Testing quantitative genetic hypotheses about the evolutionary rate matrix for continuous characters

Aim: Provide a new multivariate hypothesis testing approach for the evolution of continuous characters in a phylogenetic context. Background: Brownian motion is the most commonly used model for the evolution of quantitative traits. Under multivariate Brownian motion, the evolution of multiple continuous traits can be described by an evolutionary rate matrix in which the diagonal elements determine the rate of evolution for individual characters, while the off-diagonal elements determine the extent to which different characters co-evolve. Method: We present likelihood tests for two simple hypotheses about the evolutionary rate matrix: (1) equality or proportionality to a hypothetical matrix; and (2) concerted change in the rate matrix in a certain portion or portions of the phylogenetic tree. In case (1), the hypothetical matrix might be estimated from the within-species additive genetic variance-covariance matrix. In case (2), concerted change in the evolutionary rate matrix might result from shifts in ploidy level or the mutation rate. We illustrate these hypothesis tests using data from individual-based quantitative genetic simulations on stochastic phylogenetic trees. Results: Our evolutionary rate matrix estimator exhibited minimal bias. Type I errors in our likelihood-based tests for matrix equality and proportionality were very close to appropriate levels. Power to detect selection was also sufficient, except in the case of the weakest selection simulated in this study. Type I error and the accuracy of parameter estimation in the test for rate matrix heterogeneity were also adequate. © 2008 Liam J. Revell.