Extinction conditions for isolated populations with Allee effect

• Published in: Mathematical biosciences 2011-07, Vol.232 (1), p.78-86
• Main Authors: Méndez, Vicenç, Sans, Cristina, Llopis, Isaac, Campos, Daniel
• Format: Article
• Language: English
• Subjects: Allee effect; Animals; Conspecifics; Critical patch size; Ecosystem; Efecte Allee; Extinció (Biologia); Extinction; Extinction (Biology); Extinction, Biological; Matemàtica aplicada a les ciències; Matemàtiques i estadística; Mathematical models; Models matemàtics; Models, Biological; Numerical Analysis, Computer-Assisted; Population Density; Population Dynamics; Àrees temàtiques de la UPC
• ISSN: 0025-5564; 1879-3134
• DOI: 10.1016/j.mbs.2011.04.005

► We study population extinction conditions with Allee effect. ► Populations live surrounded by hostile environments. ► We describe analytically the bifurcation diagrams. ► We consider weak and strong Allee effects and discuss the ecological implications of our results. One of the main ecological phenomenons is the Allee effect [1–3], in which a positive benefit from the presence of conspecifics arises. In this work we describe the dynamical behavior of a population with Allee effect in a finite domain that is surrounded by a completely hostile environment. Using spectral methods to rewrite the local density of habitants we are able to determine the critical patch size and the bifurcation diagram, hence characterizing the stability of possible solutions, for different ways to introduce the Allee effect in the reaction–diffusion equations.