Survival and coexistence in stochastic spatial Lotka-Volterra models

A spatially explicit, stochastic Lotka-Volterra model was introduced by Neuhauser and Pacala in Neuhauser and Pacala (Ann. Appl. Probab. 9, 1226-1259, 1999). A low density limit theorem for this process was proved by the authors in Cox and Perkins (Ann. Probab. 33, 904-947, 2005), showing that certain generalized rescaled Lotka-Volterra models converge to super-Brownian motion with drift. Here we use this convergence result to extend what is known about the parameter regions for the Lotka-Volterra process where (i) survival of one type holds, and (ii) coexistence holds.