THE CONTINUUM CONCEPT OF VEGETATION ROBERT P. M c I N T O S H University Notre

Dame,

of Notre Indiana,

Dame 46556

Introduction ............................................................................................................................................................................................. 130 The individualistic hypothesis ............................................................................................................................................. 133 The continuum ............................................................................................................................................................................... 135 Evidence bearing on the continuum concept ...................................................................................................... 140 Interspecific association ................................................................................................................................................... 142 Ordination, gradient analysis, and continuum analysis ............................................................... 146 Spatial gradients ...................................................................................................................................................... 147 Environmental gradients ................................................................................................................................. 147 Species position index values ..................................................................................................................... 148 Community index values ................................................................................................................................. 150 Interpretations of unidimensional ordinations ........................................................................... 152 Multidimensional ordinations ..................................................................................................................... 153 The current state of the problem .................................................................................................................................... 159 Geometric models ................................................................................................................................................................. 161 Continuity and homogeneity .................................................................................................................................... 164 Classification and ordination .................................................................................................................................. 167 Assessment .................................................................................................................................................................................... 170 Literature Cited ................................................................................................................................................................................. 173 Acknowledgments The author is indebted to Drs. Grant Cottam and Lazlo Orloci for valuable comments on the manuscript. INTRODUCTION In his William James lectures on Philosophy and Psychology, Arthur O. Lovejoy (1936) said: "There are not many differences in mental habit more significant than that between the habit of thinking in discrete, well-defined classconcepts and that of thinking in terms of continuity, of infinitely delicate shadings-off of everything into something else, of the overlapping of essences, so that the whole notion of species ~1) comes to seem an artifice of thought not truly applicable to the fluency, the so to say universal overlapping of the real world." This difference in mental habit is conspicuously demonstrated in the literature of ecology relating to the nature of vegetation. Two distinct trends are apparent. In their most polarized forms one treats vegetation as composed of well-defined, discrete, integrated units which can be combined to form abstract classes or types reflective of natural entities in the "real world," whereas the other holds that vegetation changes continuously and is not differentiated, except arbitrarily, into sociological entities (McIntosh 1958, Ponyatovskaya 1961, Poore 1962, Whittaker 1962, Goodall 1963, Anderson 1965b, Daubenmire 1960, 1966). The reasons are not clear why such disparate views of vegetation are held by ecologists. Goodall (1954a) suggests that a preference for classification is ct~Species is used here in the philosophic rather than biological sense. 130

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developed in childhood and persists as a habitual form of thought in adulthood and (1965b) that cartographic needs made a classification more convenient. Webb (1954) comments that the biologist is so indoctrinated with the hierarchial classification of organisms that he finds it difficult to think in other ways. It is certainly true that the analogy of taxonomic and ecological classification has had a long history and still persists, though its inappropriateness has been noted (Bremekamp 1938, Cain 1947, Matuszkiewicz 1947, Webb 1954, Whittaker 1962). Whittaker (1962) says that there may be an ecology of ecologists, their preferences being regionally or culturally conditioned. How far it is possible to attribute a preference for one of the two concepts to ingrained habits of thinking is not obvious. It may be hoped that Dr. Egler's (1962) stricture is not justified. He said of the proponents of the two opposed concepts of vegetation: "Their partisans in my opinion are basically different personality types drawn from a student body because of inherent prejudices for these devious ways of thinking. The controversies between them, the misunderstandings of each other, are all on a par with racial prejudices." Since the beginning of scientific interest in vegetation and the nature of plant communities, the great majority of naturalists and botanists have in fact recognized discrete units of vegetation which they combined to form abstract classes or types (Poore 1956, 1962, Hanson 1958, Whittaker 1962, Daubenmire 1966). It must be emphatically asserted, as Goodall (1963) points out, that this widespread recognition does not validate the hypothesis of vegetational units any more than the once general acceptance of a fiat earth proved that it was fiat. In the earliest groupings for understanding of vegetational communities there were no obvious alternatives to classification, which has continued until recently as the generally accepted and almost sole way of considering vegetation. In many ways this conception of vegetation followed the pattern of development of other early explanations of natural phenomena and grew into a ruling theory as described by Chamberlin (1965). This has been called the association-unit theory (Whittaker 1956, 1962) and was so widely and uniformly accepted as true, or at least useful, that it was rarely described as a theory. Chamberlin (1965) aptly outlines the problems growing out of acceptance of a ruling theory and the difficulties which may result, particularly if an emotional attachment to the theory develops. He urges a method of multiple working hypotheses as the most desirable condition for the advance of a scientific discipline. In this sense of an alternative hypothesis the individualistic hypothesis has served as a great stimulus for creative work in vegetation studies. The purpose of this review is to trace the origins and particularly the recent development of concepts and techniques bearing on this latter view of vegetation, not to assess the entire tangled history of phytosociological studies and concepts. This has been done admirably by Whittaker (1962). It would be oversimplifying to argue that the polarity of the concepts described above represents the general state of ecological thought. A spectrum may be the more appropriate analogy. At one extreme Krajina (1961) comments that a continuum cannot replace the classification: "Every science has a classification of its subjects of research.., without classification there can be no science

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of vegetation" (cf. Daubenmire 1960). Daubenmire (1966), although admitting the continuity of vegetation, supports the community-type theory saying: '*But if there is to be such a thing as vegetation science there must be a framework for organizing, storing, and retrieving the information..." He predicts the success of that system making possible the maximum predictions about the unit. Poore (1964) asserts: "To anyone who engages in this work the most compelling feature is the way in which approximately the same combination of species occur again and again." Conard (1939), in a symposium which is one of the landmarks of the consideration of communities, said: " . . . where the association as understood in the international sense has been u s e d . . , there has been nothing in ecological inquiry which has been so fertile and so productive of results as the idea of the association. It is therefore so useful that whether logical or not, I am for it." At the other extreme are statements such as Cain's (1947) that in vegetation " . . . there are unlimited variables, combinations and permutations," or Whittaker's (1956): "Vegetation may be interpreted as a complex and largely continuous population pattern." These views are commonly qualified in such a way as to limit the apparent gap between the two extremes and a recent trend to mitigate the differences will be documented later. It is true that supporters of the individualistic hypothesis recognize certain units for practical purposes and supporters of the unitary concept recognize gradual transitions although assigning to them a minor role in vegetation. Nevertheless, there are substantive issues which divide the two groups and there has been relatively little meeting of the minds in the past two decades during which the two theories have been effectively opposed. Major (1961) comments that the split is worldwide and no amalgamation between the opposing views is apparent. There are misunderstandings requiring clarification whkh cloud the issues and prevent the necessary confrontation of the opposing views. Whittaker (1956) and Goodall (1963) emphasize the necessity for clear-cut expression and testing of the two hypotheses. The recent development of what may be termed a third force somewhat complicates the scene. The major proponents of the traditional community-type hypothesis represent various schools of thought in which the essential basis of the classification is subjective selection of representative samples of communities according to the precepts of the school (Whittaker 1962). Most of the discussion of the alternative hypotheses has posed the option of this subjective classification against various objective and quantitatively based methods which support the individualistic hypothesis. Goodall (1954b), Hughes and Lindley (1955), Dagn61ie (1960), Williams and Lambert (1959, 1960, 1961), Lambert and Williams (1962, 1966), Lambert and Dale (1964), Williams, Lambert, and Lance (1966), and Orloci (1967) propose methods for the objective classification of vegetation by various statistical methods. These latter workers are not to be identified with the classical proponents of the community-type theory. Although they often urge that vegetation may be effectively classified, their methods and precepts are entirely different and must be considered separately from the traditional classificatory concepts and methods. It seems desirable to adopt Whittaker's (1956) use of community to refer

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to a concrete individual community (or sample thereof) on the ground, and to use community-type to refer to an abstract grouping of concrete communities or samples (Langenheim 1962). Community herein will be broadly construed to refer to any assemblage of organisms or, to use Curtis' (1959) definition, "Any studiable grouping of organisms which grow together in the same place and have mutual interactions" (cf. Williams and Lambert 1959). In this sense community is akin to stand although it does not have the implication sometimes attributed to stand, viz., that it is a concrete unit of an extensive community type. It will be used throughout this paper in lieu of stand and sample. THE INDIVIDUALISTIC HYPOTHESIS The origin of the individualistic hypothesis was, like the origin of most revolutionary scientific concepts, a gradual one and is difficult to attribute to individuals or time. If it is to be linked with the name of a single individual as an Eponym (Boring 1964) in the sense of Mendelian or Darwinian it would likely be Gleasonian. Certainly in the English-language literature Gleason's expositions (1917, 1926, 1939) of the individualistic concept are major landmarks. However, Boring, appropriately enough, points out: " . . . the course of science is gradual and continuous." Curtis (1959), Ponyatovskaya (1961), and Whittaker (1962) cite numerous independent and nearly simultaneous expressions of the individualistic concept in diverse areas of Europe. As is commonly the situation after an idea is finally clearly and explicitly expressed, glimmerings of it are seen by hindsight in the work of earlier authors (Chamberlin 1877, Shreve 1915, and many others could be cited.) The independent, concurrent, and explicit development of the individualistic concept in Russia by Ramensky (1926, 1930; cf. Curtis 1959, Ponyatovskaya 1961, Whittaker 1962) is particularly striking. These separate developments and especially their complete failure for some time to materially influence the course of ecological thought in their respective areas should prove of considerable interest in studies of the history of science. It is apparent that the individualistic hypothesis did not spring full blown from the heads of the various ecologists to whom it has been attributed. Gleason's two papers entitled "The individualistic hypothesis of vegetation" (1926, 1939) are the most commonly cited, but the essential points of the concept, as well as the descriptive phrase, are explicit in his earlier (1917) paper. Gleason in his reminiscence (1953) refers to his 1926 paper, but in a footnote to that paper he traces some of the growth of the concept in his earlier work. Tansley (1920) comments adversely on Gleason's views but very little notice was taken of Gleason's earliest published exposition of the individualistic concept. Several papers of Ramensky (not available to the reviewer), one as early as 1910, are cited as expositions of the individualistic hypothesis by Ponyatovskaya (1961) although Ramensky's 1926 and 1930 papers are most frequently cited. The primary concern here is not to assert priority but to record the widespread early expression of the individualistic hypothesis and its nearly complete rejection by the leading ecologists of the day. Gleason's (1926) exposition of the concept was, in his words, "pulverized" (Gleason 1953) and in the process Nichols (1929)

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asserted the c:ommunity-type viewpoint with a quotation echoes of which are still heard today: "The only possible procedure is to select the extreme marked types of the groups and giving these careful study and description, to describe the intermediate kinds according to their positions between the types." BraunBlanquet dismissed the individualistic hypothesis when it was put forth independently in Europe (Whittaker 1962) and, in the latest edition of his book (1964), ignores recent work supporting it (Whittaker 1966). Hanson and Churchill (1961) describe it as impossible and similarly omit recent work supporting it (Mclntosh 1961). The perennial problem remains: How many intermediates must be interspersed between "types" before they are lost as types and become continuous with each other? Elton and Miller (1954) note that it is possible to destroy any classification by introducing transitional categories in sufficient numbers. In spite of repeated and widespread exposition of the individualistic hypothesis, its impact on any of the various ecological schools or traditions noted by Whittaker (1962) was marginal and the traditional unit or type concept continued to dominate the ecological literature. The general acceptance of a fundamental, and explicitly or implicitly, "natural" unit did not however result in a common standard (Ponyatovskaya 1961, Whittaker 1962, Daubenmire 1966). Daubenmire writes: "There has accumulated instead a spectrum of concepts, terms, and methods so broad as to discourage the novice and confuse even the specialist at times." The recent resurgence of the individualistic hypothesis, like its origin, is difficult to pinpoint. A major landmark is found in the American journal, Ecological Monographs, for 1947, where three prominent ecologists in separate papers endorse Gleason's viewpoint. Egler (1947) comments that he " . . . adopts wholeheartedly and without exception the individualistic concept of the plant community as developed by Gleason." He further says that he " . . . considers these all-but-forgotten papers as being of top importance in the entire development of American vegetational thought." Cain (1947) is more detailed in his justification of Gleason's hypothesis. The main burden of his argument rests on the fact that the species comprising an associational unit must have similar ranges and ecological amplitudes. Since both geographical range and ecological amplitude of species are largely individualistic, he asserts that the units which they comprise are also individualistic. Cain also reasserts Gleason's (1926) view that presumptive associations or areas of uniform structure vary in composition from place to place and that the degree of variation increases with distance making logical classification impossible. Mason (1947), in the same symposium as Cain, emphatically supports Gleason's view that association of species results from coincidence of historical events and environmental tolerances of the species. Shortly after this, Billings (1949) acknowledged the individualistic ranges and tolerances of several dominant species of shadscale vegetation and stated that vegetational boundaries are necessarily arbitrary but useful. In the nineteen-forties and fifties numerous authors in Europe and America (Hanson 1958, Curtis 1959, Ponyatovskaya 1961, Whittaker 1962) independently made more or less explicit statements suggesting doubt as to the validity of the associa-

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tion as a discrete unit and implying acceptance in varying degree of the individualistic hypothesis. Words like variation, kaleidoscope tapestry, spectrum, coincidence, gradual, transitional, and continuous appeared in the literature with increasing frequency and a new force was introduced into the perennial and sometimes acrimonious discussion about the plant community and the nature of vegetation. THE CONTINUUM The individualistic concept is commonly linked with the idea of continuity in vegetation and the continuum concept is widely regarded as a lineal descendant of the individualistic hypothesis (Matuszkiewicz 1947, 1948, Curtis and McIntosh 1951, Whittaker 1951, 1956, Brown and Curtis 1952, Ehrendoffer 1954, Dansereau 1957, Cain and Castro 1959, Cain 1960, Curtis 1959, Lindsey et al. 1961, Poore 1962, Flaccus and Ohmann 1964, Greig-Smith 1964). Curtis and McIntosh (1951) assert that the "vegetational continuum" appears to substantiate Gleason's individualistic hypothesis, and Curtis (1959) regards the evidence adduced in vegetational studies in Wisconsin as conclusive proof of Gleason's hypothesis. Whittaker (1956) interprets the continuum as evidenced in his studies as grounds for rejecting the association-type theory in favor of the individualistic hypothesis. Gleason (1953) suggests the equivalence of his concept and the continuum. Lindsey et al. (1961) comment that the purpose of their study is to test Gleason's theory and the continuum concept. However, Major (1961) and Waring and Major (1964) note that Braun-Blanquet endorsed and defended the individualistic view in spite of his major support of the community-type theory, and Goodall (1963) states that there is no necessary connection between the individualistic and continuum viewpoints. It is true, as Goodall notes, that a continuum or series of individualistic communities can be classified in a variety of ways, but this is not really at issue since it is generally conceded that arbitrary classification of a continuum is possible and sometimes useful and desirable (Curtis 1959). The individualistic hypothesis and the continuum will be regarded here as essentially equivalent and antithetic to the traditional community-type hypothesis as understood by Whittaker (1962). The terms continuous, continuity, and continuum referring to natural conditions have a long history and have been used in diverse contexts. Lovejoy (1936) refers to the principle of continuity derived from Plato and gives a definition of continuum attributed to Aristotle. In this sense the word was applied to a philosophical view of an unbroken order of nature (McIntosh 1960). The general idea of continuity as applied to vegetational systems is not new, nor is it restricted to such systems. It has been applied to soils in the catena concept (Milne 1935, Morison, Hoyle, and Hope-Simpson 1948, USDA 1951, Jenny 1958), in taxonomy in the idea of cline (Huxley 1938, Maarel and Westhoff 1964), and has been suggested in climatology (Landsberg 1958), animal populations (Clarke 1946, Bodenheimer 1958), and sociology (Hawley 1950). The oceanographic literature is a striking instance of parallellism with

