A novel phylogenetic comparative method for evaluating the strength of branch-specific directional selection.

Phylogenetic comparative methods (PCMs) have played a central role in studying the evolution of phenotypic traits. However, when a trait experienced directional selection, previous PCMs have faced a dilemma between mathematically tractable but restrictive models (i.e., simple Gaussian process models) and flexible but intractable approaches (i.e., a simulation-based process model of phenotype evolution built on population genetics frameworks). This paper proposes a novel Gaussian process macroevolutionary model, called the "branch-specific directional selection (BSDS)," for evaluating the strength of directional selection to reconcile these two approaches. This model is based on a second-order approximation of a previous simulation-based process model but has a closed-form likelihood function. This can also be extended to incorporate intraspecies variations and to linear mixed models, which are necessary for meta-analysis. We conduct numerical experiments to validate the proposed method and apply it to the brain volume of Hominidae species. The results show that the proposed methods yield statistically more reliable inferences and computational time is about hundred thousand times faster than the previous simulation-based methods. Further extensions of the BSDS model are expected to provide a clearer picture of the connection of microevolutionary processes and macroevolutionary patterns.