Publication Date

Summer 7-30-2024

Abstract

A commonly used tool for evolutionary biologists is a phylogenetic tree that represents the ancestry of a set of species and the evolution of traits. Statistical models can be used to predict the probabilities of gene trees which represent ancestral relationships of genes sampled from species. Because of this, we are able to represent the likelihood of a species tree, which represents the evolutionary history of a set of species, as a function of the counts of gene tree topologies, where each gene tree represents the ancestry of a specific genetic locus for multiple species. Because we can represent these likelihood functions as polynomials, we can also use other algebraic and calculus-based analyses. In addition to an extended analysis, we can also plot and graph these polynomials in order to visualize the likelihoods, finding maximums, minimums, shapes, curves, and even contour/hotspot maps which help us to see if there are multiple ways to maximize likelihoods. We visualize species tree likelihoods from simulated data as well as an empirical data set of over 10,000 estimated gene trees for four species of gibbons.

Degree Name

Statistics

Level of Degree

Masters

Department Name

Mathematics & Statistics

First Committee Member (Chair)

James Degnan

Second Committee Member

Yan Lu

Third Committee Member

Brent Wagner

Document Type

Thesis

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