Inference of historical changes in migration rate from the lengths of migrant tracts

After migrant chromosomes enter a population, they are progressively sliced into smaller pieces by recombination. Therefore, the length distribution of "migrant tracts" (chromosome segments with recent migrant ancestry) contains information about historical patterns of migration. Here we introduce a theoretical framework describing the migrant tract length distribution and propose a likelihood inference method to test demographic hypotheses and estimate parameters related to a historical change in migration rate. Applying this method to data from the hybridizing subspecies Mus musculus domesticus and M. m. musculus, we find evidence for an increase in the rate of hybridization. Our findings could indicate an evolutionary trajectory toward fusion rather than speciation in these taxa.