Non-local competition slows down front acceleration during dispersal evolution

TL;DR

This paper studies how non-local competition affects the speed of dispersal fronts in a reaction-diffusion model, showing that it slows down the acceleration compared to classical models, with both analytical and numerical insights.

Contribution

It demonstrates that non-local saturation mechanisms slow down front acceleration in dispersal models, revealing a new hindering effect due to the interplay of non-locality and population dynamics.

Findings

Acceleration rate is slower than in the linear case.

Non-local saturation hinders front speed.

Numerical simulations illustrate complex behaviors.

Abstract

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.