significant modifications in the way that the aggregations are organized, allowing the population to respond quickly to changes in the environment and/or colony needs. To understand the population consequences of individual trail marking and following, it is necessary to bridge the gap between properties and behaviors of the individual and the emergent properties, such as self-organization, that reside at the level of the population. The reader may wish to compare the approach in Chapter 7 by Turchin on beetle mass movement and the creation and dissolution of aggregations created by differential flux. Here, the treatment is one level down, starting with individual interactions in order to understand the resulting population patterns. Because interindividual interactions are not easily scaled up to emergent patterns by simple verbal arguments, it proves profitable to examine mathematical models. The purpose of the models is not to represent every detail and complexity of individual behavior, but rather to focus on the essential aspects of the emergent phenomena. For a prosaic metaphor, one might consider trying to explain the workings of a clock: the detailed action of every cog is a level of understanding suitable for some engineering purposes, but the basic idea that the clock acts like a pendulum or a loaded spring gives insight about the way that a clock "works," and about the essential part of the clock. Similarly, the models described in this chapter are meant to help understand and identify features of trail-following systems that permit certain kinds of collective behavior to emerge in a population. I have organized the rest of the chapter as follows: Section 18.2 deals with biological systems in which the marking and following of trails is known to

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occur. Section 18.3 is an outline of the specific phenomena which are to be explored, as well as the types of models dealing with such phenomena. In Section 18.4, a sketch of the mathematical models and a brief description of their results and references are presented. Implications are given in Section 18.5.

18.2 Trail following in social and cellular systems Trail following occurs in a myriad of biological systems. One of the most primitive examples is the family of Myxobacteria. These unicellular organisms secrete slime trails which lead to aggregation and collective gliding motility. Mathematical models and computer simulations of this population-level phenomenon have been proposed by Pfistner (1990), Stevens (1990), and Mogilner (1995). Slime molds, which aggregate to form fruiting bodies, also secrete chemical attractants, namely cyclic AMP (cAMP); however, unlike ant trails, it is likely that the rapid diffusion of small molecules such as cAMP prevents welldefined or long-lived trails from forming. The most well-known example of trail following occurs in social insects, where trail networks are used for the transmission of workers, materials, and information (Able 1980; Wynne-Edwards 1972; Holldobler & Wilson 1990). Trails are defined by the presence of pheromones laid down by the workers that either create a new trail or reinforce a preexisting one. Chemical trail following can be viewed as a special example of chemotaxis in which lateral diffusion of attractant is limited relative to the forward motion of the individual. The pheromones used by ants and termites are volatile and disappear on a timescale that varies from seconds to days, depending on the species (e.g. Bossert & Wilson 1963). Ants that cross or approach the trail are able to detect its polarity and will turn and follow it. A recent mathematical model that describes the turning response of ants appears in Calenbuhr and Deneubourg (1992) and in Calenbuhr etal. (1992). Although not social insects, many types of larvae and caterpillars are gregarious, and some form long columns defined by silk-like threads (Deneubourg et al. 1990a). Molluscs, including snails, slugs, and limpets, also secrete slime trails used for homing (Focardi & Santini 1990; Focardi et al. 1985; Tankersley 1990; Wells & Buckley 1972; Chelazzi et al. 1990). Trail following and associated chemical marking also occur in numerous mammals. Ungulates and other herding mammals have scent glands on their lower legs and feet and secrete scent along their trails. Photographs of migratory herds of elk, caribou, and wildebeest often reveal motion in single file or along a distinct set of trails (Wynne-Edwards 1972; Able 1980; Estes 1991).

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18.3 Phenomena stemming from trail following Social insects such as ants display collective behavior that appears much more organized and purposeful than the sum of individual behaviors of each ant. This type of population behavior has been called "collective decision making" and "self-organization" (see, for example, Camazine 1991; Deneubourg et al. 1989; 1990b). A goal of this chapter is to investigate how experimentally measurable properties at the level of the individual can lead to self-organization at the level of the population. Typical examples of parameters at the level of the individual might include, for example, the rates of secretion and chemical strength of the pheromone or other marker, the probability of tracking the path per unit time or distance, the degree of random motion of individuals, and their ability to sense and respond to trail markers. The size of the population and the diffusivity of the pheromone also prove to be important in defining interindividual interactions. A number of questions common to many chapters in this volume are of interest. How should we distinguish between order and disorder? What are the rules obeyed by individuals that lead to order, and what types of spatial patterns can thereby be explained? Why should certain patterns exist? Are the patterns adaptive? How would the patterns change as environmental conditions or needs of the population change? These are discussed in the context of mathematical models which are first motivated in the next section. The section is subdivided into units that deal with (18.3.1) the spatial distribution of trails and followers, (18.3.2) the choice of directions of motion, and (18.3.3) the distribution of traffic and the adaptability of the trails to diffuse exploration or concentrated migration columns. Each of these problems can be addressed from theoretical and experimental points of view, but separate approaches are required for each question.

18.3.1 Spatial patterns and density distributions within a swarm There are many descriptions of the formation of spatiotemporal patterns such as swarming in the biological literature. Figure 18.1, adapted from Rettenmyer (1963), shows the branching swarm patterns of two species of raiding army ants, Eciton hamatum and E. burchelli. Other examples are given by Schneirla (1971), Franks and Fletcher (1983), Burton and Franks (1985), and Franks (1989). It is evident that the spatial pattern can differ from one species to another, as well as from one physical location to another. Spatial patterns can also change radically over time. Figure 18.2, after Raignier and van Boven (1955), shows a time sequence in the swarming within a single colony of Dorylus. An initial mass of ants emerges from the nest in a rather disorganized, milling fashion. Gradually a direction of motion is selected and the traffic pattern is reinforced to form a sin-

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: : • . • • • : • '

;

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.1...

.'•••4

B Eciton hamatum

Eciton burchetti

Figure 18.1. Trail networks formed by swarms of the Army ants, Eciton hamatum, and Eciton burchelli. B = bivouac. Note the major trunk trails, the bifurcations, and the diffuse exploratory fan at the swarm front. Based on Rettenmeyer (1963). gle column. The population migrates outward in a nearly one-dimensional route before fanning out in an exploratory pattern at the front of the swarm, where food is collected. The spatial behavior of a swarm can be approximated by a discrete or a continuous spatio-temporal model which accounts for the density of trails, the individuals following the trails, and those milling about randomly (see Watmough & Edelstein-Keshet 1995). If one considers individuals moving in one dimension (e.g. along the length of the swarms in Fig. 18.1 or 18.2), it is possible to make explicit predictions about the density profile of the population and the speed of migration of the swarm. A typical set of equations for swarming is given in Section 18.4.2. A second approach is to treat the problem by simulating actual motion of a collection of "individuals" and then watching the time course of a "population" under a variety of conditions and parameter values. This type of simulation, called a cellular-automaton simulation, can be used to model spatial behavior of biological populations (e.g. Watmough 1992, 1996; Edelstein-Keshet et al. 1994; Ermentrout & Edelstein-Keshet 1993; Langton 1987). See Figure 18.3 for

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'I i5'!'.iVj ^!•r l i J^f : '^^r'i^•f I 'i^•^1 'i"•^ i %"•^ : 'iJ ;•^!^i"•^:f^^•j''i^•^!•i^•^:^i^•^:'i^•^:'":•^»?••^••^ J•

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Figure 18.2. Temporal sequence in the formation and eventual retreat of a swarm raid produced by a colony of Dorylus ants. The initially confused random milling eventually establishes a direction along which the swarm propagates. Sketch based on Raignier and van Boven (1955). a typical example of a trail-following simulation. Simulations are ideal for experimenting with a variety of rules and parameter regimes on resultant group behavior. However, it is sometimes difficult to understand the effects of parameter variations using simulations alone, and mathematical models prove helpful in these cases. Griinbaum (Ch. 17) uses both simulations and models to explore a phenomenon related to gregarious behavior - the ability of aggregations to detect and follow gradients in a noisy environment.

18.3.2 Selecting a preferred direction For ants, a transition from random milling and exploration, or disorder, to directed motion, or order, occurs in the early stages of directed migration (Fig.

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Figure 18.3. A computer simulation of ant-like automata following trails and obeying simple turning rules. Such simulations allow us to explore the consequences of changing rules, parameters, or turn angle distributions on the formation of pattern and type of aggression. Simulations were written by James Watmough.

18.2). This transition takes place spontaneously, through the collective motion, trail marking, and resultant following by all individuals. Clearly, in a natural setting there would be some biological biases in the development of directionality: These biases might include the distribution of food, light, or other cues that give a directional preference. But do ants or other trail followers also have an innate ability to collectively decide on a preferred direction, or to amplify minute environmental biases in finding the right direction?

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Consider the angular distribution of the trails and individuals creating them. It is possible to formulate a set of equations (see Sec. 18.4.3) that describe how this angular distribution changes with time. Suppose that all individuals are initially uniformly distributed and moving in random directions over some small region (e.g. in the early formation of a swarm). Suppose that by random fluctuation, the number of individuals moving in some particular direction is slightly higher than in other directions. The model predicts that this may cause the entire traffic pattern to shift so that this direction becomes dominant. However, the model also predicts that this effect occurs only when the right balance exists between competing influences such as affinity to the trails, defined as the likelihood of finding and staying on trails versus the tendency to fall off trails, a function of the degree of random motion of individuals, and the rate of decay of pheromone. The implication is that the mechanism of trail following can amplify and enhance even minute gradients or signals, and so serve to help select a preferred direction. A similar model was discussed by Edelstein-Keshet and Ermentrout (1990).

18.3.3 Diffuse exploration versus cohesive migration Figure 18.1 illustrates differences in trail pattern between major routes (along which steady traffic streams) and diffuse exploratory networks (the fan-shaped region) in which the trails are much longer but contain fewer followers per unit length. Both types of movement patterns are necessary, and the transitions between one type and another are of particular importance. How does a transition from a coherent to a diffuse motion take place? In a recent paper, Edelstein-Keshet (1994) shows that this behavioral transition from high to low traffic densities might be a simple consequence of sensitivity to the strength of the trail marker. The argument is based on the idea that the density of individuals along the length of a trail will influence the level of the marker and hence the affinity to the trail. The higher the affinity, the greater the density on the trails. A discussion of this idea, and of the model that deals with it, appears in Section 18.4.4.

18.4 Minimal models for trail-following behavior The mathematical models discussed in this chapter are based on the following variables and parameters:

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T(t) — total length of trails per unit area at time t F(t) = total number of followers (on trails) per unit area at time t L{t) = total number of explorers (nonfollowers) per unit area at time t v = speed of an individual a = rate of trail reinforcement by follower F = rate of decay of trail marker e = the rate of losing a trail being followed a = the rate of attraction to the trails Individuals are assumed to walk at a fixed speed, v, and are either exploratory ants or those following a trail. Both types of individuals secrete trail markers, at possibly different rates. In models in which the spatial or directional distribution of the population is of interest, the variables above are assumed to depend also on position, x, or on direction angle, 6. We initially assume that the parameters v, F, e, and a are constants. These can be thought of as mean values, as it is highly unlikely that individuals are identical. For simplicity, we consider behavior of a population in which the individuals are the same. The influence of slowly varying individual parameter values will be taken into account.

18.4.1 Basic model equations A basic framework for an ordinary differential equation model for trail following based on these variables is: AT1

— = vL + aF - TT at — =-£/+ at

aLT

dL — = eF - aLT dt

(18.1) (18.2)

(18.3)

Observe that the total number of individuals, N — L + F, is constant. It is thus possible to eliminate the third equation and to rewrite the equations in terms of F and T alone. In this model, single individuals secrete pheromone continuously and lengthen the trails (first two terms in eq. (18.1)). The decay of the trail

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marker (last term in eq. (18.1)) will cause the trail length to decrease at the back. It is assumed that the rate of decay is a linear process with rate constant T. Equations (18.2) and (18.3) describe the exchange that takes place between the number of individuals on and off the trails. The first term in each is the rate at which followers lose the trail, and the second term is the rate at which exploratory ants encounter and start to follow a trail. This model has a single equilibrium. The percentage of followers and of lost individuals at the equilibrium depends on the size of the population and on the other parameters. In the sections below I discuss how these basic equations are modified to deal with spatial, angular, and density variations.

18.4.2 One-dimensional swarm migration model By redefining variables as functions of position x and time t, one arrives at a spatiotemporal version of the above model: ^

= vL(x,t) + aF(X,t) - TT(x,t)

(18.4)

at

dF(x,t) —^-^ = dt

d[vF] ^—t - eF + aLT dx

dL(x,t) d2L = a—7 + eF — aLT dt dx

(18.5)

(18.6)

The equations are similar to those of the previous section, but now include directed motion of the followers down a one-dimensional trail (first term in eq. (18.5)), versus random motion of exploratory ants (first term in eq. (18.6)). Watmough and Edelstein-Keshet (1995) discuss the behavior of solutions that represent the advance of a swarm, i.e. a constant swarm density profile moving at a fixed speed without changing shape. We show, both numerically and analytically, that these equations admit so-called traveling wave solutions. The basic result is that the interior of the swarm consists of a high level of followers and exploratory ants, whereas the front of the swarm gradually declines in the density of both followers and explorers. The explorers are not concentrated at the front; they are distributed throughout the swarm. The speed of this collective motion depends on the size of the swarm, the rate of being attracted to trails, and the rate of losing trails (a and e).

