This doctoral dissertation is composed of three projects and four chapters. Chapter 1 presents the background theories and models in the field of population genetics that are related to these projects.

In Chapter 2, I develop a composite likelihood ratio test (CLRT) for detecting genes and genomic regions that are subject to recurrent natural selection while relaxing the assumption of free recombination. We find that the test has excellent power to detect weak negative selection and moderate power to detect positive selection. Moreover, the test is quite robust to the bias in the estimate of local recombination rate, but not to certain demographic scenarios such as population growth or a recent bottleneck.

In Chapter 3, I present a novel method, Poisson pairwise difference method (PPDM), which efficiently co-estimates the selection coefficient and mutation rate from arbitrarily correlated SFS data. We demonstrate that the PPDM log-likelihood ratio test has good power to detect positive selection and moderate power to detect weak negative selection.

Current state-of-the-art approaches for quantifying meiotic recombination rates (R) and/or identifying hotspots are mostly based on the likelihood of observed haplotypes or linkage disequilibrium (LD) patterns. In Chapter 4, I describe a flexible, efficient, and population structure robust approach via multiple linear regression and non-parametric bootstrap based on the frequency spectra of unphased single nucleotide polymorphism sites (SNPs) and provide confidence intervals of R between adjacent pairs of SNPs. No LD information is required. We evaluate this new approach via Monte Carlo simulation as well as application to the well-characterized hotspots near the human TAP2 gene and a 206-kb region on ch1q42.3 near MS32.