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. We evaluate this model's ability to reconstruct spatial histories using individual-based simulations and unfortunately find a clear bias in the estimates of dispersal rate and ancestor locations. We investigate the causes of this bias, pinpointing a discrepancy between the model and the true spatial process at recombination events. This highlights a key hurdle in extending the ubiquitous and analytically-tractable model of Brownian motion from trees to ARGs, which otherwise has the potential to provide an efficient method for spatial inference, with uncertainties, using all the information available in the full ARG.