Abstract
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. Our recent reaction-diffusion model of Amazonian tree cover confirmed this and was able to reproduce the observed spatial distribution of forest versus savanna satisfactorily when forced by heterogeneous environmental and anthropogenic variables, even though bistability was underestimated. These conclusions were solely based on simulation results for one set of parameters. Here, we perform an analytical and numerical analysis of the model. We derive the Maxwell point (MP) of the homogeneous reaction-diffusion equation without savanna trees as a function of rainfall and human impact and show that the front between forest and nonforest settles at this point as long as savanna tree cover near the front remains sufficiently low. For parameters resulting in higher savanna tree cover near the front, we also find irregular forest-savanna cycles and woodland-savanna bistability, which can both explain the remaining observed bimodality.
Highlights
First analyses of the satellite-derived MODIS Vegetation Continuous Fields (VCF) tree cover product [1] found strong evidence for the bistability hypothesis [2, 3]
While the approach in 2D is identical once one chooses a direction of propagation of any invasion front, front dynamics will, unlike in 1D, be influenced by front curvature, but this is minimal for the spatial scales considered [8, 19]
We have provided a first analytical and numerical analysis of our spatially heterogeneous reaction-diffusion model of tropical tree cover
Summary
First analyses of the satellite-derived MODIS Vegetation Continuous Fields (VCF) tree cover product [1] found strong evidence for the bistability hypothesis [2, 3]. They did this by showing that tropical tree cover data are multimodal at intermediate rainfall values, i.e. they have multiple maxima in their empirical probability distribution function. [2] found forest-savanna-treeless tristability, with an extra treeless state (about 0%). The treeless state was not found by [3], most likely because they excluded areas with bare soil.
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