Generalized linear mixed models for phylogenetic analyses of community structure

There is growing appreciation that ecological communities are phylogenetically structured, with phylogenetically closely related species either more or less likely to co‐occur at the same site. Here, we present phylogenetic generalized linear mixed models (PGLMMs) that can statistically test a wide variety of phylogenetic patterns in community structure. In contrast to most current statistical approaches that rely on community metrics and randomization tests, PGLMMs are model‐based statistics that fit observed presence/absence data to underlying hypotheses about the distributions of species among communities. We built four PGLMMs to address (1) phylogenetic patterns in community composition, (2) phylogenetic variation in species sensitivities to environmental gradients among communities, (3) phylogenetic repulsion in which closely related species are less likely to co‐occur, and (4) trait‐based variation in species sensitivities to environmental gradients. We also built a fifth PGLMM to test a key underlying assumption of phylogenetic community structure: that phylogenetic information serves as a surrogate for trait information about species; this model tests whether the introduction of trait information can explain all variation in species occurrences among communities, leaving no phylogenetic residual variation. We assessed the performance of these PGLMMs using community simulation models and show that PGLMMs have equal or greater statistical power than alternative approaches currently in the literature. Finally, we illustrate the PGLMM advantage of fitting a model to data by showing how variation in species occurrences among communities can be partitioned into phylogenetic and site‐specific components, and how fitted models can be used to predict the co‐occurrence of phylogenetically related species.