ON THE ROLE OF ALLEE EFFECT AND MASS MIGRATION IN SURVIVAL AND EXTINCTION OF A SPECIES

• 成果类型: Article
• 署名作者: Borrello, Davide
• 署名单位: University of Milano-Bicocca; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/11-AAP782
• 发表日期: 2012
• 页码: 670-701
• 关键词: locally interacting components; dependent random graphs; population-models; particle-systems; random-walks; attractiveness; time

摘要

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 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.