Stochastic modeling of morphological rate evolution: Phylogenetic regression with approximate Bayesian computation

In macroevolutionary studies, one major focus is understanding the evolution of traits. Several novel statistical models have been proposed to link the rate of evolution of one trait with another trait. In this framework, we expand the existing Brownian motion-type covariate (BM) to the Ornstein–Uhlenbeck (OU) process-type covariate that allows stabilizing selection to occur during evolution. In addition, the covariate type of the early burst (EB) process type covariate is also developed to consider the adaptive radiation phenomenon. Due to the lack of model likelihood, we propose the use of the approximate Bayesian computation (ABC) technique for the estimation of the model parameters. Simulations show that the models work well with posterior estimates close to the true parameters. The models are applied to analyze the 136 bird species data to reinvestigate how the rates of beak-shaped evolution in birds are influenced by brain mass.