title: An impulsive modelling framework of fire occurrence in a size-structured model of tree-grass interactions for savanna ecosystems.
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.
authors.affiliation: University of Yaoundé I, LIRIMA, GRIMCAPE team, Yaoundé, Cameroon.|African Center of Excellence in Information and Communication Technologies, University of Yaoundé I, Yaoundé, Cameroon.|IRD, UMI 209, UMMISCO, IRD France Nord, 93143, Bondy, France.
authors.forename: V
authors.initials: V
authors.lastname: Yatat
authors.affiliation: IRD, UMR AMAP, Montpellier, France.|Plant Systematic and Ecology Laboratory, Higher Teachers' Training College, University of Yaoundé I, Yaoundé, Cameroon.
authors.forename: P
authors.initials: P
authors.lastname: Couteron
authors.affiliation: University of Yaoundé I, LIRIMA, GRIMCAPE team, Yaoundé, Cameroon.|African Center of Excellence in Information and Communication Technologies, University of Yaoundé I, Yaoundé, Cameroon.|IRD, UMI 209, UMMISCO, IRD France Nord, 93143, Bondy, France.
authors.forename: J J
authors.initials: JJ
authors.lastname: Tewa
authors.affiliation: African Center of Excellence in Information and Communication Technologies, University of Yaoundé I, Yaoundé, Cameroon.|IRD, UMI 209, UMMISCO, IRD France Nord, 93143, Bondy, France.|University of Douala, LIRIMA, GRIMCAPE team, Douala, Cameroon.
authors.forename: S
authors.initials: S
authors.lastname: Bowong
authors.affiliation: CIRAD, UMR AMAP, Montpellier, France. yves.dumont@cirad.fr.
authors.forename: Y
authors.initials: Y
authors.lastname: Dumont
mesh_terms: D018533:Biomass; D003198:Computer Simulation; D005390:Fires; D065928:Forests; D065948:Grassland; D055641:Mathematical Concepts; D008954:Models, Biological; D006109:Poaceae / Q000254:growth & development; D014197:Trees / Q000254:growth & development
keywords: Asymmetric competition; Fire; Impulsive differential equation; Nonstandard finite difference scheme; Qualitative analysis; Savanna