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Forward progress in empirical population genetics is closely tied to the development of theory which can accomodate and keep pace with the production of genetic data. In recent years, the ability to survey genetic variation at increasingly greater resolution, across the genomes of a variety of species, has prompted new approaches to use this data for population genetic inference. While many models have historically relied on assuming independence among genetic variants in a sample of chromosomes, there are now a variety of methods which can use the non-independence among variants as a source of information. In particular, the unique combination and co-inheritance of variants on a chromosome can be used to define "haplotypes" of linked genetic variation associated with specific populations, individuals, or variants from which they are descended. The work presented here is a contribution to this class of population genetic models which describes: (1) a method to estimate the timing of adaptation for a beneficial allele, including several applications to recent human evolution, (2) an application of the same method to infer the timing of introgression for coat color alleles in North American wolves and high-altitude adaptation in Tibetans, (3) a model to infer the action of purifying selection against genetic incompatibilities in a hybrid zone, and (4) a reanalysis of genomic data from Heliconius butterflies which confirms the role of hybridization in transfering mimicry phenotypes between species.


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