Spatial patterns in genetic diversity are shaped by individuals dispersing from their parents and larger-scale population movements. It has long been appreciated that these patterns of movement shape the underlying genealogies along the genome leading to geographic patterns of isolation by distance in contemporary population genetic data. However, extracting the enormous amount of information contained in genealogies along recombining sequences has, up till recently, not been computational feasible. Here we capitalize on important recent advances in gene-genealogy reconstruction and develop methods to use thousands of trees to estimate time-varying per-generation dispersal rates and to locate the genetic ancestors of a sample back through time. We take a likelihood approach in continuous space using a simple approximate model (branching Brownian motion) as our prior distribution of spatial genealogies. After testing our method with simulations we apply it to the 1001 Genomes dataset of over one thousand Arabidopsis thaliana genomes sampled across a wide geographic extent. We detect a very high dispersal rate in the recent past, especially longitudinally, and use inferred ancestor locations to visualize many examples of recent long-distance dispersal and admixture. We also use inferred ancestor locations to identify the origin and ancestry of the North American expansion and to depict alternative geographic ancestries stemming from multiple glacial refugia. Our method highlights the huge amount of information about past dispersal events and population movements contained in genome-wide genealogies.
Fisher-KPP equation with small data and the extremal process of branching Brownian motion