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that on terrestrial vegetation in the conflict between the community-type and continuum concepts. Marine biologists from the classic work of M~Sbius (1877) through Petersen (1913) up to the present have recognized discrete communities of benthic and littoral marine organisms. Stephens (1933), Lindroth (1935), and MacGinitie (1939) are exceptions who assert an individualistic viewpoint. Among more recent authors, some support the community-type concept (Jones 1950, Caspars 1950, Hedgpeth 1957, Thorson 1957, Buchanan 1963) whereas others suggest a continuum concept (Tischler 1950, Sanders 1960, Wieser 1960, Kilburn 1961, Margalef 1962, Udvardy 1964). Sanders (1960) says: "In fact the species components of the benthic fauna in Buzzard's Bay constitute a continuum varying with the gradual change in sediment composition." Udvardy (1964) refers to a "floral continuum" of Pacific Coast benthos, Kilburn (1961) to a phytoplankton continuum. Russell (1963), discussing problems of classifying littoral zones, refers to ecological "lumpers and splitters," suggesting a range of views on marine community organization parallel to that for terrestrial communities. The terms continuous or continuum have commonly been used in vegetational studies in a general sense implying an uninterrupted series of elements passing into one another, asserting that no sharp transitions are obvious between communities and that species composition changes gradually from place to place or time to time. Perhaps the most explicit usage in ecology is the "vegetational continuum" (Curtis and McIntosh 1951). Although not formally defined, it is plainly described as a gradient of communities in which species are distributed in a continuously shifting series of combinations and proportions in a definite sequence or pattern. It is clear that these are not random combinations of species nor are they unrelated to the environment. It is specified that the continuum as proposed is a construction based on studies within a limited physiognomic type of vegetation and within a restricted floristic region. This view of the continuum is elaborated by Brown and Curtis (1952), Bray and Curtis (1957), and numerous other studies in Wisconsin summarized by Curtis (1959). Curtis, in his classic The Vegetation of IVdsconsin (1959), formally defines continuum as: "An adjectival noun referring to the situation where the stands of a community or large vegetational unit are not segregated into discrete and objectively discernable units but rather form a continuously varying series" (cf. Cain and Castro 1959, Hanson 1962, Pimentel 1963). Whittaker (1951, 1952, 1954, 1956) and Ehrendorfer (1954) also describe vegetation as a continuum in much the same sense as Curtis. Whittaker (1951) comments that: "Climax vegetation here is a complex continuum of plant populations. Individual communities are regarded as more or less similar to each other but not falling into natural groups." The continuum concept of vegetation as an outgrowth of the individualistic hypothesis has engendered considerable reappraisal of the nature of vegetation and techniques for the study of vegetation. The idea and associated terms have been widely accepted, even penetrating general ecology texts and reference books, with varying degrees of approval (Oosting 1956, Dansereau 1957, Cain and Castro 1959, Odum 1959, Phillips 1959, Hanson and Churchill 1961, Kendeigh

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1961, Hanson 1962, Lemon 1962, Ross 1962, Pimentel 1963, Greig-Smith 1964, Kershaw 1964, Spurr 1964, Voigt and Mohlenbrock 1964, Hopkins 1965, Smith 1966). The widespread adoption of the terms and explicit recognition of continuity, at least in degree, even by those who prefer to treat vegetation by means of a community type of some sort (Poore 1956, Becking 1957, Looman 1963, 1965, Daubenmire 1966) is a marked change in the climate of thought in vegetation studies. Much of what follows is concerned with the meaning of continuum and the evaluation of continuity in vegetation, so no attempt will be made at this juncture to consider all of the interpretations or justifications of these words. However, it is appropriate at this time to emphasize three general points which frequently recur in discussions of the continuum concept and often obfuscate real issues. (1) Many vegetation studies have emphasized the marked discontinuities which are encountered in the field (Hanson 1958, Whittaker 1962). It is widely assumed that it is the existence of such spatial discontinuities which demonstrates the validity of the community-type hypothesis, justifies a classification, and refutes the continuum concept. This view is exemplified in the work of Dahl (1956) which is frequently cited in support of the community-type concept of vegetation (Hanson and Churchill 1961, Poore 1962, Daubenmire 1966) : "The repeated occurrence in nature of vegetational discontinuities is the basis which makes a real classification possible. If all vegetational change were gradual each species reacting independently to the external and internal factors there would be no basis of classification only of typification. The occurrence of more or less well marked vegetational discontinuities is in the writer's opinion an indication that we have to deal with different communities which have to be analyzed separately." It is probable that most supporters of the continuum hypothesis would not agree that discontinuity in space is as frequent and well marked as Dahl suggests. But, more importantly, they assert that the existence of discontinuities on the ground is not proof that distinct community types exist or justification for rejecting the continuum concept. Proponents of the individualistic hypothesis (Gleason 1939) and of the continuum (Whittaker 1956, Curtis 1959) recognize that rather abrupt discontinuities often do occur between communities on the ground. Curtis comments that it is possible to go from forest to prairie in a few feet. Coupland (1961) recognizes that vegetation is a continuum but points out that abrupt changes in vegetation occur due to soil texture (cf. Wilde and Leaf 1955). Observations such as Coupland's are frequent and irrefutable. Abrupt vegetational changes are commonly associated with abrupt discontinuities on the ground due to a change in habitat, historical treatment, or perhaps chance. Continuous transition may occur on the ground but it is not necessary to the individualistic or continuum concept that all vegetational change be continuous on the ground or that discontinuities be absent. Greig-Smith (1964) notes that clearly distinguishable units in the field may form a continuum in the abstract. Lambert and Dale (1964) comment that continuum and continuity are confused because they are applied both to actual continuity on the ground and

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to continuity in abstract models. There is no reason why they should not be used in both senses. It is imperative, however, that it be clear how they are used. The continuum concept has quite clearly been based on the abstract community and the evidence for continuity is based on arrangements of community data in abstract patterns. Dansereau (1961) says that the continuum is as abstract as the classical association. The substantive issue is whether communities, even if frequently sharply distinct from contiguous communities on the ground, are units of a wide ranging community-type equivalent to the classical abstract association which is significantly distinctive from other community-types. In this sense, some statements concerning vegetation are clearly unhelpful, e.g., Martin's (1959) : "In some cases it is a continuum; in others it is a series of communities; in others it is a continuum at one period and distinct communities at another." Vegetation on the ground may run the gamut from clear discontinuity in one place to complete continuity in another and still be a continuum. (2) If vegetation is in fact composed of discontinuous community-types, it may be possible to achieve a unified system of classification which allows maximum prediction and is most meaningful and is universally valid (Looman 1965, Daubenmire 1966). Lambert and Dale (1964) comment that such hopes are a pipe dream. However, if classification is urged simply as a desirable convenience for mapping or information storage (Daubenmire 1966) for practical ends and specific purposes, the classification being arbitrary and directed to these specific ends (Rowe 1960), there is no contest. If classification of community units is a convention like a classification of books, there is little cause for dispute. If it is a theory, then it must be tested. It is entirely irrelevant that classification is useful and, for some purposes, necessary (Coupland 1961, Looman 1964, Flaccus and Ohmann 1964). Contrary to Rowe's (1961) intimation that supporters of the individualistic hypothesis or continuum assert that acceptance of these views rules out the possibility of classification, proponents of the individualistic or continuum hypothesis maintain that vegetational classifications are necessarily arbitrary not that they are not possible or for specific purposes useful (Gleason 1926, 1939, Curtis and Mclntosh 1951, Whittaker 1952, Curtis 1959). The crux of the difference lies in the degree to which a classification is held to represent entities which are consistently represented in vegetation and are organized and defined by processes which are inherent in the development of vegetation. If vegetation is not divided into objectively recognizable units by processes inherent in its development then it may be effectively treated as a continuum and there are practical and theoretical advantages to doing so. (3) Much of the recent support for the individualistic hypothesis comes from quantitative studies which introduced new approaches for the study of vegetation. However, it is not solely quantitative emphasis or difference in technique which produces divergent views of vegetation. The controversy existed before these were widely used. The predilections of various ecologists in their selection of study areas are of great importance. Traditionally the descriptions or sample data of community units have been taken from areas subjectively selected as typical of presumably uniform areas according to the precepts of one or another ecological school. Poore (1956, 1962) and Becking (1957), for

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example, assert that subjective selection of sample plots is a major advantage as compared with objective sampling, making it possible to select the most typical sites. McVean and Ratcliffe (1962), following Poore, subjectively select vegetational reference points (noda) in a vegetation they describe as continuous. Maarel (1966) comments that followers of Braun-Blanquet's methods select a single sample to represent the entire community. Other students of vegetation warn of the limitations of subjective selection according to a priori notions of a type. They urge objective selection of sample areas, at least within vegetation broadly defined to include a wide range of variation of the community under study, to preclude the dangers of subjective selection of only those areas which fit a preconceived notion as to what a particular community should be (Cottam and Curtis 1949, Curtis and Mclntosh 1951, Whittaker 1956, 1962). Selection of samples to fit a priori notions of a community type does not constitute evidence that vegetation consists of such types or that it does not form a continuum. Assertions that such choices are justified by the fact that they represent homogeneous, stable, climax, or more frequent communities as against the rest of the area in which the communities are presumably heterogeneous, mixed, unstable, seral, fragmentary, and less frequent are not satisfactory in the absence of evidence that the selected areas do in fact fulfill these criteria. Gimingham (1961) comments that a requisite for treatment of vegetation in terms of a continuum is the examination of all communities which fall within a frame of reference in a region or at least an unbiased sample of all known communities. Goodall (1963) states: "A first requirement in testing these hypotheses is that the data used should not have been selected in any way which may bias the results." Yet it must be recognized that critics of the continuum concept argue that it is the objective selection of communities which leads to the use of mixed, unstable, or rare species groupings that give the appearance of continuity (Poore 1962, Daubenmire 1966). This difference of opinion may be a more intransigent problem than matters of sampling technique or quantitative analysis of the data. It is extremely difficult to attack or evaluate the "Soziologischer Blick" (Becking 1957) or the "sociological eye" (Looman 1964), developed by the "right intuitive feeling by experience," which allegedly allows the detection of minute floristic differences evidenced by certain species combinations. It is apparent that selection of areas for study is not usually random and, to an extent, any vegetation study delimits a geographic area and commonly a physiognomic type of vegetation, e.g., forest, grassland, scrub, in which it is carried out. Most of the work suggesting continuity among communities refers to physiognomically delimited vegetation although Whittaker (1956), Bray (1956), Wells (1960), Langenheim (1962), Ream (1963), and Whittaker and Niering (1964) consider continuity between different physiognomic types. Gleason (1939), Whittaker (1956), Curtis (1959), and other proponents of the individualistic or continuum viewpoint recognize large scale physiognomically delimited types. It is clearly not at this level where they are at odds with the proponents of the community-type hypothesis. The difference is largely concerned with distinctions between floristically determined communities within a physiognomic vegetation

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type. In any event, establishing arbitrary geographical or physiognomic boundaries to the extent of a vegetational study allows a design which includes a wide range of community variation which is regarded as an important property of vegetation. It might be noted in passing that studies which center on subjectively chosen community-types are rarely followed up by studies which examine the relationship to these of other areas of vegetation not classed with these types. Gimingham (1961), for example, notes that little attention has been paid to variation within and interrelationships between types of the much classified heath community-type. EVIDENCE BEARING ON THE CONTINUUM CONCEPT Early support for the individualistic hypothesis and the concept of continuity in vegetation was derived from subjective impressions in the tradition of the community-type hypothesis. Daubenmire (1966) comments, in a rather pejorative way, that Gleason advanced no data in either his 1926 or 1939 papers in support of the individualistic hypothesis. This stricture could be applied equally to many papers supporting the community-type hypothesis. Gleason (1939), Cain (1947), Billings (1949), and others note the lack of common geographical ranges of species considered to be characteristic of a communitytype and suggest that such individualistic geographic ranges make a communitytype a phenomenon of a limited area at best. Whittaker (1962) cites the widespread subjective recognition of continuity among ecologists. Many recent students of diverse types of vegetation in various parts of the world have subjectively recognized continuity in vegetation without applying specific methods to demonstrate it or presenting extensive quantitative data. Horton (1956) refers to species combinations in western Canadian forests so numerous that it is pointless to attempt arbitrary classification; McMillan (1956) says no grass taxa in his studies would show coincidence of distribution; Muller (1958) describes community organization on terms of limited indeterminacy; Coaldrake (1961) suggests continuity in the coastal lowland vegetation of southern Queensland, Australia; Coupland (1961) recognizes a continuum in the Northern Great Plains region of North America as useful for defining the nature of vegetation; Burroughs (1962) suggests that mountain grassland in New Zealand constitutes a multidimensional continuum with continuously varying species composition; Johnson and Billings (1962) recognize four alpine vegetation types but comment that these blend with each other as a continuum on a topographic gradient; Langenheim (1962) says that, despite some discontinuity produced by different growth forms, vegetation of diverse physiognomic types in Colorado appears to be primarily a continuously gradating pattern; Martin and Specht (1962) find that floristically similar communities of dry sclerophyll forest in Australia form a continuum; McVean and Ratcliffe (1962) describe the vegetation of Highland Scotland as virtually continuous but recognize subjectively chosen communities as noda in the sense of Poore (1962); Harper (1962) finds soils and vegetation of upland heath areas in Scotland continuous; Richards (1963) says that studies of tropical rain forest indicate its continuum nature as do Hewetson (1955), van Steenis (1958), Shultz (1960), and

