A three species competition model as a decision support tool

An overcrowding problem of nyala, and lately also of impala in the Ndumo Game Reserve, South Africa, has been detrimental to other species and vegetation structures over a period of two decades. In the present study a deterministic model for three competing species (where two species tend to be overpopulated while the third faces probable localized extinction) is constructed, while future trends coupled with their coexistence are projected.On a mathematical basis, we seek reasons for the failure of the cropping strategies implemented by management over the last two decades, and suggest alternative, scientifical-based approaches to the calculation of cropping quotas to ensure the future coexistence of all three species. A system of three first-order nonlinear differential equations is used, with parameter values based on field data and opinions of specialist ecologists. The effect of various cropping strategies, and the introduction of a fourth species (man as a predator) to the system, is investigated mathematically. This model was implemented as a harvesting strategy in 2002, and is being continuously tested. Final assessment can only be done over a 10–15-year period, but so far indications are promising.