Clustering in cellular automata modelling tropical forest-grassland landscapes
Jan Sieber (Exeter)
This is joint work with Bert Wuyts (University of Exeter)
Cellular automata modelling fire feedback in tropical forest-grass landscapes have a combination of fast and slow processes (fire versus tree growth). Approximating the effects of the fast fires on the slow time scale leads to long-distance correlations in space, which are visible as clusters of grass and forest. These clusters violate the assumptions about absence of correlations commonly made when deriving percolation thresholds and macroscopic differential equations on the slow times scale.
We demonstrate how one can use controlled simulations to still determine closed equations. In particular, we find that the two most important percolation quantities in the model, the forest perimeter length and the "grass-weighted" forest perimeter length, are determined by forest area. Thus, one can use simple bifurcation analysis arguments to study the vulnerability of a landscape to tipping (self-accelerating forest die-back) in our cellular automaton.
Reference: Bert Wuyts, Jan Sieber (2023) Emergent structure and dynamics of tropical forest-grassland landscapes, PNAS 120 (45), e2211853120
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