The logistic model-generated carrying capacities, maximum take rates sustained off- and optimal stocking rates for Kenya's cornmercial ranches

Abstract

This paper deals with the derivation of logistic models for cattle, sheep and goats in a commercial ranching system in Machakos District' Kenya' a savannah ecosystem with average annuar rainfall of 589.3mm and an area of 1011,7ha. It involves modelling livestock population dynamics as discrete time logistic equations.with fixed carrying capacity. The fixed carrying capacities are generated endogenously using time-series ranch data, covering a period of 15 yearc, from 1987 to 2001, in a commercial ranching enterprise. The model incorporates interaction parameters, generated endogenousry. The estimation of the logistic models involves estimation of econometric models for each livestock species, followed by the recovery of the logistic models mathematically' optimisation procedures are employed to determine the optimal stocking levels and the optimat off-take levels' The model generated carrying capacities are 2 985, 791 and 201 animal units (AUs) for cattle, sheep and goats, respectively. Optimal stocking levels are l 369, ,54 and 69 AUs for cattle, sheep and goats respectively, while the optimal off-take t€vels are 857' 88 and 63 for cattle, sheep and goats, respectively. This shows that logistic models-based system analysis is applicable to the rnanagement of mixed-species commerciai ranching enterprise. Keywords: animal units, commercial ranching enterprises, livestock, species mix, logistic rnodels