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Slower recovery in space before collapse of connected populations


Slower recovery from perturbations near a tipping point and its indirect signatures in fluctuation patterns have been suggested to foreshadow catastrophes in a wide variety of systems1,2. Recent studies of populations in the field and in the laboratory have used time-series data to confirm some of the theoretically predicted early warning indicators, such as an increase in recovery time or in the size and timescale of fluctuations3,4,5,6. However, the predictive power of temporal warning signals is limited by the demand for long-term observations. Large-scale spatial data are more accessible, but the performance of warning signals in spatially extended systems7,8,9,10 needs to be examined empirically3,11,12,13. Here we use spatially extended yeast populations, an experimental system with a fold bifurcation (tipping point)6, to evaluate early warning signals based on spatio-temporal fluctuations and to identify a novel spatial warning indicator. We found that two leading indicators based on fluctuations increased before collapse of connected populations; however, the magnitudes of the increases were smaller than those observed in isolated populations, possibly because local variation is reduced by dispersal. Furthermore, we propose a generic indicator based on deterministic spatial patterns, which we call ‘recovery length’. As the spatial counterpart of recovery time14, recovery length is the distance necessary for connected populations to recover from spatial perturbations. In our experiments, recovery length increased substantially before population collapse, suggesting that the spatial scale of recovery can provide a superior warning signal before tipping points in spatially extended systems.

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Figure 1: Yeast populations with a tipping point: an experimental system to study the collapse of connected populations.
Figure 2: Early warning signals based on fluctuations show suppressed increase in connected populations.
Figure 3: Early warning signals can be classified into four categories by the nature of perturbations and measurements.
Figure 4: Recovery length provides a direct measure of critical slowing down in space.


  1. Scheffer, M. et al. Early-warning signals for critical transitions. Nature 461, 53–59 (2009)

    Article  ADS  CAS  Google Scholar 

  2. Scheffer, M. et al. Anticipating critical transitions. Science 338, 344–348 (2012)

    Article  ADS  CAS  Google Scholar 

  3. Drake, J. M. & Griffen, B. D. Early warning signals of extinction in deteriorating environments. Nature 467, 456–459 (2010)

    Article  ADS  CAS  Google Scholar 

  4. Carpenter, S. R. et al. Early warnings of regime shifts: a whole-ecosystem experiment. Science 332, 1079–1082 (2011)

    Article  ADS  CAS  Google Scholar 

  5. Veraart, A. J. et al. Recovery rates reflect distance to a tipping point in a living system. Nature 481, 357–359 (2012)

    Article  ADS  CAS  Google Scholar 

  6. Dai, L., Vorselen, D., Korolev, K. S. & Gore, J. Generic indicators for loss of resilience before a tipping point leading to population collapse. Science 336, 1175–1177 (2012)

    Article  ADS  CAS  Google Scholar 

  7. Guttal, V. & Jayaprakash, C. Spatial variance and spatial skewness: leading indicators of regime shifts in spatial ecological systems. Theor. Ecol. 2, 3–12 (2009)

    Article  Google Scholar 

  8. Dakos, V., Nes, E. H., Donangelo, R., Fort, H. & Scheffer, M. Spatial correlation as leading indicator of catastrophic shifts. Theor. Ecol. 3, 163–174 (2010)

    Article  Google Scholar 

  9. Dakos, V., Kéfi, S., Rietkerk, M., Van Nes, E. H. & Scheffer, M. Slowing down in spatially patterned ecosystems at the brink of collapse. Am. Nat. 177, E153–E166 (2011)

    Article  Google Scholar 

  10. Carpenter, S. R. & Brock, W. A. Early warnings of regime shifts in spatial dynamics using the discrete Fourier transform. Ecosphere 1, art10 (2010)

    Article  Google Scholar 

  11. Lindegren, M. et al. Early detection of ecosystem regime shifts: a multiple method evaluation for management application. PLoS ONE 7, e38410 (2012)

    Article  ADS  CAS  Google Scholar 

  12. Litzow, M. A., Urban, J. D. & Laurel, B. J. Increased spatial variance accompanies reorganization of two continental shelf ecosystems. Ecol. Appl. 18, 1331–1337 (2008)

    Article  Google Scholar 

  13. Ouyang, Q. & Swinney, H. L. Transition from a uniform state to hexagonal and striped Turing patterns. Nature 352, 610–612 (1991)

    Article  ADS  Google Scholar 

  14. van Nes, E. H. & Scheffer, M. Slow recovery from perturbations as a generic indicator of a nearby catastrophic shift. Am. Nat. 169, 738–747 (2007)

