Effect of Polytomy on the Parameter Estimation and Goodness of Fit of Phylogenetic Linear Regression Models for Trait Evolution

Abstract

Phylogenetic regression models for trait evolution incorporate phylogenetic trees for the analysis of comparative data, in order to study trait relationships among a group of related species. However, as such trees are estimated, it is unlikely that there will be no errors when describing the relationships among species. In particular, for polytomy trees, where the relationships within a particular clade of species are more/less certainly determined (hard/soft polytomy, respectively), results of comparative analyses obtained from models based on those phylogenetic trees may also be affected. In this study, through extensive simulations, the performances of several popular Gaussian process-based regression models (Brownian motion, BM; Ornstein–Uhlenbeck process, OU; early burst, EB), as well as branch-stretching models (Pagel’s (Formula presented.)), were evaluated by assessing their fit and parameter estimation performance when soft polytomies are presented on either the root or a clade with insufficient phylogenetic information. Comparisons of the models are conducted by either assessing the accuracy of the estimator of regression and model parameters, or using a measure of fit (AIC, (Formula presented.), and mean square error). It is found that, although polytomy does not significantly impact the fit and parameter estimate within a specified model, distinguishable differences and effects may be observed among trees and models. In particular, Pagel (Formula presented.) model and the OU model yield more accurate estimates and provide better fitting effects than the other models (BM, EB, (Formula presented.), (Formula presented.)). While correcting phylogeny is an essential step prior to analysis, users may also consider using more appropriate models when encountering the polytomy issue.