Spatial pattern formation in a model of vegetation-climate feedback

We consider a spatial version of Watson and Lovelock's tutorial model of vegetation-climate feedbacks (Watson A J and Lovelock J E 1983 Biological homeostasis of the global environment: the parable of daisyworld Tellus B 35 284-9). Two simple plant types compete on a hypothetical planet, stabilizing the global temperature via an albedo feedback. Numerical solutions show an alternating pattern of the two plant types. A stability analysis shows that there are two mechanisms involved in the pattern formation. A Turing-like process causes the uniform equilibrium state to be unstable to non-constant perturbations and the solution tends towards a striped pattern. This solution is then modified by a mechanism which restricts stripe length and results in subdivision. By calculating the associated temperature function we show how the maximum stripe length can be determined and the stability of different patterns assessed.