Advances in Botanical Research, Volume 2

Advances in

BOTANICAL RESEARCH

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Advances in

BOTANICAL RESEARCH Edited bu

H. D. PRESTON The Astbury Deparlnaml of Biophp-ics The University, k d s , England

VOLUME 2

ACADEMIC PRESS, INC. (tiarcourt Brace lovanovic h. 'Publishers)

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98765432

CO-UTORS

TO VOLUME 2

M. B. DALE,Departmend of Botany, The Univeraity, Southampton, England (p. 35). DEREKT. A. LAMPORT, Now at the Michigan State University Atomic Energy Commi8eion Plant Research LuboraWy, RIAS, Baltimore, Maryland, U.S.A. (p. 151). JOHN LEVY,Botany Department, Imperial College, University of Londun, 8.W.7 (p. 323). I. MLCNTON, Botany Department, University of L e d , England (p. 1). P. MAHESHWARI,Department of Botany, Univereity of Ddhi, Delhi, India (p. 219). N. S. RILNOASWAMY, Department of Botany, Univerdy of Delhi, Delhi, India (p. 219). P. A. ROELOFSEN, Laboratory of General and Technical Biology, Technological Univeruity, Delft, Netherland8 (p. 69). W. T.W~LIAMB, Department of Botany. The UniuerSitgv.8wuthampton, England (p. 36).

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In preparing the first volume of this series we were well aware that, whatever eke we were doing and however valuable and rewarding this new series might prove to be, we were inevitably adding to the burden of reading which all professional saientists, and not leaat among them, the botanists, are called upon to bear. In the prefaoe to that volume we were therefore rather careful to point out what we hoped would be found to be an approach somewhat different from that of most other texts reviewing piecemeal a whole field of study. Though we ouraelves had faith in this new venture we neverthelees waited with more than a little nervousness for the reaations of readera mainly, though not entirely, voiced by reviewers in the learned journale. In the event all the reviewers were favourable and we pmoeed to the second volume, not so much perhaps with more assurance, as with relief both that we were not too far in error in assessing the need for and the merits of the approach we outlined and that the publisher, the authors, and the editor had together made a book which fulfilled theee aims. In presenting this second volume we have in mind the comment of one reviewer that we may 6nd difficulty in maintaining the standard set in the first volume, We are sure that this second volume will set his fears at rest and we are grateful to the distinguished authora in this volume that they have spared no effort in ensuring that t h b ehould be ao. It is naturally not pomible in two volumes to cover the whole field of botany, and an editor is therefore faced a t the outset with the task of selecting topics in such a way as to achieve a fair balance in each volume between the interests of the wide variety of readers at which it is aimed. The inclusion in this volume of two articles dealing with cell walls therefore calls for comment, particularly since this happens to he our own particular interesf. An editor is inevitably guided by one overriding principle. The topics he chooses must be in course of rapid development, must be significant and must be dealt with by an author who is, and is known to be, distinguished. This l e d to a deliberate choice of author rather than of topic. The editor must, however, be ready to accept an opportun$y if one unexpectedly comes his way. In choosing the growing cell wall as one of the more important topi08 of the day the only possible author was Prof. Roelofaen and we am Vii

viii

PREFACE

more than grateful to him for the warmth with which he accepted an onerous task. This was intended to be the only article on cell walls, for although Dr. Levy’s article on the recently discovered importance of soft rot fungi is involved with cell walls this is not its only, or even its major, importance. When, however, we saw the opportunity of a “stop preas” article on the moat recent cell-wall development we hsd no hesitation in pressing Dr. Lamport to write what in our opinion is an article complementary to that of Prof. Roelofsen but is also in itself a striking example of the sudden break-through which can occur in an old problem when an enquiring mind seizes upon a new clue. One of the most remarkable developments of our time in plant science has been the way in which hitherto purely observational regions are progressively becoming experimental or even mathematical. One case of the former is included here, in the remarkable developments in embryology a t the hands of Prof. Maheshwari and his colleagues and students; and one case of the latter is given in the mathematical approach to taxonomy represented here in the work of Prof. Williams and his associates, which is now giving a new look to this somewhat bewildering field. We do not need to emphasize the impact of electron microscopy in all fields of botanical enquiry; it is represented here in its position with regard to classification in which, as in other aspects of electron microscopy, Prof. Manton has played such a prominent part. We are again grateful to the authors in this volume for the time and care with which they have prepared the artioles and have thereby smoothed our path, and our thanks are due particularly to the publishers whose quiet efficiency we deeply appreciate. Finally we are indebted in this volume as we were in Volume 1 for secretarial assistance to Mrs. E. D. White (nee Lister), this time with the able assistance of Mrs. C. J. Parker.

R. D. PBESTON

beds, 1906

CONTENTS

......................................... v .......................................................... vii

CONTRIBUTORS TO VOLUME2

PREFA~E

Some Phyletic Implicatione of Flagellar Structure in Planta I . MANTON .. Introduction ................................................. Distribution of Flagella of the 8 +2 Type ......................... .. The Heterokont versus Isokont Condition ........................ Other Aspects of Flagellar Numbers and Relative Length .......... V . F l a ~ ~ a r.aS h..............................................

I I1 I11 IV

.

........................................ ........................................... ............................................ ............................................ . ............................................... . ............................................ . .................................................. x. summery ................................................... References., ..................................................

V I Flagellar Appendages A Flagellar Spines B Flagellar Hairs C FlagellarScales VII Flagellar Beeea VIII Flageller “Roots” IX Conclueions

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6 8 10 13

13 14

17 17 18 20 20 33

Fundamental Problem8 in Numerical Taxonomy w T WILLIAMS and M . B DALE

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I Introduction I1 The Nsture end Propertiea of Claseificetions A The Basic Axiom B Monothetic and Polythetic Claseifications C Maximization D Hierarchical and Non-hierarchicalClaaaificetiona E Probabilistic and Non-probabilistic Cleeeificationa 111 The Choice of Mathematic&%l Model A Introduction: Metrics B Metric Properties of Pair-functions C Intrinsicslly Non-metric Systems D Non-EuclidmnSyateme E Conclusions IV The Beeio Euclideen Model A . Duality: The R/Q F’roblem ................................. B. Adjustmenta to the Model C Heterogeneity v. StretegyofAnSlyais .......................................... A Simplification Methods ..................................... B. Pertition C Non-hierarchical Methods D Hierarchical Methods Achowledgementa References

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1

3

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36

37 37 37 38 42 43 48 48 49 51 62 63 64 64 66 56 69 59 61 61 62

67 07

X

CONTENTS

Ultrastructure of the Wall in Growing Celle and ita Relation to the Direction of the Growth P

. .

. A . ROELOFSEN

................................................. 09 ............................................. ................... 70 70 ........ 78 ........................ 82 ................. 85

I Introduction I1 Morphological Aspects of Constitution. Synthesis and Breakdown of theprimery WEll A Constitution and Morphology of Microfibrils B Constitution of the Amorphous Matrix in Primsry Wells C Some Aspecte of Microfibril Coherence D Site of Synthesis of Prim~ryWall Substances E Questionable Evidence of Breakdown in Primary Walle I11 Survey of the Microfibrillsr Arrangement in Different Typee of Growing Celle A Freely Growing more or less Isodiawetrio Cells B Freely Growing Tubular Cells or Perts of Cells C Tissue Cells with Isodiametric Growth D Tissue Cells with Predominant Growth in Length E Tissue Cells that Predominantly Widen., F Tips of Tissue Cells with Tip Growth I V Interreletion between Growth end Wall Ultrastructure A Effect of Growth on Wall Structure B Effect of Well Structure on the Direction of Growth C Theories on the Mechenism of Orientated Jnitiel Synthesis of Cellulose Microfibrils References

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......... 89 ................................................ 91 91 ................ ................ 98 ......................... 104 .............. 106 ..................... 112 113 ......................... ............ 114 .......................... 114

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128 139 145

The Protein Component of Primary Cell Walls DEREK T

. A . LAMPORT

. A. LJcopeandDefinitione ...................................... 161 151 B. HistoricalPerspective1888-1969 ............................ 152 I1. Experimental Methods end Materi~ls............................ 165 A. Cell Suepension Cultures....................................166 I Introduotion .................................................

............................................. 167 168 I11. The Hydroxyproline-rich Wall Protein: “Extensin” .............. 180 A . Intra-cellular Location of Hydroxyproline..................... 160 B. Chemical Cheracb&tion of 4-tmnu-hydroxy-~-pIine......... 167 C. The Amino Acid Composition of Primepy Cell Walle., .......... 168 D. Enzymic Degradation and Characterizefion of Wall Protein ..... 171 E. Disdphide B r i d e in Cell-Wdl P r ~ b i n....................... 172 F. Distribution of the Hydroxyproline-rich Wall Probin in the Plant Kingdom ................................................. 174 IV. The Biosynthesia of “Extensin” ................................ 177 . A . Uptake and Incorporation of W-Proline by Intact Cells........ 177 B. ProlineHydroxylation ..................................... 184 V . Veristion of Cell-wall Hydroxyproline Content ...................188 A . Walls Isolsted from Tissue Culturw .......................... 188 B. Wells Isolated from Plsnt Psrts ............................. 189 B. WholePlante

c. Ana~yticdTechniques......................................

CIONTENTS

xi

.................. 189 ...................................... 193 ...................................... 194 ........... 198

.

V I Degredation of the Sycamore P r b 8 r y Cell Well A ChemioelDegradation B Enzymic Degradation VII A Tentative Piature of “Extensin” in the Primsry Wall VIII The Contribution of “Extensin” to Wall Form end Teneile Strength I X EnzymiaW8llProtein A hoorbio Aoid Oxidaae B Hydrolyeeee C Other Wall-bound Enzymee D How does the Wall Rind Emymtw ? X The Role of “Extensin” Aoknowledgemente Referenoes

. . ... .. .. .

200 ......................................... . 204

...................................... 204 .............................................. 206 ................................. 206 ......................... 206 ....................................... 209 ........................................... 213 ................................................... 213

Embryology in Relation to Phyeiology and Genetice P MAHESHWARI and N 9 RANQA8WAMY

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................................................. 219 ....................................................... 221 . ........................................ 221 ...................................... 223 . ............................................... 227 ........................................ 281 . .................................... 232 . ..................................... 232 ....................... 234 ..................................................... 237

I Introduction 11 Pollen A Longevity of Pollen B. GerminationofPollen C Pollen Tube 111 Control of Fertilizetion A Treetmentoftheat igma B Treatment ofthe Spyle C . Intrmvarien and in vitro Fertilization IV Embryo A Growth of Vmbryo in Relation to Seed Development B Dependence of Embryo on Endoeperm C Bpeofioity in Nutrition of Embryo V Endoeperm . A Conetituent4Jof Endoeperm B Role of Endusperm in Seed Development C CultmofEndosperm VI Embryo culture A Cultural Conditions B GrowthMedia C Applications of Embryo Culture D Limitations of Embryo Culture M I. Cultureof0vulee M I. Culture of Ovsriea and Flowera M Perthenocsrpy X Polsembryony A Adventive Embryony B EmbryonslBudding XI P ~ h e n o g eeeis n XI1 . . .g.A n X I I I Antherculfure XIV Control of Sex Expression X V Conclueions Aoknowledgementa Refe~

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........... 237 ....................... 239 ........................... 289 .................................................. 240 ................................. 240 ..................... 242 ...................................... 243 .............................................. 246 ........................................ .............................................

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247 260 266 262 263 266 278 280 280 286 296 800 801 804 309 810 310

xii

CONTENTS

The Soft Rot Fungi: Their Mode of Action and Sicanee in the Degradation of Wood JOHN LEVY

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I Introduction 323 I1 Histology of Soft Rot 329 I11 A Technique for Studying Soft Rot Fungi........................ 337 IV Mode of Action of Soft Rot Fungi 339 A Peseive Penetration and Decay Penetration 339 B . Effect of Species of Wood on the Mode of Attack by the same Fungue 340 C Effect of Species of Fungus on the Mode of Attack in the same 344 Wood D Soft Rot Fungi on Posts in Ground Contact 348 V List of Fungi known to came Soft Rot 348 VI Dieoussion 349 Acknowledgements 366 356 Referenoes AUTHOSINDEX 369 SWBJEOTINDEX .................................................... 371

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Some Phyletic Implications of Flagellar Structure in Plants I. MANTON Botany Department, Univereily of Lee&, Enghnrl 1. Introduction..

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1

II. Distribution of FhgeUe of the 9 +Z Tspe. .................................. 3 5 III. The Hebmkont veraue Isokont condition.. ................................ Iv. Other depeote of Flegellsr Nnmbera and Relative Length.. .................. a

v.

BlEgdhrlSaape

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M. W q & u Appendzigw ........... .+ ...................................... A. F h g e k Spinen ..................................................... B. FbgellmHeire

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c. Flegellsr Scales .....................................................

10 13 13 14 17 I?

........................................................ ...................................................... ia .......................................................... 20 ..............................................................20

VII. FhgellarBBaee YIII. Flr4gellar “Roote” IX. ConolUBioM,. X. Summery

References.. ...........................................................

33

I. INTRODUCJTION Discovery of the essential similarity between cilia and flagella of both plant and animal kingdoms has exposed a linguistic contradiction which impinges too closely on taxonomy to be easily resolved. So long as protistologists must refer to major p u p s of organkms as Ciliates and Flagellates, recommendation to use the one word “cilium” for the filamentous appendages of both, leaving the other word “flagellum” for the very differently constructed filamentous appendages of bacteria, is a council of perfection that can scarcely be carried out. That inextricable confusion has not resulted from this linguistic impasse ie a tribute both to the resilience of biologists and to the clear-cut basic character of the organelles themselves. Illogical verbal usage at this level is indeed harmless in the sense that it rarely, in practice, leads to a fundamental misunderstanding of facts. I n contrast, the unforeeeen obstacles to mutual comprehension that have been raieed by reoent attempts to standardize nqmenclature a t a more intimate level ie a topic about which more will be said below. In the study of cilia anp flaplla of the non-bacterial sort by electron microscopy, three periods pan conveniently be distinguished. In the firat phaae, extending roughly from 1946 (Jakus and Hall) to 1964 (Fawcett and Porter), with the most intense period from 1980 to 1982 (Manton and Clarke), the ubiquity of the 9+2 fibre pattern waa B

2

I. MANTON

established. That each member of the peripheral ring is double and not a single strand was also established at the close of the same period (Manton and Clarke, 1962; Fawcett and Porter, 1964), though general agreement that the fibres of the central pair are not similarly constructed came later. A second phase of study, beginning with Af?elius (1969) and culminating in Gibbons and Grimetone’s classio paper of 1960 (see also Gibbons, 1961a), introduced better fixation, the use of new plastics and above all the successful applioation of new electron dense stains to thin sections, thereby opening up the study of additional structures which is still continuing. The new information on flagellar bases discussed below was made possible by thia work. Lastly a third phase, involving application of negative staining to dismembered flagella, is beginning to provide details of the fine structure within individual fibres (Andr6 and Thikry, 1963; Pease, 1963). It is not the intention to review here any of these phases as such, but only to discuss those aspects of flagellar structure which may have phyletic implications. Phase 3 so far has no phyletic implications and mention of it has been made only to bring the record up to date and to alert biologists who are not themselves electron microscopists to the existence of a very interesting new field of study. Phyletic implications, where they occur, are only rarely dependent on the micro-anatomical details associated with the 9+2. They are usually dependent on ancillary structures or on other details such as relative length and arrangement of flagella, some of which have long been known, in a general way, to light microscopists. The early history of knowledge of the existence of tile heterokont condition among algae (Thuret; 1861, Pringsheim, 1866; Thuret and Bornet, 1878; Luther, 1899) can be cited in illustration of this. Endorsement of the liiht microscopist’s view using the same type of evidence seen larger is not, however, the main function of the study of fine structure. The phyletic implications that I wish to discuss here are those that could not have been effectively worked out by light microscopy unaided and on wbich the electron microscope has supplied a considerable number of entirely new criteria and with them some new points of view. Phyletically significant new criteria have occasionally been sought by deliberate electron microscopical enquiry, but usually they have been encountered incidentally as unexpeatd additions to an investigation directed primarily towards other objectives. At the start of electron microscopy (phase 1mentioned above), when the main technical method was that of shadow-cast whole mounts, the great variety of external appendages borne by plant flagella in contrast to those of animah was an incidental h d h g of this kind. The reviews published by myself in 1962, 1964 and 1966 cover sufficiently this phase of the investigation

FLAUELLAR STRUOOTURE IN PLASTB

3

of plants. Subsequent developments have however been of two kinds. There is real progress when new methods have proved to be applioclble to new types of material, but there are also some unfortunate mistakes which, for one reason or another, have begun to enter the litemture. These, if accepted as facts by the inexperienced, which is all too easily done, can impede progress substantially. It is this last consideration as much as any other which has prompted selection of the present title at this time. Finality is not yet attainable in many matters on which knowledge is rapidly growing. A progress report based on &&-hand experience may nevertheless have positive value. There will necessarily be strong personal bias in the selection of topics for discussion, since an exhaustive treatment of literature alone is not the intention. Fortunately two recent publications can be used to supplement this report. There is Pitelka’aexcellent little book on the fine structure of protista both colourless and coloured (Pitelka, 1963) and a recent algological survey by Christensen (1962) which lends itaelf admirably to discussion of phylogeny. Since the text of the latter is in Danish (an English edition is promised but not yet available) it may perhaps be of value to Englieh readers if the giat of Christensen’sphyletic scheme is reproduced in the form of a list from his table of oontents (see p. a), supplemented by his diagram (Fig. l), translated where necessary, reproduced on p. 5. 11. DISTRIBUTION OF FLAGELLA OF TEE 9+2 TYPE An important biological concept not based on flagella but summing up much information on the micro-anatomy of protoplasmic structures of other kinds is that ofthe procaryotic versus the eucaryotic cell (expressed as Procaryota and Eucaryota in Christensen’s liat). Anyone unfamiliar with these terms can usefully consult the excellent short paper by Stanier and van Niel(1962). Procaryotic cells lack membranebounded internalorganelles though they do not lack internal membranes. If organs of locomotion exist, aa in bacteria, they are never of the 9+2 type. Eucaryotic cella (i.e. cells of all the main plant and animal groups other than bacteria and blue-green algae) possess membranebounded organelles of various kinds, e.g. nuclei, mitochondria, chloroplasts. Even when oell size is reduced to within the dimenaiom common in bacteria, as in the tiny green flagellate iKrmnOnae p u d h (Manton, 1969a), the eucaryotic nature of the main cell components remains sharply distinct. The introduction of the membrane-bounded space within which biochemical activities of some kinds can be carried on in relative isolation from biochemical aotivities of other (perhaps mutually incompatible)

4

I . MANTON

kinds is clearly an evolutionary advance of the greatest importance which must have preceded most of the phyletic diversity with which modern taxonomy is concerned. Membrane-bounded spaces in the sense of ccdouble-membranea”(for fiwther discussionof this terminology see Manton, 1961) occur conspicuously in cells of blue-green algrte, notably in their pigmented regions. It is membrane systema of this type, or still more elaborate variants of them (but not simple membranes), which delimit the organelles within eucaryotic cells. Such ceUe are also the only ones to possess oilia and flagella of the 9+2 type, not, however, in all eucaryotic groups. The absence of flagella of any kind from the red algae has long been known (of. Fritsch, 1936), though this fact has scarcely disturbed the prevailing view that, apart from blue-green algae, a flagellate anoeatry lies behind all the main algal groups. An early loss of flagella is of course not difficult to imagine and the prevailing tendency to & o w Rhodophyceae (Fritsch, 1936, or Rhodophyta in the terminology of Smith, 1951), late in the soheme of major algal groups has consciously

List of mujor algal groups according to ChriStemen, 1962 PROCARYOTA Cyanophyta Cyanophyeeae EUCARYOTA ACONTA Rhodophyta

RMphyme CONTOPHORA Chromophyta

Cryptophgceae Di?WphgWZ$ B h a p h i ~ ~ ~ Cb~OPkP= H*topkJCrw*h-

Bt7Cill&C?phyC4?4W Xadwphym

Chlorophyta

p*hY-

EWkVhYLxOPhYPrmhphyeeae Chlorqphyctw

FLAGELLAR S T R U C T U R E I N P L A N T S

6

or unconsciously led to a general feeling that they are late arrivals and intrinsically specialized. Christensen (1962) is most explicit another way : specialized they undoubtedly are in many ways (somatic structure, mode of growth, life histories), but this could be mainly sign of extreme antiquity within the eucaryotic scheme, an antiquity which could have resulted from an origin before the 9+2 flagellum had been evolved. The extreme simplicity of their plastid lamellations (cf. Bouck, 1962; a180 A. D. Greenwood, personal communication) is an important additional micro-anatomical character consistent with such a view. Christensen’s phyletic scheme (Fig. 1) thus places the Rhodophyta MI the loweet and most ancient eucaryotic group, preoeding in origin the

Fro. 1. Christensen’s Phyletic scheme of probable relationehip between the main group of algae and other main groups of living organisms. Algae are indieetad by thick lines and lettera, other organisms by thin lines and letters. After Christensen, 1982.

6

I. MANTON

simplest true flagellates and ante-dating the separation of the plant and animal kingdoms. The importance of the term Aconta as opposed to Contophora is thus greater, and the term itself more significant than the mere absence versus presence of flagella had previously suggested.

111. THE HETEROKONT VERSUS ISOKONT CONDITION There is now a good deal of evidence in favour of extreme antiquity for the heterokont condition. By this is meant the possession of flagella in pairs, the two members of each pair Wering in length, type of motion and presence or absence of external appendages, and wully with the basal bodies of a pair mutually attached at a wide angle. Among pigmented forms, at both the monad and algal levels, other features of cell structure accompanying the heterokont flagellation include absence of chlorophyll 6 , presence of a rather simple internal plastid structure devoid of grana (perhaps more correctly described as plastids with a different lamellar system from that of the higher green plants), a more intimate relation between chloroplasts and endoplasmic reticulum than in organisms possessing chlorophyll byand the possession of mitochondria with micro-tubules and not flattened cristae. It is significant that some of these characters, notably the tubular equivalents of cristae, are also encountered among Protozoa. It is therefore virtually certain that the latter antedate Metazoa phyletically and that the heterokont pigmented flagellates are likely to be ancestral not only to these but to the main groups of heterokont algae and fungi also. These views are adequately expressed in Christensen’s diagram (Fig. l), and are, on fhd whole not controversial. An important innovation in Christensen’s scheme is, however, the use of the term Chromophyta to cover all groups of Contophora lacking chlorophyll b. Such an arrangement may not last permanently, but in the present state of knowledge it brings clarity where confusion previously existed and is therefore to be welcomed. In addition to the basic heterokont groups (Chrysophyceae, Xanthophyceae, Yhaeophyceac) some new names are included on which comment will be added later (pp.12, I’letc.). Attention should however be directed here to the importance of the present position of Vauckeria. That t h h familiar classroom type is closely relevant to questions of origin of the water moulds is well known, but as long as it was treated a8 a member of the green algae, a total conflict of evidence was inevitable together with a tendency to over-estimate the antiquity and relative importance of Chlorophyta versus Chromophyta, which still adversely affects phyletic thinking. The heterokont condition of the Vuwkria spermatozoid

FLAGELLAR STRUUTURE I N PLANTS

7

waa however well known to Pringsheim (1866),though at that date the concept of Heterokontae (Luther, 1899) as a group did not exist. It took nearly a century before the chemistry of pigmentation (for litemture see Strain, 1961) plus supplementary details of flagellar struoture (Kooh, 1961) could counteract the seductive influenoe of its bright green colour and lead to the realization that its true afRnitiee are with the Chromophyta. Everything that has happened since (eee especially Greenwood et al., 1967;Greenwood, 1969)has confirmed thie conclueion and there can be no doubt that the tranafer of Vaw&& to Xanthophyceae (Perke, 1962)is correct. This, it may be said in passing, could in fad have been done half a century sooner had the value of flagellar characters as phyletic indicators been better understood. The Chlorophyta (containing chlorophyll b) include the familiar isokont group^ enumerated in Christensen’s liat under Chlorophyceae together with euglenoids and some additional new p u p a which are not iaokont in flagellation. The essential unity of all the major land plants (archegoniates,gymnosperms,angiosperms)with green algae is endorsed by rapidly accumulating information about salient details of fine structure of the cell as a whole which cannot be described here (see however Manton, 1964b,c,d). This unity neverthelees depends almost certainly on chlorophyll b (and its physiological and structural conaequences) rather thah on flagellation, and though the origin of chlorophyll b as such can scarcely be discussed here it ia important to notioe the conservative treatment of thia problem given by Chriabnaen. In placing Chromophyta and Chlorophyta on a level, he is in fact avoiding a question which he might have treated differently. There are many members of the Chromophyta containing chlorophyll a but no other chlorophyll, e.g. many Xanthophyceae and Chrgeophyoeas (Bogorad, 1962). A caae might therefore perhaps have been made out for greater antiquity of some groups of Chromophyta compared with Chlorophyta had Christensen wiahed to do 80. He has wisely avoided this question, but it ia perhaps uaeful to note that an argument in favour of the converaeposition,i.e. for greater antiquity of Chlorophyte, versus Chromophyte, could scarcely have been sustained at all. It ie therefore important that in the list (p. 4) the group to be mentioned last ie no longer the Rhodophym (Rhodophyta) aa in Fritsch (1936) and Smith (1961), but the Chlorophyta themselves. With this point of view I personally am in full agreement. The origin of iaokont flagellation aa such is not aa olosely linked with the origin of the Chlorophyta aa has sometimee been thought. It ia important here to realize that the tacit assumption eometimes made by algologiets that isokont flagella are in themaelves primitive in an aeeump tion baaed on indirect rather than positive evidence. We have in fsot

8

I. MANTON

no information regarding the nature of “the primitive flagellate’’ and it is probably important to realize that while many Chlorophyceae are isokont other members of the Chlorophyta (Euglenophyceae, Loxophyceae and Prasinophyceae on Christensen’s terminology) are not. Conversely some members of the Chromophyta, notably the group of genera sopnrated from the Chrysophyaeaeby Christensen under the title Haptophyceae, are isokont, e.g. leochryuiu (Parke, l949), Chy80chrmulinu (Parke et al., 1966,1962etc.), P q r n d u m (Manton and Leedale, 1963) and the Coccolithophoridae (Parke and Adams, 1900). The differences between these and the isokont Chlorophyceae are nevertheless profound and include general features of cell organization as well as details of flagellar bases, some of which will be discussed below. The possibility must be accepted that isokonty may have arisen more than once within the Contophora, though in all 0&888 from an essentially unknown type of ancestor, and its presence is thus in some ways less informative than is heterokonty when all the various ancillaries are fully developed.

