Detecting range expansions from genetic data

We propose a method that uses genetic data to test for the occurrence of a recent range expansion and to infer the location of the origin of the expansion. We introduce a statistic for pairs of populations $psi$ (the directionality index) that detects asymmetries in the two-dimensional allele frequency spectrum caused by the series of founder events that happen during an expansion. Such asymmetry arises because low frequency alleles tend to be lost during founder events, thus creating clines in the frequencies of surviving low-frequency alleles. Using simulations, we further show that $psi$ is more powerful for detecting range expansions than both $F_{ST}$ and clines in heterozygosity. We illustrate the utility of $psi$ by applying it to a data set from modern humans and show how we can include more complicated scenarios such as multiple expansion origins or barriers to migration in the model.