It has been long recognized that population demographic expansions lead to distinctive features in the molecular diversity of populations. However, recent simulation results have suggested that a distinction could be made between a pure demographic expansion in an unsubdivided population, and a range expansion in a subdivided population, both leading to a large increase in the total number of the individuals. In order to better characterize the effect of a range expansion, I introduce a simple model of instantaneous expansion under an infinite-island model, under which I derive the distribution of the number of mutation differences between pairs of genes (the mismatch distribution), the heterozygosity, the average number of pairwise difference, and the fixation index FST. These derivations are checked against simulations, and are shown to lead to results qualitatively similar to those one would obtain after a range expansion in a 2-dimensional stepping-stone model. I then apply these results to estimate immigration rates in hunter-gather and post-Neolithic human populations from patterns of mitochondrial (mtDNA) diversity. Potential problems with this estimation procedure are also discussed.