A Stochastic and Deterministic Predator- G Prey Population Model for Sustainable Harvesting: A Case of Nile Perch Lates Niloticus and Nile tilapia Oreochromis Niloticus

Abstract

Predation by Nile perch is one of the main causes of fish stock depletion in Lake Victoria. Uncontrolled human exploitation (overfishing) of the stock leads to loss of fish biodiversity in Lake Victoria. Increasing the harvesting rates of mature Nile perch can lead to stable stationary states. However, increasing the predation rates of Nile perch can lead to unstable ecosystem. Predation, coupled with uncontrolled harvesting have been a major ecological force in shaping the present day fishing communities on Lake Victoria, in particular and other lakes at large. The challenges currently facing Lake Victoria is how to sustain the Nile perch, Nile tilapia and how to conserve and restore threatened fish species. In this study, we will apply the Lotka Volterra competition model (1925) for predator and prey population. The objective of this study is therefore to develop a predator- prey model for Nile perch and Nile tilapia based on standard Lotka- Volterra predator prey model. The methodology involves formulation of a system of ordinary differential equations where prey ratio is incorporated. in this model. The finding in this study could be used to predict and explain the effect of predation by Nile perch on tilapia so that control of Nile perch can result in conservation and restoration of threatened fish species. The model is also a contribution of knowledge in mathematical modeling.