Morphometrics, Homology, and Phylogenetics: Quantified Characters as Synapomorphies

-It has been claimed that quantified features are inappropriate for phylogenetic analysis. We consider that claim to be true under most conditions for characters discovered by commonly used morphometric methods, including outline-based and conventional multivariate methods. The most important reason these characters are unsuitable is that one of the tests of homology, the test of similarity, may be difficult to apply to them. This test is not even possible if the methods for comparing forms, such as outline-based techniques, do not ensure that the characters are located in the same part of the anatomy. Conventional methods, including principal components analysis, have no explicit basis for localizing characters. In addition, unless the transformation between forms is homogeneous, conventional methods cannot dissect transformations region by region to discover characters. However, one morphometric method, the thin-plate spline decomposed by its partial warps (TPS), finds characters that can be subjected to the same tests of homology (conjunction, similarity, and congruence) that we would apply to all other characters. Among available methods, TPS is unique in being able to locate the center and spatial extent of regional differences in shape and ensures that the same regions are compared among forms. We provide an example using the teleost fishes piranhas, in which tests of homology are applied to a synapomorphy found by the method. [Morphometrics; homology; synapomorphy; thin-plate spline; character analysis; piranha; Pygocentrus; Pygopristis; Serrasalmus.] Shape similarities among organisms Because much of our argument depends have long been recognized as having syson our meaning of homology, we begin tematic value. Whether shave features in with a brief foray into semantics. Followquantitative form can be a source of inforing a discussion of the definition of homation about phylogenetic relationships is mology, we examine several morphometric more controversial. This doubt is reflected methods and judge their potential for in the literature, particularly in the claims yielding characters appropriate for phylothat quantitative shape features cannot be genetic analyses. subjected to the same tests of homology that other characters must pass (Pimentel HOMOLOGY and Riggins, 1987). This position strikes diPatterson (1982), like Rieppel (1980), disrectly at the use of morphometrics as a tinguished between taxic homology, a feaclass of tools for phylogenetic analysis. ture of a monophyletic group, and transHerein, we argue that ,at least one morphoformational homology. The evidence of metric method is both suitable and useful taxic homologies is synapomorphies that in phylogenetic analysis because charachave passed three tests: conjunction, simiters found by it can be treated in the same larity, and congruence. Systematists who way as can characters from any other use the term "synapomorphy" for shared source. However, we also contend that derived states, whether or not shown to be many methods currently in use are indeed congruent, qualify this definition by reinappropriate because they cannot generstricting it to "corroborated synapomorate results meeting the criteria applied to phies." Systematists who use terms such as phylogenetic characters. "putative synapomorphy" to refer to the coded characters prior to testing their conE-mail: [email protected]. gruence and use "synapomorphy" specifE-mail: [email protected]. ically for those found to be congruent E-mail: [email protected]. equate homology with synapomorphy. 180 SYSTEMATIC:BIOLOGY VOL. 44 Transformational homologies refer only to characters, i.e., a particular feature interpreted as transformationally homologous to another feature. In Smith's (1990) terms, transformational homology refers to the vertical relationship among characters. A classic example of a hypothesis of transformational homology is the assertion that the incus is homologous to the quadrate. This is a relationship between characters and provides no information about relationships among taxa. In general, statements of transformational homology can be rewritten in taxic terms. The example of the incus and quadrate can be written as "the incus and quadrate are homologous as palatoquadrate 0ssifications of osteichthyans" and "the incus is homologous as the intermediate middle ear ossicle in mammals." There are two claims made in statements of transformational homology thus rewritten: (1)the features (incus + quadrate as palatoquadrate ossifications; incus as the intermediate middle ear ossicle) each characterize a monophyletic group (Osteichthyes; Mammalia), and (2) the features comprise a transformation series, i.e., a nested set of synapomorphies. These are two distinct and different kinds of statements, and we agree with Patterson that only those features that characterize monophyletic groups should be called homologues. The second kind of statement presumes that the variant characters are modifications of the symplesiomorphic feature and are thus comparable. Many long-standing debates regarding particular homologies are about transformational rather than taxic homology. It is the comparability of the structures, rather than their status as synapomorphies characterizing monophyletic groups, that is often in doubt. For example, if we were to observe a trapezoidal frontal bone in one taxon and a trapezoidal parietal bone in another, we would not judge trapezoidal form as a potentially homologous feature of the group comprising both taxa, even if these taxa form a monophyletic group, because these are not variant shapes of a symplesiomorphic bone. The shapes cannot be homologous when the parts are not phylogenetically comparable. This comparability is one aspect of the test of similarity. There are two distinct components of the test of similarity: (1)features must be judged comparable as modifications. of a symplesiomorphic character and (2) features must be judged to resemble each other "in sufficient detail" to code them as sharing a common derived condition. In our example of the two trapezoids, even if they pass the test of similarity (of shape), they fail the other, the comparability of the parts. One of the reasons Pimentel and Riggins (1987:208) opposed using morphometric characters in systematics is that they claimed it seems "obvious [that] most quantitative variables can lead only to implied homologies, i.e., transformational homologies [and] so are useless for cladistic analysis." This statement implies that morphometric variables can be arranged into transformation series but that they cannot be regarded as potential synapomorphies. However, morphometric variables obtained by some methods (but not all) are not even comparable. In some cases, the comparability of the parts is essentially unknowable, and so there can be no phylogenetic information in their shapes. This limitation is most evident in outline-based methods (those that do not employ landmarks). However, even some ways of analyzing landmark data fail to ensure that comparisons are restricted to phylogenetically comparable parts of the organism. Yet not all methods are suspect; the thin-plate spline decomposed by its partial warps allows discovery of characters that can be assessed for taxic homology. The term homology as used in morphometrics has a different meaning than it does in phylogenetic systematics. This term has most often been applied to landmarks, i.e., discrete, recognizable points on the organism. When systematists choose particular landmarks, the choice is often defended on the grounds that they sample parts of the organism judged homologous at the most inclusive level being studied. The intent is to identify homologous shape 181 1995 MORPHOMETRICS features of these comparable parts. However, in the usage of morphometrics, homology is not a hierarchical concept. Once we declare landmarks to be homologous at some phylogenetic level, all the shape variables extracted by analysis of these landmarks must be homologous at that level because, technically, landmarks and the features extracted by analysis of patterns of landmark displacements are algebraically equivalent. If landmarks are homologous at the most inclusive level of study, and the features extracted from the comparisons are algebraically equivalent to the landmarks, then we are forced to regard the shape variables as also homologous at the most inclusive level of study. For example, in the semantics of morphometrics, we could not refer to the landmarks as homologous at the level of Mammalia and call a particular shape character homologous at the level of Rodentia. This usage is in clear contrast to the usage of homology in phylogenetic systematics, where one would not oppose viewing the bones and their shapes as forming a nested set of homologies. To avoid misunderstandings due to this semantic inconsistency, we suggest replacing the term "homologous" with "corresponding" or "comparable" when referring to landmarks in a strictly mor-