Quantifying limits to detection of early warning for critical transitions

Abstract

Catastrophic regime shifts in complex natural systems may be averted through advanced detection. Recent work has provided a proof-of-principle that many systems approaching a catastrophic transition may be identified through the lens of early warning indicators such as rising variance or increased return times. Despite widespread appreciation of the difficulties and uncertainty involved in such forecasts, proposed methods hardly ever characterize their expected error rates. Without the benefits of replicates, controls or hindsight, applications of these approaches must quantify how reliable different indicators are in avoiding false alarms, and how sensitive they are to missing subtle warning signs. We propose a model-based approach to quantify this trade-off between reliability and sensitivity and allow comparisons between different indicators. We show these error rates can be quite severe for common indicators even under favourable assumptions, and also illustrate how a model-based indicator can improve this performance. We demonstrate how the performance of an early warning indicator varies in different datasets, and suggest that uncertainty quantification become a more central part of early warning predictions.

Factors Influencing the Detectability of Early Warning Signals of Population Collapse

“…We then analyzed the significance and strength of these correlations to evaluate the relative performance of different potential early warning signals in the data. This approach to forecasting critical transitions has been criticized for being statistically inefficient (Boettiger and Hastings 2012). We note that our goal was not to obtain the most efficient statistical estimator but rather to measure the effect of data corruption on the estimators currently enjoying the widest use.…”

“…Previously, something similar had been achieved using state-space models (Hefley et al 2013), but future work could also seek to include imperfect sampling in the calculation of statistical leading indicators. Alternatively, more powerful model selection approaches (proposed by Boettiger and Hastings [2012]) may be employed, which could prove less susceptible to degraded data. Such an approach could not be implemented here, as it is computationally intensive, and it would be impossible to analyze the large number of simulated and experimental data sets generated here.…”

“…However, when search efforts are low and sampling is infrequent, these statistical early warning signals are often unreliable. Thus, we additionally suggest that future analysis should seek to implicitly or explicitly include observational uncertainty or approach these issues in alternate ways (e.g., Boettiger and Hastings 2012).…”

“…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).…”

Long-term transients and complex dynamics of a stage-structured population with time delay and the Allee effect

“…There is a growing understanding that in natural ecosystems the asymptotic behavior is, in fact, rarely seen and their reported cases when a species that has been present in apparently safe numbers goes extinct suddenly and seemingly without any warning (Scheffer et al, 2001(Scheffer et al, , 2009Carpenter, 2003). One general way to explain these cases might be to relate them to catastrophic changes in the ecosystem properties such as, in mathematical terms, the disappearance of a steady state as a result of saddle-node bifurcation (Scheffer et al, 2009, Boettiger andHastings, 2012). Another scenario of regime shifts can be the existence of long-living transients, which provides an alternative explanation of sudden species extinction (Tilman et al, 1994, Schreiber, 2003.…”