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Fisher Waves and Front Roughening in a Two-Species Invasion Model with Preemptive Competition

L. O'Malley·B. Kozma·G. Korniss·Z. Racz·T. Caraco
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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 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 non-equilibrium 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 ${\cal O}(t^{-2/3})$.

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L. O'Malley, B. Kozma, G. Korniss, Z. Racz, T. Caraco. 2006-08-01. Fisher Waves and Front Roughening in a Two-Species Invasion Model with Preemptive Competition. https://doi.org/10.1103/physreve.74.041116

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