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

Authors

  • Valaire Yatat UMMISCO, LIRIMA project team GRIMCAPE, Yaounde, Cameroon. University of Yaounde I
  • Yves Dumont CIRAD, Umr AMAP, Montpellier, France
  • Jean Jules Tewa UMMISCO, LIRIMA project team GRIMCAPE, Yaounde, Cameroon. University of Yaounde I.
  • Pierre Couteron IRD, Umr AMAP, Montpellier, France
  • Samuel Bowong UMMISCO, LIRIMA project team GRIMCAPE, Yaounde, Cameroon. University of Douala.

DOI:

https://doi.org/10.11145/j.biomath.2014.04.212

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.

Author Biographies

Valaire Yatat, UMMISCO, LIRIMA project team GRIMCAPE, Yaounde, Cameroon. University of Yaounde I

PhD student, department of mathematics, laboratory of applied mathematics

Yves Dumont, CIRAD, Umr AMAP, Montpellier, France

Jean Jules Tewa, UMMISCO, LIRIMA project team GRIMCAPE, Yaounde, Cameroon. University of Yaounde I.

Pierre Couteron, IRD, Umr AMAP, Montpellier, France

Samuel Bowong, UMMISCO, LIRIMA project team GRIMCAPE, Yaounde, Cameroon. University of Douala.

Downloads

Published

2014-06-03

Issue

Section

Original Articles