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

Yatat V., Couteron P., Tewa J.J., Bowong S., Dumont Y.. 2017. Journal of Mathematical Biology, 74 (6) : p. 1425-1482.

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. (Résumé d'auteur)

Mots-clés : classification; compétition végétale; pâturages; modèle mathématique; analyse quantitative; méthode statistique; Écologie; incendie spontané; incendie de forêt; écosystème forestier; Écosystème; savane; arbre forestier; forêt; afrique

Thématique : Ecologie végétale; Foresterie - Considérations générales; Méthodes mathématiques et statistiques

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