Front pinning due to spatial heterogeneity in a reaction-diffusion model of tropical tree cover

Bert Wuyts
College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter 44QF, United Kingdom

Previous empirical work has hypothesised that tropical forest and savanna are two alternative stable states as a result of fire-vegetation feedbacks. The hysteresis associated with such dynamic implies that when an area of tropical forest is exposed to shocks such as deforestation or drought, it can remain locked into a savanna state unless it experiences large increases in rainfall. In my PhD, I have provided empirical and theoretical evidence that instead of two alternative stable states and hysteresis, there is only a predictable front, occurring at a single tipping point, the Maxwell point. This becomes clear after spatial heterogeneity and spatial interaction are taken into account.

In the presentation, I will start with some background on tropical tree cover bistability. Then, I use a simple reaction-diffusion equation with bistable reaction term to explain travelling wave fronts under homogeneous forcing and front pinning under heterogeneous forcing. After showing how the pinning location can be derived from data, I will briefly show the data analysis results. I will then finally introduce and analyse the reaction-diffusion model of Amazonian tree cover. It will become clear towards the end that spatial heterogeneity can lead to the false impression of bistability and hysteresis when in fact there is only a front.