A minimalistic model of vegetation physiognomies in the savanna biome

Abstract

We present and analyze a model aiming at recovering as dynamical outcomes of tree-grass interactions the wide range of vegetation physiognomies observable in the savanna biome along rainfall gradients at regional/continental scales. The model is based on two ordinary differential equations (ODE), for woody and grass biomass. It is parameterized from literature and retains mathematical tractability, since we restricted it to the main processes, notably tree-grass asymmetric interactions (either facilitative or competitive) and the grass-fire feedback. We used a fully qualitative analysis to derive all possible long term dynamics and express them in a bifurcation diagram in relation to mean annual rainfall and fire frequency. We delineated domains of monostability (forest, grassland, savanna), of bistability (e.g. forest-grassland or forest-savanna) and even tristability. Notably, we highlighted regions in which two savanna equilibria may be jointly stable (possibly in addition to forest or grassland). We verified that common knowledge about decreasing woody biomass with increasing fire frequency is recovered for all levels of rainfall, contrary to previous attempts using analogous ODE frameworks. Thus, this framework appears able to render more realistic and diversified outcomes than often thought of. Our model can help figure out the ongoing dynamics of savanna vegetation in large territories for which local data are sparse or absent. To explore the bifurcation diagram with different combinations of the model parameters, we have developed a user-friendly R-Shiny application freely available at : https://gitlab.com/cirad-apps/tree-grass.

Limited climatic space for alternative ecosystem states in Africa

“…4A). These feedbacks can involve fire and herbivory being enhanced by grassland states and retarded by forest states ( 10 , 11 ) or due to spatial dynamics of resource competition acting on a homogenous environmental template ( 12 ). Our analysis supports an alternative interpretation, which suggests that observations of different ecosystem states at intermediate positions on resource gradients may instead be caused by deterministic factors such as topographic gradients redistributing resources such as moisture in parts of the landscape, thereby creating microenvironments that favor either forests or savannas (Fig.…”

“…Theoretical models have demonstrated the possibility that positive feedback processes in the internal system dynamics acting on the initial ecosystem state can allow qualitatively different ecosystem states to persist in the same environmental setting (9). Heuristic models (10)(11)(12) and forecasting models (13) have supported this interpretation, as have empirical studies using remote sensing (2,3,14,15), tree basal area (16), and floristic surveys (17,18). The plausibility of the AES hypothesis is thus not in question.…”

Impulsive Fire Disturbance in a Savanna Model: Tree–Grass Coexistence States, Multiple Stable System States, and Resilience

“…The impulsive model presented in this paper not only has forest-savanna bistability, but forest-grassland bistability and bistability between woodier and grassier savanna coexistence states. Similar modeling work that uses a different parameterization of the impact of fires on trees, so as to capture age effects in a two-species model (Djeumen et al 2021;Tamen et al 2017), shows it is possible to generate a similar diversity of bistabilities with a somewhat different disturbance regime.…”

“…Given the ecological, economic and cultural value of savannas as well as their precarious ecological role, savanna ecosystems are a frequent target of modeling investigations (Accatino et al 2010;Batllori et al 2015;Baudena et al 2010;Beckage et al 2009;Djeumen et al 2021;Goel et al 2020;Patterson et al 2020;Ratajczak et al 2017;Schertzer et al 2015;Staver et al 2011a;Tamen et al 2016Tamen et al , 2017Touboul et al 2018;Wuyts et al 2019;Yatat et al 2018). In tree-grass-fire interaction models of savanna ecosystems, the impact of fire on tree and grass biomass is often represented as a continuous mortality in ordinary differential equation (ODE) models (Accatino et al 2010;Beckage et al 2009;Djeumen et al 2021;Staver et al 2011a;Touboul et al 2018) and in spatial partial differential equations (PDE) models (Goel et al 2020;Wuyts et al 2019;Yatat et al 2018). Continuous fire is an obvious simplification, and in this paper, we show that it is not equivalent to similar models with discrete fire.…”

Savanna-forest dynamics: Encroachment speed, model inference and spatial simulations

“…Here we use a combination of remote-sensing results (Sagang Takougoum et al, 2022) and dynamical models to assess forest encroachment, considering a case study in the forestsavanna transition zone of Cameroon, central Africa. We also demonstrate how, using a spatially explicit modeling approach where we simply add diffusion terms to the minimalistic temporal model of Yatat et al (2021), can give valuable and novel insight on forest-savanna dynamics.…”