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Savannas are known as ecosystems with tree cover below climate-defined equilibrium values. However, a predictive framework for understanding constraints on tree cover is lacking. We present (a) a spatially extensive analysis of tree cover and fire distribution in sub-Saharan Africa, and (b) a model, based on empirical results, demonstrating that savanna and forest may be alternative stable states in parts of Africa, with implications for understanding savanna distributions. Tree cover does not increase continuously with rainfall, but rather is constrained to low (<50%, "savanna") or high tree cover (>75%, "forest"). Intermediate tree cover rarely occurs. Fire, which prevents trees from establishing, differentiates high and low tree cover, especially in areas with rainfall between 1000 mm and 2000 mm. Fire is less important at low rainfall (<1000 mm), where rainfall limits tree cover, and at high rainfall (>2000 mm), where fire is rare. This pattern suggests that complex interactions between climate and disturbance produce emergent alternative states in tree cover. The relationship between tree cover and fire was incorporated into a dynamic model including grass, savanna tree saplings, and savanna trees. Only recruitment from sapling to adult tree varied depending on the amount of grass in the system. Based on our empirical analysis and previous work, fires spread only at tree cover of 40% or less, producing a sigmoidal fire probability distribution as a function of grass cover and therefore a sigmoidal sapling to tree recruitment function. This model demonstrates that, given relatively conservative and empirically supported assumptions about the establishment of trees in savannas, alternative stable states for the same set of environmental conditions (i.e., model parameters) are possible via a fire feedback mechanism. Integrating alternative stable state dynamics into models of biome distributions could improve our ability to predict changes in biome distributions and in carbon storage under climate and global change scenarios.