Stochastic evolution of four species in cyclic competition
arXiv:1205.6394 · doi:10.1088/1742-5468/2012/06/P06014
Abstract
We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number of particles these simple interaction rules result in a rich variety of extinction scenarios, from single species domination to coexistence between non-interacting species. Using exact results and numerical simulations we discuss the temporal evolution of the system for different values of , for different values of the reaction rates, as well as for different initial conditions. As expected, the stochastic evolution is found to closely follow the mean-field result for large , with notable deviations appearing in proximity of extinction events. Different ways of characterizing and predicting extinction events are discussed.
19 pages, 6 figures, submitted to J. Stat. Mech
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