Isolation-By-Distance-and-Time in a Stepping-Stone model

With the great advances in ancient DNA extraction, population genetics data are now made of geographically separated individuals from both present and ancient times. However, population genetics theory about the joint effect of space and time has not been thoroughly studied. Based on the classical stepping–stone model, we develop the theory of Isolation by Distance and Time. We derive the correlation of allele frequencies between demes in the case where ancient samples are present in the data, and investigate the impact of edge effects with forward–in–time simulations. We also derive results about coalescent times in circular/toroidal models. As one of the most common way to investigate population structure is to apply principal component analysis, we evaluate the impact of this theory on plots of principal components. Our results demonstrate that time between samples is a non-negligible factor that requires new attention in population genetics.