ESTABLISHMENT PROBABILITY IN FLUCTUATING ENVIRONMENTS - A BRANCHING-PROCESS MODEL

We study the establishment probability of invaders in stochastically f luctuating environments and the related issue of extinction probabilit y of small populations in such environments, by means of an inhomogene ous branching process model. In the model it is assumed that individua ls reproduce asexually during discrete reproduction periods. Within ea ch period, individuals have (independent) Poisson distributed numbers of offspring. The expected numbers of offspring per individual are ind ependently identically distributed over the periods. It is shown that the establishment probability of an invader varies over the reproducti on periods according to a stable distribution. We give a method for si mulating the establishment probabilities and approximations for the ex pected establishment probability. Furthermore, we show that, due to th e stochasticity of the establishment success over different periods, t he expected success of sequential invasions is larger then that of sim ultaneous invasions and we study the effects of environmental fluctuat ions on the extinction probability of small populations and metapopula tions. The results can easily be generalized to other offspring distri butions than the Poisson. (C) 1996 Academic Press, Inc.