© 2000 by The Society for Integrative and Comparative Biology
Morphometrics in Development and Evolution1
1 Biology Department, EEOB Group, Box 90338, Durham, North Carolina 27708-0338
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Morphometric approaches facilitate the analysis of quantitative variation in form, typically becoming most useful for the study of organisms that have completed morphogenesis and are at differing stages of growth. Recent conceptual and technical refinements in the characterization and comparison of forms have joined methodological innovations in molecular biology, embryology, and phylogeny reconstruction to advance the study of the evolution of development. Among the phenomena that have recently been examined morphometrically are developmental integration and heterochrony, discoveries that in turn raise deeper questions about the connections among disciplines and among levels of description: the relationship between morphometric variables and characters, between phenomenology and process, and the interplay (and evolutionary relevance) of genes and phenotypes. Morphometrics can continue to play a vital role in evolutionary studies of development as its results generate questions both for its practitioners and for other sorts of biologists to explore.
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The subject we were invited to address in this paper—morphometrics—is not a concept (like modularity, homology, or evolutionary novelty), or a particular set of phenomena (such as evolutionary history, or metamorphosis, or HOX genes), but rather a tool: a means of extracting information about biological material and biological processes.
Tools are not often accorded a place of their own in a symposium such as this: neither the gel rig, the PCR machine, nor the technique of in situ hybridization have been given such attention, although their contributions to advancing evolutionary developmental biology are substantial. Morphometrics is a tool of a different sort, because while the information it yields is simple in format (quantitative variables), the subject to which it is applied—morphology—and the inferential process involved are complicated: explanations for biological form are multiple, complex, and reside at several levels in the biological hierarchy.
There are various ways to approach a review of this subject. One can detail the history of methods (as e.g., Bookstein, 1993,
has done in several contexts; see also Reyment, 1996; Marcus, 1990; parts of Gould, 1966, 1977). One can provide a catalogue raisonné of evolutionary developmental findings obtained with these methods, for which the reference list alone could fill our page allocation. One can focus on current controversies over interpretation—for which a nuanced understanding of both the methods and the biological issues is important. Without any hope of giving comprehensive treatment from any one of these angles, we will touch on each in an effort to outline current issues, while pointing to sources that provide more extensive accounts.
Defining terms
We refer here not to the union of two fields (all of developmental plus all of evolutionary biology), but rather to their intersection: i.e., evolutionary developmental biology.
Morphometrics is the quantitative characterization, analysis, and comparison of biological form. Themes central to morphometrics, quantification and morphology, are prominent in other fields that can be distinguished from it: statistics can be an important component of morphometric analyses, especially when the focus is on variability, or the distribution of variation in form among individuals. But morphometrics refers to more than just the application of statistics to the study of morphology, because it entails the characterization of form (or of differences between forms).
Because morphometrics deals with continuous variation, its focus in evolutionary developmental biology is on the changing magnitude, proportion, and spatial locations of existing features, rather than specifically on the origin of novel features of morphology during development. For this reason, morphometrics has been especially useful for examining and comparing stages of growth, once morphogenesis is complete and homologous features can be identified through successive stages.
Even so, the origin of novel features is not outside the purview of morphometrics on continuous variables. At one level of description, for example, the posterior lobe of the male genital arch in different species of Drosophila is qualitatively distinct: in D. mauritiana it is "fingerlike"; in D. simulans it is "helmet-shaped." Yet the distinctive breadth and the hooklike recurvature of the lobe of D. simulans can be captured by the same set of elliptic Fourier variables used to characterize the lobe of D. mauritiana, which lacks these morphological features (Liu et al., 1996). But why bother with quantification, when the verbal language of qualitative description is more widely accessible? From one perspective, data that permit categorical, qualitative distinctions yield the clearest results: it is when patterns and distinctions are subtle that one must resort to statistics.
