Establishment probability in fluctuating environments: A branching process model

Patsy Haccou, Yoh Iwasa

Research output: Contribution to journalArticlepeer-review

61 Citations (Scopus)


We study the establishment probability of invaders in stochastically fluctuating environments and the related issue of extinction probability of small populations in such environments, by means of an inhomogenous branching process model. In the model it is assumed that individuals reproduce asexually during discrete reproduction periods. Within each period, individuals have (independent) Poisson distributed numbers of offspring. The expected numbers of offspring per individual are independently identically distributed over the periods. It is shown that the establishment probability of an invader varies over the reproduction periods according to a stable distribution. We give a method for simulating the establishment probabilities and approximations for the expected establishment probability. Furthermore, we show that, due to the stochasticity of the establishment success over different periods, the expected success of sequential invasions is larger then that of simultaneous invasions and we study the effects of environmental fluctuations on the extinction probability of small populations and metapopulations. The results can easily be generalized to other offspring distributions than the Poisson.

Original languageEnglish
Pages (from-to)254-280
Number of pages27
JournalTheoretical Population Biology
Issue number3
Publication statusPublished - Dec 1996

All Science Journal Classification (ASJC) codes

  • Ecology, Evolution, Behavior and Systematics


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