Testing for differences in rates-across-sites distributions in phylogenetic subtrees

It has long been recognized that the rates of molecular evolution vary amongst sites in proteins. The usual model for rate heterogeneity assumes independent rate variation according to a rate distribution. In such models the rate at a site, although random, is assumed fixed throughout the evolutionary tree. Recent work by several groups has suggested that rates at sites often vary across subtrees of the larger tree as well as across sites. This phenomenon is not captured by most phylogenetic models but instead is more similar to the covarion model of Fitch and coworkers. In this article we present methods that can be useful in detecting whether different rates occur in two different subtrees of the larger tree and where these differences occur. Parametric bootstrapping and orthogonal regression methodologies are used to test for rate differences and to make statements about the general differences in the rates at sites. Confidence intervals based on the conditional distributions of rates at sites are then used to detect where the rate differences occur. Such methods will be helpful in studying the phylogenetic. structural, and functional bases of changes in evolutionary rates at sites, a phenomenon that has important consequences for deep phylogenetic inference.