Methods for detecting early warnings of critical transitions in time series illustrated using simulated ecological data

PLoS ONE

Volumn 7, Issue 7, 2012, Pages

  Dakos, Vasilis ^a,b   Carpenter, Stephen R ^c   Brock, William A ^c   Ellison, Aaron M ^d   Guttal, Vishwesha ^e   Ives, Anthony R ^c   Kéfi, Sonia ^f   Livina, Valerie ^g   Seekell, David A ^h   van Nes, Egbert H ^a   Scheffer, Marten ^a  

^a WAGENINGEN UNIVERSITY   (Netherlands)

^b DEPARTMENT OF CONSERVATION BIOLOGY   (Spain)

^c UNIVERSITY OF WISCONSIN MADISON   (United States)

^d HARVARD UNIVERSITY   (United States)

^e INDIAN INSTITUTE OF SCIENCE   (India)

^f INSTITUT DES SCIENCES DE L EVOLUTION   (France)

^g UNIVERSITY OF EAST ANGLIA   (United Kingdom)

^h UNIVERSITY OF VIRGINIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CRITICAL TRANSITION; DIFFUSION; ECOLOGY; GEOGRAPHIC AND GEOLOGICAL PHENOMENA; MATHEMATICAL ANALYSIS; MEASUREMENT ERROR; PREDICTION; SENSITIVITY ANALYSIS; SIGNAL DETECTION; SIMULATION; STATISTICAL ANALYSIS; STATISTICAL MODEL; TIME SERIES ANALYSIS;

ALGORITHMS; BIOLOGY; COMPUTER SIMULATION; DIFFUSION; ECOLOGY; ENVIRONMENT; LAKES; MODELS, BIOLOGICAL; MODELS, STATISTICAL; MODELS, THEORETICAL; OCEANS AND SEAS; REPRODUCIBILITY OF RESULTS; SYSTEMS THEORY; TIME FACTORS;

EID: 84864018548     PISSN: None     EISSN: 19326203     Source Type: Journal    
DOI: 10.1371/journal.pone.0041010     Document Type: Article

References (64)

