Fisher waves and front roughening in a two-species invasion model with preemptive competition.
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)).
O'Malley
L
L
Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590, USA. omalll@rpi.edu
Kozma
B
B
Korniss
G
G
Rácz
Z
Z
Caraco
T
T
D000222:Adaptation, Physiological; D000818:Animals; D003163:Competitive Behavior / Q000502:physiology*; D003198:Computer Simulation; D003299:Cooperative Behavior; D017753:Ecosystem; D005716:Game Theory; D006790:Host-Parasite Interactions / Q000502:physiology*; D006801:Humans; D008954:Models, Biological; D011157:Population Dynamics; D011235:Predatory Behavior / Q000502:physiology*; D013559:Symbiosis