My recent paper with Alan Hastings, “Early warning signals and the prosecutor’s fallacy”, is now out in PRSB. An open access preprint can be found on the (arXiv) and accompanying (source code) for the analysis can be found on Github.
Recent papers in early warning signals
This invistigation is in a very similar spirit to two other recent papers on the subject. Kéfi et al. addresses a different kind of false positive for early warning signals, arising in systems approaching other transitions or bifurcations than the intended culprit, the saddle-node bifurcation. Peretti and Munch address the flip side, in which detection fails when it should work due to commonly-observed levels of noise.
Model-based approaches are clearly on the rise (following my own 2012 paper in PRSI and Lade and Gross 2012), with Brock and Carpenter (2012) putting forward a very similar model, and Ives & Dakos (2012) bringing in temporally heterogenous ARMA models.
Unfortunately such model-based approaches are too new to make it into either of the recent review-like comparisons of existing approaches to a common set of simulated data (Dakos et al. 2012) or empirical data (Lindegren et al. 2012).
References
Boettiger, C., & Hastings, A. (2012). Early warning signals and the prosecutor’s fallacy. Proceedings of the Royal Society B: Biological Sciences, (October). doi:10.1098/rspb.2012.2085
Kéfi, S., Dakos, V., Scheffer, M., Van Nes, E. H., & Rietkerk, M. (2012). Early warning signals also precede non-catastrophic transitions. Oikos, (June), no-no. doi:10.1111/j.1600-0706.2012.20838.x
Perretti, C. T., & Munch, S. B. (2012). Regime shift indicators fail under noise levels commonly observed in ecological systems. Ecological Applications, 22(6), 1772-1779. doi:10.1890/11-0161.1
Boettiger, Carl, & Hastings, A. (2012). Quantifying limits to detection of early warning for critical transitions. Journal of The Royal Society Interface, 9(75), 2527 - 2539. doi:10.1098/rsif.2012.0125
Lade, S. J., & Gross, T. (2012). Early Warning Signals for Critical Transitions: A Generalized Modeling Approach. (M. Pascual, Ed.)PLoS Computational Biology, 8(2), e1002360. doi:10.1371/journal.pcbi.1002360* Brock, W. A., & Carpenter, S. R. (2012). Early Warnings of Regime Shift When the Ecosystem Structure Is Unknown. (R. V. Solé, Ed.)PLoS ONE, 7(9), e45586. doi:10.1371/journal.pone.0045586
Ives, A., & Dakos, V. (2012). Detecting dynamical changes in nonlinear time series using locally linear state-space models. Ecosphere, 3(June). Retrieved from https://www.esajournals.org/doi/abs/10.1890/ES11-00347.1
Dakos, V., Carpenter, S. R., Brock, W. a., Ellison, A. M., Guttal, V., Ives, A. R., Kéfi, S., et al. (2012). Methods for Detecting Early Warnings of Critical Transitions in Time Series Illustrated Using Simulated Ecological Data. (B. Yener, Ed.)PLoS ONE, 7(7), e41010. doi:10.1371/journal.pone.0041010
Lindegren, M., Dakos, V., Gröger, J. P., Gårdmark, A., Kornilovs, G., Otto, S. a., & Möllmann, C. (2012). Early Detection of Ecosystem Regime Shifts: A Multiple Method Evaluation for Management Application. (S. Thrush, Ed.)PLoS ONE, 7(7), e38410. doi:10.1371/journal.pone.0038410