Ecological resilience is the ability of a system to persist in the face of perturbations. Although resilience has been a highly influential concept, its interpretation has remained largely qualitative. Here we describe an emerging family of methods for quantifying resilience on the basis of observations. A first set of methods is based on the phenomenon of critical slowing down, which implies that recovery upon small perturbations becomes slower as a system approaches a tipping point. Such slowing down can be measured experimentally but may also be indirectly inferred from changes in natural fluctuations and spatial patterns. A second group of methods aims to characterize the resilience of alternative states in probabilistic terms based on large numbers of observations as in long time series or satellite images. These generic approaches to measuring resilience complement the system-specific knowledge needed to infer the effects of environmental change on the resilience of complex systems.


Article metrics loading...

Loading full text...

Full text loading...


Literature Cited

  1. Bailey RM. 2011. Spatial and temporal signatures of fragility and threshold proximity in modelled semi-arid vegetation. Proc. R. Soc. B 278:1064–71 [Google Scholar]
  2. Batt RD, Brock WA, Carpenter SR, Cole JJ, Pace ML, Seekell DA. 2013a. Asymmetric response of early warning indicators of phytoplankton transition to and from cycles. Theor. Ecol. 6:285–93 [Google Scholar]
  3. Batt RD, Carpenter SR, Cole JJ, Pace ML, Johnson RA. 2013b. Changes in ecosystem resilience detected in automated measures of ecosystem metabolism during a whole-lake manipulation. PNAS 110:17398–403 [Google Scholar]
  4. Beaugrand G, Edwards M, Brander K, Luczak C, Ibanez F. 2008. Causes and projections of abrupt climate-driven ecosystem shifts in the North Atlantic. Ecol. Lett. 11:1157–68 [Google Scholar]
  5. Bel G, Hagberg A, Meron E. 2012. Gradual regime shifts in spatially extended ecosystems. Theor. Ecol. 5:591–604 [Google Scholar]
  6. Benincá E, Dakos V, van Nes EH, Huisman J, Scheffer M. 2011. Resonance of plankton communities with temperature fluctuations. Am. Nat. 178:E85–95 [Google Scholar]
  7. Benincà E, Huisman J, Heerkloss R, Jöhnk KD, Branco P. et al. 2008. Chaos in a long-term experiment with a plankton community. Nature 451:823–26 [Google Scholar]
  8. Berglund N, Gentz B. 2002. Metastability in simple climate models: pathwise analysis of slowly driven Langevin equations. Stoch. Dyn. 2:327–56 [Google Scholar]
  9. Bestelmeyer BT, Duniway MC, James DK, Burkett LM, Havstad KM. 2013. A test of critical thresholds and their indicators in a desertification-prone ecosystem: more resilience than we thought. Ecol. Lett. 16:339–45 [Google Scholar]
  10. Biggs R, Carpenter SR, Brock WA. 2009. Turning back from the brink: detecting an impending regime shift in time to avert it. PNAS 106:826–31 [Google Scholar]
  11. Bjornstad ON, Grenfell BT. 2001. Noisy clockwork: time series analysis of population fluctuations in animals. Science 293:638–43 [Google Scholar]
  12. Boerlijst MC, Oudman T, de Roos AM. 2013. Catastrophic collapse can occur without early warning: examples of silent catastrophes in structured ecological models. PLOS ONE 8:e62033 [Google Scholar]
  13. Boettiger C, Hastings A. 2012. Quantifying limits to detection of early warning for critical transitions. J. R. Soc. Interface 9:2527–39 [Google Scholar]
