Award Date


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mathematical Sciences

First Committee Member

Amei Amei

Second Committee Member

Chih-Hsiang Ho

Third Committee Member

Malwane Ananda

Fourth Committee Member

Guogen Shan

Number of Pages



The fidelity of DNA sequence data makes it a perfect platform for quantitatively analyzing and interpreting evolutionary progress. By comparing the information between intraspecific polymorphism with interspecific divergence in two sibling species, the well established Poisson Random Field theory offers a statistical framework with which various genetic parameters such as natural selection intensity, mutation rate and speciation time can be effectively estimated. A recently developed time-inhomogeneous PRF model has reinforced the original method by removing the assumption of stationary site frequency, but it preserves the condition that the two sibling species share same effective population size with their ancestral species. This dissertation explores a relaxation of this biologically unrealistic assumption by hypothesizing that each of the two descendant species experienced a sudden change in population size at the times of divergence from their most recent common ancestor. Statistical inference of the various genetic parameters are made under a hierarchical Bayesian framework and carried out with a multi-layer Markov chain Monte Carlo sampling scheme. To meet the intensive computational demand, a R program is integrated with C++ code and a parallel executing technique is designed to run the program with multiple CPU cores.


Statistics and Probability

File Format


Degree Grantor

University of Nevada, Las Vegas




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