Phylogenetic Curved Optimal Regression for Adaptive Trait Evolution

Abstract

Regression analysis using line equations has been broadly applied in studying the evolutionary relationship between the response trait and its covariates. However, the characteristics among closely related species in nature present abundant diversities where the nonlinear relationship between traits have been frequently observed. By treating the evolution of quantitative traits along a phylogenetic tree as a set of continuous stochastic variables, statistical models for describing the dynamics of the optimum of the response trait and its covariates are built herein. Analytical representations for the response trait variables, as well as their optima among a group of related species, are derived. Due to the models’ lack of tractable likelihood, a procedure that implements the Approximate Bayesian Computation (ABC) technique is applied for statistical inference. Simulation results show that the new models perform well where the posterior means of the parameters are close to the true parameters. Empirical analysis supports the new models when analyzing the trait relationship among kangaroo species.

The origins of mammal growth patterns during the Jurassic mammalian radiation

“…This correlation must be accounted for when comparing the growth rates of extant and fossil mammals of differing body size. The correlation was here accounted for by using phylogenetically informed nonlinear regression (PGNLR) (37) to compare log-transformed mean body mass (g) and log-transformed mean width of first recorded cementum growth layer group (μm) for each extant taxon studied here (n = 21). The first recorded growth layer group was chosen as this most reliably represents the maximum growth rate of the respective taxon and is least likely to be biased by the pattern of growth rate reduction experienced by extant mammals.…”

“…A phylogenetic subset of the extant mammals sampled was downloaded from https:// vertlife.org (data S1) representing their phylogenetic relationships. This was inputted into a nonlinear (exponential) regression model between log-transformed body mass and log-transformed mean first increment width using the methodology of Jhwueng and Wang (37). Four phylogenetically informed models were compared using the approximate Bayesian computation: an exponential model using Brownian motion for phylogenetic trait evolution (OUGBM), an exponential model using the Ornstein-Uhlenbeck process for phylogenetic trait evolution (OUGOU), a linear model using Brownian motion (OUBM), and a linear model using the Ornstein-Uhlenbeck process (OUOU).…”