Sensitivity of a methematical model used to optimize revenue in a predation-competative farming environment

Abstract

Sheep farmers in the Cape Midlands region of South Africa frequently sustain stock losses through predation by caracal lynx. Further losses are incurred when hyrax compete with sheep for available pasture. Hyrax constitute the natural prey for lynx with the result that culling either hyrax or lynx has complicated feedback effects. In order to investigate the spill-over problems from the natural predator-prey system on farming revenue, a differential equations model was previously formulated, comprising the sectors Hyrax, Lynx, Sheep, Pasture and Revenue and an optimization procedure was used to determine the optimal culling rate policy for farmers. The purpose of this paper is to investigate the numerical, behavioural and policy sensitivity of this model to parameter uncertainty.