Mathematical Analysis of Predator-Prey Dynamics in the Kainji Lake Fisheries Ecosystem

The Kainji Lake ecosystem in Niger State, North Central Nigeria, hosts one of West Africa's most productive inland fisheries, yet the population dynamics of key predator and prey fish species are poorly understood quantitatively, limiting the scientific basis for sustainable harvest management. This study develops and analyses a modified Lotka-Volterra predator-prey model incorporating carrying capacity for prey populations, harvesting terms for commercially targeted species, and a Holling Type II functional response to characterise feeding saturation dynamics. Biological parameters including intrinsic growth rates, predation rates, and carrying capacities are estimated from acoustic survey and commercial catch data provided by the Kainji Lake Research Institute spanning 2018 to 2023. Equilibrium analysis identifies conditions for coexistence of predator and prey populations and characterises the stability type of the coexistence equilibrium through linearisation and Lyapunov methods. Bifurcation analysis identifies the critical harvesting rate beyond which the predator population faces local extinction, estimated at 0.42 per unit biomass per year for the dominant predator species Lates niloticus. Optimal sustainable yield is computed as the harvesting level that maximises long-run catch while maintaining ecosystem stability. Simulations demonstrate that current commercial harvesting rates for Nile perch exceed the computed maximum sustainable yield by approximately 18 percent. Keywords: predator-prey model, Lotka-Volterra, fisheries dynamics, Kainji Lake, bifurcation analysis.