Publication Date

Spring 4-13-2017


Phylogenetic comparative methods have been used to test evolutionary signals through trait evolutionary processes. Traditionally, biologists use one phylogenetic tree as a tool to handle dependent data for the traits of interest and hence utilize one gene only. However, it is more informative if the evolutionary processes of a trait are presented by phylogenetic trees reconstructed by the DNA alignments from more than one gene. In this work, we explain and develop two methods involving modeling the trait evolutionary processes: (a) two gene trees via the Brownian motion (BM) model; and (b) two gene trees via the Ornstein-Uhlenbeck (OU) model. For presentation purposes, these two models obtain evolutionary signals from both gene trees and then utilize the variance-covariance matrix of the error terms through the phylogenetic generalized linear model approach. For parameter estimation purposes, we develop the two gene trees model for one trait by using two different Bayesian approaches: (a) the adaptive Metropolis-Hastings (AMH) approach; and (b) the approximate Bayesian computation (ABC) method. The simulations from this study indicate that, under the two gene trees BM model with one trait, the AMH approach performs well on gene trees with longer internal branch lengths regardless of the number of taxa, whereas the ABC method only performs well on small numbers of taxa. In addition, we find that the AMH approach also performs well on gene trees with larger numbers of taxa regardless of the branch lengths and topologies. To illustrate the two methods, we analyze data of grain width of rice varieties that are associated with two major genes: GW2 and qSW5 under artificial selection, which implies that the BM model is a wrong model because it ignores selection. However, when applying model selection, according to both AIC and BIC, between the one gene tree model versus two gene trees model, we find that: (i) the one gene tree BM model has the lowest AIC and BIC; and (ii) the two gene trees OU model is better than the one gene tree OU model. Since the grain width is under artificial selection, the assumptions of the two gene trees OU model seem more applicable to the real case as it could capture more evolutionary signals from the data.

Degree Name


Level of Degree


Department Name

Mathematics & Statistics

First Committee Member (Chair)

James Degnan

Second Committee Member

Ronald Christensen

Third Committee Member

Joseph A. Cook

Fourth Committee Member

Li Li




Two gene trees trait evolutionary model, phylogenetic trees, Ornstein-Uhlenbeck, Brownian motion, dependency, adaptive Metropolis-Hastings (AMH) approach, approximate Bayesian computation (ABC) method, rice varieties.

Document Type