Emergent structure, dynamics and abrupt transitions in a cellular automaton of tropical forest and fire

It is thought that tropical forests can exist as an alternative stable state to savanna. Therefore, perturbation by climate change or human impact may lead to crossing of a tipping point beyond which there is rapid large-scale forest dieback that is not easily reversed. Modelling studies of alternative stable tree cover states have either relied on mean-field assumptions or not included the spatiotemporal dynamics of fire, making it hard to compare their output to spatial data. In this talk, we analyse a microscopic model of tropical forest and fire and show how dynamics of forest area are linked to its emergent spatial structure. We find that the relation between forest perimeter and area determines the nonlinearity in forest growth while forest perimeter weighted by adjacent grassland area determines the nonlinearity in forest loss. Together with the linear changes, which are independent of spatial structure, these two effects lead to an emergent relation between forest area change and forest area, defining a single-variable ordinary differential equation. Such a relation between pattern and dynamics enables empiricists to assess forest stability and resilience directly from a single spatial observation of a tropical forest-grassland landscape.