  14. Brock WA, Carpenter SR. 2006. Variance as a leading indicator of regime shift in ecosystem services. Ecol. Soc. 11:9 [Google Scholar]
  15. Brock WA, Carpenter SR. 2010. Interacting regime shifts in ecosystems: implication for early warnings. Ecol. Monogr. 80:353–67 [Google Scholar]
  16. Brock WA, Carpenter SR. 2012. Early warnings of regime shift when the ecosystem structure is unknown. PLOS ONE 7:e45586 [Google Scholar]
  17. Carpenter SR, Brock WA. 2006. Rising variance: a leading indicator of ecological transition. Ecol. Lett. 9:308–15 [Google Scholar]
  18. Carpenter SR, Brock WA. 2010. Early warnings of regime shifts in spatial dynamics using the discrete Fourier transform. Ecosphere 1:10 [Google Scholar]
  19. Carpenter SR, Brock WA. 2011. Early warnings of unknown nonlinear shifts: a nonparametric approach. Ecology 92:2196–201 [Google Scholar]
  20. Carpenter SR, Brock WA, Cole JJ, Kitchell JF, Pace ML. 2008. Leading indicators of trophic cascades. Ecol. Lett. 11:128–38 [Google Scholar]
  21. Carpenter SR, Brock WA, Cole JJ, Pace ML. 2014. A new approach for rapid detection of nearby thresholds in ecosystem time series. Oikos 123:290–97 [Google Scholar]
  22. Carpenter SR, Cole JJ, Pace ML, Batt R, Brock WA. et al. 2011. Early warnings of regime shifts: a whole-ecosystem experiment. Science 332:1079–82 [Google Scholar]
  23. Chisholm RA, Filotas E. 2009. Critical slowing down as an indicator of transitions in two-species models. J. Theor. Biol. 257:142–49 [Google Scholar]
  24. Cline TJ, Seekell DA, Carpenter SR, Pace ML, Hodgson JR. et al. 2014. Early warnings of regime shifts: evaluation of spatial indicators from a whole-ecosystem experiment. Ecosphere 5:102 [Google Scholar]
  25. Contamin R, Ellison AM. 2009. Indicators of regime shifts in ecological systems: What do we need to know and when do we need to know it?. Ecol. Appl. 19:799–816 [Google Scholar]
  26. Cooper WS. 1984. Expected time to extinction and the concept of fundamental fitness. J. Theor. Biol. 107:603–29 [Google Scholar]
  27. Dai L, Korolev KS, Gore J. 2013. Slower recovery in space before collapse of connected populations. Nature 496:355–58 [Google Scholar]
  28. Dai L, Vorselen D, Korolev KS, Gore J. 2012. Generic indicators for loss of resilience before a tipping point leading to population collapse. Science 336:1175–77 [Google Scholar]
  29. Dakos V, Bascompte J. 2014. Critical slowing down as early warning for the onset of collapse in mutualistic communities. PNAS 111:17546–51 [Google Scholar]
  30. Dakos V, Carpenter SR, Brock WA, Ellison AM, Guttal V. et al. 2012a. Methods for detecting early warnings of critical transitions in time series illustrated using simulated ecological data. PLOS ONE 7:e41010 [Google Scholar]
  31. 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:E153–66 [Google Scholar]
  32. Dakos V, Scheffer M, van Nes EH, Brovkin V, Petoukhov V, Held H. 2008. Slowing down as an early warning signal for abrupt climate change. PNAS 105:14308–12 [Google Scholar]
  33. Dakos V, van Nes EH, D'Odorico P, Scheffer M. 2012b. Robustness of variance and autocorrelation as indicators of critical slowing down. Ecology 93:264–71 [Google Scholar]
  34. Dakos V, van Nes EH, Donangelo R, Fort H, Scheffer M. 2010. Spatial correlation as leading indicator of catastrophic shifts. Theor. Ecol. 3:163–74 [Google Scholar]
  35. Dakos V, van Nes EH, Scheffer M. 2013. Flickering as an early warning signal. Theor. Ecol. 6:309–17 [Google Scholar]
