by Nobuyuki Kutsukake and Hideki Innan
This chapter discusses the fundamental structure and advantages of the approximate Bayesian computation (ABC) algorithm in phylogenetic comparative methods (PCMs). ABC estimates unknown parameters as follows: (i) simulated data are generated under a suite of parameters randomly chosen from their prior distributions; (ii) the simulated data are compared with empirical data; (iii) parameters are accepted when the distance between the simulated and empirical data is small; and (iv) by repeating steps (i) to (iii), posterior distributions of parameters will be gained. Because ABC does not necessitate mathematical expression or analytic solution of a likelihood function, ABC is particularly useful when a maximum-likelihood estimation is difficult to conduct (a common situation when testing complex evolutionary models and/or models with many parameters in PCMs). As an application, we analysed trait evolution in which a specific species exhibits an extraordinary trait value relative to others. The ABC approach detected the occurrence of branch-specific directional selection and estimated ancestral states of internal nodes. As computational power increases, such likelihood-free approaches will become increasingly useful for PCMs, particularly for testing complex evolutionary models that deviate from the standard models based on the Brownian motion.