T.H. Fay and J.C. Greeff (South Africa)
Mathematical model, population dynamics, competition, stability.
In the Ndumo Game Reserve in KwaZulu-Natal, South Africa, the over-crowded nyala and impala populations have a detrimental effect on smaller competing species and vegetation structures. Officials have been trying to control their numbers with culling over the last two decades, without success. In this study a mathematical model is developed to describe the dynamics of these competing species, in order to investigate reasons for the failure to control their numbers, and seek alternative culling programs for effective management, in order to prevent extinction of smaller species such as bushbuck and red duiker in the reserve. A system of three first-order nonlinear differential equations is used, with parameter values based on field data and opinions of specialists in the fields of ecology. The effect of various culling strategies, and the introduction of a fourth species (man as a predator) to the system, is investigated mathematically, in combination with phase plane analyses to visually illustrate expected outcomes of different culling strategies over time. This allows the wildlife manager (with little or no mathematical background) to evaluate the options suggested without actually killing the animals, or to investigate the effect of deviations from a chosen program.
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