Abstract For over 30 years, a debate has raged among anthropologists about the origins of anatomically modern humans. At first the debate centered on fossil evidence, but in the past 10–15 years population geneticists have entered the fray. One model, the multiregional evolution model, posits a gradual transition from Homo erectus to anatomically modern humans throughout the Old World. In contrast, the recent African origin model hypothesizes that anatomically modern humans arose from a small, isolated population in Africa, spread out of Africa, and replaced indigenous H. erectus populations in Eurasia and Australasia. A primary objection, from a population genetics perspective, to the multiregional model is that the genetic data suggest a small effective population size for humans. This effective size is on the order of 10 000. Effective population size has a complex relationship with census size, but it has been argued that, assuming that effective size is roughly equal to the number of breeding individuals in human populations under standard demographic conditions, 10 000 breeding individuals could not have occupied much of the Old World throughout the Pleistocene and remained a cohesive species via gene flow. However, this argument is not valid if one considers population extinction and recolonization, which might have played an important role in human history during the Pleistocene. With population extinction and recolonization, the inbreeding effective population size can be small and the census size extremely large. In this paper, I will show that under conditions of population extinction and recolonization, an effective population size of 10 000 suggested by genetic data is compatible with a large census size consistent with the multiregional model.