Fisher waves and front roughening in a two-species invasion model with preemptive competition

Authored by Thomas Caraco, G Korniss, L O'Malley, B Kozma, Z Racz

Date Published: 2006

DOI: 10.1103/physreve.74.041116

Sponsors: Hungarian Academy of Sciences United States National Science Foundation (NSF)

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

Abstract

We study front propagation when an invading species competes with a resident; we assume nearest-neighbor preemptive competition for resources in an individual-based, two-dimensional lattice model. The asymptotic front velocity exhibits an effective power-law dependence on the difference between the two species' clonal propagation rates (key ecological parameters). The mean-field approximation behaves similarly, but the power law's exponent slightly differs from the individual-based model's result. We also study roughening of the front, using the framework of nonequilibrium interface growth. Our analysis indicates that initially flat, linear invading fronts exhibit Kardar-Parisi-Zhang (KPZ) roughening in one transverse dimension. Further, this finding implies, and is also confirmed by simulations, that the temporal correction to the asymptotic front velocity is of O(t(-2/3)).

Tags

Dynamics selection kinetics growth stability States Propagation Phase-change Nucleation Interfaces