  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.
