An impulsive modelling framework of fire occurrence in a size-structured model of tree–grass interactions for savanna ecosystems
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.
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dig-cirad-fr-5823312024-01-28T23:49:13Z http://agritrop.cirad.fr/582331/ http://agritrop.cirad.fr/582331/ An impulsive modelling framework of fire occurrence in a size-structured model of tree–grass interactions for savanna ecosystems. Yatat Valaire, Couteron Pierre, Tewa Jean Jules, Bowong Samuel, Dumont Yves. 2017. Journal of Mathematical Biology, 74 (6) : 1425-1482.https://doi.org/10.1007/s00285-016-1060-y <https://doi.org/10.1007/s00285-016-1060-y> An impulsive modelling framework of fire occurrence in a size-structured model of tree–grass interactions for savanna ecosystems Yatat, Valaire Couteron, Pierre Tewa, Jean Jules Bowong, Samuel Dumont, Yves eng 2017 Journal of Mathematical Biology F40 - Écologie végétale K01 - Foresterie - Considérations générales U10 - Informatique, mathématiques et statistiques forêt arbre forestier savane écosystème écosystème forestier incendie de forêt incendie spontané écologie méthode statistique analyse quantitative modèle mathématique pâturages compétition végétale classification http://aims.fao.org/aos/agrovoc/c_3062 http://aims.fao.org/aos/agrovoc/c_3052 http://aims.fao.org/aos/agrovoc/c_6825 http://aims.fao.org/aos/agrovoc/c_2482 http://aims.fao.org/aos/agrovoc/c_1374842133961 http://aims.fao.org/aos/agrovoc/c_3045 http://aims.fao.org/aos/agrovoc/c_34150 http://aims.fao.org/aos/agrovoc/c_2467 http://aims.fao.org/aos/agrovoc/c_7377 http://aims.fao.org/aos/agrovoc/c_32660 http://aims.fao.org/aos/agrovoc/c_24199 http://aims.fao.org/aos/agrovoc/c_5626 http://aims.fao.org/aos/agrovoc/c_35264 http://aims.fao.org/aos/agrovoc/c_1653 Afrique http://aims.fao.org/aos/agrovoc/c_165 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. article info:eu-repo/semantics/article Journal Article info:eu-repo/semantics/publishedVersion http://agritrop.cirad.fr/582331/7/art%253A10.1007%252Fs00285-016-1060-y%28edite%29.pdf text Cirad license info:eu-repo/semantics/restrictedAccess https://agritrop.cirad.fr/mention_legale.html https://doi.org/10.1007/s00285-016-1060-y 10.1007/s00285-016-1060-y info:eu-repo/semantics/altIdentifier/doi/10.1007/s00285-016-1060-y info:eu-repo/semantics/altIdentifier/purl/https://doi.org/10.1007/s00285-016-1060-y |
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F40 - Écologie végétale K01 - Foresterie - Considérations générales U10 - Informatique, mathématiques et statistiques forêt arbre forestier savane écosystème écosystème forestier incendie de forêt incendie spontané écologie méthode statistique analyse quantitative modèle mathématique pâturages compétition végétale classification http://aims.fao.org/aos/agrovoc/c_3062 http://aims.fao.org/aos/agrovoc/c_3052 http://aims.fao.org/aos/agrovoc/c_6825 http://aims.fao.org/aos/agrovoc/c_2482 http://aims.fao.org/aos/agrovoc/c_1374842133961 http://aims.fao.org/aos/agrovoc/c_3045 http://aims.fao.org/aos/agrovoc/c_34150 http://aims.fao.org/aos/agrovoc/c_2467 http://aims.fao.org/aos/agrovoc/c_7377 http://aims.fao.org/aos/agrovoc/c_32660 http://aims.fao.org/aos/agrovoc/c_24199 http://aims.fao.org/aos/agrovoc/c_5626 http://aims.fao.org/aos/agrovoc/c_35264 http://aims.fao.org/aos/agrovoc/c_1653 http://aims.fao.org/aos/agrovoc/c_165 F40 - Écologie végétale K01 - Foresterie - Considérations générales U10 - Informatique, mathématiques et statistiques forêt arbre forestier savane écosystème écosystème forestier incendie de forêt incendie spontané écologie méthode statistique analyse quantitative modèle mathématique pâturages compétition végétale classification http://aims.fao.org/aos/agrovoc/c_3062 http://aims.fao.org/aos/agrovoc/c_3052 http://aims.fao.org/aos/agrovoc/c_6825 http://aims.fao.org/aos/agrovoc/c_2482 http://aims.fao.org/aos/agrovoc/c_1374842133961 http://aims.fao.org/aos/agrovoc/c_3045 http://aims.fao.org/aos/agrovoc/c_34150 http://aims.fao.org/aos/agrovoc/c_2467 http://aims.fao.org/aos/agrovoc/c_7377 http://aims.fao.org/aos/agrovoc/c_32660 http://aims.fao.org/aos/agrovoc/c_24199 http://aims.fao.org/aos/agrovoc/c_5626 http://aims.fao.org/aos/agrovoc/c_35264 http://aims.fao.org/aos/agrovoc/c_1653 http://aims.fao.org/aos/agrovoc/c_165 |
spellingShingle |
