Stochastic evolution of four species in cyclic competition

We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number N 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 N , 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 N , with notable deviations appearing in proximity of extinction events. Different ways of characterizing and predicting extinction events are discussed. PACS numbers: 02.50.Ey,05.40.-a,87.23.Cc,87.10.Mn Stochastic evolution of four species in cyclic competition 2