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, ; Thiele, 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, 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.
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. 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.
One difficulty identified by Bookstein is that changes in shape are not commutative: As Rohlf , modifying an example offered by Bookstein, 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. 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. 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, ; see also discussion of human chin in Gould, 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, , 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.
Outline analysis is another approach to analyzing shape. CV1 displays shape changes that primarily affect the width of the corolla tube and the location of dorsal and lateral petals. Histomorphometry of bone involves obtaining a bone biopsy specimen and processing of bone specimens in the laboratory, obtaining estimates of the proportional volumes and surfaces occupied by different components of bone. Appendix A. J Herpetol — Simpson et al Combining the Tools of Geometric Morphometrics.
Rohlf and Bookstein have clarified important mathematical considerations; Zelditch et al. Neither the mathematical nor the biological issues are simple, and neither lends itself to dogmatic prescription.
This volume is based on the NATO Advanced Study Institute, "Advances in Mor phometries" held in 11 Ciocco, Tuscany, Italy from July , , and directed . Editors: Marcus, L.F., Corti, M., Loy, A., Naylor, G.J.P., Slice, D.E. This volume is based on the NATO Advanced Study Institute, "Advances in Mor phometries" held in 11 Ciocco, Tuscany, Italy from July , , and directed by Leslie F. Marcus. The "Advances in Morphometries.
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. 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. 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.
Crustacean ontogeny and diversity as depicted by Haeckel right , Thompson top left; reprinted with the permission of Cambridge University Press , and Huxley bottom, left; Problems of Relative Growth, p. Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide.
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References Publications referenced by this paper.
Morphometrics and phylogenetics: principal components of shape from cranial modules are neither appropriate nor effective cladistic characters. Dimension Reduction and Selection of Landmarks.
Introduction to Outlines. Paul D. Sampson, Fred L. Bookstein, Florence H. Sheehan, Edward L. David Dean, Leslie F. Marcus, Fred L. Spline Curves and Surfaces for Data Modeling. Edgels and Tangent Planes in Image Warping.
Front Matter Pages N9-N9. Fluctuating Asymmetry in Mus musculus Subspecific Hybridization. Correspondence between Interlandmark Distances and Caliper Measurements. Some Applications of Geometric Morphometrics to Ostracoda.