What is gained from a quantitative description is precision in the ability (a) to recognize forms that are intermediate, (b) to judge degrees of proximity or similarity to other forms, and (c) to extrapolate or predict hypothetical, experimental, or nonexistent extremes. In the example mentioned above, the ordination scheme provided by applying principal components analysis to elliptical Fourier coefficients from digitized outlines of the posterior lobe in Drosophila places F1 hybrids, remarkably, directly in between the parental types of D. mauritianus and D. simulans; backcrosses fall in correspondingly intermediate positions. As a consequence, a univariate score can be associated with each morphology, and the genetic architecture of the trait (which may be subject to sexual selection, and is one of the earliest to diverge at speciation) can be examined through the mapping of quantitative trait loci (Liu et al., 1996).
The strength of these quantitative techniques is their ability not only to provide a faithful representation of the forms being examined, but also to aid discovery. A quantitative characterization is especially useful if it abstracts elements of form that turn out to be biologically important.
In a different example, using cusp tips as landmarks on seals' teeth, Jernvall (2000) found that variation in the positions of the three main cusps of a tooth predicts the absence, presence, and location of auxiliary cusps. This in turn provided a test of a patterning cascade model of tooth development organized by inhibitory fields.
It is the links in this path of inference, from raw data to patterns (as revealed by morphometric variables that are obtained in a morphometric analysis); from patterns to phenomena (such as morphological integration, heterochrony, or heterotopy); and from phenomena to causal agents (such as genetic linkage, chemical inhibition, and/or natural selection) that have raised the most questions, sparked the greatest controversy, and provided the field with its greatest scientific and intellectual rewards.
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Even "[t]he approach now referred to as traditional morphometrics or multivariate morphometrics is only a few decades old" (Rohlf and Marcus, 1993
, p. 129). Advances in the theory and application of morphometrics have been accelerated by technological advances in computing, which have allowed more complex manipulations to be applied more rapidly to ever larger sets of data.
Technical literature on morphometrics has burgeoned thanks largely to refinements introduced by practitioners of geometric morphometrics, who have also reviewed the history of their discipline both frequently and thoroughly (e.g., Bookstein et al., 1985; Rohlf and Bookstein, 1990; Bookstein, 1991; Richtsmeier, 1992; Marcus et al., 1993, 1996; Dryden and Mardia, 1998). Software and other information are freely disseminated on the web (http://life.bio.sunysb.edu/morph/), which has links to bibliographies with abstracts, and to list-servers inviting discussion of current issues.
In his "history of a method, not of findings," Bookstein (1993, p. 20) tied the current state of morphometric analysis to two distinct traditions: (1) the biometric, statistical tradition of Galton and Pearson, which applied the algebra of multivariate statistics (especially covariance matrices) to sets of distance (or area, angular, or volume) measurements taken on a sampling of individuals; and (2) more geometric approaches exemplified by the transformation grids of D'Arcy Thompson (1942), which preserve and analyze differences in spatial arrangements of landmarks.
Geometric methods, which are applied to data collected in the form of two- or three-dimensional coordinates of landmark points, have engendered particular enthusiasm because they allow recovery and visual display of spatial information that is not captured by sets of distance measurements. Moreover, the mathematical shape space within which the techniques of Procrustes analysis and the thin-plate spline operate readily accommodates the approximations required for use of standard techniques of multivariate statistics. Geometric methods can be subdivided into two main categories: methods of superimposition (including Procrustes analyses and what Bookstein refers to as the method of shape coordinates), and methods of deformation (including various attempts to quantify D'Arcy Thompson's transformations, Bookstein's technique of biorthogonal grids, the thin-plate spline, and certain applications of finite element analysis) (Dryden and Mardia, 1998). Methods of superimposition apply a global transformation (which affects the location, orientation, etc. of the entire figure) to map the landmark points of one form onto another, and report the residual variation for each point after this point-for-point mapping. By contrast, methods of deformation decompose the mathematical transformation into geometrically orthogonal components that affect different geometric scales. Deformations are shown as spatially continuous across the entire form, allowing one to visualize changes as affecting, and distributed across, the form as a whole, rather than applied to the landmark points individually. The geometry of a form may also be preserved in a series of coordinates that are not taken as individual landmark points with individual correspondence to single points on other forms, but rather represent a continuous outline. Curves (such as the trigonometric polynomials of elliptic Fourier analysis) may be fit to such an outline, and then compared through statistical analysis of their parameters.