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18.4.3 Orientation of individuals and selection of swarming direction To study the directions of motion of individuals and ask how individual turning probabilities affect the angular distribution of the population and its trail networks, I define F(6,t), L(6,t) = F or L individuals currently moving in direction 6 T(6,t) = density of trails made by individuals moving in direction 6 K{9,6') - probability that individual moving in direction 6 will turn and follow a trail in direction 6' R(0,6') = probability that individual moving in direction 6 will randomly turn in direction 6' Then a set of equations for these variables would be 37(0,0 dt

= vL{6,t) + aF(6,t) ~ TT(6,t)

(18.7)

dF(6,t) = -eF + aT(e,T)K* L dt

(18.8)

dL(d,t) _ eR * (F + L) - aLK * T dt

(18.9)

In these equations the terms K*T, K*L, and R*(F + L) are known as convolutions. These are integrals that sum up all the possible transitions from one direction to another. For example, K*L=

[ K(d,9')L(6',t) dd

(18.10)

is the net rate at which individuals initially moving in any direction would turn and follow a unit length of trail whose direction is 6. If there are many trails in this direction, i.e. T(6,t) is large, this would clearly increase the likelihood of such turns, and hence the term aT(6,t)K*L appears in the equation for the rate at which followers (at angle 9) are accumulating. A similar interpretation for other terms in the equations can be made. Information about turning probabilities of individuals can be ascertained by experimental manipulation. Equations such as these can be analyzed to address the selection of a preferred direction. Using linear stability theory, and assuming small initial bias in one or several directions, we can then seek conditions under which such small biases

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180 theta

225

270

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360

180 •fche-ta

223

270

315

360

Figure 18.4. Models for angular distributions of the directions of motion in a population (see Section 18.4.3) can describe how a set of preferred directions could arise spontaneously. Shown here are numerical simulation of the angle distribution equations for the trails and the followers starting from a nearly uniform initial distribution. With time, a particular direction (given as an angle out of 360°) and the vertical axis is the density of trails or followers oriented along that direction.

can become amplified. Typically, only a limited range of individual parameters leads to the ability to select a dominant direction. If individuals have a high tendency for directional persistence, the formation of a directed migration column is favored. Figure 18.4 shows a typical numerical simulation of the equations given above. The graphs represent angular distributions. A nearly flat initial distribution means that, in the beginning, ants move about in all directions with

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nearly equal probabilities. Later, preferred directions develop. This is shown by the peaked distributions. The angle(s) at which peaks appear are the dominant direction(s) of motion. This is shown by the peaked distributions. The method of analysis and simulations for this model are analogous to those of EdelsteinKeshet and Ermentrout (1990).

18.4.4 Adaptable trails: light and heavy traffic patterns The variables in the models are defined as densities (of individuals, of trails, etc.) per unit area. However, the traffic volume along the trails is given by the number of followers per unit length of the trail, defined as: 5(0 = F(t)IT{t) = number of followers per unit length of trails Because each individual on a trail secretes trail marker, or has the same probability of secreting trail marker, the variable S can also represent the chemical strength of the accumulated marker. Thus, we could describe the dichotomy between "strong" (cohesive) and "weak" (exploratory) trails, or between hightraffic and low-traffic trails, by high or low values of this quotient. The fanshaped migration front of army ants, which consists of a highly reticulated meshwork, would be an example of a network of weak exploratory trails, whereas the trunk trail formed from the nest along which steady traffic flows would be a strong, cohesive trail. Because ants respond to pheromone signals in a graded way, the rate of finding trails, the rate of reinforcing a trail, and the fidelity to the trail (or conversely, the rate at which followers lose the trails they are following) is likely dependent on the strength of the trail. This can easily be incorporated into the model by modifying the parameters defined in Section 18.4.1, previously taken as constants. Edelstein-Keshet (1994) argues that one reasonable assumption is that the rate of getting lost (e) diminishes as the strength of the trail increases. For example, e drops off exponentially as a function of S, such that e= e(S) = Eexp(-bS) = Eexp(-bF/T)

(18.11)

E is the maximal rate of losing a trail and b is the rate of decline of trail loss per unit increase in trail strength. Replacing the previously constant value of e with this functional form results in a variety of behavioral outcomes. Figure 18.5A, B, and C illustrate three possibilities obtained by varying the parameters E and b. In Figure 18.5A the equilibria include one representing weak trails (close to the horizontal axis) and one representing strong trails (close to the vertical axis). Different initial conditions (e.g. different initial ratios of follower ants and lost

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1 1

Trail Density Figure 18.5. Phase plane diagrams for the behavior of the model in Section 18.4.4. The horizontal axis is trail density and the vertical axis is follower density. The dark point on the upper left of (A) and (C) represents a steady state for which F/T is high, i.e. a strong trail network. The dot on the lower right in (A) and (B) represents a steady state in which F/T is low, i.e. a weak trail network. The curves are trajectories that summarize how both F and T change from any given initial values to their eventual (steady-state) levels. The model predicts that slight changes in the parameters governing tendency for random turns, E, and sensitivity to trail pheromone, b, can lead to these transitions in population behavior. (A) Both weak and strong trails can occur, but their formation depends on the initial numbers of followers and trails. (B) Only weak trails occur. (C) Only strong trails occur.

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ants) lead to different eventual outcomes. In Figures 18.5B and 18.5C, the trails are eventually exclusively weak (18.5B) or strong (18.5C). A transition from one case to the other can occur as slight variations are made in the parameters of the individual motion. For example, by increasing E, which is associated with the tendency to make random turns, and thus promoting a tendency to lose trails being followed, a transition to loose, exploratory-type, low-traffic trails is made. By increasing b, the sensitivity to trail strength, a transition to strong, hightraffic trails can occur. The implication of this result is that the parameters associated with the individual behavior and with acuity of the trail-detection mechanism can result in directed, global population behavior. For more detail see Edelstein-Keshet (1994).

18.5 Discussion The manifestation of an emergent pattern is a defining characteristic of animal aggregations. Edges, spatial arrangement, and directionality of movement embody our visual concepts of swarms, flocks, and schools. And yet these groups are made up of selfish individuals acting on their own behalf (see Ch. 11 by Hamner & Parrish for a discussion of individuals versus group cohesion), and rarely, if ever, aware of the group as a whole. An examination of the ways in which individual behavior can shape, and can be shaped by, an emergent pattern is therefore crucial to understanding aggregation. Although this chapter has concentrated on a specific mechanism (trail marking) operating in a particular taxa (the ants), the methods presented here apply to many other types of aggregation (and mechanisms involved in their creation and maintenance), including fish schools, bird flocks, and herds of terrestrial animals. The models and simulations presented in this chapter reveal several underlying concepts uniting individual to "group" behavior. First is the idea that the interactions of many similar units, each obeying fairly simple rules, can lead to complex emergent patterns of organization at the population level. The particular signals used to relay information between individuals, and the rules of motion or interaction, are no doubt case specific and can be much more general than those described here for ants. A second concept of wide applicability is the idea that a given pattern can emerge only if a balance exists between competing influences. For example, in schools of fish there is a tendency for group cohesion but the cohesion may be disrupted when a predator attacks. (See the "fountain" or "flash expansion" discussed in Pitcher & Parrish 1993). In the case of chemical communication by trail marking, the pheromone should be sufficiently long-lived to transmit the signal, but also volatile so that outdated signals are not confused with newer

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ones. The ants should be good at following the trails, but not too good. Getting temporarily lost may ultimately lead to encountering a stronger and more rewarding route. Similar to other animal aggregations, especially those relevant to migration, a trade-off exists between faithfully following the preceding individual versus more flexible "individualistic" strategies. Like terrestrial animals, ants remain on surfaces, whether the surface of the soil or the surface of branches and twigs on a bush. Thus, in a sense, ants live in a two-dimensional world, or a highly constrained three-dimensional one. It could be argued that ant swarms are therefore not true examples of three-dimensional aggregations. However, like the more truly three-dimensional cases of fish schools or midge swarms, the challenges posed by trying to understand how group cohesion is maintained is the same, even though the geometry is in a sense simpler. One might anticipate that the "rules" being used by individuals in an aggregation may be quite similar, whether the animals are sensing and moving along two- or three-dimensional tracks. The literature on chemical signaling in social insects and on self-organization in ants is a wide and interesting one. The reader may wish to consult a few sources cited below for more detailed background information. For properties of pheromonal signaling, and especially of diffusion, see Wilson (1962) and Bossert and Wilson (1963). For self-organization in ants, see Deneubourg et al. (1989, 1990b), Aron et al. (1989, 1990a,b), Pasteels et al. (1986, 1987a,b), Calenbuhr and Deneubourg (1992), Calenbuhr et al. (1992), and Franks et al. (1991). For details of the mathematical formulation, analysis, and predictions of models discussed in this paper, see Edelstein-Keshet (1994) and EdelsteinKeshet et al. (1994). Simulations of spatial patterns and swarming behavior appear in Watmough (1992), Watmough and Edelstein-Keshet (1995), Deneubourg et al. (1989), Franks and Bossert (1983) (army ant raiding swarms), Deneubourg et al. (1990b) and Aron et al. (1990a,b) (other species of ants). To date, many of the simulations described by Deneubourg and his group focus on ants moving on artificial bridges (with decisions to be made at forks). While this is an artificial situation, it is attractive from the point of view of validating their models by experimental tests. The simulations described by Watmough deal with free motion of ants emanating from a nest. These can be used to explore how changes in individual parameters might affect trail morphology. More recent modeling work by Watmough (1996) extends ideas of collective behavior to the case of honeybees. The models described in this chapter and expanded on in companion papers identify a minimal list of parameters that describe how trail markers interact with trails and with each other. These parameters include properties of the (1) chemical signal (decay rate, F), (2) the followers (mean time a path is followed,

Trail following as an adaptable mechanism

299

l/e; sensitivity to trail strength, b), (3) the exploratory ants (random motility /x; tendency to accept trail, a), and (4) the population (total size, N). Applying this model to other types of animal aggregations less dependent on chemical signaling (for example, Ch. 14 by Dill et al.) would necessarily require system-specific replacements. Testing whether the simple models can account for the gross features (if not the fine details) of an emergent pattern would require either measuring or estimating the set of parameters. In general, this is difficult to accomplish. Indeed, as discussed in Edelstein-Keshet et al. (1994), it is not currently possible to find values for all of the trail-following parameters from the literature on any one ant species. The pattern of environmental effects has not been explicitly included in any of the models presented in this chapter. However, environmental effects (e.g. homogeneous versus patchy food distributions) impinge on the population by changing the behavior of individuals, and this can be incorporated as causing slight shifts in parameters of individual movement described in this chapter. Part of an experimental procedure for measuring the above parameters would be to observe how their values might vary with changes in environmental conditions. Trail pheromones illustrate one mechanism used to coordinate behavior of individuals in a group. Other equally important mechanisms are common; there are pheromones that attract worker bees to their queen (e.g. queen-bee pheromone; see Watmough 1996), there are species that swarm in response to a physical marker (e.g. see Ikawa & Okabe Ch 6) or in response to gradients of light (Yen & Bryant Ch. 10), nutrients (Griinbaum Ch. 17), etc. In higher organisms, advanced sensory systems such as vision (in birds) or pressure difference (in fish) probably play much more dominant roles in establishing and fine-tuning animal aggregation. Scent trails and pheromone signals are a form of olfactory communication. As such, they are among those mechanisms that evolved earliest. Thus, studying these (relatively primitive) systems gives clues about ways that organisms could achieve self-organization at the dawn of life, when the more advanced physiological systems had not yet appeared. One would like to suggest a future goal of bringing experiment and theory together. Ideally, measurement of the individual parameters of trail followers, together with experimental manipulation of trail pheromones and of population size, would permit model validation or would suggest improved models. Unfortunately, other than a limited number of cases, most pheromones remain unidentified, and many species of trail forming ants (e.g. the army ants) fail to thrive under laboratory conditions. Thus the establishment of a good experimental system for studying and manipulating trail followers is still a primary goal in pursuing these problems.

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Leah Edelstein-Keshet

Acknowledgments This work has been carried out under support from the National Sciences and Engineering Research Council of Canada, grant number OGPIN 021. I would like to thank James Watmough and G. B. Ermentrout for discussions during various stages of this project.

