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A minimalistic model of vegetation physiognomies in the savanna biome

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  • Djeumen, I.V. Yatat
  • Dumont, Y.
  • Doizy, A.
  • Couteron, P.

Abstract

We present and analyze a model aiming at recovering, as dynamical outcomes of fire-mediated 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 with respect to the African context and retains mathematical tractability, since we restricted it to the main processes, notably tree–grass asymmetric 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 bifurcation 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 verified for all levels of rainfall, contrary to previous attempts using analogous ODE frameworks. Thus, our framework appears able to render more realistic and diversified outcomes than often thought of regarding ODE. 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.

Suggested Citation

  • Djeumen, I.V. Yatat & Dumont, Y. & Doizy, A. & Couteron, P., 2021. "A minimalistic model of vegetation physiognomies in the savanna biome," Ecological Modelling, Elsevier, vol. 440(C).
    • Handle: RePEc:eee:ecomod:v:440:y:2021:i:c:s0304380020304452
    DOI: 10.1016/j.ecolmodel.2020.109381
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    References listed on IDEAS

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    1. Mahesh Sankaran & Niall P. Hanan & Robert J. Scholes & Jayashree Ratnam & David J. Augustine & Brian S. Cade & Jacques Gignoux & Steven I. Higgins & Xavier Le Roux & Fulco Ludwig & Jonas Ardo & Feetha, 2005. "Determinants of woody cover in African savannas," Nature, Nature, vol. 438(7069), pages 846-849, December.
    2. Accatino, Francesco & De Michele, Carlo, 2013. "Humid savanna–forest dynamics: A matrix model with vegetation–fire interactions and seasonality," Ecological Modelling, Elsevier, vol. 265(C), pages 170-179.
    3. Marten Scheffer & Steve Carpenter & Jonathan A. Foley & Carl Folke & Brian Walker, 2001. "Catastrophic shifts in ecosystems," Nature, Nature, vol. 413(6856), pages 591-596, October.
    4. Beckage, Brian & Gross, Louis J. & Platt, William J., 2011. "Grass feedbacks on fire stabilize savannas," Ecological Modelling, Elsevier, vol. 222(14), pages 2227-2233.
    5. Tchuinté Tamen, A. & Dumont, Y. & Tewa, J.J. & Bowong, S. & Couteron, P., 2017. "A minimalistic model of tree–grass interactions using impulsive differential equations and non-linear feedback functions of grass biomass onto fire-induced tree mortality," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 133(C), pages 265-297.
    6. Koenker, Roger & Park, Beum J., 1996. "An interior point algorithm for nonlinear quantile regression," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 265-283.
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