LONG DISTANCE DISPERSAL AND ALLEE EFFECT IN A BIOLOGICAL INVASION

We present a mathematical model which couples a population growth dynamic subject to an Allee effect and a long distance dispersal process. First we analyzed the local dynamic through the equilibria and their stability. For the spatial dynamic we used numerical simulations, that allowed us to observe the spatial expansion of the population and to track the spatial displacement of the invasion front. This permitted us to calculated the expansion speeds. We determined the influence of the Allee effect, reproductive capacity and the long distance dispersal an the invasion speeds. We observed that an Allee effect turns accelerating expansion speeds into constant speeds. Expansion speeds decreases with Allee effect intensity but increases with the reproductive capacity of the population. Our results show that While dispersal contributes to expansion speeds, it also turns the population more susceptible to extinction.