19 Metabolic models of fish school behavior - the need for quantitative observations WILLIAM MCFARLAND AND AKIRA OKUBO

19.1 Introduction There is extensive literature on fish schooling emphasizing school architecture and how behavioral interactions drive school structure. In fact, studies of schooling have focused almost exclusively on biotic forces - predation, foraging, reproduction-experienced by schoolers (see review in Pitcher & Parrish 1993). How schoolers interact with the physical environment has received little attention, despite the fact that physiological constraints can have a dramatic effect on survivorship in the short term. For example, how the physiology of schooling organisms affects the chemistry and nutrient loads of the water masses that they occupy has been virtually ignored. Changes in water chemistry can alter the quality of the environment such that it is locally inhospitable. Field observations reveal that fish schools can alter dissolved respiratory gases (McFarland & Moss 1967) and increase ammonium and nutrient concentrations (Oviatt et al. 1972; Meyer et al. 1983; Bray et al. 1986), and that their foraging activities can greatly reduce zooplankton concentrations (Bray 1980; Koslow 1981; Hamner et al. 1988). It is entirely possible that physiological constraints may place limits on school size, density, shape, and internal arrangement. Unfortunately, few investigations demonstrate what effect(s) these metabolically related changes may have on schooling behaviors (Moss & McFarland 1970). Although the structure of a fish school can be influenced by innumerable factors, McFarland and Moss (1967) suggested that many of the dynamic internal changes observed in school structure and shape could be a response to lowered ambient oxygen and/or increased carbon dioxide concentrations. If decreased oxygen, increased carbon dioxide, and increased ammonium levels in the water can be deleterious to fish, then individual movements within dense schools may be modifications to minimize the exposure to deleterious conditions. As conditions worsen and/or spread throughout the volume of the group, the sum of indi-

301

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William McFarland andAkira Okubo

vidual behavioral modifications should change school structure. The obvious solution, dissolution, will be balanced by biotic forces selecting for continued group membership (e.g. predation). Given the constraint of continued school existence, the physiological hypothesis implies that there should be a maximum size to fish schools that is dependent on water flow, school density, and individual rates of metabolism. In this chapter we describe an advection-diffusion-reaction (A-D-R) model for oxygen concentration as a function of school size. We contrast the predictions of the A-D-R model against a simple linear model, and test the validity of both against available field data for striped mullet, Mugil cephalus. Migrating striped mullet form extremely dense, polarized schools, varying in size (mea-

(A)

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303

sured as length of axis of travel; longitudinal axis) from tens to hundreds of meters (McFarland & Moss 1967). Large schools of mullet can be found migrating from lagoons along the Gulf of Mexico coast to the open Gulf during the spawning season. School structure may change markedly as a function of distance from the leading edge (Fig. 19.1). The A-D-R model incorporates variables such as oxygen diffusivity, swimming speed, fish size, school density, and school size, all of which are derived from field measurements/observations on mullet (when available) or other schooling species. Field measurements of oxygen reduction

(B) Figure 19.1. Surface photograph of a striped mullet school during a reproductive migration from Corpus Christi Bay, Texas to the open Gulf of Mexico. (A) densely polarized individuals near the front of the school; (B) breakdown in school structure near the trailing edge of the school.

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William McFarland andAkira Okubo

for the mullet as well as distance from the leading edge at which school structure begins to break down are from a previous study (McFarland & Moss 1967).

19.2 Density in mullet schools Although the spacing and density within fish schools have been widely studied in laboratories (Breder 1954; Pitcher 1973, 1986; Rottingen 1976; Graves 1977; Pitcher & Partridge 1979; Partridge 1980), few measurements exist for schools in the sea. Although fish density usually refers to the number of fish per volume of water, a more convenient measure is nearest-neighbor distance (NND), which is related to mean body length (L) by NND = a*L. The proportionality constant (a) ranges from 0.7 to about 1.2, depending on age and species. The most realistic model of packing (i.e. volume of fish plus surrounding water volume) predicts a total volume per fish of 0.6 L3 (Pitcher & Partridge 1979). Density is then the inverse of total volume per fish. Using this calculation, schools of adult striped mullet, which have a mean body length of 25-30 cm, should therefore have from 62 to 107 fish/m3. Increasing school swimming velocity tends to produce a more compact school (Abrahams & Colgan 1985). Because our model is based on migrating mullet, we choose 100 fish/m3, or 0.1 fish/1, as a typical density value. For 30 cm mullet, the mean volume of fish alone is estimated as 360 cc (Adkins et al. 1979), or 3.6 * 10~4 m3. Thus 100 striped mullet would only occupy 3.6% of a cubic meter.

19.3 Mullet school velocity School velocity is dependent on behavior (e.g. feeding, migration) and has been determined both experimentally and analytically. The migration velocity of various species of fish whose body size is approximately 30 cm ranges from 5 to 35 cm/sec. The optimum swimming velocity for fish of body length (BL) of 30 cm was estimated to be 30 cm/sec by Webb (1977) and 32-42 cm/sec by Ware (1978), or 1 to 1.5 BL/sec. Webb (1975) suggests a maximum speed of 120 cm/sec. Estimating typical velocity as a function of body size can also be determined analytically using Reynolds number (Re), the relationship of fluid flow past a body: Re = U*L/v

(19.1)

where U is velocity, L is a length measurement of the animal (e.g. BL), and v is dynamic viscosity. A diagram of Reynolds number (Re) versus body size (L) for motile organisms from bacteria to whales (Okubo 1987) yields a regression of Re = 270*L 1 8 6

(19.2)

Metabolic models offish school behavior

305

Where U = 0.01 cm2/sec and L is expressed in cm. By rearrangement: U (cm/sec) = 2.7 *L 1 8 6

(19.3)

Thus, for a 30-cm mullet the swimming velocity predicted by the regression (If) is 50.3 cm/sec or just under 2 BL/sec. Although this value is strictly applicable to individual fish rather than a school, field observations reveal that the schools seldom move more rapidly than 1 or 2 body lengths per second. For our model, we therefore assume a typical range in velocity of a migrating school of striped mullet to be between 30 and 50 cm/sec.

19.4 Oxygen consumption of swimming mullet The rate of oxygen depletion of the school is a function of both school and individual parameters. School shape, density, and size will all affect depletion rate, as will the rate of water turnover with the school volume. Individual oxygen consumption is a species-specific function of metabolic rate and weight. Data that relate oxygen consumption to swimming speed are available for several species of fish. For instance, Tytler (1969) obtained the relationship Y = 58.9 * 10o«v

(19.4)

for haddock, where Y is oxygen consumption in mg/kg * H at 10°C, and V is specific swimming speed (BL/sec). The value of 0.33 has also been obtained with other species, but the coefficient 58.9 is species and temperature dependent. Jones (1976) published a general relationship of oxygen consumption to specific swimming speed (V), body weight (W), and temperature (7): AR = 0.025 * W°08 exp(0.081 *T+ 0.76V)

(19.5)

where AR is the active rate of oxygen consumption in kJ/day. Because metabolism involving 1 ml O2 releases 0.021 kJ, by substitution: AR = 1.19 * W08 exp(0.081 * T + 0.76V) ml O2/day = (8.27 * 10-4 ) * W°8 exp(0.081 * T + 0.76V) ml 0 2 /min

(19.6) (19.7)

Therefore, for a 30-cm striped mullet weighing 360 g, and migrating through an October-November water temperature of approximately T = 25°C (Adkins et al. 1979) oxygen consumption would be: 1.49 ml 02 /min for U = 30 cm/sec and 2.47 ml 0 2 /min for U = 50 cm/sec.

(19.8)

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William McFarland and Akira Okubo

19.5 Modeling oxygen consumption within a mullet school The metabolic model describes the changes in oxygen availability throughout the school, as oxygen is transported and diffused by physical forces and consumed by the fish in the school. We start with an advection-diffusion-reaction equation in three dimensions, where the coordinate system is fixed to the leading edge (X = 0) of the migrating school. Advection is primarily due to school swimming velocity, diffusion is due to mixing along the periphery created by turbulence within the school, and the reaction component results from oxygen consumption of school members. For simplicity, we assume that oxygen distribution attains a steady state. This assumption is valid because the time scale of lateral and vertical mixing (i.e. oxygen diffusion at edges other than the leading edge) is considerably longer than the time scale of oxygen replacement through advection in the direction of travel through a school. As a result, we feel it sufficient to consider an averaged oxygen concentration along the longitudinal axis of a school for comparison with the field data (McFarland & Moss 1967), greatly simplifying our system of equations. For the concentration of oxygen as a function of school length {(,) averaged over the lateral and vertical extent of a mullet school: D*—±-U*—L-a dx1 dx i2/~'

= 0

(O^x^t)

(19.9)

(€*Sx^€)

(19.10)

AC*

D*—£-U*—dx

=0 dx

where C{ and C2 are the averaged oxygen content of water within the school and behind the school, respectively. D and U are diffusivity and advection velocity, and a is the oxygen consumption rate by a school member (= AR * school density). Equation (19.9) describes the balance among the longitudinal diffusion of oxygen (first term), advection of oxygen (second term), and the reaction loss due to oxygen consumption of school members (third term). This equation is applied within the school, i.e. the longitudinal axis x ranges from zero to € (length of fish school). Equation (19.10) describes the balance between the longitudinal diffusion of oxygen (first term) and advection of oxygen behind the school (second term), i.e. x ranges from (, to €0, where €Q is that distance behind the school where the oxygen concentration essentially regains the ambient concentration Co. Judging from the field data (McFarland & Moss 1967), we chose € as 150 m, and €0 as 195 m, so that k = €
(19.11)

Metabolic models offish school behavior

307

when x = £Q, Cx = C o

(19.13)

dC,

when x = I, C. = C9

dCn

L

— =—(19.14) dx dx Conditions (19.11) and (19.12) simply state that at the front of the school (x - 0) and at the distance €0 behind the school, the oxygen concentrations are at the ambient level. Condition (19.13) states that at the tail end of the school the oxygen concentrations within and just behind the school must have the same value and smoothly vary such that the spatial gradients of oxygen must be the same. For convenience nondimensionality is introduced to the set of equations by letting x'=x/i, C[= C{/Co, and C2 = C2/C0. Equations (19.9) to (19.13) then become: 1

^ - 4 * ^ 7 - 8

«_ki _ dx

and

l

„, «^2 dx

= 0

(19.14)

(O^JC'^1)

n^x'^k)

= 0

(19 15)

for the following boundary conditions: whenx'=0, C,'= 1

(19.16)

whenjt'=lt= 1.3,C 2 '= 1

(19.17)

whenx'= 1, C,'= C2 anddC^/dx'^

dC2'ldx'

(19.18)

where q is the nondimensionalized advection velocity (= U * €/D), and 8 is the nondimensionalized oxygen consumption rate (= (a* (,2)I{D * Co)). Solutions of (19.14) to (19.18) are obtained by 8 C(x)

= l

:,x

\

S

* ei3"

+

\q ~

1)g

" :|: (^

C2{x') = 1 - 4 * • +22(3! - XY * (e13" - **)

\\

(1919)

(19-20)

These solutions can be compared with the field data by choosing values for the parameters 8 and q, where 81q = (a/C0)(£/U)

(19.21)

81qi = (a/C0)(D/LR)

(19.22)

William McFarland andAkira Okubo

308

D is chosen as 60 m2/min inside the school, and 300 m2/min outside the school, € is 150 m, and U ranges from 30 to 50 cm/sec. Thus q ranges from 45 to 75; within the school 8/q = 0.24 and 8/q2 = 0.0054 (U = 30) and 0.0032 (U = 50), and behind the school 8/q2 = 0.0268 (U = 30) and 0.0160 (U = 50). Because q » 1 advection processes dominate and the oxygen concentration decreases linearly from the front of the school with distance through the school. At the trailing edge of the school oxygen content reaches a minimum and the effect of diffusion becomes important, resulting in quick recovery of oxygen levels to ambient values when x > t (Fig. 19.2). The A-D-R model provides a reasonable prediction of reality as based on the field data (Fig. 19.2). Field descriptions provide examples of changes in mullet school shape, continuous turnover of the position of school members, and on some occasions the actual disruption and breakup of large schools into smaller schools (McFarland & Moss 1967; Fig. 19.1). Further, the reduction of oxygen and consequent increase in carbon dioxide from the collective metabolism of the school can be sensed by individual fish (Moss & McFarland 1970). The disruption of schools and loss of organized polarization at the rear of these schools (see Fig. 19. IB) can be attributed to the rather severe changes in respiratory gases demonstrated by the field data. Unless individual fish in the rear of such schools attempt to reposition themselves, they will suffer severe physiological constraints. Repositioning may include a change in interfish distance, polarity, and/or swimming

FRONT

cm/sec 30 50

o 0.5

I

I

I

I

O.5

I

•

x/a

i

l

1.0

l

1.5

Figure 19.2. Relative reduction in environmental oxygen within a migrating mullet school. X is the distance from the front of a school; € is the length of a school from leading to trailing edge. School swimming velocities in cm/sec are represented by solid (30 cm/sec) and dashed (50 cm/sec) lines. C is the oxygen concentration at distance X; Co is the ambient oxygen concentration outside the school. Circles are field data collected from migrating schools of striped mullet (McFarland & Moss 1967).