Taking a different tack in focussing more on findings than on methods, we may segregate past studies according to biological subject. One can identify the roots of modern evolutionary developmental morphometrics in the study of two types of ontogenetically relevant patterns: (1) the ontogenetic trajectory, as illustrated by growth curves, and embodied in the allometric tradition of Huxley (1932; see also Gould, 1966, and caveats in Godfrey and Sutherland, 1995a, b), and whose evolutionary modification can sometimes be described as heterochrony (Gould, 1977; Alberch et al., 1979; Klingenberg, 1998); and (2) morphometric variability or covariance (Olson and Miller, 1958) assessed on samples of organisms at single stages of growth, and taken as indices of canalization, constraint, or morphological integration. The computational techniques employed by these two types of studies are not necessarily distinct, and the two subjects intersect where, for example, size or any other morphometric variable is considered a proxy for the time or stage of development, or where changing patterns of integration are examined through ontogeny. In the next section we briefly describe several examples of each of these two types of study. The choice is biased toward recent examples that illustrate creative ways in which morphometric techniques have been used to clarify evolutionary developmental phenomena that in turn can be placed in a broadly interdisciplinary explanatory framework.
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Ontogenetic trajectories for differing modes of growth
For objects like molluscan shells, which exhibit accretionary growth, as well for the overall form of a plant, where growth occurs by modular addition, the shape of the adult itself embodies its ontogenetic trajectory. Stone (1998)
used three different morphometric representations to compare a set of (hypothetical; simulated) gastropod shell morphologies: (1) He applied principal components analysis (PCA), a standard multivariate morphometric technique, to traditional morphological variables (heights, widths), thereby treating the shells as sets of static objects. (2) For another PCA he used the dynamic parameters (rates of whorl expansion, translation) from a mathematical model of the shell as a growing helix. (3) In a third analysis, the shell was examined in longitudinal section, and its ontogeny represented by a series of points arranged in zig-zag, each point occupying the center of a whorl sectioned at 180° intervals. The varying spatial configuration of these points (each configuration representing an ontogenetic trajectory) among different shells was then compared using thin-plate splines—a technique that has more commonly been applied to the analysis of purely spatial variation. Not surprisingly, the three techniques segregated specimens into the same groupings, and in doing so highlighted different features of morphology. This study illustrates in a simple manner how the same information (form) can be expressed in different ways, and how the manner in which a form is represented can influence both our description and our conceptualization of how forms change.
A different mode of growth is exhibited by holometabolous insects, where appendages of adults develop from imaginal disks which undergo most of their growth during a brief phase immediately before metamorphosis. Although allometric relationships (differences in relative sizes of body parts) usually imply differences in relative growth rates (Huxley, 1932), Nijhout and Wheeler (1996) observed that the processes producing allometric variation in holometabolous insects must differ from those of other types of animals, in which one or both structures are growing continuously (whether intermittently or gradually). Growth in imaginal structures takes place not only abruptly, but also within essentially a closed system, as the animal does not feed during metamorphosis. Nijhout and Wheeler proposed that some unusual features of allometry in ants and beetles, including curvilinearity and discontinuity, result from this mode of growth in which body parts compete for resources. Models of growth they developed that involve body parts in competition for resources succeeded in producing a diverse array of allometric curves with many of the complex features characteristic of holometabolous insects. Competition also provides a mechanistic basis for understanding asymmetries (Klingenberg and Nijhout, 1998) and negative covariation in the sizes of different structures. A tradeoff in resource allocation to morphological structures was demonstrated experimentally in beetles and in butterflies (Nijhout and Emlen, 1998). This collection of studies illustrates a productive interplay of morphometric analysis with experimentation and modelling. Further morphometric characterization (e.g., comparative analyses of spatial and temporal growth gradients within entire animals or within individual disks) may point to links with other mechanistic factors (e.g., domains of gene expression associated with hormonal switches) amenable to experimental analysis.
