Savannas are characterized by a competitive tension between grasses and trees, and theoretical models illustrate how this competitive tension is influenced by resource availability, competition for these resources, and disturbances. How this universe of theoretical possibilities translates into the real world is, however, poorly understood. In this paper we indirectly parameterize a theoretical model of savanna dynamics with the aim of gaining insights as to how the grass-tree balance changes across a broad biogeographical gradient. We use data on the abundance of trees in African savannas and Markov chain Monte Carlo methods to estimate the model parameters. The analysis shows that grasses and trees can coexist over a broad range of rainfall regimes. Further, our results indicate that savannas may be regulated by either asymptotically stable dynamics (in the absence of fire) or by stable limit cycles (in the presence of fire). Rainfall does not influence which of these two classes of dynamics occurs. We conclude that, even though fire might not be necessary for grass-tree coexistence, it nonetheless is an important modifier of grass: tree ratios.