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Walker (1966). Churchill (1955) and Beschel (1964) recognize Arctic Tundra as forming a continuous series of transitions; Campbell and Dick-Peddie (1964), in the tradition of Gleason's famous Mississippi River transition, sample along the Rio Grande River north to south and find that the vegetation forms a continuum with gradual and imperceptible changes between dominant and subdominant species; Dansereau (1964) describes continuity in temperate rain forest of New Zealand; Maarel and Westhoff (1964) and Maarel (1966) refer to the extremely complex continuum nature of dune vegetation in the Netherlands; Buck (1964) considers woody vegetation of the Wichita Mountains, Oklahoma, as a continuum; Yoshioka (1964) finds continuity in deciduous and conifer forests in Japan; Scott (1965) describes, in the South of England, a loosely ordered complexity of vegetation on shingle beach which supports the individualistic hypothesis; Vogl (1966) (cf. Good 1965) comments that species cross apparent zones in California salt marsh in a continuous manner; Klikoff (1967) describes a continuum on a topographical gradient in the Sonoran desert. Many ecologists obviously find it meaningful to consider vegetation as a continuum. Cushing (1965) comments that the continuum approach is welcome to the paleoecologist. Some ecologists consider that vegetation constitutes a continuum but find it more useful to classify it (Hanson 1958, Coupland 1961, McVean and Ratcliffe 1962, Poore 1962, Daubenmire 1966). Principal support for the continuum concept, however, comes from extensive and intensive quantitative studies using a wide variety of analytic and synthetic techniques for the study of vegetation (Goodall 1952, 1962, Curtis 1959, Whittaker 1962). Among the earliest of these are the pioneer papers of Ramensky (1930), Matuszkiewicz (1947, 1948), and other European workers. These studies published in Russian and Polish were largely unknown to most ecologists until similar, independent studies brought them to light and reinforced their findings. Curtis (1959) comments that Matuszkiewicz (1948) produced the first vegetational continuum. It is striking that similar techniques and interpretations appeared, largely independently, in diverse places. These techniques stem from the renewed interest, apparent in recent years, in quantitative and objective methods for the sampling and analysis of plant communities. It is not clear just why individuals in diverse places became interested in ordination methods. It may be that the general confusion and lack of agreement among diverse schools of ecology (Whittaker 1962, Daubenmire 1966) precipitated a search for alternatives to traditional classification methods and for more objective techniques. It has been implied (Poore 1962, Daubenmire 1966) that the support for the continuum is a consequence of methods of sampling and analysis. It does seem clear that a predilection shared by the proponents of the continuum is the mass collection of large amounts of quantitative data (Egler 1954, Curtis 1959) and an emphasis on variation as an important aspect of vegetation. Proponents of the continuum concept have generally favored ordination methods. It does not follow, as Goodall (1963) points out, that these are necessarily linked. The essential relationships of species to species or communities to communities, which are the basis of vegetation study, are amenable to analysis

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by either or both classification or ordination methods. The basic problem remains in the interpretation of the results and particularly in relating the results of vegetational analyses to the environment. Implicit in the comparison of sets or classes of objects are the notions of correlation and similarity. Certain properties go together in a somewhat restricted fashion and the result is a class of similar objects. This is inherent in the traditional view of community units. Thus the basic approaches to the study of vegetation are directed at the ideas of correlation and similarity. Recent work in which the continuum concept is an issue continues these basic approaches and is of two general types. (1) Examination of correlation or association of species to determine to what degree they are aggregated into discrete groups distinct from other groups. (2) Comparison of communities to assess the degree of similarity between them. These comparisons may be generally recognized as either of two types. (a) Communities may be compared by direct analysis of the available floristic data to evaluate the degree of similarity or relationship between two or more communities. Species composition is considered as the basis of comparison in these techniques. Whittaker (1954), McMillan (1956), Rowe (1960), and Goff and Cottam (In press) call attention to certain problems inherent in this assumption. (b) Communities may be compared by relating them through information derived from sources other than the vegetation itself, usually attributes of the physical environment. The variations in detail and emphasis on the above themes are myriad and all may be used in a single study or mixed in a single technique. The discussion of the validity of the continuum concept revolves around studies using the basic approaches suggested above and their interpretation as demonstrating: i) individualistic distribution of species; 2) similarity between communities; 3) continuity or discontinuity between communities. INTERSPECIFIC ASSOCIATION

The traditional view of a community as a coordinated group of species which commonly occur together forming aggregations which can be defined and subjectively recognized in the field has led to attempts to accomplish this definition objectively. Since the essence of the idea is mutual association and interaction of species, it suggests that measures of correlation or of association would reveal such natural aggregations. These have been reviewed by Goodall (1952, 1965a), Fager (1957), Whittaker (1962), Greig-Smith (1964), and Dagn~lie (1965a, b). Pearson's coefficient of correlation (r) (Stewart and Keller 1936, Tuomikoski 1942, Dawson 1951, Watt 1960, Box 1961, Beschel and Weber 1962, Anderson 1965a, Schmid 1965) has not been widely used because of the labor of computation and its assumption concerning the underlying probability of paired observations (Cole 1949, Vries 1953, Greig-Smith 1964). Tests of association or mutual occurrence of species such as chi-square (X 2) or Cole's Index (1949) have been used frequently in community analysis based on qualitative data. Re-

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sults of such studies have been variously treated and interpreted to suggest a continuum or used as a basis for classification. In some instances the matrix of association values is simply inspected and the incidence of significant association or their lack noted (Greig-Smith 1952, Shanks 1953, Jones 1955, Pr~cs~nyi 1958, Kershaw 1959, 1960, Dagn~lie 1962a, Cook and Hurst 1963, McDonough 1963, Beaman and Andresen 1966). Species are normally considered as associated pairs but Hale (1955), Cole (1957), Greig-Smith (1952, 1964), and Gilbert and Wells (1966) consider joint associations of more than two species. Greig-Smith notes some groups of associated species but expresses doubts as to the concept of the community as a complex organism. Sexton, Heatwole, and Knight (1964) use chi-square to relate animal species to structural features of vegetation. Gilbert (1953), Gilbert and Curtis (1953), Hale (1955), Guinochet (1955), Bray (1956), Struik and Curtis (1962) arrange the matrix of association values by inspection. Species with high positive association are placed close together and those with negative association far apart. Groups of species which have high positive association with each other thus become more readily visible, usually along the diagonal. Gilbert and Curtis and Struik and Curtis interpret the resultant matrix of association values in studies of forest herb species as a continuously shifting gradient supporting the individualistic hypothesis. Hale, studying corticolous cryptogams, discerns relatively distinct groups in his matrix (cf. Vasilevich 1962). In some instances the significant associations between species are represented in the form of a two-dimensional "constellation" (Vries, Baretta, and Hamming 1954) with lines connecting species which are significantly associated (Vries 1953, Vries, Baretta, and Hamming 1954, McIntosh 1957, 1962, Welch 1960, Agnew 1961, 1962, Juh~isz-Nagy 1963, Groenewoud 1965b, Dale 1966, Kowal 1966, Yarranton 1966). Looman (1963) constructs a three-dimensional model which is shown from three directions. Beals (1965b) uses the negative and positive square root of chi-square as a measure of the ecological distance between species. Using this measure, Beals constructs a two-dimensional ordination of species by a technique similar to that of Bray and Curtis (1957) (see below). Instead of taking communities as reference stands, he uses different species. Beals also compares the results of chi-square with those produced by Cole's index (1949). By grouping communities according to segments of a slope gradient and recalculating chi-square, he shows that many of the association values lose their significance, demonstrating the importance of topography in affecting distribution. Such figures attempt to place the species with positive associations close together, those with negative associations far apart. The inference is that the model is a spatial representation of the ecological relations of the species. Groups of species become apparent if several members are mutually associated and if they have few positive associations with species outside of the group. The number of significant positive associations within a group of species as a proportion of the total possible number may be used as an index of the cohesion of the group, e.g., between four species there are six possible associations. It is not

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possible to represent the species relationships in proportion to the magnitude of the X ~ association index in Euclidean space, for X 2 is not a metric function. Its use as a distance measure results in distortion the exact extent of which is difficult to determine. Some authors have interpreted such figures as representing species groups (Agnew 1961, JuMsz-Nagy 1963, Looman 1963, Dale 1966); others (Vries, Baretta, and Hamming 1954, McIntosh 1957, 1962) state that the diagram does not justify the recognition of groups of species existing as combinations in nature. The problem is that there is no way of objectively subdividing such a diagram or validating the apparent clusters unless they are grossly isolated. Members of one suggested group may have sufficient significant associations with other groups to vitiate the validity of subjectively determined groups. Kershaw (1964) reproduces Agnew's (1961) species association diagram and asserts that three groups of species are immediately obvious. This assessment does not have the same immediacy to every reader. Another problem lies in the fact that pairs or groups of species which are significantly associated in one study may be independent in another so the associated pairs or groups are not constant (McIntosh 1962, Cook and Hurst 1963). In some situations chi-square may be calculated between species and classes of an environmental characteristic, e.g., soil moisture (Quarterman and Keever 1962) or range condition (Cook and Hurst 1963). More objective methods of assessing matrices of interspecific associations have been proposed by Goodall (1953a), Hopkins (1957), Fager (1957), Williams and Lambert (1959, 1960, 1961), Lambert and Williams (1962), and Gilbert and Wells (1966). Hopkins, by a series of eliminations, concentrates the positive associations and identifies groups of associated species which he terms "basic units." Communities are allotted to basic units as their composition approximates that of the basic unit (Juhllsz-Nagy 1963, Boscain and Soran 1965). Fager identifies "recurrent groups" of species by a method based on ranking species in order of number of significant positive associations. Goodall and Williams and Lambert use the chi-square test of interspecific association as a basis for identifying groups of species (or communities) by elimination of association (GoodaIl) or reducing it to specified levels (Williams and Lambert). The essential assumption is that the resultant groups are homogeneous or relatively so, and can be treated as classificatory units. Goodall's approach has been used by Hosokawa (1955), Rayson (1957), McIntosh (1962), and Looman (1963) and is discussed by Williams and Lambert (1959), Greig-Smith (1964), and Kershaw (1964). The methods of Goodall and Williams and Lambert achieve an objective division by identifying discontinuity (presence or absence of species) between communities (Harberd 1960). "Normal association-analysis" (Williams and Lambert 1959) divides a group of communities into subgroups. "Inverse analysis" (Williams and Lambert 1961) uses the association matrix to divide the species into groups. "Nodal analysis" (Lambert and Williams 1962) seeks coincidences between "Normal" and "Inverse" analyses as a basis for identifying nodal groups of species and communities. These are described (Lambert and Dale 1964) as comparable to the subjectively defined "noda" of Poore (1956, 1962) in his

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method of "successive approximation." Ivimey-Cook and Proctor (1966), however, regard the nodum of Williams and Lambert as quite different from that of Poore. The techniques of Williams and Lambert are reviewed by Harberd (1960) and Greig-Smith (1964) and have been used by Kershaw (1961), Ramsay and DeLeeuw (1964), Gittins (1965c), Grunow (1964), Beals (1965b), IvimeyCook and Proctor (1966), Boaler (1966), Gimingham, Pritchard, and Cormack (1966), Gilbert and Wells (1966), and Crawford and Wishart (1966). Kershaw compares association-analysis with his own technique of co-variance analysis which uses quantitative rather than qualitative data. He raises the question of the use of only qualitative data in the analysis of vegetation since it ignores the attribute which is fundamental to the meaning of vegetation, namely the relative quantities of the component species. Gittins compares the results of association-analysis with an ordination using the method of Bray and Curtis (1957) (see below) and finds that they give substantially the same interpretation. He notes that the association-analysis does not show the degree of relationship between the groups recognized. Gimingham, Pritchard, and Cormack (1966) compare inverse analysis with a two-dimensional ordination using the method of Bray and Curtis (1957) and find that they both arrive at the same general conclusions. Ivimey-Cook and Proctor compare the traditional phytosociological approach with association-analysis which they suggest is, in some ways, a mechanized version of traditional phytosociology. They review a number of limitations of association-analysis. One point which is emphasized is that division of data by association-analysis does not necessarily indicate a lack of continuity. Boaler (1966), in fact, uses association-analysis to segregate a vegetational sample into groups which he interprets as a continuum, each group merging imperceptibly into the adjacent groups. An important problem in the use of chi-square as an index of association is the effect of quadrat size upon the measure of association. Lambert and Williams (1962) suggest that quadrats be large in relation to the size of the plants. Changing the size of quadrat changes the magnitude of the measure of association and may even change the sense. Dawson (1951), Kershaw (1961), GreigSmith (1964), Beals (1965b), Groenewoud (1965a), Gittins (1965c), Gimingham, Pritchard, and Cormack (1966), and Yarranton (1966) call attention to this problem. Greig-Smith says that information based on data from one quadrat size only is incomplete and difficult to interpret. Yarranton suggests the use of a point sample technique which, however, requires physical contact between the two species which are to be tested for association. Goodall (1965a) describes two methods which test interspecific association by means of distance measures. None of the several methods of vegetation analysis based upon chisquare tests of interspecific association has been examined carefully in respect to the effect of quadrat size on its results and their interpretation. Kershaw (1961) shows the effect of quadrat size on association-analysis and comments that the final groupings are influenced by the size of the quadrat. Bray (1956), Fager (1957), and Gilbert and Wells (1966) note that the chi-square does not measure biotic association per se but rather amplitude of

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distributional overlap. It is influenced by the number as well as the size of the samples. If areas are included in which only one or neither of a pair of species is present the magnitude of the chi-square will change. In this way it is influenced by the heterogeneity of the communities included. This is, however, what Goodall (1954b) and Williams and Lambert (1959) are dealing with and their techniques are designed to reduce the heterogeneity evidenced by the interspecific association. None of the above methods has been used extensively in a variety of vegetation types or repetitively in a similar vegetation type to ascertain the consistency with which groups of species may be identified. The techniques of Goodall and Williams and Lambert are intrinsically methods for classification and may be used to classify anything in which there is a significant association between any of the components, i.e., which is heterogeneous. As such they may prove useful as suggested in several trials noted above and where it is clear that utility or the convenience of the user is the prime requisite for the selection of a method (Lambert and Dale 1964). Williams, Lambert, and Lance (1966) note wide differences in the results of association analysis and other quantitative classification techniques using different coefficients and comment that the only test of the efficacy of a method is that it serve the purpose of the user and produce a clear cut hierarchy. ORDINATION, GRADIENT ANALYSIS, AND CONTINUUM ANALYSIS

