Quantifying and comparing phylogenetic evolutionary rates for shape and other high-dimensional phenotypic data

Many questions in evolutionary biology require the quantification and comparison of rates of phenotypic evolution. Recently, phylogenetic comparative methods have been developed for comparing evolutionary rates on a phylogeny for single, univariate traits (σ2), and evolutionary rate matrices (R) for sets of traits treated simultaneously. However, high-dimensional traits like shape remain under-examined with this framework, because methods suited for such data have not been fully developed. In this article, I describe a method to quantify phylogenetic evolutionary rates for high-dimensional multivariate data (σ2mult), found from the equivalency between statistical methods based on covariance matrices and those based on distance matrices (R-mode and Q-mode methods). I then use simulations to evaluate the statistical performance of hypothesis testing procedures that compare σ2mult for two or more groups of species on a phylogeny. Under both isotropic and non-isotropic conditions, and for d...