Metabolic models offish school behavior

309

speed. Often toward the rear of mullet schools roiling of the water surface by individual fish can be observed. This behavior may actually relate to attempts to obtain atmospheric oxygen through the upper pharyngeal chamber (Hoese 1985) and to off-gas carbon dioxide via the gills and/or pharyngeal chamber. Schooling species without such unique respiratory adaptations may experience loss of school structure at smaller school sizes. In this sense, there should be a critical maximum school dimension at a given school density and swimming speed, beyond which individual fish cannot function optimally because of the physiological constraints imposed by the group. For migrating mullet, this appears to be about 75-100 m (McFarland & Moss 1967). Field data on metabolically produced changes in ambient oxygen levels of the water by striped mullet revealed reductions for small schools of longitudinal dimensions of 4-9 m of 1.7 to 5.3%, medium schools of 15-30 m of 7.2 to 10.7%, and large schools of 75-300 m from 9.1 to 28.8% (see Table 1 in McFarland & Moss 1967). A linear model of oxygen concentration as a function of school size predicts large reductions which greatly exceed the few field measurements available (Fig. 19.3). This may be due to the increasing importance of lateral and vertical mixing of oxygen from outside (ambient levels) to inside the rear of the school (i.e. diffusion), which is ignored by the linear model but addressed in the A-D-R model.

y LINEAR MODEL--.

0.3-_

> A-D-R MODEL / /^ ^— ^

•

—

•

—

^

"

—-" / ^ ^

^0.2 O I O°0.1 - *

•

• • i

i

-

I I I I i I I 100 200 SCHOOL LENGTH |m|

I

I

I

I

300

Figure 19.3. Comparison of the A-D-R model and a linear model to field data collected on the amount of oxygen used as a function of school size measured as total length of the longitudinal axis (£ in previous figure). Circles are field data collected from migrating schools of striped mullet (McFarland & Moss 1967).

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William McFarland and Akira Okubo

19.6 Discussion The advection-diffusion-reaction model provides a reasonable description of the metabolic impact of schools of mullet, on oxygen reduction in the water through which they travel. In general, simplified models support the hypothesis that group metabolism can have a dramatic effect on environmental oxygen levels and, therefore, can directly affect the behavior of school members and consequent school structure. For large schools, the interaction between threedimensional structure and species-specific physiological constraints becomes increasingly important in estimating the in situ distribution of dissolved oxygen. Metabolism by fish not only uses oxygen and produces carbon dioxide, but in most fish nitrogenous wastes are excreted across the gills as ammonium ions. In striped mullet schools as large as those encountered in Texas (McFarland & Moss 1967), ammonium excretion may act synergistically with reduced oxygen and increased carbon dioxide to effect the dramatic changes in behavior observed at the rear of these schools. For example, if mullet excrete similar amounts of ammonium as detected from schools of blacksmith, Chromis punctipinnis (Green & McFarland, 1994), then the ammonium concentrations should reach levels of > 100 /uM/1 at the rear of schools that exceed 150 m in length. Fish residing in the rear of a school may not only have to deal with added physiological stress due to toxic changes in dissolved gases, but may also suffer higher energetic costs associated with swimming farther to encounter the same amount of food relative to their leading cohorts. Because oxygen tension declines from the front to rear within fish schools, such an increase in metabolism may have further deleterious effects on rearguard fish. Even though the changes in oxygen tension are not sufficient to be lethal (McFarland & Moss 1967; Moss & McFarland 1970), chronic alterations in respiratory gases lower the capacity of many fishes to maintain constant swimming speed (Fry 1947). Fish at the rear of a medium to large school could suffer a reduced ability to be as active as their forward school mates which, in turn, should increase their susceptibility to predation. The turnover of individuals observed in many schools, and particularly in the rear portions of migrating mullet schools, serves to expose all members to the positionally dependent advantages and disadvantages of the various physiological constraints imposed on the individual by the group (see also Romey Ch. 12). The dearth of information about the physiological impact of fish schools on their immediate environment emphasizes the need to gather accurate field data on school structure and metabolism for several schooling species and under a variety of field conditions. Gathering precise field data on school dimensions and the dynamics of internal school structure and measuring metabolic impact(s)

Metabolic models offish school behavior

311

throughout each school (i.e. oxygen, carbon dioxide, ammonia, etc.) presents a major technical challenge. In spite of the need for more data from the field, we suggest that the A-D-R model presented here could be more precisely tested with studies of fish schools under controllable conditions, as in the laboratory rather than in the field. Other considerations concerning the physiology of fish schools need to be addressed. Is there some lower oxygen threshold for each schooling species that effects significant internal changes in the school? Do some species partially avoid this threshold by accumulating an oxygen debt that is amortized at night when the school structure breaks down? Do many schooling species use atmospheric oxygen, as suggested for mullet (Hoese 1985)? Do schooling fish roil the surface, as seen in mullet and menhaden, to increase gas diffusion into and out of the surface layer? Finally, questions arise as to whether group metabolism equals the sum of the individuals - which reopens Schlieper's much older suggestion that group metabolism might actually be less than the sum of each school member when measured alone. Such may well be the case in tightly packed schools because of improvements in hydrodynamics (Weihs 1984). It is questionable, however, that metabolic reductions that issue from schooling would be sufficient to counteract the metabolic impact of a large fish school.

Acknowledgments We are grateful to the National Science Foundation for support of the workshop which stimulated this collaborative project. This chapter is contribution 163 of the Wrigley Marine Science Center, and contribution 942 of the Marine Sciences Research Center, State University of New York, Stony Brook.

Symbols NND = nearest neighbor distance L = body length of fish (usually expressed in cm); also BL € = length of fish school expressed in meters RE = Reynolds number = U * Llv U = swimming velocity (usually in cm/sec), which also equals the advection velocity as used in the model v = kinematic viscosity in cm2/sec Y = oxygen consumption in mg/kg*//

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William McFarland andAkira Okubo

V — specific swimming speed in BL/sec AR = active rate oxygen consumption (expressed in various units) D = diffusivity expressed in m2/min Co, CVC2= mean oxygen values in front of, within, and behind school § = nondimensionalized oxygen consumption rate q = nondimensionalized advection velocity a = oxygen consumption rate by a school member [= AR * (0.1 fish/1)]

20 Social forces in animal congregations: Interactive, motivational, and sensory aspects KEVIN WARBURTON

20.1 Introduction Until relatively recent times there has been a strong tendency for studies of animal congregations to emphasize the properties of the group rather than the fact that all such groups are composed of independent individuals (Pitcher & Parrish 1993). This is partly because the collection of data from identified members of dynamic, often large, and three-dimensional groups is not a straightforward matter. However, since natural selection operates mainly upon the individual, it is important to develop interpretations on the structure-function relationships of groups in terms of the imperatives and constraints which impinge on individuals (Magurran 1993). To this end, it is relevant to consider how social interactions and whole-group dynamics are influenced by changes in the motivational state of individuals in response to internal and external factors. This raises questions concerning the types of information to which congregating individuals respond, as well as the translation mechanisms which mediate between sensory inputs and emergent behavior. Motivational analyses can therefore provide a framework within which the highly dynamic changes in an animal's internal state, themselves affected by a wide range of external factors, may be used to interpret group processes. A central aim in attempts to assess the fitness consequences of group cohesion and coordination must be an appreciation of the mechanisms whereby members of a group interact. In other words, understanding how animals group can help us understand why they do so (Partridge et al. 1980). As with other behaviors, an instructive approach is to pose questions regarding the number of internal causal factors which underlie the behavior, how they interact, how they are affected by external cues, and how they change over time (Colgan 1993). Several authors have proposed that group cohesion is maintained primarily by an interplay of attractive and repulsive forces operating between neighboring 313

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Kevin Warburton

individuals. Models which invoke a set of modulated attractive and repulsive forces can be used to describe typically observed movement patterns of grouping animals. The origins of these social forces and their sources of variability have been less frequently considered. A theme developed in this chapter is that certain types of attraction-repulsion models can shed light on motivational tendencies of grouping individuals. They can thereby help to explain grouping at a more fundamental level than purely descriptive movement models (which have often been used as building blocks in larger models of group structure and function). They can also account for phenomena at the group level in terms of the consequences of interactions between group members. The present intentions are (1) to examine various models of attraction-repulsion interaction and compare their predictions; (2) to consider how interindividual spacing, as determined by the balance between attractive and repulsive tendencies, is modified by internal and external factors; (3) to review relevant characteristics and constraints of the sensory channels through which information on such factors is received; and (4) to consider ways in which hypotheses regarding social forces can be tested empirically, with the aim of gaining insight into movement decision rules and a better understanding of the sensory-motor basis of grouping behavior. This chapter is somewhat biased toward aquatic vertebrates, reflecting both the main interests of the author and an abundant literature on fish schooling and shoaling. It focuses on the interactive processes occurring within groups and not their higher-order consequences (cf. Turchin 1989a).

20.2 Models of attraction and repulsion 20.2.1 Group dynamics and social forces Okubo (1986) described the movement dynamics of animal groups in terms of interactions between three categories of biological forces, analogous in some ways to a Newtonian analysis of physical forces: 1. External forces (those emanating from outside the group). These include pressure for dispersal and mate finding as well as physiological or behavioral responses to environmental conditions. In the present context this category would also include searching movements and "random" walking unrelated to group interactions. 2. Internal forces (those emanating from interactions between numbers of the group). 3. Frictional forces acting on an animal as it moves. These are assumed to be linearly related to the velocity when the Reynolds number is small (i.e. with

Social forces in animal congregations

315

relatively small organisms), but quadratic with respect to velocity when the Reynolds number is large (relatively large animals). The main interest here is in forces of the second type. Specifically, when animals are within communication range and social forces are the only determinants of movement, an individual closer than a given distance from another will tend to move away from it (repulsion) and one which is farther than a given distance will tend to approach it (attraction). The boundary between the zones of repulsion and attraction then occurs at an equilibrium distance, where repulsion switches to attraction. The concept of an "equilibrium distance" is similar to that of "individual distance," which may be defined as the distance at which another individual provokes aggressive or avoidance behavior (Hediger 1955; Brown 1975). In practice, the personal space kept free around an animal may be asymmetrical, being likely to be larger in front than behind (Brown 1975).

20.2.2 Threshold tendency models Assumptions regarding the existence of an equilibrium distance lead to two distinct interpretations of attraction and repulsion in animal congregations. In "threshold tendency" models, the approach tendency is activated only when the separation of individuals exceeds the equilibrium distance, and the avoidance tendency operates only within the equilibrium distance (Warburton & Lazarus 1991). There is a simple correspondence between motivational tendency and behavior, so that the tendency-distance relationship is identical to the behavior-distance relationship. Decisions to approach or avoid depend on whether the distance separating an individual from another member of the group is greater or less than the equilibrium distance. The strength of movement may be constant (where movement strength is a step function of separation distance), or attraction and repulsion may increase monotonically as the difference between the separation and equilibrium distances departs from zero (Fig. 20.1a,b). The threshold tendency approach has frequently been used as one component of larger-scale simulations of grouping dynamics. For example, Thompson et al. (1974) used such assumptions in a "social movement" subroutine as part of a simulation model of bird flocking. They defined a movement reaction (MR) by one bird relative to another as: MR = (t - d)ea('-d)

(20.1)

where t is the threshold distance, d is the separation distance, and a is a scaling constant. The shape of this monotonic function is upwardly convex, the degree of convexity depending on the exponent.

316

Kevin Warburton

(a) ED

(b)

ED

(c) A R -

A-R-

Separation distance

Figure 20.1. Tendency-distance models. Dashed lines indicate attraction (A) and repulsion {R) tendencies; solid lines indicate resultant cohesion functions (A-R). ED is the equilibrium distance, (a) Threshold tendency model (step function); (b) threshold tendency model (monotonic function); (c) continuous tendency model.

