Detecting correlation between characters in a comparative analysis with uncertain phylogeny

The importance of accommodating the phylogenetic history of a group when performing a comparative analysis is now widely recognized. The typical approaches either assume the tree is known without error, or they base inferences on a collection of well-supported trees or on a collection of trees generated under a stochastic model of cladogenesis. However, these approaches do not adequately account for the uncertainty of phylogenetic trees in a comparative analysis, especially when data relevant to the phylogeny of a group are available. Here, we develop a method for performing comparative analyses that is based on an extension of Felsenstein's independent contrasts method. Uncertainties in the phylogeny, branch lengths, and other parameters are accommodated by averaging over all possible trees, weighting each by the probability that the tree is correct. We do this in a Bayesian framework and use Markov chain Monte Carlo to perform the high-dimensional summations and integrations required by the analysis. We illustrate the method using comparative characters sampled from Anolis lizards.