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

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

2010-03-20

arxiv.org/abs/1003.3922v3

Mathematics

Probability

27 pages

Scientific paper

We use interacting particle systems to investigate survival and extinction of a species with colonies located on each site of Z^d. In each of the four models studied, an individual in a local population can reproduce, die or migrate to neighbouring 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 non-trivial invariant measures for each model.

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