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

L. O’Malley, B. Kozma, G. Korniss, Z. Rácz, and T. Caraco
Phys. Rev. E 74, 041116 – Published 19 October 2006

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(t23).

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Received 1 August 2006

DOI:https://doi.org/10.1103/PhysRevE.74.041116

©2006 American Physical Society

Authors & Affiliations

L. O’Malley1,*, B. Kozma1,†, G. Korniss1,‡, Z. Rácz2,§, and T. Caraco3,∥

  • 1Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590, USA
  • 2Institute for Theoretical Physics—HAS, Eötvös University, Pázmány sétány 1/a, 1117 Budapest, Hungary
  • 3Department of Biological Sciences, University at Albany, Albany, New York 12222, USA

  • *Electronic address: omalll@rpi.edu
  • Permanent address: Laboratoire de Physique Théorique (UMRdu CNRS 8627), Bâtiment 210, Université Paris-Sud, 91405 OrsayCedex, France. Electronic address: kozmab@th.u-psud.fr
  • Electronic address: korniss@rpi.edu
  • §Electronic address: racz@general.elte.hu
  • Electronic address: caraco@albany.edu

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 74, Iss. 4 — October 2006

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×