In this paper I will review twenty years of work on the question: When is there coexistence in stochastic spatial models? The answer, announced in Durrett and Levin [Theor. Pop. Biol. 46 (1994) 363–394], and that we explain in this paper is that this can be determined by examining the mean-field ODE. There are a number of rigorous results in support of this picture, but we will state nine challenging and important open problems, most of which date from the 1990’s.
"Coexistence in stochastic spatial models." Ann. Appl. Probab. 19 (2) 477 - 496, April 2009. https://doi.org/10.1214/08-AAP590