Modeling the dynamics of soil erosion and vegetative control — catastrophe and hysteresis

Wildfire events and anthropogenic activities such as agriculture and livestock grazing may denude the landscape from vegetation cover, resulting in systems prone to soil loss and degradation. Soil dynamics is an intricate process balanced between pedogenesis, which is a relatively slow process, and erosion which depends on many inert (e.g., soil texture, slope, precipitation, and wind) and biological factors such as vegetation properties, grazing intensity, and human disturbance. We develop here a theoretical model of the global dynamics of the interactions between vegetation and soil. Assuming a double feedback between them—plants control erosion, and soil availability facilitates plants growth—a system of nonlinear differential equations is derived, and the outcomes are investigated. The range of realistic parameter values were taken from the literature. Complex properties emerge from this model. For some ranges of parameter values, the model predicts one of two types of steady states—full recovery of vegetation cover or a degraded barren system. For another range of parameter values, bistability appears. We identify the parameter combinations which determine the qualitative behavior of the system and the threshold values beyond which the system becomes bistable. The model predicts that certain ecosystems are highly stable. Others might be bistable transitioning between these two states through perturbations. Therefore, the possibly of hysteresis as parameters vary arises, as well as the ability of the system to shift between steady states, possibly leading to sudden and dramatic changes.