Analysing Shrub Encroachment in the Southern Kalahari: A Grid-Based Modelling Approach

1. Shrub encroachment is reducing the carrying capacity of arid grasslands in southern Africa for cattle. Although shrub-encroachment is known to occur as a result of the selective overgrazing of grasses by cattle, the interactions between rainfall and grazing are not well understood. Both the quantity and sequence of rainfall events are likely to influence the growth rates and competitive abilities of shrubs and grasses. 2. Shrub encroachment is a slow process and animals are stocked at low densities in arid regions. Thus, field experiments for determining stocking rates that avoid shrub encroachment under various rainfall scenarios are almost impossible to replicate. We used a grid-based simulation model to investigate the shrub-grass dynamics of the southern Kalahari under various realistic rainfall scenarios and stocking rates of domestic livestock. The simulation experiments addressed the following questions: (1) Does simulated cattle grazing lead to shrub encroachment? (2) Over what time scale does the process take place? (3) Are the dynamics of vegetation-change continuous in relation to grazing pressure or do they show a threshold behaviour? 3. Simulation results indicated that the answers to all three questions depended on the quantity and sequence of rainfall. Simulated cattle grazing led to shrub encroachment under all rainfall scenarios, once stocking rates exceeded a threshold determined by long-term mean annual rainfall. 4. The stocking rate threshold for shrub encroachment was less distinct (i.e. shrub cover in different simulation experiments had a higher coefficient of variation) under xeric than mesic climatic scenarios. This is because either competition from the herbaceous layer or rain may limit shrub establishment. In relatively mesic scenarios, where shrub encroachment was limited mainly by grass competition, the grazing of grasses beyond a certain threshold led to an almost deterministic increase in shrub cover. However, under xeric climates, where rainfall was lower and more stochastic, the rate of shrub encroachment in response to a given intensity of grazing became less predictable. 5. The most significant finding of the simulation experiments was that, although the stocking rates currently recommended by pasture scientists are unlikely to lead to shrub encroachment within 20 years, they have a high probability of bringing about shrub encroachment within a century. These findings applied to most of the rainfall scenarios found in