1. Lenton TM, Held H, Kriegler E, Hall JW, Lucht W, et al. (2008) Tipping elements in the Earth's climate system. Proc Nat Acad Sci USA 105: 1786-1793.
2. Scheffer M, Carpenter S, Foley JA, Folke C, Walker B, (2001) Catastrophic shifts in ecosystems. Nature 413: 591-596.
3. McSharry PE, Smith LA, Tarassenko L, Martinerie J, Le van Quyen M, et al. (2003) Prediction of epileptic seizures: Are nonlinear methods relevant? Nat Med 9: 241-242.
4. Scheffer M, (2009) Critical Transitions in Nature and Society. Princeton, New Jersey: Princeton University Press.
5. Bestelmeyer BT, Ellison AM, Fraser WR, Gorman KB, Holbrook SJ, et al. (2011) Analysis of abrupt transitions in ecological systems. Ecosphere 2: 129.
6. Scheffer M, Bascompte J, Brock WA, Brovkin V, Carpenter SR, et al. (2009) Early-warning signals for critical transitions. Nature 461: 53-59.
7. Livina VN, Lenton TM, (2007) A modified method for detecting incipient bifurcations in a dynamical system. Geophys Res Lett 34.
8. Dakos V, Scheffer M, van Nes EH, Brovkin V, Petoukhov V, et al. (2008) Slowing down as an early warning signal for abrupt climate change. Proc Nat Acad Sci USA 105: 14308-14312.
9. Drake J, Griffen B, (2010) Early warning signals of extinction in deteriorating environments Nature 467: 456-459.
10. Carpenter SR, Cole JJ, Pace ML, Batt R, Brock WA, et al. (2011) Early warnings of regime shifts: a whole-ecosystem experiment. Science 332: 1079-1082.
11. Kramer J, Ross J, (1985) Stabilization of unstable states, relaxation, and critical slowing down in a bistable system. J Chem Phys 83: 6234-6241.
12. Tredicce JR, Lippi GL, Mandel P, Charasse B, Chevalier A, et al. (2004) Critical slowing down at a bifurcation. Am J Phys 72: 799-809.
13. Veraart AJ, Faassen EJ, Dakos V, van Nes EH, Lurling M, et al. (2012) Recovery rates reflect distance to a tipping point in a living system. Nature 481: 357-359.
14. Lenton TM, (2011) Early warning of climate tipping points. Nature Clim Change 1: 201-209.
15. Hastings A, Wysham DB, (2010) Regime shifts in ecological systems can occur with no warning. Ecol Lett 13: 464-472.
16. Carpenter SR, Brock WA, (2011) Early warnings of unknown nonlinear shifts: a nonparametric approach. Ecology 92: 2196-2201.
17. Wissel C, (1984) A universal law of the characteristic return time near thresholds. Oecologia 65: 101-107.
18. Strogatz SH, (1994) Nonlinear Dynamics and Chaos- With Applications to Physics, Biology, Chemistry and Engineering. Reading: Addison-Wesley Publishing Company.
19. Held H, Kleinen T, (2004) Detection of climate system bifurcations by degenerate fingerprinting. Geophys Res Lett 31.
20. Kleinen T, Held H, Petschel-Held G, (2003) The potential role of spectral properties in detecting thresholds in the Earth system: application to the thermohaline circulation. Ocean Dynamics 53: 53-63.
21. Box GEP, Jenkins GM, Geinsel GC, (2008) Time Series Analysis Forecasting and Control. New Jersey: Wiley.
22. Ives AR, Dennis B, Cottingham KL, Carpenter SR, (2003) Estimating community stability and ecological interactions from time-series data. Ecol Monogr 73: 301-330.
23. Carpenter SR, Brock WA, Cole JJ, Kitchell JF, Pace ML, (2008) Leading indicators of trophic cascades. Ecol Lett 11: 128-138.
24. Schroeder M, (1991) Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise: Freeman.
25. Biggs R, Carpenter SR, Brock WA, (2009) Turning back from the brink: Detecting an impending regime shift in time to avert it. Proc Nat Acad Sci USA 106: 826-831.
26. Peng C-K, Buldyrev S, Havlin S, Simons M, Stanley H, et al. (1994) Mosaic organization of DNA nucleotides. Phys Rev E 49: 1685-1689.
27. Lenton TM, Livina VN, Dakos V, van Nes EH, Scheffer M, (2012) Early warning of climate tipping points from critical slowing down: comparing methods to improve robustness. Philos Transact A Math Phys Eng Sci 370: 1185-1204.
28. Carpenter SR, Brock WA, (2006) Rising variance: a leading indicator of ecological transition. Ecol Lett 9: 311-318.
29. Guttal V, Jayaprakash C, (2008) Changing skewness: an early warning signal of regime shifts in ecosystems. Ecol Lett 11: 450-460.
30. Engle RF, Hendry DF, Trumble D, (1985) Small-sample properties of ARCH estimators and tests. Can J Econ 18: 66-93.
31. Engle RF, (1982) A general approach to Lagrange multiplier model diagnostics. J Econom 20: 83-104.
32. Seekell DA, Carpenter SR, Pace ML, (2011) Conditional heteroscedasticity as a leading indicator of ecological regime shifts. Am Nat 178: 442-451.
