• Approximate Bayesian computation (ABC);
  • phenotypic evolution;
  • phylogenetic comparative methods;
  • simulation-based likelihood computation

Phylogenetic comparative methods (PCMs) have been used to test evolutionary hypotheses at phenotypic levels. The evolutionary modes commonly included in PCMs are Brownian motion (genetic drift) and the Ornstein–Uhlenbeck process (stabilizing selection), whose likelihood functions are mathematically tractable. More complicated models of evolutionary modes, such as branch-specific directional selection, have not been used because calculations of likelihood and parameter estimates in the maximum-likelihood framework are not straightforward. To solve this problem, we introduced a population genetics framework into a PCM, and here, we present a flexible and comprehensive framework for estimating evolutionary parameters through simulation-based likelihood computations. The method does not require analytic likelihood computations, and evolutionary models can be used as long as simulation is possible. Our approach has many advantages: it incorporates different evolutionary modes for phenotypes into phylogeny, it takes intraspecific variation into account, it evaluates full likelihood instead of using summary statistics, and it can be used to estimate ancestral traits. We present a successful application of the method to the evolution of brain size in primates. Our method can be easily implemented in more computationally effective frameworks such as approximate Bayesian computation (ABC), which will enhance the use of computationally intensive methods in the study of phenotypic evolution.