Analytic and simulation studies were carried out in order to predict the average geographic area occupied by alleles in a continuously distributed population. The properties of three statistics were investigated: the sum of the squared distances between members of allelic classes, the sum of the root mean squared distances, and the sum of the squares of the numbers of alleles. The expectations of these quantities can be obtained analytically from both stepping-stone and branching diffusion models. The predictions of these two models are similar for wide ranges of parameter values and are consistent with the simulation results from a stepping-stone model. These results suggest that measures of the geographic distribution of alleles can be useful for estimating average dispersal distances at loci, such as minisatellite and microsatellite loci, at which mutation rates are high enough that they can be estimated with confidence.