Population Genetic Effects of Recent Admixture

Admixture has played an important role in shaping genetic diversity in many human populations. Quantifying these effects is important not only for answering historical questions, but also for detecting selection, mapping disease genes, and estimating recombination rates. Many existing methods for estimating admixture times use spatial information from the genomes of admixed individuals, such as the distribution of admixture tract lengths or the two-point covariance function of their local ancestries. I first discuss some theoretical results about the length distribution of admixture tracts. I use simulations to show that, for recent admixture events, no existing population genetic model approximates this length distribution well. I introduce a new model, based on dyadic intervals, which is accurate in this regime more mathematically tractable. I then show how the distribution of admixture proportions within a population, as estimated by programs such as STRUCTURE, gives information about the population's admixture history and relate the moments of this distribution to the theory of multi-locus linkage disequilibria. Finally, I show how measures of three-locus linkage disequilbria can be used to improve on the resolution of existing admixture history inference methods