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... Full description

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 $\left( {\sigma _{mult}^2} \right)$, 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 $\sigma _{mult}^1$ for two or more groups of species on a phylogeny. Under both isotropic and non-isotropic conditions, and for differing numbers of trait dimensions, the proposed method displays appropriate Type I error and high statistical power for detecting known differences in $\sigma _{mult}^1$ among groups. In contrast, the Type I error rate of likelihood tests based on the evolutionary rate matrix (R) increases as the number of trait dimensions (p) increases, and becomes unacceptably large when only a few trait dimensions are considered. Further, likelihood tests based on R cannot be computed when the number of trait dimensions equals or exceeds the number of taxa in the phylogeny (i.e., when p> N). These results demonstrate that tests based on $\sigma _{mult}^1$ provide a useful means of comparing evolutionary rates for high-dimensional data that are otherwise not analytically accessible to methods based on the evolutionary rate matrix. This advance thus expands the phylogenetic comparative toolkit for high-dimensional phenotypic traits like shape. Finally, I illustrate the utility of the new approach by evaluating rates of head shape evolution in a lineage of Plethodon salamanders.