Time-Dependent Random Effect Poisson Random Field Model for Polymorphism within and Between Two Related Species

TIME-DEPENDENT RANDOM EFFECT POISSON RANDOM FIELD MODEL FOR POLYMORPHISM WITHIN AND BETWEEN TWO RELATED SPECIES by Shilei Zhou Dr. Amei Amei, Examination Committee Chair Associate Professor of Mathematical Sciences University of Nevada Las Vegas Molecular evolution is partially driven by mutation, selection, random genetic drift, or combination of the three factors. To quantify the magnitude of these genetic forces, a previously developed time-dependent fixed effect Poisson random field model provides powerful likelihood and Bayesian estimates of mutation rate, selection coefficient, and species divergence time. The assumption of the fixed effect model that selection intensity is constant within a genetic locus but varies across genes is obviously biologically unrealistic, but it serves the original purpose of making statistical inference about selection and divergence between two related species they are individually at mutation-selection-drift inequilibrium. By relaxing the constant selection assumption, this dissertation derives a within-locus random effect model in which the selective intensity of non-synonymous mutation in a gene is treated as a iii random sample from some underlying normal distribution and applies a Bayesian framework to make statistical inference about various genetic parameters. Also, a new N-ADAM-mixing Markov chain Monte Carlo sampler is created to provide better sampling strategy and fastens the convergence speed. Furthermore, to conquer the computational cost of the developed model this dissertation proposes a MPI parallel computing scheme which boosts the calculation speed by ten times.