Résumé
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.