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

Abstract

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.

Figure 1.—

The distribution of migrant tract lengths after the advent of admixture. Models where previously isolated populations begin exchanging migrants at rate N_em = 0.1 100, 200, or 300 generations ago are compared against the case in which populations exchange migrants at a constant rate N_em = 0.1 with no prior isolation (the single migration rate, “equilibrium” model). Depicted here is the relative abundance of migrant tracts for 0.01-cM histogram bins between 0.5 (the minimum/threshold tract length) and 5 cM. Also shown is the agreement between theoretical predictions (lines) and tracts from 1000 simulated replicates with N_e = 10,000 (shapes).

Figure 2.—

Power to test demographic hypotheses. Shown here first are tests comparing the migration rate change model to the null model of a constant migration rate, for histories involving decreasing (A) or increasing (B) migration rates. For histories involving decreasing migration rates, power to reject a model with m₁ constrained to be zero is shown (C). For histories involving increasing migration rates, power to reject a model with m₂ constrained to be zero is shown (D). Significance was gauged by comparing the difference in log-likelihood scores between models to data simulated under the null model. Each data set consisted of 100 simulated haploid genomes, and a threshold tract length of 0.5 cM was used.

Figure 3.—

Distribution of demographic parameter estimates. Results from the analysis of simulated migrant tract data are shown, including median estimates (diamonds) and 95% confidence intervals (the 2.5 and 97.5 percentiles of the distribution of estimates) for (A) m₁, (B) m₂, and (C) T. The order of parameter sets is the same in each panel (i.e., the far left estimates are for true values of m₁ = 0, m₂ = 1E−5, and T = 100).

Figure 4.—

Migrant tract lengths found in M. m. domesticus and M. m. musculus, compared to constant migration rate expectations.