Competition between stochasticity and determinism in a Lotka-Volterra prey-predator 2D Lattice model

Abstract

We investigate the differences in prey-predator dynamics arising in a stochastic lat- tice model as a result of determinism(in the form of strategies for prey and predator with an aim to optimize the respective fitness) and stochasticity (in which the move- ment of the two entities is governed by highest random hopping weights assigned to neighboring cells). By means of Monte Carlo procedure, we simulate the model defined on a regular square lattice and discern the phase transition from an active state (where both species coexist) to an absorbing state(where one or both of the species are extinct). We find out that in a system with dominant predation, intro- ducing intelligence in prey confers an additional advantage in terms of fitness which leads to their greater presence across sites on the lattice as compared to the preda- tors who occupy fewer sites.Also, as we keep on increasing the probability of a prey to adopt the strategy of hopping to the neighboring site with the minimum number of predators, we find that predators vanish quicker than the situations where preys adopt a more random approach in hopping to the sites.