This is a model of forest stability and transitions, inspired by:
Global Resilience of Tropical Forest and Savanna to Critical Transitions
Marina Hirota, Milena Holmgren, Egbert H. Van Nes, Marten Scheffer
It has been suggested that tropical forest and savanna could represent alternative stable states, implying critical transitions at tipping points in response to altered climate or other drivers. So far, evidence for this idea has remained elusive, and integrated climate models assume smooth vegetation responses. We analyzed data on the distribution of tree cover in Africa, Australia, and South America to reveal strong evidence for the existence of three distinct attractors: forest, savanna, and a treeless state. Empirical reconstruction of the basins of attraction indicates that the resilience of the states varies in a universal way with precipitation. These results allow the identification of regions where forest or savanna may most easily tip into an alternative state, and they pave the way to a new generation of coupled climate models.
The paper is worth a read. It doesn’t present an explicit simulation model, but it does describe the concept nicely. I built the following toy model as a loose interpretation of the dynamics.
Use a Synthesim override to replace Forest Cover with a ramp from 0 to 1 to see potentials and vector fields (rates of change), then vary the precipitation index to see how the stability of the forest, savanna and treeless states changes:
Start the system at different levels of forest cover (varying init forest cover), with default precipitation, to see the three stable attractors at zero trees, savanna (20% tree cover) and forest (90% tree cover):
Start with a stable forest, and a bit of noise (noise sd = .2 to .3), then gradually reduce precipitation (override the precipitation index with a ramp from 1 to 0) to see abrupt transitions in state:
forest savanna treeless 1f.mdl (requires an advanced version of Vensim, or the free Model Reader)
forest savanna treeless 1f.vpm (ditto; includes a sensitivity file for varying the initial forest cover)