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Analysis and application of linkage disequilibrium in population and statistical genetics

Linkage disequilibrium (LD) is the non-random association of alleles at different genetic loci. This dissertation consists of three projects that relate to the analysis and application of LD on various topics within population and statistical genetics. Various measures of LD have been proposed in the literature, each with different arguments favoring its use. Chapter 2 employs a theoretical approach to examine mathematical properties of five different measures of LD. These results help place the use of various LD statistics into their proper contexts, and provide a mathematical basis for comparing their values. Next, the presence of LD in genomes can be leveraged for a number of different applications in statistical genetics. Chapter 3 examines one such example in genetic imputation. Specifically, we ask the question of how to optimally select a subset of a study sample for sequencing when choosing an internal reference panel for imputation, in order to maximize the eventual imputation accuracy. We compare two algorithms—maximizing phylogenetic diversity (PD) and minimizing average distance to the closest leaf (ADCL)—and conclude that while both algorithms give better imputation results as compared to randomly selecting haplotypes to be included in the reference panel, imputation accuracy is the highest when minimizing ADCL is used as the method for panel selection. Finally, LD in genomes can produce genetic signatures that may be suggestive of certain demographic processes. Genetic linkage results in the preservation of homozygous segments in the genome that are produced as the result of genomic sharing, which can then be detected as runs of homozygosity (ROH). Chapter 4 analyzes the distribution of ROH lengths in a sample of worldwide Jewish and non-Jewish populations, and employs a model-based clustering method to classify the ROH in a given population into three classes (short, intermediate, and long) based on length. Furthermore, for a subset of the Jewish populations in this study, we were able to obtain estimates of demographic rates of consanguinity (as indicated by the rates of close-relative unions). We find that the level of consanguinity in those populations is predictive of long ROH, thus finding genetic signatures of mating patterns that existed in a population's history. Making use of theoretical, computational, and statistical approaches, these chapters together provide a wide-ranging account of different aspects of LD, as related to their respective applications within the field.