Monte Carlo methods for inference in population genetic models
Anderson, Eric C., 1970-
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This dissertation describes novel applications of Monte Carlo and Markov chain Monte Carlo (MCMC) techniques to statistical inference in problems from the field of conservation genetics. The inference problems are motivated by issues arising in the conservation and management of trout and salmon. The first half of the thesis deals with estimating effective population size and related quantities from temporally spaced samples of genetic data. A likelihood function for organisms with discrete generations is developed, based on the Wright-Fisher model and a hidden Markov chain formulation. Importance sampling methods for computing this likelihood are presented and applied to published data on Drosophila. Some modeling assumptions implicit in the use of the Wright-Fisher model are detailed, and a new model for genetic inheritance, based on a Polya urn scheme, is presented and characterized. Methods are developed using this model for the MCMC estimation of the likelihood or posterior probability for the effective size of a population or for the ratio lambda of the per-generation number of effective breeders to census breeders in a population. The Polya urn model forms the basis for a probability model of allele frequency change conditional on lambda in salmon populations. Specifying this model in terms of a large directed graph simplifies the application of a single-component Metropolis-Hastings algorithm for computing the posterior distribution of lambda. The method is applied to genetic data simulated upon the census counts of a threatened salmon population in Idaho, demonstrating that the method allows precise estimates of lambda with such data.The second half of the thesis focuses on approaches to inference within populations of recently-hybridized populations. First, I extend the methods of PRITCHARD et al. (2000) to allow inference of pure and admixed categories of individuals in structured populations. Finally, I develop methods based on explicit modeling of recent hybridization and evaluate the potential for using genetic data to distinguish F1, F 2 and backcrossed hybrid categories among sympatric, hybridizing populations.