Codes and data of Long transients may be temporary visits of hidden alternative stable states

Ecosystems can fluctuate around a stable equilibrium or be in a transient state (the period toward a stable state). In practical applications, transient states may be mistakenly regarded as stable states, or vice versa, especially when multiple positive feedbacks are involved, which produce much more complex system equilibrium behavior than a single positive feedback. However, our current understanding remains limited. Using a long-term restoration project in the Tengger Desert as the study object, this study employed a minimal model to explain a long “transient state” of a dryland ecosystem after restoration under the effects of two positive feedbacks (water-vegetation and erosion-vegetation). The results indicated that the transient state, a shrub-dominated state, might be an alternative stable state maintained by water-vegetation positive feedback. Shifts in dominance between the two positive feedbacks caused the ecosystem to shift from a shrub-dominated state to a herbaceous-dominated state. The shrub-dominated state was masked due to the mechanisms of dominance shifting by the two positive feedbacks, a phenomenon we refer to as a “hidden alternative stable state”. This work proposes a novel perspective to study system dynamics – a switch of multiple positive feedbacks, and discovers a new explanation to transient state – temporary visits of hidden alternative stable states, which could significantly benefit practical ecosystem interventions.