The dynamics of a fisheries model with feeding patterns and harvesting: Lates niloticus and Oreochromis niloticus in Lake Victoria

摘要

In this study, we develop a model based on a standard Lotka-Volterra prey–predator model that is used to predict and explain the effect of predation by the Nile perch on Nile tilapia. The effect of harvesting of both the Nile perch and Nile tilapia on the population dynamics of the fish species is investigated. The model incorporates three developmental stages (i.e. young, juveniles and mature) of each species and the effect of preference of the Nile perch for either young or juveniles Nile tilapia is pointed out. Lake Victoria being a vast lake, the carrying capacity is not a vital parameter considered in the model. Both qualitative and numerical analyses of the model are carried out. The results of this study show that predation by the Nile perch is one of the main causes of fish stock depletion in Lake Victoria. The findings further show that uncontrolled human exploitation (over fishing) of the stock leads to loss of fish biodiversity in Lake Victoria. The basic predation numbers R0, show that increasing the harvesting rate of the mature Nile perch leads to stable stationary states. However, increasing the predation rates of the Nile perch leads to unstable ecosystem.