On the extinction of a colonizing species.

Abstract Stochastic models are used to analyze the colonization or extinction of a population growing on a limit source of food. It is shown that there exists a critical size of the population such that if the initial size of the population is above this level, the population is bound to colonize. On the other hand, if the population size is below this critical size, either extinction takes place with an average time of extinction of the order of the reciprocal of the birth rate per individual for low-density population, or the existence of the population is guaranteed for an immensely long time. The size of the established population if it escapes rapid extinction depends on the amount of food available.