Fast and Flexible Estimation of Effective Migration Surfaces

An important feature in spatial population genetic data is often “isolation-by-distance,” where genetic differentiation tends to increase as individuals become more geographically distant. Recently, Petkova et al. (2016) developed a statistical method called Estimating Effective Migration Surfaces (EEMS) for visualizing spatially heterogeneous isolation-by-distance on a geographic map. While EEMS is a powerful tool for depicting spatial population structure, it can suffer from slow runtimes. Here we develop a related method called Fast Estimation of Effective Migration Surfaces (FEEMS). FEEMS uses a Gaussian Markov Random Field in a penalized likelihood framework that allows for efficient optimization and output of effective migration surfaces. Further, the efficient optimization facilitates the inference of migration parameters per edge in the graph, rather than per node (as in EEMS). When tested with coalescent simulations, FEEMS accurately recovers effective migration surfaces with complex gene-flow histories, including those with anisotropy. Applications of FEEMS to population genetic data from North American gray wolves shows it to perform comparably to EEMS, but with solutions obtained orders of magnitude faster. Overall, FEEMS expands the ability of users to quickly visualize and interpret spatial structure in their data.