A variety of techniques have been developed for relating communities to each other. Essentially these are methods for condensing and synthesizing large amounts of ecological data which have become increasingly available as sampling techniques have become more rapid and effective. The most widely used means to this end is classification. The alternative is called ordination, a name proposed by Goodall (1954a) and Ehrendorfer (1954) and previously used by Ramensky (1930). An ordination is an arrangement of communities, species, or environments in sequence which it is hoped will reveal maximum information about the relationships among them and which will also reveal such classes as may exist. Like a classification, an ordination is an abstract construction and the most important consideration is the interpretation of the results. A clear understanding of the specific premises and effects of particular techniques is important to the interpretation. The crucial question raised by Dr. Grant Cottam at the International Botanical Congress at Edinburgh is: "What does it all mean ?"--and the answer lies in the insight of the ecologist, not in the method. Ecological judgment, has not, as some have feared, become computerized. Whittaker (1952, 1956) has proposed the general term "gradient analysis" to describe ordination methods which concentrate on the construction and study of gradients of species, communities, or environment. McIntosh (1958) suggested that the term gradient analysis was applicable to ordinations of communities on environmental gradients (direct gradient analysis of Whittaker), and "continuum analysis" has been used, as noted below, for ordinations on the basis of species composition which is essentially a phytosociological procedure (Whittaker's indirect gradient analysis). The terminology is unimportant, but

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the different bases which have been employed for construction of ordinations should be clear. Diverse techniques have been used and several may appear in the same article. The citations below indicate that a given technique is used in the reference cited, not that it is the only or even the major technique used. Spatial Gradients

In the most direct sense transects may be placed along an actual spatialenvironmental gradient and the characteristics of the communities examined at various points along the sequence. Here the ordination is a geographical one, the communities being contiguous or not but in either instance located by spatial position (Bray 1956, Dahl 1956, Mandossian and McIntosh 1960, Laessle and Monk 1961, Lindsey et al. 1961, Beschel and Weber 1962, Beschel, Weber, and Tippett 1962, Berglund 1963, Schmid 1965, Vogl 1966). The transect is of course a standard method of examining relation of species or communities to the actual conditions on the ground, and may reveal discontinuity or continuity. As emphasized earlier, the distribution of communities as a continuum on the ground is not the major point at issue. However, studies of spatial distributions of plant communities or their component populations across presumed zonations or boundary areas between communities, especially on apparently continuous environmental gradients, may bear directly on important aspects of community organization and theory, e.g., competition, the role of the dominant. Environmental Gradients

In a number of methods the aim is to develop abstract arrangements of communities which are not spatially contiguous nor ordered in any way related directly to their spatial position. One of these ordinates communities by direct alignment on an environmental factor or factor complex as measured or estimated within each community. This is "direct gradient analysis" in Whittaker's phraseology. Environmental gradients which have been used are: 1) soil moisture (Partch 1949, 1962, Curtis 1955, Maycock and Curtis 1960, Maycock 1961, 1963); 2) altitude (Whittaker 1952, 1956, Langenheim 1962, Mowbray 1966); 3) slope facing (Okutomi 1958, Langenheim 1962); 4) steepness of slope (Row 1963, Beals 1965b); 5) height above stream (Horikawa and Okutomi 1959, Mowbray 1966); 6) soil type (Harper 1962); 7) snow cover (Hansen 1930); 8) flooding incidence (Willis et al. 1958); 9) soil nutrients (King 1962, Beals and Cope 1964). Pennak (1942), Bodenheimer (1958), and Whittaker and Fairbanks (1958) in similar ways show distributions of animal populations on salinity gradients. Usually values of a gradient are scaled linearly, but Whittaker and Fairbanks use a logarithmic scale. Bray (1958) applies a log10 scale of light intensity. Rowe (1956) also uses a log scale of moisture index values but does not arrange communities directly on the moisture gradient (see below). Hale (1952) ordinates constancy of corticolous cryptogams against height on tree stem. Langenheim (1962) shows the distribution of subjectively determined physiognomic communities by means of a coincidence index which is the ratio of the total area occupied by the community to the area of an environmental character, e.g., altitudinal zone, slope exposure, or geological substrate.

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The early gradient diagrams of Rasmussen (1941) provide an insight into problems of interpretation. Ross (1962) sees them as suggesting sharp separation of biomes, whereas Spurr (1964) comments that they show the impracticability of recognizing different forest zones, the species showing overlapping population distribution. The most thorough ordinations based directly on environmental data for each community are those of Loucks (1962), who synthesizes several measurements of moisture, nutrients, and local climate into unit expressions called scalars. Communities are placed directly on the environmental scalar according to their index value as derived from the environmental data. Loucks relates these environmental ordinations to vegetational ordinations (see below). Waring and Major (1964) in some instances arrange communities directly along environmentally determined gradients of minimum available moisture and replaceable calcium as well as using other ordination methods (see below). Environmental gradient approaches derive from the tradition, particularly in forestry, of using site conditions as a basis for prediction of silvicultural capability and management planning. It is not implied that environmental gradients are functionally independent of the community but that the measurements and ordinations are derived independently from a consideration of the species present (see below). The correspondence between the two may be sought for assessing the validity of using one to predict the other (Loucks 1962). Species PositJop~ Index Values

A second major ordination or gradient analysis approach arranges communities in sequence according to their composition. Whittaker calls this "indirect gradient analysis." A specific variant of this method has been called "continuum analysis" (Gounot 1961, McIntosh 1958, 1962, Anderson 1963, Bannister 1966a, Buell et al. 1966, Anderson et al. 1966). The technique was not designed to analyze a continuum but was developed as a means of expressing quantitatively a pattern of relations among communities suggested by preliminary grouping and ordering methods. These were the leading dominant method (Curtis and McIntosh 1951, Horikawa and Okutomi 1955, Curtis 1959, Rice and Penfound 1959, Bray 1960, Anderson 1963, Itow 1963, Maycock 1963, Buell et al. 1966, Davidson and Buell 1967) and the strip method (Curtis and McIntosh 1951, Clausen 1957a, Gimingham, Pritchard, and Cormack 1966). These methods respectively arrange groups of communities defined by their leading dominant(s), or individual communities on a gradient by inspection of composition data. Species are assigned weighting values according to the relative position of the peak of a curve of the distribution of a quantitative measure of each species. This value is used in calculating a weighted compositional index value (weighting value times a measure of each species) which locates each community on a gradient or ordination axis. The essence of this and similar approaches is that the actual position of each community in the ordination is determined by its specific composition. Whittaker (1954) and Swindale and Curtis (1957) comment on the use of weighted indices. One of the early uses of a weighted index value called it the "climax adapta-

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tion number" (Curtis and McIntosh 1951, Brown and Curtis 1952, Kucera and McDermott 1955). The word climax was later dropped (Christensen, Clausen, and Curtis 1959, Curtis 1959). This usage has been criticized and alternative terms suggested, e.g., "ecological sequence number" (Cain and Castro 1959), "continuum number" (Anderson 1963), "habitat adaptation number" (Buell et al. 1966, Davidson and Buell 1967), "species position index value" (Goff and Cottam, In press). Although appropriate enough in its original context, climax adaptation number gives the misleading implication that the vegetational continuum is necessarily a successional sequence, which it is not (Whittaker 1956, Curtis 1959, Wells 1960, Anderson 1963). "Species position index value" has the advantage of being non-committal as to the basis of the value and will be used here in preference to the other descriptive terms. It simply describes a numerical assessment of a single species or group of species on a gradient. Species position index values have been determined in a variety of ways. Some approaches are based on sociological relations using vegetational data only. Species may be weighted by their ecologic position relative to a climax dominant (Curtis and McIntosh 1951, Brown and Curtis 1952, Parmalee 1953, Ware 1955, Anderson 1963). Swindale and Curtis (1957), following Guinochet (1955), calculate an index of joint occurrence between species. These are arranged in order of high to zero joint occurrence and the sequence divided into four groups. The number of the group is used as a weighting value. Agnew (1961) in an analogous approach constructs an interspecific association diagram using chi-square in which he recognizes five groups of species to which he assigns weighting values. Bray (1956) calculates an index of joint occurrence of species which he uses to arrange species in a linear order by inspection. He arbitrarily divides this into four groups. Dix and Butler (1960) calculate a matrix of community similarity coefficients using the Kulczynski (1927) coefficient of similarity (see below), ordinate the matrix by inspection, and divide it into five groups of communities which they use to assign weighting numbers to species with maximum frequency in each group. Gilbert and Curtis (1953) weight herb species by the segment of a continuum gradient, based on trees, in which the herb species reaches its maximum presence. Species position index numbers may also be assigned by the position of the species on a measured or subjectively determined environmental scale. Use of species weighting numbers as determined by their adaptation to the environment is simply an ordering of species or species groups and is an adaptation of the traditional use of indicator species. It is similar to the differential species group composed of species which occupy similar ranges on environmental gradients (Ellenberg 1956) but the groups here are used as a basis for classification. Groenewoud (1965a) comments that such a classification need not assume discontinuity but may divide a catena into segments. Bakuzis (1959) reviews the literature, particularly the European forestry material, relating to this usage. Waring and Major (1964) also review the use of species as indicators of ecological conditions and discuss certain theoretical aspects. Kittredge (1938) and King (1962) assign species indicator numbers according to soil groups. Numerous ecologists assign values according to position on a moisture scale

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(Raabe 1949, Whittaker 1952, 1956, Christensen 1954, Curtis 1955, Rowe 1956, Whitford 1958, Christensen, Clausen, and Curtis 1959, Rice and Penfound 1959, Whittaker and Niering 1965, Buell et al. 1966, Davidson and Buell 1967, Dix and Smeins 1967). Habeck (1959) selects groups of indicator species which are common components of different communities on a moisture gradient. Knight (1965) also uses a moisture scale but ranks morphologicalfunctional types rather than species. Whifford (1951) ranks species according to estimated light intolerance classes. Bray (1958) groups measured light intensity values into four classes on a log10 basis and weights species by the class in which they reach their highest frequency (cf. Waring and Major 1964). Hosokawa (1964) uses compensation point for weighting species. A number of gradients have been devised based on species response to disturbance. Dyksterhuis (1946, 1949, 1958), Ramensky et al. (1956), Cawley (1958, 1960), Horikawa and Itow (1958), Dix (1959), and Itow (1960, 1963) use susceptibility to grazing. Beals and Cottam (1960), Habeck (1960), and Beals, Cottam, and Vogel (1960) consider preference as deer browse. Lindsey et al. (1961) list susceptibility of species to suffocation by flooding. Bakuzis (1959) uses the term "synecological value" to refer to the " . . . adaptation to or requirements for essential environmental factors (under competitive conditions) of species, species groups or whole communities." He ranks species in five classes on synthesized scales of moisture, nutrients, heat, and light. Such an arrangement of species he calls an "ecological row." Waring and Major (1964) also locate species along various environmental scales representing complex gradients of moisture, nutrients, light, and temperature. They use species of subjectively selected community types of widely different physiognomy ranging from grassland through chaparral, deciduous oak forest to redwood forest. Some of their environmental gradients are derived from elaborations of direct measurements of the environment; others (temperature) are derived from weather bureau records of areas in which a particular physiognomic communitytype dominates. Community Index Values

Vegetation responds to changes in the environment by changes in the qualitative and quantitative characteristics of species populations and in species composition. These, of course, are the premises for the use of species as indicators. Any specific habitat contains a group of species responding in complex, and in part undetermined, ways to numerous factors of the environment and, also, modifying the environment in varying degrees (Kittredge 1948, Major 1951, Gorham 1955, Jenny 1958). Whittaker (1954) comments that Major outlines the theoretical approach to "gradient analysis." Species position index values always carry a burden of indicator value even when they are not explicitly weighted according to the relation to an environmental factor or factor complex. Limitations to the validity of these values are considered by Whittaker (1954), McMillan (1956), Waring and Major (1964), and Goff and Cottam (In press). A community may be placed in a gradient of communities by calculating a composite index value for the community as a whole. The composite index value

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of a community may be the average of the weighting values of the species (i.e., qualitative data) or it may be the sum of the products of the species weighting values and a quantitative measure of the species, e.g., frequency, density, cover, or a composite measure such as the importance value (Curtis and McIntosh 1951). Some authors use all species for which data are available; others (Curtis 1955) select a few species or even one (Horikawa and Okutomi 1957) as indicators of particular environmental ranges. In general, multiple species combinations are preferable as a basis of indication because the ecological optima and amplitude of a species are commonly influenced by other species (Ellenberg 1952) and the combination makes a better indicator of the habitat complex than a single indicator species. Species with narrow amplitudes of tolerance are commonly preferred. Wide-ranging species which are not considered good indicators of the environmental gradient being used may be excluded (Ellenberg 1952, Rowe 1956). Whittaker and Niering (1965) and Waring and Major (1964) also omit species with broad ecological amplitudes and bimodal species. King (1962) omits species with maximum occurrence in the mid-range of the gradient, thus increasing the effect of those at the extremes. Goff and Cottam (In press) review many of the problems inherent in species and community index values. There has been little study of the effect of these practices on the resulting distributions of composite index values. In any event, a range of composite index values for a series of communities permits their arrangement along a gradient in the order of their community index values. The "continuum index" (Curtis and McIntosh 1951, Brown and Curtis 1952, Parmalee 1953, Lindsey et al. 1961, Anderson 1963, Buell et al. 1966), presence index (Curtis 1955), composition index (Curtis 1959, Swindale and Curtis 1957, Goff 1964), synecological index (Bakuzis 1959, Pluth and Arnemann 1965), the moisture gradients of Whittaker (1956) and Whittaker and Niering (1965), and the several vegetation indices of Waring and Major (1964) are of this type. Some of the community indices have been used as a frame of reference for other data. The hardwood tree continuum of Southern Wisconsin (Curtis and McIntosh 1951) has been used in studies of forest herbs (Gilbert and Curtis 1953, Randall 1953), soil microfungi (Tresner, Backus, and Curtis 1954, Christensen, Wittingham, and Novak 1962), cryptogams (Hale 1955), geographical distribution of forest communities (Whitford and Salamun 1954), and bird populations (Bond 1957). The northern-hardwood forest tree continuum of Wisconsin has been the basis for studies of cryptogams (Culberson 1955) and soil microfungi (Christensen 1960). The prairie continuum (Curtis 1955) formed a base for studies of phenology, life form, and life-history characteristics (Butler 1954) and of soil microfungi (Orpurt and Curtis 1957). Whitford and Salamun (1954) and Buell et al. (1966) find that the community index value based on saplings is generally higher than that for trees, suggesting a successional trend. In several instances, environmental factors are found to be related to the continuum ordination (Curtis and McIntosh 1951, Brown and Curtis 1952, Curtis 1959). Curtis (1959) links various continuum sequences in composite linear ordinations. Knight's (1965) index based on

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structural-functional characteristics (e.g., height, root system) related to a moisture scale corresponds with Curtis' (1955) prairie compositional index. Use of such non-taxonomic criteria as a basis for calculation of index values affords a means of comparing communities having completely different floras, relating similar structural-functional attributes to environmental gradients, and continues the traditional use of non-taxonomic criteria pioneered by Raunkiaer and recently extensively developed by Dansereau (1951, 1957). The lowland forest continuum index (Christensen, Clausen, and Curtis 1959) is used by Habeck (1960) to show shifts in the peak of presence of understory species influenced by deer browse.

