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

About 14, 000 years ago, Lake Victoria contained 500 species. Of these original species, 200 have become extinct and 200 are on the endangered species list (DuHamel, 2004). Predation coupled with poor harvesting methods has caused a big economic loss on most Ugandan lakes in particular and the world at large. In this study, we formulate 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 with harvesting of both species. The model incorporates three developmental stages (i.e young, juveniles and mature) of each species. Both qualitative and numerical analyses of the model have been 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 (overfishing) of the stock has also lead to loss of fish biodiversity in Lake Victoria. The basic predation numbers show that increasing 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.