A major goal of human population genetics is to understand our evolutionary history from genetic data. With the advances made in whole-genome sequencing, ancient DNA, and broader spatial sampling efforts, we are faced with new sets of challenges to: (1) visually represent population genetic data and (2) to develop theoretical results for handling new dimensions in the sampling process, such as time. With the increased pace of technological innovation and sampling in human genetics, the development of new theory and data representations are key to extracting deeper biological understanding from such rich data sources. In Chapter 1, we develop a new representation of multi-population allele frequency data to highlight the geographic distribution of human genetic variation from a variant-centric perspective. In Chapter 2, we derive theoretical results for the implications of serial-sampling on genealogical ancestry at multiple genetic loci, with close applications to genotype imputation. In Chapter 3, we focus on the genetic history of the Kodava population in south India as a case study to assess population origin hypotheses and south Indian demographic history. The work here suggests new methods for the analysis of human genetic data, as well as new theoretical developments to understand the spatio-temporally sampled datasets that are becoming increasingly commonplace in human population genetics.



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