Improving phylogenetic regression under complex evolutionary models

Phylogenetic Generalised Least Square (PGLS) is the tool of choice among phylogenetic comparative methods to measure the correlation between species features such as morphological and life-history traits or niche characteristics. In its usual form it assumes that the residual variation follows a homogenous model of evolution across the branches of phylogenetic tree. Since a homogenous model of evolution is unlikely to be realistic in nature, we explored the robustness of the phylogenetic regression when this assumption is violated. We did so by simulating a set of traits under various heterogeneous models of evolution, and evaluated the statistical performance (type I error -the % of tests based on samples that incorrectly rejected a true null hypothesis- and power -the % of tests that correctly rejected a false null hypothesis) of classical phylogenetic regression. We found that PGLS has good power but unacceptable type I error rates. This finding is important since this method has been increasingly used...