by Pierre de Villemereuil and Shinichi Nakagawa
There is much in common between the aim and tools of the quantitative geneticist and the comparative biologist. One of the most interesting statistical tool of the quantitative genetics is the mixed model framework, especially the so-called animal model, which can be used for comparative analyses. In this chapter, we describe the Phylogenetic Generalised Linear Mixed Model (PGLMM), which encompasses Phylogenetic (Linear) Mixed Models (PMM). The widely used Phylogenetic Generalised Least Square (PGLS) can be seen as a special case of PGLMM. Thus, we demonstrate how PGLMM can be a useful extension of PGLS, hence a useful tool for the comparative biologist. Especially, we show how the PGLMM can tackle issues such as (i) intra-specific variance inference, (ii) phylogenetic meta-analysis, (iii) non-Gaussian traits analysis, and (iv) missing values and data augmentation. Further possible extensions of the PGLMM and applications to phylogenetic comparative analysis are discussed at the end of the chapter. We provide working examples, using the R package MCMCglmm, in the Online Practical Material (OPM).