A Stochastic Model for the Interbreeding of Two Populations Continuously Sharing the Same Habitat

We propose and solve a stochastic mathematical model of general applicability to interbreeding populations which share the same habitat. Resources are limited so that the total population size is fixed by environmental factors. Interbreeding occurs during all the time of coexistence until one of the two population disappears by a random fluctuation. None of the two populations has a selective advantage. We answer the following questions: How long the two populations coexist and how genetically similar they become before the extinction of one of the two? how much the genetic makeup of the surviving population changes by the contribution of the disappearing one? what it is the number of interbreeding events given the observed introgression of genetic material? The model was originally motivated by a paleoanthropological problem concerning the interbreeding of Neanderthals and African modern humans in Middle East which is responsible for the fraction of Neanderthal genes (1-4%) in present Eurasian population.