NON-LOCAL COMPETITION SLOWS DOWN FRONT ACCELERATION DURING DISPERSAL EVOLUTION

We investigate super-linear spreading in a reaction-diffusion model analogous to the Fisher-KPP equation, but in which the population is heterogeneous with respect to the dispersal ability of individuals and the saturation factor is non-local with respect to one variable. It was previously shown that the population expands as O(t³/²). We identify a constant a^*, and show that, in a weak sense, the front is located at a^*t³/². Surprisingly, a^* is smaller than the prefactor predicted by the linear problem (that is, without saturation) and analogous problem with local saturation. This hindering phenomenon is the consequence of a subtle interplay between the non-local saturation and the non-trivial dynamics of some particular curves that carry the mass to the front. A careful analysis of these trajectories allows us to characterize the value a^*. The article is complemented with numerical simulations that illustrate some behavior of the model that is beyond our analysis.