IV. OTHERASPEUTB OF

B’LAGELLAR

NUMBEW AND RELATIVE LENGTH

The uniflagellate condition, encountered sporadically in many groups, is sometimes manifestly a secondary development by suppression of one member of a former (usually heterokont) pair. An extremely clear example of this is the brown alga Dictyota (Manton, 1969c)in which the uniflagellate spermatozoid retains a basal body for the hind member of a heterokont pair which fails to develop further. The single flagellum is clearly the of members of the Chrysophyceae such as Mdequivalent of the front flagellum of their heterokont relatives within the same group (Pihlka, 1949).It is possible that the single flagellum of fungi such as A l h y c m or OZpidium is aim&& the equivalent of t b hind flagellum of a former heterokont pair, but this is less certain. On the other hand, the nature of the single flagellum in green flagellah such as Pedinmnonas, Fig. 4, (Ettl and Manton, 1964), hficronumae (Manton and Parke, 1900),hfowmmtiz,Fig.6, etc.,is entirely uncertain. These organisms are small and apparently simple. They lack sexual processes and often lack true starch, though they posseas chlorophyll 6. The single flagellum they contain could be primitive. Whether this is in fact the case is however almost impossible fo prove. The special case of Euglena can be dismissed &om this category. While it is probable that all members of Euglenophyceae will eventually prove to be biflagellate (G. F. Leedale, personal communication), it is well established (Pdngsheim, 1966; Leedale, 1966) that all representatives, both aolourlessand coloured,previously described as hawing aaingle

FLAGELLAR STRUUTURE I N P L A N T S

9

flagellum bifurcate at the base, are biflagellate, though the moond flagellum if3 80 short that it fails to omerge from the oantll (formerly termed reservoir or gullet). Much elementary teaching could usefully be corrected on these points. Multiple flagella (beyond two) have certainly been achieved independently more than once and major phyletic conclusions based on this character have to be made with caution. The best known examples of multiple flagella are at present Oedoqonium (Hoffman and Manton, 1962, 1963) among algae and the gametes of many archegodate land plants (compareMsntonandClarke,1961a,withMmton, l952,1959b), all chlorophyll b-containing organism. The quadriflagellate condition is however a special case which should perhaps be mentioned first. It might have been expected that a group of four equal flagella would have been directly related (as a relatively simple precursor) to a large ring such a8 that of Oehqorjium (Fig. 10). This however is not 80. A recent study carridout in detail from this point of view (Manton, 1964a) has shown that at least in 8tigeoclonium and D r a v m U i a (members of the Chdophorales 8emu Christensen) the quafdrifiagellate condition is achieved by the grouping of two isokont flagellar pairs in a mirror image relation (Fig. 11A) and the same is almost certainly true for Ulothriz (Manton, 1962). Other quadriflagellate green cells, e.g. P y ~ a milnonas (Manton et at., 1963),Platymonas, 8 p ,may relate back to uniflagellate or biflagellate relatives in which flagellar number has increased in a different manner. Some information about these will be given below (pp. 9,11,17 etc.). It is enough to say here that the grouping of fourflagella seems to have occurred within the green algae many times and few, if any, are in a direct line towards either Oedogonium or a fern s*rmatozoid. While the origins of the special types of multifbgellate motile oelh characteristic of Oedogonium on the one hand and many land plants on the other are therefore still obscure, a positive finding relevant to the latter is perhaps important. The biflagellate condition of bryophyte spermatozoids is sometimes (e.g. 8phugnum, Manton and Clarke, 1962) undoubtedly the expression of two flagella of different lengths, attached at different points on the cell and therefore not a pair in either the isokont or ordinary heterokont mnse. Whether this oonditioa is primitive or specialized (i.e. due to reduction from a multiflagellate type) is unknown but it indioates that flagellar number is not in itself the moat significant character, but rather the overall symmetry of the cell. The spermatozoids of archegoniates are fundamentally aaymmetrical no matter whether they are bi- or multiflagellate. There is therefore no ease for attributing an isokont ancestry to them. The common textbook practice of treating C?damydummaa aa an unequivocally primitive

10

I. M A N T O N

type is thus valid, if at all, only for certain groups of green algae but not for the mainstream of phyletic change leading to the vegetation of the land. It is perhaps important to note that flagellar size as such is not directly connected with flagellar number, though minor phyleticallydetermined differences exist. In the large compound zoospores of Vaucheriu (Greenwood, et el., 1967) the average length of the shorter member of each flagellar pair was 9-8p and of the longer member 11.1 p. In Oedogonium, for which abundant numerioal data have ale0 been assembled (Hoffmann and Manton, 1962, 1963),an averago length of 174 p was encounterod both in epermatozoids with 30 flagella per cell and in Z O O E ~ O ~with ~ E over 120. The biflagehte gametes of bryophytea may give measurements of slightly greater length, e.g. 20p for both Marchantia (Manton, 1962) and 8phagnum (Manton and Clarke, 1962), but those of a fern (Dryoylleris) are only slightlylessthanthisat 18p (MantonandClarke, 196la;Manton, 1969b), though flagellar numbers in ferns may reach three figures. Uniflagellate cells are more varied, though lese so if the exceptional condition of the very reduced species Nicronumas puailb (see below and Fig. 6A) is excluded. P e a l i v rniw (Fig. 4A)with a cell only a few microns larger than N.puailb has a length for its single flagellum ranging from 10-17 p according to conditions. The extreme shortness of the hind flagellum in many heterokont members of the Chromophyta iR thus a sign of fundamental asymmetry of the cell as a whole, since it is in no way conditioned by flagellar number as such.

V. FLAGELLAR SHAPE The only feature of flagellar Rhape of importance in the present context is that of the tip. ThiR region, however, oannot be effectively studied by light microscopy uncontrolled by electron microscopy since flagellar tips are often the sites of structural breakdown either in vivo or after fixation, leading to artifacts of very peculiar kinds which need to be recognized for what they are before conclusions can be drawn. If distal breakdown ocour~without rupture of the flagellar membrane, osmotic swelling may lead to apparently spherica1 apices which have been desoribed aa such more than once by light microscopists (see for example Strasburger, 1880,for Vuucheria).Discussion of this artifact in relation to bryophyte epermatozoids will be found in Manton and Clarke (1962).On the other hand the flagellar membrane may beoome wholly or partially stripped offleading to an appearance aa of a long distal thin hair. This artifact is almost certainly in part the r w n for the special term “acronematic”, introduced by Deflandre (1934)for

FLAUELLAR S T R U C T U R E IN PLANTS

11

flagella lacking lateral hairs, since the early drawing8 of stained flagella (e.g. Fischer, 1894) show extreme developments of this kind whioh are mrtainly paztly artifacts in the light of subsequent eleotron mioroscopical investigations. The most extreme o w e of all, in which the whole flagellum is disrupted, displaying its fibrillar oompition, ie usually recognized for what it is (oompare for example Ballowitz, 1888, with Manton, 1960, and Manton and Clarke, 19/51), but even extreme disruption commonly starts at the flagellar tip and may not affect the base. Since the component fibrils of a disrupted flagellum are individually below the limit of effective resolution with the light microscope unless dried,suoh a flagellum in a stained preparation may appear to show a faint, splayed, distal extremity on a more densely staining narrower base. Another complictction that has to be remembered is that of occwional abnormalities which may simulate one or other of these conditions. An early example (in Fucw 8erratw) of an exceptional plant giving a long terminal “hair” as a genuinely structural addition to the front flagellum of its male gametes which other plants of the same species do not normally show, was illustrated in Manton and Clarke (1961~).When therefore a similar condition is described for the zoospores of Chordaria on the coast of Denmark (Petersen et al., 1968), such a description nee& to be followed up by a re-investigation of the same species in another locality before the suspicion of structural abnormality in the material can be excluded. Abnormalities and damage apart, there may be other difficulties in determining the true shape of flagellar apices in dried material examined optically or electron microscopically.The flagellum itself may be coated in some way and its tip not directly visible. The apparently te-1 tuft, of hairs described for M&mnnmua 8qu.amata (Manton and Parke, 1960), Pyrarnimmw, etc. (Manton et al., 1963), belongs to this category and further information about thew genera will be given below (see also Fig. 9). Knowledge of the internal structure is also probably more necessary to interpretation than has generally been recognized and this has rarely been provided for the flagellar apices in plants (see however Roth and Shigenaga, 1964, for some pertinent details for animals). The smoothly tapered cilia of ferns and some bryophytes seem likely to depend on the early termination of the two central strands followed by gradual petering out of the strands of the peripheral ring (evidencefrom dismembered speoimens, Manton and Clarke, 1961a, 1962). In other cases, notably AZicrowwncce pwilkc, Fig. 6A (Manton, 1969a), the central strancb are prolonged beyond those of the peripheral ring giving a long and slender but membranebounded terminal extremity, suggesting a hair-point when seen with

12

I. MANTON

the light microscope. One of the commonest types of flagellar ending8 is, however, shortly mucronate (Fig. 2B),but there is no information on the internal tip structure in any of the organisms with tips of this kind and it is therefore impossible to know whether a mucro L only a short “hair-point” or a genuinely separate morphological category. I personally suspect the latter, but morphology alone provides insufficient guidance in this’case. While therefore it is probable that phyletic information may ultimately be obtainable from apical shapes of more than one kind, there is only one context at present in which these seem likely to be important in the immediate futuk. Among small green flagellates in the group provisionally assigned to Loxophyceae by Christensen, the long “hairpoint” of Nicromoms pmilh has already been mentioned. It is roughly 2 p long on the tip of a flagellum only about 1p long. The hair-point is smoothly covered by the flagellar membrane and is unquestionably not an artifact (Fig. 6A). This peculiar little organism, the smallest known true flagellate, remained for several years in an anomalous taxonomic position (for furfher discussion, see Manton and Parke, 1960). Two other recently investigated genera of small green flagellates are nevertheless showing (Fig. 6) with four signs of bridging this isolation. In Sp-sir, flagella and Mononu;cstix with one flagellum (Fig. 6B), each flagellum is effectively bipartite ,possessing a long distal extremity conspicuously thinner than the almost equally long proximal part. This feature waa correctly recorded by light microscopy at leaat for Spemul-aie (Korschikoff, 1913) and ie undoubtedly a good morphological character. Since an affinity between these genera and M. pueilh can almoet certainly be justified on other grounds it is probable that these oharao. teristic flagellar apices may prove to be useful phyletio indicators within this group when more is known. However, it is precisely for this reason that the continued u88 of the word “acronematicJJfor any of these flagellar types, even those last discussed, is undesirable. The term suggests the presence of a terminal hair comparable to the lateral hairs which will be discussed in the next section, which is in fact never the caw. The word Peitechenge&8d (whiphh flagellum) is not inappropriate for the hind flagellum of a heterokont pair (Fig. 2A) a8 a contrast to F&mmrqek?e,! (hairy flagellum, Fig. 2B)for the front flagellum of the same pair. In all other cases ordinary botanical language is greatly to be preferred, e,g. mucronate, tapering or bipartite. For the most frequently needed distinction, that between hairless and hairy (with lateral hairs), latinized words such as glabrous and hirsute or their translated equivalents are available for use in languages such as French which lack a

PLAGELLAR STRUCTURE I N P L A N T S

13

simple vernacular word for “hairy”. My recommendation is therefore strongly that “acronematic” should be deleted from the vocabulary. Further comments on nomenclature will be found in the next motion.

VI. FLAGELLAR APPEXDAGES Information on flagellar appendages of the sort variously termed Flimmer or mastigonemes (see below) dates from the nineteenth century, more eapeoially Loeffler (1889) and Fisoher (1894). Qood reviewrt of the light microscopy will be found in Petersen (1929), Vlk (1931) and Deflandre (1934), with important personal observations by Petersen (1918) and Koch (1951). Apart from this brief list of excellent papers, the first fifty years after Loeffler were on the whole dominated by indifference if not frank disbelief by most botanists. The importance of electron microscopy in changing this picture has been reviewed several times, see especially Pitelka (1949, 1963) and also Manton (1952, 1954, 1956), and no attempt will be made to diacuas the whole field again. Consideration can nevertheless usefully be given t o topics not adequately covered by previous reviews and some of these are indeed to be found in relation to each of the more diverse categories of flagellar appendages encountered in plants, namely, spines, hairs of various kinds, and scales. A. FLAGELLAR SPINES

th el^^ spines are of special phyletic interest in relation fo certain more recent observations on the nature of the primitive Fucoid to be disoussedbelow (pp. 19-20). Thereareonlythreeknowncases,allmembeFs of the brown algae. There R i a Ringle spine on the front flagellum in Hinucntlralia (Manton el al., 1953) and another in a 8irnihr portition in Xiphqhura (Manton,1956), a Fucoid from the southern hemisphere. I n the third example, Diclyola (Manton et al., 1963), there GIa row of spines. A spine seem to be an excrescence caused by a lump of some unknown material borne on one of the peripheral fibm and therefore beneath the flagellar membrane. A phyletic interpretation is not available for Dictyota though the character waa of importance in determining the plane of “symmetry”* aa passing between but not through the two central strands (Manton, 1959). A phyletic interpretation

*

That strict bilateral symmetry does not exist in fbgella follows from the demonetration of spiral aqmmetry so clearly made for flagellar beses by Gibbone (1961). Gibbons and Grimetone (1960) and others. Nevertheleae the central strands per ae have 8 symmetrydoftheir own m d e fixity of position in relation to other attributes of e flagellum which it ie impo.tent to determine. Tbie ie therefore the sense in which the words “fhgeUar eymmetry” rn intended in the present context.

14

I. M A N T O N

supporting a common origin for X i p h p h m a and Himanthalia, on the other hand, is a matter of considerable btereet. Xip?uq~homdiffere from Himccnthalia in lacking the basal “button” and is therefore probably more primitive. It is otherwise not dissimilar since it mnsists essentially of dichotomous ribbon-like thalli with conoeptacles on both surfaces as in HimanthuZkz. An a w t y between these two genera in spite of their present wide geographical separation could be argued on general morphological grounds. The demonstration that they share a character as unusual as that of their flagehr spine nevertheless gives force to this comparison in a way which is perhaps important. B. FLAOELLARHAIRS

FZageZlar hair8 have recently become a serious source of confusion aa a result of three entirely different factors, namely, the nomenclature, the accidental introduction of errors of fact into the literature and genuine increases of knowledge. Nomenclature can at this point be relegated to a footnote” since my own strong recommendation, a8 already explained, is to discard for the time being all special terms except perhaps tho two oldest (Flirnmergei88d and Peit8chengei88d) limiting these however to the special case of the two differentiated members of a heterokont pair in the mnventional heterokont groups (Xanthophyceae, Chrysophyceae, Phaeophyceae and the water moulds). For the appendages themselves in these and other cases the word “hair”, at least to readers of English, is unambiguous and I propose to use it in the account which follows since it carries no overtones suggesting uniformity in all contexts which a single specially coined technical term such as “mastigoneme” inevitably does. The scepticism of biologists in accepting the concept of b i r a on flagella at all is connected with the obvious diffioulty in distinguishing fixation artifacts fiom real structures which are at or just below the threshold of visibility with the light microscope. A mistake of a Werent kind is exemplified by Thalaasomonae Butcher, a genus of small green flagellates, described (Butcher, 1969) as possessing full heterokont flagellation. However, this description has recently been shown (Parke and Rayns, 1964) to be due to confmion betwoen two *The more commonly encountered terms other than IrlhmrgeisseZ end Peitachengeiesel(Fiecher, 1894) were introduced by Deflandre (1934) end englicized by Pitelke (1049). who ale0 lists them in Pitelke (1963). On this terminology, the noun w t i g o n e m denotea 8 &gellar hair of any khd; the adjmtive pantonemtk denotes e f h g e h n which when Been in profile ehowa hsh on both sides; 8 t h h m ~ a C Aagellum with bira on one aide only; end amonematic 8 terminal hair (diecuseed on p. 12). Other terms, of which there are an increasing number, do not yet 8igniScSntly effect the general literetuw.

FLAQHILLAR STRUOTURID I N P L A N T S

15

different organism present together in the same culture, namely, a pigmented organiem identioal with Micromo7~cs8qtubmatQ (Menton end Parke, 1960) and a much larger colourless chrysophyoean predator. This naturally displayed hairs on its front flagellum of the normal heterokont type charaoteristic of Chrysophyceae, when examined electron microsoopioally by another observer whose miorographs wem reproduced. The genus Th.akceeomonas has thus to be rejected aa a nomen confusurn, synonymous otherwise with Xkwmunaa 8quu&, and all statements based on it, claiming the presence of true heterokont flagellation in a member of the green algae, should be deleted also. This does not, however, mean that hairy flagella as such are absent from members of the Chlorophyta and indeed there are hairs of more than one kind and in several different types of arrangement. For comparison Fig. 2 illustrates the type of hair present on a true Ff!irnwrgeissef! of a brown alga, in this case represented by the front flagellum of the zoospore of Scytoeiphon. The hairs are co&1ge,arranged in two rows (one on each side of the flagellum), but becoming sparaer towards the tip which is shortly mucronate. Each hair appears to be bipartite with a slender distal extremity emerging from a somewhat thicker proximal part. Whether these slender extremities are present in life or represent molecular threads ejected from the centres of tubes (the thicker bases) as a fixation artifact is unknown. F i p 4, on the other hand,illustrates the very different type of hair present on the single flagellum of the type-species of Pedinomrmc~e(Loxophyceae within the Chlorophyta8ewu Christensen).Thereare again two rowsof lateral hairs, but each hair is sothin aa to make the detachedbacterialflagellumpresent in the same field appear coarse in comparison. Moleculer threads are again suggested, though in this case the idea of a f h t b n a r t W i s m o r e difficultto introduce in view of their very regular arrangement. What effect, if any, their presence may have on the mechanics of swimming is impossible to determine, but a substantial mechanical effect seems excluded for threads as thin as this. In a somewhat similar caw, Chlorochitridim t u b e r c u b Vischer (Pedinomonacr tuberculata (Vischer) Cams), the hairs are more numerous and longer (Manton and Parke, 1960) but they are individually no thicker than in P, minor. Their exact arrangement in ChZorochitridion should be re-examined, since the “plume-like” appearance might in that o w have been caused by an all-over hairiness rather than by restriction of the hairs to two ranks. This possibility is excluded for P.m i w (rig. 4) and also for a true li”limmergei88d since the alignment of the point6 of origin of hairs, either singly or in tufts, w(t8 clearly demonstrated at an early date (Manton and Clarke, 1966;see also Manton et aZ., 1952). The special flagellar characteristicsof the euglenoids have often been

16

I. M A N T O N

illustrated (see especially Mainx, 1928; Manton, 1962; and may be taken as generallyknown. Thelimitation of the longest hairs to oneside of the flagellum (Fig. 3) was detected by Fischer (1894) and hae not subsequently been seriously disputed. Nevertheless to w e the name PZimmergeisseZ for this as well as for the front flagellum of a hetemkont alga is almost certainly ill-advised. Not only is the arrangement of hairs different but the individual hairs, not separately visible with the light microscope which can detect only hair tufts in a stained preparation, are very slender and, though longer and more copious than in the type species of Pdinommure, are definitely not comparable either in structure or in arrangement with the hairs of the heterokont algae and fungi. The presence of thick hairs of more than one kind has, however, also been recorded on unequivocal evidence within the Chlorophyta. Among members of the Volvocales the surface of the whole cell, both wall and flagellar membrane, is sometimes covered by a close tomentum, at least when seen in the iixed condition (Fig.7). The evidence of dividing ceUs (Fig. 7D) indicates that this apparent tomentum is almost certainly derived from material deposited upon the new daughter cells before liberation from the old wall of the mother cell. An extreme case (Fig. 8) is that of Haemtococcus pluvialis which has not yet been studied developmentally but which has a very conspicuous tomentum limited to the flagellttr surfaces only. The hairs in this c a m are very translucent when examined in whole mounts (Fig, 8A) though they were recorded as present as early as 1961 (Miihlpfordt and Peters). I n sections on the other hand they are extremely compicuouc(, Wme being apparently compound and curly. They cover the flagellar surface all over including the tip, but they are not an integral part of its structure since they are clearly related to a separate layer of material of unknown nature laid upon the surface. A different type of thick hair (Rg. 9) has been encountered among many genera of Christensen's new group Prasinophyceae (see List p. 4) and also in some colourless Cryptomonads, notably Chilomonae (Pitelkaand Schooley, 1966). Examples illustrated here are on the tip of the flagellum of illicrommras s q u a m t a (Fig. 9A), the surface of the flagellum in Heteromastix (Fig. 9B)and scattered fiee on the field near a group of flagella from which they have become detached in H&ephmra (Fig.9C).Such hairs are often slightly curved and tapered at both ends. They commonly show a pattern of transverse s t ~ t i o m when seen in section and they have recently been shown, in the special case of Heteromaetix (Manton et al., 1965), to be msnuftlcturod in vesicles within the body and to be depoeited thenos, together with scales, upon the surface.

FLAGELLAR STRUCTURE I N P L A N T S

17

C. FLAGELLAR SCALES

These last examples lead naturally to some of the most peculiar flagellar appendages so far discovered, namely, jlagellccr scales (Fig. 9). These were first encountered in Micromonas s q w w t a (Manton and Parke, 1960)as a single layer of fairly large scales covering the whole of the cell including the single flagellum (Fig. 9A). For some years this remained a unique occurrence, but now many other cases are known (Figs. 9B and 9C), with possible consequences to the taxonomy and nomenclature (includingthe naming of M . aqwmata itself) which have not yet been fully determined. Nephr08ehi8 gilva (Parke and R a p s , 1904) has a single layer of fairly large scales over body and flagella, though here the flagellar scales are not quite like those on the body, and the flagella themselves are two, somewhat unequal in length. Still more complex examples with scales in two layers (Fig. 11B) and with morphological differences affecting both layers according to location on the organism have been encountered in Pyramimonae, Hahaphaera, Pteromonas,Heteromastix,Prasimladw, Plutymonm to name only a few for which the facts have been published or are nearly ready for publication (Manton et aE., 1963; Manton et al., 1905; M . Parke and I. Manton, unpublished). It is possible that Christensen’snew group Prasinophyceae may eventually be used to oontain them all, though t o do so will involve bisecting the genus Micromonas since M . pwilkc, the t p species discussed on p. 12, has already been assigned to Loxophyceae. These problems need not, however, seriously affect a general botanist. The grouping of difficultgenera into larger units is a special taxonomic exercise which not many people will want to undertake. The important point in the present context is not the names but rather the undoubted fact that flagellar scales as well as flagellar hairs seem likely to provide some phyletic information of a new and interesting kind even though this has not yet been completely assimilated into the nomenclature of any existing system.

VII. FLAGELLAR BASES The use of flagellar bases as phyletic indicators is only just beginning. The absence of the central strands was the only significant observation before the introduction of0the improved methods mentioned under phase 2 (p. 2), but these, in the hands of Gibbons and UrimrJtone (1900), gave results of such dazzling clarity that they have remItined unchallenged. These authors showed among other things that, in the flagellar bases of certain colourless endoparasites, the peripheral strands became triplets instead of the doublets present in the 9+2 region. Each triplet group when seen in transverse section appeared tilted radially, C

18

I. MANTON

giving the type of spiral asymmetry referred to above, and within this region of tilted triplets or at least for a considerable part of it an elaborate central pattern, sometimes referred to as the “cartwheel pattern”, occupied the centre of the basal body. These observations have been substantially confirmed by other workers on several animals and plants and, until recently, major diversity was not bclieved to occur. Nevertheless there is diversity, at least among algae. That the flagellar bases of certain green algae are not identical in all respects with those of Gibbons and Grimstone’s material has been imperfectly shown in a general way several times. Some good transverse and longitudinal sections through the transition region in a species of Polytoma (colourless relative of Chlamydomonas) published by Lang ( 1 963), and two detailed studies by myself, carried out independently on several pigmented algae (Manton, 1964a,b), have clarified the factual position. There is no doubt that Gibbons and Grimstone’s triplet strands (Fig. 11G) and a form of the cartwheel pattern (Fig. 11H) are present in all these bases, the cartwheel pattern being characteristic of the extreme lower end of a flagellar base, but the transition region between base and flagellum proper shows a spectacular stellate pattern which was not observed by Gibbons and Grimstone. In the green algae, and indeed probably in most if not all chlorophyll b-containing organisms, the stellate pattern is so strongly developed as t.0 arrest the attention (Fig. l l D ) , but elsewhere it has to be looked for with care even when present and it is not yet known whether indeed it is always present outside the Chlorophyta and land plants. In a search for it among the Chromophyta it was found with difficulty (Fig. 11C) in Prymnesium parvum (formerly Chrysophyceae, now Haptophyceae sensu Christensen). The flagellar base of this organinm nevertheless proved to be so unlike those of both Gibbons and Brimstone’s material and the members of the green algae studied that a view of any one of three or four different levels would have differentiated it phyletically at a glance. Nevertheless even here the extreme base had triplet strands and a cartwheel pattern in no way different from that of almost any other plant or animal. The fixity of the 9+2 thus seems to be shared by some but not all the structural features of flagellar bases and it R i certain that these will repay closer study in a wider range of forms than have hitherto been examined.

VIII. FLAGELLAR “ROOTS” The phyletic signficance of the fibrous appendages internal to the cell, which radiate from the region of the flagellar barns, repreuents a new field which has only recently been effectively studied in plants.

FLAGELLAR STRUOTURE I N PLANTS

19

Only a limited number of examples are yet known in detail, but these are all in their various ways important. One of the simplest to describe though by no means the simplest t o explain is Oedogonium. The well-known crown of cilia in the zoospore and spermatozoids of this familiar green alga were studied in detail b y Hoffman and Manton (1962, 1963) who showed not only the fibrous substructure giving stability to the ring (Fig. 1OB) but the presence of radiating roots arising singly between each pair of ciliary bases and therefore equal in number to the cilia themselves (Fig. lOA). Each root proved to be bipartite (Fig. IOC) with a relatively short rod of crossbanded densematerial underlying a ribbon of three tubes or coated fibres running longitudinally beneath the plasmalemma for possibly the whole length of the body. No exactly similar case has yet been encountered elsewhere since in other green algae there are normally two kinds of roots arranged alternately no matter what the total number of cilia (flagella) may be, i.e. whether one (Pedinomonua), two anisokont ( H e t e r o w t i x ) , two isokont (Chaetomorpha) or four isokont (Stigeoclonium, Darprnaldia, Ulothrix). Roots of all these genera contain tubes or coated fibres in very definite numbers. The commonest fibre number ie two (Fig. 1lE), encountered in all these genera though in each case in only two of the four roots present. The other two roots, arranged alternately with these in tt cruciform manner, have been Rhown to possess five fibres (Fig. 1IF) in Stigeoclonium, Draparnaldia, Ulothrix (Manton, 1952; Manton et al., 1955; Manton, 1964s) and three fibres in Pedimmna.9 (Ettl and Manton,, 1964) and probably Chaelomorpha (Manton et al., 1955). This degree of numerical uniformity was unexpected and is difficult to explain except perhaps in terms of an ultimately monophyletic origin for very diverse chlorophyll 6-containing organisms now distributed in several different sections of Chlorophyceae, F’rasinophyoeae and Loxophyceae. This sqbject therefore deserves further attention with the expectation that the exact phyletic meaning may become better interpretable when more is known. The same may be said for flagellar roots in members of the Chromophyta, though here the pattern just outlined is not repeated. Instead we have some extremely peculiar but equally characteristic structures which have been studied most fully among brown algae. Thn need for doing so was determined by the existence of a special organ, the 00called proboscis attached to the flagellar apparatus of Fucuis (Manton and Clarke, 1951c), in a position apparently identical with that of an internal “root” detected later (Manton, 1959~)in the uniflagellate spermatozoid of Dictyota. This matter has recently been explored in greater detail (Manton, 1964c) with the discovery that the proboscis

20

I. M A N T O N

of Fucus is indeed homologous with a special type of internal root present generally in brown algal zoospores as well as in the male gametes of more primitive Fucoids, notably Halidrys and C‘ystoseira. The phyletic importance of this is considerable, since it indicntos among other things that Fueus itself is more specictlized thtin has sometimus been thought, while Cg~toseiruis Rubstantially more primitive.

