A mathematical model of browse and herbage production in communal grazing lands of semi-arid regions - Nhlengetfwa, Melusi (Department of Mathematics and Applied Mathematics, 2017)
The main purpose of this work is to extend an existing model of growing cattle and grass production in a semi-arid rangeland.The existing model which is basically Dye's (1983) model in differential equation form handles: i) the growth and performance of cattle measured in terms of weight, ii) the initiation of grass growth in early rainy season and its utilisation by the cattle . This model is being extended to simulate woody plants in addition to the grass and to simulate browsing by goats. The densities of vegetation and the stocking rates of both types of animals are being considered. Our model (SAVANNAS) will predict animal productivity in relation to rainfall and density of woody plants (or vegetation condition). A rainfall data file is being used to generate rain which divides into infiltration and run-off. Athough generally dry, semi-arid regions are agriculturally productive, more especially in terms of animal products. An understanding of the climatic conditions by the farmers is all what it takes. It is unfortunate that in these regions, rainfall, being the main driving force behind animal productivity, is unreliable in that it varies both within and over the years. It is in this regard, therefore, that models be built to simulate semi-arid environments. Such models, when run for several (semi-arid) representative rainfall years could be used by farmers. For instance, a model like SAVANNAS will be run for three rainfall years namely 1980/81, 1981/82 and 1982/83, which, respectively represent: very high, about average and very low rainfall (by semi-arid standards). SAVANNAS simulates processes that operate on widely different time scales. The growth and consumption of herbage and leaves and twigs of woody plants are modelled on a daily basis, while the numbers and ages of woody plants are updated every 120 days. The year is divided into four seasons, with the rainy season beginning in September and initiating herbage re-growth. SAVANNAS simulates herbage biomass, which means it allows the re-establishment of the previous year's grass plants . It divides woody plants into age cohorts with the first cohort being seedlings mainly, and the last cohort being adult trees which are usually out of the browsing range of herbivores. It is a model that has a focus on the effects of vegetation (woody plants and grass) on each other and the effects of the animals on vegetation and viceversa. Without overlooking their effects on vegetation production, fires are not considered in SAVANNAS. This is because in communal lands heavy grazing does not allow the accumulation of sufficient dry herbage for fuel.