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Published online by Cambridge University Press:  27 April 2017

P. David Polly
Departments of Geological Sciences, Biology, and Anthropology, Indiana University, 1001 E. 10th Street, Bloomington, Indiana 47405, USA 〈〉
Gary J. Motz
Department of Geological Sciences and Center for Biological Research Collections, Indiana University, 1001 E. 10th Street, Bloomington, Indiana 47405, USA 〈〉
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Focusing 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.

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Copyright © 2017, The Paleontological Society 

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