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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Consequences of the Allee effect for behaviour, ecology and conservation.

Philip A. Stephens, William J. Sutherland (1999)

Warder C. Allee brought attention to the possibility of a positive relationship between aspects of fitness and population size 50 years ago. Until recently, however, this concept was generally regarded as an intriguing but relatively unimportant aspect of population ecology. Increasing appreciation that Allee effects must be incorporated into models of population dynamics and habitat use, together with recent interest in the implications of sociality for conservation, have shown that for ecology and conservation the consequences of the Allee effect are profound. The Allee effect can be regarded not only as a suite of problems associated with rarity, but also as the basis of animal sociality.

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Inverse density dependence and the Allee effect.

Franck Courchamp, Tim H. Clutton-Brock, Bryan Grenfell (1999)

The Allee effect describes a scenario in which populations at low numbers are affected by a positive relationship between population growth rate and density, which increases their likelihood of extinction. The importance of this dynamic process in ecology has been under-appreciated and recent evidence now suggests that it might have an impact on the population dynamics of many plant and animal species. Studies of the causal mechanisms generating Allee effects in small populations could provide a key to understanding their dynamics.