Differences in intrinsic growth rates of different body parts in a growing animal may produce the more familiar examples of allometry that involve not tradeoffs, but positive covariation. Allometry in such cases may be isometric or negative (i.e., growth of one body part only keeps pace with, or even lags behind growth in another), but all body parts are typically larger in larger individuals. Marcus and McCune (1999) suggested that the mechanisms that cause correlated growth may provide an explanation for the evolutionary loss of swords in swordtail fishes. Despite widespread preferences of females (even in swordless species) for males with swords, swords may be reduced and lost, if selection for characters correlated with the absence of swords overcomes sexual selection favoring them. If swords have been lost, the preferences for them need not have preceded existence of the trait. An examination of correlations between parameters of growth in multiple species of swordtails (Marcus and McCune, 1999) points to several possible targets of selection, if one can assume that phenotypic correlations reflect underlying genetic covariances.
Variation and correlation
Variability, or rather its absence, may be taken as evidence of canalization or constraint, while covariation suggests integration or causal interdependency (Olson and Miller, 1958. For a thorough and thoughtful review of the subject of morphological integration see Chernoff and Magwene's afterword to the 1999 reprinting of this classic work.)
There are many studies that have used morphometric covariation to infer integration, but the research programs of two individuals, James Cheverud and Miriam Zelditch and their respective colleagues, are especially noteworthy for their extensive and constructive engagement with the topic and its biological implications.
Cheverud's work links morphological integration to quantitative genetic theory through the arguments of Lande (1979) and Wagner (1996; see also Riska, 1986): Functionally and developmentally related traits are expected to evolve together, and to give rise to genetic correlations congruent with functional and developmental relationships. Where selection favors functional and developmental integration of phenotypic characters, it can be expected to favor both pleiotropy (at the individual level) and genetic integration (as assessed in a quantitative genetic framework, and resulting in a coordinated response to selection). Moreover, morphological integration facilitates adaptive evolution. Cheverud (1996) pointed to empirical studies of an array of characters that suggest that phenotypic, genetic, and environmental components of morphological integration are higher among functionally and developmentally related traits than in unrelated ones. His own work suggests this is the case for skulls of several groups of primates (e.g., Cheverud, 1995). In addition he and his colleagues (Cheverud et al., 1997) have tied patterns of morphological covariation in mandibles of laboratory mice to particular chromosomal regions. A mapping of quantitative trait loci (QTLs) associated with morphometric variation in the mandible suggests that portions of the mandible that are within the same morphologically and functionally integrated unit also tend to share QTLs.
The work of Zelditch and her colleagues has focused on spatial patterns of integration, and how these change in ontogeny. For example, Zelditch and Carmichael (1989) used confirmatory factor analysis to evaluate competing hypotheses that predict different patterns of morphological integration. In cotton rats, structures developing from the same branchial arch strongly covary during early phases of development, but later (just before weaning—but in advance of any changes of diet) patterns of integration become more evident between structures that will need to function together during mastication. In other studies on this species, Zelditch et al. (1992) used the deformation technique of the thin-plate spline to describe ontogenetic transformations and decompose them into elements reflecting spatial deformations at progressively more local scale. In contrast to Cheverud's findings, in this analysis no developmental units corresponding to the standard division of the skull into facial and basicranial regions emerged. Fink and Zelditch (1996) also used the thin-plate spline to examine evolutionary changes in ontogenetic features in piranhas, and found considerable dissociation (and little preservation) of spatial integration across lineages.
Integrating different disciplines such as genetics or phylogenetics with complex characterizations of morphology is a challenging business, so it is not surprising that these studies, which are noteworthy for their success in bringing new perspective to interpretation of morphology, have also received a share of criticism (as well as some vindication) for the assumptions they make, for particular applications of statistics, and for their interpretations of patterns (e.g., Willis et al., 1991; Roff, 1996). The chain of reasoning that begins with observation of morphology—and leads through decisions on what morphometric data to collect, how to analyze them, how to interpret numerical and geometric patterns that are revealed, and what biological agents are causally most relevant to explain them—is long and complex, providing opportunities at many stages for conflict in judgement to arise. Of special interest to evolutionary developmental biology are questions about which, whether, and how morphometric variables evolve—and to what extent mathematical constructs have biological relevance and should be reified (Reyment, 1990). In the next section we examine some heated discussion that has centered on the interpretation of morphometric variables as phylogenetic characters: where quantification is helpful, where it differs, and where it does not, from other ways of treating morphological observations.