IX. CONCLUSIONS

It is thus clear that flagellar characters have value as phyletic indicators in many more ways than could have been known even ten years ago. Emphasis can nevertheless usefully be laid here on two major sources of confusion which must at all costs be avoided if the full value of these somewhat unfamiliar criteria is to be utilized. One is the type of careless mistake leading to seriously erroneous records as discussed on p. 14 with respect to “Thahsomonae”, and the other is premature systematization of nomenclature which can obscure genuine and phyletically significant differences under the artificial unity of a system of Latin names, as discussed under flagellar apices (p. 12) and flagellar hairs (p. 14). The two most important attributes for work of this kind are meticulous care in recording and an open mind in interpreting. Given these, together of course with reasonable botanical knowledge and manipulative skill, accumulated information will almost automatically clarify interpretation provided that it is collated with other sources of evidence. It cannot be emphasized too strongly, however, that for phyletic interpretations there is no a priori guidance as to what characters will in themselves be of major and what of minor importance. Only when the work is finished will this become apparent. It is essential therefore to use information from fine-structure as additions to the pool of knowledge provided by general morphology, biochemistry, life histories, etc., so that phyletic conclusions when reached are based on all the evidence and conflict with none. Knowledge of very few plant groups is in this happy state and therefore it may assist a general reader without first-hand experience of the particular characters under discussion if a summary of what I personally regard as reasonably well authenticated conclusions in the present state of knowledge be appended.

X. SUMMARY (1) Absence of flagella in the case of Red Algae, combined with other facts of fine structure (notably the platid lamellations) in which members of this group seem primitive, is I believe correctly interpreted

FLAGELLAR STRUCTURE I N PLANTS

21

(Christensen, 1962) as indicating greater relative antiquity for this group than for any other type of pigmented algae after Blue-Green Algae. (2) On thesubject of isokont versus heterokont flagellation, the following points have been brought out. (a) Heterokonty in the strict sense is not found in Chlorophyta though it occurs in several groups of’ organisms lacking chlorophyll 6, collectively termed Chromophyta by Christensen (19f32),together with their colourless tlorivativen, notably the water moulds. The Chromophyta are tLt leant an d t l and could be oltlcr than the Chlorophyta. ( b ) lxokonty H i found in the Huptophyceae among Chromophyta and in the Chlorophyceao among Chlorophyta. There is no close affinity between these two groups. Anisokont members of the Chlorophyta occur in the Euglenophyceae, the Loxophyceae and the Prasinophyceae. The fundamental asymmetry of the motile cells of land plants points to an anisokont ancestry within the Chlorophyta, for which therefore Chlamydomonas is not on the direct line. ( c ) This means that the nature of the “primitive flagellate” within the Contophora is unknown, but it must not be assumed that it contained chlorophyll b and it need not have been isokont. (3) External flagellar characters of value as phyletic indicators include : (a) apical structure (especially in certain anisokont greens), ( b ) flagellar spines (brown algae), (c) flagellar hairs (different in Chlorophyta from Chromophyta but of value in different ways in both), ( d ) flagellar scales. (4) Internal flagellar chaructw of value an phyletic indimtore include : ( a ) flagellar bases (different in Chlorophyta and Chromophyta), ( 6 ) flagellar roots (different in Chlorophyta and Chromophyta). ( 5 ) A special case for which the sum of flagellar characters (including external morphology and the micro-anatomy of roots) has given important new insight is in the Fucales, where Cyatoseim now appears t o be more primitive and Fucua less so than has commonly been thought.

22

I. M A N T O N

LEGENDS OF FIQURES 2-11 FIG.2. Scytosiphon zoospore to show normal heterokont flagellation. A: showing part of the body with a romplete hind flagellum (Peitschengeissel) and part of the hairy front flagellum (Flimmergeissel); micrograph C5933, x 15,000. B: the tip of a front flagellum, C3706, x 20,000 (Bfter Manton 1964r). FIG.3. Euglena apirogyra flagellar tip x 20,000 (courtesy Dr. G. F. Leedalc).

FIG.4. Pedinomonae minor. A: complete cell showing the single flagellum, 5797 /21, ~3000. 13: flagellar tip showing very fine lateral hairs with an S-shaped detached bacterial flagellum lying awow the wpecimen; mirrograph C5006, ~ 3 0 , 0 0 0(after Ettl and Manton, 1964). B:

h a . 5. A : Micronionnr pueilh Hection of a complete re11 xE0,000 (after Manton, 1959). Yottomtinliz eczeca (courtesy 1)r. J. H. Belchor). Micrograph C5015, x 20.000,.

Pro. 6. l~lugellsrtips from R freshwatcr plankton sample (courteay 1)r. H. Ettl); two dagells from ~tL‘hlrrmydomonnn species below; four flagella with long “hair-pointa” from a Spermloroopin cell abovo. Micrograph C3028, X 15,000. PIG. 7. Chloropnium ronue (courtesy Dr. H. Ettl). A: transverse section of a flagellum ahowing the superficial tomentum; micrograph C3137, X 50,OOO. B: oblique longitudinal section of a flagellum near the surface of the subtending cell, both showing tomenturn; C3151, ~40,000.C: longitudinal section through a cell tip with emerging flagellum t o show distribution of tomentum and differing thicknesses of wall layers below; C3170, x40,OOO. I): part of two daughter cells within the mother cell wall to show probable origin of tomentum; C3156, X40,000. FIG.8. Haemutococcus pluvialis (courtesy Dr. H. Ettl). A: shadowcast flagellar tip showing very transparent tomentum (contrast with the detached spine of another organism top right), C7299, ~30,000.B: transverse section of a flagellum with tomentum attached to a separate layer of material outside the plasmalemma; C8208, ~60,000.C: oblique longitiidinal sertion of a flagellum with tomentum (N.B. the lower end of the profile is not a flagellar tip); C7439, x 40,000.

Fro. 9. Examples of flagella with hairH and wcalen. A: Micrornrmna eqmmulo, x30,CNN (after Parke & Rayna 1964). B: Hetrromu8lix rotunda, x30,WK) (after Manton el ul., 11965). C: Halosphnera sp. (courtesy Dr. M. Parkc), mic-rograph BW2r5, ~30,000. Fro. 10. Ocdogonium cardiaeum npermatozoicl (aftor Hoffman and Mariton, 1963). A: flagellar ring with bases and ‘ ‘ m O t H ” , X 16,000. B: section whowing the cartwheel p&ton, in flagellar bases and the various fibrow hands connecting them together, xf%,fw). (;: two adjacent ‘‘mots” cut transversely showing in each the nolid rod below and tho ribbon of three fibres or tubes above, Xm,oOo.

Frcr. 11. Flagellar bases and “roots” in variouH algae. A: Stigeoclonium Hertion of a tip of a settling zoospore ~30,000 (from Manton, 1964a). B: Heleromaslix dovclb wction o f a flagel. lum covered with two scale-layers (see also Pig. BB); micrograph C5552, x 100,CXw). C: the “stellate pattern” in Prymnenium parvum, X 100,OOO (after Manton. 1964h). L): the “st&ate pattern” in Stigeockmium, X 150,000 (after Manton. 1984b). E :Stigeoeloniurn, two-strandd root, ~ 5 0 , 0 0 0(after Manton, 1984a). F: Sligeoclonium, five-stranded root, x IOO,ooO (after Manton, 1964a). G: triplet strands from the middle region of&flagellar base of P r ~ w i ~ m p r v u m ; micrograph C4238, x 100,OOO. H: triplet strands and cartwheel pattern a t innemoet end of flagellar base of Prymnesium parvum; micrograph C4613, x 1OO.OOO.

Fro. 3. Euglena.

Fro. 3. Euglena.

FIG.5. Micrononae and Monomaetix.

FIG.6. 8permatozoopie and Chkzmydomnas.

Fio. 7. Chloroqniurn rome.

29

FXQ.8. Uaemaloeoccua.

FIG.10. Oedogonium.

FIG.11. FIagellar “roots” and flagellar bases.

B L A Q E L L A R STRUOTUR‘BI IN PLANTS

53

REPERENOES A d d , J. and Thi&y, J. P. (1963). J. M h ~ p i 2,s 71-80. Afzelius, B. (1969). J. Bwphya. Bioohem. Cytol. 5, 289-78. Bdlowitz, E. (1888).AT&. dk.A M . 82, 401-73. Bogorad, L. (1982). I n "Physiology and Bioohemistry of Algae” (R.A. h*, ed.). AccEdemio P m , New York. Bouok, (3. B. (1962).J . OSU BWl. lQ1,153-70. Butoher, R. W. (1969). An introduotory account of the smaller algae of Brithh O O M t d Wetere. Part I. Fkh. Invest. hd.8er. 4. Chriateneen, T. (1962). Botanik. Bind 11: Syetemtik Botamk, Nr. 2, A b r . 1-178. Munkegeerd, Copenhegen. Dei%uuh,0. (1934). C.R. A d . Rcd., Paria, 198, 497-8. Ettl, H. and Menton, I. (1964). Nowa Hedw@a. In the preae. Fawoett. D. W. end Pgrt-ar, K. R. (1964). J. Morph. 94,221-82. Fieoher, A. (1894). Pringa?&m’e Jahrb.f. +a. Bot. XirVI. 187-236. Frifech,F.E. (1936).“structureesldreproductionof the Algee.”Vol.I.Wbri+ Gibbons, I. R. (1961a). J. Biophya. Bwchern. Cytol. 11, 179-205. Gibbona, I. R. (1961b). N d w e , Lond. 19, 1128-9. 7, Gibbona, I. R. and Grimatone, A. V. (1960). J. Bhphye. Biochem. U@. 879-716. Greenwood, A. D. (1969).J. exp. Bot. 10, 56-88. Greenwood, A. D., Manton, I. and Clarke, B. (1967).J. exp. Bot. 8,71-86. H o ~L.,and Manton, I. (1962). J. EXP.Bot. 18, 443-9. Hoffmsn, L.and Menton, I. (1963).Amer. J. Bot. 60. Jakus, M. A. and Hall, C. E. (1948). BioZ. Bull. 91, 141-4. Koch, W. (1961).J . E k h a Mitohell eci. SOC.87, 123-31. Korechikoff, A. A. (1813).Ber. dtsch. bot. Qw. 81, 174. Lang, N. J. (1963).J. cell. Bwl. 19, 631-4. Leedale, G. F. (1964).Arch. Mikrobiol. In the preaa. Loeffler, F. (1889). Zbl. Bakt. 6, 209-24. Luther, A. (1899). K . Bvenska, Vetensk A M . L@ud. 24, 1-22. Maims, F. (1928). Arch. ProtLqtenk. IJL, p. 306. Manton, I. (1960).Demonstration of compound cilia in a fern aperm8tozoid by meene of the ultra-violet microscope. J. exp. Bot. I,89-70. Menton, 1.(1962).The fine structure of plant cilia. R p p . Roc. exp. Bwl. 8,300-19. Manton, I. (1954). Microsnstomy of cilia, flagella etc. 139. Recent work on the internal structure of plant cilia. Proc. Int. Confevmce on EZectron Micro-

-,

London. 694-9.

Manton. I. (1966).In ‘lCellulsr Mechanism in Differentiation mid Growth’’, @. Rudnick, ed.). Princeton, U.8.A. Manton, I. (19698). Electron microscopical observetione on 8 very amall fl8geht.e. The problem of C h r d i m gnceilla Butcher. J . Mar. biol. A M . U.K. 88. 319-33. Manton, I. (196Qb).Observations on the mi&oantatomy of the spermatozoid of the Bracken Fern.(Pteridiwnaqudinwn.)J . Bwphya. B i o c b . Cytol. 6,413-18. Manton, I. (19690).Obeervationa on.the internal structure of the spermatozoid of Ddclyola. J. exp. BOt. 10, 448-61. Manton, I. (1961). P l a t Cell 8tmcture, In “Contemporery Botanioal Thought” (MoLeod and Cobley, eds.) pp, 171-97. Oliver and Boyd, London. Manton, I. (19848). ~bsewationson the Ane structure of the zooapore and young gemling of Stigeoolonium.J . exp. Bot. 16, 399-411. Msnton, I. (1964b). The poeeible signi5usnce of aome detaile of flagellar baeee in plants. J . R.nric?.. 800. 111,82,279-80. Mmton, I. (1964~).A contribution towarda underatanding of “the primitive Fucoid”. New PWZ. 68, 244-64. Manton, I. (1964d). Obeervstions with the electron microeoope on the division cycle in the flagellate Prymneeium p a r u n . J. R. Mh.6oc. 88, 317-26.

34

I. MANTON

Manton, I. and Clarke, B. (1960). Electron miaroscopical observatione on the spermetozoid of FUGUE. Nature, Lo&. 160, 973. 8 fern Manton, I. and Clarke, B. (196la). Demonstration of compowld C i h eprmetozoid with the electron microscope. J. Wp. Bat. 2, 126-8. Manton, I. end Clarke, B. (1061b). Electron microscopical observations On the zoospores of Pylaielb and Lanrimrb. J. q. Bot. 2, 242-0. Manton, I. and Clarke, B. (10610). An eleatron miorowope etudy of the sp-tozoid of Fucw aewatw. Ann. Bot. N.B. 15, 461-71. Manton, I. end Clarke, B. (1962). An electron miommope study of the spennetozoid of19phgnum.J. exp. Bot. 8,206-75. Manton, I. and Parke, M. (1860). Further observetione on small green fl&lab with special reference to possible relatives of 0-m Mlla Butohm. J . MW. h i . AEE.U.H. a 9 , 2 7 ~ ~ Manton. I., Clarke, B. end Greenwood, A. D. (1953). Further observatiom With the electron miarwoope on spermatozoids in the Brown Algae. J. c ~ pBat. . 4, 310-29. b t o n , I., Clarke,B. and Greenwood, A. D. (1965). Obeervationswith the eleotron microscope on biciliate end quadriciliate zoospores in Green &m. J . q B O ~6,. 126-8. Manton, I., Oates, K. and Perke, M.(1963). Observations on the fine structure Of the Pyramimorure stege of Hahaphaera end preliminary observations on three species of Pyramimonae. J. Mar. bwl. Aae. U . K . 48, 225-38. Manton, I., Clarke, B., Greenwood, A. D. snd Flint, E. A. (1962). Further observations in the struoture of plant, cilie, by a combination of Visual and electron microscopy. J. exp. Bot. 3, 204-16. Manton, I., Raym, D. G., Ettl, H. and Parke, M. (1066). Further observations on green flagellates with scaly flagella: the genus Heterommtiz Korshikov. J. Mar. biol. Aas. U.K.45, 241-66. Muhlpfordt, H. and Peters, D. (1061). 2001.Anz. 16 (Suppl.) 163-0. Parke, M. (1949). J , Mar. Biol. Aaa. U.K. 28, 266-86. Parke, M. (1962). J. Mar. biol. Aaa. U.K.32, 407-620. Parke, M. and Adams, I. (1060). J. Mar. Biol. Aaa. U.K.89, 263-74. Parke, M. and R a p , D. a. (1964). Studies on Marine Flagellates. VII. Nephro. aebnie gilwa sp. nov. and some allied forma. J. Ma?.. biol. Am. U.K. In the press. Parke, M.,Lund, J. W. Q. end Manton, I. (1062). Arch. Mikrobiol. 42, 838-52. Perke, M., Manton, 1. end Clarke,B. (1066). J . Mar. Liiol. Rae. U.K. 84,579-608. Pea~e,D. C. (1063). J . cell. BWl. 18, 313-26. Petersen, B. (1918). k w k . Ndurh. For. 69, 346-7. Petereen, B. (1029). Bot. Ti&&. 40,373-89. Petersen. J. €3.. Caram, B. and Haneen, J. B. (1968). Bot. Tidssb. 64, 67-60. Pitelka, D. R. (1940). Uniw. C d q . Publ. 2002.68, 377-480. Piteh, D. R. (1963). “Electron-microscope etruature of Protom8.” Pergamon h, Oxford. Pitelka, D. R. end Schooley, C. N. (1966). Univ. Cdif. Publ. 2002.61, 79-128. Pringeheim, E. a. (1948). BWZ. Rev. 28, 46-61. Pringsheim, E. G. (1966). N o ~ Acts a Leop. CWOZ.18.1-188. m h e i m , N. (1866). M d . A M . Wku. Berlin. 133-66. Roth, L. E. and Shigenege, Y. (1064). J. cel2. Bwl. 20, 240-70. Bmith, 0.M. (1061). Menu81 of Phycology. N.8. 27, Ohmica Botunim 00. W d W , Maaa. Stanier, R. Y. and van Niel, C. B. (1062). Arch. Mikrobiol, 4a, 17-36. strain, H.H.(1061). In “Menual of Phyoology” ( a. 116. Bmith, ed.) p. 262. Cronioe Bot~nic& CO., W81tham, Maasaehueette. Strasburger, E. (1880). Znltbildzcngund 2-w. 3rd edition. Jena. Thuret, G. (1861). Recherches sur lea Zoospores dea Alguw. Ann. 8ei. W . (bot.) 38 10, 1-13. Thuret. a.md %ma+, Ti! ‘11S’711\ “F+.4- DL----l-A---- r t D-21

Fundamental Problems in Numerical Taxonomy

.

W. T. WILLIAMS and M B . DALE Department of Botany. The Univeraity. 8outhamptm. Bngland

.

............................................................. 86 .................................. 87 . ............................... ;..................... a7 B. Monothetio and Polythetic Clwi5~lltione.................................87 C. Maximizcltion ......................................................... 88 D. Hierarchical and Non-hierclrahical Clessiflmtione........................... 42 E. Probabilfstic and Non-probabllisttoClwifirntiom.......................... A3 I11. The Choice of Mathemstioel Model.......................................... 48 A . Introduction: Metrica .................................................. 48 B. Metric Properties of Pair-functions ...................................... 49 C. Intrinaidy Non-metrio Byatam ........................................61 D. Non-Euclidean Syntamn................................................. 52 E. Concluaionn ........................................................... 63 IV. The BM~C Euclidesn Model ................................................. 54 A . Duslity: The R/Q Problem .............................................. 64 B. Adjustments to the Model .............................................. 66 C. Heterogeneity......................................................... MI V. Strategyofhlysis ....................................................... 60 A. Simplification Methods ................................................. 69 B. Partition ............................................................. 61 C. Non-hierarchical Metbode ..............................................81 L). Hierarchical Methods .................................................. 82 Acknowledgements........................................................ 67 Referenw ..............................................................87 I

.

Introduction

I1 The Nature and Propertien of Clessiflcutione A TheBaeicAxiom

I. INTRODUCTION In any field of endeavour which transgrosoos the boundary between fundamental and applied disciplinefl there tend to be two alternative approaches: the user’s approach. “What do I wish to do. and how can it best be done?” and the more fundamental “What can most efficiently be done. and what can it be used for?” The approaches are more different than is commonly realized. and both are necessary. Them refleotions are prompted by the appearance of the firet major text-book devoted to numerical taxonomy. that due to Bokal and Sneath (1964). This will provide an admirable introduction for those botanists wishing to enter this rapidly developing field; and it is no denigration of this important work to suggest that the authors are less rigorous in their examination of the methods than they are in their Uee and htemreta-

W. T. WILLIAMS A N D M . B. D A L E

36

tion, for it is with these latter aspects that they are primarily concerned. The user’s interests in plant ecology are similarly met by Greig-Smith (1964) and, in a more limited context, by an article which to some extent complements our own (Lambert and Dale, 1964). Excellent bibliographies have been provided for taxonomy by Sokal and Sneath (1964) and for ecology by Goodall (1962) and Greig-Smith (1964). Our intention is different. The newcomer to this field is faced with a formidable diversity of methods, all apparently fullilling closely similar functions. It is nevertheless our contention that the number of fundamentally distinct methods is very small, and that criteria can be erected which will olarify the distinctions between them, and between their numerous variants. This is tho aim of this communication. We shall not be concerned with the problem of allocation to an existing classification, which is the province of discriminant analysis. Although all the methods we shall discuss are in principle applicable to botanical problems, few have yet been ao applied; our references will therefore of necessity be drawn from a wide variety of disciplines. Symbols used will be conventional; but in the 2 x 2 contingency table arising from the possession ( J , K )or lack (j,k)of two attributes J and K, two conventions now exist for the number of individuals in each class: the alternatives are set out below:

SJ

-J

SK

a

6

-K

C

d

+J

-J

(J)

Scheme (i)is older, and has long been used in elementary statistical texts; scheme (ii) is used by Sokal and Sneath. The latter is more informative, but is clumsy in algebraic expressionsand in our experience is easily misread. When such a table is at issue, we shall therefore adhere to the (a,b,c,d)convention.

FUNDAMENTAL PROBLEMS I N NUMERICAL TAXONOMS

37

TI. ‘I‘HIGNATUREAND PROPERTIES OF CLASSIFICATIONS A. THE BASIC AXIOMS

Most, ge~i(wtldixcurrsionn o t i c:lrcndicr~t h r two co~icc~iwd tto clc?fina. t’o (tistiiigiiirrli bctwcon, csistiirg typw of clrwnification; such , for examplc, are tlie discussions in Lawrence (IYGl), Beckner (196Y), Gilmour (1961)and Sokal and Srisatli (1964).It is important for our purposes, however, to establish the minimum requirements which all cliissifications must meet, and wc rcstnte tlie problem as follows. A population consist8 of elerncnts, each of which can be iridividually described by reference to a predetermined list of “relevant characteristics”. This population is subdivided into sets of elements. what requirements must be fulfilled by these sets for the subdivision to rank as a classification? We submit that the following axioms will suffice. iuid

(1) Within every many-membered set there must be, for every member of the set, at least one other membes with which it shares at least one relevant characteristic. (2) Membership of the set may not itself be a relevant Characteristic. (3) Every member of any one set must differ in at least one relevant characteristic from every member of every other set.

Axiom (1) introduces a concept of “likeness” and ensures that tin elenlent cannot be classified if nothing is known about it. Axiom (2) has two important ConsequenceH. First, division into groups defined solely as possessing a stated nuniber of membcrs (such a8 dividing a population into groups of ten, or dividing it equally into eight parts) is excluded ; secondly, all classifications mu& be open-ended-there may be no known members to add to a set, hut it must not be impowittlle by definition to add more. Axiom (3) not orily cnsurm that identicah cannot be distributed between different sctq, hit makes provision for the Mingle-membered set. Although these axioms will suffice to define a classification, they are not in general sufficient to define one which is useful. We therefore need to discover what additional constraints must be imposed to enable our classification to meet specific external requirements, and it is from this point of view that we now proceed to examine some of the basic problems in numerical taxonomy. B. MONOTHETIC AND POLSTHETIC CLASSIFICATIONS

These terms were introduced by Sneatll (1962) to replace Beckner’fi (1959)terms “monotypic” and “polytypic” (without changing Beckner’s definit.ions),since these terms have other meanings. The Nets in a mono-

38

W. T . WILLIAMS A N D M. B . DALB

thetic classification are completely defined by the presence or absence of specific characteristics. Since such classifications are always generated in practice by successive sub-division, it follows that there must always be at least one set all of whose members share at least one relevant charaoteristic. It is quite possible to oonstruct a population, classifiable by reference to the axioms, from which no such set can be extracted; in such a case monothetic classification is impossible. Monothetic classifications may nevertheless be useful. They have proved valuable in ecology, where the concept of “indicator species” has long been familiar; they may well be needed in criminology, in which a decision may have to be taken quickly and based on as few attributes as possible. They are normally unacceptable in taxonomy; in medical taxonomy, for instance, one does not wish a man to be treated for the wrong disease because he has one aberrant symptom. The occasional criticism that monothetic systems produce misclassification is, however, invalid, since the criticism automatically assumes that a polythetic system is desired, and the argument is circular. The real objection to manothetic classifications is that they assme a property of the population which it may not in fact possess. Polythetic classifications imply no properties beyond those invoIved in the basic axioms, and are therefore always possible. 0. MAXIMIZATION

1. principlee of maximization The basic axioms will serve to define a large number of alternative cla&kations, And a further constraint is needed to select from among these. The constraint universally required by users is that, in a sense yet to be defined, the members of any one set are to be as alike as possible and as unlike the members of other sets as possible. Differences within sets are to be minimized, differences between sets are to be maximized. Formal work in this field, usually loosely known a8 “maximization”, has been largely confined to discriminant situations, particularly in the field of pattern recognition (vide, e.g. Sebestye~, 1962); but the diverse methods of numerical taxonomy are simply variant methods of maximization. The method8 fall into two fundamentally distinot groups.

i. r%f-~tnLcturingmpdhodi~ (u)A function of the relevant characteristics ia defined between paim of elements. ( b ) An element may be either a member of a population or an entire set; if a set, then the set may be defined by one of its members, by all

BUNDAMENTAL PROBLIDMS I N NUMERIUAL TAXONOMY

39

of its members, or by an element constructed from all of its members. (c) Sets are to be construoted so that the funotion is minimum (or maximum) within them, maximum (or minimum) between them, or both.

ii. Derived-~tmturing?ne.t)wda (a) A function is defined between pairs of relevant oharaoteristios over a given set of members. (b) A characteristic, or a group of characteristics, is found for which the funotion, or a derivative of the function, is maximal. (c) Sets of members are defined in relation to the oharacteristic(e) so selected.

For certain purposes it is desirable that the analysis oan be “inverted”, in the sense that the elements and characteristias change plaaes. For this to be possible the data must fulfil certain oonditions which we explore later (Section IV A). The apparent diversity of methods in the literature largely concerns self-structuring methods, and in these the diversity is largely one of the function selected. Monothetic methods necessarily employ derived-structuring. 2. Intern1 and external ch&$cationa It is assumed in the foregoing paragraph that the members as defined by their relevant oharacteristics form a self-sufficient set within which maximization is to be effected; such systems, which comprise almost the wholo of existing literature in numerical taxonomy, we shall call “internal” classifications. It may nevertheless be desired to impose a restraint in the form of an external element or set of elements (selfstructuring) or an external characteristio or set of oharacterietics (derived-structuring). In such casm the maximization is entirely between the reference unit on the one hand and the internal eete on the other, the internql sets needing only to satbfy the besic olassifiwtory axioms. The process of maximization is, however, itself different from the all-internal case. The pkimary maximization is of the range of the selected function, in that the internal sets are to be as like or unlike as possible to the reference sef. The main use of these “external” classificatiom is likely to be predictive; if the population is heterogeneous in the sense we shall define in Section IV C, they will be more powerful than the classical regrmsions taken over the whole population. Their possible application t o problem in plant ecology is also under investigation. The only example known to us in the literature iu the derived-structure “predictive attribute ctnalysis” of Macnaughton-Smith (19SS), with whom we are currently collaborating in the development of more general S Y E ~ I W .

