Comparing evolutionary rates for different phenotypic traits on a phylogeny using likelihood.

In recent years, likelihood-based approaches have been used with increasing frequency to evaluate macroevolutionary hypotheses of phenotypic evolution under distinct evolutionary processes in a phylogenetic context (e.g., Brownian motion, Ornstein-Uhlenbeck, etc.), and to compare one or more evolutionary rates for the same phenotypic trait along a phylogeny. It is also of interest to determine whether one trait evolves at a faster rate than another trait. However, to date no study has compared phylogenetic evolutionary rates between traits using likelihood, because a formal approach has not yet been proposed. In this article, I describe a new likelihood procedure for comparing evolutionary rates for two or more phenotypic traits on a phylogeny. This approach compares the likelihood of a model where each trait evolves at a distinct evolutionary rate to the likelihood of a model where all traits are constrained to evolve at a common evolutionary rate. The method can also account for within-species measurement error and within-species trait covariation if available. Simulations revealed that the method has appropriate Type I error rates and statistical power. Importantly, when compared with existing approaches based on phylogenetically independent contrasts and methods that compare confidence intervals for model parameters, the likelihood method displays preferable statistical properties for a wide range of simulated conditions. Thus, this likelihood-based method extends the phylogenetic comparative biology toolkit and provides evolutionary biologists with a more powerful means of determining when evolutionary rates differ between phenotypic traits. Finally, I provide an empirical example illustrating the approach by comparing rates of evolution for several phenotypic traits in Plethodon salamanders.