Multi-Response Phylogenetic Mixed Models: Concepts and Application

The scale and resolution of trait databases and molecular phylogenies is increasing rapidly. These resources permit many questions in macro evolution and ecology to be addressed with the right statistical tools. Phylogenetic mixed models (PMM), particularly multi-response (MR) implementations, offer great potential for analyses of trait evolution. While flexible and powerful, these models can be conceptually challenging. The literature describing PMM is also highly technical, creating additional barriers for many biologists. Here we present an accessible and practical guide to the PMM. We begin by outlining key concepts in mixed modelling, emphasising the use of covariance matrices to model correlative structure in the data. We present a simple notation for PMM, of which phylogenetic generalised least squares (PGLS) is a special case. We outline the limitations of single-response (SR) models such as PGLS for characterising patterns of trait variation, and emphasise that MR models will often be a preferable approach to analyses involving multiple species traits. Using simulated data and visual examples, we demonstrate the capacity of MR-PMM to partition trait covariance into phylogenetic and independent components. We discuss interpretation, prediction, and model validation, including methods based on leave-one-out cross validation. We then apply this approach to a real-world data set of leaf traits in Eucalyptus to show how MR-PMM can offer a more nuanced understanding of trait correlations compared to SR approaches. Finally, we highlight common pitfalls and offer practical recommendations to analysts. To complement this material, we provide an online tutorial including additional examples, as well as side-by-side implementations in two popular R packages, MCMCglmm and brms.