Modeling of a predator prey dynamic system with harvesting using the lattice gas approach

Abstract

This paper uses the lattice gas model to incorporate spatial and stochastic elements in a prey-predator dynamic system. In this system, the habitat is partitioned in two adjacent patches, one of them being a prey reserve. The habitat is populated by two competing prey and a common predator. In the reserve, prey harvesting is prohibited. In the other patch, harvesting of one of the prey is allowed at a constant quota rate. The evolution of the system is investigated using local species interactions. The effect of different levels of constant quota harvesting are investigated using the lattice gas approach, first by the mean field approximation method and then by simulation. The system attains a stable equilibrium below a threshold constant harvest value on condition that the survival rate of the non-harvested prey exceeds that of the harvested prey. Furthermore, the predator biomass conversion rate for the non-harvested prey should be more than that for the harvested prey. If the aforementioned conditions are not met, the population of the harvested prey outside the reserve declines to extinction in finite time. This paper concludes that the maximum constant harvest level for stable species populations can be significantly increased by introducing harvesting for the non harvested prey. Key words: Prey, predator, constant quota harvest, lattice gas model.