Abstract. Geographic variation may ultimately lead to the splitting of a subdivided population into reproductively isolated units in spite of migration. Here, we consider how the waiting time until the first split and its location depend on different evolutionary factors including mutation, migration, random genetic drift, genetic architecture, and the geometric structure of the habitat. We perform large-scale, individual-based simulations using a simple model of reproductive isolation based on a classical view that reproductive isolation evolves as a by-product of genetic divergence. We show that rapid parapatric speciation on the time scale of a few hundred to a few thousand generations is plausible even when neighboring subpopulations exchange several individuals each generation. Divergent selection for local adaptation is not required for rapid speciation. Our results substantiates the claims that species with smaller range sizes (which are characterized by smaller local densities and reduced dispersal ability) should have higher speciation rates. If mutation rate is small, local abundances are low, or substantial genetic changes are required for reproductive isolation, then central populations should be the place where most splits take place. With high mutation rates, high local densities, or with moderate genetic changes sufficient for reproductive isolation, speciation events are expected to involve mainly peripheral populations.Key words. Centrifugal speciation, holey adaptive landscapes, mathematical modeling, parapatric, peripatric.Received March 19, 1999. Accepted January 27, 2000.The geographic range sizes of most species are much larger than the typical dispersal distances of individuals (or gametes). This creates an opportunity for the generation and maintenance of extensive genetic differences among geographic populations of the same species in spite of migration. Several factors contribute to these processes. Because each specific mutation is a very rare event, whereas the number of possible mutations is enormous, different mutations will appear in different geographic areas. Mani and Clarke (1990) refer to this factor as ''mutational order.'' Additional divergence will be created by stochastic factors affecting survival and reproduction, which are commonly referred to as ''genetic drift.'' Finally, variation in abiotic and biotic conditions can result in systematic differences in selection regimes that operate in different parts of the species range to augment geographic differentiation. Extensive geographic variation is well documented for most species (e.g., Endler 1977;Avise 1994). A classical example of extreme geographic differentiation are ''ring species'' (e.g., Mayr 1942Mayr , 1963Wake 1997), where genetic differences between some neighboring populations result in strong reproductive isolation.Generation of geographic variation is a necessary step in most scenarios of speciation. Here, we concentrate on parapatric speciation, that is, speciation with some gene flow between neighboring su...