  36. DeAngelis DL. 1980. Energy-flow, nutrient cycling, and ecosystem resilience. Ecology 61:764–71 [Google Scholar]
  37. DeAngelis DL, Waterhouse JC. 1987. Equilibrium and nonequilibrium concepts in ecological models. Ecol. Monogr. 57:1–21 [Google Scholar]
  38. DeVantier LM, De'ath G, Done TJ, Turak E. 1998. Ecological assessment of a complex natural system: a case study from the Great Barrier Reef. Ecol. Appl. 8:480–96 [Google Scholar]
  39. Donangelo R, Fort H, Dakos V, Scheffer M, van Nes EH. 2010. Early warnings for catastrophic shifts in ecosystems: comparison between spatial and temporal indicators. Int. J. Bifurc. Chaos 20:315–21 [Google Scholar]
  40. Drake JM, Griffen BD. 2010. Early warning signals of extinction in deteriorating environments. Nature 467:456–59 [Google Scholar]
  41. Elser JJ, Elser TJ, Carpenter SR, Brock WA. 2014. Regime shift in fertilizer commodities indicates more turbulence ahead for food security. PLOS ONE 9:e93998 [Google Scholar]
  42. Fung T, Seymour RM, Johnson CR. 2013. Warning signals of regime shifts as intrinsic properties of endogenous dynamics. Am. Nat. 182:208–22 [Google Scholar]
  43. Fussmann GF, Ellner SP, Shertzer KW, Hairston NG. 2000. Crossing the Hopf bifurcation in a live predator-prey system. Science 290:1358–60 [Google Scholar]
  44. Gandhi A, Levin S, Orszag S. 1998. “Critical slowing down” in time-to-extinction: an example of critical phenomena in ecology. J. Theor. Biol. 192:363–76 [Google Scholar]
  45. Gardiner CW. 2004. Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences New York: Springer [Google Scholar]
  46. Gelcich S, Hughes TP, Olsson P, Folke C, Defeo O. et al. 2010. Navigating transformations in governance of Chilean marine coastal resources. PNAS 107:16794–99 [Google Scholar]
  47. Grasman J, Van Herwaarden OA. 2010. Asymptotic Methods for the Fokker-Planck Equation and the Exit Problem in Applications Berlin/Heidelberg, Ger: Springer-Verlag [Google Scholar]
  48. Grimm V, Wissel C. 1997. Babel, or the ecological stability discussions: an inventory and analysis of terminology and a guide for avoiding confusion. Oecologia 109:323–34 [Google Scholar]
  49. Guttal V, Jayaprakash C. 2008. Changing skewness: an early warning signal of regime shifts in ecosystems. Ecol. Lett. 11:450–60 [Google Scholar]
  50. Guttal V, Jayaprakash C. 2009. Spatial variance and spatial skewness: leading indicators of regime shifts in spatial ecological systems. Theor. Ecol. 2:3–12 [Google Scholar]
  51. Hansen MC, DeFries RS, Townshend JRG, Carroll M, Dimiceli C, Sohlberg RA. 2003. Global percent tree cover at a spatial resolution of 500 meters: first results of the MODIS vegetation continuous fields algorithm. Earth Interact. 7:1–15 [Google Scholar]
  52. Hanson FB, Tuckwell HC. 1978. Persistence times of populations with large random fluctuations. Theor. Popul. Biol. 14:46–61 [Google Scholar]
  53. Hastings A. 2004. Transients: the key to long-term ecological understanding?. Trends Ecol. Evol. 19:39–45 [Google Scholar]
  54. Hastings A, Wysham DB. 2010. Regime shifts in ecological systems can occur with no warning. Ecol. Lett. 13:464–72 [Google Scholar]
  55. Held H, Kleinen T. 2004. Detection of climate system bifurcations by degenerate fingerprinting. Geophys. Res. Lett. 31:L23207 [Google Scholar]
