It is thought that tropical forests can exist as an alternative stable state
to savanna [1,2]. 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 [3-5]. Empirical evidence for
bistability due to fire-vegetation feedbacks relies on tree cover bimodality in
satellite-observed data [1,2], but this may also be explained by spatial
heterogeneity [6], or by biases in the data [7,8]. Theoretical evidence for
bistability [9-11] does not consider the interaction of fire with the
vegetation landscape. Focusing on landscapes consisting of tropical forest and
grassland, we show that the microscopic rules of fire and vegetation spread (as
proposed by [12]) lead to an emergent relation between macroscopic forest
structure and dynamics. This relation defines a landscape-scale balance
equation of forest area change in which the forest perimeter determines the
nonlinearity in forest growth while the forest perimeter weighted by adjacent
grassland area determines the nonlinearity in forest loss. We demonstrate that
our equation enables analysis of resilience or abrupt shifts for a given
landscape, using only the landscape state at a single point in time and
measurable parameters of the underlying microscopic spatial processes, thereby
avoiding the problems associated with reliance on bimodality

Sieber, Jan

Wuyts, Bert

Proceedings of the National Academy of Sciences

English

arXiv

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

arXiv.org e-Print Archive

Emergent structure and dynamics of tropical forest-grassland landscapes

This is the final version. Available on open access from the National Academy of Sciences via the DOI in this recordData, Materials, and Software Availability:
Algorithm data have been deposited in Github (https://github.com/b-wuyts/fgba) (51).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 hypothesized mechanism for such bistability is 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, 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.Engineering and Physical Sciences Research Council (EPSRC)European Union Horizon 202

Emergent structure and dynamics of tropical forest-grassland landscapes

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