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Savannas are mixed tree-grass ecosystems whose dynamics are predominantly regulated by resource competition and the temporal variability in climatic and environmental factors such as rainfall and fire. Hence, increasing inter-annual rainfall variability due to climate change could have a significant impact on savannas. To investigate this, we used an ecohydrological model of stochastic differential equations and simulated African savanna dynamics along a gradient of mean annual rainfall (520–780 mm/year) for a range of inter-annual rainfall variabilities. Our simulations produced alternative states of grassland and savanna across the mean rainfall gradient. Increasing inter-annual variability had a negative effect on the savanna state under dry conditions (520 mm/year), and a positive effect under moister conditions (580–780 mm/year). The former resulted from the net negative effect of dry and wet extremes on trees. In semi-arid conditions (520 mm/year), dry extremes caused a loss of tree cover, which could not be recovered during wet extremes because of strong resource competition and the increased frequency of fires. At high mean rainfall (780 mm/year), increased variability enhanced savanna resilience. Here, resources were no longer limiting and the slow tree dynamics buffered against variability by maintaining a stable population during ‘dry’ extremes, providing the basis for growth during wet extremes. Simultaneously, high rainfall years had a weak marginal benefit on grass cover due to density-regulation and grazing. Our results suggest that the effects of the slow tree and fast grass dynamics on tree-grass interactions will become a major determinant of the savanna vegetation composition with increasing rainfall variability. [ABSTRACT FROM AUTHOR]