Methods for Detecting Early Warnings of Critical Transitions in Time Series Illustrated Using Simulated Ecological Data

Dakos, Vasilis; Carpenter, Stephen R.; Brock, William A.; Ellison, Aaron M.; Guttal, Vishwesha; Ives, Anthony R.; Kéfi, Sonia; Livina, Valerie N.; Seekell, David A.; Nes, Egbert H. van; Scheffer, Marten

doi:10.1371/journal.pone.0041010

Cited by 794 publications

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References 61 publications

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“…For example, we found strong fluctuations in nonlinearity estimates, especially in the exploitation scenario (electronic supplementary material, figure S2f). Changes in variance and autocorrelation can also be unreliable in the presence of short time series [51], high levels of stochasticity [57], fast changing stress drivers [54,58] or due to portfolio effects [56] and life-history strategies [59]. Further research is needed to find if similar constraints hold for the elevated nonlinearity indicator we propose here.…”

Section: Discussionmentioning

confidence: 84%

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Elevated nonlinearity as an indicator of shifts in the dynamics of populations under stress

Dakos

Glaser

Hsieh

et al. 2017

J. R. Soc. Interface.

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Populations occasionally experience abrupt changes, such as local extinctions, strong declines in abundance or transitions from stable dynamics to strongly irregular fluctuations. Although most of these changes have important ecological and at times economic implications, they remain notoriously difficult to detect in advance. Here, we study changes in the stability of populations under stress across a variety of transitions. Using a Ricker-type model, we simulate shifts from stable point equilibrium dynamics to cyclic and irregular boom-bust oscillations as well as abrupt shifts between alternative attractors. Our aim is to infer the loss of population stability before such shifts based on changes in nonlinearity of population dynamics. We measure nonlinearity by comparing forecast performance between linear and nonlinear models fitted on reconstructed attractors directly from observed time series. We compare nonlinearity to other suggested leading indicators of instability (variance and autocorrelation). We find that nonlinearity and variance increase in a similar way prior to the shifts. By contrast, autocorrelation is strongly affected by oscillations. Finally, we test these theoretical patterns in datasets of fisheries populations. Our results suggest that elevated nonlinearity could be used as an additional indicator to infer changes in the dynamics of populations under stress.

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Section: Discussionmentioning

confidence: 84%

“…Therefore, it is expected that these indicators (as any other indicator) would also change in a continuous way. For this reason, interpretations of changes in dynamics could only be based on parallel monitoring and comparison among multiple indicators [51].…”

Section: Discussionmentioning

confidence: 99%

Elevated nonlinearity as an indicator of shifts in the dynamics of populations under stress

Dakos

Glaser

Hsieh

et al. 2017

J. R. Soc. Interface.

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“…Such early warning signals include an increase in the standard deviation of a population's size, a decrease in the return rate of a population to its mean after a perturbation, and an increase in the autocorrelation of a population's demographic fluctuations (Dakos et al 2012a). These generic leading indicators arise from mathematical properties of stochastic dynamical systems as they approach a tipping point and appear to be present in vastly different systems, including stock markets, global climatic change, and populations (for a review, see Scheffer et al 2009).…”

Section: Introductionmentioning

confidence: 99%

“…This may take the form of time series that cover a short period with relatively frequent sampling, time series that cover a longer period of time with more infrequent sampling, or irregular sampling through time. Irregular temporal sampling is of particular concern, as many statistical leading indicators require data that are sampled at regular intervals (Dakos et al 2012a). Irregularly sampled data must therefore be interpolated to create evenly spaced data, which may introduce artificial autocorrelation (Boettiger and Hastings 2012).…”

Section: Introductionmentioning

confidence: 99%

“…To address this, we first simulated data using a model previously shown to exhibit early warning signals prior to a regime shift (Dakos et al 2012a) and then corrupted this perfect data by simulating search regimes and search frequencies. We identified which early warning signals are most robust to subsampling of the data and what portion of the habitat must be searched (or frequency of sampling must be employed) before trends in early warning signals were reliably identified.…”

