The spatial mixing of genomes in secondary contact zones

Recent genomic studies have highlighted the important role of admixture in shaping genome-wide patterns of diversity. Past admixture leaves a population genomic signature of linkage disequilibrium (LD), reflecting the mixing of parental chromosomes by segregation and recombination. These patterns of LD can be used to infer the timing of admixture, but the results of inference can depend strongly on the assumed demographic model. Here, we introduce a theoretical framework for modeling patterns of LD in a geographic contact zone where two differentiated populations have come into contact and are mixing by diffusive local migration. Assuming that this secondary contact is recent enough that genetic drift can be ignored, we derive expressions for the expected LD and admixture tract lengths across geographic space as a function of the age of the contact zone and the dispersal distance of individuals. We develop an approach to infer age of contact zones, using population genomic data from multiple spatially sampled populations by fitting our model to the decay of LD with recombination distance. To demonstrate an application of our model, we use our approach to explore the fit of a geographic contact zone model to three human genomic data sets from populations in Indonesia, Central Asia, and India and compare our results to inference under different demographic models. We obtain substantially different results from those of the commonly used model of panmictic admixture, highlighting the sensitivity of admixture timing results to the choice of demographic model.