    Article  Google Scholar 

  15. May, R. M. Thresholds and breakpoints in ecosystems with a multiplicity of stable states. Nature 269, 471–477 (1977)

    Article  ADS  Google Scholar 

  16. Scheffer, M., Carpenter, S. & Foley, J. A. Folke, C. & Walker, B. Catastrophic shifts in ecosystems. Nature 413, 591–596 (2001)

    Article  ADS  CAS  Google Scholar 

  17. Staver, A. C., Archibald, S. & Levin, S. A. The global extent and determinants of savanna and forest as alternative biome states. Science 334, 230–232 (2011)

    Article  ADS  CAS  Google Scholar 

  18. Isbell, F., Tilman, D., Polasky, S., Binder, S. & Hawthorne, P. Low biodiversity state persists two decades after cessation of nutrient enrichment. Ecol. Lett. (2013)

  19. Holling, C. S. Resilience and stability of ecological systems. Annu. Rev. Ecol. Syst. 4, 1–23 (1973)

    Article  Google Scholar 

  20. Scheffer, M. Critical Transitions in Nature and Society (Princeton Univ. Press, 2009)

    Google Scholar 

  21. 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 Dyn. 53, 53–63 (2003)

    Article  ADS  Google Scholar 

  22. Brock, W. A. & Carpenter, S. R. Interacting regime shifts in ecosystems: implication for early warnings. Ecol. Monogr. 80, 353–367 (2010)

    Article  Google Scholar 

  23. Boettiger, C. & Hastings, A. Early warning signals and the prosecutor’s fallacy. Proc. R. Soc. Lond. B 279,. 4734–4739 (2012)

  24. Rietkerk, M., Dekker, S. C., De Ruiter, P. C. & Van de Koppel, J. Self-organized patchiness and catastrophic shifts in ecosystems. Science 305, 1926–1929 (2004)

    Article  ADS  CAS  Google Scholar 

  25. Kéfi, S. et al. Spatial vegetation patterns and imminent desertification in Mediterranean arid ecosystems. Nature 449, 213–217 (2007)

    Article  ADS  Google Scholar 

  26. Gore, J., Youk, H. & Van Oudenaarden, A. Snowdrift game dynamics and facultative cheating in yeast. Nature 459, 253–256 (2009)

    Article  ADS  CAS  Google Scholar 

  27. Fernández, A. & Fort, H. Catastrophic phase transitions and early warnings in a spatial ecological model. J. Stat. Mech. P09014 (2009)

  28. Sole, R. V., Manrubia, S. C., Luque, B., Delgado, J. & Bascompte, J. Phase transitions and complex systems. Complexity 1, 13–26 (1996)

    Article  Google Scholar 

  29. Ries, L., Fletcher, R. J., Battin, J. & Sisk, T. D. Ecological responses to habitat edges: mechanisms, models, and variability explained. Annu. Rev. Ecol. Evol. Syst. 35, 491–522 (2004)

    Article  Google Scholar 

  30. Harper, K. A. et al. Edge influence on forest structure and composition in fragmented landscapes. Conserv. Biol. 19, 768–782 (2005)

    Article  Google Scholar 

  31. DeCarlo, L. T. & Tryon, W. W. Estimating and testing autocorrelation with small samples: a comparison of the c-statistic to a modified estimator. Behav. Res. Ther. 31, 781–788 (1993)

    Article  CAS  Google Scholar 

  32. Legendre, P. & Fortin, M. J. Spatial pattern and ecological analysis. Vegetatio 80, 107–138 (1989)

    Article  Google Scholar 

  33. Moran, P. A. P. Notes on continuous stochastic phenomena. Biometrika 37, 17–23 (1950)

    Article  MathSciNet  CAS  Google Scholar 

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We would like to thank D. Vorselen, T. Krieger, D. Seekell, M. Pace and members of the Gore laboratory (A. Sanchez, M. Datta, E. Yurtsev, T. Artemova, K. Axelrod and A. Chen) for comments on the manuscript. T. Krieger performed initial simulations for the connected populations. Y. Zhang and O. Ornek collected preliminary data for the experiment to measure recovery length. This work was supported by a Whitaker Health Sciences Fund Fellowship (to L.D.), a Pappalardo Fellowship (to K.S.K.), an NIH R00 Pathways to Independence Award (NIH R00 GM085279-02), an NIH New Innovator Award (NIH DP2), an NSF CAREER Award, a Sloan Research Fellowship, the Pew Scholars Program and the Allen Investigator Program.

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Authors and Affiliations



L.D., K.S.K. and J.G. designed the study. L.D. performed the experiments and analysis. K.S.K. and J.G. assisted with the analysis. L.D., K.S.K. and J.G. wrote the manuscript.

Corresponding authors

Correspondence to Lei Dai or Jeff Gore.

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The authors declare no competing financial interests.

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Dai, L., Korolev, K. & Gore, J. Slower recovery in space before collapse of connected populations. Nature 496, 355–358 (2013).

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