Driver-system state interaction in regime shifts: A model study of desertification in drylands

An ecosystem may abruptly switch into a contrasting stable state at a critical threshold under the effect of external drivers, a phenomenon called regime shifts. However, drivers are generally assumed to be independent of system states, and thus associated driver-system state interaction is largely ignored when studying regime shifts. With dryland ecosystems as study objective, this study used a mean field model with drift potential as driver to investigate the influences of driver-system state interaction on dynamics of regime shifts. Our results showed following three aspects of influences of the interaction. (1) The interaction pushed the equilibria of regime shifts as a whole into higher drift potential, especially for the forward path. Under annual rainfall of 150 mm, 300 mm and 500 mm, tipping points of the upper branches moved forward 140 VU, 151 VU and 152 VU with strength of the interaction of 200 VU relative to these with strength of the interaction of 0 VU, respectively. (2) The interaction could expand the bi-stability region of regime shifts in driver space, e.g., from 125 VU (annual rainfall of 150 mm), 181 VU (annual rainfall of 300 mm) and 209 VU (annual rainfall of 500 mm) under the interaction of 0 VU up to 145 VU, 257 VU and 290 VU under the interaction of 200 VU, respectively. (3) The interaction might repel ecosystems away from the middle range of system states. These results suggest that the driver-system state interaction should be considered in the studies of regime shifts, and thus to better understand, predict and combat desertification in practice.