40

W. T. WILLIAMS A N D M , B. D A L E

3. Simultaneous alternative chsi$cations: clump Suppose the system be restricted by the requirements ( i ) that maximization shall extract only one sub-set from the population, and (ii) that this sub-set shall be subject to a specified constraint; the constraint normally imposed is that the subset must contain a specified element or group of elements which will act a8 its nucleus. Such a subset is normally termed a “clump” and the remainder of the population is without interest. Let this process be successivly repeated on the entire population by specifying a new constraint on each occasion ;the ultimate result is a set of clumps. This set is sometimes loosely termed an “overlapping olassification”, but such an extension of the term “classification” is not to be recommended; the clumps need not exhaust the population, and any one element can, and usually does, occur in more than one clump. Systems of this type are particularly associated with the work of Needham (vide,e.g. Needham, 1962; Needham and Jones, 1964) on linguistic data arising from problems in documentation and information retrieval ; but they have also found some application in anthropology and medicine (Bonner, 1964). They have been developed to meet circumRtances in which simplicity and speed of computation are more important than power, and they may well require re-examination before they can satisfy the more rigorous demands of plant taxonomy and ecology. A system of clumps can similarly be generated by the use of a changing external criterion as constraint. The groups delimited by the “deme” terminology (Gilmour and Heslop-Harrison, 1954) of plant taxonomy together form a system of precisely this nature, but it seems never to have been the subject of numerical study. We shall not be further concerned with clump systems in this article. 4. Weighting Sokal and Sneath (1964) accept the Adansonian postulate that “every character is of equal weight”. We need not so restrict ourselve8, and we shall first distinguish between a primi and a posteriori importance.

i. Importance a priori Classifications in, for example, modical or criminological corrtoxtn may be used as guides to action; in such cases particular characteristics may be of overriding importance. It might be regarded as undmirable to send epileptics to prison, no matter what their other characteristics suggested. Such cases do not disturb the systems we are considering, since they do not alter the classifications, but only the UBB that ie made of them. It has, however, frequently been suggested (wide, e.g.

FUNDAMENTAL PROBLEMS IN N U M E R I C A L T A X O N O M Y

41

Proctor and Kendrick, 1963)that characteristics should be assigned a differential importance from prior knowledge of the field ; as we have already pointed out (Williams et al., 1984) this destroys the objectivity which is the single most valuable feature of numerical taxonomy, and we cannot recommend it. ii. lmportunce a posteriori Derived-structuring methods maximize some function of the characteristics. After maximization, therefore, each characteristic will be associated with a numerioal value which reflects its contribution to the overall maximization, and which may therefore be regarded as tt measure of its importance. The application of this concept presents different problems in different systems, and the situation may best be explorcd by comideration of firstly, monothetio derived-struoture, and secondly, polythetio self-structure. (a) Mmthetic derived-etructure.If a population is such that it contains many shared charaoteristias and 80 can be defined as a set of final classes, a very large number of alternative monothetic classifications is possible. The characteristics used may be selected solely for external convenience, or even indiscriminately, and there is no internal maximization. Such are the “special claasifications” (into, e.g., food- or fibreplants) and the dichotomous keys in floras. These, which are in fact perfectly good external classifications, are commonly termed“artificia1”. It is therefore tempting to equate “artificial” with “absence of internal maximization”; but we defer to the views of Sneath (in Zitt.) to the effect that the terms “natural” and “artificial” have been so variously used that to provide them with new statistical definitions would confuse rather than clarify the situation. In contraat to these classifications, the method of Aseociation Analysis, whose properties are discussed in Section V D 2, ie a monothetio method whose defining CharacteriRtics have been obtained by a process of internal maximization. The characteristios now differ in a p8teriori importance, and this has by some workers been regarded an “weighting”. (b) Polythetic self-structure. Here again it is theoretically possible to effect classification without maximization, but since most real-life populations already themselves satisfy our Axiom (1) for a classification, the solution is usually trivial. A single maximization is therefore necessary in practice. All the “similarity” methods discussed in Sokal and Sneath (1964) are of this type : they use the least maximization which is in practice essential. However, the first step in such an analysb might be a derived-structure maximization, so that the characteristics were aa a first step provided with “importance” measures; a second

42

W.

T. WILLIAMS A N D X. B . DALE

maximization, using these weighted characteristics, would be necessary to complete the classification. The only such doubly-maximizedmethods known to us are those in whose development we have ourselves collaborated (Macnsughton-Smith et al., 1964; Williams et ul., 1964). 5. Unintentional weighting: “nui~ancecorrelations” The selection of attributes is not itself the concern of numerical taxonomy. Nevertheless, methods which employ derived-structure functions are prone to difficulties arising from so-called “nuisance correlations”-groups of attributes linked for reasons unconnected with the purpose of the analyeis. This problem does not arise in those ecological studies in whiah the attributes are plant species, since these are necessarily different things. The questionnaires of sociologiortl studies, however, normally contain much redundant information ; this is deliberate, since a question which may be avoided in one form may be answered readily in another. Some of the attributes are therefore logically linked, and these linked groups may dominate the subsequent analysis. It must be remembered that questionnaires have not normally been deaigned with modern numerical methods in mind, and the increasing use of these methods will doubtless in time iduence the design of questionnaires; but meanwhile the problem exists. The nature of the problem, however, has not always been clearly understood. The objection,to these links is simply that they can be known to be links without recourse to analysis ;if they could not be so known they would be of interest. It does not follow that they are in every caw easily recognized, and a preliminary numerical analysis may serve to este;blieh them. This is possible if the system is such that elements and chamteristics can change places, so that the characteristior, can be grouped into sets; if such a set inescapably suggests the hypothesis that the mombercl are linked for reasona-auch as intrinsic redundancy in a questionnaire -in which the investigator is not interested, the group can be replaced by one or more of its members or by a new attribute constructed from all of them. Despite statements to the contrary in tho literature, we submit that the objection to nuisance correlations does not lie in their logically necessary links; the sole criterion is the interest or otherwise of the wer. D. HIERARCHICAL AND NON-HIERILRCHICJAL CLASSIFICATIONS

Hierarchical classifications are of very real advantage to the taxonomiat, since they enable him to compare taxa at any desired level. This has probably contributed to the fact that the vast majority of existing numerical methods are hierarchical in nature. However, it

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43

may also generate a requirement that each level in division is aesoaiated with some measure which shall fall as the hierarohy deswnds. It is not always realized that this places an additional oonstraint on the ohoioe of maximizing function ; some functions (notably Euclidean distanoee and information statiatios) possess this property, whereas others (most of the derived-structure ooefficients and the “statistioal distance” coefficients) do not. The term “reticulate classification” seems .to include two quite different concepts. The f h t ia the unmaximized external classification with an embarrassing choice of alternatives, such aa arises in classifying books; this need not concern us. Truly reticulate claasifications arise out of an interest in inter-set relationships after division into sets has been complgted. If only the inter-set functions are required, a completely non-hierarchical method could be used; but, as shdl later point out, the choice of such methods is extremely restricted. In most caaes, therefore, both the hierarchy and the inter-set functions are of interest, and the problem is to generate either from the other. We ahall later demonstrate that maximization may, or may not, be uniform over the entire mathematical model in me. If it is uniform, as with unweightd Euclidean distances or information statiatios, no difficulty arises : inter-set functions and hierarohical divisions are everywhere oompatible. In those methods with which we ourselves have been associated, the maximization is deliberately non-uniform over the model; in these cases, which are hierarchical, no compatible inter-set function has yet been defined (vide Sections I11 D (i)(ii)).It is not permissiblo to define a completely new function,laincethe original hierarchical maximization may then fail; this is the cauae of the “recombination of aets” difficulty which Goodall (1953a) experienced in his pioneer studies in divisive methods. E. PROBABILISTIC AND NON-PROBABILISTIC CLASSIB+ICATIONE

This particular dichotomy has generated more confusion-and probably more rancour-than any other. It underlines the commonlyexpressed doubts a~ to whether these methods can, or cannot, be classed as statistics, and so has caused Greig-Smith (1964) to use the term “quantitative” and Sokal and Sneath (1964) and ourselves to fall back on “numerioel”. It underlies, too, the misgivings that authors frequently express concerning the “significance” of their results. The difficulty has been exacerbated by the fact that modern statistios is almost entirely concerned with estimates of probability, so that if well-known statistical parameters-x* or the correlation coefficient, for example-are uaed for maximizing, it is aaeumed that these am

44

W . T . W I L L I A M S A N D M . B. D A L E

estimates which should be associated with measures of probability. I n fact, the methods of numerical taxonomy are not, or need not be, probabilistic systems at all, but hypothesis-generating systems. We shall outline the two alternative approaches.

I . The non-probabilistic approach From this point of view, the methods of numerical taxonomy may be regarded as stemming from a branch of statistics of respectable antiquity-that concerned with finding mathematical formulations which will serve as a concise and economical description of an otherwise intractably oumbersome mass of data. Though superficially so dissimilar, their logical relatives are to be found among such projects as the fitting of Pearson curves to actuarial data (Elderton, 1938); the search for a flexible growth-curve (Richards, 1969; Nelder, 1961); and the application of contagious Poisson distributions to distributions of plants in the field (Archibeld, 1948).The fitting of regression lines is itself a member of the mme family, extended by the probabilistic concept of the significance of the parameters which the fitting requires. Now, these concise mathematical descriptions can with perfect validity be used to generate hypotheses concerning the nature of the data, but only if two conditions are rigidly satisfied. First, aa always, the hypotheses must be capable of being tested; secondly, any test must depend on new observations, and cannot again use the data from which the hypothesis was generated. Generation of the hypothesis may not be used as its own evidence; we forbear to cite examples of this practice, contenting ourselves by remarking that they can be found in biological literature. The precise statistical context of these methods can most clearly be demonstrated by comparing a vegetation survey in ecology with an agronomic experiment in, say, mineral nutrition. In the agronomic context the hypothesis is set from previous experience, and this determine8 the details of an experiment, which issues in a quantity of data; etatistical methods are applied to thaw data in order to test the hypotheHis-ueually in the form of the probability of obtaining a given deviation from a null hypothe6iB by chance alone. Tn tho ecological context, although experience may have informed its collection, the data is the starting-point ; function6 are elected and appropriately maximized in order to reduce the data to eimplor form; thin simpler form is used to generate a hypothesis-often in the form of “there is a change of some sort in this region”; and the hypothesis is tested by new, direct observations in the field. Examples of this type of hypothesisvalidation may be found in the work on Association Analysis (Williams and Lambert, 1960).

B U N D A M E N T A L YBOBL10MS 1N N U M E R I U A L T A X O N O M Y

46

Nor is validation difficult in applied taxonomy. In medicine, for example, the individuals classified may be diseme-producing organisms, or symptoms; in criminology they are normally delinquents. I n these cases the hypothesis takes the form of a suggestion for treatment. It may be remarked in passing that the power of the mathematical methods used is all-important in these fields, for although falsification of a hypothesis might gratify a dispassionate experimenter, it is apt to be disastrous if a human individual is concerned. The problem is more difficult in “classical” taxonomy. Here it is tempting to enunciate a phylogenetic hypothesis, normally based on inter-set functions, but fossil records are such that hypotheses of this type are rarely testable (vide, e.g. Sneath and Sokal, 1962). The basic requirement of taxonomy aemu stricto is stability, both of the membership of sets and of the pattern of characteristics that their members display within them. I n the first case (the membership of sets), addition of new characteristics followed by re-maximization should not ohange the membership of the sets. In the eecond (the pattern of characteristics), let a new element be disooverod whom chctracteristios are imperfectly known; if from the known chasacteristics it can be allocated unequivooally to an existing set, the pattern of its remaining characteristics, when these are examined, should conform to the pattern for the set. On this approach, therefore, the methods of numerical taxonomy are hypothesh-generating systems; and a hypothesis-generating system is neither valid nor invalid. Probability enters only, if indeed it enters at all, in the testing of the hypotheses that are generated. This approach exposes a possible danger, which we do not believe taxonometric writing has always avoided. This is that computer classifications might be regarded aa in some sense absolute-as “objective” and therefore “better”. They are not objective, since they depend on the user’s personal choice of maximizing function; and they are only better if they can be shown to fulfil a stated requirement more efficiently.

2. The probabilistic approach It is, &B we shall show, easy to conceive of probahilietio clamificatione in theory; but we are here concerned to defend tho thesitc that auch classifications are usually both impracticable and unprofitable. Fimt, it should be noted that a probabiliRtic classification requiree a null hypothesis; this will normally take the form of stating that the pairfunctions available for maximization in a given population or set could have been generated by a random process. The null hypothesis cannot, in fact, be independent of the function selected for maximization,

46

W. T. WILLTAMS A N D M. B. DALHl

i. DifJicultiea inherent in null hypothea Since the null hypothesis depends on the maximizing function, it will be convenient to select two well-known cases for consideration. (a) Multivariate nomnal popubtiom. In this case the null hypothesis would state that the observed variation in characteristics could have been generated by a set of independent normal variates, usually the characteristics themselves. The function available for test would probably be the correlation matrix. Now, Bartlett’s (1950) test for the roots is not available if the matrix is singular, and experience suggests that it is sensitive to departures from normality. To demand that all the coefficients be individually significant is nomally regarded aa too stringent ; and Goodall (19G3a) has in effect suggested that the ooefficients be themselves treated as normal deviatos, so that the proportion of them which exceeds the individual signifioanoe level be regarded &B a test of significanoe of the whole matrix. There is, in fact, no simple, unequivocal and robmt test available. ( 6 ) Qualitative populations. The function used (though others are available) is often related to the Euclidean diRtance between elements (or set centroids) plotted in an n-dimensional space where the j t h co-ordinate for an element is 1 if it possesses the j t h attribute and 0 if it lacks it. The problem now is to state a null hy&hesis at all. Use of the binomial expansion would imply that possession of all characteristics was equally likely; and the solution obtained by Rohlf (1962) for even n makes assumptions as to the distribution of the frequencies. If we assume, however, that the hypothesis should not involve the frequencies, an obvious solution would be to retain the frequency totals and to construct from them the entirely dissociated class-frequencies; that is, the numbers of individuals that would be required in all possible sub-classes if, without change in the total numbers possessing each attribute, all pairs of attributes were to have zero association. It is straightforward, though tedious, so to calculate the probabilities (for 0,1, d2)in the two-characteristic case; but the resulting algebraio expressions are extremely cumbersome, and lend little hopo of extension. In any case, construction of the general null population may present formidable difficulties. If we write (A) for the number of individuals possessing attribute A, (AB) for the number posmsing both A and B, and so on, then in the oompletely dissociated population W C .

N

*.

.)

( 4 * ( B )((7... .

=x

“3

Unfortunately, for more than two characteriafics, this relationship is necessary but not s d c i e n t (vide, e.g. Yule and Kendall, 1960), and oannot therefore be UBePx M a generating function.

F UNDAM INT A L PROBLIMS I N N U Y I R I O A L TAXONOMY

47

It has been suggested to UB (Macnaughton-Smith, in W.) that information statistics might provide a solution of the qualitative problem, in view of their remarkable additive propertiea and their relationship to x*. Let a p u p of n individuals be specified by the possession or lack of p attributes, and let the number possessing the j t h attribute be a,; we have made preliminary ObservationA, using ecological data, on the behaviaur of the statistic: I = Iyn log It-

E [u, log a,+(n-aj)

log (n-tzj)l*

j-1

Ecological data not uncommonly contain groups of identical or nearidentical individuala, and these groups may vary greatly in size; the data will have the properties of a stratified, rather than of a random, sample. Unfortunately, we find that the stati8tio above is seneitive to this particular form of non-randomnew, and is therefom unduly senaitive to set size--sets tend to be fused if they contain comparable numbers of membera. This is incompatible with our second classificatory axiom, since it implies that a function of the set may determine the allocation of one of its members. This difficulty may be removed by normalizing for group size, though, in some forma of analysis, a t the expense of replacing it by the generation of an “ambiguity” problem related to that arising from unweighted Euclidean diatanwa (Section V D 3 (i)). Nevertheless,these statistics have many desirable properties and would repay further investigation. (c) GoodaZl’8 coe&ien$. Very recently Goodall (1964) has proposed a probabilistic similarity index. For every pair of individuals, the probability that the two are as similar as in fact they are is calculated for each attribute separately , and the attribute-probabilities then combined. The method is cumbersome for qualitative b t a , but it is the only method known to us which ia in principle applicable to mixed data i.e. data in which the attributes are 80 unlike that any common scaling would be unrealietic. No example of it8 use has yet been published. ii. AelicaliOn Of $WObabili8tic Ch8$C&iO?l% Suppose an appropriate criterion of significance, and therefore an appropriate null hypothesis, to be available; and s u p p a a popubtion to have been divided by maximization into two eete whose dididididididididididididididididkincfio fails to reach signihance. It still does not follow that the division should not be effected. For the population may be so intractably large that the best possible sub-diviaion, though non-significant,may be mom uaeful than none at all. However, although the overall characbristicpattern may not define a significantdifference, sub-seta of charmbh-

48

W . T . WILLIAMS A N D M. B . D A L E

tics may exhibit stability (this phenomenon may occur if the population exhibits n o h , which are briefly discussed in Section I V C 4). I n either case, it is the usefulness of the division which will be of importance; the division will therefore in any case be subjected by the user to a second, pragmatic, test which will override the fist, probabilistic, test. We are therefore not convinced that any useful purpose is served by the probabilistic test, quite apart from its inherent difficulties. 111, THECHOICEOF MATHEMATICAL MODEL A. INTRODUOTION : METRIOS

The ultimate test of a numerical method is whether the u8er fin& it useful. However, all mothods are of some we to the usor; and if he ie to bear the sole responsibility of deciding between them, he will be faced with an immense amount of empirical work,still with no assuranm that the method may not fail under extreme conditiona-as, we believe, some existing “similarity” methods have s h a d y failed. The literature contains many despondent remarks on the paucity of available information relating to comparison of methods. This is particularly true of the pair-functions themselves, often loosely classed as “similarity coefficients”. The best-known have been reviewed by Goodman and Kruskal (1954, 1959), Dagnelie (1960) and Sokal and Sneath (1904); but it k doubtful whether even these extensive collections are complete. The problems would be relatively unimportant if all such functions were jointly monotonic, in the sense that, if element-pairs are so ordered that one function forms a monotonic series (i.e. a series which either increases or decreases over the whole of its length), the remainder will also be monotonic, To take only three well-known functions, 2a/(%+b+c), (a+d)/(a+b+c+d), and the correlation coefficient, it ie easily shown that no one of these is jointly monotonic with either of the other$. A choice is therefore necesmy; and the testing diffioulty oan be overcome, at lea& in part, if the methods and function8 are required to fulfil appropriate mathematical conditions. We consider it essential that any meamre used for maximization should define a model, and, if possible, a model in Euclidean space. The advantages of such Rystems are threefold. First, many simple, robust and powerful methods are available in Euclidean systems that are not available outside them. Secondly, as mentioned in Section I1 D, they have hierarchical advantages. Thirdly, and perhaps most important, our daily experience gives us an intuitive perception of Euclidean systems, and thereby enables us to grasp their properties and to predict these properties in extreme cases. If the function is such that it is not known

FUNDAMENTAL PROBLEMS I N N U Y E R I U A L TAXONOMY

49

to be associated with any particular probabilistic or spatial model (models which me neither probabilistic nor spatial are possible, but we know of no published work on them) we propose that it must, aa a minimum requirement, be a metric; it will then necessarily define a spaoe whose properties oan be explored. We deal in this motion with the general problem of metrios, and it will be oonvenient Brat to etate the conventionaldefinitione. The subject is fully dieoueaedin geometrioal texts; the formulation we use ia substantially that of Kelley (1965). De$dtion. A numerical function d(z,y) of pairs of points of a eet E is said to be a metric for E if it satisfies these oonditions: (1) d(z,y) = 4Y,430 (symmetry) (2) d(z,z)
where true we shall call qua&-metric. In the oontext of numerical taxonomy, metrio properties may fail for two remons : the characteristics may be intrinsically metric but the pair-function selected is not; or only a pair-function exists, and this is not metric. We deal with these cases in order. B. METRIU PROPERTIES OF PAIR-FUNUTIONS

It would be unprofitable to examine the properties of all the many functions in the literature, and we shall largely conhe our observations to the three moat familiar: (a+d)/(a+b+c+d); 2a/(%+b+c); and the correlation ooeffiaient.

I . ia+d)/(a+b+c+d)

This is the coefficient normally used by Sneath. Using the model mentioned in Section I1 E 2(i)b, and following Soh1 and Sneath in writing d for the Euclidean distance between the two points, the ooefficient is equal to (1-A*/N). It is baaed on a Euclidean metrio and satisfies the requirements we have suggested. 2. 2a/(2a +b +c) This coefficient is probably among the oldest in the literature; it specifies the ratio between the number of charaderiefics common to two elements and the arithmetic mean of the numbers possessed by eaoh. It is monotonic with the coefficient a/(a+b+c), used by Sneath for the purpose of exoluding double-negative matches; the intention Ic

50

W. T. WILLIAMS AND 116. B. D A L l

here, in the context of our model, is to prevent points being gmupd solely beoause they are near the origin. Enumeration of the I)-oh&raoteristic case for either coefficientwill immediately demonstrate that the ooeffioients are quasi-metric ; they are also necessarily semi-metrio, and thus do not Ratisfy our requirements on either oount. It is of intent& to note that Sokal and Sneath (1964) no longer recommend the exolwion of double negativea. The earlier coefficient can be ueed to generate a different model. If, in the ordinary 2 x2 table, we have (2a+b+c)#N, there must be Ia-dl double-positive or double-negative matches ; there may be more but there cannot be less. If the coefficient is written in the form:

it may be regarded as derived from a distance whose dimensions am scaled to remove all logically-necessary matches. The dimensions of the model now change from place to place, so that the model is nonEuclidean; it could be topologically embedded in a Euclidean space of not more than 2N dimensions, but we are not ourselves competent to explore the utility of this approach.

3. The correhtion coeficient Several alternative models have been suggested for this funotion, only one of whioh fulfils our requirements. First, it should be noted that of the four requirements for a metric, simple unsigned derivativea of this coefficient (such as (1-r)) fail t o satisfy requirements (2)and (3), and cannot therefore be handled in this way (its semi-metric properties are of value if “shape” coefficients are r e q u i r e d 4 Rohlf and Sokal, 1963). A model commonly used in factor analysis, however (vide, e.g. Cattell, 1962), supposes the points to be rigidly attached to their ,co-ordinate axes by extensible perpendichrs. If the axes are now rotated about the origin until all correlations are zero, the final angles between them will be the inverse cosines of the original coefficiente. These angles between pairs of lines now serve to define a Euolidean space with oblique axes ;providing this model is in me, our requiremente tm therefore satisfied.

4. Aeymmetric fU%i?b?&? Goodall (1963b), in the c o w of an emmination into the phytosociological concept of “fidelity” , has suggested that twymmetrio funotions would be of value in this mntext. Several euoh funotions am in fact on record in the literature, although only Goodall appem to have appreciated their nature and possible applioation. 80 far aa we 5m

FUNDAMENTAL PROBLEMS IN N U M I R I O A L T A X O N O M Y

61

aware, no practicable strategy for the maximisetion of aaymmebrio functions has ever been suggested or even sought; unldl this ia done, further investigation of their properties will remain unproilttable. U. INTItINSIOALLY NON-METRIO SYSTEMS

In the previous section it has been assumed that all characteristics are, or can be regarded as being, measurable; failure of metricity ia due only to the calculation of a measure which is not a metric. We are here concerned with two problems of greater fundamental difficulty; firat, the case in which individual characteriatioa, though they exist, cannot be provided with a simple measure; and secondly,the caw in which characteristics do not exist, though a pair-function between elements does. 1. I n d i ~ d dCharWteTi8tiGB This situation arises when all that can be measured in respect of a given characteristic is some cornparison between two elementacommonly in the form of a difference or a ratio. It is then neceaaary to operate on these comparisons in such a way m to generate a metric which will uniquely order the elements along that ahmaateriatic considered a8 a dimension. This problem, usually known as “scaling”, is of great importance in psychometric work, and hae given rise to 4n extensive literature ; the reoent communiwtion by Phillips (1903) will aerve as an introduction to the field. We h o w of no botanical work of this type; but since comparative measures are not unknown in taxonomic descriptions,the methods may yet prove applicable, and botanists should be aware of their existence. 2. I80laled pair-functim Consider a sociological study in which has been recorded, for the members of each pair of individuab in a group, the number of times they met each other in a given period; all that is available for analysis is a pair-funotion. Functions of this type are often semi-metrio (some pairs of individuals never meet) and are almost alwaye quaai-metric. The problem is to generate a Euclidean system of hypothetical characteristice such that the distances between elements shall be related to the original pair-functions. A solution itl provided by the “proximity analyais” of Shepard (1962tt,b).This generates a system of coo-ordinates, of the lowest order which will permit a unique solution, such that the Euclidean distances between the elements are monotonic with the original pair-funotions. The solution is iterative, and a oomputer

62

W . T . WILLIAMS A N D M . B . D A L E

program exists. Again, we know of no published botenical applioations, but the method might conceivably be of interest in competition studies where the records took the form of the number of times pairs of species were in contact.

D. NON-EUCLIDEAN SYSTEMS

1.

I~TdUCtiOn

A Euclidean space is necesmrily metric, but the converse is not true. It will be convenient to begin with a conventional definition : A Euclidean space of order n is the set of all n-tuples (q. . , xi . z,,) where all xi are real numbers and where the distance between two points

.

n is given by [d(z,y)]Z = Z(xj-yi)z. It can be shown that such i =1 distances are metrics. There are three obvious ways in which Euclidean properties may be lost. Firstly, n itself may not be constant, so that the dimensions vary locally; this is the situation for the coefficient discussed in Section I11 B 2 above. Secondly,the n-tuples may be constrained in some way, e.g. to the surface of a sphere ;we know of no application in numerical taxonomy. Thirdly, the distance function may fail; in the cmes we shall consider, the distance-function holds within sets, but fails between some or all of them. The space defined is thus locally Euclidean, and hence (if varying continuously) Riemannian; and no difficulty arises unless inter-set functions are required. We shall disouse briefly three rnethode in which this type of problem arises.

2. Examples (i) Attempts to we “8tati8tical distance" The group of statistia of which the Mahalanobis Dzis the bestknown is essentially probabilistic in concept; it relates inter-& distance to a common within-set function, and involves the postulation of a common dispersion matrix for the two sets. If the sets are manifestly unlike, this is an unrealistic assumption; end if such a matrix ie artificially constructed, it may well be singular. It is not uncommon (cf. Harberd, 1962) to postulate that the common dispersion matrix is an identity matrix, and to regard the Euclidean distance so calculated as a derivative of the Mahalanobis statistic; we ourselves believe this fo represent an unrealistic model, and consider that, as suggesw by Kendall(1957), a Riemannian metric is needed.

