Abstract
Spatial population genetic data often exhibits 'isolation-by-distance,' where genetic similarity tends to decrease as individuals become more geographically distant. The rate at which genetic similarity decays with distance is often spatially heterogeneous due to variable population processes like genetic drift, gene flow, and natural selection. 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 model 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). With simulations, we show conditions under which FEEMS can accurately recover effective migration surfaces with complex gene-flow histories, including those with anisotropy. We apply FEEMS to population genetic data from North American gray wolves and show it performs favorably in comparison to EEMS, with solutions obtained orders of magnitude faster. Overall, FEEMS expands the ability of users to quickly visualize and interpret spatial structure in their data.
Highlights
The relationship between geography and genetics has had enduring importance in evolutionary biology
Details on the Fast Estimation of Effective Migration Surfaces (FEEMS) model are described in the Materials and methods section, at a high level, we assume exchangeability of individuals within each sub-population and estimate allele frequencies, bfjðkÞ, for each sub-population, indexed by k, and single nucleotide polymorphism (SNP), indexed by j, under a simple Binomial sampling model
With the estimated allele frequencies in hand, we model the data at each SNP using an approximate Gaussian model whose covariance is, up to constant factors, shared across all SNPs—in other words, after rescaling by SNPspecific variation factors, we assume that the set of observed frequencies at each SNP is an independent realization of the same spatial process
Summary
The relationship between geography and genetics has had enduring importance in evolutionary biology (see Felsenstein, 1982). One fundamental consideration is that individuals who live near one another tend to be more genetically similar than those who live far apart (Wright, 1943; Wright, 1946; Malecot, 1948; Kimura, 1953; Kimura and Weiss, 1964). This phenomenon is often referred to as ‘isolation-by-distance’ (IBD) and has been shown to be a pervasive feature in spatial population genetic data across many species (Slatkin, 1985; Dobzhansky and Wright, 1943; Meirmans, 2012). Geographic features can influence migration in localized regions leading to spatially heterogeneous patterns of IBD (Bradburd and Ralph, 2019)
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