An impulsive modelling framework of fire occurrence in a size-structured model of tree-grass interactions for savanna ecosystems

The generation mechanism of Turing-pattern in a Tree-grass competition model with cross diffusion and time delay

In this paper, we study the general mechanism of Turing-pattern in a tree-grass competition model with cross diffusion and time delay. The properties of four equilibrium points, the existence of Hopf bifurcation and the sufficient conditions for Turing instability caused by cross-diffusion are analyzed, respectively. The amplitude equation of tree-grass competition model is derived by using multi-scale analysis method, and its nonlinear stability is studied. The sensitivity analysis also verified that fire frequency plays a key role in tree-grass coexistence equilibrium. Finally, the Turing pattern of tree-grass model obtained by numerical simulation is consistent with the spatial structure of tree-grass density distribution observed in Hulunbuir grassland, China.

Mathematical modeling of forest ecosystems by a reaction-diffusion-advection system: impacts of climate change and deforestation

We present an innovative mathematical model for studying the dynamics of forest ecosystems. Our model is determined by an age-structured reaction-diffusion-advection system in which the roles of the water resource and of the atmospheric activity are considered. The model is abstract but constructed in such a manner that it can be applied to real-world forest areas; thus it allows to establish an infinite number of scenarios for testing the robustness and resilience of forest ecosystems to anthropic actions or to climate change. We establish the well-posedness of the reaction-diffusion-advection model by using the method of characteristics and by reducing the initial system to a reaction-diffusion problem. The existence and stability of stationary homogeneous and stationary heterogeneous solutions are investigated, so as to prove that the model is able to reproduce relevant equilibrium states of the forest ecosystem. We show that the model fits with the principle of almost uniform precipitation over forested areas and of exponential decrease of precipitation over deforested areas. Furthermore, we present a selection of numerical simulations for an abstract forest ecosystem, in order to analyze the stability of the steady states, to investigate the impact of anthropic perturbations such as deforestation and to explore the effects of climate change on the dynamics of the forest ecosystem.

Evasion of tipping in complex systems through spatial pattern formation

[Figure: see text].

Increased aridity drives post-fire recovery of Mediterranean forests towards open shrublands

Recent observations suggest that repeated fires could drive Mediterranean forests to shrublands, hosting flammable vegetation that regrows quickly after fire. This feedback supposedly favours shrubland persistence and may be strengthened in the future by predicted increased aridity. An assessment was made of how fires and aridity in combination modulated the dynamics of Mediterranean ecosystems and whether the feedback could be strong enough to maintain shrubland as an alternative stable state to forest. A model was developed for vegetation dynamics, including stochastic fires and different plant fire-responses. Parameters were calibrated using observational data from a period up to 100 yr ago, from 77 sites with and without fires in Southeast Spain and Southern France. The forest state was resilient to the separate impact of fires and increased aridity. However, water stress could convert forests into open shrublands by hampering post-fire recovery, with a possible tipping point at intermediate aridity. Projected increases in aridity may reduce the resilience of Mediterranean forests against fires and drive post-fire ecosystem dynamics toward open shrubland. The main effect of increased aridity is the limitation of post-fire recovery. Including plant fire-responses is thus fundamental when modelling the fate of Mediterranean-type vegetation under climate-change scenarios.