A tribute to the use of minimalistic spatially-implicit models of savanna vegetation dynamics to address broad spatial scales in spite of scarce data

Abstract

The savanna biome encompasses a variety of vegetation physiognomies that traduce complex dynamical responses of plants to the rainfall gradients leading from tropical forests to hot deserts. Such responses are shaped by interactions between woody and grassy plants that can be either direct, disturbance-mediated or both. There has been increasing evidence that several vegetation physiognomies, sometimes highly contrasted, may durably coexist under similar rainfall conditions suggesting multi-stability or at least not abrupt transitions. These fascinating questions have triggered burgeoning modelling efforts which have, however, not yet delivered an integrated picture liable to furnish sensible predictions of potential vegetation at broad scales. In this paper, we will recall the key ecological processes and resulting vegetation dynamics that models should take into account. We will also present the main modelling options present in the literature and advocate the use of minimalistic models, capturing only the essential processes while retaining sufficient mathematical tractability and restricting themselves to a minimal set of parameters assessable from the overall literature.

Spatial self-organisation enables species coexistence in a model for savanna ecosystems

“…Previous modelling of the savanna biome using nonspatial ODE and impulsive differential equations models (see [100] for a review) has successfully identified a range of different mechanisms that stabilise species coexistence based on key differences between grasses and trees. Examples include disturbances that affect species asymmetrically, such as different functional responses in the description of grazing and browsing [84] or variations in the species' susceptibility to fires [101]; an age structure of trees with different competitive abilities of tree seedlings and adult trees [4,27]; or resource niche separation [92].…”

Species coexistence in resource-limited patterned ecosystems is facilitated by the interplay of spatial self-organisation and intraspecific competition

“…Indeed, the consideration of spatial effects in the ecohydrological dynamics changes which species' intraspecific competition is responsible for species coexistence. In a nonspatial setting, a common approach to model coexistence of herbaceous and woody species in savannas [28], strong intraspecific competition of the (locally) superior species creates a resource niche for a second species and thus facilitates coexistence ( Fig. 3.1).…”

A minimalistic model of vegetation physiognomies in the savanna biome

“…In Africa, they particularly occur between 100 mm and 1500 mm (and sometimes more) of total mean annual precipitation (Lehmann et al [2011], Baudena and Rietkerk [2013]), that is along a precipitation gradient leading from dense tropical forest to desert. There is widespread evidence that fire and water availability are variables which can exert determinant roles in mixed tree-grass systems (Scholes and Archer [1997], Yatat et al [2018b] and references therein). Empirical studies showed that vegetation properties such as biomass, leaf area, net primary production, maximal tree height and annual maximum standing crop of grasses vary along gradients of precipitation (Penning de Vries and Djitèye [1982], Abbadie et al [2006]).…”

“…Along the rest of this gradient, rainfall is known to influence indirectly the fire regime through what can be referred to as the grass-fire feedback (Yatat et al [2018b], Scholes [2003] and references therein): grass biomass that grows during rainfall periods is fuel for fires occurring in the dry months. Sufficiently frequent and intense fires are known to prevent or at least delay the development of woody vegetation (Yatat et al [2018b], Govender et al [2006]), thereby preventing trees and shrubs to depress grass production through competition for light and nutrients. The grass-fire feedback is widely acknowledged in literature as a force able to counteract the asymmetric competition of trees onto grasses, at least for climatic conditions within the savanna biome that enables sufficient grass production during wet months.…”

“…Some of them explicitly considered the influence of soil water resource on the respective productions of grass and woody vegetation components (see the review of Yatat et al [2018b]). Most of the models also incorporated the grass-fire positive feedback, several of them distinguishing firesensitive small trees and shrubs from non-sensitive large trees (Higgins et al [2000], Beckage et al [2009], Baudena et al [2010], Staver et al [2011], Yatat et al [2014Yatat et al [ , 2018b), while the rest stuck to the simplest formalism featuring just grass and tree state variables (Van Langevelde et al [2003], D 'Odorico et al [2006], Higgins et al [2010], Accatino et al [2010], Beckage et al [2011], Yu and D'Odorico [2014], Tchuinté Tamen et al [2014], see also the review of Yatat et al [2018b]). Models featuring the grass-fire feedbacks have shown that complex physiognomies displaying treegrass coexistence (i.e.…”