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ABSTRACT: Early warning signals (EWS) of regime shifts are challenging in cases where the true natural data-generating process is uncertain. Nonparametric drift-diffusion-jump models address this problem by fitting a general model that can approximate a wide range of data-generating processes. Drift measures the local rate of change. Diffusion measures relatively small shocks that occur at each time step. Jumps are large intermittent shocks. Total variance combines the contributions of diffusion and jumps. Nonparametric methods are well suited to emerging technology for automated, high-frequency sensors. Total variance is the most precisely measured indicator. Jump intensity appears to be a useful EWS. Estimates of the drift are highly uncertain unless long time series with many regime shifts are available. EWS computed from drift estimates (such as autocorrelation coefficients or return rates) have low precision and should be used with caution. Nonetheless, in the current state of knowledge, it is premature to disregard any potential EWS.
Ecology 12/2011; 92(12):2196-201. · 4.85 Impact Factor
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S R Carpenter,
J J Cole,
M L Pace,
R Batt, W A Brock,
T Cline,
J Coloso,
J R Hodgson,
J F Kitchell,
D A Seekell,
L Smith,
B Weidel
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ABSTRACT: Catastrophic ecological regime shifts may be announced in advance by statistical early warning signals such as slowing return rates from perturbation and rising variance. The theoretical background for these indicators is rich, but real-world tests are rare, especially for whole ecosystems. We tested the hypothesis that these statistics would be early warning signals for an experimentally induced regime shift in an aquatic food web. We gradually added top predators to a lake over 3 years to destabilize its food web. An adjacent lake was monitored simultaneously as a reference ecosystem. Warning signals of a regime shift were evident in the manipulated lake during reorganization of the food web more than a year before the food web transition was complete, corroborating theory for leading indicators of ecological regime shifts.
Science 05/2011; 332(6033):1079-82. · 31.20 Impact Factor
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ABSTRACT: Regime shifts are large, long-lasting changes in ecosystems. They are often hard to predict but may have leading indicators which are detectable in advance. Potential leading indicators include wider swings in dynamics of key ecosystem variables, slower return rates after perturbation and shift of variance towards lower frequencies. We evaluated these indicators using a food web model calibrated to long-term whole-lake experiments. We investigated whether impending regime shifts driven by gradual increase in exploitation of the top predator can create signals that cascade through food webs and be discerned in phytoplankton. Substantial changes in standard deviations, return rates and spectra occurred near the switch point, even two trophic levels removed from the regime shift in fishes. Signals of regime shift can be detected well in advance, if the driver of the regime shift changes much more slowly than the dynamics of key ecosystem variables which can be sampled frequently enough to measure the indicators. However, the regime shift may occur long after the driver has passed the critical point, because of very slow transient dynamics near the critical point. Thus, the ecosystem can be poised for regime shift by the time the signal is discernible. Field tests are needed to evaluate these indicators.
Ecology Letters 03/2008; 11(2):128-38. · 17.56 Impact Factor
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ABSTRACT: 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.
Ecology Letters 02/2006; 9(3):311 - 318. · 17.56 Impact Factor
