Cyclic competition of four species: mean field theory and stochastic evolution
| Autor: | Clinton H. Durney, S. O. Case, Royce K.P. Zia, Michel Pleimling |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2010 |
| Předmět: |
education.field_of_study
Extinction Statistical Mechanics (cond-mat.stat-mech) Population Populations and Evolution (q-bio.PE) General Physics and Astronomy FOS: Physical sciences 01 natural sciences 010305 fluids & plasmas Competition (economics) Set (abstract data type) Mean field theory Simple (abstract algebra) Product (mathematics) FOS: Biological sciences 0103 physical sciences Master equation Statistical physics 010306 general physics education Quantitative Biology - Populations and Evolution Condensed Matter - Statistical Mechanics Mathematics |
| Popis: | Generalizing the cyclically competing three-species model (often referred to as the rock-paper-scissors game), we consider a simple system of population dynamics without spatial structures that involves four species. Unlike the previous model, the four form alliance pairs which resemble partnership in the game of Bridge. In a finite system with discrete stochastic dynamics, all but 4 of the absorbing states consist of coexistence of a partner-pair. From a master equation, we derive a set of mean field equations of evolution. This approach predicts complex time dependence of the system and that the surviving partner-pair is the one with the larger product of their strengths (rates of consumption). Simulations typically confirm these scenarios. Beyond that, much richer behavior is revealed, including complicated extinction probabilities and non-trivial distributions of the population ratio in the surviving pair. These discoveries naturally raise a number of intriguing questions, which in turn suggests a variety of future avenues of research, especially for more realistic models of multispecies competition in nature. 6 pages, 4 figures, to appear in EPL |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|