Abstract Aim Tropical savanna ecosystems are uniquely characterized by the co-dominance of both trees and grasses. An operational understanding of the ecological processes involved in maintaining this condition is essential for understanding both the functioning of savanna systems as well as their potential response to environmental change. A simple model is presented to explore the potential for a demographic mechanism of long-term tree persistence and temporal physiognomic stability in the Brazilian cerrado. Location The model is developed based on data from the humid cerrado of Brazil. Methods In contrast to many existing models of tree–grass dynamics a model is presented which is based on data from the humid cerrado of Brazil, which is both qualitatively and quantitatively different from many of the more arid savannas of the palaeotropics. The model focuses on the dynamics of a synthetic tree population, with particular attention given to reproduction, seedling establishment and fire effects; with separate sub-models for grass production, fire and rainfall. Results The model successfully predicts coexistence across the full range of observed vegetation physiognomies, but only under limited conditions. Under coexistence conditions, the dynamics of the tree population are characterized by long periods of gradual decline, punctuated by occasional bursts of growth. However, in agreement with earlier studies, the model consistently over-predicts domination by the tree component. Fire is identified as an overriding factor in determining model behaviour, and the response of reproduction and sapling recruitment to variance in the frequency of fire ignition is identified to be of potential importance in the functioning of the Brazilian cerrado. The key dynamics of the model which promote tree–grass coexistence are consistent with a number of established determinants of ecological resilience in savanna systems. Main conclusions The model identifies the importance of the effective exploitation of rare opportunities for favourable recruitment (e.g. exclusion from fire) by the tree population, in promoting coexistence within a predominantly adverse environment. Support is provided for an alternative demographic mechanism of tree–grass coexistence in the cerrado (the storage effect), which is not based on the limiting assumption of niche partitioning through differences in rooting depth. The results are consistent with those presented by recent modelling work based on the more arid savannas of southern Africa. The model presented here differs in the emphasis given to particular environmental and life-history attributes which are critical in determining the tree–grass balance, but provides further general support for the potential role of demographic mechanisms (such as the storage effect) in determining the structure of tropical savannas. Despite having clear limitations, models can serve as valuable heuristic tools to aid the integration and exploration of existing data sets as well as our present understanding of key ecological processes.