FUNDAMENTAL PROBLEMS IN NUM’IORIOAL T A X O N O M Y

63

ii. weighted polfietic & d a r n This method (Maonaughton-Smithet al., 1964) employs a Euclidem model with axes scaled by a p t e r i o r i importance me&Bures.As in the previous case, the scaling depends on the dispersion (or cornlation) matrix, but it is the individual axes which are affected. New scales &FB calculated before each sub-division; as a reault, any two sets derived by sub-division of a single set share the same metric, but this is not true of set-pairs in general. The final model resembles a Riemannian system in being locally Euclidean; bu6 the space is now divided into blocks with the local metric changing abruptly at the boundaries, and may best be described aa a “disjoint metric space”. Although models of this general type have received some attention from topologists, we have been unable to trace any work on the metrization of such a space. The diiliculty is exacerbated by the fact that the space remains undefined between sets. iii. Aeeociution A?ldg&8 Since this is a puro derived-structure method, no measure .)f intor-sot distance arises naturally from the maximization. Again, however, the axes vary in a poakriom‘ importance from set to set, and a Euclidecm metric would be unrealistic. E. CONOLUSIONS

We may now conveniently classify the acceptable ooefficients under three headings : 1. Information stat&8tica These can be maximized over the whole model; as a result, they automatically provide inter-set functions and progressively-falling hierarchy measures. Their relationship with x* permits them to be used in a probabilistic context. If our misgivings (Section I1 E 2(i)b) as to their dependence on set-size prove to be unfounded, or can be overcome, they will be very attractive; but more work is needed. 2.’ E‘uclihn CEialancecr These, too, can be maximized over tho whole model, and provide inter-set functions and hierarchical measures with the desired properties. They aeem likely to be probabilistically intractable, but we have given reaaons (Section I1 E 2(ii))for regarding this as relatively unimportant. Compared with the doubly-maximized coeffioienta they appear to lack power, especially in populations defined by small numbers of characteristica.

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3. Riemannh and diejoint-ape fundions It is our opinioii that these provide the moet Fealistio models mid the most powerful methods for olassifioation;but work on inbr-aet funotioris is badly needed, #or the biologist (inoluding the p m n t authom) the mathematioe required for suoh work is out of reaoh; but the d i f l i o u i t i e ~ are not entirely mathematical. In the probabilistio o w , since the dispersion matrices are known to be different, what is the null hypothesis which is fo be tested? In methods using sub-division with changing weights, what properties is an inter-set funotion required to possees? Before the geometers oan be expected to collaborate, the users must be prepared to consider theae questions.

IV. T m BASIOEUULIDEAN MODEL A. DUALITY: THE R/& PROBLEM We have already given reasons for our preference of a Euolidean model; this is not incompatible with essentially Riemannian or disjoint models, shoe the region of space undergoing maximization is always locally Euolidean. We therefore now oonsider the problems that arise in setting up suoh a model. We begin with n elements (which we shall henceforth uall idvidmh) specifled by p uharacteristics (whioh we shall henceforth call attributes, a term we use in an extended sense to inolude variables and variates). Provided all attributes can be given values, either inherently or by the methods of generation outlined in Section I11 C, the sy~temis symmetrioal; the data-matrix can be transposed so that the individuals and attributes exohange status. Two models immediately present themselvee: a set of rc points in a p-spsce, or a set of p points in an n-space. This duality haa given rise to the symboh R and &. Unfortunately, two mutally incompatible traditions aa to the definition of these symbols exist side-by-side in the literature; and this oonfusion-to which we have ourselves contributed-must now be resolved. The early workers in factor analysis oommonly refer to a model in which the individuals am points imagined as in a spaae apeofled by co-ordinate axes representing attributes: this is our n points in a p-space that we shall for the moment mll an attribute-space. The arithmetical operations were oarried out on a matrix of correlations (or oooaeionally 00variances) between attributes. Suoh a method ww oalled an R-method. Later, the entire prome WM transposed for oertain purpoees; the model is now p points in an n-space that we ehall for the moment ortll an individual-spaoe, and the arith6tical operatiom were octrried out on a matrix of correlations between individuals. This waa a 0-method.

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This now is the problem: do R and Q refer to the model or the matrix? In the early work there was no obvious ambiguity; but oonaider a matrix of Euolidean distances between individuale. Shoe it is a matrix between individuals, it hi Q; but since it is bmed on a model in the attribute-space, it is R. Sokal and Sneath (1964) define the symbols unequivooally by the matrix, and the individual-diatanoe matrix is, for them, Q; but in all publications from our laboratory we have d e h e d the symbols by the model, and the individual-distance matrix has been, for us, R. We have now decided that the Sokal-Sneath definition should prevail, for two rewons. First, the widespread circulation that their book will deservedly attain will ensure that many taxonomists previously unfamiliar with the symbols will first meet them in the Sokal-Sneath sense; and to attempt to assert a rival definition would cause unjustifiable confusion. Secondly, there is some historical precedent. Most early work obtained approximate solutions for principal axes by the “centroid” method. Although this opemtes arithmetically on an attribute-combtion matrix, it is based on a model in the individual-space;but it hw always been known as R, though by the Southampton definition it would be &. We suggest, then, that R and & refer to the matrix; but it w i l l still be oonvenient to have symbols for the model, and we suggest the symbols A (for a model in the attribute-space) and I (for a model in the individual-spaoe). It seem likely that the indecision frequently expressed concerning the relative merits of R and Q-methods stems partly from inadequate understanding of the models implied, and we believe that the introduction of the new symbols will olarify the situation. A matrix of interindividual distances and an inter-individua! oomlation matrix are both &; but the former implies relationships between points in an A-space, the latter between angles in an I-space. An attribute-oorrelation matrix is R,and an individual-distancemtrk ie Q; but both am A - s p w models, the first ooncerned with angles and the second with points. In fact, two @methods may require models which differ from each other more fundamentally than do some It/& pairs. B. ADJUSTMENTS TO THE: MODEL

V i r t d l y all numerical methods involve diEcultiss oonwrned with the dimemione of physioal quantities. Only in truly qwlitative data do these difS.Oultiesnot arise; whatever the nature of the quantities which have been diohotomized, addition of either rows or mlumns of the datamatrix is interpretable in terms either of the number of individuclls possessing an attribute or of the number of attribute p o d by an

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individual. If the data is quantitative and not all in the same units, addition of attributes across a single individual is not teohnioally possible. This difficulty arises immediately in Euclidean distances or principal components in the A-space, and in correlation coefficients (“betweenpersons”) in the I-space. It is discernible,too, in the tendenoy to regard principal components as “taking out” a proportion of a variance constructed by the illegitimate addition of sepmate variances. It is the invariable, and inevitable, convention in numerical taxonomy to regard all attributes as dimensionless, and hence available for ethmetioal manipulation; but the highly autocratic nature of this convention must be clearly realized. Methods which involve the addition of different attributes are not, in general, invariant under changes in scale of the co-ordinate axes. The initial scaling of axes is thus irrevocable, and will in a sense determine the results of the analysis. Euolidean distanoes are very sensitive to the scales of the axes, but independent of the position of the origin ;principal oomponents are very sensitive to both. In the o&ae of Euolidean distances we have, we believe (Maanaughton-Smith et al., 1964; Williams et al., 1964), turned this sensitivity to sale to advantage, though at the expense of ending the analysis with a disjointspace model. There tend to be two schools of thought concerning principal components, those who leave the variances unohanged and those who standardize them all to unity; one advantage of such standardization is that it renders the variates genuinely dimensionless. It would be equally permissible to standardize the variates by “importance” measuros as in the case of our scaled distances; this might conceivably increase the power of the method, but it haa never been tried. In factor analysis it is usual to rescale the factors to unit variance after their extraction. The position of the origin is a far mom intractable problem, since in highly heterogeneous data there is no obvious “best” place for its location. It is traditional to take the decision appropriate to the multivariate normal distribution and locate the origin at the common mean; we ourselves have no better solution to offer. U. HETEROOENRITY

1. Introduction If material is presented for claesification, it must be suspected of being heterogeneous in aome way. In the context of our model, this heterogeneity may take two forms. In the h t , all attributes may be meaningful for, and measurable on, all individuals; but attributes, either singly or in linked groups, may be markedly polymodal. I n the

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A-epaoe model, the points form discrete galaxies (we d h o w the possibility of non-galactic heterogeneity below). In the aeoond, $he attributes may, again either singly or in groups, beoome &em.If only the zero or non-zero nature is at stake (qualitative dab) them ia no difficulty; the diffloulty arisee when measurable attributee am sometimes zero. For the ooncept of “zero” embraces two quite dietinot concepts-that whioh happens to be zero and that which must be zero: the number of haira on the third pair of legs be zero in an inseot, but it muat be zero in man. In many cases the pattern of zeros and nonzeros is itself of primary importance.

2. The data-Ch88&3 Since data may be homogeneous, or heterogeneous in either or both of two ways, we find it convenient to distinguish fom classes of data. C h 8 1. &-ordinates measurable on all axes; no sub-populations everywhere zero on sub-sets of axes; dietributions substantially unimodal on all axes. Claas 2. Co-ordinates measurable on all axes ;no sub-populations everywhere zero on sub-sets of ams; polymodal on at least some axes, the points forming galaxies in the A-space. Class 3. Qualitative data, the oo-ordinatestaking only the values 0 or 1; sub-populations exist which are everywhere zero on eub-set8 of ares. C h 8 4. &-ordinates measurable on all axes; sub-populations exht which are everywhere zero on sub-sets of axes; diatributionson the non-zero axea may be polymodal.

CLaSs 1, of courae, approaches the multivariate norma1 distribution, and is of no interest in classificatory problems. CIaSs 2 data is the raw material of taxonomy, so long as the individuale are known to be oloeely similar. Bince random sampling of individuals of widely disparate nature would be pointless for taxonomic purposes, this requirement is normally fulfilled. Class 3 is the familiar “presence-or-absend’ data of the ecologist ;perhaps because of the modesty of ita mathematical demands, it has been extensively studied by “biological” biometrioians. Moreover, owing to the rebtive ease with which such data can be analysed, it is frequently generated from Class 4 data by dichotomizing the variatee. It has, however, been pointed out to us by MaonaughtonSmith (in Zitl.) that this raisee a new difficulty. In ecology the 1/0 situation is truly asymmetrical, in that only the preeencee carry useful information, but this is not true in sociology; if 1 is taken to repremnt drunkenness, 0 represents sobriety, and both am meaningful. It

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remains only to say that Class 4 data are normal in sociology, and in ecology if a measured attribute (such &B peroentage cover) is d.

3. Trampotition of data-chases The data-classes are not necessarily invariant under trctnspodtion. Classes 1 and 2 may become inter-converted under A / I tranepoaition; so may Clasees 9 and 4, with certain limitations. The nature of the

data may thua appear to change markedly when transposed. We believe that thia is one c a w of the prevailing uncertainty regarding B/Q differenma : an R/Q difference is inherently likely to be greater if it dso involves an A / I difFerenoe.

4. Noda The term “nodum” was apparently introduced by Poore (1966) in the context of phytosociology; its numerical implications have so far been examined only in the cam of monothetio olassifioations of Clase 8 data (Williams and Lambert, 19618; Lambert and William,1962). This concept is, however, most easily illuatrated in Class 2. Consider points in a 3-spac13,disposed within two elliptioal cylindera whose long axes are parallel to the Z-axis. The projection on the (X,Y)-plane will show two sharply-definedgalaxies; projections on the other two planee will show no strikingly galactic structure, and may not even separate the two cylindem. A nodum, in our dehition, is an enumeration both of a set of points and of the set of &xesin which the pointa constitute a galaxy or “cluster”. In Class 3 data, a nodum consists of an enumeration of a set of individnala and of a set of attributes for which they are substantially all non-zero. Noda may be regarded as foci around which the population is varying; they are potentially of great value as a basia for sheddingperipheral information. Unfortunately, no general method of extracting them ie yet known. We now incline to the view that the solution provided by Willi~msand Lambert (1961a) is open to objeotiona; it is in any oase applicable only to monothetic situatione. One of UB (Dale, 1904) has carried out a preliminary inveatigation into the oharaoteriaation and combinatorid properties of noda, but the problem is a6 yeb far from solution. The d%culty is more fundamental than may appear at firet sight, The existing method involves aetting up the fwo modela (n pointa in p-spaoe and p pointa in n-space) and cohting the reaulte; but the mnoept of a nodum &B “central” infomtion intrinsically requiree that the individuals and attributes be manipulated simulteneously. This is impossible 80 long &B either ia regarded &B a set of pointa in a apace defined by GO-ordinate axes of the other. Deepite our advocaoy

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of a Euolidean model, and despite its inoontesbble power, the searoh for nodd teobniquea may yet force us to abasdon spatial models and seek methods of maximhing some funotion of a da.b-matrix whioh ehall be symmetrioal ES regards rows and oolumne.

5. N o n - g ~ t i Cheterogewity In Class 2 data, the pinla need not olustm into galexiee; they might, for example, be dispereed along intatwined filaments, or on the surfam of oonoentrio sphem. We me not aware that m y suoh data have been reported (except, of oourse, in eoologioal situations where pattern on the ground is at issue); but if it were to be suspeoted a psrtiouhr stirategy of analysis is indimtecl (vide Beotion V D I(%) below).

V. STRATEGY OF ANALYSIS A. BIIIIPLIFIUATION METHODS

By “simplifiwtion” we intand Borne means of r e d u h g the dimensions of the original Euolidean model, so that the data (ULIL be dhphyed in a small number of dimemions with the minimum loss of information. The p r o m may fl any of three quite distinot funotions, though these are seldom olwrly distinguished in the literature. 1. 8ubjeetive clmaa$cation of c o m ( p b data A taxonomist may legitimatelynot wish to invoke objeotive numerid methode, preferring for some specifio purpose to utilize his own knowledge and experienoe to delimit taxonomioally intrautable m~terial. The data may nevertheless be speoified by too m y attributes for the iaxonomist fo handle oonfidently; the requirement is to find transkmations of the original attributm whioh o m be graphed in two or three dimeneions. Prinaipal oomponent analysis ia oommonly uded for this purpose, but ie intrimically liable to prodm a dilemma. If fhe clispereion matrix is d, the data is in no way dbtorbd; but if any of the attributes have appmaiably higher variance th&nthe remainder, these attributes will dominate the analysis, 80 providing information which oould have been more simply obtained by univariate inapeofion. If, on the other hand, the oorrehtion matrix ie usedit normally isthe data being o b i f i e d is not the original data. The Hotelling solution oommonly given in test-booksinvolves two suodaeeivesh-tions to unit vtwhnce-kt of the attributes, then ot the oompnenband so atill further distorte the originel dab. Feotor analysis h w oomsionally been u88d for the =me purpose, but the elementa being so olsaified are further removed again from t h

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W . T. WILLIAMS A N D Y. B . D A L B

specified by the original data. However, the cme reported by Pettett (1960)~of a population of Viola spp. whioh showed marked disoontinuity on the first factor but not on the fist component, iS potentially of great interest, and would merit further investigation. Relatively crude approximations to such methods exist in the literature ; the method of Curtis (1969), for example, can be regarded aa an approximation to a component analysis with the origin outside the population, at the point of intersection of the tangent-planes perpendicular to the axes of the hyper-ellipsoid. The coefficient used is the quantitative counterpart of 2a/(2a+b +c) and is thus non-metric. Such methods were unavoidable while computing facilities were limited ;now that fast programmes exist for the calculation of large dispersion or correlation matrices, and for the extraction of their roots and vectors, there is little point even in such approximations as the centroid solution.

2. Preliminary evaluation of data A non-probablistic approach in practice necessarily assumes that there ie heterogeneity to be found ;but it may well be desired to explore the general configuration of this heterogeneity, whether or no it is everywhere sharply-dehed, and whether or no it is galactio. Unlws the data is exceptionally aomplex, the first two or three principal components will normally provide the information required.

3. Generation of “underlyingfactor” hypothesw It may be desired to erect hypotheses more far-reaching than those [Section I1 E I] which are purely classificatory; such hypothesee normally take the form of postulating the existence of a small number of underlying “factors” which would be sufficient to generate the interrelationships within the entire numerical system under study. It is natural to explore the simplest possible hypotheses-i.e. those that can be contained in the smallest number of postulated factors-with due regard to Kendall’s (1967) warning that “this seems to w u m e on Nature’s part a much more indulgent behaviour than we have my right to expect”. If classical methods are in use-aa distinct from those maximum likelihood methods (Lawley and Maxwell, 1963) which do not require rotation-the appropriate solution is iterated communalities, double standardization and rotation to simple structure. Rotation normally aims at providing the simplest possible relationship between old and new axes; but it may instead be required to seek the simplest possible relationship between individuals and new axes-the solutione are not necessarily identical. In cases of extreme heterogeneity, Dale (1964) has shown that there may be no factor-analytic solution : there may be no real values of the communalitiw which will substantially

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reduce the order of the matrix, and the oentroid iteration of communalities may fail to oonverge, These methods are ourrently out of favour, probably as a result of the inoautioua olaizps whioh have in the past been made for them. They do not “rev8&1” or “demonstrate” any struoture in the data, and we deprecatethe tendency to “identify” the factors which are extracted. If they me regarded purely ae hypothesis-generatingsystems fheir use is unexoeptionable, and they are potentially of great power. B. PARTITION

Attributes may be suoh that not only are they present or absent (and the pattern of presences or absences important) but they may also, if pment, be meaeurable. Buch situations are more oommon then is usually realized. In partioular, the data of plant eoology are of this type if a mwure suoh as percentage cover is in use. They arise in pure taxonomy if, for given t p of specimens (suchas herbarium speoimens), some attributes oamot be observed; and they arise in sociology if parts of a questionnaire are not answered. Essentially, the data is of Class 4, and the primary need is to ascertain whether the major heterogeneity is qualitative or quantitative. We have suggested elsewhere (Williams and Dale, 1962) a method by which this may be effected, but the computation is heavy and no computer programme exists at present. The method consists essentially of a partition into qualitative and quantitative elements; it can be extended without M c u l t y to the threefold system (known/unknown): (if known, presentlabsent): (if known and present, then measured). We incline to the opinion that Class 4 data should normally be partitioned-i.e. eeparated into Class 2 and clese 3 elements-before numerical analysis; but the methods of subsequent analysis will require modification from their normal forms, and no investigation of this kind has yet been attempted. C. NON-MERAROHIUAL METHODS

The most familiar non-hierarchical method is that whioh u888 canonical variates (h, 1952) for the comparison of ~ O U P Sof individuals. Recent examples are mainly zoological, though the method haa been wed successfullyon Populus, Betulcc and UZmu.9 spp. by J.M.R. Jeffers (personal oommuuioation)andhiscobborators. Like all methods relate3 to the Mahahnobis D*strttistic,it is not applicable to i n d i v i d d or to groups not known a pimi to be sufficiently aimilar to sham a common within-group dispersion matrix, and its defailed aoneideration is therefore oufside the scope of this article.

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Component analysis and factor analysis me non-hierarohiwl, but are normally made the basis of subjeotive daasification: completely objeotive non-hierarohioal methob, suoh as the “multi-dimemdona1 group analysis” under development by R.Janoey (pereon4oopmunication), seem to be extremely rare. We have a3ready pointed out (8eotion I1 D) that hierarchical ohwilloations are oommonly regarded aa deairable by the users,and it ia preambly for this reason that they dominate the literature. Despite their intrinsio theoretioal intereet, we inoline to the View that non-hiermchicalmethods are of limited value in numerical taxonomy. A n exception should perhaps be made for the method assooiated with Tanimoto : but this, though non-hierarohical, is closely related to oertain hierarchical systems, and it will be more convenient to defer its consideration to the section which follows. D. EXERARUHIOAL METHODS

1. General CmLeiderations

i. Pairs Hierarchical methods are oompletely dominated by the concept of all possible pairs of points or of axes. There is no difficulty in conceiving methods bamd on all possible triangles or tetrahedra of points, or all possible solid angles. We know of no work of this type. It would involve far more computation than do the pair-system, and until it is oertak.1 that a11 possible power has been extracted from such systems, it is doubtful whether more oomplex methods are worth pursuing.

ii. Direction The analysis m y either begin with the entire population and progressively break it down (divisive methods), or begin with the individuals and progressively fuse them (aggIomerative methods). The relative idvantages and disadvantagee are best disonssed in connexion with speoific systems; it is only necessary here to point out that, if a hiemrohical classification is required, monothetio methods cannot (except in a trivial sense)be agglomerative ;after the fbt groups have been formed there may be no attribut6 by whioh they ortn be fused. iii. Sorti?q The problem here may be reduced to that of defhing a distance between a point and a set of points, and is parficuhrly relevant to the agglomerative methode. Three methods are in u88. In the first, the distance is defined as that between the point and the neeseet member of the set (“neareat-neighbow” sorting). 8inoe this u888 only 8 small

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part of the available information concerning the set, the method is normally regarded as lacking in power. It is, however, computationdy very economical, requiring the calculation of @(a-1) diabnoes, and it is the only form of sorting which will eluoidate non-gahotio heferogeneity. In the second method, the distance is defined &B the average of all the distttnces between the point and the individual membera of the set. It requires the ca.louhtion of (1c-1)~dietanoes or averagea of distances, but demands complex sorting procedures to use the oalouhtions economically. It is nevertheless the only method whioh has regard to set density. h t l y , the set may be represented by the ooordinates of its centroid. This also requires (a-l)a oaloulations, but the computational strategy is very simple; it is our opinion that the simplicity and elegance of strategy that this method allows conclusively justifiee its use. 2. Momthetic eub-cEivieiue: “iwaociationa d y & ” For detailed accounts of the uae of the method, see Williams and Lance (1968), Willi~msand Lambert (1969, 1960, 198lb). It uses derived-structure maximization; zajkis calculated between every pair of attributes j and k (in terms of the number of individuals possessing

or lacking them singly or jointly) and the B U ~ .%bis formed of all k#J the 2 9 whioh involve a particular attribute j.Sub-division is on the attribute for which

$jxa,k ie maximum.Sincefor the 2 x 2 case%a = Nra,

’

. T ~ , ~in ; this form the method ie kZ3 possibly applicable to quantitatively-specified data (vide Dele, 1964, for a method of subdivision on a quantitative variable) but no work of this type has yet been undertaken. The original investigations in

the parameter may be regarded as

fact used Ir,&laa sub-didion-parameter ;but private oommunicationa k#j from H. Shin (usingamultiple-regressionmodel)and from P. MacnaughtonSmith (using an information-theory model) have independently demonstrated that Zra is the efficient parameter if the greateat reduotion of residual variance is required. Lawley (aZit&) haa pointed out that, aa originally suggested, Z(rJmay be regarded as a crude approximation to a factor analysis (using averoid communalifies), and thue may perhaps be treated aa a monothetic approximation to an essentially polythetic system. Empirical trials on ecological d ~ t ah v e suggested it is less sensitive that Zlrl has in fact cercain advantages:in p&i&r to the presence of “outlying” individuals, whose innate similarities it may preeel.ve. The more effioientBY*tend8 to split off outl*g indivi-

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W . T . WILLIAM8 A N D M. B . D A L E

duals as single-membered sets, thus hgmenting the analysis. Further comparative tests on different types of data are desirable. The method has now been used in variety of contexts and appears robust in that it is not unduly sensitive to occasional errom in transcription of data. It is, however, extremely sensitive to “nuisance correlations” as defined in Section I1 C 4 ; because of the large contributions that such correlations can make to Zr*, they are intrinsically liable to dominate the analysis. The largest individual x k has been u a d as a memure of “rank” for each successive sub-division, and Williams and Lambert (1900) give reasons for not using more sophisticated parameters. The measure is nevertheless unsatisfactory, since it does not neoessarily fall with the hierarchy; this is particularly troublesome at the lower levels of subdivision. We have some reason to believe that

kz-;xajk

would be a better

measure, and we propose to subject this possibilityto empirical test.

3. Polythetic ccggherative: “aimihrity” amty8ea Most of the published accounts of such methods use parameters which we consider unsatisfactory for reasons given in Section I11 B, often combined with inevitable but relatively inefficient hand-sorting; these methods need no critical examination. We shall also exclude information statistics and the Goodall probablistic coefficient, since no fully developed methods are yet in use. With these provisos, there are currently only three genuinely distinct methods, associated respectivelywith Sneath, with Tanimoto and with ourselves. We consider these in turn.

i. Sneuth: unweighted methods References: Sneath (1967); Sneath and Cowan (1968); Sokal tLnd Sneath (1904). The earlier work used the quaeimetria aoeffioient a/(a+b+c), though in his more recent writing heath, like ourselves, inclinea towards the fully metric (a+d)/(a+b+c+d); the earlier work also used nearest-neighbour sorting as a computational convenience, though here also Sneath concedes the greater power of group-sorting techniques when computational facilities are available. The important feature of his methods is the strict adherence to the Adaneonian postulate that, unless there is some special rewon for so doing, all attributes are equal and should not be weighted. A ditIioulty immediately arises if only few attributes are available or if many of the attributes are lacked or possessed by nearly ad the individuals: the intrinsic information content per individual is 60 low that it is impossible to specify the “best” fusion at any stage. Sneath has always made it

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66

clear that his methods are not applicable to such data, and stresees that the number of attributes used should not be less than about 40. Despite the undoubted sucoesses that his methods have achieved with suitable data, we believe that this limitation ia a severe and undesirable restriction on the wide application of the method. It is clear that this restriction can be overcome if further information can be imported into the system at the individual level, which will necessarily involve some form of weighting. On the assumption that a piori importance measures are undesirable, the only remaining s o m of information ia contained in such a posteriori measures as can be obtained from the population as a whole. The remaining two methods offer Werent solutions to this problem. ii. Tanimto: weighted individmla Tanimoto (1968); Rogers and Tanimoto (1960). This method in fact uses a quasimetric coefficient, but this is not important in the present context. The coefficients are summed for all individuals, thus providing an a po.deriori importance measure for each individual; the individuals with the highest values are used as “apices” for beginning the aggomerative process. Unfortunately, the existing sorting process is non-hierarohical and involves decisions on the part of the operator, and, aa Sokal and Sneath (1964) point out, the increasing tendency to separate operator from computer renders “steered” programmes undesirable. h p i t e the early successes of the method, its sorting strategy requires revision ; if its concept of information-importing can be combined with the use of a fully-metric coefficient and a mechanioal (and preferably hierarchical) sorting system, the method, already of great intrinsio interest, might be a widely applicable strategy of coneiderable power.

iii. W i l l i a m et al. : weighted attributa Williams, Dale and Macnaughton-Smith (1964). This method ~ 8 8 8 Euclidean distances in an A-space with axes permanently scaled by the a pogteriori importance measure of Association Analysia, i.e. k+j& z Its succeeeful classification of a 6-attribute population demonstrates that it is free from the attribute limitations of Sneath’s unweighted method. Its chief demerit is the use of invariant weighta: the a n a l p h is necessarily dominated by what may loosely be regarded aa “firstfactor” relationships. 4. Polythetic divi8ive Several.authors (wide, e.g., Regcigno and Maccaccaro, 1960; C o c h n P

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and Hopkins, 1961;Macnaughton-Smithetal., 1964) have considered the general problem of finding what is in some sense the beat of all p s i b l e alternative sub-divisions; but the only practical method known fo US is that of Edwards (1963). This calculates between/within partitions of Euclidean distances for all possible sub-diviaiona into two p u p s . Since there are 2n-1-1 such sub-divisions, the method is neoesedy limited to a small number of individuals; and shoe the distanaes unweighted, some diffidties due to ambiguity may be expot6d at low levels of diviaion. If the number of individuals is to be increaeed to reahtic proportions, some form of “directed search’, is inevitable. The Macnaughton-Smith et al. “dissimilarityanalysis” finds,in accordanoe with a stated criterion, the individual least representative of the pophtion aa a whole; this individual is then used aa the basis for a sub-population, and the remaining individuals allocated sequentially to this sub-population or to the remainder of the population. The “objectively-weighted Euclidean distance” of Section V D 3(iii)above has been used as criterion in the preliminary trials. The method has two advantages. Firat, the computation required, though still considerable, is considerably less than iS required for an ‘MI possible sub-divisions” method. Secondly, the weights for the axes can be recalculated for each successive sub-division, thus removing the “first-fact~r~’ dependence of the corresponding agglomerative method. The present criterion has the disadvantage of defining a disjoint-space model. 5. Genera2 conclwione If a monothetic classification is desired, association analysis is olearly indicated; if monothetic clasRification is acceptable, and if p 4 IZ (as is often the case), the computation required is less than for othor methods, and association analysis is again indicated. If a polythetic classification is essential, a sub-divisive method which will provide the major discontinuities at the beginning of analysis is obvioualy preferable; we can only say that “dissimilarity analysis” ahowe considerable promise, though further development and experience is necessary before it can be uIuc888Nedly recommended. It is in the agglomerative field that we find ourselves most at vazianoe with current practice. We believe that the completely unweighted methods lack power, and are only suitable where very sharply defined heterogeneities exist ; we suspect that the “cloudy clusters’7 stigmatizsd in a recent h l i b discussion (1962, p. 268) as “a criticism not of the method, but of the material” may yet be found to be due to uaing a. method of insufEcient power. Furthermore, we oonaider that weights calculated internally from the data contravene only the letter, and not

FUNDAMENTAL PROBLEMS IN NUMERIOAL T A X O N O M Y

07

the spirit, of the Adansonian postulatea: Admaon oould hardly have foreseen the possibility of internal weighting. It will not have esoaped notice that we inoline towcmls the u88 of methods in whose developments we have o d v m been oonoerned. This is inevitable, sinoe had we not been dissatisfied with exiating methods we should not have been led to devise our own. It does not follow that we are right :when all the programmes am freely available, the mre will decide.

h K N 0WLEDQMENTS

We are indebted to many mathematicians and statisticians for their patient assistanoe, among whom we pmtioularly wish to aokuowledge the help of M i . P. Maonaughton-Smith, Dr. F. Rhodes and Mrs. N. Wilson;but these must not be held responsible for any heretical views we may have expressed. We are also greatly indebted to Dr.P. H. A. Sneath for enabling the senior author to read Lsokal and Sneath’s book in proof. The arfiole inoorporates material arising from work &d out by one of UB (M.B.D.)during the tenure of a D.S.I.R. Studentahip.

