Time scale of resilience loss: Implications for managing critical transitions in water quality

Autoři: Ryan D. Batt aff001;  Tarsha Eason aff004;  Ahjond Garmestani aff005
Působiště autorů: National Research Council, United States Environmental Protection Agency, Cincinnati, Ohio, United States of America aff001;  Rensselaer Polytechnic Institute, Department of Biological Sciences, Troy, New York, United States of America aff002;  Rutgers University, Department of Ecology, Evolution, and Natural Resources, New Brunswick, New Jersey, United States of America aff003;  United States Environmental Protection Agency, Office of Research and Development, Research Triangle Park, North Carolina, United States of America aff004;  United States Environmental Protection Agency, Office of Research and Development, Cincinnati, Ohio, United States of America aff005;  Utrecht Centre for Water, Oceans and Sustainability Law, Utrecht University School of Law, Utrecht, Netherlands aff006
Vyšlo v časopise: PLoS ONE 14(10)
Kategorie: Research Article
doi: 10.1371/journal.pone.0223366


Regime shifts involving critical transitions are a type of rapid ecological change that are difficult to predict, but may be preceded by decreases in resilience. Time series statistics like lag-1 autocorrelation may be useful for anticipating resilience declines; however, more study is needed to determine whether the dynamics of autocorrelation depend on the resolution of the time series being analyzed, i.e., whether they are time-scale dependent. Here, we examined timeseries simulated from a lake eutrophication model and gathered from field measurements. The field study involved collecting high frequency chlorophyll fluorescence data from an unmanipulated reference lake and a second lake undergoing experimental fertilization to induce a critical transition in the form of an algal bloom. As part of the experiment, the fertilization was halted in response to detected early warnings of the algal bloom identified by increased autocorrelation. We tested these datasets for time-scale dependence in the dynamics of lag-1 autocorrelation and found that in both the simulation and field experiment, the dynamics of autocorrelation were similar across time scales. In the simulated time series, autocorrelation increased exponentially approaching algal bloom development, and in the field experiment, the difference in autocorrelation between the manipulated and reference lakes increased sharply. These results suggest that, as an early warning indicator, autocorrelation may be robust to the time scale of the analysis. Given that a time scale can be shortened by increasing sampling frequency, or lengthened by aggregating data during analysis, these results have important implications for management as they demonstrate the potential for detecting early warning signals over a wide range of monitoring frequencies and without requiring analysts to make situation-specific decisions regarding aggregation. Such an outcome provides promise that data collection procedures, especially by automated sensors, may be used to monitor and manage ecosystem resilience without the need for strict attention to time scale.

Klíčová slova:

Algae – Ecosystems – Chlorophyll – Lakes – Surface water – System stability – Water quality – Fertilization


1. Scheffer M, Hosper SH, Meijer ML, Moss B, Jeppesen E. Alternative Equilibria in Shallow Lakes. Trends Ecol Evol. 1993;8(8):275–9. doi: 10.1016/0169-5347(93)90254-M 21236168

2. Beckage B, Ellingwood C. Fire feedbacks with vegetation and alternative stable states. Complex Systems. 2008;18(1):159.

3. Frank KT, Petrie B, Choi JS, Leggett WC. Trophic cascades in a formerly cod-dominated ecosystem. Science. 2005;308(5728):1621–3. doi: 10.1126/science.1113075 15947186

4. Staver AC, Archibald S, Levin S. Tree cover in sub-Saharan Africa: rainfall and fire constrain forest and savanna as alternative stable states. Ecology. 2011;92(5):1063–72. doi: 10.1890/10-1684.1 21661567

5. Botsford LW. The Effects of Increased Individual Growth-Rates on Depressed Population-Size. Am Nat. 1981;117(1):38–63.

6. Spencer PD, Collie JS. Effect of nonlinear predation rates on rebuilding the Georges Bank Haddock (Melanogrammus aeglefinus) stock. Can J Fish Aquat Sci. 1997;54(12):2920–9.

7. Dakos V, Scheffer M, van Nes EH, Brovkin V, Petoukhov V, Held H. Slowing down as an early warning signal for abrupt climate change. P Natl Acad Sci USA. 2008;105(38):14308–12.

8. Scheffer M, Bascompte J, Brock WA, Brovkin V, Carpenter SR, Dakos V, et al. Early-warning signals for critical transitions. Nature. 2009;461(7260):53–9. doi: 10.1038/nature08227 19727193

9. Wissel C. A Universal Law of the Characteristic Return Time near Thresholds. Oecologia. 1984;65(1):101–7. doi: 10.1007/BF00384470 28312117

10. Held H, Kleinen T. Detection of climate system bifurcations by degenerate fingerprinting. Geophys Res Lett. 2004;31(23).

