Reaction fronts in persistent random walks with demographic stochasticity

TL;DR

This paper investigates reaction fronts in models of organisms with persistent movement and demographic stochasticity, showing how finite population effects influence wave speed and proposing a generalized Lévy walk model.

Contribution

It introduces a discrete particle model with persistent random walk and logistic growth, linking it to the Reactive Cattaneo Equation and extending to Lévy walks for transport.

Findings

Finite-population effects slow down propagation speed.

The Reactive Cattaneo Equation accurately describes large populations.

A new expression for front speed in Lévy walk models is proposed.

Abstract

Standard Reaction-Diffusion (RD) systems are characterized by infinite velocities and no persistence in the movement of individuals, two conditions that are violated when considering living organisms. Here we consider a discrete particle model in which individuals move following a persistent random walk with finite speed and grow with logistic dynamics. We show that when the number of individuals is very large, the individual-based model is well described by the continuous Reactive Cattaneo Equation (RCE), but for smaller values of the carrying capacity important finite-population effects arise. The effects of fluctuations on the propagation speed are investigated both considering the RCE with a cutoff in the reaction term and by means of numerical simulations of the individual-based model. Finally, a more general L\'evy walk process for the transport of individuals is examined and an expression for the front speed of the resulting traveling wave is proposed.