  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. 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.
