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Abstract: Generalizing the cyclically competing three-species model often referred toas the rock-paper-scissors game, we consider a simple system of populationdynamics without spatial structures that involves four species. Unlike theprevious model, the four form alliance pairs which resemble partnership in thegame of Bridge. In a finite system with discrete stochastic dynamics, all but 4of the absorbing states consist of coexistence of a partner-pair. From a masterequation, we derive a set of mean field equations of evolution. This approachpredicts complex time dependence of the system and that the survivingpartner-pair is the one with the larger product of their strengths rates ofconsumption. Simulations typically confirm these scenarios. Beyond that, muchricher behavior is revealed, including complicated extinction probabilities andnon-trivial distributions of the population ratio in the surviving pair. Thesediscoveries naturally raise a number of intriguing questions, which in turnsuggests a variety of future avenues of research, especially for more realisticmodels of multispecies competition in nature.



Autor: Sara O. Case, Clinton H. Durney, Michel Pleimling, R.K.P. Zia

Fuente: https://arxiv.org/







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