Application of Fitted Polynomial Functions to Modeling Contours Derived from Mammalian Mandibular and Dental Morphology

Abstract

Three sets of test data were used to evaluate the utility of fitted polynomial functions for systematic investigations of morphological differences among species. In the first, a sample of New World leaf-nosed bats (Phyllostomidae), jaw shape was closely approx- imated by a second-order polynomial; two of the resultant parameters showed significant differences among included species according both to taxonomic group (tribe) and dietary preference, while the third coefficient revealed different patterns of variation in asymmetry among species. Population samples of two species, Artibeus jamaicensis and Glossophaga soyi- cina, indicated that directional asymmetry is present in the jaw of both species. In the third example, molar cusp (paracone) shape was compared among samples of Cretaceous mar- supials, using fourth-order polynomials. Discriminant function analysis was moderately suc- cessful in distinguishing among species and produced phylogenetically intelligible species groupings. For both the phyllostomids and the Cretaceous marsupials, the procedure yielded continuously distributed character variables (either the function coefficients themselves or factor scores derived from multivariate analysis) that have systematic applications; examples using discrete coding for parsimony-based cladistic analysis are given. For second-order poly- nomials modelirng structures that are ideally symmetrical (as in the example of the phyllos- tomid bats), both direction and magnitude of asymmetry are indicated; some of the standard