### Abstract

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 language | English |
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Pages (from-to) | 254-280 |

Number of pages | 27 |

Journal | Theoretical Population Biology |

Volume | 50 |

Issue number | 3 |

DOIs | |

Publication status | Published - Dec 1996 |

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### All Science Journal Classification (ASJC) codes

- Agricultural and Biological Sciences(all)
- Ecology, Evolution, Behavior and Systematics

### Cite this

*Theoretical Population Biology*,

*50*(3), 254-280. https://doi.org/10.1006/tpbi.1996.0031

**Establishment probability in fluctuating environments : A branching process model.** / Haccou, Patsy; Iwasa, Yoh.

Research output: Contribution to journal › Article

*Theoretical Population Biology*, vol. 50, no. 3, pp. 254-280. https://doi.org/10.1006/tpbi.1996.0031

}

TY - JOUR

T1 - Establishment probability in fluctuating environments

T2 - A branching process model

AU - Haccou, Patsy

AU - Iwasa, Yoh

PY - 1996/12

Y1 - 1996/12

N2 - 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.

AB - 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.

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U2 - 10.1006/tpbi.1996.0031

DO - 10.1006/tpbi.1996.0031

M3 - Article

C2 - 9000490

AN - SCOPUS:0030475823

VL - 50

SP - 254

EP - 280

JO - Theoretical Population Biology

JF - Theoretical Population Biology

SN - 0040-5809

IS - 3

ER -