Rescaled Lotka-Volterra models converge to super-Brownian motion
  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. 
J. Theodore Cox and Edwin A. Perkins