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Previous work indicates that tropical forest can exist as an alternativestable state to savanna. Therefore, perturbation by climate change or humanimpact may lead to crossing of a tipping point beyond which there is rapidforest dieback that is not easily reversed. A hypothesised mechanism for suchbistability is a feedback between fire and vegetation, where fire spreads as acontagion process on grass patches. Theoretical models have largely implementedthis mechanism implicitly, by assuming a threshold dependence of fire spread onflammable vegetation. Here, we show how the nonlinear dynamics and bistabilityemerge spontaneously, without assuming equations or thresholds for fire spread.We find that the forest geometry causes the nonlinearity that inducesbistability. We demonstrate this in three steps. First, we model forest andfire as interacting contagion processes on grass patches, %using a cellularautomaton showing that spatial structure emerges due to two counteractingeffects on the forest perimeter: forest expansion by dispersal, and foresterosion by fires originating in adjacent grassland. Then, we derive alandscape-scale balance equation in which these two effects link forestgeometry and dynamics: forest expands proportionally to its perimeter, while itshrinks proportionally to its perimeter weighted by adjacent grassland area.Finally, we show that these perimeter quantities introduce nonlinearity in ourbalance equation and lead to bistability. Relying on the link between structureand dynamics, we propose a forest resilience indicator that could be used fortargeted conservation or restoration.

Emergent structure and dynamics of tropical forest-grassland landscapes