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 system’s 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 that—although the two mechanisms differ—flickering 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.
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Acknowledgements
We thank Serguei Saavedra and the two anonymous reviewers for helpful comments. We are grateful to Steve Carpenter and Tim Cline for providing us with the planktivorous data for Fig. 1c from the Cascade Project at the University of Wisconsin-Madison, funded by US NSF. We also thank John Drake for allowing us to use the zooplankton data in Fig. 1d. VD is supported by a Rubicon fellowship from the Netherlands Science Foundation (NWO). EvN and MS acknowledge funding from an Advanced ERC grant awarded to MS.
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Dakos, V., van Nes, E.H. & Scheffer, M. Flickering as an early warning signal. Theor Ecol 6, 309–317 (2013). https://doi.org/10.1007/s12080-013-0186-4
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DOI: https://doi.org/10.1007/s12080-013-0186-4