Multistability and tipping: From mathematics and physics to climate and brain—Minireview and preface to the focus issue

The turbidity of lakes is generally considered to be a smooth function of their nutrient status. However, recent results suggest that over a range of nutrient concentrations, shallow lakes can have two alternative equilibria: a clear state dominated by aquatic vegetation, and a turbid state characterized by high algal biomass. This bi-stability has important implications for the possibilities of restoring eutrophied shallow lakes. Nutrient reduction alone may have little impact on water clarity, but an ecosystem disturbance like foodweb manipulation can bring the lake back to a stable clear state. We discuss the reasons why alternative equilibria are theoretically expected in shallow lakes, review evidence from the field and evaluate recent applications of this insight in lake management. Copyright © 1993. Published by Elsevier Ltd.

Regime shifts are substantial, long-lasting reorganizations of complex systems, such as ecosystems. Large ecosystem changes such as eutrophication, shifts among vegetation types, degradation of coral reefs and regional climate change often come as surprises because we lack leading indicators for regime shifts. Increases in variability of ecosystems have been suggested to foreshadow ecological regime shifts. However, it may be difficult to discern variability due to impending regime shift from that of exogenous drivers that affect the ecosystem. We addressed this problem using a model of lake eutrophication. Lakes are subject to fluctuations in recycling associated with regime shifts, as well as fluctuating nutrient inputs. Despite the complications of noisy inputs, increasing variability of lake-water phosphorus was discernible prior to the shift to eutrophic conditions. Simulations show that rising standard deviation (SD) could signal impending shifts about a decade in advance. The rising SD was detected by studying variability around predictions of a simple time-series model, and did not depend on detailed knowledge of the actual ecosystem dynamics.