11. Livina VN, Lenton TM. A modified method for detecting incipient bifurcations in a dynamical system. Geophys Res Lett. 2007;34(3).

12. Dai L, Vorselen D, Korolev KS, Gore J. Generic Indicators for Loss of Resilience Before a Tipping Point Leading to Population Collapse. Science. 2012;336(6085):1175–7. doi: 10.1126/science.1219805 22654061

13. Drake JM, Griffen BD. Early warning signals of extinction in deteriorating environments. Nature. 2010;467(7314):456–9. doi: 10.1038/nature09389 20827269

14. Veraart AJ, Faassen EJ, Dakos V, van Nes EH, Lurling M, Scheffer M. Recovery rates reflect distance to a tipping point in a living system. Nature. 2012;481(7381):357–U137.

15. Gsell AS, Scharfenberger U, Ozkundakci D, Walters A, Hansson LA, Janssen ABG, et al. Evaluating early-warning indicators of critical transitions in natural aquatic ecosystems. P Natl Acad Sci USA. 2016;113(50):E8089–E95.

16. Spanbauer TL, Allen CR, Angeler DG, Eason T, Fritz SC, Garmestani AS, et al. Prolonged instability prior to a regime shift. PLoS One. 2014;9(10):e108936. doi: 10.1371/journal.pone.0108936 25280010

17. Carpenter SR, Cole JJ, Pace ML, Batt R, Brock WA, Cline T, et al. Early Warnings of Regime Shifts: A Whole-Ecosystem Experiment. Science. 2011;332(6033):1079–82. doi: 10.1126/science.1203672 21527677

18. Pace ML, Batt RD, Buelo CD, Carpenter SR, Cole JJ, Kurtzweil JT, et al. Reversal of a cyanobacterial bloom in response to early warnings. P Natl Acad Sci USA. 2017;114(2):352–7.

19. Kefi S, Dakos V, Scheffer M, Van Nes EH, Rietkerk M. Early warning signals also precede non-catastrophic transitions. Oikos. 2013;122(5):641–8.

20. Spears BM, Futter MN, Jeppesen E, Huser BJ, Ives S, Davidson TA, et al. Ecological resilience in lakes and the conjunction fallacy. Nat Ecol Evol. 2017;1(11):1616–24. doi: 10.1038/s41559-017-0333-1 29038522

21. Biggs R, Carpenter SR, Brock WA. Turning back from the brink: Detecting an impending regime shift in time to avert it. P Natl Acad Sci USA. 2009;106(3):826–31.

22. Boettiger C, Hastings A. Tipping points: From patterns to predictions. Nature. 2013;493(7431):157. doi: 10.1038/493157a 23302842

23. Dakos V, Carpenter SR, Brock WA, Ellison AM, Guttal V, Ives AR, et al. Methods for Detecting Early Warnings of Critical Transitions in Time Series Illustrated Using Simulated Ecological Data. Plos One. 2012;7(7).

24. Kefi S, Guttal V, Brock WA, Carpenter SR, Ellison AM, Livina VN, et al. Early Warning Signals of Ecological Transitions: Methods for Spatial Patterns. Plos One. 2014;9(3):213–7.

25. Kefi S, Rietkerk M, Alados CL, Pueyo Y, Papanastasis VP, ElAich A, et al. Spatial vegetation patterns and imminent desertification in Mediterranean arid ecosystems. Nature. 2007;449(7159):213–5. doi: 10.1038/nature06111 17851524

26. Batt RD, Carpenter SR, Cole JJ, Pace ML, Johnson RA. Changes in ecosystem resilience detected in automated measures of ecosystem metabolism during a whole-lake manipulation. P Natl Acad Sci USA. 2013;110(43):17398–403.

27. Porter J, Arzberger P, Braun HW, Bryant P, Gage S, Hansen T, et al. Wireless sensor networks for ecology. Bioscience. 2005;55(7):561–72.

28. Porter JH, Nagy E, Kratz TK, Hanson P, Collins SL, Arzberger P. New Eyes on the World: Advanced Sensors for Ecology. Bioscience. 2009;59(5):385–97.

29. Hampton SE, Strasser CA, Tewksbury JJ, Gram WK, Budden AE, Batcheller AL, et al. Big data and the future of ecology. Front Ecol Environ. 2013;11(3):156–62.

30. Levin SA. The Problem of Pattern and Scale in Ecology. Ecology. 1992;73(6):1943–67.

31. Frossard V, Saussereau B, Perasso A, Gillet F. What is the robustness of early warning signals to temporal aggregation? Frontiers in Ecology and Evolution. 2015;3:112.

