Assessing the affinities of fossils using canonical variates and generalized distances

Abstract

Canonical variate analysis and generalized distances are commonly used multivariate statistical techniques for assessing the comparative morphology of living and fossil primates. Some common pitfalls of these methods when used to analyze fossil specimens are: (1) ignoring the possibility that a fossil belongs to a group other than one of the predefined reference samples (i.e., restricted versus unrestricted approaches to classification), (2) misinterpreting probabilities of group membership (i.e., posterior versus typicality probabilities), and (3) failing to understand how sample sizes influence multivariate ordinations in trying to effectively illustrate the morphometric affinities of a fossil (i.e., weighted versus unweighted analyses with fossils entered indirectly or directly into the analysis). To better understand canonincal variate analysis and generalized distances, the workings of these methods are portrayed graphically as a series of rotations and rescaling of data plotted in a multivariate data space. The influence of sample sizes and the importance of higher-numberer canonical variates are emphasized. Simple examples taken from the literature illustrate how the different approaches to including a fosil in canonical variate analysis may affect the multivariate results upon which physical anthropologists base their interpretations of the fossil's morphology.