REPBIRENUES h h i b e l d , E. E.A. (1948). Ann. Bot. N.S. IS, 221. ABLIB Conference on Cleseification (1962). AaZib Proo. 14, 216. Bartlett, Y. 8. (1960). B.J.P. SWkt. 8, 77. Beckner. M. (1969). “The Biologid WSY of Thought”. Columbia Universify Prees, New York. Bonuer, R E. (1984). I.B.M. J . 8,22. Cattell, R.B. (1962). “Factor Andpis”. Harper & Bros., New York. Cochran, G.and Hopfrine, C. E. (1981). BiometriOe 17, 10. Curtis,J.T.(1969). “The Vegetationof Wisconsin”.University of Wisconsin Press. Dagnelie, P. (1980). Bull. Hem. Can%phytogeogr. B 6, 7. Dale, M. B. (1964). Ph.D. The&, University of Southampton. Edwards, A. W. F. (1903). 5th I d . Cwj. BiomStrh (Cambridge, 1963). Elderton, W. P.(1938). ‘‘FrequencyCurvee and Correlation”, 3rd ed. Cambridge. cfiknow, J. 8. L. (1961). Nature, Loncl. 168. 400. Oihow, J. 8. L.end HaIop-Befiieon, J. (1964). U e n d a 87, 147. aoodsll, D. W.(1@638).A d . J . Bot. I,89. Goodall, D.W. (1963b). Auet. J . Bot. I,434. ooodall,D.W. (1982). Ebot. B 4; 10. Goodall, D. W.’(1984).N&re, M .203. 1098. Uoodmsn, L.A. and Krusksl, W. H.(1964).J . Amer. aldiat. A@#.40,732. Goodman, L.A. and h k d , W. H.(1969). J . A m r . slabist. AM. 04,128. Om&-Smith, P. (1964). “QwmtitmtivePlant Ecology”. Butterworthe, Landon. Wberd, D. J. (1962). J . E d . 60, 1.

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Kelley, J. L. (1966).“General Topology”. Van N o s t w d , New York. Kendall, M. G. (1967).“A Course in Multivariate Analyaid’. G m , London. Lambert, J. M. and Dale, M. B. (1964). “Advences in Ecologictll Reeeeroh,” Vol. 2. Academic Preas, London. Lambert, J. M. and Williams,W. T. (1962).J. EwZ. 80, 776. Lawley, D. N. and Maxwell, E. A. (1963). “Fsctor A d y s i a 88 6 Btetisticsl Method”. Butterworth, London. Lawrence, G. H. M. (1961). “Taxonomy of Vaeculer Plants”. Mmmillsn, New York. Macnaughton-Smith, P. (1963).Biornetrka 19,364. Mmnaughton-Smith, P., Williams, W. T., Dale, M. B. and Mockett, L. 0. ( 1964). Nuhre, Lond. Needham, R. M. (1962).In “Information Processing 1962”,p. 284.North Holland Publishing Co. Amsterdam. Needham, R. M. and Jones, K. 8. (1964).J . Document. 20,6. Nelder, J. A. (1961).B i m & 17, 89. Pettett, A. (1960). Ph.D. Thesis, Univcrsity of Southampton. Phillip, J. P. N. (1963).Nature, Lond. 200, 1347. Poore, M. E.D. (1966).J. Ewl. 48,226, 246, 606. Proctor, J. R. and Kendrick, W. B. (1903).Ntbtwe, Lond. 187, 716. R m , C. R. (1962).“Advanced Statistical Methods in Biometric h e a r c h . ’ ’ W h y , New York. Rescigno, A. and Meooaccaro, G. A. (1960). The Information Content of Biological ClaesScations. I n “Symposium on Information Theory”. Butterworth, London. Richards, F. J. (1969).J . ezp. Bot. 10, 290. Rogers, D.J. and Tanimoto, T. T. (1960).Science 182, 1116. Rohlf, F.J. (1962).Ph.D. Thesis, University of Kanses. Rohlf, F. J. and Sokal, R. R. (1963).Kana. Univ. 815.BuU. Sebestyen, G. 8. (1962).‘‘Daision-making Processea in Pattern h o g n i t i o n ” . Mmmillan, New York. P q c h t r i k a 27, 126. Shepard, R. N. (1962~). Shepesd, R.N. (1962b).P8ychomelrika. 27, 219. Sneath, P.H.A. (1967).J . g m . Microfiol. 17,201. Sneath, P.H.A. (1962).Symp. SOC.gen. Microbiol. 12, 283. Sneath, P.H.A. and Cowan, S. T. (1969).J. gem Mii7robiOZ. 19,651. Sneath, P.H.A. and Sokal, R. R. (1962).Nature, Land. 198, 865. Sokal, R.R. and Sneath, P. H. A. (1964). “Numerical Taxonomy”. W.H.Freeman, San Francisco and London. Tanimoto, T. T. (1968).“An Elementary Matherrmtical Theory of Claurifioclti4n end Prediction”. I.B.M.Corp., New Ymk. Williams, W. T. and Dale, M. B. (1962).Nahre, Lmcd. 198, 602. William, W. T. and Lambert,J. M. (1969).J . E d , 47, 83. Williams, W. T. and Lambert, J. M. (1960).J. E d . 48,689. Williams, W. T. and Lambert, J. M. (1961a).Nature, Lond. 191,202. William, W. T. and Lambert, J. M. (1961b). J . Ecol. 49,717. Williems, W. T. and Lance, G. N. (1968).Nature, h n d . 182, 1766. William, W. T., Dale, M. B. and Maonaughton-Smith, P. (1964).Nature, Laul. 201, 426.

Yule, 0. U. and Kendell, M. G. (1960). “An Introduction to the Theorg of Ststistics”. Grifh, London.

Ultrastructure of the Wall in Growing Cells and its Relation to the Direction of the Growth * P. A. ROELOFSEN

Laboratory of Gmml and Technical Biology,Tech-cal Delft, Netherlad

Univerdty,

I. Introduction ............................................................. 69 11. Morphological Aspects of Constitution, Synthesis and Breekdown of the Primary

Well .................................................................. 70 A. Constitution and Morphology of Microfibrile., ............................. 70 B. Comtitution of the Amorphoue Matrix in Primary Walls 78 C. &me Aepeots of Microfibril Cbherence .................................... 82 D. Site of Byntheeb of Primary Wall Substances. ............................. 68 E. Qnwtionable Evidence of Breakdown in Primary W& 80 III. Burvey of the Mim5brlllm Arrangement in Different Types of Qrowing Cells.. 91 A. Freely Qrowing more or less Iaodiametric Celle 91 B. Freely Qmwing Tubular Cells or Parts of Cells.. ........................... 98 C. Tieaue Cells with Iaodiemetrio Urowth ................................... .lo4 D. Tissue Cells with Predominant Growth in Length ..........................lo5 E. Tiesue Cells that Predominsntly Widen.. ................................ .112 F. T i p of "issue Cells with Tip Urowth .................................... .113 IV. hterreletion between Urowth and Wall Ultrastructure ....................... .114 A. Effeut of Omwth on Wall Structure ..................................... .114 B. Effect of Well Structure on the Direction of Urowth.. ..................... .I28 C. Theories on the Meahanism of Orient&tedInitial Synthesis of Cellulose Microfibrilel30 References .............................................................. .146

....................

..................... ... .............................

I. INTRODUOTION This review deals with the present knowledge of the submicrosmpia st;ructure of growing Geus of Thallophyta and Cormophyta and the interrelation between this and the direction of surface growth. Also morphological aspects of constitution, synthesis and breakdown of cell wall substances will be discussed. As 8 rule only literature more recent than 1969 will be mentioned. For older literature and for electron micrographic documentation of structures, the reader is referred to the monographs of Frey-Wyssling (1959) and Roelofaen (1959), and to the reviews of Setterfield and Bayley (1961), Wardrop (1962) and Northcote (1963). The review is restricted to a consideration of the primary w t l l , which is defined as the part of the wall that is produced by a cell or by its parent cell while growing in surface. The s d 9 y wall is defined as the part produced after growth has ceased and is more compact. The growing cell may sometimes, or locally, produce more wall The survey of literature p r t a i i g to this review was concluded in June 1 W .

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material than is needed to compensate for wall extension, which results in thickening. Hence thickened primary w& do exist, so that thickening cannot be adopted as a criterion for the definition of a secondary wall. However, there still remain transitions between primary and secondary wall layera as defined above, since growth may cease slowly. Then an intermediate layer may occur, called the transition layer (Uebergangslamelle), which has the more compact structure. typical of the secondary wall but shows signs of extension, such as wide spacings between microfibrillar bundles and crossed interwoven bands. Probably the low extensibility of this layer is aofually the cause of the cessation in growth. Naturally, the wall of a freely growing cell and the outer wall of an epidermal cell consist of one primary wall, whereas walls in tissues consist of two primaries. Their outermost parts are fused to form the middZe lamella, easily recognizable by its non-birefringence due to the absence of cellulose, and by microchemical reactions, etc. The partition wall between daughter cells embodies the cell plate, but in growing cell walls,e.g. in the side walls in the files of daughter cells in primary meristems, the cell plate has disappeared completely. *

11. MORPHOLOGICALASPEOTS OF

CONSTFlWTION, SYNTHESIS AND

BREAKDOWN OF TEE PRIMARY W u

All growing plant cell walls consist of a f r a m m k of microjibrile of either cellulose or chitin or, more rarely, another plysaccharide, embedded in a continuow matrix of usually amorphous and highly swollen substances. The microfibrils are necessary to bear the stress in the wall due to turgor pressure. This has been extensively treated by Frey-Wyssling (1952,1969, p. 306). For instance in wheat mots with cells of 16 p diameter and turgor pressures of 3 atm, wall stresses of 30-60 kg/cmz occur. I n a V u h i u cell of 10 mm diameter at only 1 atm, however, it is a formidable 20,000 kg/cm*, since the stress is proportional to the diameter. Therefore the wall stress in ba&& is at the most 1 kg/cm,. This permits the absence of any fibrihr component in bacterial walls ; with those species which do produce cellulose, this arises in the culture medium. A. CONSTITUTION AND MORPHOLOGY OB MICROFIBRILS

7. Celluloee micro$br&Ee

In the primary walls of all Cormophyta, of all algae of which the ultrastructure will be discussed here and of the Ollrnyoetes, cellulose

U L T R A S T R U O T U R E O F THE WALL I N G R O W I N G UBILLS

71

ie the sole miorofibrillar component. Its amount varies between 20 and 30% (see below). Since i&e chemical and physical properties of oeuulose have been treated in detail in the monographs cited above (ale0 in Treiber, 1967; Ruhland, 1958; Honeymctn, 1969), it may suffim to mention here only

properties relevant from a morphological point of view.

mElem6/lary fibril'

X)x70h

Fro. 1. Diagram of the otruoture of oellulcme microfiW. A and B: generally ocoepted itrnotrve and dimensions. C: with "elementary fibrils" t~coordiagto Frey-Wpling. Now oelluloric polyas&uidea locsted d i n g to preeton (1962).

Ae is shown diagrammatically in Fig. 1, the miorofibrile are very long with respect to their diameter, at least several p, unbranched and somewhat flattened. Their width hae been estimrcted by most authors at 100-300 A, their thickness at 60-1OOA. The microfibrils consist of a bundle of parallel, equally unbranched, cellulose (&1-4 glucan) chain molecules, with lengths varying between about a half and several p. In tramverse section there are about three of these chains per square mp.

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Some two-thirds of each microfibril may be considered c r y s t a k e since it produces X-ray interferences. The crystal structure is of aa called cellulose I, which occurs only in nature and is probably the only crystalline form occurring in nature. The remaining third is less well, or not at all, ordered (no regular hydrogen bonds between adjacent chains) and is called semi- or paracrystalline. A small part of this is probably localized in very small regions throughout the crystal lattice (no crystal is 100% perfect). The main part, however, occurs firstly in short segments at intervals alon the length of the microfibrils, thus separating crystallites 300-600 long, and secondly, at the surface (see Fig. 1). Despite this crystallinity the microfibrils can make curves down to 1400 A in dirtmeter (Muhlethaler, 1960) due to their thinness and, probably, to the paracrystalline regions. Frey-Wyssling’s concept (1969, pp. 17, 114; by-Wyssling and Miihlethaler, 1963) of microfibril structure is somewhat Werent, see Fig. 1(C). He envisages “elementaryfibrils” of 35 x36 A (30 x70 Ain the original concept), each having thin paracrystalline sheaths, which would either occur freely, or be aggregated, thus forming the thicker microfibrils usually found. In our view the evidence supports the first concept. Firstly, the thickness of 36 A as determined by Miihlethaler (1960, cf. also Ohad et a,?.,1962), might, according to Colvin (1963), be a considerable underestimate. Also data from X-ray and electron diffrcldion diagrams have often permitted the conclusion that the crystallites were much thicker (e.g. Preston, 1962). I n that case, however, the fibrils would no longer be “elementary”, but just common micro5brils, and there would be little difference between the two concepts, ~ince it is commonly aocepted that microfibrils tend to aggregate into bundles. Secondly, in the range of 36-200 A all thicknesses seem to occur (cf. Giinther, 1960) and not only multiples of 36 A. The occurrence of smoothly tapering ends in growing microfibrils with a thickness of more than 100 A (see below) also seems a t variance with the concept. Further, cellulose, which is attacked chemically or enzymrttically, disintagrates in pieces of much more than 35 A thick (see, for example, Norkrans and R&nby, 1966). Since paracrystalline regions may be supposed to be primary points of attaok, crystallites of 36 A thickness are to be expected in them caws. The non-crystalline condition of the surface of the microfibrile is of great importance for their coherence. Within the crystallites all OH-groups, three in each glucose-anhydride monomer, are involved in hydrogen bonds which interconnect the cellulose chain molecules. At the surface, however, many of them become available. These may bind to the paracrystalline surfaces of other microfibrib. The great strength

x

U L T R A S T R U U T U R E O F T H E W A L L IN G R O W I N G OELLS

73

of cellulose fibres, both wet and dry, demonstrates the extent of this bonding. I n most secondary and in all primary walls, however, hemicelluloses and pectic substances are associated with the microfibril surface, as indicated in Fig. 1. Part of these are held so tenaciously that it is notoriously difficult to obtain pure cellulose from such cell walls (Adams and Bishop, 1955). These substances are more hydrophilic than cellulose; this means that more hydroxyl groups are involved in hydrogen bonds with water molecules and fewer will be available for hydrogen bonding between microfibril surfaces. Therefore, in the presence of water the microfibril coherence is reduced as compared with pure cellulose (in the dry condition coherence is increased, but this does not occur in living cell walls).

FIG. 2. Growing extrscellular cellulose microfibrils in a culture of Acelolmcter Zylinum. Note the tapering ends along about 0-6 p and the blunt points. A: from Millman and Colvh (1961); B: from Colvin and Dennis (1964).

For the biochemistry of cellulose synthesis we refer to reviews of Setterfield and Bayley (1961) and Neufeld and Hassid (1963; cf. also Elbein et al., 1964). The morphological aspects of microfibril formation have mainly been studied in young cultures of Aeebbacter xylinum, which produces cellulose extracellularly. It waa started by Miihlethaler (cf. Frey-Wyssling, 1959, p. 123) and carried on mainly by Colvin and co-workers (e.g. Colvin and Beer, 1960; MiUmaa and Colvin, 1901; Colvin, 1963, 1964a).Around clean bacteria under favourable conditione microfibrils less than 0.6 ,uin length appear within half a minute. These elongate constantly, but except at the two ends, the final diameter Qf 150-200 A, is very soon attained. The microfibrils are often twisted, and both ends taper for about 0.5 p, but not indefinitely, 90 that the very points are blunt (see Fig. 2). At 34°C the growth velocity of each microfibril is on the average 2 ,u per min, but there are faster growing ones, since after 1.5 m h microfibrils of 8 ,u are to be found. At 25OC the growth velocity is about F*

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P. A . ROELOFSEN

half of this. Whether one or both tips grow is unknown, but the similar morphology would suggest the latter. Some authors (originally Miihlethaler, and more recently Ohad el al., 1962) reported that the microfibrils arose from slimelike or granular prestages that were supposed to be, at least partly, amorphous cellulose molecules. This was denied by Colvin and co-workers (most recently Colvin, 1963) who observed the formation of microfibrils remote from amorphous materials which they considered to be excreted proteins, etc, Using labelled glucose they failed t o find the postulated intermediate cellodextrins and, moreover, demonstrated the formation of microfibrils from an excreted soluble low molecular precursor by a similarly excreted bacterial enzymatic system (Khan and Colvin, 1961 ; Colvin, 1964a). Colvin and co-workers therefore favour the hypothesis of tipbiosynthesis of the microfibrils, the addition of glucose monomers to the ends of the cellulose chains, exposed a t the tapered microfibril ends. The crystalline ordering of the chains would then follow tbe growing molecules. This hypothesis was originally proposed by the author (1968) on the following considerations. (a)Microfibril formation from preformed cellulose molecules should, just as in the production of synthetic cellulose fibres, give rise f a interconnected microfibrils with a crystal structure (cellulose 11) different from that found in nature. (b) The “unusual” tip-biosynthesis would make the formation of the unusual crystal lattice and the formation of unbranched microfibrils more comprehensible. Since enzymatic synthesis of polysaccharides is as yet known to occur only at the non-reducing molecule ends, the hypothesis suggested that the molecule ends at the growing tips would all be non-reducing ones and this, in its turn, would require that the commonly accepted crystal structure with so-called an tiparallel molecule chain orientation should be rejected and replaced by one with parallel chain orientation. The latter suggestion had in fact been proposed long ago, but had been rejected on insufficient grounds (cf. discussion in the paper by Preston, 1964).

We thought that it also implied that the microfibrils should @OW at one tip only, the non-reducing one (“reducing” on p. 188 of our monograph is an error). However, while writing this article it occumd to us that a microfibril might equally start with chain8 growing in opposite directions. While moving away from the “tail to tail” mid& part, both ends will soon become non-reducing ;at least to a large extent, since antiparallel molecules of 0.5 ,u length at most (the tapering ends) might be incorporated in the growing microfibril. (A small number of

ULTRASTRUCTURE O F THE WALL IN GROWING CELLS

78

the cellulose molecules are actually about this length, cf. Marx-Figini and Schulz, 1963.) Colvin (1964b) has determined the isotope-labelling and reducing activity of microfibril ends, and concludes that all tips are similar. As discuesed, this does not solve the parallel-antiparallel, nor the one or two enzymes problem.

Fro. 3. The inner cell wall surface of a plasmolyzed cell of C h e t o m o t p b melagmiurn. Note tapering ends of microfibrils covering microfibrils running in main direction and ends covered with files of granular bodies (from Prei and Preston, lO6la).

How cellulose microfibrils in plants are formed is unknown, but the occurrence of soluble precursors (Colvin, 1961; Webb and Colvin , 1963; Elbein et a,!., 1964) and, ae is apparent in Figs. 3 and 4, of similar tapering ends with blunt points, suggest a similar mechanism. It certainly does not suggest that in plants, microfibrils would be formed in a way any different from that in bacteria, e.g. be modelled within or along microtubules (see pp. 85, 141).Tip growth ie also suggested by the intertwining of the microfibrils in plant cell walls as e.g. the one depicted in Fig. 3. The twisted microfibrillar bundles frequently observed also suggest tip growth, but the twisting might have occurred during drying (Millman and Colvin, 1961). Finally, the striking alignment of microfibrils in many cell walls would be quite comprehensible

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on the basis of growth of tips through pre-existing interfibrillar spaces. Such template action of pre-existing microfibrils was also observed in Acetobacter cellulose formed on agar (Millman and Colvin, 1961). However, this template phenomenon, if occurring in plant cell walls, is evidentlysubordinate to some other orienting mechanism (see p. 139). Growth of microfibrils in thickness not only at the tapering ends, but all along their length, has been postulated several times (cf. Roelofsen, 1959, p. 29), but most emphatically by Gunther (1960), who in the protonema of Funaria found thicker microfibrils on the outer wall surface (as compared with the inside) and in old protonemata (as

FIG.4. Cellulose microfibrile with tapering end regions and blunt points at the edge of B perforation, formed to reloase swarmem in a cell of Chm!mwrpha melagmiurn. CrScLe in microfibrils are artefacts (from Frei and Preston. 198111).

compared with young ones). These remlts do not, in our view, prove the point, but certainly merit attention. 2. Chitin microjibrib Chitin is found in all fungi, except Obmycetes and lome exceptional cases (cf. Roelofsen, 1959, p. 40; Northcote, 1963). It doe# not occur in algae, as is still asserted in recent encyclopaedicworks and probably never occurs together with cellulose. (The presence of cellulose in the chitin containing fungys Rhizidimyces was reported by Fuller (1960) and Fuller and Barshad (1960), but this is based only on X-ray ring diagrams, which have more than once led to misinterpretation.) Chemical and physical properties of chitin are discussed in the monographs already mentioned and by Foster and Webber (1960). Recent literature on biosynthesis is mentioned by Jawomki et a,?.

ULTRASTRUCTURE

O F THE W A L L IN Q R O W I N Q CELLS

77

(19631, on crystal structure by Dweltz (1960) and Rudall (1963). From our point of view it is relevant that chitin microfibrils are usually very similar to those of cellulose in length, diameter, probable flatness, chemical resistance and crystallinity. Here too, the microfibril surface will probably be paracrystalline and will more readily bind polymers from the non-fibrillar matrix. However, in cell walls which contain small quantities of chitin, like those of many yewts, the chitin is not fibrillar but granular (Houwink and Kreger, 1953). In such walls another fibrillar component often occurs, viz. glucan (see below). Very long and rather thicker are the curious so-called “mycofibrila” discovered by Liese and Schmid (1962, 1963). They are formed extracellularly by wood-rotting fungi, both when grown on wood and on agar. However, their chemical constitution is BR yet unknown. The chitin content of fungal walls varies greatly. One yeast (Schizoeacchromyc,cee)contains no chitin, baker’s yeast only about O-lyo(Korn and Northcote, 1960), Phycomycea sporangiophores 30%, Allornycee mycelium as much as 60% (Aronson and Machlis, 1959). This applies to full-grown cell walls; growing ones have not been analysed. They probably differ greatly, since in young mycelium of Allontycae, which still would have contained non-growing walls, considerably less chitin was found than in old mycelium. 3. Micro$brils of other materiala

In Cormophyta the sole non-cellulosic microfibrillar cell wall substance known is the mannan in the endosperm of palm seeds (Meier, 1958; also Roelofsen, 1959, p. 56). These cells will not be discussed in this review since they do not grow and, moreover, have not been studied sufficiently. Furthermore in certain collenchyma cells pectin has been found to occur in the form of axially orientated crystallites. In the “pectin skeletons”, obtained after extraction of cellulose and hemicellulose, short aggregated microfibrils occurred. However, these might have arisen after the chemical treatment (Roelofsen and Kreger, 1951; Roelofsen, 1959, p. ‘72) and their original presence is questionable. In nearly all green, red and brown algae studied so far, cellulow is the sole microfibrillar component. In some green algae (Bryopie, Caulerpa, Penicillua, Udoteu, Halimeda) and in two red algae (Pmphyra and Banqia) the microfibrilsconsist of B- 1,3-linkedxylan ;while in some other green algae (Codium, Amtabularia, Dmyccla&us,Ba&pa.ura) and in the “cuticle” of Porphyra the crystalline wall component is /3-1,4linked mannan (identical with that found in palm seeds) but no microfibrils have been detected ( h iand Preston, 1961c, 1964). Furthermore in the green algae Hydrodictyon and Halicyetie the microfibrile probably consist of a partly crystallized mixture of cellulose, and mannan and

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P. A . ROELOFSEN

xylan respectively (Roelofsen, 1959, p. 228; Kreger, 1960; Northcote et al., 1960).* Until recently it was accepted that alginic acid, universally found in brown algae as well as cellulose,occurred in orientated (birefringent)but amorphous state. Recently, however, Frei and Preston (1962) showed that one component of it, polyguluronic acid, partly occurred in the native walls in orientated crystallites. As far as is known at present, however, these are not incorporated into microfibrils. The situation seems more or less comparable with that of the related pectin in collenchyma cell walls. Finally we have to mention the glucan microfibrils demonstrated in the walls of yeasts. They seem to be very short, nearly granular, at least in the untreated cell walls (Houwink and Kreger, 1953; Roelofsen, 1959 p. 304). In the chemically treated walls conspicuous aggregation occurs. There is about 30% glucan in yeast cell walls, so it certainly is an important structural component, unlike the chitin, of which often only traces occur. Yeast glucan is probably a linear polymer with both /?-1,3 and /?-l,S links; like cellulose it tenaciously associates with other substances, viz. mannan and protein (see below). It seems relevant that all these non-cellulosic and non-chitinous microfibrils differ in appearance from cellulose and chitin microfibrils. The latter are clearly individual, easily separable, somewhat stiff threads. The former appear to be more supple, are often short and seem sometimes to be interconnected. Torn edges of cell walls never show the fringe of loose microfibrils, which are typical of cellulosic walls. B. CONSTITUTION OF THE AMORPHOUS MATRIX IN PRIMARY WALL8

The matrix in which the microfibrillar framework i H embedded consists of a highly hydrated molecular network of a number of polymeric Substances, viz. polysaccharides and polyuronides, intermixed with a minor amount of proteins and lipids. Meristematic cell walls have often been analysed. Unfortunately the available analytical methods, even for separating such main groups a8 cellulose, hemicelluloses and pectic substances, lack specificity, mainly since these substances associate readily and since each group contains molecules varying greatly in molecular weight, the hemicellulosefl also varying in chemical constitution. The separation of these hemicellulose components is even more difficult. Since glucose oocurs both in cellulose and in some hemicelluloses and uronic acids occur both in the latter and in pectic substances, the analysis cannot be based upon the quantitative constitution of the hydrolysate of the whole cell wall. This * Xylan microfibrils show the exceptional feature of negative birefringence (Frei and Preston, 1%).

