Searching for patterns in rate of molecular evolution using phylogenetic pairwise contrasts

Understanding variation in molecular evolutionary rates among species offers insight into the forces shaping evolution, and can inform phylogenetic models and molecular dating. Explaining this variation is challenging, however. Analyses must account for phylogenetic relationships, correlated species traits, and features of substitution rate estimates that standard approaches like phylogenetic generalised least squares (PGLS) do not address. Notably, substitution rates describe change accumulated over time along the lineages of a phylogeny, where shorter branches have higher variance in substitution rate estimation. Traits like body mass, by contrast, are instantaneous measurements and are therefore properties of nodes or tips, rather than branches. Here, we formalise an approach that overcomes these problems using phylogenetic pairwise contrasts (PPC). By comparing differences between pairs of taxa, we avoid estimating traits at internal nodes. Pairs are sampled from a phylogeny so that the edges connecting them do not overlap with any other pairs, generating comparisons that can be analysed using a linear regression. Simulations show that PPC tolerates measurement error in both traits and substitution rates while keeping its false positive rate close to nominal. PGLS, by contrast, is poorly calibrated for finding covariates of substitution rate, with up to 35% of replicates yielding p<0.01 when no true association exists. We "ground-truth" PPC using empirical datasets, corroborating the well-established negative correlation between body size and substitution rate in flowering plants and mammals. This work offers a straightforward, reliable method for linking substitution rates to biological traits, implemented in the R package phylowise.