Modeling vegetation patterning on sloped terrains: The role of toxic compounds

Vegetation patterning processes taking place on sloped terrains are here investigated through a class of three-compartments 1D reaction–advection–diffusion models enclosing the effects associated with the presence of toxic compounds. Focus is given to the transition from a uniformly-vegetated area to the desert state which occurs through the formation of an intermediate state characterized by non-stationary vegetation stripes. To this aim, linear stability analysis is addressed to characterize the mechanism of wave instability, responsible for the emergence of oscillatory Turing patterns. In detail, the analysis provides the critical value of the main control parameter as well as the wavelength and the migration speed at the onset of instability. Moreover, multiple-scale weakly nonlinear stability analysis is performed to describe the time evolution of the pattern amplitude close to the bifurcation threshold. Theoretical investigations are complemented by numerical simulations carried out for an extension of the Klausmeier kinetics that explicitly takes into account the interaction between autotoxicity and vegetation biomass. Numerical results provide several insights on how the interplay among mean annual rainfall, plant mortality and plant’s sensitivity to toxicity gives rise to different ecological scenarios.