U L T R A S T R U C T U R E O F T H E W A L L I N Q R O W I N Q CELLS

79

unsatisfactory situation explains why the results of analyses of the same object by different investigators using different methods usually differ considerably, often more than the analyses of different objecta by the same investigator. Roelofsen (1959, pp. 2, 127) and Setterfield and Bayley (1961) gave summaries of quantitative analyses. Some more recent analyses have been compiled in Table I. Regarding these data the following pointa TABLEI Quantitative Chemical Analyaee of Growing Cell Walk Publisherl Bince 1960 (Valuearepreaent yo of total dry wall) Number of HemiPedic reference. Cellulose eelluloee aubatance Protein Lipid Lignin

Object --

h’adaonia (yeaat)

>6l

3-6

46 33 46 63 40 26 39 13 40 mixed 46 with 80

26 17 16

26

Avena coleoptile Avena coleoptilo Allium. root Pieurn, stem Acer pepl., cambium Nitella opm NiteUa tranalucena Cham auatralia Hydrodictyon afric.

10

4

30 30 29 37 17

9

2.8

<30 26 28

4

+

4 11 4

7

-

8

11

9

*Reference numbers (1) Bishop et al. (1968),pectic substances corrected according to King and Bayley (1063).(2) Ray (1062).(3) CRlCdRtedfkOm Jeneen and Ashton (1060). (4) Matchett and Nance (1982). (6) Thornber and Northcote (1961, 1062). (6) Probine and Preston (1081). (7) Anderson and King (1961). (8) Northcote el d.(1960). (9) Dyke (1984).

should be noticed. The corrected pectin content of Avenu ooleoptiles is more in line with the earlier results of Alberaheim and Bonner (1969) and of Jansen et al. (1960); and with the recent results of Ray and Rottenberg (1964), who found 4% galacturonic acid incorporated in pectin and 2% glucuronic acid in xylan-hemicelluloses. The finding of lignin in cambium and its high cellulose content indicates the admixture of secondary walls. This probably applies even more to the walls of Nitella translucens and Chara; the “lignin” in these cases must have been some other substance. I n these algae the pectic substances would be wholly westerified, which the authors relate to their auxin insensitivity. In Hydrodictyon the hemicellulose is mannan and pectin is less than 6% in amount. The hemicellulose of Nadeonia contains equel quantities of glucose and mannose, probably occurring aa microfibrillar

80

P . A . ROELOFSEN

glucan and amorphous mannan, as in other yeasts. Chitin in this caae is at most 0.4y0. If both recent and older tmalyses are considered and any extreme values are neglected, it can be stated that, usually, primary walls of Cormophyta contain 20-30% cellulose, 3 5 5 0 % hemicelluloses, 10-20y0 pectin substances, 3-10% proteins and 2-7% lipids. Avena coleoptiles are exceptional in having very low pectin and very high hemicellulose contents. Collenchyma walls are exceptional in containing more than 40% pectin. In recent years a number of investigations were concerned with the changes in wall components during growth and induced by auxin (Galston and Purves, 1960; Setterfield and Bayley, 1961 ; Thimann, 1963; Ray, 1962; Probine and Preston, 1962; King and Bayley, 1963). In some objects an increme of hot water soluble substances, especially pectic substances, and an increase of methylation of the pectin, was found; however, in others it was not. Other cell-wall components did not change significantly in amount and constitution ; neither did the amount and the distribution of calcium. This does not, however, disprove the eventual role of these substances in plasticization of the wall for growth, since the physical properties of polymers may be profoundly changed by slight, so far undetected, chemical changes. Since the amorphous matrix is involved in the coherence of the microfibrils, the chemical constitution may be briefly mentioned. The hemicelldoses are a mixture of polysaccharides, some of which contain glucuronic acid. They may involve straight chain homopolymers, e.g. mannan, galactan, glucan, xylan and araban, or these may bear other monomers, usually in short side-chains but sometimes also in the main chain, so that heteropolymers arise, e .g. glucomannan, galactomaman, arabinoxylan and arabinogalactan. Glucuronic acid or its methylester may be attached to some heteropolymers as side chains, e.g. glucuronoxylan and arabinoglucuronoxylan. In marine algae sugar sulphates are usually incorporated in the hemicelluloses. Each of these polymers varies greatly in degree of polymerization (DP) and hence in solubility. On the average the DP is 100-300, corresponding to a maximum length of 500-1500 A, which is short as compared with t h e microfibril dimensions. The pectic substances of the Cormophyta are straight chain polymers of galacturonic acid and of its methylester. The solubility in neutral water is less in fractions with higher DP, lower methyl and higher calcium content. For chemical details of the amorphous polysaccharides the reader is referred to the reviews of Aspinal (1959, 1962), Kreger (1962, algae

U L T R A S T R U U T U R E O F THE W A L L IN G R O W I N G UELLS

81

only) and Northcote (1963,algae and fungi), and for papers on the biosynthesis to Setterfield and Bayley (1961)and Neufeld and H W (1963). Special attention has been given in recent years to cell wall proteh, whose presence has now been conclusively proved (see Roelofaen, 1969, p. 77; Newoomb, 1963; Dyke, 1964). The embodiment of proteins in walls also follows from the occurrence in the wall of enzymes (Newcomb, 1963). In some cases the enzymes were shown to be present only in cell wall fractions isolated from tissue homogenatee. Since adsorption of proteins certainly occurs, the evidence in such cmes can never, in our opinion, be conclusive. More convincing is the demonstration of the occurrence of metabolic turnover within the cell wall, e,g. by Matchett and Nance (1962).Also the secretion of enxymes into the culture medium by both tissue cultures and intact plant roots (e.g. Constabel, 1963; Chang and Bandurski, 1964)involves the presence of proteins, at least temporarily, in the wall. With yeasts and other fungi, many exocelluhr enzymes and enzymes attached to the wall have, of course, been known for a long time. Possibly significant with regard to cell wall plasticization is a cell wall protein, probably non-enzymatic, that wm found in the cell walls of both plant tissue cultures and, to a lesser estent, normally grown plants. Its discovery was due to an extraordinary high content of the unusual amino acid hydroxyproline (Lyndon and Steward, 1963; Newcomb, 1963;Steward and Chang, 1963).It has been supposed that this protein is involved in the control of growth by forming labile cross linkages between the cellulose (Brown, 1963;Lamport, 1963,see p.212 of this book); also, that it would cement the cells together in the middle lamella (Ginzburg, 1961).The latter supposition does not c o r n pond with the possibility that the cells of many tissues can be separated with substances that do not react with proteins, like calcium binding agents (Letham, 1962)and purified pectinase preparations (Zaitlin and Coltrin, 1964). The protein of yeaat cell wall was also studied recently (Nickereon et! al., 1961; Northcote, 1962; Dyke, 1964). With careful extraction glucan-protein and glucan-mannan-protein complexes are obtained. Glucosrcmine would act as a binding agent in them. The protein dnot contain hydroxyproline. Although its cystein costent is small it would, according to Nickerson and Falcone (1956),be involved in the strengthening of the coherence of the glucan microfibrils in the cell wall by forming disulpbide bridges. Breaking these bonds by a reducing enzymrttic system would weaken the wall fabric in the s p t where a bud is to be formed. Brown (1963)has postulated that in higher plants the breaking of protein disulphide bonds is also involved in growth.

82

P. A . R O E L O F S E N 11. SOME ASPEOTS OF MIUROFZBRIL OOXERENOB

Growth is the yielding of the wall to the stress generated by the turgor pressure. The stress is born by the microfibrils and by the coherence between these. The coherence will be highest between microfibrils that are in direct contact. It will probably decrease sharply with an increase of the interfibrillar distance shoe it then becomes dependent on the strength of the bonding of hemicelluloses, pectic substances rtnd possibly proteins. Since the molecular chain length of hemicelluloeee, for example, varies between 600 and 1500& smallinterfibrillar distanms will require the participation of two of these to establish one link, and this number would increase proportionately with distance. The binding of hemicelluloses to the paracrystalline microfibril surface is ratber strong, as is seen by the dWcdty in purifying oellulose, but in all probability the points of contact between two hemicellulose moleoules in the amorphous interfibrillar material are too limited to establish strong links. In electron micrographs the “cellulose skeletons” obtained after extraction of most other substances look very compact, but this is due both to shrinkage as a result of extraction and desiccation, and to a comparativelygreat depth of focus in the electron microscope. In order to estimate the true volume percentage of oelluloee in the untreated wall, one has to take into consideration the highly hydrated condition of the intersbrillar substances as compared with cellulose. In 1892 Cohn found 61-72% water in collenchyma. Corn coleoptile walls contain about 60% water (Roelofsen, 1969, p. 127, the water content of 90%, often quoted, is without any experimental basis). In contact with water, pure cellulose contains only about 16% water, which is wholly restricted to the paracrystalline regions. Accepting a total water content of 60% and 30% cellulose on dry weight, the interfibrillar substances would contain about 67% watm and would oompy about 90% of the total volume. The cellulose would occupy about lo%, which implies that the mean distance between microfibril s u r f a c ~ ~ would be about four times their diameter, that ie 600-1000 A. This is an average of the whole wall; the middle lamelb does not contain cellulose. The outer parts of the primary wall contain much less than the inner ones, as is apparent from electron micrographs of cell wall sections (cf. Setterfield and Bayley, 1968). If the innem& layer would contain 76% cellulose on a dry weight basis, this would occupy about half of the volume. The mean intedibrillar diatmm would be less than their diameter; there would be considertcble direot contact, with many interfibrillar links involving only one mole& of hemicellulose. In the middle and outer layers many more weaker linka,

ULTRASTRUUTURE O F T H E W A L L IN GROWING UELLS

83

involving more than one molecule per link, will occur (see Fig. 5). Besides the amount of amorphous substances, the degree of alignment of the microfibrils naturally will also be very important with regard to their coherence. A network of microfibrils orientated at random will, like a piece of felt, be equally extensible in all directions. With two crossed microfibrillar directions the network will, like textile fabric, be least extensible in these directions and most extensible (more than a random network) in the directions bisecting the angles between the microfibrillar directions. Finally, a wall with more or less parallel microfibrils only will extend with difficulty parallel to these and with

Meon dislonce lW&-------

Cellulose content of: 75 1.%, 50 vol. %

------30w.'L,K)vDI.%

------15w.%,5wl.%

Fra. 6. Diagram of the role of interfibrillary eubatances in the coherence of mimofibrilr, at varying callulose oontent.

w e at right angles. We will see that all these possibilities are actually realized in growing walls. The only bonds possible betwean polysaccharides are hydrogen bonds between two hydroxyl groups (I)or between one hydroxyl and the 0-atom of either pyrmose or furanose-rings or of the glycosidic bridge (11). In chitin there might, in addition, exist hydrogen bonde between two NH-CO-groups of the acetylglucosamine monomers (111) or involving one of these. The carboxyl groups of uronides or of uronic acids in hemialldosea may bind hydroxyl groups, both when ionized (IV) or non-ionized (V). Relatively strong double bonds may occur between two non-ionized

P. A . R O E L O F S E N

84

(- )OOC

Hb

\

CH,

\N-CH,-CH,-N

/\

/\

CH,

\

W++)

/ \

COO(-)

(-)OOC

(VW

\

/ C

/

bH

,’

p

I

I (VIII)

carboxyl groups (VI), but only in an acid medium. Since proteins have both peptide-groups and several kinds of H-donating and H-accepting groups in side chains, they may form complexeswith all polysaccharides. Not only protons (H-ions) are attracted by the free electron pairs of electronegative atoms like 0 and N, but also metal-atoms and metalions that may incorporate such pairs in the outer electron shell. Many metals can take up four, six or even more of such electron pa&. In this way metal-complexes, called chelates, may be formed with molecules having two or more electron-donating atoms. Calcium and magnesium, the main metals in plant cell walls, are known to decrease the plasticity of primary cell walls and it has been supposed that they are involved in the growth-promoting action of auxin. This would induce the production of some chelating agent that would bind the atoms that previously connected two uronic acid groups in pectic substances or in acid hemicelluloses (see BurstrUm, 1963). Usually the possibility of the binding of acid groups only ia considered. It may be remembered, however, that by binding an anionio group like carboxyl, the a f i i t y of the metal for hydroxyl oxygen or for nitrogen increases, as is demowtrated by the Ca-EDTA complex (VII), the complexing of calcium by lactic acid, gluconic acid, etc. Therefore it is likely that in cell walls calcium and magnesium a t o m form metal bridges not only between uronic acid or otheranionicpups,

UL T RAS T RU C T U R E O F THE W A L L I N G R O W I N G CELLS

I

86

but also between these and hydroxyl groups of polysacoharidee, including cellulose (VIII). The co-ordinative binding properties of many other bivalent and trivalent metals, e.g. copper, zinc, aluminium, iron and silver are much greater. These may bind OH-groups in a natural medium without the help of carboxyl groups. Belford e l al. (1959) showed that heavy metals are taken up in a more or less crystalline arrangement on the surface of cellulose fibres in amounts that parallel their content of xyhn. Of these metals, however, only traces are found in natural cell walls. D. SITE OF SYNTHESIS OF PRIMARY W A L L SUBSTANCES

It will appear below that cellulose microfibrils are, in all probability, synthesized partly between plasmalemma and the inner wall surface (strict apposition) and partly within the wall veryneartheinnersurfbce. Considered submicroscopically the latter process is intussusception, but considered on a microscopic scale it still is apposition. In the following discussion we will use the term apposition in the latter sense except where specifically stated otherwise. Amorphous cell wall polysaccharides are probably synthesized outside the plasmalemma. In at least one instance ( N i W ) this process occurs, as in the caw of cellulose, at or near the inner wall surface, but in higher phnta probably throughout the growing wall. The grounds leading to these conclusions are as follows. (a) If cellulose microfibrils were synthesized in the cytoplasm, free microfibrils should have been observed regularly in the electron micrographs of section through growing cells as for instance those of Bayley and Setterfield and co-workers (cf. Roelofsen, 1959, pp. 142, 150, leO), which is not the cam. Moreover, the strict apposition this would mply does not correspond with the considerable interwining of the microfibrils, nor with the covering of microfibrile that very probably were the youngest ones, see Fig. 3. Thia Ruggests that microfibrils are formed on the spot by tip growth as in the formation of bacterial cellulose. This interwining comprises several microfibrih. Therefore a thickness of say 600 A of the innermost part of the wall must be able to synthesize them throughout (Frei and Preston, 19618; Preston, 1964), at least, in this particular case. In yeaet, intimate contact between glucan microfibrils and particles at the outer surface of the plasmalemma has been reported (Moor and Miihlethaler, 1963). The microtubles discovered recently by Ledbetter and Porter (1963) near growing walls and by Hepler and Newcomb (1964) near secondaq thickenings probably do not synthesize cellulose, but are related only to the orientation of the growth of cellulose microfibrils w i t h the

86

P. A . ROELOFSEN

wall. One of the electron micrographs of the first-mentioned paper is reproduced in Fig. 28. This point will be discussed in Section IV C. (b) The molecules of both cellulose and other wall plysaccharides are insoluble, so that they cannot diffuse. Thus, if they would be synthesized endoplasmatically, this would imply strict apposition, unless (i) there would either occur numerow tiny cytoplasmh protrusions into the wall, or (ii) there would occur outward flow of the interfibdar substances through the pores of the microfibrillar network. Possibility (i) must be rejected. Electron microscopy has revealed a distinct, continuous plasmalemma, which only enfers the wall at plasmodesmata (of. Buvat, 1963; Newcomb, 1963). The tiny threada between wall and plasmolyf ed protoplast, originally described by Hecht, always correspond with plasmodesmata (Sitte, 1963). Also the plasmic “invaginations”, reported by Frey-Wyssling (1962) and celled plasmic papillae, are, in our view, curved entrances of plasmodeernrcta. They were demonstrated only in oblique sections of very young, shrunken walls, which explains their abnormal shape. Similar Str’UCtUreS occur in the micrographs of, for example, Strugger (1967), who apparently also considered them to be plasmodesmata. Plrtsmodesrrmfa are numerous, but nevertheless there are far too few to explain wall growth by intussusception. Moreover, they are grouped in a limited number of primary pit fields, which are not centres of growth but “centres of stagnancy”, as will appear later (p. 117). The wall grows between these (cf. Roelofsen, 1969 p. 133). Finally there are growing walls without any plasmodesmata, e.g. those of tips showing intrusive growth, of fungi, and of green algae. Possibility (ii)seem very unlikely, since there is no pressure gradient normal to the wall (for consideration of tangential gradients see p. 116 and Fig. 18). Consequently, cytophmic synthesis implies strict apposition. However, as will appear below, the btter ie unlikely and, henoe, exophmatic synthesie is more probable. The considerable activity of cytoplasmic organelles like the endoplasmic reticulum, the dictyosomes and their vesicles, probably pertaim to the production and the transport to the walI of precursore of cell wall substances, of co-enzymes and of eynthmizing enzymes, needed for synthesis outside the plasmalemma. (c) In Acelobacter xylinum, ceilulose microfibrils arise extracellularly. Cellulose molecules naturally are too insoluble to pass the wall and in fact enzymatic synthesis in the culture medium, from an excrefed soluble precursor and from a similar precursor extraoted from green Plants, been reported (see p. 74). This does not prove anything

ULTRASTRUCTURE O F T H E WALL IN G R O W I N G CELLS

87

about the site of synthesis in higher plants, but is at least consistent with exoplasmatic synthesis. (d) The investigations of Ordin et al. (1967) and Jansen et a2. (1960) on pectin methylation, of Margerie and €'6aud-Lenoel(I 961) on cellulose and of Matchett and Nance (1962) on cellulose, hemicellulose and pectic substances, indicate metabolic turnover of these cell wall substances. This clearly suggests synthesis outside the plasmalemma, although in our view it is not strictly proved. There might be breakdown of existing wall substances by hydrolysing enzymes, accompanied by apposition of new wall substances that has been synthesized in the cytoplasm. (e) Setterfield and Bayley (1959) followed the site of cell wall synthesis during growth by means of autoradiographs of sections of Avenu coleoptile segments that had been incubated in tritium-labelled sucrose for several hours. Labelled cell wall material appeared not only

FIG.6. Autoradiographs of transverse sertions of the epiderml wall of Avena coleoptiles, grown for 21 h on tritiated sucrose. A : unextracted wall, containing 76"/n non-cellulorce.

B: wall extracted with acid and alkali, containing about 40% non-cellulose (from h t t e d e l d and Bayley, 1969). 1

at and in the inner part of the wall, but also elsewhere throughout the depth of the thick outer epidermal walls. This is apparent in Fig. 6A. Figure 6 B is of a section that was treated to remove mogt of the noncellulose, but still contained 40%. Since the non-cellulose molecules cannot diffuse into the wall and probably do not flow through it either, synthesis everywhere within the wall is clearly indicated. This does not, in our view, apply to cellulose since in the section of Fig. 6B a large amount of non-cellulosic material was present. Moreover Bahmer (1958) concluded from autoradiographs of parenchyma cells of coleoptiles, subjected to a similar treatment, that there wm no cellulose synthesis within the wall rJince the edge thickeningfi (see Fig. 14) lagged behind in labelling (as also Heen in the autoradiographn published by Setterfield and Bayley, 1957, 1959). (f) Green (1968a) exposed Nitella cells for short periods to tritiumcontaining water and, by comparing the radio-activity on the outer

88

P. A . ROELOFSEN

and the inner sides of the cleaned walls, showed that new wall material, apparently both cellulose and non-cellulose, must, have been added to the wall at or very near the inner surface. This observation is consistent with both apposition of materials synthesized in the cytoplasm and synthesis immediately outside the plasmalemma. Evidently, the site of synthesiH of at least non-cellulosic material is different in Nitella as compared with the Avena coleoptile. (9) Both the so-called multinet structure found in tubular c e b (Figs. 12 and 14)involving a difference in microfibrillar orientation between inner and outer lamellae in crossed polylamellate walls (Figs. 10, 13 and 15), and the peeling off of outer lamellae in many algae, are only comprehensible on the basis of the apposition of the microfibrils, either in the strict sense or in the sense of being formed both on and within the wall near the inner surface. See Section IV A 5. ( h ) On the other hand, the retention of the thicknew of the middle lamella during growth ie only comprehcneihle on the haUiH of either outward migration of its constituents through the interfibrillar spaces, which Beems unlikely, or synthetiis in or near the middle lamella. This is discussed on p. 117. (i) If intuwusception of cellulose microfibrils were to occur at a greater distance from the inner surface, then one would expect the occurrence of cellulose in the middle lamella of all tissue cells and the non-existence of walls with separate cellulose lamellae. What would occur if cellulose microfibrils were to be formed throughout the wall is demonstrated by the completely interwoven structure of the cellulose films of Acetobacter xylinum. A microfibril in this felt-like structure cannot be ascribed to one particular bacterium, whereas in plant tissues, for each microfibril a cell can be indicated to which it belongs. It should be mentioned here that Bayley et al. (1957), studying the outer epidermal wall of the Avena coleoptile, and Beer and Setterfield (1958), studying collenchyma cells, concluded that intumusception of cellulose within these thick polylamellate walls seemed likely on certain morphological grounds. Their conclusion regarding the epidermal wall wan, however, criticized by Bolliger (1969) and in our view the origin of the structure of collenchyma cells is more readily comprehensible without accepting intussusception (see p. 111). The previouN discussion mainly concerned polysaccharide~.Chitin microfibrils are probably also formed at or near the inner wall nurfam, but thiH is based only on the multinet structure of Y h y m y c e s sporangiophores. Wall proteins are presumably synthenized in the cytoplasm, nince the ribosomes and RNA needed do not, as far as is known, occur in cell walls. The hydroxyproline, however, seems to be formed by oxidation

ULTRASTRUCTURE O F THE W A L L IN G R O W I N G CELLS

89

of proline that was incorporated in wall protein (Lamport, 1963). Nothing is known of the site of synthesis of wall lipids. E. QUESTIONABLE EVIDENCE OF BREAKDOWN IN PRIMARY WALLS

Evidently, full-grown walls may occasionally be dissolved physiologically, e.g. in cross walls of wood vessels, lysigenous oil cavities, the flesh of ripening berries, endosperm of seeds, eta. (see Kiister, 1966, pp. 139, 726; Frey-Wyssling, 1969, p. 77). Recently Wartenberg (1963) reported cell wall attack in starving epidermal cells. To our knowledge, none of these cases have been studied electron-optically, so that we do not know the morphological changes of the cellulose microfibrils. When attacked by fungal cellulase they disintegrate into pieces 300 A long and 150 A thick (Meier, 1965; Norkrans and Ranby, 1966). We do not know these changes in chitin microfibrils either. The diHsolution of the partition wall in zygotes of P h y m y c a was studied by SaRsen (1962), but the morphology of the attack of the chitin microfibrils it!jnot revealed. Breakdown of cell wall substance in primary walls, going beyond the plasticization of the amorphous interfibrillar substances, has, in our view, not been proven to exist. Until a few years ago it was often considered that in meristematic cells plasmodesmata aroee by dissolution of at least the amorphous matrix and by either a pushing aside, or else a dissolution, of the microfibrils (see e.g. Frey-Wysslhg, 1959, p. 68). However, in the partition walls between daughter cells, cytoplasmic connections have now been shown to persist during the formation of the cell plate, thus giving rise to the plasmodesmata (of. Buvat, 1963). Also in the side walls of apical meristem cells, for example, plasmodesmata very probably do not arise by dissolution of cell wall substance. Up to 1967 they were either thought to be absent in the youngest stages, or to exist as invisibly thin plasmic threads (Meeuse, 1957). Later they were also found here (Strugger, 1957; Frey-Wyssling, 1962; other literature in Krull, 1960; Newcomb, 1963; Buvat, 1963). As will appear later (p. 117) they ure formed it1 the dividing parent cell cell by the cleaving of existing plltsmodcHrrit~Lti that were widened as a result of wall exteneion. One case of dissolution of wall material in the formation of I ~ u H ~ ~ ( J desmata is evident, viz. of the callow platelet8 at both sides of the pores in the sieve plates of growing sieve vcfisel elements (Esau et al., 1962). Cellulose and other wall mdwtanoeN, originally prerjcnt at thcnc pore sites, need not have been dissolved (see p. 120). Two cases of perforation of growing walh of lower plants huw: ttccn studied electron-optically. Firstly, the perforation of ChcLetorwy~hu cells for the release of swarmers. According to Frei and Prefiton (196la) the cytoplasm protrudes into the wall by pufihing microfibrils anide and

90

P . A . ROELOFSEN

apparently by digestion of the matrix substanoes and the last few wall larnellae only are burst through. Meanwhile the deposition of wall lamellae goes on. but there are two differences with normal lamelhe. Firstly, the microfibrils are oriented at random, as compared with the strictly parallel arrangement of normal IameUaa (Fig. 13). Secondly, they end at the perforation, as is clearly demonstsated in the electron micrograph of Fig. 4. Note the tapering ends of about 0.6 p in length similar to those found with growing microfibrils, both of C - p b (Fig. 3) and of Acetobacter (Fig. 2). This indicates that they were being synthesized. If they were being attacked, disintegration in pieces would probably occur. (The ruptures visible in the miorofibrils in Fig. 4 are not signs of' breakdown. According to Preston, they are arbifacts caused by the electron beam.) Secondly, we may mention the perforation of the wall of yeaeta in the formation of buds. It has been mentioned already (p. 81) that, at the site where the bud is to be formed, the wall would (according to Nickerson and Falcone, 1960) be plasticized by a reducing enzymatic system. The wall yields abruptly and a naked protoplasmic sphere ie extruded. According to the authors the glucan microfibrils are displaced into a circular rim at the base of the sphere. The latter fonns a wd, expands and is thrown off after a separating wall htw been laid down. The circular r i m s remain visible like a bud scar in the parent cell and a birth scar in the bud, see Fig. 9. If the perforation of a growing wall is to be considered the result of an extreme local extension identical in principle with growth, and if even this does not aeem to require true breakdown of cell wall substances, then it seem unlikely that normal growth would do so. cells may in fact elongate so fast that there can be no question of ohemical change; for instance, when the cellulose parts of the cells of Tr&cizntia stamina1 hairs attain a threefold length in half a minute, or when stamina1 filaments of grasses elongate sixfold in several minufee (eee p. 114).A1so the fact that the chemical compoeition of a rapidly growing wall often does not differ from that of a dower growing one tiow not s ~ p p ~the r t idea of chemical change. It does not disprove it either, for synthesis might just compensate breakdown in both slow and rapidly growing walk Matchett and Nance (1962) demonstrated metabolic turnover of 0eU wall substances, including cellulose, by a decrease of radioactivity during growth. This wm stimulated by auxin. It waa interpreti3d as indicating increased rates of breakdown and of resynthesis of wall components. However, in our view, this still does not prove the occurrence of true breakdown, since it was not demonstrated that the turnover could not be ascribed to mere exchange of monomers between

ULTRASTRUOTURE OF T H E W A L L I N GROWING U ELLS

91

the cell-wall substances and their precursors for synthesis, oatdysed, of course, by the synthesizing enzymes present in the wall. Enzymetic synthesizing reactions often are reversible. Hydrolytio reactions are w a rule practically irreVereible and if it were demonstrated, therefore, that e.g. c e l l h e , chithaw, h e m i d u lases Or pectinme were present and active in the well, breakdown would have to be accepted. As far a~ we know, of all these enzymes only c e l l b h w been demonstrated in growing tissues (Ruhland, 1968; Gascoigne and Gaacoigne, 1960; Maclachlan and Perrault, 1964). However, whether it occurs in the cell wall and is aotive them, is unknown. Mrtclachlan and.Young (1962) postulated the breakdown of cell wall in growing pea stems, but the evidence 1388108 quesfionable. Moreover, in view of the slownees of the attack of insoluble celluloee by known cellulases it seems hard to understand a degradation of microfibrils that is rapid enough to be effective in plasticization of primary walls. Also, disintegrated microfibrils have not been observed. A limited depolymerization or side-chain removal of matrix materiala aeems more likely as the basis of plasticization.

