Efeito Allee e dispersão não local em processos de invasão

Abstract

The main goal of this dissertation is to analyze the role of Allee effect in processes of populations invasion for species that reproduce in discrete time steps and perform longrange movement. These phenomena are described by integrodifference equations, discrete in time and continuous in the space. Initially, we present a model for a single invasive species, whose growth is affected by a strong Allee effect. We found, through numerical simulations, that the speed of invasion increases with in reasing dispersal rate and intrinsic growth rate and decreases with increasing intensity of the Allee effect. Then we analyze a predatorprey model for invasion in which the prey is influenced by a strong Allee effect and the predator, is a specialist. The non-local dispersion of both spe ies is described by the Laplace redistribution kernel. We observed, through numerical simulation, that the coupling of the dispersion in this model can make the invasion process possible for dynamical parameters for wich, in the local dynamics, only the extinction of both species was possible. We present the several scenarios of invasion and estimate the corresponding speed of invasion. Finally, we conclude that the dispersion process is crucial for the occurrence of a population invasion and the presence of the strong Allee effect makes patchy invasion possible, characterized by forming a complex spatial pattern.