Invasion dynamics of super invaders: elimination of Allee effects by a strategy at the range boundary

We consider a reaction-diffusion model with free boundaries in one space dimension for a single population species with density u(t, x) and population range [g(t), h(t)]. The equations governing the evolution of the range boundary are deduced from the biological assumption that the species maintains its population density at a fixed positive level at the range boundary by advancing or retreating the fronts. Our mathematical results suggest that the Allee effects are eliminated if the species maintains its population density at suitable levels at the range boundary, namely with such a strategy at the range edge the species can invade the environment successfully with all admissible initial populations, exhibiting the dynamics of super invaders. Numerical simulations are used to help understand what happens if the population density levels at the range boundary are maintained in other ranges.