On the usefulness of a minimalistic model to study tree-grass biomass distributions along biogeographic gradients in the savanna biome

TL;DR

This study introduces a simple yet effective mathematical model using two differential equations to simulate and analyze the diverse vegetation states in savannas along rainfall and fire frequency gradients, capturing complex dynamics like bistability and tristability.

Contribution

The paper presents a minimalistic ODE-based model that accurately reproduces various long-term vegetation states and transitions in savannas, improving understanding of tree-grass interactions across biogeographic gradients.

Findings

Model captures monostability, bistability, and tristability in savanna vegetation.

Reproduces known effects of fire frequency on woody biomass.

Provides a bifurcation diagram linking rainfall, fire, and vegetation states.

Abstract

We present and analyze a model aiming at recovering as dynamical outcomes of tree-grass interactions the wide range of vegetation physiognomies observable in the savanna biome along rainfall gradients at regional/continental scales. The model is based on two ordinary differential equations (ODE), for woody and grass biomass. It is parameterized from literature and retains mathematical tractability, since we restricted it to the main processes, notably tree-grass asym-metric interactions (either facilitative or competitive) and the grass-fire feedback. We used a fully qualitative analysis to derive all possible long term dynamics and express them in a bifur-cation diagram in relation to mean annual rainfall and fire frequency. We delineated domains of monostability (forest, grassland, savanna), of bistability (e.g. forest-grassland or forest-savanna) and even tristability. Notably, we highlighted regions in which two savanna equilibria may be jointly stable (possibly in addition to forest or grassland). We verified that common knowledge about decreasing woody biomass with increasing fire frequency is recovered for all levels of rainfall, contrary to previous attempts using analogous ODE frameworks. Thus, this framework appears able to render more realistic and diversified outcomes than often thought of. Our model can help figure out the ongoing dynamics of savanna vegetation in large territories for which local data are sparse or absent. To explore the bifurcation diagram with different combinations of the model parameters, we have developed a user-friendly R-Shiny application freely available at : https://gitlab.com/cirad-apps/tree-grass.