Canis dirus and Smilodon Procrustes coordinates

The primary goal of this paper is to examine and rationalize different integration metrics used in geometric morphometrics, in an attempt to arrive at a common basis for the characterization of phenotypic covariance in landmark data. We begin with a model system; two populations of Pleistocene dire wolves from Rancho La Brea that we examine from a data-analytic perspective to produce candidate models of integration. We then test these integration models using the appropriate statistics and extend this characterization to measures of whole-shape integration. We demonstrate that current measures of whole-shape integration fail to capture differences in the strength and pattern of integration. We trace this failure to the fact that current whole-shape integration metrics purport to measure only the pattern of inter-trait covariance, while ignoring the dimensionality across which trait variance is distributed. We suggest a modification to current metrics based on consideration of the Shannon, or information, entropy, and demonstrate that this metric successfully describes differences in whole shape integration patterns. Our new metric allows detailed comparison of the hyperellipses occupied by the two populations in morphospace (which is a form of covariance space). Finally, the information entropy approach allows comparison of whole shape integration in a dense semilandmark environments, and we demonstrate that the metric introduced here allows comparison of shape spaces that differ arbitrarily in their dimensionality and landmark membership.

Methods
These data comprise two dimensional landmark data from left jaws of the dire wolf, Canis dirus, from Rancho La Brea, California. The landmarks were digitized from photographs of the specimens.