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A vigorous debate has emerged over whether it is legitimate to use morphometric variables in systematics, particularly in character-based methods of phylogeny reconstruction. The issues include the following:
Use of character data in cladistic parsimony analysis entails delimitation and coding of discrete character states. How can, and should, such a categorical decision be made where the ranges of variation for different taxa appear partially to overlap?
Variability in character-states is most evident for characters (such as many morphometric variables) that are measured on a continuous scale; yet Stevens (1991) has pointed out that many supposed qualitative characters can more fundamentally be viewed as quantitative. Rae (1998) has argued that identical logic applies to both continuous and discrete characters if data are coded using methods that are objective and repeatable.
Even for characters that are clearly delineated into qualitatively distinct states, taxa can show overlapping distributions if they are polymorphic. Ultimately, in fact, all taxa and traits are potentially polymorphic, although discerning, documenting, or ruling out polymorphism may require exhaustive sampling. Traits would not evolve if they did not exhibit variation.
Although in practice it is individual specimens that are scored for characters, the evolving unit whose history is reconstructed in studies of systematics is the population or taxon (Roth, 1991; Thiele, 1993). Strictly speaking, the characters we use in a phylogenetic analysis should be characteristics of a population, and a population-level character (even if the population is monomorphic) is always a statistical distribution.
Different coding schemes carry different assumptions, and imply different things about the nature of character transformation in evolution; they also have different consequences for the number of trees, amount of homoplasy, and degree of resolution obtained in the analysis (Wiens, 1999). A shift in the statistical distribution of states of a character may be seen as an evolutionary event: a population is changed (evolves, if the change is heritable) even by the loss of a few individuals at one end of a range of variation. We may choose to recognize such a shift as an event worth distinguishing with the coding of a character-state change, or we may not. If we do so, we give weight to that character in the analysis, and we must ask if that weight is commensurate with what is recognized as a step for other characters.
We must also ask whether we can reasonably hypothesize a relation of homology for states of different populations that are coded as similar. This may entail homology of particular character-values exhibited by individuals, but it need not. In coding two populations the same because they have similar distributions of (for example) femur lengths, we hypothesize that the common ancestral population also had that distribution. This hypothesis (like any hypothesis of homology) may be false, and if there are good reasons to expect such a hypothesis to be false, the coding scheme or even the entire character may be deemed unsuitable for incorporation in an analysis. Pimentel and Riggins (1987) considered morphometric characters to be problematic not only because of overlapping ranges of variation, but also because they are "vague": it is difficult to be confident that a length of x mm actually means the same thing in two cases, because there are multiple ways (with differing morphology) of achieving that state. The consequence for phylogenetic analysis of incorporating a false hypothesis may be additional homoplasy in the analysis, or additional support provided for an incorrect conclusion. While morphometric data are not different in principle from data more traditionally coded as characters (Swiderski et al., 1998), they may be especially vulnerable to errors in homology assessment, and their evolution may more readily lend itself to modelling in a continuous framework (Felsenstein, 1988). The difficulty here, of course, is identifying an appropriate model.
The problem of homologising morphometrically-defined character states has received more fundamental criticism: that irrespective of their distributions or the overlap amongst them, and apart from the possibility of error when homology is assessed, morphometric variables simply cannot be homologised, and are intrinsically unsuitable for use in phylogenetic analysis. Bookstein (1994) put it emphatically: "the languages of systematics and biometrics must remain incommensurate" (p. 198, p. 225); "no biometric method developed for the analysis of measurable characteristics of single organisms...can be turned validly to...the reconstruction of evolutionary history" (p. 203); "My argument is...a declaration that the attempt to link the one [morphometrics] to the other [systematics] is futile." (p. 204); "the languages of homology and of morphometrics are mutually incomprehensible" (p. 224); etc.
