Improving phylogenetic regression under complex evolutionary models - Mazel, Florent (Ecology, 2016)
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 the 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 evaluating 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 in comparative analyses over the last decade. To address this issue, we propose a simple solution based on transforming the underlying variance-covariance matrix to adjust for model heterogeneity within PGLS. We suggest that heterogeneous rates of evolution might be particularly prevalent in large phylogenetic trees, whilst most current approaches assume a homogenous rate of evolution. Our analysis demonstrates that overlooking rate heterogeneity can result in inflated type I errors, thus misleading comparative analyses. We show that it is possible to correct for this bias even when the underlying model of evolution is not known a priori.