Sakai (1973) and Suzuki and Sakai (1973) (discussed by Okubo 1980) described a model of fish schooling in which a step function was used to separate zones of mutual repulsion and attraction. Repulsion strength varied linearly with interindividual distance and attraction was assumed to be constant between the equilibrium point and a specified maximum distance. Additional influences included in the model were a random force, a forward thrust (a tendency to continue forward at a given velocity), and an arrayal force (a tendency for neighboring animals to equalize their velocities when they are within a sphere of influence). The model was able to simulate a range of different types of group motion, such as amoebic movement (when the random force exceeds the forward force and the shape of the near-circular group fluctuates but the center of mass hardly moves), group rotation (when the forward thrust exceeds the ran-

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dom force and a doughnut-shaped group rotates about an empty center), and rectilinear motion (when an arrayal force is added to the other forces, forming a tight, cohesive, directed group). A somewhat different approach was taken by Huth and Wissel (1992), who distinguished three concentric zones about a simulated subject fish (Fig. 20.2): (a) an inner zone of repulsion (within a radius of c. 0.5 body lengths), (b) a middle zone (c. 0.5-2.0 body lengths) where the subject attempted to orient itself parallel to a neighbor entering the zone, and (c) an outer zone (c. 2.0-5.0 body lengths) of attraction. A fourth zone (d), namely a sector of interior angle c. 30 degrees immediately behind the fish, was also identified. If all the fish's neighbors were located in area d then they could not be perceived and the fish reacted by searching (making a random turn). Fish schools simulated by this model displayed characteristics of real schools: namely, a high degree of parallel orientation and strong cohesion. The distribution of distances to neighbors was also similar to those of real schools, but unlike real schools (Partridge et al. 1980) the nearest-neighbor distribution did not decrease to zero at a finite separation distance. This was thought to be due to a simplifying assumption that the velocity of each fish could be chosen independently of its neighbors, producing a repulsive behavior which was too weak. A simulation model of schooling developed by Aoki (1982) incorporated similar assumed zones of approach and avoidance.

Figure 20.2. Areas of interaction around a member of a fish school, according to Huth and Wissel (1992). (See text for details.)

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A common feature of the threshold tendency approach, therefore, is the postulation of a fixed repulsion zone around each individual in the group; however, it may also appear in other forms - such as in movement rules of the type "if the size of a conspecific image on the retina is too small then approach; if the image size is too large then avoid." See, for instance, the loom of Dill et al. (Ch. 14). Despite their advantages of simplicity and the possibility of obtaining empirical agreement with observed behavior patterns, threshold tendency models of attraction and repulsion remain summary descriptions of phenomena which may have a complex and interactive basis. If they are to reflect reality, threshold tendency models require that animals estimate the separation distance, compare it with a reference (equilibrium) distance, and subtract one from another to determine the magnitude and direction of the resultant tendency. An alternative class of models ("continuous tendency" models - Warburton & Lazarus 1991) assume that attraction and repulsion tendencies coexist, and that both vary simultaneously with distance. In this case, it is the sum of the two effects which determines the resultant behavior at a given distance (Fig. 20.1c). In terms of neural processing requirements, continuous tendency models are more parsimonious than threshold tendency models because they simply demand the estimation of interindividual separation distance, coupled with appropriate distance-tendency translation mechanisms. They are also more likely to be realistic because both tendencies are in operation at the same time, which accords with ethological evidence that approach and avoidance tendencies are often in conflict (Baerends 1975). 20.2.3 Continuous tendency models In the context of fish schooling, Parr (1927) first interpreted group cohesion in terms of a balance between attractive and repulsive forces, but he did not formulate expressions for those forces. Breder (1951) later developed a mechanistic approach and considered the use of gravitational formulae similar to those applied in studies of magnetism and electrostatics to describe the mutual attraction of merging schools. Thus, f=k

K

(m, * m,) ' ,. 2>

(20.2)

where/equals force, k is a constant, and m, and m2 are two particles or masses separated by a distance d. Breder (1951) speculated that mx and m2 could represent the number of fishes in the two schools, that the constant k could be ignored, and that the smaller group should move faster since it is attracted to a larger "mass." Breder also

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noted that a physical analogy could help to explain the very existence of schools and other aggregations: because a uniform distribution of mutually attractive items is gravitationally unstable, fishes should form dense masses with large vacant spaces in between. Breder (1951) cited the results of Japanese studies in support of these conjectures. In particular, the work of Tauti and Hudino (1929) with Leuciscus hakuensis revealed that the attractive power of a group decreased with distance, that a moving aggregation was more attractive than a static one, and that a large group had a greater attractive influence than a small one (see also Kennleyside 1955b). More recent experiments by Hager and Helfman (1991) demonstrated that minnows preferred larger shoals, but only where all test shoals were relatively small. Avoidance of small shoals was more marked in the presence of predatory threat. In subsequent papers, Breder (1954, 1959) elaborated his previous ideas. He started with an assumption that both attractive and repulsive forces operating between individual fishes varied inversely with the power of interindividual distance:

c

~ f- ~ 7-

(203)

where a equals attraction, r equals repulsion, d equals the separation distance, m and n are exponents, and c equals cohesiveness (i.e. the sum of attraction and repulsion). Breder (1954) suggested that repulsion might vary inversely as the square of the distance, as in Coulomb's law of magnetism and electrostatics. He noted that, although the exponent could theoretically take any value, with n = 2 the repulsive strength increased rapidly with a small departure below the equilibrium distance, as would appear to be required in the case of fish schooling in close proximity. The effect of reducing the size of the exponent is to lessen the slope of the cohesion curve as it crosses the distance axis and to increase the average spacing between fish. It is unlikely that the exponent would reach the third power; using another physical analogy, Newton pointed out that this would cause the planets to move away from the sun in spiral paths. Breder (1954) also argued that because attraction is more effective than repulsion at long distances, the exponent m for the attractive force should be less than the repulsion exponent n. Further, as attraction seems to be mediated largely by vision (at least in fish), it might be practically independent of distance up to the limits of visibility, and m could be assumed to be zero (i.e. the value a could be treated as a constant). Thus, the original equation reduces to

c = a-ji

(20.4)

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Because r involves two objects (individual fish or schools), this may be expressed as c —a—

(r, * r2)

(20.5)

When c is plotted against distance this gives an upwardly convex curve, with the attractive force rapidly reaching a plateau (Fig. 20.3). In this case, fish are very sensitive to variations in separation distance only when they are close together. Based on observations of two-fish groups of roach, mullet, and chromis, Hemmings (1966) concluded that close swimming coordination could be adequately described by three motor patterns, namely (1) an exploratory tendency, where either fish would swim in any direction away from the other; (2) a returning tendency, where if it was not followed, the fish swimming away would turn and swim back to the other; and (3) a following tendency, where when one fish swam away it would usually be followed by the second fish. These tendencies were interpreted as an action-reaction system, where pattern 1 constituted the action. Hemmings's scheme does not describe movements within the "optimum or preferred" separation distance, where mutual repulsion should be greatest. While pattern 1 may be interpreted as an internal repulsive force and patterns 2 and 3 as internal attractive forces (as in Okubo's 1986 scheme), it is difficult to determine the extent to which exploratory movements are the product of attraction to environmental factors, or if returning movements are influenced by repulsion by

f -8

-12

-16 0

4

8

12

Distance Figure 20.3. Graph of the cohesion equation c = a — rx rjd2, where r, = r2 = 3 and a=\. (From Breder 1954). (See text for details.)

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external stimuli. This problem of interpretation highlights the general point that the relationship between motor patterns and internal states can be quite complex. Although he did not attempt to quantify the strength of these tendencies, Hemmings conceived of them as increasing or decreasing nonlinearly with separation distance (Fig. 20.4). The corresponding resultant behavior function would be upwardly convex. Hemmings's scheme could be incorporated into models of cooperative behavior (e.g. "tit-for-tat" interactions) between fish inspecting potential predators - Dugatkin 1988; Milinski et al. (1990). Synchronization in bird flocks has been similarly interpreted in terms of the interaction of different tendencies, although not necessarily in exactly the same way. For example, Crook (1961) described two main factors, namely social facilitation (copying) and a following (directionally oriented) reaction. Warburton and Lazarus (1991) reasoned that although the form of component attraction and repulsion curves could not be known a priori or measured directly, natural selection should favor resultant attraction-repulsion relationships which maximize group cohesion. They simulated the effects of a family of resultant functions having a range of shapes, including strongly convex, linear, and strongly concave. Cohesion was defined in terms of spacing (mean interindividual distance) and an index of group elongation, high cohesion being associated with low mean values and low variation in those measures. Their results showed

R1 + R2

u ©

c o OS

o

SO

SI

S2

Separation distance between two fish Figure 20.4. Hemmings's (1966) proposed basis of visual contact between two schooling fish. Al (action), exploratory tendency of first fish; Rl (reaction), following tendency of first fish; Rl (reaction), following tendency of second fish; SO, optimum or preferred separation between fish; SI, separation when Al = Rl + R2, with two fish swimming freely; S2, separation when A1 = Rl, with one fish free and the other caged but visible. (From Hemmings 1966).

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that as long as social forces were present all models led to stability in group structure, but that cohesion was best served by an upwardly convex behavior-distance function. However, this was highly conditional on the relative magnitudes of the maximum levels of attraction and repulsion, as well as on the shape of the resultant curve: a strongly asymmetrical function, with maximum repulsion exceeding maximum attraction (as proposed by Breder 1954), was distinctly inferior to one where the maximum levels of the two tendencies were equal. Thus, both the relative amplitudes and the attenuation characteristics of interactive social forces may be subject to selection.

20.2.4 Harmonic models Formal models of fish schooling dynamics have often used a similar operational framework to the exploratory-returning-following interpretation of Hemmings (1966) to examine patterns of spacing fluctuation as distinct from descriptions of average structure. In modeling a two-fish school, Okubo et al. (1977) incorporated frictional forces (proportional to velocity), a harmonic force relative to the equilibrium position, and a "swimming force" per unit mass. In this model, one fish was assumed to follow the other and to respond to changes in the acceleration of the first fish with a small but finite time lag (latency). A theoretical spectral density function was well fitted to data on the cyprinid Gnathopogon elongatus with a latency of 0.2 sec. This model was similar to a linear dynamic model applied to insect swarming (Okubo 1986), except that in fish schooling the forces between fish were closely related with a small time lag while in insect swarming each insect was subject to an independent random force. However, as Okubo (1986) pointed out, schooling models such as this one may need modification before they can be applied to multifish schools, because individual differences and leadership behavior are more marked in very small groups (Partridge 1980; Fitzsimmon & Warburton 1992), and the correlation between the instantaneous velocities of individuals in the group increases with school size and school density (Partridge 1980). Breder's (1954) simplifying assumption that all fish in a school can be regarded as equipotential cannot therefore be strictly upheld. The relative instantaneous orientations and positions of animals within the group will have a strong influence on their ability to attract or repel their neighbors. Empirical observations and simulation models suggest that only relatively few neighbors (most importantly, the nearest) need to be monitored for maintenance of group cohesion (Partridge & Pitcher 1980; Warburton & Lazarus 1991; Huth & Wissel 1992; Parrish & Turchin Ch. 9). Flocking hens show similar priorities, individuals looking more directly at nearest

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than second-nearest neighbors, and facing their nearest neighbor more as the separation distance decreases (McBride et al. 1963). Spectral analysis of the separation distance in Gnathopogon swimming in groups of 2 to 8 revealed a long periodicity of 10-20 sec, which was attributed to alternating movements of approach and withdrawal, and a short periodicity of 2-4 sec, which was interpreted in terms of small-scale movements for the fine adjustment of position to maintain a desirable interfish distance of about 1 body length (Aoki 1980). Aoki attributed the relatively uniform density distribution across the school to a balance between convergence and dispersion as the fish apparently avoided areas of local high density. In a later paper on the harmonic behavior of Gnathopogon and mullet, Aoki (1984) showed that the observed power spectra agreed well with theoretical results derived from linear differential models. In particular, nonrandom fluctuations of nearest-neighbor distance were well described by the following model:

d

i - -i

(2a6)

at k where r is the deviation from the equilibrium distance and & is a time constant. In other words, the deviation decreased at a rate proportional to the deviation. If the movement tendencies of the fish are proportional to velocity, then this would imply a linear cohesion function and attraction will increase with distance. On the other hand, if tendencies are proportional to acceleration (from the analogy with physical forces and the relationship force = mass X acceleration), this would imply that the resultant tendency is independent of separation distance.

20.3 Sensory modalities mediating the attraction-repulsion system Information on extrinsic and intrinsic factors may reach animals via a number of pathways. Candidate sensory systems include vision, hearing, the lateral line system of fish and aquatic amphibians, touch, olfaction, gustation, electroreception, and temperature sensitivity. Information exchange efficiency through a given channel is strongly dependent on the nature of the transmitting medium (Schilt & Norris Ch. 15). Light is transmitted relatively poorly through water; even in the clearest water, visual contrast decreases rapidly with distance (Loew & McFarland 1990). On the other hand, hearing is potentially more efficient in aquatic environments because sound is transmitted much better in water than in air (Popper & Coombs 1980). It is likely that aquatic animals "hear" rather than "see" their most distant horizons.

