Emergent structure and dynamics of tropical forest-grassland landscapes

TL;DR

This paper demonstrates how the nonlinear dynamics and bistability of tropical forest and grassland landscapes emerge spontaneously from the geometry of forests, without assuming explicit fire spread thresholds, highlighting the role of spatial structure in ecosystem stability.

Contribution

The study introduces a novel model linking forest geometry to dynamics, revealing spontaneous bistability and proposing a resilience indicator based on landscape structure.

Findings

Forest geometry causes nonlinear feedback leading to bistability.

A new balance equation links forest perimeter and dynamics.

A resilience indicator based on structure is proposed.

Abstract

Previous work indicates that tropical forest 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 forest dieback that is not easily reversed. A hypothesised mechanism for such bistability is a feedback between fire and vegetation, where fire spreads as a contagion process on grass patches. Theoretical models have largely implemented this mechanism implicitly, by assuming a threshold dependence of fire spread on flammable vegetation. Here, we show how the nonlinear dynamics and bistability emerge spontaneously, without assuming equations or thresholds for fire spread. We find that the forest geometry causes the nonlinearity that induces bistability. We demonstrate this in three steps. First, we model forest and fire as interacting contagion processes on grass patches, %using a cellular automaton showing that spatial structure emerges due to two counteracting effects on the forest perimeter: forest expansion by dispersal, and forest erosion by fires originating in adjacent grassland. Then, we derive a landscape-scale balance equation in which these two effects link forest geometry and dynamics: forest expands proportionally to its perimeter, while it shrinks proportionally to its perimeter weighted by adjacent grassland area. Finally, we show that these perimeter quantities introduce nonlinearity in our balance equation and lead to bistability. Relying on the link between structure and dynamics, we propose a forest resilience indicator that could be used for targeted conservation or restoration.