title: Improving phylogenetic regression under complex evolutionary models.
abstract: Phylogenetic Generalized 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 percentage of tests based on samples that incorrectly rejected a true null hypothesis] and power [the percentage 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, while 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.
authors.forename: Florent
authors.initials: F
authors.lastname: Mazel
authors.forename: T Jonathan
authors.initials: TJ
authors.lastname: Davies
authors.forename: Damien
authors.initials: D
authors.lastname: Georges
authors.forename: Sébastien
authors.initials: S
authors.lastname: Lavergne
authors.forename: Wilfried
authors.initials: W
authors.lastname: Thuiller
authors.forename: Pedro R
authors.initials: PR
authors.lastname: Peres-NetoO
mesh_terms: D005075:Biological Evolution; D003198:Computer Simulation; D049810:Genetic Speciation; D008954:Models, Biological