P. Haccou et Y. Iwasa, ESTABLISHMENT PROBABILITY IN FLUCTUATING ENVIRONMENTS - A BRANCHING-PROCESS MODEL, Theoretical population biology, 50(3), 1996, pp. 254-280
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.