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. 
C. H. Durney, S. O. Case, M. Pleimling, and R. K. P. Zia
cond-mat.stat-mech q-bio.PE