Various ecological and other complex dynamical systems may exhibit abrupt regime shifts or critical transitions, wherein they reorganize from one stable state to another over relatively short time scales. Because of potential losses to ecosystem services, forecasting such unexpected shifts would be valuable. Using mathematical models of regime shifts, ecologists have proposed various early warning signals of imminent shifts. However, their generality and applicability to real ecosystems remain unclear because these mathematical models are considered too simplistic. Here, we investigate the robustness of recently proposed early warning signals of regime shifts in two well-studied ecological models, but with the inclusion of time-delayed processes. We find that the average variance may either increase or decrease prior to a regime shift and, thus, may not be a robust leading indicator in time-delayed ecological systems. In contrast, changing average skewness, increasing autocorrelation at short time lags, and reddening power spectra of time series of the ecological state variable all show trends consistent with those of models with no time delays. Our results provide insights into the robustness of early warning signals of regime shifts in a broader class of ecological systems.
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V.G. is supported by a Ramalingaswamy Fellowship from the Department of Biotechnology, Government of India and the Ministry of Environment and Forests, Government of India.
All authors contributed equally to this manuscript and the names are listed in alphabetical order.
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Guttal, V., Jayaprakash, C. & Tabbaa, O.P. Robustness of early warning signals of regime shifts in time-delayed ecological models. Theor Ecol 6, 271–283 (2013). https://doi.org/10.1007/s12080-013-0194-4
- Regime shifts
- Critical transitions
- Alternative stable states
- Delay differential equations
- Early warning signals
- Power spectra