A phylogenetic comparative method for studying multivariate adaptation

Phylogenetic comparative methods have been limited in the way they model adaptation. Although some progress has been made, there are still no methods that can fully account for coadaptation between traits. Based on Ornstein-Uhlenbeck (OU) models of adaptive evolution, we present a method, with R implementation, in which multiple traits evolve both in response to each other and, as in previous OU models, to fixed or randomly evolving predictor variables. We present the interpretation of the model parameters in terms of evolutionary and optimal regressions enabling the study of allometric and adaptive relationships between traits. To illustrate the method we reanalyze a data set of antler and body-size evolution in deer (Cervidae).