Interpretations of Unidimensional Ordinations The results of the various techniques of ordination or gradient analysis described thus far are arrangements of communities in sequence. Each community is located relative to other communities directly on an environmental gradient or on a synthetic compositional gradient which may or may not incorporate an environmental factor or factor complex. The position of the individual community on the synthetic compositional gradient is a resultant of the contributions of each of the component species used in calculating the community index value. These are treated as linear sequences although they may be combined to form two- or three-dimensional figures (see below). The distribution of the communities along such gradients, when they are not selected on a priori grounds as members of a class of communities, is generally rather uniform although not necessarily random. It would be readily possible to create a cluster of communities on such a scale by selecting numerous "more or less" similar communities and placing them on the ordination. Such sequences of communities are the "vegetational continuum" of Curtis and McIntosh (1951), the "compositional index" of Curtis (1959), and the "composite transect" of Whittaker (1956). Much of the early interpretation of vegetation as a continuum, substantiating the individualistic hypothesis, rests upon the distribution of species populations on such gradients when quantitative measures of the species are plotted on the gradient axis. For the most part they form curves approximating a normal distribution although some may be skewed or truncated. The rationale and interpretation of these curves have been considered by Curtis (1959) and Whittaker (1954, 1956). Centers of individual species distribution located as maximum value, mean, or mode, as well as limits of curves of different species, are scattered along the ordination axis and clusters of species peaks or boundaries are not strongly evidenced. The continuous change of species populations along objectively determined gradients of environmental factors or of community composition constructed in various way and the extensive overlappings of the curves of several species are interpreted as arguing against the community-type concept. Groenewoud (1965a) illustrates the complex relations between species having different quantitative distributions on a gradient axis. The similarity between communities which are close together on the ordination axis is seen as only approximate, due to the continuous change in species populations, and similarity decreases with distance along the axis. The lack of similar curves and boundaries

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for several species is interpreted as arguing against the concept of a homogeneous community extending along a gradient until it gives way abruptly to another homogeneous community. These patterns of overlapping curves substantiating earlier views of the individualistic responses of species to environmental phytosociological gradients are commonly interpreted as supporting the individualistic hypothesis and the continuum concept of vegetation (Ramensky 1930, Curtis and McIntosh 1951, Whittaker 1952, 1954, 1956, Curtis 1959, Anderson 1963, Rabotnov 1966). MullJdimensional Ordinations

The early ordinations or gradient analyses use various of the methods outlined above. A common assumption of unidimensional ordinations is that communities are arranged along the single axis according to their relative similarity. The poles of this axis have communities which differ maximally from each other and intermediate positions on the axis are occupied by communities intermediate between the poles. Presumably proximate communities on the axis are similar to each other. It soon became apparent that linear ordinations are inadequate and that communities which are proximate on a unidimensional ordination are not necessarily similar to each other; neither are species with proximate curves on the axis necessarily ecologically related. Representation of vegetation on a single dimension results in a foreshortening or distortion. The complex relationships inherent in vegetation require multidimensional methods of representation (Whittaker 1952, 1956, Goodall 1952, 1954b, McIntosh 1957, Bray and Curtis 1957, Curtis 1959, Dagn~lie 1960, Gimingham 1961, Greig-Smith 1964, Kershaw 1964, Buell et al. 1966). Various studies have represented vegetation in multidimensional patterns and there are many variations in approach. The most direct method simply selects two or more independently derived environmental or compositional gradients and uses them as coordinates. Whittaker (1952, 1954, 1956, 1960) and Whittaker and Niering (1964) construct two-dimensional ordinations, putting together environmental gradients of moisture and altitude. Bakuzis (1959) and Bakuzis and Hansen (1965), using the method of "synecological coordinates," plot communities or habitat attributes such as soils in two-dimensional gradients of synthetic environmental factors, e.g., moisture, light, nutrients. Bakuzis shows the distribution of species frequency in two-dimensional "ecographs" which are similar to the contour patterns of species distributions of Curtis (1959). Loucks (1962) plots two-dimensional graphs showing the distribution of communities on pairs of synthetic scalars of moisture, nutrient relations, and local climate representing approximations of three dimensions of environment. Waring and Major (1964) plot frequency of species in two-dimensional diagrams of combinations of their synthetic environmental gradients. Beals and Cope (1964) show the distribution of species in two-dimensional patterns of soil calcium and organic matter gradients. Itow (1963) constructs two-dimensional ordinations using a rather involved combination of grouping communities to provide indicator species, the Kulczynski (1927) similarity index to compare the groups, and species weighting values based on the groups to construct a compositional

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index on which the individual communities are ordinated. Compositional index values of the communities are plotted on bilateral axes of topographic steepness and age of grazing and isorhythms drawn to define the communities in a manner similar to that of Whittaker (1956). Recent applications of various methods of multivariate analysis to vegetational studies Have introduced a new dimension (literally and figuratively) into the problems of vegetational theory. These methods have been used to support both classification and continuum viewpoints (Matuszkiewicz 1948, Goodall 1953b, 1954b, Hughes and Lindley 1955, Bray and Curtis 1957, Curtis 1959, Williams and Lambert 1959, 1960, 1961, Dagn~lie 1960, 1961, 1962b, 1965a,b, Hughes 1961, Harberd 1962, Lambert and Williams 1962, 1966, Greig-Smith 1964, Lambert and Dale 1964, Gittins 1965a,b,c, Groenewoud 1965a, Austin and Orloci 1966, Orloci 1966, Williams, Lambert, and Lance 1966, Goff and Cottam In press). The use of multivariate techniques in ecology has been reviewed by Dagn~lie (1960) and Greig-Smith (1964), and is discussed by Lambert and Dale (1964). The most widely used and discussed multidimensional ordination technique which has been interpreted in support of the continuum hypothesis is that developed by Bray and Curtis (1957), and used, with variations, by Bond (1957), Clausen (1957a), Okutomi (1958), Curtis (1959), Burgess (1959, 1961), Beals (1960, 1965a), Beals and Cottam (196o), Maycock and Curtis (1960), Bray (1961), Loucks (1962), Christensen (1963), Looman (1963), Ream (1963), Ayyad and Dix (1964), Ashton (1964), Mclntosh and Hurley (1964), Nelson and Burgess (1964), Gittins (1965a,b), Larsen (1965), Monk (1965, 1966), White (1965), Bannister (1966a,b), Gimingham, Pritchard, and Cormack (1966), Swan and Dix (1966), Crawford and Wishart (1966), Hulett, Coupland, and Dix (1966). Numerous variations of the Bray and Curtis ordination technique have been devised. Loucks (1962) uses the methods of Bray and Curtis to establish vegetation gradients and relates these to the environmental scalars mentioned above. Species distributions on the vegetational ordinations correspond with those on the environmental ordinations. Ream (1963), in a study of vegetation of the Wasatch Mountains, divides stands into four types based on their physiognomy. Each physiognomic type is ordinated separately. These ordinations are used to divide each physiognomic type into arbitrary community types. Prevalent species (Curtis 1959) of each of these are determined. Finally, a Kulczynski (1927) index is calculated for each individual community on the basis of the prevalent species. These are used to produce a secondary ordination of the community types. Itow (1963), Ramsey and DeLeeuw (1965b), and Crawford and Wishart (1966) first classify communities, then ordinate them using the Bray and Curtis technique. Gimingham, Pritchard, and Cormack (1966) ordinate groups of stands selected by the leading dominant, using the mean composition for each group as the basis for comparing the groups. Monk (1965, 1966) uses soil-nutrient data rather than compositional data in the index of similarity. He thus plots the distribution of species in an environmental ordination rather than the reverse which is more common. Gittins (1965b) constructs an ordination of species rather than the

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more usual ordination of communities. Beals (1965b) also produces twodimensional ordinations of species, rather than communities, using the square root of chi-square of species association as the basis of a distance measure. The axis construction is similar to that of Bray and Curtis. Hole and Hironaka (1960) produce a three-dimensional model based on soil-profile data. There are three essential elements of the Bray and Curtis and similar types of ordination: 1) the qualitative or quantitative data representing the communities being compared; 2) a measure of similarity which is used to compare the composition of communities; 3) a technique for constructing or determining the axes or gradients on which communities are located with respect to each other. The resulting ordinations are influenced by and must be evaluated with respect to each of these three elements (Curtis 1959, Orloci 1966). The Bray and Curtis technique has been used with qualitative data, e.g., presence (Christensen 1960, Christensen, Whittingham, and Novak 1962), but more commonly with quantitative data of diverse types, the latter either applied directly or scaled in various ways. Clausen (1957b) compares the effect on ordinations of frequency, relative frequency, and presence. Bannister (1966a) compares ordinations based on cover, frequency, cover plus frequency, Domin estimates (see Cain and Castro 1959), and a transformation of Domin estimates. He finds considerable similarity between the ordinations. Gimingham, Pritchard, and Cormack (1966) compare ordinations using mean cover and frequency values. The pattern of distribution on a two-dimensional ordination is similar but the groupings suggested by the magnitude of the similarity index values are somewhat different. Bray and Curtis (1957) use relative values, the highest value for a species being scaled to 100 (cf. Whittaker 1952). Burgess (1961) examines the behavior of the Kulczynski (1927) index in samples of a prairie catena by averaging matrix values for different block (aggregate sample) sizes. He omits the common, wide-ranging grass species from his calculations. If the block size is too large, he finds that the continuum nature of the prairie community is lost. If it is too small the effect of clumping due to the clonal nature of the prairie species results in large fluctuations of species curves on the ordination axis. The measure of similarity, according to Burgess, is a function of the distance between the blocks and the size. Lambert and Dale (1964) argue that qualitative data is more efficient than quantitative data, at least for classifications. Relatively little has been done to compare the effect of the type of data on the resulting ordinations. Orloci (1966) compares the effect of qualitative and quantitative data (frequency) on the ordination using different techniques for axis construction. He finds that fiequency data emphasize ecological gradients and discontinuity as compared to qualitative data. Goff and Cottam (In press) compare the effects of relative frequency, relative density, and basal area and density and find little difference in the effect on the community index value. Gimingham, Pritchard, and Cormack (1966) construct two-dimensional ordinations using frequency and mean cover values and find the results similar except in minor respects. Corollary to the choice of sample data is the problem of what species to use in any of the techniques based on compositional data. In some instances, as

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noted above, all species are included; in others only a portion of the total composition is used. Curtis and Mclntosh (1951), Whittaker (1952), and Maycock (1963) consider only trees in forest studies; Gilbert (1953), Gilbert and Curtis (1953), and Bray (1960) use herbaceous species to ordinate forests; Culberson (1955) ordinates trees on the basis of cryptogams; Christensen, Whittingham, and Novak (1962) ordinate five forest stands by soil microfungi. Some studies use selected indicator groups of species (Curtis 1955, Habeck 1959, Dix and Butler 1960). Bray and Curtis (1957) demonstrate that it is not necessary to include all species to get meaningful distributions. They use selected trees, shrubs, and herbs (cf. Beals and Cottam 1960, Nelson and Burgess 1964). Some authors omit species of wide ecological amplitudes or bimodal distributions on ecological gradients (Ellenberg 1952, Rowe 1956, Whittaker and Niering 1964). Anderson (1963) eliminates a single species which he regards as a secondary colonizer, a practice criticized by Daubenmire (1966). Burgess (1961) eliminates the dominants; Waring and Major (1964) criticize the use of the Kulczynski (1927) index, and presumably similarity indices in general, because of species replaceability as indicators. It appears that the general validity of ordination studies to date will not be greatly influenced by the selection of data or the species used. However, continuing studies are needed to clarify the effect of data and/or species selection on the resulting ordinations and particularly to indicate the type and amount of data which will produce meaningful ordination results with the least effort. The relationship of communities is measured by various indices of similarity or coefficients of community (Gleason 1920, Kulczynski 1927, Sorenson 1948, Raabe 1952, 1957, Whittaker 1952, Bray 1956, Bray and Curtis 1957, Clausen 1957b, Bourdeau 1961, Greig-Smith 1964, Orloci 1966, Williams, Lambert, and Lance 1966). These indices or their complements are used to indicate a distance between communities in a spatial pattern related to their ecological similarity. The most widely used similarity index in ordination procedures is that variously attributed to Sorenson, Kulczynski, or Gleason and apparently derived from Czekanowski (1913). It is here called the Kulczynski index. Its most 2w common expression is ~ where a is the sum of the quantitative measures of the species in one community, b is the sum for a second community, and w is the sum of the lesser values for the species which are present in both of the communities (cf. Williams, Lambert, and Lance 1966). This index has been used to classify communities (Sorenson 1948, Hanson 1955, Evans and Dahl 1955, Hanson and Dahl 1957, Hurd 1961, Bliss 1963) as well as for ordinating communities in the method of Bray and Curtis. Brodo (1961) calculates Kulczynski index values for corticolous communities and ordinates these by inspection (cf. Mueggler 1965). Ramsay (1964) constructs a diagram based on Kulczynski index values which is similar to the "constellation" diagrams described above. He compares the resultant species groups with groups originally based on chi-square values of associated species (Ramsey and DeLeeuw 1964). Beals (1965a) modifies the Kulczynski index, adding a factor for growth forms of lichens. Gimingham, Pritchard, and

