Bistability and the theory of life, rainforests and (almost) everything

This talk describes work with current PhD students Bert Wuyts and Nicolas Verschuren.

Reaction-diffusion models have been proposed since the work of Alan Turing as a model for spatial patterning. These are the combined effects of natural phenomena that want to diffuse in space at the same time as undergoing local-level interactions.

This talk considers two such problems for which the local interaction naturally produces bistability between a low-intensity and a high-intensity state. The first problem, in collaboration with Bert, concerns data on rainforest/savana bistability. Recent studies in high profile journals suggest a possible climate-induced tipping point leading to desertification of the rainforest. By looking at additional data on closeness to human impact, we show that the data in pristine regions instead displays spatially separated regions of rainforest and savanna, controlled by average rainfall levels. We are using reaction-diffusion models of local bistability of tree density together with fire diffusion predicts sharp fronts (Maxwell points) that explain these data.

The second problem, in collaboration with Nicolas, concerns how cells develop polarity, the first step to them forming inhomogeneous structures that go to make up the rich diversity of cell types seen on earth. A fundamental mechanism involving small G-proteins in active and inactive forms is revisited and shown to lead to subcritical Turing patterns. The subcriticality leads to bistability between patterned and nonpatterned states which results in either sharp fronts or localised structures. A mixture of Hamiltonian normal-form and asymptotic methods can explain these results.