  56. Hewitt JE, Thrush SF. 2010. Empirical evidence of an approaching alternate state produced by intrinsic community dynamics, climatic variability and management actions. Mar. Ecol. Prog. Ser. 413:267–76 [Google Scholar]
  57. Hirota M, Holmgren M, van Nes EH, Scheffer M. 2011. Global resilience of tropical forest and savanna to critical transitions. Science 334:232–35 [Google Scholar]
  58. Holling CS. 1973. Resilience and stability of ecological systems. Annu. Rev. Ecol. Syst. 4:1–23 [Google Scholar]
  59. Holling CS. 1996. Engineering resilience versus ecological resilience. Engineering Within Ecological Constraints PC Schulze 31–43 Washington, DC: Natl. Acad [Google Scholar]
  60. Hsieh CH, Reiss CS, Hunter JR, Beddington JR, May RM, Sugihara G. 2006. Fishing elevates variability in the abundance of exploited species. Nature 443:859–62 [Google Scholar]
  61. Ives AR. 1995. Measuring resilience in stochastic systems. Ecol. Monogr. 65:217–33 [Google Scholar]
  62. Ives AR, Dakos V. 2012. Detecting dynamical changes in nonlinear time series using locally linear state-space models. Ecosphere 3:58 [Google Scholar]
  63. Kéfi S, Dakos V, Scheffer M, van Nes EH, Rietkerk M. 2013. Early warning signals also precede non-catastrophic transitions. Oikos 122:641–48 [Google Scholar]
  64. Kéfi S, Guttal V, Brock WA, Carpenter SR, Ellison AM. et al. 2014. Early warning signals of ecological transitions: methods for spatial patterns. PLOS ONE 9:e92097 [Google Scholar]
  65. Kéfi S, Rietkerk M, Alados CL, Pueyo Y, Papanastasis VP. et al. 2007. Spatial vegetation patterns and imminent desertification in Mediterranean arid ecosystems. Nature 449:213–17 [Google Scholar]
  66. Keitt TH, Lewis MA, Holt RD. 2001. Allee effects, invasion pinning, and species' borders. Am. Nat. 157:203–16 [Google Scholar]
  67. 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 Dyn. 53:53–63 [Google Scholar]
  68. Kosten S, Vernooij M, van Nes EH, Sagrario MÁG, Clevers JGPW, Scheffer M. 2012. Bimodal transparency as an indicator for alternative states in South American lakes. Freshw. Biol. 57:1191–201 [Google Scholar]
  69. Krkosek M, Drake JM. 2014. On signals of phase transitions in salmon population dynamics. Proc. R. Soc. B 281:20133221 [Google Scholar]
  70. Kuehn C. 2013. Warning signs for wave speed transitions of noisy Fisher–KPP invasion fronts. Theor. Ecol. 6:295–308 [Google Scholar]
  71. Lade SJ, Gross T. 2012. Early warning signals for critical transitions: a generalized modeling approach. PLOS Comput. Biol. 8:e1002360 [Google Scholar]
  72. Lahti L, Salojärvi J, Salonen A, Scheffer M, De Vos WM. 2014. Tipping elements in the human intestinal ecosystem. Nat. Commun. 5:4344 [Google Scholar]
  73. Leigh EG Jr. 1981. The average lifetime of a population in a varying environment. J. Theor. Biol. 90:213–39 [Google Scholar]
  74. Leung HK. 2000. Bifurcation of synchronization as a nonequilibrium phase transition. Physica A 281:311–17 [Google Scholar]
  75. Lever JJ, van Nes EH, Scheffer M, Bascompte J. 2014. The sudden collapse of pollinator communities. Ecol. Lett. 17:350–59 [Google Scholar]
  76. Lewontin RC. 1969. The meaning of stability. Diversity and Stability in Ecological Systems: Report of a Symposium Held May 26–2813–24 Springfield, VA: Clearinghouse for Federal Scientific and Technical Information [Google Scholar]
  77. Lindegren M, Dakos V, Gröger JP, Gårdmark A, Kornilovs G. et al. 2012. Early detection of ecosystem regime shifts: a multiple method evaluation for management application. PLOS ONE 7:e38410 [Google Scholar]
