Modeling rate of adaptive trait evolution using Cox–Ingersoll–Ross process: An Approximate Bayesian Computation approach

Abstract: Over the past decades, the Gaussian process has been widely used to study trait evolution. In particular, two members of Gaussian processes, Brownian motion and the Ornstein-Uhlenbeck process, have been frequently applied for describing continuous trait evolution. Models have been proposed to study the impact on the optimum of a trait by other traits. Applying the Cox–Ingersoll–Ross (CIR) process on rate of evolution, which prevents rates from becoming negative, is a potentially useful extension developed here as the OUBMCIR and OUOUCIR models. Since the likelihood functions of the OUBMCIR and the OUOUCIR are intractable, a heuristic algorithm for parameter estimation and inference under Approximate Bayesian Computation (ABC) is proposed. Simulation studies show that new models perform well. Empirical analysis using several datasets from literature also provides evidence of the validity and utility of the new models.