Adaptive trait evolution in random environment

Abstract

In past decades, Gaussian processes has been widely applied in studying trait evolution using phylogenetic comparative analysis. In particular, two members of Gaussian processes: Brownian motion and Ornstein-Uhlenbeck process, have been frequently used to describe continuous trait evolution. Under the assumption of adaptive evolution, several models have been created around Ornstein-Uhlenbeck process where the optimum θ y t of a single trait y t is influenced with predictor x t . Since in general the dynamics of rate of evolution τ y t of trait could adopt a pertinent process, in this work we extend models of adaptive evolution by considering the rate of evolution τ y t following the Cox-Ingersoll-Ross (CIR) process. We provide a heuristic Monte Carlo simulation scheme to simulate trait along the phylogeny as a structure of dependence among species. We add a framework to incorporate multiple regression with interaction between optimum of the trait and its potential predictors. Since the likelihood function for our models are intractable, we propose the use of Approximate Bayesian Computation (ABC) for parameter estimation and inference. Simulation as well as empirical study using the proposed models are also performed and carried out to validate our models and for practical applications.

Modelling Trait-dependent Speciation with Approximate Bayesian Computation

“…Hence, alternative methods need to be employed, numerically solving an ODE system [20,22,31] or ABC (e.g. [10,27,42] and see a review in [28])…”

“…It turned out that looking at the sample mean and variance of the trait values was the best option. Statistics based on tips' means and variances have already been considered in the PCM setting [10,27,42]. However, the situation is different in the previous two cases.…”

“…Earlier, in a similar spirit just the variances inside clades were compared [10]. Similarly in [27] the mean and variance of the difference between tip measurements are calculated.…”

Phylogenetic Curved Optimal Regression for Adaptive Trait Evolution

“…Hansen et al [ 20 ] developed a popular model (OUBM model) for phylogenetic adaptive trait evolution where the response trait variable is assumed following an Ornstein–Uhlenbeck (OU) process dynamic where the optimum of the response trait is assumed with a linear relationship with Brownian motion (BM) covariates. Later, various scientists made further efforts to expand the OUBM model of Hansen et al via considering an Ornstein–Uhlenbeck process covariates (OUOU model) [ 21 , 22 ], a Cox–Ingersoll–Ross process for rate evolution [ 19 ], or extending the OUBM model to the multivariate case [ 23 , 24 , 25 ].…”

Building an adaptive trait simulator package to infer parametric diffusion model along phylogenetic tree

“…The paper focuses on the implementation of methods for adaptive trait evolution in Jhwueng and Maroulas [10] , Jhwueng and Maroulas [11] and Jhwueng [12] , building from Hansen et al. [9] .…”