Fixation in a cyclic Lotka-Volterra model
  We study a cyclic Lotka-Volterra model of N interacting species populating a d-dimensional lattice. In the realm of a Kirkwood approximation, a critical number of species N_c(d) above which the system fixates is determined analytically. We find N_c=5,14,23 in dimensions d=1,2,3, in remarkably good agreement with simulation results in two dimensions. 
L. Frachebourg and P. L. Krapivsky