We show that a sequence of stochastic spatial Lotka–Volterra models, suitably rescaled in space and time, converges weakly to super-Brownian motion with drift. The result includes both long range and nearest neighbor models, the latter for dimensions three and above. These theorems are special cases of a general convergence theorem for perturbations of the voter model.
"Rescaled Lotka–Volterra models converge to super-Brownian motion." Ann. Probab. 33 (3) 904 - 947, May 2005. https://doi.org/10.1214/009117904000000973