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On the role of Allee effect and mass migration in survival and extinction of a species

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Abstract

We use interacting particle systems to investigate survival and extinction of a species with colonies located on each site of $$\mathbb {Z}^d$$. In each of the four models studied, an individual in a local population can reproduce, die or migrate to neighboring sites. We prove that an increase of the death rate when the local population density is small (the Allee effect) may be critical for survival, and that the migration of large flocks of individuals is a possible solution to avoid extinction when the Allee effect is strong. We use attractiveness and comparison with oriented percolation, either to prove the extinction of the species, or to construct nontrivial invariant measures for each model.

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Allee effects in stochastic populations

(2002)
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Ten lectures on particle systems

(1995)
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Ergodic theorems for coupled random walks and other systems with locally interacting components

(1981)
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Author and article information

Journal
20 March 2010
2012-05-14
10.1214/11-AAP782
1003.3922

IMS-AAP-AAP782
Annals of Applied Probability 2012, Vol. 22, No. 2, 670-701
Published in at http://dx.doi.org/10.1214/11-AAP782 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
math.PR q-bio.PE
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