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My studies at Florida State University focused on using computers and statistics to solve problems in population genetics. I have created models and algorithms that have the potential to improve the statistical analysis of population genetics. Population genetical data is often noisy and thus requires the use of statistics in order to be able to draw meaning from the data. This dissertation consists of three main projects. The first project involves the parallel evaluation an model inference on multi-locus data sets. Bayes factors are used for model selection. We used thermodynamic integration to calculate these Bayes factors. To be able to take advantage of parallel processing and parallelize calculation across a high performance computer cluster, I developed a new method to split the Bayes factor calculation into independent units and then combine them later. The next project, the Transition Probability Structured Coalescence [TSPC], involved the creation of a continuous approximation to the discrete migration process used in the structured coalescent that is commonly used to infer migration rates in biological populations. Previous methods required the simulation of these migration events, but there is little power to estimate the time and occurrence of these events. In my method, they are replaced with a one dimensional numerical integration. The third project involved the development of a model for the inference of the time of speciation. Previous models used a set time to delineate a speciation and speciation was a point process. Instead, this point process is replaced with a parameterized speciation model where each lineage speciates according to a parameterized distribution. This is effectively a broader model that allows both very quick and slow speciation. It also includes the previous model as a limiting case. These three project, although rather independent of each other, improve the inference of population genetic models and thus allow better analyses of genetic data in fields such as phylogeography, conservation, and epidemiology.
A Dissertation submitted to the Department of Scientiﬁc Computing in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy.
Includes bibliographical references.
Peter Beerli, Professor Directing Thesis; Anuj Srivastava, University Representative; Gordon Erlebacher, Committee Member; Alan Lemmon, Committee Member; Dennis Slice, Committee Member.
Florida State University
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