Estimating recent migration and population-size surfaces

In many species a fundamental feature of genetic diversity is that genetic similarity decays with geographic distance; however, this relationship is often complex, and may vary across space and time. Methods to uncover and visualize such relationships have widespread use for analyses in molecular ecology, conservation genetics, evolutionary genetics, and human genetics. While several frameworks exist, a promising approach is to infer maps of how migration rates vary across geographic space. Such maps could, in principle, be estimated across time to reveal the full complexity of population histories. Here, we take a step in this direction: we present a method to infer maps of population sizes and migration rates associated with different time periods from a matrix of genetic similarity between every pair of individuals. Specifically, genetic similarity is measured by counting the number of long segments of haplotype sharing (also known as identity-by-descent tracts). By varying the length of these segments we obtain parameter estimates associated with different time periods. Using simulations, we show that the method can reveal time-varying migration rates and population sizes, including changes that are not detectable when using a similar method that ignores haplotypic structure. We apply the method to a dataset of contemporary European individuals (POPRES), and provide an integrated analysis of recent population structure and growth over the last approximate to 3,000 years in Europe. Author summary We introduce a novel statistical method to infer migration rates and population sizes across space in recent time periods. Our approach builds upon the previously developed EEMS method, which infers effective migration rates under a dense lattice. Similarly, we infer demographic parameters under a lattice and use a (Voronoi) prior to regularize parameters of the model. However, our method differs from EEMS in a few key respects. First, we use the coalescent model parameterized by migration rates and population sizes while EEMS uses a resistance model. As another key difference, our method uses haplotype data while EEMS uses the average genetic distance. A consequence of using haplotype data is that our method can separately estimate migration rates and population sizes, which in essence is done by using a recombination rate map to calibrate the decay of haplotypes over time. An additional useful feature of haplotype data is that, by varying the lengths analyzed, we can infer demography associated with different recent time periods. We call our method MAPS for estimating Migration And Population-size Surfaces. To illustrate MAPS on real data, we analyze a genome-wide SNP dataset on 2224 individuals of European ancestry.