Inference of historical migration rates via haplotype sharing

Abstract

Summary: Pairs of individuals from a study cohort will often share long-range haplotypes identical-by-descent. Such haplotypes are transmitted from common ancestors that lived tens to hundreds of generations in the past, and they can now be efficiently detected in high-resolution genomic datasets, providing a novel source of information in several domains of genetic analysis. Recently, haplotype sharing distributions were studied in the context of demographic inference, and they were used to reconstruct recent demographic events in several populations. We here extend the framework to handle demographic models that contain multiple demes interacting through migration. We extensively test our formulation in several demographic scenarios, compare our approach with methods based on ancestry deconvolution and use this method to analyze Masai samples from the HapMap 3 dataset.

Availability: DoRIS, a Java implementation of the proposed method, and its source code are freely available at http://www.cs.columbia.edu/~pier/doris.

Fig. 1.

An IBD segment (blue) is co-inherited by two present day individuals from a common ancestor that lived four generations in the past. Recombination shortens the IBD segment, as meiotic events occur along the lineage between the two individuals

Fig. 2.

Two demographic models that involve two populations and migration between them. In model (a), the populations have the same constant size N_e, and exchange individuals at the same rate m. In model (b), a population of constant ancestral size N_atot splits G generations in the past, resulting in two populations whose sizes independently fluctuate from and individuals to and individuals during G generations. During this period, the populations interact with asymmetric migration rates m₁₂ and m₂₁

Fig. 3.

True versus inferred parameters for the model in Figure 2a. Estimates were obtained using Equation (10)

Fig. 4.

Inference of recent effective population size using Equation (3), which neglects migration. The ratio between inferred and true population size (y-axis) increases as the migration rate (x-axis) is increased, approaching the sum of population sizes for both populations (twice the true size)

Fig. 5.

Results of the evaluation of our method on synthetic populations with demographic history depicted in the model of Figure 2b. Higher variance in the method’s accuracy is observed because of limited sample sizes and increased population sizes. Higher migration rates further decrease the rate of coalescent events in the recent generations (Fig. 5b), resulting in additional uncertainty. However, no significant bias is observed in the inference

Fig. 6.

We simulated a chromosome of 150 cM for 600 individuals using the model in Figure 2a, setting population sizes to 4000 and 12 000 diploid individuals, with a migration rate of 0.04. IBD sharing was extracted directly from the simulated genealogy (diamonds), or inferred trough GERMLINE using perfectly phased (circles) or computationally phased (triangles) chromosomes

Fig. 7.

The model used to simulate admixed populations

Fig. 8.

We created several simulation genotype datasets using the model in Figure 7, varying G_s while keeping , and using constant populations of size 5000 or 10 000 diploid individuals. We inferred the value of m using PCAdmix + Tracts, or GERMLINE + DoRIS, here reported as a function of G_s

Fig. 9.

We created several datasets using the model in Figure 7, varying G_s from 200 to 6000, and using with population sizes of 10 000 diploid individuals. We inferred the value of m using PCAdmix + Tracts from phased genotype data