Defensive alliances in spatial models of cyclical population interactions
Abstract
As a generalization of the three-strategy Rock-Scissors-Paper game dynamics in space, cyclical interaction models of six mutating species are studied on a square lattice, in which each species is supposed to have two dominant, two subordinated, and a neutral interacting partner. Depending on their interaction topologies, all imaginable systems can be classified into four (isomorphic) groups exhibiting significantly different behaviors as a function of mutation rate. In three out of four cases three (or four) species form defensive alliances that maintain themselves in a self-organizing polydomain structure via cyclic invasions. Varying the mutation rate, this mechanism results in an ordering phenomenon analogous to that of magnetic Ising systems. The model explains a very basic mechanism of community organization, which might gain important applications in biology, economics, and sociology.
- Publication:
-
Physical Review E
- Pub Date:
- October 2001
- DOI:
- 10.1103/PhysRevE.64.042902
- arXiv:
- arXiv:cond-mat/0103625
- Bibcode:
- 2001PhRvE..64d2902S
- Keywords:
-
- 87.23.Cc;
- 05.10.-a;
- 05.40.Fb;
- 64.60.Ht;
- Population dynamics and ecological pattern formation;
- Computational methods in statistical physics and nonlinear dynamics;
- Random walks and Levy flights;
- Dynamic critical phenomena;
- Condensed Matter - Statistical Mechanics;
- Quantitative Biology
- E-Print:
- 4 pages, 3 figures