  78. 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 [Google Scholar]
  79. Livina VN, Lenton TM. 2007. A modified method for detecting incipient bifurcations in a dynamical system. Geophys. Res. Lett. 34:L03712 [Google Scholar]
  80. Maltby L, Blake N, Brock TCM, van den Brink PJ. 2005. Insecticide species sensitivity distributions: importance of test species selection and relevance to aquatic ecosystems. Environ. Toxicol. Chem. 24:379–88 [Google Scholar]
  81. Matsumoto G, Kunisawa T. 1978. Critical slowing-down near transition region from resting to time-ordered states in squid giant axons. J. Phys. Soc. Jpn. 44:1047–48 [Google Scholar]
  82. Murray JD. 2002. Mathematical Biology: I. An Introduction Berlin: Springer-Verlag [Google Scholar]
  83. Oborny B, Meszéna G, Szabó G. 2005. Dynamics of populations on the verge of extinction. Oikos 109:291–96 [Google Scholar]
  84. O'Regan SM, Drake JM. 2013. Theory of early warning signals of disease emergence and leading indicators of elimination. Theor. Ecol. 6:333–57 [Google Scholar]
  85. Perretti CT, Munch SB. 2012. Regime shift indicators fail under noise levels commonly observed in ecological systems. Ecol. Appl. 22:1772–79 [Google Scholar]
  86. Pimm SL. 1984. The complexity and stability of ecosystems. Nature 307:321–26 [Google Scholar]
  87. Pomeau Y. 1986. Front motion, metastability and subcritical bifurcations in hydrodynamics. Phys. D Nonlinear Phenom. 23:3–11 [Google Scholar]
  88. Rietkerk M, Dekker SC, de Ruiter PC, van de Koppel J. 2004. Self-organized patchiness and catastrophic shifts in ecosystems. Science 305:1926–29 [Google Scholar]
  89. Rietkerk M, van de Koppel J. 2008. Regular pattern formation in real ecosystems. Trends Ecol. Evol. 23:169–75 [Google Scholar]
  90. Rinaldi S, Muratori S. 1992. Slow-fast limit cycles in predator-prey models. Ecol. Model. 61:287–308 [Google Scholar]
  91. Rinaldi S, Scheffer M. 2000. Geometric analysis of ecological models with slow and fast processes. Ecosystems 3:507–21 [Google Scholar]
  92. Rosenzweig ML. 1971. Paradox of enrichment: destabilization of exploitation ecosystems in ecological time. Science 171:385–87 [Google Scholar]
  93. Sæther BE, Engen S, Islam A, McCleery R, Perrins C. 1998. Environmental stochasticity and extinction risk in a population of a small songbird, the great tit. Am. Nat. 151:441–50 [Google Scholar]
  94. Scheffer M. 2009. Critical Transitions in Nature and Society Princeton, NJ: Princeton Univ. Press [Google Scholar]
  95. Scheffer M, Bascompte J, Brock WA, Brovkin V, Carpenter SR. et al. 2009. Early-warning signals for critical transitions. Nature 461:53–59 [Google Scholar]
  96. Scheffer M, Carpenter SR, Foley JA, Folke C, Walker B. 2001. Catastrophic shifts in ecosystems. Nature 413:591–96 [Google Scholar]
  97. Scheffer M, Carpenter SR, Lenton TM, Bascompte J, Brock W. et al. 2012a. Anticipating critical transitions. Science 338:344–48 [Google Scholar]
  98. Scheffer M, Hirota M, Holmgren M, van Nes EH, Chapin FS. 2012b. Thresholds for boreal biome transitions. PNAS 109:21384–89 [Google Scholar]
  99. Seekell DA, Carpenter SR, Cline TJ, Pace ML. 2012. Conditional heteroskedasticity forecasts regime shift in a whole-ecosystem experiment. Ecosystems 15:741–47 [Google Scholar]
  100. Seekell DA, Carpenter SR, Pace ML. 2011. Conditional heteroscedasticity as a leading indicator of ecological regime shifts. Am. Nat. 178:442–51 [Google Scholar]