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Cormack (1966) use the reciprocal of the Kulczynski index as a measure of distance. Recent evaluations of the Bray and Curtis technique have been critical of the index of similarity used and their technique of axis construction (Dagn~lie 1960, Lambert and Dale 1964, Dale 1964, Williams and Dale 1965, Austin and Orloci 1966, Orloci 1966, Williams, Lambert, and Lance 1966). The com2w plement of the similarity l-a- ~ -

used by Gray and Curtis as a measure of dis-

tance between communities in the construction of the ordination does not, as Curtis (1959) noted, give values which are directly proportional to the relationship. Austin and Orloci (1966) show that this value is non-Euclidean. They advocate the Euclidean measure of distance

(Xij - Xlh) ~ 1/2 as a measure

of the distance between communities (Orloci 1966). Xlj and Xih represent the species scores in communities j and h respectively. Newbould (1960) and Ramsay and DeLeeuw (1964) use the Euclidean distance to show the relations of communities or species groups respectively (cf. Vasilevich 1963). Distance is used by Swan and Dix (1966) as an estimate of how well a three-dimensional figure constructed by the Bray and Curtis technique represents the Kulczynski index values of the original matrix. They report a highly significant correlation between distance and the corresponding Kulczynski index values for corresponding pairs. The problem of an ordination technique is to simplify the matrix of similarity index (or other) values and derive from it one or more axes such that the position of each community relative to them conveys the maximum information about the vegetation. A number of approaches have been tried. Clausen (1957a) attempts to arrange communities by inspection in a two-dimensional framework so that their spacing represents their similarity index value, and finds it impossible. Various methods of axis construction are described by Clausen (1957a,b), Bray and Curtis (1957), Maycock and Curtis (1960), and Beals (1960). Characteristically one extreme community is designated to represent one end of an axis and a community which is maximally different from it the other end. In some instances composite end communities are used. Clausen (1957b) and Bray (1961) note that if one or two very unusual communities are introduced into the data these will become the end communities and the remainder will cluster near the center of the axis. Beals and Cottam (1960) state that two-dimensional ordinations produce a major gradient on the diagonal. Gittins (1965a) also notes that the constructed axes are not the principal axes of variation and rotates the constructed axes 45 ~. Austin and Orloci (1966) comment that the selection of extreme end stands may produce axes which do not lie in the principal axes of variation of the data. Dale (1964) and Austin and Orloci (1966) assert that the axes of the Bray and Curtis ordination are not perpendicular, thus distorting the relations between the communities and in the resulting models. Austin and Orloci (1966) propose an ordi-

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nation technique using Euclidean distance as the measure of similarity, and Orloci (1966) describes the geometry of determining perpendicular ordination axes. The selection of a technique for determining the axes on which the communities or species are distributed is, perhaps, a more important problem in ordination studies than the selection of data or correlation coefficient. The pioneer effforts described above are currently being reexamined and alternative and improved methods of axis construction developed. Bray and Curtis (1957) comment that their technique of axis construction was adopted in lieu of factor analysis because of problems in the latter of heavy computational labor in handling large amounts of data, disadvantages of Pearson's r as the correlation coefficient, and difficulties of interpretation. The great increase in availability of computer facilities and programs has obviated the first difficulty and allows exploration of diverse techniques and combinations of techniques which were impossible before, and cofficients other than "r" are being used with variants of factor analysis. The difficulties of interpretation and evaluation of the results of various techniques remain; but recent efforts are directed towards application of factor analysis to ordination of vegetation (Goodall 1954b, Hughes and Lindley 1955, Dagn~lie 1960, Greig-Smith 1964, Groenewoud 1965a, Austin and Orloci 1966, Orloci 1966, 1967, Goff and Cottam In press). Cattell (1965a,b) gives a detailed account of factor analysis and its role in biological research. GoodaIl, Hughes and Lindley, and Dagn~lie explore the use of factor analysis to analyze matrices of correlation coefficients. Greig-Smith reviews various methods of factor analysis. Recent efforts center on a variant of factor analysis known as principal components analysis which identifies sequentially the major axes of variation in a matrix of coefficients of community relations. Groenewoud (1965a) compares principal component analysis of two different correlation matrices. One of these is compared with an ordination using the Bray and Curtis method. He also explores the possibilities of classifying the ordinations produced by the principal components analysis. In one set of communities he finds clustering, in a second, larger, set he finds no indication of clustering (i.e., a continuum). Groenewoud proposes the combination of an ordination technique and a classification technique based on the ordination. Austin and Orloci (1966) compare a principal components ordination with a Bray and Curtis ordination and with a perpendicular axis ordination based on the Euclidean distance and constructing perpendicular ordination axes. They note that principal component analysis produces an ordination with more restricted continuity than the Bray and Curtis technique. Orloci (1966) compares principal components ordination with his own position vectors technique and the perpendicular axis ordination proposed by Austin and Orloci (1966). The principal components analysis is the most efficient but takes longer to compute than the position vectors technique. He comments that ordinations based on quantitative (frequency) data and qualitative data are different, the former being more revealing of gradients and discontinuities. Orloci (1966) also notes that the correlation coefficient and variance-

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covariance which are satisfactory when used in analyses of communities on the basis of correlations among the species are less efficient when applied to analyses of species on the basis of the correlations among the communities; the first ordination axis does not represent the maximum variation. He proposes a weighted similarity coefficient which accounts for the maximum variation in the latter. Orloci (1967) ordinates centroids of clusters of communities, defined through a classification technique, by a principal components analysis. Goff and Cottam (In press) compare a sequence of species position index values derived from five ordination techniques, including principal components, and find them similar. Studies using the Bray and Curtis and similar techniques have commonly been interpreted as supporting the continuum concept. Looman (1963) is an exception. When quantitative values of species are plotted on the gradients in one-, two-, or three-dimensional ordinations, the distribution of species is represented by curves, polygons or circles, and spheres respectively and the distribution resembles an intergrading series of curves, circles, or spheres, each with independently determined positions. The first axis according to Bray and Curtis (1957), for example, shows a high correlation with the earlier linear continuum for the same deciduous hardwood forest communities (Curtis and McIntosh 1951). In the two- and three-dimensional representations based on axes constructed in the various ways described above, the centers of species distributions derived from the ordinations of communities are individualistically distributed, no species occupy exclusive areas, and distinct clustering of species is not apparent. The patterns of species are ordered in respect to the several axes, the populations commonly tapering away from a center of maximum density to approximately concentric areas of lesser abundance. The phytosociologically determined gradients are usually correlated with one or more environmental factors or factor-complexes. The continuum is more recently represented as a multidimensional pattern of environmental and vegetational gradients more amenable to ordination than classification. Greig-Smith (1964) comments that evidence from ordination studies " . . . points increasingly to the individualistic viewpoint of the community as being more satisfactory." THE CURRENT STATE OF THE PROBLEM The individualistic hypothesis and continuum concept have been variously assessed and criticized. At worst they have been simply ignored (Braun-Blanquet 1964). Contrary to the early tendency to see the continuum concept and the community-type hypothesis as mutually exclusive, they are viewed more recently as simply a matter of preference or even as complementary. Numerous statements suggest that there is no real conflict between the continuum concept and classification. Oosting (1956) notes that such opinions have inhibited but little the use of systems of classification. Becking (1957) says: "There is no real incompatibility between the concept of the continuum and that of discontinuity (ZM). Authors of the ZM School grant that associations intergrade extensively." He attributes the differences to personal preference, research objectives, and methodology. He suggests, however, that Vries (1953) and Vries,

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Baretta, and Hamming (1954) provide mathematical proof for discontinuity of grassland communities when, in fact, Vries says: "Yet one sees practically everywhere connections, though they are not so pronounced everywhere. This does not indicate, in my opinion, that plant communities conceived as combinations of species are sharply delimited in nature." Martin (1959) comments that forests exhibit a little of both concepts and therefore he says it is unfruitful to debate the point. Selleck (1960) notes that classifications and ordinations can coexist. Hanson and Churchill (1961) say that gradual transition does not invalidate abstract classification but requires recognition of more classes. Egler (1954) points out that recognition of numerous categories of variation and subdivision in a community is only a step from the idea of continuously varying vegetation. Krajina (1961) attributes the contradiction to an apparent misunderstanding. Major (1961) states that the difference between these views is a question of degree: "All users of continua do recognize some units; all users of associations do recognize some transitions." Kendeigh (1961) says the two concepts are not incompatible. Ponyatovskaya (1961), translated by Major, indicates no necessarily absolute contrast between them: "In the future a more complete development of the two trends must take place through further synthesis of both" (i.e., thesis-antithesis-synthesis). Ovington (1962) states that the ecosystem concept can encompass the continuum but does not exclude classification. Rowe (1960) and Poore (1962) emphasize the utilitarian advantages of classification. Poore (1964) regards both concepts as extreme and ideal. Goodall (1963) provides a balanced discussion of the three apparent antitheses: 1) classification and continuum, 2) individualistic and integrated community, and 3) continuous intergrading in the field and distinct boundaries. He suggests that none of these are mutually exclusive but any of the alternatives may be applicable in degree. Looman (1963) indicates that the gap between the continuum and the Zurich-Montpellier approach is not so wide as it may appear to be and emphasizes the possibilities of bridging it. Lambert and Dale (1964) suggest that the differences between the two views are based on a misunderstanding as to the nature of vegetation and propose an approach which defines "noda" as basic vegetational units and effects a compromise between the opposing concepts of vegetational continuum and discrete communities. Spurr (1964) says that there is little justification for either extreme view. Watt (1964) cites the apparently polar views of Gleason and Clements and searches for common ground as a basis for rapprochement and a new working hypothesis by injecting Gleason's views with those of Clements. Aleksandrova (1965) comments that the continuum is not incompatible with recognition of uniform phytocoenoses connected by continuous transitions. Anderson (1965b) asks, why all of the " . . . controversy over a non-existent problem ?" According to Anderson, neither approach is better nor more correct but the choice depends upon the purpose of the investigator. However, he notes an acid test of methodology: the extent to which it aids in understanding the ecological complexity of the biosphere. It is just this acid test which makes the choice of methodology dependent upon something other than the purposes of the investigator. The acid test is whether there are

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some methods which elucidate the complexities of vegetation and its relationships to the environment more effectively than others and which are more productive of insights into ecological problems. The test must be a public one, not simply the satisfaction of the investigator. The fact that it is convenient to recognize community-types for forest or grassland management, classification or mapping, or filing and data recovery purposes is simply irrelevant, as noted in the introduction. It is eminently true, as Goodall (1963) emphasizes, that ordination methods and continuum concept are not inextricably linked. Continua can be classified if heterogeneous (see below) (Curtis 1959, Goodall 1963, Lambert and Dale 1964); ordination methods will reveal discontinuity as well as continuity. Groenewoud (1965a) ordinates and then classifies; Orloci (1967) classifies and then ordinates. Much of the mitigation of the differences between the opposing views cited above, however, does little to bridge the gap of understanding. This incorporates differences in the understanding of vegetation as an object of study and of the nature and purposes of the scientific study of vegetation. It is difficult to see no incompatibility between the concept of the association of Becking (1957) or Looman (1965) and the continuum of Bray and Curtis (1957) or Whittaker (1956). Poore (1956) and Daubenmire (1966) agree that vegetational variation is continuous but assert that something produces well-marked communities. Poore (1962) equates the objectively selected end stands of Bray and Curtis with his subjective noda, but Bray and Curtis use the end stands as "sighting points" to which the rest of the vegetation is related; this remains an undeveloped prospect in Poore's approach. Daubenmire's "typal communities" are predicated upon intuitive selection of representative stands of a monodimax, stable community. The noda of Lambert and Dale (1964), although quantitatively defined by a rigorous statistical method, now replaced by an improved method (Williams, Lambert, and Lance 1966), do not effectively result in a compromise as Lambert and Dale had hoped. General consideration of the continuum concept and development of newer methods of analysis of vegetation date only from the nineteen-fifties. Attempts to study vegetation using various techniques of multivariate analysis and information theory and adequately exploiting the computer have barely begun. There is much to be done to clarify issues which divide the proponents of the opposing hypotheses. Disputes between them have often been based on a lack of common understanding. It is not necessary to anticipate an ultimate acceptance of either hypotheses, or of any methodology as optimal, but it seems premature to declare no contest until the contest has been held on the same field with some common ground rules. GEOMETRIC MODELS

Discussion of vegetation is replete with expressed or implied analogies which illustrate the author's point of view, although they do not necessarily lend credence to his position. One of the grand old analogies of ecology is that of the community as an organism or quasi-organism, suggesting that the community has the integration and unity of an individual organism and that vegeta-

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tion is comprised of individual, discrete communities (Cain 1939). Vegetation is sometimes described as a mosaic (Watt 1947, Jenny 1958), implying that it is composed of discrete, clearly bounded areas (tessera) in a repeating pattern. A recent usage carries heavenly implications likening communities to constellations (Vries, Baretta, and Hamming 1954) or galaxies (Poore 1956, Goodall 1963). The implied clustering of groups of communities, distant from other groups, suggests a satisfying discreteness and ease of recognition that, unfortunately, is not commonly encountered in studies of vegetation on earth which, as Webb (1954) says, hovers between the continuous and discontinuous. Poore (1956) also uses the analogy of a net, the knots or intersections suggesting a cluster of typical communities in a regular pattern which can be used as base points or "noda" to which other less frequent or less well defined communities may be related. Vegetation has been visualized as a spectrum (Brown and Curtis 1952, Webb 1954), suggesting unbroken continuity, the communities being designated by a quantitative unit or wavelength. Unfortunately this analogy implies a linear sequence appropriate to the early continuum analysis but inadequate for multidimensional representations. Hanson and Churchill (1961) use an analogy of youth and old age to suggest classes of vegetation, which also implies a satisfying dichotomy. Williams and Lambert (1961) use the analogy of a painting, the pigments representing plant species but the important characteristics of the vegetation residing in the relationships of the colors and forms, e.g., in the matrix of correlation coefficients. The weakness of this analogy lies in the school of painting one envisions, whether classical, impressionist, modern geometric, or pop art. An analogy is a kind of verbal model (Forest and Greenstein 1966) which attempts to convey an enlightening insight into the vegetation in terms of something else which is presumably more familiar and more readily understood. Ordinations are geometrical models of the set of relationships between entities such as communities, species, or habitat complexes. The entities which are ordinated, "ordinants" in the sense of Goff and Cottam (In press), are conceived as points in one- to multidimensional geometrical models, their spatial relations representing their ecological relations. The aim of the model is to simulate the relations between the ordinants. It is not clear that a set of points in a volume of vegetational space will prove satisfying to some ecologists as a definition of a concrete association (Goodall 1963) but it may be regarded as such. Geometric or other mathematical models do not represent reality but rather an abstract space interposed between reality and the model which Nooney (1965) calls "imagery." In effect, the model attempts to translate an abstraction into mathematical terms. The issue is not whether the model fits reality but how well it fits a hypothesis about reality. The model must be consistent with respect to mathematics but its worth depends on its compatibility with our verified knowledge of vegetation. In all but the simplest examples the geometric model is a much simplified version of the actual matrix of relations. Goodall (1954a, 1963, 1965b) and Groenewoud (1965a) discuss the ecological interpretation of geometric models. It is around these, their construction, and their interpretation,

