Unifying Deterministic and Stochastic Models in Drylands

Abstract

Understanding the causes and effects of spatial vegetation patterns in semi-arid ecosystems is a fundamental problem in ecology, especially because these can be used as early predictors for catastrophic shifts such as desertification. Empirical studies of the vegetation cover in some areas such as drylands and semi-arid regions have revealed the existence of vegetation patches of broadly diverse sizes. Different explanatory mechanisms, such as plant-plant interactions and plant-water feedback loops have been proposed to rationalize the emergence of such patterns, yet a full understanding has not been reached. Using a stochastic model for vegetation and water dynamics, we show that emergence of vegetation patches with broadly distributed sizes are promoted in a robust way depending on the stochastic pressure. From a practical viewpoint, this may be of importance to characterize real data gathered using remote sensing and predict the effects that changes in environmental conditions may have in real ecosystems.