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Shrub encroachment, i.e. the increase in woody plant cover, is a major concern for livestock farming in southern Kalahari savannas. We developed a grid-based computer model simulating the population dynamics of Grewia flava, a common, fleshy-fruited encroaching shrub. In the absence of large herbivores, seeds of Grewia are largely deposited in the sub-canopy of Acacia erioloba. Cattle negate this dispersal limitation by browsing on the foliage of Grewia and dispersing seeds into the grassland matrix. In this study we first show that model predictions of Grewia cover dynamics are realistic by comparing model output with shrub cover estimates obtained from a time series of aerial photographs. Subsequently, we apply a realistic range of intensity of cattle-induced seed dispersal combined with potential precipitation and fire scenarios. Based on the simulation results we suggest that cattle may facilitate shrub encroachment of Grewia. The results show that the severity of shrub encroachment is governed by the intensity of seed dispersal. For a high seed dispersal intensity without fire (equivalent to a high stocking rate) the model predicts 56% shrub cover and 85% cell cover after 100 yr. With fire both recruitment and shrub cover are reduced, which may, under moderate intensities, prevent shrub encroachment. Climate change scenarios with two-fold higher frequencies of drought and wet years intensified shrub encroachment rates, although long-term mean of precipitation remained constant. As a management recommendation we suggest that shrub encroachment on rangelands may be counteracted by frequent fires and controlling cattle movements to areas with a high proportion of fruiting Grewia shrubs.