Complexity and coexistence in a simple spatial model for arid savanna ecosystems

Tree-grass coexistence is broadly observed in tropical savannas. Recent studies indicate that, in arid savannas, such coexistence is stable and related to water availability. The role of different factors (from niche separation to demographic structure) has been explored. Nevertheless, spatial mechanisms of water-vegetation interactions have been rarely taken into account, despite their well-known importance for vegetation distribution. Here, we introduce a spatial model including tree and grass biomass dynamics, together with soil and surface water dynamics. We consider two water-vegetation feedbacks. Grasses increase water infiltration into the soil, while tree shadow limits evaporation, and both mechanisms increase soil water availability, leading to positive feedbacks. The infiltration feedback can also lead to spatial pattern formation. Despite the fact that trees and grasses compete for the same resource, namely water, we observe stable coexistence as a possible model outcome. The system displays a complex behavior, with multiple stable states and possible catastrophic shifts between states, e.g., patterned grassland, bare soil and forest. In our model, coexistence is always linked with multi-stability and spatial pattern formation, driven by grass infiltration feedback. Given such complex model solutions, we expect that, under real conditions, heterogeneities and disturbances, acting on the multi-stable states, may further foster coexistence.