Quantifying macro-evolutionary patterns of trait mean and variance with phylogenetic location-scale models

Shinichi Nakagawa , Ayumi Mizuno , Coralie Williams , Malgorzata Lagisz , Yefeng Yang, Szymon Marian Drobniak

Understanding how both the mean (location) and variance (scale) of traits differ among species and lineages is fundamental to unveiling macroevolutionary patterns. Yet, traditional phylogenetic comparative methods primarily focus on modelling mean trait values, often overlooking variability and heteroscedasticity that can provide critical insights into evolutionary dynamics. Here, we introduce phylogenetic location-scale models (PLSMs), a novel framework that jointly analyzes the evolution of trait means and variances. This dual approach captures heteroscedasticity and evolutionary changes in trait variability, allowing for the detection of clades with differing variances and revealing patterns of adaptation, diversification, and evolutionary constraints. Extending PLSMs to a multivariate context enables simultaneous analysis of multiple traits and their covariances, facilitating the testing of hypotheses about evolutionary trade-offs, pleiotropy, and phenotypic integration. By modelling covariances between phylogenetic effects in both the \emph{location} and \emph{scale} parts, we can discern whether changes in one trait’s mean or variance are associated with changes in another’s, thereby offering deeper insights into the mechanisms driving trait co-evolution, and co-divergence or ``contra-divergence". We also describe how an extended version of PLSMs incorporating within-species variability can enhance our understanding of trait convergence and divergence arising from ecological and environmental factors. Our framework provides an innovative and flexible tool for exploring macro-evolutionary patterns by jointly modelling trait means and variances. Importantly, PLSMs can be used to reassess almost all previously published comparative data, providing new evolutionary insights and enriching our understanding of the diversity of life.