We study a lattice model of a prey-predator system. Mean-field approximatio
n predicts that the active phase, i.e., one with a finite fraction of preys
and predators, is a generic phase of this model. Moreover, within this app
roximation the model exhibits quasi-oscillations resembling Lotka-Volterra
systems. However, Monte Carlo simulations for a one-, two-, and three-dimen
sional versions of this model do not support this scenario and predict that
at a certain value of some parameter the model enters the absorbing state,
i.e., a state where the entire population of predators dies out and the mo
del is invaded by preys. Simulations for the one-dimensional version indica
te that the transition into the absorbing state belongs to the directed per
colation universality class. (C) 2000 Elsevier Science B.V. All rights rese
rved.