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Grass feedbacks on fire stabilize savannas

Author

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  • Beckage, Brian
  • Gross, Louis J.
  • Platt, William J.

Abstract

Savannas commonly consist of a discontinuous cover of overstory trees and a groundcover of grasses. Savanna models have previously demonstrated that vegetation feedbacks on fire frequency can limit the density of overstory trees, thereby maintaining savannas. Positive feedbacks of either savanna trees alone or trees and grasses together on fire frequency have been shown to result in a stable savanna equilibrium. Grass feedbacks on fire frequency, in contrast, have resulted in stable equilibria in either a grassland or forest state, but not in a savanna. These results, however, were derived from a system of differential equations that assumes that fire occurrence is strictly deterministic and that vegetation losses due to fire are continuous in time. We develop an alternative formulation of the grass-fire feedback model that assumes that fires are discrete and occur stochastically in time to examine the influence of these assumptions on the predicted state of the system. We show that incorporating fire as a discrete event can produce a recurring temporal refuge in which both grass and trees co-occur in a stable, bounded savanna. In our model, tree abundance is limited without invoking demographic bottlenecks in the transition from fire-sensitive to fire-resistant life history stages. An increasing strength of grass feedback on fire results in regular, predictable fires, which suggests that the system can also be modeled using a set of difference equations. We implement this discrete system using modified Leslie/Gower difference equations and demonstrate the existence of a bounded savanna state in this model framework. Our results confirm the potential for grass feedbacks to result in stable savannas, and indicate the importance of modeling fire as a discrete event rather than as a loss rate that is continuous in time.

Suggested Citation

  • Beckage, Brian & Gross, Louis J. & Platt, William J., 2011. "Grass feedbacks on fire stabilize savannas," Ecological Modelling, Elsevier, vol. 222(14), pages 2227-2233.
  • Handle: RePEc:eee:ecomod:v:222:y:2011:i:14:p:2227-2233
    DOI: 10.1016/j.ecolmodel.2011.01.015
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    Citations

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    Cited by:

    1. Chen-Charpentier, B. & Leite, M.C.A., 2014. "A model for coupling fire and insect outbreak in forests," Ecological Modelling, Elsevier, vol. 286(C), pages 26-36.
    2. 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.
    3. 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).
    4. Blanco, Carolina Casagrande & Scheiter, Simon & Sosinski, Enio & Fidelis, Alessandra & Anand, Madhur & Pillar, Valério D., 2014. "Feedbacks between vegetation and disturbance processes promote long-term persistence of forest–grassland mosaics in south Brazil," Ecological Modelling, Elsevier, vol. 291(C), pages 224-232.
    5. 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.

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