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that much of the recent discussion of the continuum versus the community-type concept of vegetation revolves. The crucial problems of ordinations as geometrical models are the basis of their construction, the identification of one or a few variables (axes), and the interpretation of the resultant distribution as it relates communities and environment (Bray and Curtis 1957, Beals 1960, Poore 1962, Goodall 1963, 1965b, Groenewoud 1965a, Austin and Orloci 1966, Orloci 1966). The geometrical model is an abstract space. Like the continuum, it does not have a direct connection with a physical vegetational space. The vegetation may be considered as the set of points or vectors in the vegetational space if the dimensions are the species encountered (Goodall 1963, Groenewoud 1965a). If quantitative data are used, an infinity of possible points exists in the abstract space. If the points representing concrete communities are uniformly distributed in such a space they would constitute a continuum and no classification or, indeed, ordination would be possible. Goodall notes that not all portions of the space are in fact equally filled, since the continuum as generally understood is a limited area of vegetation space. A continuum is expre3sed in a model by a single cluster of points representing the continuously changing communities. If these points form a single hyper-ellipsoid clu_~ter, this constitutes a continuum and the major axes can be determined. If points are clustered in several groups in limited portions of the abstract space without intermediate points, community-types may be identified. The galaxy analogy is most suggestive here. If the dusters of points are viewed as galaxies and the ratio of intragalactic distance (i.e., diameter) to intergalactic distance approximates the one to twenty ratio of galaxies in space, then the discontinuity would be most satisfying. Goodall (196%) notes that the identification of communities will depend upon the range of communities examined. A limited number carefully selected may produce reasonably distinctive clusters. As the range of communities included is increased and intermediate points appear, the distinctiveness of the clusters will disappear. If the clusters are closer than the galaxy analogy suggests, points in adjacent portions of two clusters may be clo~er to each other than they are to points in the far side of their own cluster. Poore (1962) says that points representing communities must be distributed at random in order to demonstrate a continuum (cf. Ivimey-Cook and Proctor 1966). This is not so. Goodall points out that the entire multidimensional space can be described as a continuum but it does not follow that all portions will be represented by vegetation. Curtis and McIntosh (1951) note that not all possible combinations are realized, only some (Juhfi.sz-Nagy 1964). Hence, actual vegetation in being may be represented by points which occupy only a limited portion of the model. If these are not aggregated into clusters the vegetation may be said to constitute a continuum. The difficulty lies in determining what constitutes clustering. Poore (1956) notes that communities in the continuum are not uniformly distributed; quite apart from questions rising out of techniques of construction of the model, it is not clear that they need be. Certainly some species combinations may be more frequent in an area than others. Hence it may be that certain sections of a geometric model will have more points and intermediate

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areas fewer. Is the location with fewer points to be regarded as having less biological validity? k may be that site conditions in the study plot are unequally represented or, by chance or choice of the investigator, only limited portions of the extant vegetation are sampled. The choice is commonly justified by assertions that only climax, stable, homogeneous, or widespread communities should be studied but such choices may be expected to produce more or less discrete clusters. Chance is more difficult to assess. If one visualizes a geometric model in which the points represent combinations of trees and herbs characteristic of the oak openings (savanna) of the midwestern United States, the disposition of points in a geometric model is no more fixed than is the vegetation. At the present time the combination of trees and prairie herbs characteristic of oak openings is poorly represented on the ground; but oak forests are relatively well represented. Hence the model would suggest a clustering of numerous points representing oak forest and only a sparse scattering representing oak opening. One hundred years ago oak openings were much more widespread (Curtis 1959) and oak forest less so. The distribution of concentration in the cloud of points would have changed markedly as a matter of historical accident. The relative incidence of points is not, as Goodall (1963) suggests, an effective guide to discrete community-types. That some areas of a model are somewhat more densely filled with points representing actual vegetation than others can be accounted for on a number of grounds, none of which lend credence to any particular area of more dense point concentration as having more claim to constituting a community-type than another area of less dense point concentration. If a space corresponding to impossible species combinations interrupts the cluster of points it can be regarded as a discontinuity. It may be said that the oak openings and forests are neither homogeneous nor stable and that the vagaries of the point cluster are simply a consequence of inappropriate selection of communities for study. These along with prairie have been the dominant vegetation over thousands of square miles for extended periods of time and the selection of putatively stable or climax communities for study would, even if possible, leave out of account the majority of the vegetation of the region. CONTINUITY AND HOMOGENEITY Goodall (1963) suggests two reasons for differential distribution of points in geometric models: 1) more frequent occurrence of particular site conditions, and 2) greater stability of certain species combinations. The first creates no particular problem from the individualistic or continuum point of view. It is generally recognized that relatively similar habitats may have relatively similar communities. If certain site conditions are absent from the study area, are less frequent or simply less frequently sampled, the resultant cloud of points will represent this. The second is the basis for much difference of opinion regarding the continuum concept. The traditional view of the community-type emphasizes the existence of homogeneous and presumably stable communities. Goodall (1952) interprets this view as requiring homogeneity as the first criterion for a community. Dahl and Hada~ (1949) consider more or less homogeneous com-

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munities recognized by the trained eye of the plant sociologist (of. Lambert and Williams 1962). The difficulty is that there is no agreement among plant ecologists about the measurement or estimation of homogeneity or even its existence. It is not possible here to review the extensive literature on homogeneity (Goodall 1952, 1954b, Greig-Smith 1964, Wright 1965). The lack of a common understanding of homogeneity is, in part, the reason for the lack of meeting of the minds noted at the International Botanical Congress at Montreal (Major 1961). Major, reviewing the differences between the community-type and continuum concepts, comments that he has been driven back to the stand of vegetation as the fundamental unit and that we need data from homogeneous stands of vegetation. Gounot (1961) asserts that the study of homogeneous units must precede a test of the continuum. Poore (1964) calls for a measure of homogeneity as one of the important requirements of ecology. Daubenmire (1966), in an essay critical of the continuum concept, emphasizes that his study sites are of maximum homogeneity and in a pristine and stable condition. He calls for recognition of "potential" homogeneity. Cottam and McIntosh (1966) assert that this cannot be done. Whittaker (1956) comments that it is impossible to demonstrate homogeneity in plant communities by statistical means, and few studies attempt statistical assessment of homogeneity of communities. Representations of homogeneity such as Raunkiaer's "law," although dearly useless, keep rising like the Phoenix (McIntosh 1962). Curtis and McIntosh (1951) and others (Curtis 1959) use chi-square to test for homogeneity of the common dominant trees in forest studies. Goodall (1961) evaluates an Australian scrub community for homogeneity and finds none. Poore (1962) and Greig-Smith (1964) comment that Goodall's samples are taken from a single community and suggest a test of his approach in more diverse vegetation. Wright (1965), using Goodall's variance method, finds evidence of homogeneous vegetation in two physiognomically different areas of the Sonoran Desert. Some critics of the continuum suggest that continuity is an artifact given by the incorporation of heterogeneous communities into the study (Poore 1962, Daubenmire 1966). Poore contrasts the relative uniformity of the sites of Dahl (1956) with the fifteen acres used by Curtis (1959) for forest stands. This seems an unwarranted comparison since DahI studies snow-fieId vegetation at a grossly different scale of plant size and spacing. Frequently proponents of intuitively recognized homogeneity are dealing with small-scale vegetation where it is possible to stand in it and obtain a bird's-eye view. Those working in largescale vegetation, particularly tropical forest, are less likely to recognize homogeneous units on subjective grounds. In any event, criticisms of continuum interpretations based on size and lack of homogeneity of forest communities do not apply to the studies in grassland and other small-scale vegetation (Curtis 1955, Gimingham 1961, Anderson 1963, Gittins 1965a). The methods of Goodall (1953a) and of Williams and Lambert (1959, 196i) accept heterogeneity as commonplace if not universal, and are designed to abstract relatively homogeneous groups by objective statistical techniques. Lambert and Dale (1964), incorporating the views of Williams and Lambert,

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regard the concept of the continuum as having little value. They state that equating heterogeneity with discontinuity has caused confusion among ecologists. According to Lambert and Dale, continuity in the statistical sense requires that all communities contain the same species, i.e., communities are discontinuous if differing by one species. They provide an alternative definition in the terminology of set theory by which vegetation is discontinuous only if the communities have no species in common. Neither definition is, as the authors note, particularly useful and they urge that the idea of continuity be replaced by heterogeneity. Williams, Lambert, and Lance (1966) refer to "rather continuous data (as is frequent in ecology)" and "more continuous vegetational data," implying degrees of continuity, although it is not clear that this usage adopts the earlier definition given by Lambert and Dale. It should be noted that they are using homogeneity in the sense of similarity, not in the sense of spatial homogeneity (Greig-Smith 1964, McIntosh, In press). A statistically homogeneous vegetation is necessarily continuous and communities selected in it would produce a hypersphere of points in a geometric model (Goodall 1963, Groenewoud 1965a). Such a hypothetical continuum does not exist in vegetation and would be useless if it did. A heterogeneous vegetation may be discontinuous or continuous. A vegetational continuum is defined (Curtis and McIntosh 1951, Whittaker 1951, 1956, Curtis 1959) as a continuously changing series of communities and is quite unambiguously heterogeneous. It is possible for communities at the extremes of a continuous series to be florisfically completely unlike. It is also possible for floristically identical communities to form a continuous series by reason of shifts in proportions of species. Odum (1959) comments that a continuum does not continue indefinitely; sooner or later, he says, a different set of plants and animals is apparent. He refers to this as a natural discontinuity. The individualistic hypothesis and the continuum concept agree that one set of organisms may be replaced by another on a gradient. The problem, however, lies in whether changes in a series of communities are abrupt or gradual, i.e., continuous or discontinuous. It is true that the proponents of a continuum do not define the meaning of continuous in a rigorous mathematical sense. It is not clear that such a definition is useful in an ecological context. The vegetational continuum as a series of stands positioned on a gradient of environmental values or of weighted community values is a continuous series since the community can take any measured or calculated position even though the species data may be qualitative and discontinuous in Lambert and Dale's sense. Ecologists using the term continuous infer gradual changes in proportions and combinations of species. Discontinuity infers a local steepening of the gradient, indicated by abrupt and coincident changes in the quantity or kinds of species. Identification of discontinuity by the absence of a single species is, in a sense, trivial since it follows by definition and is unassailable. Discontinuities in an ecological sense as breaks between community units must be defined by more than one species and the geographic ranges and ecological amplitudes of the several species should coincide. Qualitative data has a built-in discontinuity, a species is either present or absent, i.e., 1 or 0. The interpretation of absence as a zero value, however, is

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not uniform. Greig-Smith (1964) regards it as essentially the lowest of a continuous series of quantitative values. Lambert and Dale (1964) disagree, holding that zero or absence is distinctively a qualitative value. Absence is quite explicitly zero if the investigator has a complete census of the community. However, if he is dealing with a sample of the community, absence is dependent upon sample size and number. Goodall (1954a) comments that presence or absence can be interpreted as an index of value of a continuous variable. CLASSIFICATION AND ORDINATION

The relative merits of methods of ordination and classification and the validity of what they demonstrate about the nature of vegetation have been discussed at length. Daubenmire (1960, 1966) contends that the ordination methods of Curtis and McIntosh (195I) and of Whittaker (1956) create an artifact of continuity by inclusion of heterogeneous, unstable, and seral communities and the use of " . . . methods of analysis or of subsequent data manipulation that can completely determine the nature of the conclusions reached." Using data from only "pristine," "stable" communities of "maximum homogeneity," Daubenmire asserts that he shows vegetation to consist of distinctive "typal communities" which can be readily classified but which are lost upon disturbance. The problem resides in the identification of the communities which are pristine, stable, maximally homogeneous, and which, presumably, represent the climax, and in the interpretation of the qualities of homogeneity and stability. It would appear that such selection not only determines the nature of any conclusions reached but in fact follows from conclusions already reached. Poore (1962) comments that the Bray and Curtis method of ordination demonstrates that vegetation can be treated as a continuum, not that it is a continuum. According to Poore, the appearance of continuity is given by lack of uniformity of communities, methods of sampling, incorporation of successional communities, and methods of analysis. Poore, like Daubenmire, says that he omits unstable, fragmentary, heterogeneous (mosaic), and ecotone communities, and he emphasizes subjective selection of communities classified as "noda." Looman (1965) asserts that vegetational continuity is '*exclusively successional" and that discrete pioneer associations converge on a monoclimax. He makes a peculiar distinction between continuity which is seral and "overlap" which is continuity between habitat types. In the latter, the continuity is recognized but it is subject to steeper gradients at certain points of a habitat factor or complex (trigger factors). This is similar to Daubenmire's (1966) recognition of continuity but with plateau-like areas separated by areas of steeper gradients. Presumably the vegetation changes abruptly at the latter and only slightly on the plateau-like areas of the gradient. Daubenmire, Looman, and Poore hold that classification and the kind of continuity they envision are not contradictory, and Looman uses methods ranging from those of the BraunBlanquet school to those of Bray and Curtis. Looman (1965) provides a definition of association which he claims will, with methodological adaptations of the Braun-Blanquet system, make possible a "universally valid classification." Daubenmire, Looman, Poore, and others (Williams and Lambert 1959, 1961,