111. SURVBY OF THE MIUROFIBRILWLR ARMGEXENT IN DIFFERENT TYPESOF GROWINGCELLS In our monograph (Roelofsen, 1959,pp. 134-160,273-305)the microfibrillar structure of growing cells of lower and higher plants has been described in detail and documented with electron miorographs. Here we will try to summarize this knowledge by giving schematic drawings of the structural types known so far. Since many lower plants and mamy types of tissue cells of higher plants have not been studied, or not sufficiently, this review will necessarily be very inwmplefe. In 80 fiGr as the diagrams are baaed on recent papers, these will be cited; for older papers, our monograph might be consulted. Freely growing cslls and tissue cells are treated separately since the former, not being infiuenoed by adjacent cells, are structurally simpler. Miarofibrils alwaye lie mom or less parallel to the plane of the w d . With random or isotropic orientation there is an abeenoe of preference for any direction within this plane. It will be undersfood further that e.g. “random layer”, “orientated layer”, etc., are corruptionsof: “ b p r being constituted of microfibrile orientated at random”, an #‘parallel in a certain direction”, respectively. A. FREELY GROWING MORE OR LESS ISODIAMBTBIU OELLB

This group includes yeasts, some algae and young stegm of other algae and fungi. There are four structural types. Type lA, Fig. 7, is the most simple type conceivable. There a m (3

92

P . A . ROELOFSEN

A

FXQ. 7. Structural type 1 of isndiametric cells. A: more or I ~ k lE y growingecelisof algae and fungi; B: t h e cells.

randomly orientated microfibrils all around the cell end through the whole depth of the wall. Probably the meah Will be wider at the outer surface as a result of extension combined with apposition, but thie has not been observed. The outer surface is covered by e cuticls-lh amorphous granular material that disappears on treatment with alkali. In some cases the cells are truly free, in other cams they are fixed at one or both ends. Probably the walls of a great many Unicellular algae and fungal stages have this microfibrillar structure, but only very few have been studied, viz. Chlorelh pyremidosa (Northcote and Godding, 1958), the youngest sporeling stage of some algae ( V h h , Dictgmphiwia, Chaedmwrpha, Cludupha, 8pongvnwrpb and A m W M , me Nicalai and Preston, 1959) and young stages of the fungi Wwp&&m (&onson and Preston, 196Ob) and A w c m (Aronson and Preston, 19604. In C h h e l h , r 5 m m p h and A c r o e i p h h pmumably young and old cell w a b have the same structure notwithstendingthat the twolatter ones elongate (see p. 101). In the other algae, however, radically different lamellar appear very soon (types 4 and 7) but if they are plaamolymi, the retracted protoplasts again produce this efrudmal type of wall (Frei and Preston, 1962a). In Hydrodictym ufricunwn, young cells are tubular (w p. NO),but older cells become more and more spherical and, mrreaponding)y, acquire the isotropic wall atructure of t p 1A (Breen, 1963b).

U L T R A S T R U C T U R E OR T H E W A L L I N G R O W I N G C E L L S

93

Sometimes the structures of different parts of one cell belong to different types. In young P h y m p + ssporangiophores, the tip is blown up to a spherical SporCLngium with, again, ieotropio structure, whereas the growth-zone below it had and will keep quit6 a different strudmm (seep. 100).

/Ifit

-

l@A

Birefringence in Holicystis

Fro. 8. 8tructural type 2 ie a8 lA, but lamellab. Found in Ha&&, induced globoid celle of Nit&.

red algae, colchioin-

Type 2, Fig. 8 is similar to type IA, but there am many isotropio lamellae separated by amorphous material. This is typioal of all spherical or barrel-shaped cells of fhmentoue and also thalloid red algae (Myers and Preston, l969b;Dawes d al., 1961),of which in particular Uri~thaia$oeculoea(Hyers et d.,1966), Rhim?ymenia palmata (Myers and Preston, 1959s)and € € e b n i & M caZifomica (Dawes et al., 1961)have been studied. 8trictly, the c d b of thrtlloid red algae should not be mentioned here but in &&ion IIC. Apparently, the growth in tissue ha8 no significant struotural consequences,except that pits &re present (see Myers et d., 1959). Experimentrtlly this structure was obtained with internodal cells of Nitella (otherwisetype 6) by cultivation in water with 0.35~0colohicide (Green,1962, 196%). The cells of Halicyeti8 ovalie are probably built in this way, but ody the outer and the inner surfaces have been observed (Roelofeen, 1959, p. 282).These walle differ in being built up of three polyhmellatelayers, of which the middle one ia exceptional in exhibiting negative double refiaotion, see Fig. 8. Except for cell walls containing wax, this eeemed to ooour in one other case only, viz. in CauZerp (see e.g. Dippel, 1898, p. 240).Its cause was obscure, but now it is evident that it is due to the negative birefringence of xylan microfibrib, as WLW found and expleined recently by Frei and Preston (1964), see also Bryopk etc., p. 77.

94

P . A . ROELOBSEN

Type 3 (Fig. 9) represents the wqll structure of non-myceliumforming yeasts (literature cf. Roelofsen, 1969, p. 304; Hagedorn, 1964; MacClary, 1964). In chemically untreated cell walls, the short randomly orientated, possibly interconnected glucan microfibrils, are visible only on the inside of the wall. The outer side is covered by a grmuhr, lipid-rich material that may be removed by treatment with alkali. The wall is usU&uytwo-layered, the inner one being rich in gluoan, the outer in mannan. Each cell has one birth scar (always at one of the ends of the egg-shaped cells) and a varying number (up to about 100) of bud scars. As far as known, young cells without bud scars and fullgrown cells with bud scars have the same cell wall structure.

6 t h scar

Fro. 9. Structural type 3 is

as l A , but with birth scar8 and

mycelium-forming yeasts.

bud

BCU~.

repreeenting uou.

In the scars a concentric orientation of microfibrib ia Vieible, especially in the rims; in the centre is a little dent. Such a ~otlrlike structure was also observed in hyphas of the fungus PoZy&a!w (eee p. 98). The perforation of the wall prior to budding haa been discussed on p. 90. Type 4, Fig. 10, represents the big (up to 4 cm in diameter) coenocytic (multinuclear) cells of several Valonia s p e c k and the cells (about 0.5 mm) constituting the thallus of D i d y m p M famhaa. Very probably a similar structure occurs in iaodiametrio cells of related genera. There is a gradual transition to tubular wlb with the wme crosswise polylamehte walls described under type 7, Fig. 13. The diagram is based on literature mentioned in our monograph (1959, p. 274). The aplanospore has a cellulose-free wall with a, granular ~ d a 0 8 . The finst cellulose lamella deposited on its inside is felt of randomly arranged microfibrils embedded in an amorphous matrix. This stage was mentioned under type 1, p. 92. Unlike waUs of some other algae

U L T R A S T R U O T U R E O F THE W A L L IN OROWING CELLS

96

Amorphous wall aplanospore

I

Successive larnellae deposited with increasing parollelism

Lamelloe 4,7,10 etc., less dense, sometimes missing

[

Effect of growth on successive lomelloe

FIG.10. Btructurd type 4, found in eella of V a h h spec. div., tbllue mlla of LXc@qhu&a and related gonera.

and of higher plants, this cannot extend very much, 80 that it is torn soon by the extension of the cell. Before this occurs, a lamella of amorphous material followed by a second cellulose lamella (2 in Fig. 10) has been deposited, again on the inside. In the latter the cellulose ie more or less orientated in a flat left-handed (S)helix around the cell. This direction is marked A in Fig. 10. Pollowing this, amorphoue material end then lamella No. 3 is deposited. Its direction, B, is more or less along the meridians from the base of the cell converging to s

96

P . A . ROELOFSEN

“pole” at or near the top. The sharp angle a between A and B varied between 67” and 89” in one cell that waa studied in detail. On to the inner side of lamella No. 3, amorphow material and then lamella No. 4 is (at least may be, see below) deposited, b v h g microfibrillar direction X. Thk intersocte the obtuse angle between A and B and hence is in a right-handed (Z) helix around the cell, also oonverging at the pole. Then again a lamella with direction A is deposited md 80 on ABX ABX, etc. The sets A and B are alwaye well developed and always present, but the X-lamella are thin and sometimes they may even be missing, so that the sequence may be an irregular one, e.g. A B A B X, etc. The degree of regularity varies in different s p e c b and even in cells of the same species. Also the helix angles vary considerably. In growing and full-grown cells there are 20-40 cellulose lamellae present. Each is about 0.4 p thick. The first couple of lamelbe a m laid down with an increasing d e b e of fibrillar alignment. AU are separated by thin lamellae of amorphous hemicellulosicand polyuronide material, so that they can be separated easily after mild maceration. As a result of more or less isodiametric externion of the cell, lamella No. 7 is torn soon to isolated patches that are thrown off. The orientated lamellae are also torn, but initially only along lines parallel to their main orientation, so that broad fissures arise (see Fig. 10).Later, teare normal to these also appear so that pieces are formed that peel off. In Dictyo8phueGa there is a very regular three-lamella repeat and all lamellae are equally developed. Taken strictly, thew cells am not freely growing and should be mentioned in Section 111E. It ehould be noted that no orientated streaming of protoplasm could be observed in the living cells mentioned in this section. ’

B. FREELY UROWlNU TUBULAR CELLS OR PARTS OF UEUB

A tubular cell may arise as a result of either tip growth, or growth in the aide wall only, or both. 1.

Tubular celle with tipgrowth only

Pollen tubes and root hairs of land plants certainly grow in this way and probably also hyphae of fungi, rhizoids of aIgae and fungi and the protonema of mosses. Recent papers confirming this are of &rmack et al. (1963, root hair), Rosen e.t al. (1964, p l l e n tube) and 8trnnk (1983, hyphae). For other literature we refer to our monograph (1969 p. 188) and that by Frey-Wysshg (1969, p. 83). The structure of the tip may, as shown diagrammatically in Fig. 11 under type 6, vary in detail. After a cutiole-like amorphous maa has been removed, the outer surface usually shows randomly orientated microfibrilcl (X), but sometimes more or less a d y orientated ones (Y).

U L T R A S T R U C T U R E OF T H E W A L L IN OROWING UIELLS

87

The inner side of the tip has in no case been observed electron-optioally but, as judged from the birefringence of the whole wall, the microfibrils here are usuaJly also orientated isotropically (A), sometimeg, however, transversely (B) Since the tubular part does not grow, the outer surface is the same as at the tip, either X or Y. Underneath, the secondary thickening

.

& A : FUIIY isotropic or

Cuticle

1’ May be lomallole

Fro. 11. Btructural type 6, found in tip of frcely growing w l l ~or of per& of cell8 and of tieaue wlle with intrusive growth.

is often visible, better, of course, when observed from the inner side. Its orientation is usually axial, sometimes croeswiae or transverse. In exceptional cmes no secondary thickening is deposited. We will now discuss the structure of the various objects as far aa it has been studied. Concerning root hairs of land plants some recent publications have been added to the ones mentioned in our monograph (1969, pp. 140,160) :Belford and Preston (1961, on 8imyie),Dawes and Bowler (1969, on Raphanue) and Scott el al. (1963a, on Raphanw, Bramica, Triticum and Cucurbita). In nearly a11 oakw a combination of the structures X with either A or B wag found in the tip. In R a p h w one author found type Y,others X. Different shapes of the tip may explain this (me p. 127). The root hair of Tritznea bogotenai8 wa8 studied by Roelofaen and %lorn6 (1980). Here again the combination XB waa found. Bince the random structure is retained in the tubular part, it can be upp posed that, as with land plants, this part does not grow. The inner surfiwe, presumably a secondary thickening, is irregular but predominently transverse in orientation, which is exceptional. AB is well known, the protoplasm streams lengthwise. The protonema of Funaria hygrometrica wm studied electron-optically by Gunther (1960). The combination XA waa found both in the tip

98

P. A . ROELOFSEN

and in the tubular part. Extension here is presumably by tip growth only, though Giinther herself does not report about the site of growth. Pollen tubes have, as far as is known (cf. Roelofsen, 1969, p. 168; Sassen, 1964),also the combination XA. This may occur in the tubular part, but also type 6A (p. 100).Probably,themisnosecondarythickening. Tips of fungal hyphae show at their outer surface a random orientation (Roelofsen 1969, Fig. P210; Aronson and Preston, 1960a,b; Strunk, 1963). In some tips of hyphae of PoEystidue, Strunk (1983) found a concentric structure with a pore-like centre, that would be centre of growth. These structures also occurred in aide walls. They look like bud scars in yeasts and this raises the question whether they are scars of thrown-off branches and whether tips showing it were actually growing. Rhizoids of Alhkycm have structure Y at their tips (Aronson and Preston, 1960a).Structure XA was also found in the tips of rhizoids of sporelings of Chaetmorphct and Chdophora and, as already mentioned on p. 89, in the bulges formed in full-grown oeh prior to the perfor&tion of these spots for the release of Bwarmera. Probably isotropic structure also occurs in the hemispherical apical cell of Nitella, but this is only deduced from its isotropy between crossed nicols (Green, 1968b). The red algae present a problem in that we do not know if the tubular cells occurring in many species have been formed by tip growth only, or if there also was elongation in side walls. All wall lamelhe were reported to be isotropic (Myers and Preston, 1969a,b; Dawea et d., 1961). If we accept this (the micrographs published by the h t mentioned authors do show orientation), it suggests restriction of the growth to the tip of the apical cells, since pasaive axial reorientation would presumably occur if the sidewalls would elongate (see Section I V A 5). Lack of knowledge concerning the localization of growth also hampers classification of the structure of the green algae A C T W $ ~ ~ U and Spongmpha, which is like that of the red algae (Nimbi and Preston, 1959). They are therefore also proviBionally classified under tip growth. Also unknown is the eitc of growth in elongated celh of brown aka%. According to Dawes et al. (1961)(for older literature cf. Roelofsen, 1969, p. 297) a thin outer layer is isotropic, the rest of the wall is axially oriented. Perhaps the latter is “secondary wall”. 2 . Tubular cells growing in sidewalls only Tbere are two structural types in these cells, depending on the initkl orientation of the microfibrils deposited at the inside.

U L T R A S T R U U T U R E O F THM W A L L IN Q R O W I N G O l L l i S

90

(a) New microfibrile &po&ted with t m w e ~ s eOtientatiOn. AU freely growing tubular cells that grow in the tubular part and in which new microfibrils are deposited in transverse orientation have the structural type 6. It is visible in the electron micrograph of Pig. 23 and shown schematically in Fig. 12.

Cu tide

- ---May

tM:

or intermediate

Intermediate

May be lomellale

(N/!c//u)

Fro. 12. Structural type 6, called multinet ntructcvo. k”ount1 iu all frwly

growing

oelb

that elongate in lltteral walle cmd in which the initial cclluloso orientation is cunetantly traneverse.

On the inner wall surface the structure is comparatively compact and the microfibrils are orientated more or lees transvemely (if there is spiral growth, the mean orientation is according to a flat helix, me p. 132). After removing the cuticle, either a very widely meshed mimfibrillar network R i visible, with the microfibrils running more or lee8

100

P. A . ROELOFSP1N

lengthwise (A) or a less widely meshed network with microfibrils running in all directions (B), or a structure transitional between them. The intermediate part of the wall always ahows a gradml transition between the inner and the outer surface. I n some oases regulasly crossed structures as in C appear as a transitioml stage, or on the inner surface when the elongation ends, aee p. 128. This is known as multinet structure (Roelofsen and Houwink, 1963) (although the walls represented by Figs. 10, 13 and 16 would be more entitled to that name). This term was given since the wall may be imagined to consist of a number of nets with varying wideness of mesh and varying orientation of microfibrils. Usually, however, there are no separate nets, but one three-dimensional network. As will be disoussed in Section IV A 5 (b), the multinet structure arises aa a result of p d v e reorientation of the transversely orientated microfibrils deposited at the inner surface (see Fig. 23). Free cells of higher plants that grow in this way and that have been cltudied electronoptically are restricted to two, viz. the ceb of the stamina1 hairs of Tradeecuntia virginica and the arms of the stellate aerenchyma cells in the medulla of young leaves of Jumw eJu8ua (of. Roelofsen, 1969,p. 146-149). In Juncwr (Rg. 22)the outer surface waa according to type A ; in Tradacantia, type B waa seen on very young cells, and type A on full-grown cells that also had extended through endosmosis (see p. 132). Among fungal cells, the growing zone of the sporangiophom of Phywmyces blakes1eeacnu.a in the stage with sporangium belonge to thie type (cf. Roelofsen, 1959,p. 298).The outer surfaoe is aa B in the middle part of the growth zone and more like A after full extension further down. Below the growth zone (more than 2 mm below the sporangium) the axially oriented secondary wall is deposited on the inner side. Of the algae, the cells of Nitella (Green, 1968b, 1960a;Probine and Preston, 1961;Limaye et al., 1962)and 8pirogyra (Limye ei! aZ., 1962) can be mentioned. In both, the outer surface is, &B A. The Nit& wall is lamellate and the central lamellae have in fact structures intermediate between the innermost and outermost ones (Probine and %ton, 1961). Transverse orientation was also observed in ToZypelb by Fridvalgky (1968),but in To~ypdlopsisand in two species of C h a , thirn only occurred in the outer part of the wall, the inner one showing axial or steep helical orientation (Fridvaleky, 1967, 1960). Thh, in our view, suggests secondary thickening, which, &R far &B we know, waa not reported 80 far in Algae. Hydrodiclyon is provisionally classified here since the cells are also tubular, negatively birefringent and without the striations typical for the crossed lamellate walh of type 7. However, unpublished eledton

U L T R A S T R U C T U R E O F T H E WALL I N U R O W I N U (3ELLS 101

micrographs (prepared by B. J. Spit) only showed a microfibrillar reticulum with, at least in young cells, a low degree of orientation. Cross walls have only beon studied in Tradacantia and Nilella. Both have random orientation. There are many phmodesmata in the former, but they seem to be lacking in the latter caae (eee a h hiohart, 1962). As far as has been observed, protoplasm streaming in all these ceb was either more or leas lengthwise, or irregular, never transverse. (b) New microfibrib depo8ited in larnellae with al&mting helical micro$brillar miendation. When tissue celh are exoluded (see p. 104) only algal cells fall into this group, namely C w h , C w p h u and probably also the related R?&oclonium and other genera of the Siphonocladales with tubular cells. These are arranged in files, forming filaments, which are unbranched in Chaetmwrph and branched in CZudoplwra. All cells are multinucleate, and so may divide and grow. I n C w l w r a a major part of the growth is located in the tip of the apical cell, which usually falls off in Chaetmwtpha. The submicroscopic structure has been studied exclusively by Nicolai and Preston and co-workers (cf. Roelofeen, 1969, p. 284; Nicolai and Preston, 1969; Frei and Preston, 1961a,b). As mentioned on p. 94 the swarmem, after settling, first acquire a cellulose lamella with random orientation, as in F’ig. 7. Soon, however, the polarity which the cell apparently develops is also expressed in the wall. A lamella is laid down with a flat helical microfibrillar orientation and having a “pole” somewhere near the top of the cell. This stage is quite similar to that of a young sporeling of V a h i a (Wg. 10) in which only the lamellae nos. 1 and 2 are present. Then, however, the sporelings of C h a d w p h a and CWphora elongate and acquire a wall that is, at least in detaib, different. It is represented in Fig. 13 rn structural type 7. The wall is built up of cellulose-rich layers separated by thin amorphous layers. The former consist of several lamellae (total number of lamellae is several tenths). In each lamella the microfibrils are parallelly orientated in an oblique direction with respect to the cell axis, thus running in helices around the cell. As in Valania, there are always two p directions and, in some major sets A and B, in flat and s t ~ oblique species of both genera, a third direction, X, that b b o t a the o b t w angle between A and B. In most species A and X form S-helicteR; B, a Z-helix, ie as drawn in Fig. 13, but in C l a d q h a polVera A iR Z and B and X are S. Since new Iamellae are laid down on the inner surfaoe only, the outer lamellae in any cell are extended more than the inner ones. The extension is in an oblique direction, in most species Z-helical, with an average a~ is indicated in Fig. 13. This causes the cell and the whole

102

P. A . KOELOFSEN Birefringence

Rotation

\,

fe

2

.Cellulose ond

~

Amorphous layers

1

I

!I

Steepness

Outer

+4 -4 +4

Alignment-

Spacing+

+ + +

I

Middle

Inner

/

Average oricnlotion of upper growlh wall spiral of cellin

\

Y

Effects of elongation on structure of lornelloe (Outer compored with inner)

Fro. 13. Structural type 7, found in C'hdophora, C'haelomorpha and other Siphonocladales with tubular cells and alternating initial cellulose orientation.

filament to rotate around its axis and it aho cawes the clrsngm in orientation and in alignment in the cellulose lamellae &R indicated. This evidently requires some slipping past one another of adjacent lamellae. Outermost lamellae may be 80 torn that they peel off. In rapidly growing cells the A lamellae always have flatter, and the B lamellae steeper, microfibrillar orientation aa compared with slower growing cells. When growth stops in the autumn, all lamellae are similar to the outer lamellae of growing celh. By then the cells have also become more or less barrel-shaped so that they might a h be classified with ceUs of F'ulonia in type 4. During the stage of widening the initial orientation of the A lamellae becomes steeper and that of the

U L T R A S T R U C T U R E O F T H E W A L L I N Q R O W IN O C ELLS

103

B-lamellae flatter, just contraxy to the difference observed when a cell increases its growth rate. Whether this also occure in the la,mellae while being displaced outwardly, is questionable. The sign of rotation during widening has not been reported. As in V&ntizc, there is no orientated protoplasm streaming. 3. Tubular cells growing both in the tip and in sidemlla

These naturally are merely combinations of type 5 (Fig. 1 1 ) with either 6 (Fig. 12) or 7 (Fig. 13). The cotton hair shows a combination of 5 XB with 6 A. I n full-grown hairs the crosswise structure 6 C has been observed at the inner surface. The struoture of the tip is demonstrated by Figs. 24 and 26. The hairs of Ceiba pentandra and A8ckp’a.s cornudi exhibit in the tubular part, like cotton, the structural type 6 A. Their tips have not been studied ;nor has the tip of the apical cell of Traderrcantiastamina1 hairs. Immature sporangiophores of Phycmym (with no sporangium yet), also grow both at the tip and in the tapering part ,down to 2 mm below the tip (Castle, 1968; cf. Roelofsen, 1969, p. 298). Electron-optioally, structure 6 B was observed; the inner surface waa sometimes aa 6 C. The tip was not studied by means of this method, but since it is negatively birefringent its structure probably R i according to type 5 XB. In the apical cell of Cbdophora filaments, a struoture as 6 XA waa fourid. ‘I’his merges into the crossed polylamellate structure of type 7 (Frei and Preston, 1961a). Rhizoids of this alga, apical celh of red algae and the protonema of Funaria were provisionally chsified in the group with tip growth only, but in reality it is not known whether these do not grow below the tip. The green alga Bryopsis (a large coenocytic call,Rhaped like a feather) was, until recently, studied with the polarization and the interference microscopes only (Kuster, 1933; Green, 1960b), so that its structural pattern is only partly known. The results indicate that the tubular parts have a structure as in type 6 A and that the tips of the main axis and of the laterals are as in type 5 B. Green’s (1963b) revised Rtructural model of Rryop.6~does not hold, since Kiister (1933) had observed a reverml of the double refraction on stretching and releasing the flaccid cells. This is evidence of traneverse orientation. The condition in Byopsits has been resolved by Frei and Preston (1964) who show that the negative birefringence of the xylan microfibrils is overcompensated by the positive birefringence of glucan chains which lie parallel to them. Electron micrographs show

104

P. A . R O E L O F S E N

that the microfibrils lie in fact almoRt at random with only a slight tendency towards transverse orientation. It s e e m unknown whether growth is confined to the tips in B ~ g q e i e cells, or occurs in the tubular parts as well. The multinet-like structure points to the latter possibility. Green (1902, 1903a) has induced Nitella internodal cells to produce lateral protuberances by surrounding them with a tight jacket provided with a hole. These induced laterals are negatively birefringent throughout with respect to their axis. This suggests a combination of types 0 A and 5 B. U. TISSUE UELLS WITH 180DIAMETRIU GROWTH

Although more or less isodininotric cells oocur very frequently, the submicroecopic structure of both the growing and the full-grown walls has received little attention. Since tho cell faces are isotropic in surface view, it has tacitly been accepted that the microfibrile are randomly orientated both in primary and in secondary walk. Thus the stru&ural type 1 A (Fig. 7) would apply, only with pits and