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Within visual range, the mean reactive distance of fishes increases asymptotically with stimulus size (Hester 1968; Ware 1973). Together with limitations on light availability (e.g. in cave environments, the deep sea, and at night) and penetration (e.g. in turbid environments), this means that vision can be relied upon only over a relatively short distance surrounding the subject. At close range there is abundant evidence that vision is an important means of monitoring other individuals and maintaining cohesive groups (e.g. in fish and dolphins - Shaw 1978; Norris & Schilt 1988). These considerations imply that for aquatic animals, vision has limitations in terms of the identification of, and attraction to, distant conspecifics. It is also possible that chemical senses aid in the process of congregation (Keenleyside 1955b; Hemmings 1966), but the diffusive nature of their stimuli prevents them being useful in accurately estimating distances to, and directions of, mobile conspecifics. Dolphins produce signature whistles (at least in captivity) which are more multidirectional than their beamed echolocation clicks (K. Schulz, pers. comm.) and which may be used to maintain local contact and parallel spacing. The role of hearing in schooling fish needs further investigation, but few sounds have been recorded from schooling species (Hawkins 1986). Of the various mechanoreceptor systems, the lateral line appears to be the most heavily involved in the maintenance of school cohesion (Bleckmann 1986). The lateral line is sensitive to water displacements and pressure waves caused by pulsating, vibrating, or moving objects, which would necessarily include the fin movements of shoaling neighbors. Water displacements decrease inversely with the cube of distance from the source and are the basis of the so-called nearfield effect. The motion of objects also produces pressure changes of two types: near-field pressure changes associated with near-field motion (which attenuate inversely with the square of the distance) and far-field pressure changes (which decay inversely with distance and are the basis of hearing - Bleckmann 1986). The rapid attenuation of the near-field effect means that relevant receptors would have to be unrealistically sensitive to be useful at ranges greater than a few body lengths. Similarly, far-field pressure vibrations are unlikely to be strong enough to stimulate the lateral line (Bleckmann 1986). However, when a fish is close to a source of vibration, the relative movement of the medium may vary considerably along the length of the fish and provide detailed information on the direction and distance of the source (Denton & Gray 1983). Aquatic invertebrates also rely on mechanoreception: for example, copepods have antennal setae which project in three planes and can detect local vibrations in three-dimensional space (Yen & Nicoll 1990). In zooplankton, communication seems to occur mainly via the relatively slow transmission of mechanosensory or chemical cues (Yen & Bundock Ch. 10). Although these senses may be used for food finding or predator avoidance, they are doubtful candidates for

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swarm maintenance. However, zooplankton also exhibit responses to light since swarms loosen by night (Clutter 1969; Shaw 1978; Hamner & Carleton 1979), and in the case of large crustaceans such as krill, individuals finding themselves isolated at some distance from the main congregation reestablish contact using rapid directed movements (Hamner, pers. comm.), which are probably mediated by vision. Using sensory deprivation techniques, involving temporarily blinding and/or sectioning the lateralis nerves of schooling saithe, Partridge and Pitcher (1980) examined the respective roles of vision and the lateral line. Blinded fish exhibited greater nearest-neighbor distances (NNDs) than control fish, while lateralis sectioned fish schooled at lower NNDs than controls. Therefore, vision appeared to be associated with attraction and the lateral line with repulsion. Schooling was eliminated only by simultaneous blinding and lateralis sectioning, but not by either in isolation (see also Pitcher et al. 1976). Correlations between the speed or heading of a particular fish and the speed or heading of other fish a short time before indicate what standard of reference a fish uses to adjust its velocity (Partridge 1982). The strongest correlation is that involving a number of neighbors (not just the nearest) and the square or cube of the distance from the subject fish (Partridge 1982). If fish attend primarily to visual information, then the correlation should depend on the area of an image projected onto the retina (see Dill et al. Ch. 14) and thus with the square of the distance. Alternatively, if discrimination is via the near-field lateral line modality, then it should be affected by its strong attenuation characteristics and depend on the cube of the distance. The fact that the best correlations occur with exponents somewhere between two and three suggests that both modalities are employed. These deductions do not support Breder's (1954) speculation that attraction can be treated as a constant, but rather provide evidence for a dynamic balance between opposing forces. Evidence for the interplay of coexisting forces comes also from other sensory deprivation experiments — for example, fish reduce their spacing distance when separated by a glass sheet (Hemmings 1966). A system involving multiple sensory modalities must incorporate a method for resolving conflicting information. Schooling fish are presented with conflicting information about the velocity of neighbors from their lateral line and vision whenever they turn; in such circumstances, they pay more attention to visual cues (Partridge & Pitcher 1980). It is likely that the swarming behavior of flying insects is mediated by vision or mechanoreception. In migrating locust swarms cohesion is maintained by insects at the edge of the swarm consistently orienting toward the interior (Betts 1976). Interactions between individuals in midge swarms have also been

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recorded (Okubo 1986). In pine beetles, swarming is a two-stage process, namely (1) directed flight in response to volatile chemicals from the host tree and to visual cues, and (2) congregation in response to sex-specific pheromones (Geiszler et al. 1980; Turchin Ch. 7). By contrast, in crawling insects, spacing is often maintained by touch; thus, crawling flies maintain at least two leg lengths between individuals (Sexton & Stalker 1961). In the case of most birds and terrestrial mammals, spacing interactions are apparently carried out using information obtained predominantly by visual means. This is a significant departure from the simultaneous use of two or more modalities common in aquatic animals such as fish. The fact that the transmission of visual signals is much better through air than water suggests that land animals have experienced relatively weak selective pressures to evolve "backup" systems to detect movement patterns in conspecifics at close range as well as for attraction at greater distances. However, vision as the single sensory modality regulating aggregation presents several potential sources of systematic error. Monocular ungulates may have difficulty with depth perception and body size, and therefore at a given distance image sizes of animals in a given group may vary widely (Partridge & Pitcher 1980). Thus, vision must transmit different types of information simultaneously. One likely type of information would be derived from the size of the retinal image of a conspecific (or some feature thereof). This is also consistent with mechanisms of attraction of predators toward their prey. There is evidence that fish use the apparent size of prey (i.e. the area of the image projected on the retina regardless of the distance of the prey from the eye) to make early orientation decisions (Wetterer 1989). (Note, though, that attraction is directly proportional to image size in prey selection but inversely proportional to image size in schooling.) However, at a later stage of the same process, predators are able to assess real prey size more accurately, possibly by using parallax (Li et al. 1985) or binocularity (Wetterer 1989). In a similar way, Ingle (1967) distinguished between (1) visual processes which are involved in orientation to a moving object and (2) those by which animals evaluate the identity or activity of the object. Grouping animals may be able to estimate distance by using parallax or binocularity or by monitoring other visual cues, such as the color or shape patterns on a neighbor's body. Norris and Schilt (1988) suggested that in dolphins, a small change in the angle of a pectoral fin (a dolphin's diving plane) instantly signals a change of the animal's direction in three dimensions and noted that such fins are normally dark against a light body field or move across a dark-light pattern edge. The production and perception of such subtle movements allows neighbors to escape from predators in a rapid and coordinated manner. Other types of signals

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might include movements of the dark bars, fin-markings and silvery surfaces of fish, or the head markings and wing bars of birds (e.g. Keenleyside 1955b; Muntz 1990). When a predator approaches, the normal response of a prey group is to tighten. This should have the effect of maximizing message transmission speed by increasing the ability to detect subtle signals (Norris & Schilt 1988). At the same time, it is important that a given individual does not need to move either eyes or head to detect signaling neighbors. Even eye movement is too slow a process to be accommodated in the extremely rapid events of predator avoidance. Furthermore, such eye movements could themselves confound accurate assessment of a neighbor's movements (Norris, pers. comm.). Under these circumstances, constraints on the speed and accuracy of transmission would thus tend to select for maintenance of a minimum distance between neighbors so as to maximize information transfer efficiency. Therefore, group cohesion might involve two distinct types of process, explicable in terms of (1) an attraction tendency which varies continuously with distance, and (2) a threshold tendency mechanism, where the equilibrium distance is subject to continual refining as short-term conditions (e.g. the sudden appearance of a predator) change. It is worth noting that this latter process would overcome the main objection to threshold tendency models, namely the need to store an independent reference (equilibrium) distance in memory (Warburton & Lazarus 1991). The possibility that some animals may be able to rely exclusively on such a threshold tendency mechanism for the maintenance of cohesion requires rigorous testing.

20.4 Real-life factors mediating attraction and repulsion, and their effects on group cohesion In the above models, interest has centered mainly on explaining essential features of group dynamics or interpreting relatively short-term data sets obtained in an unvarying environment. To return to Okubo's (1986) classification, interactions between attractive and repulsive tendencies are examples of internal group effects. However, interindividual spacing is not fixed for a number of species (Crook 1961); obviously tendencies are not constant but may be modified, over a change of time scales, by a number of other influences. The definition of internal factors as those which are integrally involved in the ongoing grouping processes draws attention to the essential cues involved in interaction. Fish may use sizes, color patterns, or trajectories of neighbors to assess distance, bearing, velocity, or acceleration. Thus, effects of external factors can be regarded as superimposed on the primary interaction processes. Together, internal and external factors define a multivariate complex in motivational space.

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What then are the most important external factors affecting spacing dynamics, and how do they interact with the internal influences? Although there is a plethora of relevant external factors, some common themes emerge. Predominant among these are the twin imperatives of food-finding and predator-avoidance and the various trade-offs between the two which characterize animal groups (e.g. Dill & Fraser 1984; Lima 1985; Romey Ch. 12). In the realm of food-finding, the dispersion of an aggregation often reflects that of its food resource (Crook 1961; Brown 1975) so that heterogeneous habitats may support higher population densities and closer spacing (Fretwell & Lucas 1970; Hazlett 1975). Hungry birds are known to follow others flying to a food source (DeGroot 1980) and flocking is often more prevalent when food is scarce, as in cold winters (Pulliam et al. 1974). Hungry animals may also investigate areas which others have exposed as being profitable (area-copying - Krebs et al. 1972; Pitcher & House 1987), while animals which are concentrating on feeding may either tolerate closer approaches by conspecifics (Crook 1961) or move farther apart. However, food is not the only motivating factor. Thus starvation need not affect the spacing of resting animals (e.g. the perching behavior of birds such as chaffinches Marler 1956). In the realm of predator-avoidance, a common response to the approach of a potential predator is to close ranks (and in some cases, clump with others in the group - Kennleyside 1955b; Meinertzhagen 1959; Goss-Custard 1970). Close packing into a conspicuous mass may sometimes serve as an aposematic device (i.e. act as a deterrent to predators by advertising unpleasant consequences of attack), as in caterpillars of the cinnabar moth on ragwort and in tight congregations of the venomous catfish Plotosus (Driver & Humphries 1988). This tightening response appears to be more effective as an antipredator strategy in pelagic species than in benthic, cryptic prey or in palatable terrestrial species, because of differences in the likelihood of prey detection and attack by predators (Driver & Humphries 1988). Reliable evidence as to the effect of fish school size on schooling density is limited. However, some studies (Nursall 1973; Partridge et al. 1980; Smith & Warburton 1992) indicate that mean spacing may vary inversely with group size. Perhaps in highly dynamic situations, predatoravoidance may be better served by improved locomotory freedom than by group contraction. Regardless of predation pressure, tight spacing in small groups subject to social and random forces can also be predicted on theoretical grounds, as long as the number of neighbors to which an individual responds does not vary greatly with group size (Warburton & Lazarus 1991). There is some evidence that schooling fish of a given species tend to group together less densely as their mean body size increases (Breder 1965; Dupee & Warburton in prep.). There is also evidence to the contrary (Van 01st & Hunter

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1970), but as discussed by Symons (1971a), this may be due to the inaccurate estimation of nearest-neighbor distances from two-dimensional photographs. Decreasing density may relate to improved maneuverability, but it is also consistent with a relaxation associated with reduced vulnerability to predators as body size increases. By aggregating in groups, animals reduce the need for individual vigilance and therefore improve their ability to obtain a favorable trade-off between their investments in foraging and predator-avoidance (Magurran & Pitcher 1983; Caraco 1983). Smith and Warburton (1992) interpreted short-term changes in the spacing of shoaling blue-green chromis, Chromis viridis, in these terms, and showed that mean nearest-neighbor distance decreased during the course of a three-minute feeding bout. This appeared to be independent of effects due to changes in the dispersion of prey (swarming brine shrimp), because the fish shoals continued to contract after their prey were fully dispersed throughout the test tank. Abrahams and Colgan (1985) interpreted induced changes in the shape of a school of blackchin shiners, Notropis heterodon, similarly as a trade-off between predator-avoidance and hydrodynamic efficiency. In affecting the spacing behavior of animals, although not generally thought of as structuring passive congregations, individual recognition and social status are often influential. Individual distances in bird, fish, and primate species increase with social dominance (King 1965; Gibson 1968; Thompson 1969). Marler (1956) demonstrated that in chaffinches the distance at which aggression occurred depended on dominance and sex. Schilt and Norris (Ch. 15) discuss sensory integration systems in cetaceans where interanimal distances may be regulated by social communication. The above considerations suggest that the basic form of a tendency-distance relationship is likely to be determined mainly by internal cohesion factors, which are important in the continuous monitoring of the relative positions of neighbors. In contrast, most external factors operate independently of distance, and therefore can be understood as variables which may change the intensity of attraction or repulsion tendencies but not the general form of the tendency-distance curve. The most important exception may be direct predatory threat, which is likely to vary quantitatively as the predator approaches. The density and threedimensional structure of schools vary according to predator presence/absence as well as the time since the last attack (Abrahams & Colgan 1985; Dupee & Warburton in prep.). The time spent at a food patch by shoaling minnows confronted by an approaching model pike predator was linearly related to the distance of the perceived threat (Magurran et al. 1985). These results suggest that the modifying effect of such an external factor will be to increasingly sharpen the slope of the attraction curve, and thus the resultant cohesion curve, as the predator approaches. Therefore, animals in the group would be likely to become more

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sensitive to the predator's movements, as well as to clump more strongly, as the predator advances. Reactions to other group members having differing dominance status may also be distance dependent, but little is known about dominance relationships within passive congregations. The likelihood that, in general, external factors may affect spacing by modifying the relative strengths of attraction or repulsion in a straightforward, additive fashion means that, in principle, the form of tendency-distance relationships underlying the cohesion process can be revealed by comparing the cohesion characteristics of a given group in the presence and absence of the modifying factor.

