Spatial feedbacks and the dynamics of savanna and forest

Theoretical models and empirical analyses have combined to suggest that, for some ranges of climate, alternative stable states in vegetation structure may be possible: positive feedbacks with fire may differentiate savanna from forest, while positive feedbacks with hydrological processes may differentiate grassland from savanna. However, existing models have largely failed to include spatially explicit fire spread, dispersal, and hydrological processes, and as such ignore key features of vegetation systems. In this paper, we incorporate spatial and stochastic effects to form a comprehensive and realistic description of the dynamics of vegetation growth. By using novel computational tools such as path-sampling, we investigate the effect of noise and spatial coupling on the stability and the dynamics of forest-savanna transitions. Spatial effects change model behaviors: We find that spatial interactions between savanna and grassland result in the eventual nucleation and propagation of one of the states to invade the other. Which state wins depends on parameter values, which in turn depend on environmental conditions. Meanwhile, transitions between savanna and forest occur much less frequently, because an event such as a period of fire suppression in savanna or a fire in forest must be larger to successfully invade a landscape; this results in transitions between savanna and forest that, although not strictly history dependent, look temporally similar to hysteresis because the time lags involved in transitions are so large.