A Method for Assessing Phylogenetic Least Squares Models for Shape and Other High-Dimensional Multivariate Data

Abstract

Studies of evolutionary correlations commonly use phylogenetic regression (i.e., independent contrasts and phylogenetic generalized least squares) to assess trait covariation in a phylogenetic context. However, while this approach is appropriate for evaluating trends in one or a few traits, it is incapable of assessing patterns in highly multivariate data, as the large number of variables relative to sample size prohibits parametric test statistics from being computed. This poses serious limitations for comparative biologists, who must either simplify how they quantify phenotypic traits, or alter the biological hypotheses they wish to examine.In this article, I propose a new statistical procedure for performing ANOVA and regression models in a phylogenetic context that can accommodate high-dimensional datasets. The approach is derived from the statistical equivalency between parametric methods using covariance matrices and methods based on distance matrices. Using simulations under Brownian motion, I show that the method displays appropriate Type I error rates and statistical power, whereas standard parametric procedures have decreasing power as data dimensionality increases. As such, the new procedure provides a useful means of assessing trait covariation across a set of taxa related by a phylogeny, enabling macroevolutionary biologists to test hypotheses of adaptation, and phenotypic change in high-dimensional datasets. K E Y W O R D S :Geometric morphometrics, macroevolution, morphological evolution, phylogenetic comparative method.In comparative biology it is generally accepted that the evaluation of evolutionary correlations among traits requires a phylogenetic perspective. Because of shared evolutionary history, species in a phylogeny are not independent (Felsenstein 1985;Harvey and Pagel 1991; Felsenstein 2004;Revell et al. 2008;Pennell and Harmon 2013). This leads to phenotypic similarities among taxa, whose expected covariance may be described in proportion to their shared ancestry under a specified model of trait evolution (Felsenstein 1985;Grafen 1989;Martins and Hansen 1997;Rohlf 2001). As a consequence, statistical procedures that assess patterns of covariation among traits from cross-species data must take the evolutionary relationships among taxa into consideration during the analysis, so that the lack of independence among species may be properly accounted for (Revell 2010). In these circumstances, when evolutionary correlations among traits are identified via phylogenetic comparative methods, such correlations provide important evidence of adaptation and inform on the evolutionary causes of phenotypic change (Garland et al. 1992;Rüber and Adams 2001;Pennell and Harmon 2013), as the potential effect of shared evolutionary history may be ruled out.Over the past several decades, numerous analytical approaches have been developed to account for phylogenetic nonindependence while assessing patterns of trait covariation (Cheverud et al. 1985;Felsenstein 1985;Grafen 1989;Martins and Hansen 1997;Diniz-F...

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