Fluctuations and correlations in lattice models for predator-prey interaction
Abstract
Including spatial structure and stochastic noise invalidates the classical Lotka-Volterra picture of stable regular population cycles emerging in models for predator-prey interactions. Growth-limiting terms for the prey induce a continuous extinction threshold for the predator population whose critical properties are in the directed percolation universality class. We discuss the robustness of this scenario by considering an ecologically inspired stochastic lattice predator-prey model variant where the predation process includes next-nearest-neighbor interactions. We find that the corresponding stochastic model reproduces the above scenario in dimensions 1<d⩽4 , in contrast with the mean-field theory, which predicts a first-order phase transition. However, the mean-field features are recovered upon allowing for nearest-neighbor particle exchange processes, provided these are sufficiently fast.
- Publication:
-
Physical Review E
- Pub Date:
- April 2006
- DOI:
- 10.1103/PhysRevE.73.040903
- arXiv:
- arXiv:q-bio/0508043
- Bibcode:
- 2006PhRvE..73d0903M
- Keywords:
-
- 87.23.Cc;
- 02.50.Ey;
- 05.40.-a;
- 05.70.Fh;
- Population dynamics and ecological pattern formation;
- Stochastic processes;
- Fluctuation phenomena random processes noise and Brownian motion;
- Phase transitions: general studies;
- Quantitative Biology - Populations and Evolution;
- Quantitative Biology - Quantitative Methods;
- Condensed Matter - Statistical Mechanics;
- Physics - Physics and Society
- E-Print:
- 5 pages, 4 figures, 2-column revtex4 format. Emphasis on the lattice predator-prey model with next-nearest-neighbor interaction (Rapid Communication in PRE)