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Abstract
Spatial population genetic models are useful tools to study the impact of geographical processes, such as migration and population structure, on genetic variation in humans and other species. Several research areas in human biomedical genetics are intertwined with spatial processes, particularly when considering variants affected by natural selection. In this dissertation, I will examine how spatial population genetic models can provide insight in two such areas: (i) the spread of adaptive viral lineages in epidemics, and (ii) the identification of deleterious variants associated with disease traits from large genetic samples. First, in Chapter 2, I review a long history of theoretical modeling related to the spread of adaptive alleles in spatial populations, and discuss how such models could be adapted to study variants of concern in SARS-CoV-2 and similar viruses. In Chapters 3 and 4, I turn to the second question of characterizing deleterious variants from genetic samples. In particular, I focus on the role of spatially uneven sampling designs on ascertained allele frequencies of rare, deleterious variants. In Chapter 3, I present a population genetic model for the distribution of carriers of deleterious alleles in a structured population – accounting for dispersal, drift, selection, mutation, and uneven spatial sampling simultaneously – and derive key properties of the site frequency spectrum (SFS) as well as downstream quantities. In Chapter 4, I provide an empirical analysis of how spatially uneven sampling impacts sampled allele frequencies, and compare these results to expectations under the model of Chapter 3 using a likelihood-based framework. In sum, the work presented here demonstrates the utility of spatial population genetics-based approaches for studying problems of biomedical interest, and suggests new approaches for improving such models and their application as the availability of genetic data continues to grow.