Résumé
In this work, we improve a previous minimalistic tree-grass savanna model by
taking into account water availability, in addition to fire, since both factors
are known to be important for shaping savanna physiognomies along a climatic
gradient. As in our previous models, we consider two nonlinear functions of
grass and tree biomasses to respectively take into account grass-fire
feedbacks, and the response of trees to fire of a given intensity. The novelty
is that rainfall is taken into account in the tree and grass growth functions
and in the biomass carrying capacities. Then, we derive a qualitative analysis
of the ODE model, showing existence of equilibria, and studying their stability
conditions. We also construct a two dimension bifurcation diagram based on
rainfall and fire frequency. This led to summarize different scenarios for the
model including multi-stabilities that are proven possible. Next, to bring more
realism in the model, pulsed fire events are modelled as part of an IDE
(Impulsive differential Equations) system analogous to the ODE system.
Numerical simulations are provided and we discuss some important ecological
outcomes that our ODE and IDE models are able to predict. Notably, the
expansion of forest into tree-poor physiognomies (grassland and savanna) is
systematically predicted when fire return period increases, especially in mesic
and humid climatic areas.