Fisher waves and front roughening in a two-species invasion model with preemptive competition
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) .
- Publication:
-
Physical Review E
- Pub Date:
- October 2006
- DOI:
- 10.1103/PhysRevE.74.041116
- arXiv:
- arXiv:q-bio/0608001
- Bibcode:
- 2006PhRvE..74d1116O
- Keywords:
-
- 05.40.-a;
- 87.23.Cc;
- 68.35.Ct;
- Fluctuation phenomena random processes noise and Brownian motion;
- Population dynamics and ecological pattern formation;
- Interface structure and roughness;
- Quantitative Biology - Populations and Evolution;
- Condensed Matter - Statistical Mechanics
- E-Print:
- 8 pages, 5 figures