A simple dynamic model relating forest area in a region, its contribution to dry season precipitation and the effect on its own establishment was developed. The model equation shows hysteresis between forest and savannas as a function of imported dry season precipitation. Regions are either dominated by forests or savannas, with each ecosystem showing stability despite changes in imported dry season precipitation. Deforestation beyond a certain threshold value, however, could cause a collapse of forest ecosystems and replacement by savannas in marginal areas. The predictions of this model corroborate pollen core analysis in the Amazon basin, where historical stability of tropical forest cover has been shown despite global climate change.