Mathematical Analysis of a Size Structured Tree-Grass Competition Model for Savanna Ecosystems

Valaire Yatat, Yves Dumont, Jean Jules Tewa, Pierre Couteron, Samuel Bowong

Abstract


Several continuous-time tree-grass competition models have been developed to study conditions of long-lasting coexistence of trees and grass in savanna ecosystems according to environmental parameters such as climate or fire regime. In those models, fire intensity is a fixed parameter while the relationship between woody plant size and fire-sensitivity is not systematically considered.In this paper, we propose a mathematical model for the tree-grass interaction that takes into account both fire intensity and size-dependent sensitivity. The fire intensity is modeled by an increasing function of grass biomass and fire return time is a function of climate. We carry out a qualitative analysis that highlights ecological thresholds that summarize the dynamics of the system. Finally, we develop a non-standard numerical scheme and present some simulations to illustrate our analytical results.

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DOI: http://dx.doi.org/10.11145/j.biomath.2014.04.212

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ISSN 1314-7218 (online)
ISSNĀ 1314-684X (print)

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