Currently available phylogenetic methods for studying the rate of evolution in a continuously valued character assume that the rate is constant throughout the tree or that it changes along specific branches according to an a priori hypothesis of rate variation provided by the user. Herein, we describe a new method for studying evolutionary rate variation in continuously valued characters given an estimate of the phylogenetic history of the species in our study. According to this method, we propose no specific prior hypothesis for how the variation in evolutionary rate is structured throughout the history of the species in our study. Instead, we use a Bayesian Markov Chain Monte Carlo approach to estimate evolutionary rates and the shift-point between rates on the tree. We do this by simultaneously sampling rates and shift-points in proportion to their posterior probability, and then collapsing the posterior sample into an estimate of the parameters of interest. We use simulation to show that the method is quite successful at identifying the phylogenetic position of a shift in the rate of evolution, and that estimated rates are asymptotically unbiased. We also provide an empirical example of the method using data for Anolis lizards.

The adaptive landscape and the G-matrix are keys concepts for understanding how quantitative characters evolve during adaptive radiation. In particular, whether the adaptive landscape can drive convergence of phenotypic integration (i.e., the pattern of phenotypic variation and covariation summarized in the P-matrix) is not well studied. We estimated and compared P for 19 morphological traits in eight species of Caribbean Anolis lizards, finding that similarity in P among species was not correlated with phylogenetic distance. However, greater similarity in P among ecologically similar Anolis species (i.e., the trunk-ground ecomorph) suggests the role of convergent natural selection. Despite this convergence and relatively deep phylogenetic divergence, a large portion of eigenstructure of P is retained among our 8 focal species. We also analyzed P as an approximation of G to test for correspondence with the pattern of phenotypic divergence in 21 Caribbean Anolis species. These patterns of covariation were coincident, suggesting that either genetic constraint has influenced the pattern of among-species divergence or, alternatively, that the adaptive landscape has influenced both G and the pattern of phenotypic divergence among species. We provide evidence for convergent evolution of phenotypic integration for one class of Anolis ecomorph, revealing yet another important dimension of evolutionary convergence in this group.