32. Green OO, Garmestani AS, Allen CR, Gunderson LH, Ruhl JB, Arnold CA, et al. Barriers and bridges to the integration of social-ecological resilience and law. Front Ecol Environ. 2015;13(6):332–7.

33. Cline TJ, Seekell DA, Carpenter SR, Pace ML, Hodgson JR, Kitchell JF, et al. Early warnings of regime shifts: evaluation of spatial indicators from a whole-ecosystem experiment. Ecosphere. 2014;5(8).

34. Kleinen T, Held H, Petschel-Held G. The potential role of spectral properties in detecting thresholds in the Earth system: application to the thermohaline circulation. Ocean Dynamics. 2003;53(2):53–63.

35. Carpenter SR, Ludwig D, Brock WA. Management of eutrophication for lakes subject to potentially irreversible change. Ecol Appl. 1999;9(3):751–71.

36. Carpenter SR. Eutrophication of aquatic ecosystems: Bistability and soil phosphorus. P Natl Acad Sci USA. 2005;102(29):10002–5.

37. Carpenter SR, Kinne O. Regime shifts in lake ecosystems: pattern and variation: International Ecology Institute Oldendorf/Luhe, Germany; 2003.

38. Fussmann GF, Ellner SP, Shertzer KW, Hairston NG. Crossing the Hopf bifurcation in a live predator-prey system. Science. 2000;290(5495):1358–60. doi: 10.1126/science.290.5495.1358 11082063

39. Serizawa H, Amemiya T, Enomoto T, Rossberg AG, Itoh K. Mathematical modeling of colony formation in algal blooms: phenotypic plasticity in cyanobacteria. Ecol Res. 2008;23(5):841–50.

40. Vos M, Kooi BW, DeAngelis DL, Mooij WM. Inducible defences and the paradox of enrichment. Oikos. 2004;105(3):471–80.

41. Batt RD, Brock WA, Carpenter SR, Cole JJ, Pace ML, Seekell DA. Asymmetric response of early warning indicators of phytoplankton transition to and from cycles. Theor Ecol-Neth. 2013;6(3):285–93.

42. Wilkinson GM, Carpenter SR, Cole JJ, Pace ML, Batt RD, Buelo CD, et al. Early warning signals precede cyanobacterial blooms in multiple whole-lake experiments. Ecol Monogr. 2018;88(2):188–203.

43. Brock WA, Carpenter SR. Variance as a leading indicator of regime shift in ecosystem services. Ecol Soc. 2006;11(2).

44. Johnson WE, Hasler AD. Rainbow trout production in dystrophic lakes. The Journal of Wildlife Management. 1954;18(1):113–34.

45. Carpenter SR, Cole JJ, Hodgson JR, Kitchell JF, Pace ML, Bade D, et al. Trophic cascades, nutrients, and lake productivity: whole-lake experiments. Ecol Monogr. 2001;71(2):163–86.

46. Holmes EE, Ward EJ, Wills K. MARSS: Multivariate Autoregressive State-space Models for Analyzing Time-series Data. R J. 2012;4(1):11–9.

47. R Core Team. R: A Language and Environment for Statistical Computing (version 3.3. 2). R Foundation for Statistical Computing, Vienna. 2016.

48. Furnas MJ. In situ growth rates of marine phytoplankton: approaches to measurement, community and species growth rates. J Plankton Res. 1990;12(6):1117–51.

49. Gillooly JF. Effect of body size and temperature on generation time in zooplankton. J Plankton Res. 2000;22(2):241–51.

50. Boettiger C, Hastings A. Early warning signals and the prosecutor’s fallacy. Proceedings of the Royal Society B: Biological Sciences. 2012;279(1748):4734–9. doi: 10.1098/rspb.2012.2085 23055060

51. Dakos V. Identifying best-indicator species for abrupt transitions in multispecies communities. Ecological Indicators. 2018;94:494–502.

52. Bestelmeyer BT, Ellison AM, Fraser WR, Gorman KB, Holbrook SJ, Laney CM, et al. Analysis of abrupt transitions in ecological systems. Ecosphere. 2011;2(12).

53. Brock WA, Carpenter SR. Early Warnings of Regime Shift When the Ecosystem Structure Is Unknown. Plos One. 2012;7(9).

54. Litzow MA, Mueter FJ, Urban JD. Rising catch variability preceded historical fisheries collapses in Alaska. Ecol Appl. 2013;23(6):1475–87. doi: 10.1890/12-0670.1 24147417

55. Eason T, Garmestani AS, Stow CA, Rojo C, Alvarez-Cobelas M, Cabezas H. Managing for resilience: an information theory-based approach to assessing ecosystems. J Appl Ecol. 2016;53(3):656–65.

Článek vyšel v časopise


2019 Číslo 10