Migration or random walk in a prey-predator system is studied by pair approximation (PA) theory and computer simulations. Both theory  and simulations indicate that prey’s migration is disadvantageous to prey. On the other hand, the effect of predator’s migration is rather complicated. The migration of predators allows them to persist over a wide range of parameters in both the PA theory and the simulation on a random network. However, it usually has negative effects on the persistence of predators in the simulation on a lattice.

pair approximation, prey-predator system, random walk, stochastic cellular automata.