Section: Introductionmentioning

confidence: 99%

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Factors Influencing the Detectability of Early Warning Signals of Population Collapse

Clements

Drake

Griffiths

et al. 2015

The American Naturalist

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The recent description of potentially generic early warning signals is a promising development that may help conservationists to anticipate a population's collapse prior to its occurrence. So far, the majority of such warning signals documented have been in highly controlled laboratory systems or theoretical models. Data from wild populations, however, are typically restricted both temporally and spatially due to limited monitoring resources and intrinsic ecological heterogeneity -limitations that may affect the detectability of generic early warning signals, as they add additional stochasticity to population abundance estimates. Consequently, spatial and temporal subsampling may serve either to muffle or magnify early warning signals. Using a combination of theoretical models and analysis of experimental data, we evaluate the extent to which statistical warning signs are robust to data corruption. Online enhancements: appendixes, zip file.abstract: The recent description of potentially generic early warning signals is a promising development that may help conservationists to anticipate a population's collapse prior to its occurrence. So far, the majority of such warning signals documented have been in highly controlled laboratory systems or in theoretical models. Data from wild populations, however, are typically restricted both temporally and spatially due to limited monitoring resources and intrinsic ecological heterogeneity-limitations that may affect the detectability of generic early warning signals, as they add additional stochasticity to population abundance estimates. Consequently, spatial and temporal subsampling may serve to either muffle or magnify early warning signals. Using a combination of theoretical models and analysis of experimental data, we evaluate the extent to which statistical warning signs are robust to data corruption.

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Variance and Rate‐of‐Change as Early Warning Signals for a Critical Transition in an Aquatic Ecosystem State: A Test Case From Tasmania, Australia

et al. 2018

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Critical transitions in ecosystem states are often sudden and unpredictable. Consequently, there is a concerted effort to identify measurable early warning signals (EWS) for these important events. Aquatic ecosystems provide an opportunity to observe critical transitions due to their high sensitivity and rapid response times. Using palaeoecological techniques, we can measure properties of time series data to determine if critical transitions are preceded by any measurable ecosystem metrics, that is, identify EWS. Using a suite of palaeoenvironmental data spanning the last 2,400 years (diatoms, pollen, geochemistry, and charcoal influx), we assess whether a critical transition in diatom community structure was preceded by measurable EWS. Lake Vera, in the temperate rain forest of western Tasmania, Australia, has a diatom community dominated by Discostella stelligera and undergoes an abrupt compositional shift at ca. 820 cal yr BP that is concomitant with increased fire disturbance of the local vegetation. This shift is manifest as a transition from less oligotrophic acidic diatom flora (Achnanthidium minutissimum, Brachysira styriaca, and Fragilaria capucina) to more oligotrophic acidic taxa (Frustulia elongatissima, Eunotia diodon, and Gomphonema multiforme). We observe a marked increase in compositional variance and rate‐of‐change prior to this critical transition, revealing these metrics are useful EWS in this system. Interestingly, vegetation remains complacent to fire disturbance until after the shift in the diatom community. Disturbance taxa invade and the vegetation system experiences an increase in both compositional variance and rate‐of‐change. These trends imply an approaching critical transition in the vegetation and the probable collapse of the local rain forest system.

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Methods for Detecting Early Warnings of Critical Transitions in Time Series Illustrated Using Simulated Ecological Data

Cited by 794 publications

References 61 publications

Elevated nonlinearity as an indicator of shifts in the dynamics of populations under stress

Elevated nonlinearity as an indicator of shifts in the dynamics of populations under stress

Factors Influencing the Detectability of Early Warning Signals of Population Collapse

Variance and Rate‐of‐Change as Early Warning Signals for a Critical Transition in an Aquatic Ecosystem State: A Test Case From Tasmania, Australia

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