33. Brock WA, Dechert W, Scheinkman J, LeBaron B, (1996) A test for independence based upon the correlation dimension. Econom Rev 15: 197-235.
34. Johannes M, (2004) The statistical and economic role of jumps in continuous-time interest rate models. J Finance 59: 227-260.
35. Bandi F, Nguyen T, (2003) On the functional estimation of jump-diffusion models. J Econom 116: 293-328.
36. Hardle W, (1990) Applied Nonparametric Regression. Cambridge, England: Cambridge University Press.
37. Horsthemke W, Lefever R, (2006) Noise-Induced Transitions: Theory and Applications in Physics, Chemistry, and Biology. Berlin: Springer.
38. Ives AR, Dakos V (in press) Detecting dynamical changes in nonlinear time series using locally linear state-space models. Ecosphere.
39. Box GEP, Jenkins GM, Reinsel GC, (1994) Time Series Analysis: Forecasting and Control. Englewood Cliffs, New Yersey USA: Prentice-Hall.
40. Harvey AC, (1989) Forecasting, structural time series models and the Kalman filter: Cambridge University Press.
41. Self SG, Liang KY, (1987) Asymptotic properties of maximum-likelihood estimators and likelihood ratio tests under non-standard conditions. J Am Stat Assoc 82: 605-610.
42. Stram DO, Lee JW, (1984) Variance-components testing in the longitudinal mixed effects model. Biometrics 50: 1171-1177.
43. Livina VN, Kwasniok F, Lenton TM, (2010) Potential analysis reveals changing number of climate states during the last 60 kyr. Clim Past 6: 77-82.
44. Livina VN, Kwasniok F, Lohmann G, Kantelhardt JW, Lenton TM, (2011) Changing climate states and stability: from Pliocene to present. Climate Dynam 37: 2437-2453.
45. May RM, (1977) Thresholds and breakpoints in ecosystems with a multiplicity of stable states. Nature 269: 471-477.
46. Noy-Meir I, (1975) Stability of grazing systems an application of predator prey graphs. J Ecol 63: 459-482.
47. van Nes EH, Scheffer M, (2007) Slow recovery from perturbations as a generic indicator of a nearby catastrophic shift. Am Nat 169: 738-747.
48. Dakos V, van Nes EH, D'Odorico P, Scheffer M, (2011) Robustness of variance and autocorrelation as indicators of critical slowing down. Ecology 93: 264-271.
49. Hasselmann K, (1976) Stochastic climate models, Part I: Theory. Tellus 28: 473-485.
50. Thompson JMT, Sieber J, (2011) Predicting climate tipping as a noisy bifurcation: a review. Int J Bifurcat Chaos 21: 399-423.
51. Theiler J, Eubank S, Longtin A, Galdrikian B, Farmer JD, (1992) Testing for nonlinearity in time-Series- the method of surrogate data. Physica D 58: 77-94.
52. Halley JM, Kugiumtzis D, (2011) Nonparametric testing of variability and trend in some climatic records. Clim Change 109: 549-568.
53. Dakos V, Kéfi S, Rietkerk M, van Nes EH, Scheffer M, (2011) Slowing down in spatially patterned ecosystems at the brink of collapse. Am Nat 177: E153-E166.
54. Livina VN, Ditlevsen PD, Lenton TM, (2012) An independent test of methods of detecting system states and bifurcations in time-series data. Phys A 391: 485-496.
55. Thompson JMT, Sieber J, (2011) Predicting climate tipping as a noisy bifurcation: a review. Int J Bifurcat Chaos 21: 399-423.
56. Lade SJ, Gross T, (2012) Early warning signals for critical transitions: A generalized modeling approach. PLoS Comput Biol 28: e1002360.
57. Oborny B, Meszena G, Szabo G, (2005) Dynamics of populations on the verge of extinction. Oikos 109: 291-296.
58. Guttal V, Jayaprakash C, (2009) Spatial variance and spatial skewness: leading indicators of regime shifts in spatial ecological systems. Theor Ecol 2: 3-12.
59. Dakos V, van Nes E, Donangelo R, Fort H, Scheffer M, (2010) Spatial correlation as leading indicator of catastrophic shifts. Theor Ecol 3: 163-174.
60. Rietkerk M, Dekker SC, de Ruiter PC, van de Koppel J, (2004) Self-organized patchiness and catastrophic shifts in ecosystems. Science 305: 1926-1929.
61. Kéfi S, Rietkerk M, Alados CL, Pueyo Y, Papanastasis VP, et al. (2007) Spatial vegetation patterns and imminent desertification in Mediterranean arid ecosystems. Nature 449: 213-217.
62. Maestre FT, Escudero A, (2009) Is the patch size distribution of vegetation a suitable indicator of desertification processes? Ecology 90: 1729-1735.
63. Carpenter SR, (2002) Regime Shifts in Lake Ecosystems: Pattern and Variation. Oldendorf/Luhe, Germany.
64. Clark JS, Carpenter SR, Barber M, Collins S, Dobson A, et al. (2001) Ecological forecasts: An emerging imperative. Science 293: 657-660.