| dc.description.abstract | The key to sustained production in rangelands entails a good understanding of the carrying
capacity of the land, the determination of the proper species mix and the proper stocking
levels.Despite the mention of carrying capacity in many rangeland research literatures not much
has been done in the way of developing empirical tools for its determination, leading to poor
ranch management strategies, which inevitably result in sub-optimal productivity which may
errantly obliterate commercial ranching as a viable use of rangelands. Most ranching enterprises
determine their stocking rates based on the historical stocking rates and trial and error method
(Pratt and Gwynne, 1977) or through the adjusting the stocking rates depending of range
condition and trend (Herlocker, 1999). This study employs the use of bioeconomic modeling to
study cattle and sheep enterprises,providing an alternative empirical approach to the
determination of carrying capacity, stocking rates and maximum sustained yield (MSY).
These models are constructed based on the discrete time logistic equations, where the annual
growth of the herd (Ht) is modeled as dependent on initial population (Ht), the intrinsic growth
potential of the herdr, interspecies and intraspecies interaction parameters. Offtake was used as
the control variable in the equation. Data covering 14 years from Konza ranch was used to
validate the models using regression analysis. A fixed rainfall based logistic model was also
developed to modellivestock population growth based on annual precipitation and estimated
using the same data. The models are mathematically solved to provide the carrying capacity
solution of cattle and sheep as well as optimal species mix and optimal stocking rate.
Both the cattle and the sheep fixed carrying capacity models provided a good overall fit for the
data with F ratio of 22.6 and 9.1; with corresponding R2 value of 0.79 and 0.6respectively.
Intrinsic rate of growth parameters were both significant (P<0.05). Interspecies interaction was
supplementary from the model and the simulated carrying capacity for cattle was 3.43 acres/AU
and the simulated MSY for cattle and sheep was 2548AU and 33.59AU respectively.
The study revealed that the ranch's stocking rate for cattle and sheep islower than the simulated
stocking rates and provides an optimal solution that should improve production of the ranch. The
discrete - time logistic models provide good ranching simulations, endogenously estimating the
growth parameters of the livestock populations and providing optimal solutions for ranching
objectives.From this study, animal numbers fluctuated widely depending on the annual rainfall
suggesting that forage production was primarily driven by rainfall.
The discrete time logistic models simulated livestock growth convincingly but the models can be
further modified to account for other factors affecting livestock growth including varying forage
resources from season to season. The rainfall based fixed carrying capacity model does not
provide a good fit for livestock enterprises in spite of its success in the study of wildlife
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