The promise and challenge of spatial inference with the full ancestral recombination graph under Brownian motion.

Spatial patterns of genetic relatedness among samples reflect the past movements of their ancestors. Our ability to untangle this history has the potential to improve dramatically given that we can now infer the ultimate description of genetic relatedness, the ancestral recombination graph (ARG). By extending spatial theory previously applied to trees, we generalize the common model of Brownian motion to full ARGs, thereby accounting for correlations in trees along a chromosome while efficiently computing likelihood-based estimates of dispersal rate and genetic ancestor locations, with associated uncertainties.