Estimating population split times and migration rates from historical effective population sizes
The estimation of effective population sizes (Ne) through time is of fundamental interest in population genetics, but the interpretation of Ne as the effective number of breeding individuals in the population is challenged by the effect of population structure. In fact, variation in Ne reported in many studies may be a consequence of changes in migration rates between populations rather than changes in actual population size. We address this long-standing problem here by constructing joint models of population size changes, migration, and divergence that can adjust temporal estimates of Ne and estimate the actual Ne of a local deme connected to another population through migration. We also develop a method for estimating divergence times and migration rates taking into account complex scenarios of changing population sizes. We apply the method to previously published data from humans, and show that, when taking migration and changes in Ne into account, the estimated divergence between the San and Dinka populations is approximately 108 kya, and not 255 kya as reported in a previous study. Using simulations, we demonstrate that the previously reported and surprisingly old estimates of divergence between San and Dinka is in fact caused by a quantifiable estimation bias due to changes in Ne through time.