A numerical model to solve single-species invasion problems with Allee effects

The population dynamics problems considered here describe propagation of travelling population fronts that represent either single-species invasion or single-species retreat. The influence of the weak and strong Allee effect is analyzed on the spread of a single species invading organism in a one-dimensional domain. This problem is mathematically modelled by a non-linear advection–diffusion–reaction transport equation, which is numerically solved by using the finite element method. The resulting numerical model is stable and accurate for a wide range of parameters. Some scenarios of single species invasion are investigated so as to evaluate the interaction of travelling population fronts under different parameter values, allowing to derive numerically whether they can reverse or block the species invasion, and to predict the speed of an invasion.