One difficulty identified by Bookstein is that changes in shape are not commutative: As Rohlf (1998, modifying an example offered by Bookstein, 1994) explained, we can imagine two shape variables, A and B, each of which undergoes a change in value. Starting with a single initial form, if A is changed first, and then B, the result will not be the same as if the two events had occurred in different sequence (B and then A). "Thus the biological meaning of a shape change in a shape variable depends upon the values of the other shape variables" (Rohlf, 1998, p. 156). While this is an interesting and useful observation, it is not clear what the implications are for homology or phylogeny reconstruction. The general issue of context-dependence described in the quotation is not peculiar to morphometric variables: for example, the effect of a mutation at a locus to an alternative allele often depends upon the genetic background in which it occurs.
A second problem with shape variables is illustrated by the fact that formally, for any set of three differently shaped triangles (each triangle being an OTU), there are an indefinite number of shape measures that are consistent with (make it possible to justify) arrangement of the triangles into any possible permutation. Geometry alone appears unable to offer a unique scheme of ordering; hence "one needs to justify that the selected variables are each of particular biological interest in comparison to an infinite number of other possible shape variables." (Rohlf, 1998, p. 156). This sound advice applies equally to any features (qualitative or quantitative) identified on an organism. What we most easily recognize as landmark points or anatomical structures are not guaranteed always to be coherent units in an evolving phenotype (Cartmill, 1982; see also discussion of human chin in Gould, 1977). In some instances one may with equal justification homologise aspects, features, qualities, and abstract variables, if there is evidence of phylogenetic continuity of information (Roth, 1984, 1991).
The debate over use of morphometric variables as characters, while at times contentious in tone, has been constructive in bringing several issues to the fore. Rohlf and Bookstein have clarified important mathematical considerations; Zelditch et al. (1998) have pointed out that the complications arising from these considerations, and the assumptions they require, are no different in principle from those posed by other types of data that are regularly used by systematists. Neither the mathematical nor the biological issues are simple, and neither lends itself to dogmatic prescription. As the features of morphology represented by morphometric variables become more abstract and removed from immediate intuition, and as they partition variation in novel ways, results can become more easily confounded with artifacts. An understanding of the mathematical properties of morphometric tools, and the sources of variation to which they are and are not sensitive, is vital if they are to be used properly, especially now that fast computers and wide distribution of software have placed these tools in the hands of biologists from diverse specialties. Still, judgement, care, and consciousness of assumptions are important components of any analysis of complex phenomena. Clarity of communication becomes essential.
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Morphometrics is an evolving discipline, providing increasingly powerful techniques for quantitative characterization and comparison of anatomies. Recent enhancements include the development of geometric morphometrics, techniques that more directly preserve geometry and the spatial relationships among landmark points and contours of a form. As manipulations of data have moved beyond simple bivariate regression through more elaborate calculations, the importance of a solid grounding in both the mathematical and the biological issues is underscored: it is essential to keep in mind both the properties of the tools one is using, and the biological questions one intends them to answer.
Morphometrics has been used in both inferential and exploratory modes—that is, both for testing specific predictions, and for discerning patterns in data that in turn raise new questions or point to new hypotheses. As a mechanism for extracting (or abstracting) patterns from morphological data, morphometrics has a great deal to offer evolutionary studies of developmental biology. To date it has been especially successful in clarifying organizational principles of the phenotype: from patterns of morphological variation can be inferred such phenomena as morphological integration or heterochrony, which are patterns at a higher level of generality. It will be of particular interest to know where, when, and how often these phenomena are found, as more biological systems come under scrutiny.
Most exciting is the conceptual link that morphometric characterizations may be able to provide between morphology and the genetic, developmental, and evolutionary processes and factors that influence it. Some of the examples described here illustrate how morphometrics has provided a first step on a path of inference that leads from morphology to explanations (e.g., natural selection; pleiotropy) drawn from other disciplines. To date, molecular genetics and experimental developmental biology have been most effective in dealing with qualitative or categorical differences. As entire genomes become sequenced and their physiological structure and architecture become understood, however, more complex phenotypic traits, whose variability is best described in quantitative terms, will become accessible to analysis. For this, morphometrics is the natural language.
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1 From the Symposium Evolutionary Developmental Biology: Paradigms, Problems, and Prospects presented at the Annual Meeting of the Society for Integrative and Comparative Biology, 4–8 January 2000, at Atlanta, Georgia.
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