  101. Strogatz SH. 1994. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering Reading, MA: Addison-Wesley [Google Scholar]
  102. Suweis S, D'Odorico P. 2014. Early warning signs in social-ecological networks. PLOS ONE 9:e101851 [Google Scholar]
  103. Suzuki K, Yoshida T. 2015. Ecological resilience of population cycles: a dynamic perspective of regime shift. J. Theor. Biol. 370:103–15 [Google Scholar]
  104. Takimoto G. 2009. Early warning signals of demographic regime shifts in invading populations. Popul. Ecol. 51:419–26 [Google Scholar]
  105. Tirabassi G, Viebahn J, Dakos V, Dijkstra HA, Masoller C. et al. 2014. Interaction network based early-warning indicators of vegetation transitions. Ecol. Complex. 19:148–57 [Google Scholar]
  106. Turing AM. 1952. The chemical basis of morphogenesis. Philos. Trans. R. Soc. B 237:37–72 [Google Scholar]
  107. van de Koppel J, Gascoigne JC, Theraulaz G, Rietkerk M, Mooij WM, Herman PMJ. 2008. Experimental evidence for spatial self-organization and its emergent effects in mussel bed ecosystems. Science 322:739–42 [Google Scholar]
  108. van de Leemput IA, van Nes EH, Scheffer M. 2015. Resilience of alternative states in spatially extended ecosystems. PLOS ONE 10:e0116859 [Google Scholar]
  109. van de Leemput IA, Wichers M, Cramer AOJ, Borsboom D, Tuerlinckx F. et al. 2014. Critical slowing down as early warning for the onset and termination of depression. PNAS 111:87–92 [Google Scholar]
  110. van der Heide T, Bouma TJ, van Nes EH, van de Koppel J, Scheffer M. et al. 2010. Spatial self-organized patterning in seagrasses along a depth gradient of an intertidal ecosystem. Ecology 91:362–69 [Google Scholar]
  111. van Nes EH, Hirota M, Holmgren M, Scheffer M. 2014. Tipping points in tropical tree cover: linking theory to data. Glob. Change Biol. 20:1016–21 [Google Scholar]
  112. van Nes EH, Scheffer M. 2004. Large species shifts triggered by small forces. Am. Nat. 164:255–66 [Google Scholar]
  113. van Nes EH, Scheffer M. 2007. Slow recovery from perturbations as a generic indicator of a nearby catastrophic shift. Am. Nat. 169:738–47 [Google Scholar]
  114. Vandermeer J. 2011. The inevitability of surprise in agroecosystems. Ecol. Complex. 8:377–82 [Google Scholar]
  115. Vandermeer J, Yodzis P. 1999. Basin boundary collision as a model of discontinuous change in ecosystems. Ecology 80:1817–27 [Google Scholar]
  116. Veraart AJ, Faassen EJ, Dakos V, van Nes EH, Lürling M, Scheffer M. 2012. Recovery rates reflect distance to a tipping point in a living system. Nature 481:357–59 [Google Scholar]
  117. von Hardenberg J, Meron E, Shachak M, Zarmi Y. 2001. Diversity of vegetation patterns and desertification. Phys. Rev. Lett. 87:198101 [Google Scholar]
  118. Wang R, Dearing JA, Langdon PG, Zhang E, Yang X. et al. 2012. Flickering gives early warning signals of a critical transition to a eutrophic lake state. Nature 492:419–22 [Google Scholar]
  119. Wissel C. 1984. A universal law of the characteristic return time near thresholds. Oecologia 65:101–7 [Google Scholar]
  120. Wouters N, Dakos V, Edwards M, Serafim MP, Valayer PJ, Cabral HN. 2015. Evidencing a regime shift in the North Sea using early-warning signals as indicators of critical transitions. Estuar. Coast. Shelf Sci. 152:65–72 [Google Scholar]

Data & Media loading...

Supplementary Data

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error