Extending phylogenetic regression models for comparing within‐species patterns across the tree of life

Abstract Evolutionary biologists characterize macroevolutionary trends of phenotypic change across the tree of life using phylogenetic comparative methods. However, within‐species variation can complicate such investigations. For this reason, procedures for incorporating nonstructured (random) intraspecific variation have been developed. Likewise, evolutionary biologists seek to understand microevolutionary patterns of phenotypic variation within species, such as sex‐specific differences or allometric trends. Additionally, there is a desire to compare such within‐species patterns across taxa, but current analytical approaches cannot be used to interrogate within‐species patterns while simultaneously accounting for phylogenetic non‐independence. Consequently, deciphering how intraspecific trends evolve remains a challenge. Here we introduce an extended phylogenetic generalized least squares (E‐PGLS) procedure which facilitates comparisons of within‐species patterns across species while simultaneously accounting for phylogenetic non‐independence. Our method uses an expanded phylogenetic covariance matrix, a hierarchical linear model, and permutation methods to obtain empirical sampling distributions and effect sizes for model effects that can evaluate differences in intraspecific trends across species for both univariate and multivariate data, while conditioning them on the phylogeny. The method has appropriate statistical properties for both balanced and imbalanced data. Additionally, the procedure obtains evolutionary covariance estimates that reflect those from existing approaches for nonstructured intraspecific variation. Importantly, E‐PGLS can detect differences in structured (i.e. microevolutionary) intraspecific patterns across species when such trends are present. Thus, E‐PGLS extends the reach of phylogenetic comparative methods into the intraspecific comparative realm, by providing the ability to compare within‐species trends across species while simultaneously accounting for shared evolutionary history.