Promoting the use of phylogenetic multinomial generalised mixed-effects model to understand the evolution of discrete traits.

Phylogenetic comparative methods (PCMs) are fundamental tools for understanding trait evolution across species. While linear models are widely used for continuous traits in ecology and evolution, their application to discrete traits, particularly ordinal and nominal traits, remains limited. Researchers sometimes recategorise such traits into binary traits (0 or 1 data) to make them more manageable. However, this risks distorting the original data structure and meaning, potentially reducing the information it initially contained. This paper promotes the use of phylogenetic generalised linear mixed-effects models (PGLMMs) as a flexible framework for analysing the evolution of discrete traits. We introduce the theoretical foundations of PGLMMs and demonstrate how univariate and multivariate versions of binary PGLMMs, which might be more familiar to evolutionary biologists, can be conceptually extended to model ordinal and nominal traits. Specifically, we describe ordered and unordered multinomial PGLMMs for ordinal and nominal traits, respectively. We then explain how to interpret regression coefficients and (co)variance components, including associated statistics (e.g., phylogenetic heritability and correlation) from PGLMMs for discrete traits. Using real-world examples from avian datasets, we illustrate the practical implementation of PGLMMs to reveal evolutionary patterns in discrete traits. We also provide online tutorials to guide researchers through the application of these models using Bayesian implementations in R. By making complex models more accessible, we aim to facilitate a more precise and insightful understanding of the evolution and function of discrete traits, which have received relatively limited attention in evolutionary biology so far.