20.5 Models of attraction and repulsion which describe the effects of motivational change Several studies have assumed or deduced the existence of an interplay between opposing forces of social interaction, and some have suggested what typical characteristics of a combined resultant function might be like. Understanding the form of the component attraction and repulsion functions, and thereby gaining a clearer insight into the motivational and sensory basis of group cohesion, is a worthwhile aim. However, it is complicated by the fact that it is possible to observe directly the outcome of an interaction between the two opposing tendencies, but not the tendencies themselves. The intention here is to explore a possible solution to this problem by formulating predictions regarding changes in the resultant cohesion curve which would be expected in response to variation in external cohesion factors. These predictions could then be tested empirically (e.g. by observing interactions in a group under a systematically modified external factor). Figure 20.5 illustrates a generalized continuous tendency attraction-repulsion system where attraction increases and repulsion decreases with interindividual distance (henceforth called a Type 1 system). For simplicity, the two tendencies are assumed to vary linearly, but the same general argument developed here also holds for convex or concave curves. If the slope of the attraction function decreases due to a change in motivational state (as in response to variation in an extrinsic factor), then the strength of the attraction tendency at a given distance (A in Fig. 20.5) will fall and the individuals concerned will tend to space themselves farther apart. The range of the repulsion effect may be affected in a similar way, reducing the distance DRmax, and reducing the average spacing between individuals. In Type 1 systems, the resultant tendency moves from net repulsion (when individual spacing is less than the equilibrium distance ED) to net attraction (beyond ED). Additional distance-related effects, such as the attenuation of light or sound, or the masking of distant images by near neighbors, will reduce

Social forces in animal congregations

D

331

max

DRmax

R

Distance Figure 20.5. Generalized attraction-repulsion system where attraction increases to a maximum (at maximum distance, Omax) and repulsion decreases to zero with increasing interindividual distance. ED (filled circle): equilibrium distance. Solid lines indicate original attraction and repulsion curves, dashed lines indicate modified conditions, and heavy lines indicate resultant functions. Modified conditions result from reduced attraction at a given distance (and hence reduced slope of the attraction function), and/or a reduced range over which repulsion operates. Points a and b indicate maximum repulsion distances (DR ) under original and changed conditions respectively.

the amplitude of net attraction beyond distance Dmax and are not included in the basic model. Figure 20.6 illustrates an alternative attraction-repulsion system (Type 2), where the shape of the resultant tendency is similar to that of Type 1, but where attraction decreases with distance. As a result, at extreme distances a decrease in net attraction is explicit in the model. Variation in the range of attraction and/or repulsion (i.e. change in the slopes of the component functions) affects three potentially measurable factors, namely (1) the equilibrium distance, (2) the amplitude of the resultant function on the attraction axis, and (3) the overall range of the resultant on the distance axis. Because combinations of these qualitative effects differ depending on whether attraction, repulsion, or both attraction and

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R Distance (a)

(b)

(c)

Figure 20.6. Generalized attraction-repulsion system where both attraction and repulsion decline to zero with increasing interindividual distance. Modified conditions (dashed lines) as follows: (a) reduced attraction range; (b) reduced repulsion range; (c) ranges for both attraction and repulsion reduced in proportion. Heavy continuous or dashed lines indicate resultant functions.

repulsion functions are perturbed, various perturbation possibilities may, in principle, be identified from the nature of the resultant's response. In other words, comparisons of grouping behavior observed under different conditions may provide insight into the underlying interaction mechanism. Details of these effects for Type 1 and Type 2 systems are documented in Table 20.1. For a given type of system, perturbation possibilities (five for Type 1 and six for Type 2) can be uniquely characterized, except that variations in maximum repulsion and repulsion range have the same qualitative effect. Certain combinations of effects are common to both types of systems, but in only one case do these common effects arise from a common cause (namely a proportionally equal reduction in maximum attraction and maximum repulsion). These observations suggest that, if used in tandem with a knowledge of external factors and candidate sensory modalities, such effects may prove useful in deducing the structure of attraction-repulsion systems. In essence, Table 20.1 summarizes a set of testable predictions as to how the observable relationship between social movements (measured in terms of instantaneous velocities or accelerations) and separation distance varies in response to external stimuli.

20.6 Conclusion Theoretical studies have the potential to provide insight into the underlying processes of social cohesion, where individual processes cannot be measured

Table 20.1. Impact of changes in attraction (A) and/or repulsion (/?) characteristics on the form of the resultant cohesion function. DAmax and DRmia are the distances over which the component attraction and repulsion tendencies operate. +, increase; —, decrease; n.c, no change. *, both characteristics changed in proportion in each case. Impact on resultant Change (decrease) Attraction-repulsion model

Repulsion

Attraction

A increases, R decreases with distance

and A

max

aIld

max*

Equilibrium distance

Net attraction amplitude

Overall range (distance)

n.c.

n.c.

n.c.

n.c.

+ n.c.

n.c.

+

n.c.

n.c. *max*

Distance R

-R

max

A and R both decrease with distance

DA. DR DA

*

and

max

max

/ Distance

^max A * max

R and

n.c.

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Kevin Warburton

independently of their collective effect. Models can help to erect a conceptual framework for motivational hypotheses of grouping, define theoretical possibilities, and develop testable predictions. In many cases, predictions regarding three-dimensional processes can be projected readily from simpler twodimensional models. Theoretical and simulation models incorporating the assumption that cohesion in animal congregations is the product of an interplay between attractive and repulsive tendencies have successfully reproduced, and therefore helped to explain, several aspects of group dynamics. Threshold and continuous tendency models, respectively, represent synthetic and analytic approaches to modeling cohesion. Both are capable of illuminating group processes, but they embody different assumptions as to the neural abilities of animals. Harmonic models have proved useful in teasing apart interactive movement patterns with different periodicities. Cohesion curves have often been assumed to be upwardly convex. Simulated groups having this feature show strong cohesion characteristics. Such a relationship is biologically plausible because it implies that the attraction and/or repulsion tendencies approach their values beyond Dmax gradually and because animals do not need to be increasingly sensitive to relative position as separation distance increases (which would be especially difficult for animals with monocular vision). An empirical procedure with potential for validating tendency-distance relationships is the analysis of trends in movement characteristics (e.g. velocity, acceleration, latency, or probability of movement) with respect to distance to neighbors or the group centroid. Parrish and Turchin (Ch. 9) found that shoaling blacksmith, Chromis punctipinnis, avoid their nearest neighbors when at close range (<10 cm), but show a gradual, near-linear increase in net attraction to the school centroid as their distance to the centroid increases. A study of swarming midges (Okubo et al. 1977) yielded a relationship between mean acceleration and normalized distance from the swarm center which was close to linear, although there was some indication of increasing acceleration with distance (Fig. 20.7). This is suggestive of an upwardly concave cohesion function. The observed acceleration-distance relationship was apparently due to the nature of the interaction forces themselves, as opposed to the changing number of conspecifics a midge would perceive as it moved from the center to the periphery of the swarm. The departure of these results (and also those of Aoki's 1984 harmonic analysis) from the often assumed convex cohesion model illustrate the need for further studies on a much wider range of grouping animals before generalizations regarding the prevalence of different tendency-distance relationships can be attempted. Indeed, present cohesion hypotheses may be too simplistic. The possibility exists that functionally opposite tendencies may exhibit mutual inhibition which is nonlinearly related to ten-

Social forces in animal congregations

335

2000

1000

cm/sec

-1000

- 3 - 2 - 1 0 1 2 3

Normalized distance Figure 20.7. Mean acceleration of swarming midges vs. normalized distance from the swarm center (from Okubo et al. 1977).

dency strength. Thus, motivational hypotheses should be used to guide future analyses of mechanisms at work in particular cases, rather than as blanket explanations (Baerends 1975). In principle, the underlying shape of component tendency-distance curves could be inferred from changes in the form of the resultant curve in response to known variation of external factors. However, such an approach would be subject to the usual complications of motivational analysis, including uncontrollable variation in responsiveness, individual differences, and the fact that stimuli can both release and prime responses (see Colgan, 1993, for a discussion). As a qualitative analysis, however, the exercise would be illuminating. Information on both internal and external cohesion factors is transduced through an animal's senses. Thus, characteristics of any distance-related response are strongly influenced by the physical constraints of relevant perceptual cues (e.g. the size and rate of movement of a visual image projected on the retina; see Dill et al., Ch. 14) and the efficiency of information transfer. Signal attenuation can vary substantially with the transmission medium, and this helps to account for differences in the sensory modalities employed by aquatic and terrestrial animals. An improved grasp of the motivational and sensory bases of animal grouping behavior will depend on the progress which can be achieved in several complementary fields, involving the further development and empirical validation of cohesion models, the clarification of sensory abilities (e.g. through neurophysiological experiments, sensory deprivation manipulations, and signal-reaction

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relationships), and psychological investigations of perception-tendency translation systems. The business of relating these diverse sources of information represents a fascinating challenge in its own right, not least because behavioral programs and their underlying neurophysiological mechanisms need not be totally isomorphic (Baerends 1975). Such studies will help to focus attention on the individual as well as the group and should allow us to address such questions as: How do the attraction-repulsion systems of individuals within a group differ? Do such differences reflect the dominance status or other characteristics of group members? What are the consequences for cohesion and coordination of the group as a whole and for the decisions individuals make about time allocated to feeding, vigilance, and other activities? Finally, can one fail to be repelled by any suggestion that such questions are unattractive?

Acknowledgments I am very grateful to John Lazarus, Stewart Evans, Ken Norris, Carl Schilt, and Ken Schulz for providing me with helpful information on the grouping behavior of birds and dolphins.

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Subject index

acoustic diffraction tomography, 21 acoustic techniques, 27-35; three-dimensional, 30-5 acoustic visualization, 62-5 active aggregation, 108; definition of 3 advection-diffusion-reaction model, 254, 302, 306-9 (see also diffusion, reaction-diffusion) aggregation; cues for, 251; definition of, 2; evolution of, 159; evolutionary aspects, 253; foraging, 167; indices of, 109; mating, 166; mechanical advantages, 167; positional effects, 168; predation, 167; sensory modality, 323-7; terms of, 1; visual signals, 326-7 aggregation device, 226 (see also attraction, external source) aggregation rate, 148-9 alignment, 273 (see also polarization) amplification, 230, 293 angular distribution, 266, 268, 290, 294 aposematism, 180, 328 asocial aggregation, 226 attenuation, 322, 335 attraction, 4, 127, 137; cues for, 115, 144; external source, 81; gravitational model, 318; influences on, 115, 136; visual mediation, 319 attraction field, 115 attraction focus, 116, 131 (see also attraction, external source; congregation focus) attraction-repulsion models, 314, 330-2, 333 attractive bias, 115, 120-3

chemical signals, 282, 298 chemotaxis, 251, 260, 285 chorus-line hypothesis, 76, 227 cognition, 242 cohesion, 160, 258, 273, 313, 318-9; curves, 334; definition of, 321; internal factors, 329; lateral line, 324; trail strength, 295 collective behavior, 282 (see also epiphenomena; group response); sensory cues, 299 collective decision making, 272-3, 278, 286 (see also information transfer; social taxis) collective searching, 278 (see also information transfer; social taxis) collinearity, 37-8 computerized tomography, 18,21 (see also inversion techniques) confusion effect, 167, 181,238-9 congregation, 108, 226; definition of, 4; properties of, 5-6 (see also emergent property, epiphenomena) congregation focus, 115, 132 (see also attraction focus) congregation rules, 139-40 (see also traffic rules) continuous tendency models, 318-22 continuum model, 249-50, 252, 273, 287 control frame, 40, 54 (see also calibration techniques, reference unit) control points, 39 convolutions, 293 cooperation, 178 cooperative hunting, 233 coordination, 313 copepod swarm, 145 coplanarity, 37-8 correspondence, 25 (see also matching; photogrammetry) cost benefit ratio, 168, 198-9 cost benefit threshold, 169

binocular vision, 326 bird flock, aerodynamic hypotheses, 70-2; cluster formation, 70, 76-85; internal structure, 78; line formation, 68, 70-6; optical resolution of, 72-4; radar resolution of, 74—5; V-formation, 69 calibration, 90 calibration frame, 58 (see also control frame; reference unit) calibration techniques, 39—40 camera, digital, 46; metric, 38; nonmetric, 39; semi-metric, 39 cellular-automaton simulation, 287 chemical defense, 180

density, effect of satiation, 201-2 (see also positional preferences, hunger); fish school, 304 density distribution, 110 density gradient, 122-3 detection range, 265 (see also perception distance)