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Hanson and Churchill 1961) urge classification as the most effective and even necessary or exclusive means of analysis of vegetation. Poore (1962) develops a method of vegetation analysis called "successive approximation" of which he says: "Its principles are the same as classification and the method, if applied extensively, leads inevitably to a classification of the phenomena being studied." The analogy is frequently brought to bear on the problem. Poore (1962) notes the advantage of distinguishing between hot and cold; Hanson and Churchill (1961) use youth and old age. Unfortunately, none of these criticisms of the continuum concept or ordination methods consider the full range of data and technique which have been used to support it. It should be noted that continuity is not restricted to seral communities, as is explicitly asserted by Curtis (1955, 1959) and Whittaker (1956). Methods of classification and ordination have sometimes been regarded as mutually exclusive and linked respectively with the community-type concept and continuum concept. The methods are not always so clearly demarked. As noted earlier, an initial classification may lead to an ordination (Curtis and McIntosh 1951, Curtis 1955), an ordination may be classified arbitrarily into segments (Curtis 1959, King 1962), or a more involved sequence of classification and ordination procedures developed (Ream 1963, Groenwoud 1965a, Orloci 1967). Goodall (1963) and Greig-Smith (1964) consider ordination and classification methods and agree that they are not necessarily incompatible. Goodall, GreigSmith, and Groenewoud suggest that ordination is preferable as an initial procedure. Lambert and Dale (1964) agree that ordination and classification are not mutually exclusive as methods, but take the opposite viewpoint of their utility as an initial procedure on the grounds that most vegetation is heterogeneous and ordination methods computationaIly cumbersome. It is not clear that ordination methods are generally more cumbersome than classification methods or less appropriate for heterogeneous vegetation. Both are in such a state of flux that it is difficult to make effective comparison. It also appears that Lambert and Dale misread Greig-Smith in saying that he implies that classification is the most generally useful method. Greig-Smith says that the results of an ordination "may conceivably indicate" that this is so. It is unlikely that proponents of classification by any of the traditional phytosociological methods and premises have much sympathy with newer approaches to objective, numerical classification techniques. Some clearly would say, with the Duchess in Alice in Wonderland, "Oh, don't bother me; I never could abide figures." Both groups adopting a classification approach, however, express doubts about the premises, utility, or methods of the continuum concept but on quite different grounds. Proponents of the continuum concept share with developers of numerical methods of classification a common view of objective sampling and a preference for quantitative methods of analysis of vegetation as distinct from subjective classification. Lambert and Dale (1964) suggest that persons favoring the community-type concept propose classifications, those favoring the continuum concept adopt ordination methods. The community-type hypothesis is one with the tradition of subjective classification, but proponents of objective classifications (Goodall, Dagn~lie, Harbert, Hughes, Williams,

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Lambert, Dale, etc.) hold no brief for classifications of this kind, A preference for classification is built into any methodology which starts witb subjectively recognized communities as parts of an abstract entity or uses a methodology which can produce only a classification. The genesis of the continuum concept is not so clear. In some instances it derived from initial classifications in which boundaries were difficult to ascertain. Ordination methods were generated as a secondary consequence of failure to find an effective basis for classification rather than an initial preference for continuity. After various initial successes, personal choice may have operated in the selection of ordination methods in preference to traditional classifications. In certain schools of phytosociology classification is an end in itself, the aim being a taxonomy of vegetation. A similar point of view is expressed by proponents of objective, numerical methods of classification who have little else in common with the traditional schools of ecology. There is no assumption by the latter group that there is one generally applicable or universal classification. Lambert and Dale (1964) comment that classifications should be produced quickly and efficiently in relation to particular regional problems and then be discarded once their purposes have been served. Williams, Lambert, and Lance (1966) comment that choice of methods is dependent more upon the convenience of the user than on preconceptions as to continuity or discontinuity: if the prime requirement is to produce vegetational units which can be used for mapping or description, then classificatory methods are more applicable." They note that a particular classification technique may not work well on "more continuous vegetational data." It is true that a method of vegetation analysis will be judged by how well it achieves its end. If vegetational types are the desired end then classification methods may be most effective. A continuum, being intrinsically heterogeneous, can be arbitrarily classified or can be objectively classified by the association-analysis methods of Williams and Lambert9 Ivimey-Cook and Proctor (1966) suggest a number of limitations in the classifications so produced and compare the results with those produced by traditional phytosociological methods. They suggest that association-analysis is a mechanized technique comparable to the intuitive mental process of recognition of characteristic species "Kennarten." It is difficult to see that these methods effect a compromise between the opposed concepts of the vegetational continuum and the traditional community type (Lambert and Dale 1964). They do provide a third alternative of an objective method of producing dear-cut classifications using qualitative data and statistical methods appropriate to this type of data. Greig-Smith (1964) comments that the important difference between communities lies in the amounts of different species. It is certainly easier to classify by considering only qualitative data because presence or absence alone provides an inherent discontinuity. When quantities of the species are considered it is more difficult to establish classes on the basis of the continuous variables which are introduced. Much remains to be done in clarifying the use of qualitative and quantitative data of various kinds in the newer objective methods of classification and ordination and their effect on the resultant ecological interpretations. 9

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The newer numerical classification methods have been interpreted in some quarters as being more efficient than ordination techniques. What seems apparent is that the newer methods of both classification and ordination are still in a state of development which requires that judgment be withheld. Lambert and Date (1964), for example, reviewing the basic methods of numerical classification, comment that subdivisive methods are to be preferred on theoretical grounds. Williams, Lambert, and Lance (1966) compare the results of association-analysis (a subdivisive-monothetic method) with information-analysis (an agglomerative-polythetic method), and find the latter to be greatly superior. West (1966) develops a system of classification based on the Kulczynski similarity coefficient and using cluster analysis by the weighted-pair method (Sokal and Sneath 1963). Coefficients are determined between highly similar community pairs and then between these and other communities forming progressively more inclusive (i.e., less similar) groups. This produces synecological units he calls "coenons." West plots populations of several species along the sequence of communities in his dendrogram and comments that they do not yield bell-shaped curves like those commonly represented in continuum diagrams. Since the dendrogram is not designed to ordinate stands, there is no reason to expect such curves. Sokal and Sheath comment that the abscissa of a dendrogram has no special meaning, merely separating the original entities which are being classified. A common difficulty of classification methods is that they do not show the relationship of the groups which are produced by the classification. Orloci (1967) develops an agglomerative method for classification of plant communities which can be used with either qualitative or quantitative data, unlike information-analysis which uses qualitative data only. Following classification, Orloci ordinates the centroids of the classification units produced. A major problem raised in recent discussion of vegetation analysis is whether the results of such studies demonstrate anything about the nature of vegetation. Williams, Lambert, and Lance (1966) assert that the best criterion for selecting a method is that it serve its purpose. If the user wants to classify he selects a classification method, if he wishes to ordinate he uses an ordination method. In the few comparisons of numerical classification and ordination methods available (Gittins 1965c, Gimingham, Pritchard, and Cormack 1966), the basic ecological interpretations are substantially the same. However, these comparisons are based on ordination and classification methods which are dated. It appears that the methods of ordination which have been most extensively utilized in developing the continuum concept are now being supplanted by other and more sophisticated methods of ordination, none of which have been extensively utilized in vegetation studies to date. Methods of numerical classification have been developed rapidly in the past decade but none extensively applied to diverse vegetation. Williams and Dale (1965) review methods of numerical classification, some of which have been applied to ecological data, and clarify the distinctions between them. ASSESSMENT

The main difficulty in selecting among ordination or numerical classification methods or making a choice between them is finding the most effective ways of

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assessing their worth. Nooney (1965) suggests criteria by which mathematical models must be judged (cf. Forest and Greenstein 1966). They must have consistency, tradition, and computability with respect to mathematics. These attributes are difficult for most ecologists to judge although effort or cost of computability may influence his choice. It is perfectly clear, however, that mathematical elegance per se is of little worth to the ecologist. He is more interested in the other criteria of judgment, namely validity, generality, and prediction ability with respect to ecological reality. This does not infer an absolute reality, only an image or theory of that reality which must conform to the observable facts of the ecological situation. It may be accepted that objective classifications, in the sense they are considered by Goodall (1963) and Lambert and Dale (1964), and ordinations are not mutually exclusive and may, in fact, be complementary. It does not, however, seem desirable that the assessment of results of ecological methods be primarily utilitarian, e.g., mapping. The basis of choice is not easily discernable, even as between similar methods. Williams, Lambert, and Lance (1966), for example, revert to the "acid test" of ecological interpretability and suggest two alternative methods for comparing the results of analyses produced by different methods of classification. One compares the results of two or more analyses with interpretations based on prior ecological experience. The second, which they elect, erects an intuitive classification and compares the results of the analyses with the groupings of the intuitive classification. Essentially, quadrats and species are catalogued on the basis of prior experience into "standard units." Uncertain or ecotonal situations are left uncategorized. The groups produced by each analysis are compared with the standard units. If a group incorporates at least one-half of the total number of the standard units of one type before a mistake is made and a unit of another type is included, it is recognized as a standard grouping. This demonstrates that groupings can be formed and that these coincide with and may elaborate on predetermined groups. It is not clear what residuum remains uncategorized. Williams, Lambert, and Lance do not consider justifiable the effort of attempting an external measure to compare the ecological significance of several analyses. Validation of a phytosociologically based classification or ordination usually hopes to relate it to environmental variables, preferably independently analyzed. Very few attempts have been made to do this. Loucks (1962) attempts to relate independently derived ordinations of environment and communities. There has been extensive work on development of numerical methods of classification, but relatively little assessment of these in an ecological sense. Ordination methods have not been so extensively developed but the spectrum of methods available has been applied in much more extensive and diverse ecological situations. Evaluation of the efficacy of methods is an important aspect of current work in vegetational analysis. It is also important that these be directed effectively to increased understanding of ecology. The function of a classification, whether of the traditional kind or the more recent numerical type, or of an ordination is to arrange or organize a set of observations and to seek meaningful patterns of relationships. The classification or ordination is essentially an explanatory device to elucidate a large mass of

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observations whether qualitative and subjective or quantitative and objective. The major problem which currently faces the ecologist is selecting the most meaningful from among the diverse types of models of vegetation, constructed with different data inputs. The ecologist must not be forced into a mold created by abstract mathematics but the various models, mathematical and otherwise, should serve to sharpen his critical judgment of ecological concepts. Many different constructions can be imposed upon a given set of raw data. A model, unlike a poem, is not just to be. Its function is to mean and it takes on meaning only in the context of a theory. The community-type hypothesis and the continuum hypothesis may not be the only possible bases for a vegetational theory. They both need clarification and to be related to other ecological theories. Gause (1936) asks: "Why are intermediate combinations of organisms impossible under intermediate conditions ?" Watt (1947) refers to Gause's demonstration that certain species live together in stable combinations only in definite proportions. Hutchinson (1953) considers the production of discontinuous biological zonation on a continuous environmental gradient. Becking (1957) and Hanson and Churchill (1961) assert that competition between species creates communities more sharply defined than the environment. It is sometimes inferred that entire communities may compete with other communities (Odum t956, Odum, Cantlon, and Kornicker 1960, Buell and Martin 1961). Wells (1960) considers that there is considerable evidence for continuum-type gradations within vegetation of a similar physiognomy, but suggests a sharp transition between climax vegetation types of different physiognomy enforced by competition of the dominants. Whittaker (1956, 1964), however, comments that steep transitions between communities occur but are exceptional and are not based on competitive exclusion. McIntosh (1963) and Whittaker (1964) call attention to the large number of situations in which species populations overlap broadly along a variety of gradients with gradual changes in density of species resulting in gradual and continuous change of community composition. Whittaker (1964) suggests that plants have evolved to produce a scattering of distributional centers in habitat-space and, by inference, in vegetational-space, producing intergrading species mixtures of species rather than clusters of associates. According to Goodall (1963), if a number of species tend to grow together they will create "a self-intensifying, self-accelerating" process, bringing pressure on other species to adapt and developing an integrated evolving community-unit. Theories of population dynamics are explicitly or implicitly involved in much of the discussion of the opposed views of community-type and continuum. Competition, the role of the dominant, the effect of disturbance upon vegetation are commonly introduced to support either position or to call for compromise. Goodall (1954a) and Anderson (1965b) assert that human disturbance and intensive selection over long periods give rise to sharp boundaries and more clearly differentiated vegetation types. Watt (1964) suggests that the control of the dominant is destroyed by disturbance (grazing), allowing more play for coincidence and fortuitous juxtaposition, inferring less well-defined communities. Daubenmire (1966) states that disturbance weakens discontinuities, and this in

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proportion to its degree, and that undisturbed vegetation consists of more distinctive types. The interaction of evolution and community organization referred to by Goodall (1963) and Whittaker (1964) is a frequently encountered theme. Bates (1960), noting limited progress in community analysis, states that ecology and evolution will have to blend completely, the function of ecology being to describe existing conditions, and evolution to explain how they got that way. Waddington (1961) comments: " . . . a fully comprehensive theory of evolution must see it as a series of changes in communities, and in the types of organisms which comprise them." Orians (1962) asserts that evolution seems to be the only real theory of ecology today, and comments that animal ecologists are adopting the community approach which has been intensively and extensively used by plant ecologists for decades. Baker (1966) calls for both ecological and evolutionary studies, suggesting that original associations become more coordinated and community homeostasis improves as these evolve. It is unfortunate that a distinction is commonly made between phytosociology and ecology (Egler 1954, Poore 1962, Whittaker 1962, Looman 1964, Walter 1964). Phytosociology, particularly in continental Europe, is usually regarded as community systematics and as distinct from ecology. Whittaker contrasts the literature of phytosociology with that of British ecology. Poore comments that the logical processes of community classification are distinct from their explanation. Many ecologists, particularly animal ecologists, have ignored phytosociology and its contribution to community theory. Elton and Miller (1934), on the other hand, note the need to relate the principles of classification of communities to those which govern population problems. Curtis (1959) says: "It is the task of phytosociology to describe the combinations of plants that do occur in each region of the world, to find how they came into being and how they maintain themselves, to relate them to their physical environment and to reach an understanding of the material and energy changes which occur within them." Theories of population dynamics and of evolution are increasingly being brought to bear on ecology and on community theory. Not infrequently these are used to make predictions about communities or their properties. The basic function of vegetational analysis is to assess the validity of such predictions and to test their ecological implications. These sometimes assert what should occur in nature. The effectiveness of a technique of classification or ordination or models derived from them is best judged by how it relates to concepts and models in related areas of population and evolution and how effectively it contributes to a theory of community organization. LITERATURE CITED AGNEW, A9 D. Q. 1961. The ecology of Juncus effusus L. in North Wales9 Jour. Ecol. 49: 83-102. 9 1962. A study of the oak forests of Gara Mountains, Mosul Liwa. Proe. Iraqi Sci. Soc. 5: 31-43. ALEKSA~DROVA,V. D. 1965. The problem of distinguishing phytocoenoses in a vegetative continuum. Bot. Zhur. 50: 1248-1259.

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