Publication Date

Spring 4-15-2022


This dissertation includes two main topics. The first uses measurement error modeling to improve upon an existing method of inferring species trees from gene trees that were estimated with error. The second involves extending the parametric bootstrap (PB) approach, which was previously shown to work well for one- and two-way analysis of variance models with unequal variance and unbalanced data (heteANOVA), to multi-factor heteANOVA models. An overall framework using PB is presented. For each topic, the underlying theory is shown, and simulations and applications to empirical data are presented, demonstrating improvement over earlier methods. The proposed species tree inference method shows that species tree inference can be improved in the presence of gene tree estimation error, and the new method may be useful for inferring starting trees for other possibly slower methods. The PB methods developed here provide a viable alternative to transforming data to meet the equal variance assumption.

Degree Name


Level of Degree


Department Name

Mathematics & Statistics

First Committee Member (Chair)

James Degnan (Co-Chair)

Second Committee Member

Guoyi Zhang (Co-Chair)

Third Committee Member

Fletcher G. W. Christensen

Fourth Committee Member

Jeffrey C. Long




species tree inference, measurement error modeling, Bayesian methods, ANOVA, unequal variance, multiple comparisons

Document Type



James Degnan and Gouyi Zhang were co-chairs of the committee.