Content area
Full Text
Theor Ecol (2013) 6:309317 DOI 10.1007/s12080-013-0186-4
ORIGINAL PAPER
Flickering as an early warning signal
Vasilis Dakos & Egbert H. van Nes & Marten Scheffer
Received: 13 February 2013 /Accepted: 11 April 2013 /Published online: 28 April 2013 # Springer Science+Business Media Dordrecht 2013
Abstract Most work on generic early warning signals for critical transitions focuses on indicators of the phenomenon of critical slowing down that precedes a range of catastrophic bifurcation points. However, in highly stochastic environments, systems will tend to shift to alternative basins of attraction already far from such bifurcation points. In fact, strong perturbations (noise) may cause the system to flicker between the basins of attraction of the systems alternative states. As a result, under such noisy conditions, critical slowing down is not relevant, and one would expect its related generic leading indicators to fail, signaling an impending transition. Here, we systematically explore how flickering may be detected and interpreted as a signal of an emerging alternative attractor. We show thatalthough the two mechanisms differflickering may often be reflected in rising variance, lag-1 autocorrelation and skewness in ways that resemble the effects of critical slowing down. In particular, we demonstrate how the probability distribution of a flickering system can be used to map potential alternative attractors and their resilience. Thus, while flickering systems differ in many ways from the classical image of critical transitions, changes in their dynamics may carry valuable information about upcoming major changes.
Keywords Resilience . Critical transition . Critical slowing down . Alternative stable states . Regime shift . Stochasticity
Introduction
Theory predicts that, close to tipping points, the return to equilibrium upon small perturbations will slow down (Wissel 1984; Strogatz 1994; Scheffer et al. 2009). In stochastic environments, this will tend to be reflected in higher temporal autocorrelation and variance of the fluctuations in the state of a system (Held and Kleinen 2004; Carpenter and Brock 2006; Scheffer et al. 2009). However, this picture of a critically slowed down world prior to a transition could be the exception rather than the rule. As most systems are embedded in highly stochastic environments, they may start to flicker between the basins of attraction of their potential alternative states far before bifurcation points at which critical transitions occur. Under such...