The role of Allee effects for Gaussian and Lévy dispersals in an environmental niche (Q6584145)

This work presents a comprehensive analysis of the influence of spatial stochastic dispersal on the population dynamics, which takes into account the Allee effect. The paper is supplied with a clear and substantial discussion of the biological and mathematical backgrounds of the considered phenomenon, which is followed by the rigorous mathematical consideration of spatial and spatiotemporal effects. Among the principal results are the analysis of stationary spatial solutions (an elliptic problem), which characterizes the survival chances of a dispersed population, and spatiotemporal problems, which take into account not only Brownian random walks leading to the classical diffusion but also anomalous random walk process in the form of superdiffusive Lévy flights revealed actually in the modern investigation of animal movements.