An impulsive modelling framework of fire occurrence in a size-structured model of tree–grass interactions for savanna ecosystems

Valaire Yatat Pierre Couteron 1 J. Tewa S. Bowong 2 Yves Dumont 1
1 UMR AMAP - Botanique et Modélisation de l'Architecture des Plantes et des Végétations
2 LIRIMA - Laboratoire International de Recherche en Informatique et Mathématiques Appliquées
Abstract : Fires and mean annual rainfall are major factors that regulate woody and grassy biomasses in savanna ecosystems. Within the savanna biome, conditions of long-lasting coexistence of trees and grasses have been often studied using continuous-time modelling of tree–grass competition. In these studies, fire is a time-continuous forcing while the relationship between woody plant size and fire-sensitivity is not systematically considered. In this paper, we propose a new mathematical framework to model tree–grass interactions that takes into account both the impulsive nature of fire occurrence and size-dependent fire sensitivity (via two classes of woody plants). We carry out a qualitative analysis that highlights ecological thresholds and bifurcation parameters that shape the dynamics of the savanna-like systems within the main ecological zones. Through a qualitative analysis, we show that the impulsive modelling of fire occurrences leads to more diverse behaviors including cases of grassland, savanna and forest tristability and a more realistic array of solutions than the analogous time-continuous fire models. Numerical simulations are carried out with respect to the three main ecological contexts (moist, mesic, semi-arid) to illustrate the theoretical results and to support a discussion about the bifurcation parameters and the advantages of the model.
Keywords : Savanna Fire Asymmetric competition Impulsive differential equation Qualitative analysis Nonstandard finite difference scheme
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https://hal.umontpellier.fr/hal-02194380
Contributeur : Yannick Brohard <>
Soumis le : jeudi 25 juillet 2019 - 14:32:21
Dernière modification le : samedi 27 juillet 2019 - 01:22:06

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UNIV-MONTPELLIER | INRA | AGROPOLIS | CIRAD | INRIA2017 | INRIA | B3ESTE | AMAP

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Valaire Yatat, Pierre Couteron, J. Tewa, S. Bowong, Yves Dumont. An impulsive modelling framework of fire occurrence in a size-structured model of tree–grass interactions for savanna ecosystems. Journal of Mathematical Biology, Springer Verlag (Germany), 2017, 74 (6), pp.1425-1482. ⟨10.1007/s00285-016-1060-y⟩. ⟨hal-02194380⟩

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