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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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          Most cited references 17

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          Allee effects in stochastic populations

           Brian Dennis (2002)
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            Ten lectures on particle systems

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

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                Author and article information

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

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                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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