Fronts, Irregular Cycles and Bistability in a Reaction-Diffusion Model of Tropical Tree Cover

Observed bimodal tree cover distributions at particular environmental conditions and theoretical models indicate that some areas in the tropics can be in either of the alternative stable vegetation states forest or savanna. However, when including spatial interaction in nonspatial differential equation models of a bistable quantity, only the state with the lowest potential energy remains stable. If bistability cannot be rejected, differential equation models will therefore need an extra feature. Here we show via analysis and simulation of a reaction-diffusion model how bimodal tree cover distributions can arise. When savanna tree cover is low, there is a front separating forests from savannas, which is determined by external forcings. At higher savanna tree cover, irregular cycles develop near the front in which forests can persist for centuries to millenia after which they are replaced by savannas in decades. This is not bistability but it does lead to bimodality and implies that rapid unpredictable tree cover change can occur without exogenous change. Bistability of forest cover does not occur in our simulations unless the model is sufficiently discrete. We do find bistability of savanna tree cover, in absence of forest, under a regime of high fire occurrence and high savanna sapling recruitment.