Data from: A method for assessing phylogenetic least squares models for shape and other high-dimensional multivariate data

Studies of evolutionary correlations commonly utilize 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 utilizing 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.