The Logistic Model-generated carrying capacities, maximum sustained off-take rates and optimal stocking rates for Kenya.

Abstract

This paper deals with the derivation of logistic model for cattle, sheep and goats in a commercial ranching system in Machakos District, Kenya, a savannah ecosystem with average annual rainfall of 589.3  159.3mm and an area of 10,117ha. It involves modeling livestock population dynamics as discrete-time logistic equations wiyh fixed carrying capacities. The fixed carrying capacities are generated endogenously using time-series ranch data, covering a period of 15 years, from 1987 to 2001, in a commercial ranching enterprise. The model incorporates interaction parameters, generated endogenously. The estimation of the logistic models involves estimation of econometric models for each livestock species, followed by the recovery of the logistic model mathematically. Optimisation procedures are employed to determine the optimal stocking levels and the optimal off-take levels. The model-generated carrying capacities are 2,985, 791 and 201 animal units (AU) for cattle, sheep and goats, respectively. Optimal stocking levels are 1,369, 154 and 69 Aus for cattle, sheep and goats, respectively, while the optimal off-take levels are 857, 88 and 63 for cattle, sheep and goats, respectively. This shows that the logistic model-based system analysis is applicable to the management of mixed-species commercial ranching enterprises.