F40 - Écologie végétale K01 - Foresterie - Considérations générales U10 - Informatique, mathématiques et statistiques forêt arbre forestier savane écosystème écosystème forestier incendie de forêt incendie spontané écologie méthode statistique analyse quantitative modèle mathématique pâturages compétition végétale classification http://aims.fao.org/aos/agrovoc/c_3062 http://aims.fao.org/aos/agrovoc/c_3052 http://aims.fao.org/aos/agrovoc/c_6825 http://aims.fao.org/aos/agrovoc/c_2482 http://aims.fao.org/aos/agrovoc/c_1374842133961 http://aims.fao.org/aos/agrovoc/c_3045 http://aims.fao.org/aos/agrovoc/c_34150 http://aims.fao.org/aos/agrovoc/c_2467 http://aims.fao.org/aos/agrovoc/c_7377 http://aims.fao.org/aos/agrovoc/c_32660 http://aims.fao.org/aos/agrovoc/c_24199 http://aims.fao.org/aos/agrovoc/c_5626 http://aims.fao.org/aos/agrovoc/c_35264 http://aims.fao.org/aos/agrovoc/c_1653 http://aims.fao.org/aos/agrovoc/c_165 F40 - Écologie végétale K01 - Foresterie - Considérations générales U10 - Informatique, mathématiques et statistiques forêt arbre forestier savane écosystème écosystème forestier incendie de forêt incendie spontané écologie méthode statistique analyse quantitative modèle mathématique pâturages compétition végétale classification http://aims.fao.org/aos/agrovoc/c_3062 http://aims.fao.org/aos/agrovoc/c_3052 http://aims.fao.org/aos/agrovoc/c_6825 http://aims.fao.org/aos/agrovoc/c_2482 http://aims.fao.org/aos/agrovoc/c_1374842133961 http://aims.fao.org/aos/agrovoc/c_3045 http://aims.fao.org/aos/agrovoc/c_34150 http://aims.fao.org/aos/agrovoc/c_2467 http://aims.fao.org/aos/agrovoc/c_7377 http://aims.fao.org/aos/agrovoc/c_32660 http://aims.fao.org/aos/agrovoc/c_24199 http://aims.fao.org/aos/agrovoc/c_5626 http://aims.fao.org/aos/agrovoc/c_35264 http://aims.fao.org/aos/agrovoc/c_1653 http://aims.fao.org/aos/agrovoc/c_165 Yatat, Valaire Couteron, Pierre Tewa, Jean Jules Bowong, Samuel Dumont, Yves An impulsive modelling framework of fire occurrence in a size-structured model of tree–grass interactions for savanna ecosystems |
description |
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. |
format |
article |
topic_facet |
F40 - Écologie végétale K01 - Foresterie - Considérations générales U10 - Informatique, mathématiques et statistiques forêt arbre forestier savane écosystème écosystème forestier incendie de forêt incendie spontané écologie méthode statistique analyse quantitative modèle mathématique pâturages compétition végétale classification http://aims.fao.org/aos/agrovoc/c_3062 http://aims.fao.org/aos/agrovoc/c_3052 http://aims.fao.org/aos/agrovoc/c_6825 http://aims.fao.org/aos/agrovoc/c_2482 http://aims.fao.org/aos/agrovoc/c_1374842133961 http://aims.fao.org/aos/agrovoc/c_3045 http://aims.fao.org/aos/agrovoc/c_34150 http://aims.fao.org/aos/agrovoc/c_2467 http://aims.fao.org/aos/agrovoc/c_7377 http://aims.fao.org/aos/agrovoc/c_32660 http://aims.fao.org/aos/agrovoc/c_24199 http://aims.fao.org/aos/agrovoc/c_5626 http://aims.fao.org/aos/agrovoc/c_35264 http://aims.fao.org/aos/agrovoc/c_1653 http://aims.fao.org/aos/agrovoc/c_165 |
author |
Yatat, Valaire Couteron, Pierre Tewa, Jean Jules Bowong, Samuel Dumont, Yves |
author_facet |
Yatat, Valaire Couteron, Pierre Tewa, Jean Jules Bowong, Samuel Dumont, Yves |
author_sort |
Yatat, Valaire |
title |
An impulsive modelling framework of fire occurrence in a size-structured model of tree–grass interactions for savanna ecosystems |
title_short |
An impulsive modelling framework of fire occurrence in a size-structured model of tree–grass interactions for savanna ecosystems |
title_full |
An impulsive modelling framework of fire occurrence in a size-structured model of tree–grass interactions for savanna ecosystems |
title_fullStr |
An impulsive modelling framework of fire occurrence in a size-structured model of tree–grass interactions for savanna ecosystems |
title_full_unstemmed |
An impulsive modelling framework of fire occurrence in a size-structured model of tree–grass interactions for savanna ecosystems |
title_sort |
impulsive modelling framework of fire occurrence in a size-structured model of tree–grass interactions for savanna ecosystems |
url |
http://agritrop.cirad.fr/582331/ http://agritrop.cirad.fr/582331/7/art%253A10.1007%252Fs00285-016-1060-y%28edite%29.pdf |
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