PATTERNS AND PROCESSES IN MORPHOSPACE: GEOMETRIC MORPHOMETRICS OF THREE-DIMENSIONAL OBJECTS

Abstract

AbstractFocusing on geometric morphometrics (GMM), we review methods for acquiring morphometric data from 3-D objects (including fossils), algorithms for producing shape variables and morphospaces, the mathematical properties of shape space, especially how they relate to morphogenetic and evolutionary factors, and issues posed by working with fossil objects. We use the Raupian shell-coiling equations to illustrate the complexity of the relationship between such factors and GMM morphospaces. The complexity of these issues re-emphasize what are arguably the two most important recommendations for GMM studies: 1) always use multivariate methods and all of the morphospace axes in an analysis; and 2) always anticipate the possibility that the factors of interest can have complex, nonlinear relationships with shape.