Different strategies of evolution in a predator-prey system

We propose a lattice model of evolution of a predator-prey system. Both spe cies in order to survive must cat. The prey cats the grass growing in unlim ited quantities on most of the cells of the lattice. On the remaining cells the prey find cover against predators, but not food. We compare four activ e strategies-the prey move in the direction of grassy cells, they move away from the predators, the predators move in the direction of the prey and bo th species move in the direction of their respective food resources. These strategies are compared with random wandering of both species. We show that the character of the asymptotic stationary state depends on the initial co ncentrations of predators and prey, density of the shelter for the prey and on the strategy adopted, The predators are more vulnerable to the proper c hoice of the strategy. The strategies which lead in most cases to the extin ction of predators and prey are those in which the predators are searching the prey. (C) 2001 Elsevier Science B.V. All rights reserved.