Ecosystem regime shifts are commonly regarded as abrupt global transitions from one stable state to another, induced by slow environmental changes or by global disturbances. However, the disturbances that ecosystems are subjected to, be they the results of grazing, clear-cutting, fires or infestation, are often local, affecting limited areas rather than encompassing the whole ecosystem. Such disturbances can trigger local state transitions and the formation of confined domains of the alternative state. The fate of such initial domains depends on the dynamics of their boundaries, i.e. the transition zones, or “fronts”, that separate alternative-state domains. Pattern formation theory highlights three aspects of front dynamics that are essential for understanding regime shifts in spatially extended ecosystems: (i) the motion of a single front, in terms of direction and speed of propagation, (ii) the interactions between nearby fronts, and (iii) front instabilities, e.g. saddle-node front bifurcations that result in alternative stable fronts propagating in opposite directions. These aspects have hardly been studied in ecological contexts. In this work we use mathematical models of dryland vegetation to study the implications of front motion, front interactions and front instabilities on desertification and recovery shifts in dryland ecosystems.
Results/Conclusions
Focusing on the dynamics of fronts that separate domains of bare soil and of uniform vegetation we show that fronts can change their speed and invert their direction of motion as parameters change across threshold values (so-called Maxwell points), that fronts may slow down or stop entirely when interacting with other fronts, and that an additional front, moving in a direction opposite to that of an existing front, may appear along the rainfall gradient. We further study the implications of these results to regime shifts, showing that they proceed gradually, do not necessarily culminate in the alternative state, i.e. remain incomplete, and can be reversed by local manipulations at the front zone, turning desertification fronts into recovery fronts. Since gradual regime shifts can take place far from tipping points, early warning signals base on the proximity to such points are not applicable for predicting them. Because of their slow dynamics, more significant than such signals is the development of detection and prevention methods.