  We investigate the 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. We prove that the
rate of acceleration is slower than the rate of acceleration predicted by the
linear problem, that is, without 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 at the
front. A careful analysis of these trajectories allows us to identify the value
of the rate of acceleration. The article is complemented with numerical
simulations that illustrate some behavior of the model that is beyond our
analysis.
