Deep Recovery of Effective Migration Surfaces

The isolation-by-distance (IBD) principle describes the tendency for genetic relatedness to decline with geographic distance. Although the existence IBD has long been documented in natural populations, recent analyses of spatially referenced genotype data have shown that the strength of this relationship can vary across a landscape due to geographic barriers, habitat compatibility, or other factors. Effective migration surfaces (EMS) have emerged as a popular exploratory tool for visualizing spatial patterns in IBD. However, fitting likelihood-based EMS models is often computationally demanding, requiring repeated large-scale matrix calculations. Here, we introduce Deep Recovery of Effective Migration Surfaces (dreems), a graph neural network for amortized inference of effective migration surfaces. dreems maps genetic covariance and sampling locations directly to an effective migration surface, while simultaneously providing predictive uncertainty estimates. Once trained, the network accommodates different graph sizes and sampling designs without needing to re-train. Across independent coalescent simulations that were not seen during training, dreems has roughly 10-30% lower estimation error compared to a state-of-the-art likelihood-based method, with the largest gains observed under sparse sampling designs that are commonly encountered in practice. Reanalysis of several published datasets recovers spatial patterns that are broadly consistent with earlier likelihood-based estimates, while reducing computation time by orders of magnitude.