Allee Effects and Extinction in a Lattice Model

Abstract

In the interest of conservation, the importance of having a large habitat available for a species is widely known. Here, we introduce a lattice-based model for a population and look at the importance of fluctuations as well as that of the population density, particularly with respect to Allee effects. We examine the model analytically and by Monte Carlo simulations and find that, while the size of the habitat is important, there exists a critical population density below which extinction is assured. This has large consequences with respect to conservation, especially in the design of habitats and for populations whose density has become small. In particular, we find that the probability of survival for small populations can be increased by a reduction in the size of the habitat and show that there exists an optimal size reduction.

7 pages and 8 figures

References in corpus (6)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Critical phenomena in atmospheric precipitation
• Absorbing-state phase transitions in fixed-energy sandpiles
• Extinction in population dynamics
• Epidemic spreading with immunization and mutations
• Particle Statistics and Population Dynamics