373

374

Subject index

diffusion, 10, 248, 262-3, 306 diffusion equation, 116, 249-50 diffusion models, 111 (see also Eulerian analysis) dilution effect, 167, 181 directionality, 289, 293 (see also polarization) echo counting, 27 echo integration, 27 edges, 160, 206 elective group size, 196, 205 emergent property, 81, 166, 284, 297, 299 (see also epiphenomena) emission techniques, active, 23—4; passive, 23-4 encounter rate, 259 epiphenomena, 9,254 (see also emergent property) equilibrium distance, 315, 318, 330 Eulerian analysis, 108, 110-2, 113; definition of, 11 (see also diffusion) exploratory tendency, 320 (see also attraction, external source) explorer, 292, 298 fish school, acoustic resolution of, 27-8; foveal sonar imaging of, 32^4; optical resolution of, 26; physiological constraint, 301, polarization of, 127; three-dimensional resolution of 54-5 fish school structure, 127 fluorescence imaging, 22-3 follower, 211,292,298 follower tendency, 320 forage area copying, 279, 328 Fourier transformation, 20-1, 29 fractal analysis, 111 fractal dimension, 149, 153, 156-8 fractals, 11 frame grabbing, 46 flock-school-herd (FSH), 175 (see also congregation) gradient of response, 195 gradients, 257, 276 group fidelity, 240 group fission, 82 group geometry, 240 (see also group structure) group persistence, 197 group response, 138-9 (see also emergent property); 282 group selection, 166 group shape, metabolic effects, 301 group size, 110, 146, 169-70, 234,272; effects on, 196; maximum, 302; minimum, 241; optimum, 198, 204-5, 254; stable, 204 group size preference, 205 group structure, 170, 322; facilitation of communication, 208; foraging, 233; hunger, 236; mechanical advantages, 208 (see also positional preferences); metabolic effects, 301, 308-9; ontogeny, 236; optimal, 214, 216; polarization, 227, 235; predation, 233; refuge, 236 habituation, 239 haphazard orientation, 145 (see also milling)

harmonic models, 322 holography, 22 ideal free distribution, 204 individual differences, 176, 335; aggression, 185-6; fear, 185; hunger, 184; motivation, 183; phenotypic, 183 information, 207 information gathering, 170 information propagation, 258 (see also information transfer) information transfer, 4-5, 170, 247-8, 251; efficiency, 323, 327; sensory modality, 227-8 interacting-particle model, 252 interaction forces, external, 314; frictional, 314-5, 322; internal, 314 interfish distance, 323 (see also nearest neighbor distance) internal spacing, visual cues, 227 internal state, 313 inverse square law, 208, 319 inversion procedure, 19 Lagranian analysis, 108, 110-2, 130-2, 141, 249 (see also random walk); definition of, 11 leader, 211; bird flock, 78; lack of, 284 life-dinner principle, 169, 194, 203 linear stability theory, 293 loner, 185 (see also straggler) many eyes hypothesis, 228; foraging, 198; predation, 180 (see also vigilance) mass attack, 114—5, 118—20 (see also attractive focus; pheromones) mass spawning, 166 matching, 47-50, 90, 148 (see also correspondence); probabilistic model, 91—4 maximum group size, physiological hypothesis, 302 maximum school dimension, 309 mean field model, 252 mechanoreception, 159, 324 microscopy, confocal, 22; serial, 22 milling, 235, 288 Mills crossed array, 34 model validation, 241, 299 mosquito swarm, three-dimensional resolution of, 96-100 motility, definition of, 115 motivational state, 313 nearest neighbor association, 134 nearest neighbor distance, 109, 130, 133-5, 139-40, 153, 231-2, 304, 323, 325; angular velocity, 209; bird flock, 72-4; foraging, 329; loom, 210, 318; mosquito swarm, 101; tau, 211; time to collision, 211; V-formation, 72-4 null models, 215 object density, 19 object space, 37

Subject index oddity effect, 181 open environment, 226; ocean, 61 optical techniques, 26 (see also photogrammetry) optimal group structure, fish school, 214; null models, 216; V-formation, 214 optimal position, 189, 209 (see also positional preferences) optimal sensitivity, 220 optimality theory, 189 optimum group size, 198,204-5, 254 parallax, 42, 326 passive aggregation, definition of, 3 passive congregation, definition of, 5 (see also FSH) patch dimension, 147-8 patch dynamics, 147—8 patch profitability, 252 patch scale, 258 patch size, 143 patchiness, 61, 143, 195, 196, 257 pattern, 247; balance of forces, 297; pelagic distribution, 65 perception distance, 247, 329 (see also attractive bias; gradients) pheromones, 113-5 (see also attraction; mass attack), 285, 298, 299, 326 photogrammetry, definition of, 36 phytoplankton, 144 pixel, 18 polarization, 258 population density, 112, 117 (see also density distribution) population flux, 111, 116-8 (seealso Eulerian analysis) positional effects, environmental influence, 191; foraging, 178-9; genetic constraints, 191-2; homeostasis, 177; locomotion, 178; metabolism, 310; multiple factors, 189-91 (see also optimal position); predator avoidance, 179 positional preferences, 174, 182 predator inspection, 321 predator swamping, 181 (see also dilution effect) preferred direction, 295 projection slice theorem, 20 random walk, 111, 115, 151, 260, 262-3, 314 (see also Lagrangian analysis) reaction-diffusion, 252 (see also diffusion equation) reactive distance, 324 received intensity, 20 reference unit, 96-9 (see also calibration frame; control frame) reflection techniques, 24-5 relevant detail, 249 repulsion, 4, 81, 127, 137 resolution, range, 29; spatial, 18, 25; temporal, 25 return tendency, 320 (see also attraction) Reynolds number, 314-5 rules of interaction, 255, 265, 297 (see also traffic rules)

375

scale, problem of, 237-8, 247-9 school shape, 329 school unit, 234, 241 (see also sensory integration system) schooling, deterministic model, 273; foraging benefits, 279 Schreckstoff, 185 (see also pheromones) searching behavior, 261 self-organization, 284, 286, 298 selfish herd, 182 sensitivity, 211,230, 297 sensory integration system, behavioral constraints, 239; definition of, 229; life history constraints, 242-3 separation distance, 315, 318, 321 signal propagation, spatial scale, 237 signal to noise ratio, 29, 228, 260, 263 social congregation, definition of, 5 social medium, 230; propagation characteristics, 231-3 social signals, 230 social taxis, 260 sonar, dual-beam, 28; split beam, 28 spacing dynamics, body size, 328-9; external factors, 328; group size, 328 (see also interfish distance; nearest neighbor distance) spatial behavior, 287 spatial summation, 228 spatio-temporal model, 287 spectral analysis, 323; pelagic animals, 61 stable group size, 204 state vector, 18-9 statistical mechanics, 248 stereoscopy, 42-50,91; digital, 45 stochastic processes, 250 stragglers, 138, 169 (see also loners) submersible, 169 swarm, communication within, 159; definition of, 97; mysids, 197; zooplankton, 53-6, 144 swarm maintenance, cues for, 160 swarm marker, 97, 148 (see also attraction, external source) swarm migration model, 292 swarm shape, 102 swarm structure, 160 synchrokinesis, 279 synchrony, 76-7, 171, 241-2; visual cues, 242 target strength, 27-8 theoretical models, 207, 333-4 three-dimensional tracking, 50—2; automatic, 57-9, 130; birds, 75; mosquitoes, 96, 99, 102; path sinuosity, 111; schooling fish, 128 three-dimensional visualization, 42-3, 47; copepod swarm, 146 threshold tendency models, 315-8 traffic pattern, 290 (see also trail following) traffic rules, 12, 172 (see also rules of association); fish schools, 139 traffic volume, 295 (see also trail following) trail decay, 291-2

376

Subject index

trail following, 282; function of, 282-4, 290; mammals, 284; molluscs, 285; Myxobacteria, 285; social insects, 282, 285; trade-offs, 297-8 marking, 284, 295 (see also pheromones); trail network, evolution of, 286-7; spatial pattern, 287 translation mechanisms, 313, 318 (see also information transfer) transmission techniques, 19-23 traveling wave solutions, 292 triangulation techniques, 24-5 Turing model, 253

vertical migration, 195, 238; zooplankton, 63 vigilance, 180, 329 voxel, 18 wave of excitation, 230, 237 zone of approach, 317 (see also attraction) zone of avoidance, 317 (see also repulsion) zooplankton patch, acoustic resolution of, 62-6 zooplankton swarm, 144; escape response, 194-5; resolution of 53—4, 55-6

Taxonomic index

orange roughy, Hoplostethus atlanticus, 54 roach, Rutilus rutilis, 184 saithe, Pollachius virens, 33, 182, 218, 219, 325 smallmouthed bass, 279 striped bass, Morone saxatilis, 235 striped mullet, Mugil cephalus, 183, 302-3 tuna, 240; bluefin tuna, Thunnus thynnus, 214 yellow perch, 240 zebrafish, 280

BACTERIA, 260; Myxobacteria, 285 Myxococcus xanthus, 244 BIRDS blackbird, 69 Brown Pelican, Pelecanus occidentalis, 74 Budgerigar, Melopsittacus undulatus, 75 Canada Geese, Branta canadensis, 69, 72, 74, 208, 214,215 chaffinch, 329 Dunlin, Calidris alpina, 77-8 European Starling, Sturnus vulgaris, 68, 76, 77-8, 79, 183 pigeon, 78; wood pigeon, 185 quail, 240 sanderling, 240 tit, 240 vulture, 75 White Pelican, Pelecanus erthrorhynchos, 73, 214,215

INSECTS ant, 282-3, 298; army ant, Eciton hamatum, 286-7; Eciton burchelli, 286-7; Dorylus sp., 286, 288 bark beetle, 110, 112; southern pine beetle, Dendroctonus frontalis, 114-5 caterpillar, 285; of cinnabar moth, 328 locust, 258, 325 midge, 325 mosquito, Culexpipiens pallens, 91, 96, 98-9; Culex pipiens quinquefasciatus, 103 sycamore aphid, 109 water flea, Bosmina sp., 168, 182 whirligig beetle, Dineutes sp., 184

FISH anchovy, 26, 181; northern anchovy, Engraulis mordax, 235 Australian salmon, Arripis trutta, 198 blackshin shiners, Notropis heterodon, 329 catfish, Plotosus sp., 328 chromis, blacksmith, Chromis punctipinnis, 129, 310, 334; blue-green chromis, Chromis viridis, 329 cod, Gadus morhua, 28 hammerhead shark, 26 herring, 184; blueback herring, Alosa aestivalis, 235; flat-iron herring, Harengula thrissina, 141 mackerel, Scomber sp., 26, 182; Atlantic mackerel, Scomber scombrus, 28; jack mackerel, 184; Trachurus japonicus, 26; Trachurus symmetricus, 209 minnow, 185, 329; bluntnose minnow, 184, 279; fathead minnow, Pimephales promelas, 140; Gnathopogon elongatus, 322-3; Leuciscus hakuensis, 319

MAMMALS caribou, 285 dolphin, 233, 239, 241, 242, 324, 326; Hawaiian spinner dolphin, 241 elk, 285 sheep, 240 wildebeest, 285 MOLLUSCS limpet, 285 slug, 285 snail, 285 PROTISTS slime mold, 285; Dictyoslelium discoideum, 236 ZOOPLANKTON cnidarian, 280

377

378

Taxonomic index

copepod, 195, 324; Acartia spp., 156; Cyclops abyssorum, 238; harpacticoid copepod, Coullana canadensis, 145, 150, 152, 153, 154, 155; Labidocera pavo, 160 ctenophore, 280 Daphnia sp., 181

euphausiid, 194, 195; Antarctic krill, Euphausia superba, 196, 259, 278 mysid, 56; Paramesopodopsis rufa, 197 salp, 280 sergestid shrimp, 59