The effective founder effect in a spatially expanding population
Benjamin Marco Peter, Montgomery Slatkin
The gradual loss of diversity associated with range expansions is a well known pattern observed in many species, and can be explained with a serial founder model. We show that under a branching process approximation, this loss in diversity is due to the difference in offspring variance between individuals at and away from the expansion front, which allows us to measure the strength of the founder effect, dependant on an effective founder size. We demonstrate that the predictions from the branching process model fit very well with Wright-Fisher forward simulations and backwards simulations under a modified Kingman coalescent, and further show that estimates of the effective founder size are robust to possibly confounding factors such as migration between subpopulations. We apply our method to a data set of Arabidopsis thaliana, where we find that the founder effect is about three times stronger in the Americas than in Europe, which may be attributed to the more recent, faster expansion.