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

TL;DR

This paper investigates how the Allee effect and flock migration influence species survival and extinction using particle systems, revealing critical thresholds and migration strategies for persistence.

Contribution

It introduces models demonstrating the impact of the Allee effect and flock migration on species survival, providing mathematical proofs of extinction or persistence.

Findings

Allee effect can be critical for species survival.

Migration of large flocks can prevent extinction.

Mathematical proofs of extinction and survival thresholds.

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.