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Early warning signals of extinction in deteriorating environments


During the decline to extinction, animal populations may present dynamical phenomena not exhibited by robust populations1,2. Some of these phenomena, such as the scaling of demographic variance, are related to small size3,4,5,6 whereas others result from density-dependent nonlinearities7. Although understanding the causes of population extinction has been a central problem in theoretical biology for decades8, the ability to anticipate extinction has remained elusive9. Here we argue that the causes of a population’s decline are central to the predictability of its extinction. Specifically, environmental degradation may cause a tipping point in population dynamics, corresponding to a bifurcation in the underlying population growth equations, beyond which decline to extinction is almost certain. In such cases, imminent extinction will be signalled by critical slowing down (CSD). We conducted an experiment with replicate laboratory populations of Daphnia magna to test this hypothesis. We show that populations crossing a transcritical bifurcation, experimentally induced by the controlled decline in environmental conditions, show statistical signatures of CSD after the onset of environmental deterioration and before the critical transition. Populations in constant environments did not have these patterns. Four statistical indicators all showed evidence of the approaching bifurcation as early as 110 days (8 generations) before the transition occurred. Two composite indices improved predictability, and comparative analysis showed that early warning signals based solely on observations in deteriorating environments without reference populations for standardization were hampered by the presence of transient dynamics before the onset of deterioration, pointing to the importance of reliable baseline data before environmental deterioration begins. The universality of bifurcations in models of population dynamics suggests that this phenomenon should be general10,11,12.

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Figure 1: Dynamics of representative populations from an experiment in which extinction was observed under deteriorating and constant conditions.
Figure 2: Estimated growth rate versus time for deteriorating-environment and control populations.
Figure 3: Coefficient of variation, skewness, autocorrelation, and spatial correlation in population size are leading indicators of extinction.
Figure 4: A composite early warning index comprising all four indicators is highly sensitive to the onset of critical slowing down.


  1. Fagan, W. F. & Holmes, E. E. Quantifying the extinction vortex. Ecol. Lett. 9, 51–60 (2006)

    PubMed  Google Scholar 

  2. Oborny, B., Meszéna, G. & Szabo, G. Dynamics of populations on the verge of extinction. Oikos 109, 291–296 (2005)

    Article  Google Scholar 

  3. Ludwig, D. The distribution of population survival times. Am. Nat. 147, 506–526 (1996)

    Article  Google Scholar 

  4. Lande, R. Demographic stochasticity and Allee effect on a scale with isotropic noise. Oikos 83, 353–358 (1998)

    Article  Google Scholar 

  5. Drake, J. M. Density-dependent demographic variation determines extinction rate of experimental populations. PLoS Biol. 3, e222 (2005)

    Article  Google Scholar 

  6. Melbourne, B. A. & Hastings, A. Extinction risk depends strongly on factors contributing to stochasticity. Nature 454, 100–103 (2008)

    ADS  CAS  Article  Google Scholar 

  7. Takimoto, G. Early warning signals of demographic regime shifts in invading populations. Popul. Ecol. 51, 419–426 (2009)

    Article  Google Scholar 

  8. Kendall, D. G. On the generalized “birth-and-death” process. Ann. Math. Stat. 19, 1–15 (1948)

    MathSciNet  Article  Google Scholar 

  9. Ludwig, D. Is it meaningful to estimate a probability of extinction? Ecology 80, 298–310 (1999)

    Article  Google Scholar 

  10. Dakos, V. et al. Slowing down as an early warning signal for abrupt climate change. Proc. Natl Acad. Sci. USA 105, 14308–14312 (2008)

    ADS  CAS  Article  Google Scholar 

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

    Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

  13. Baillie J. E. M., Hilton-Taylor C., Stuart S. N., eds. 2004 IUCN Red List of Threatened Species: A Global Species Assessment 10–104 (IUCN, 2004)

  14. Brook, B. W., Sodhi, N. S. & Bradshaw, C. J. A. Synergies among extinction drivers under global change. Trends Ecol. Evol. 23, 453–460 (2008)

    Article  Google Scholar 

  15. Hallam, T. G. & Clark, C. E. Non-autonomous logistic equations as models of populations in a deteriorating environment. J. Theor. Biol. 93, 303–311 (1981)

    Article  Google Scholar 

  16. Jagers, P. & Zhunwei, L. Branching processes with deteriorating random environments. J. Appl. Probab. 39, 395–401 (2002)

    MathSciNet  Article  Google Scholar 

  17. Lande, R., Engen, S. & Sæther, B. E. Stochastic Population Dynamics in Ecology and Conservation 1–118 (Oxford Univ. Press, 2003)

    Book  Google Scholar 

  18. Fussmann, G. F., Ellner, S. P., Shertzer, K. W. & Hairston, N. G., Jr Crossing the Hopf bifurcation in a live predator-prey system. Science 290, 1358–1360 (2000)

    ADS  CAS  Article  Google Scholar 

  19. Becks, L., Hilker, F. M., Malchow, H., Jürgens, K. & Arndt, H. Experimental demonstration of chaos in a microbial food web. Nature 435, 1226–1229 (2005)

    ADS  CAS  Article  Google Scholar 

  20. Carpenter, S. R. & Brock, W. A. Rising variance: a leading indicator of ecological transition. Ecol. Lett. 9, 311–318 (2006)

    CAS  Article  Google Scholar 

  21. Wissel, C. A universal law of the characteristic return time near thresholds. Oecologia 65, 101–107 (1984)

    ADS  CAS  Article  Google Scholar 

  22. 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 

  23. Guttal, V. & Jayaprakash, C. Changing skewness: an early warning signal of regime shifts in ecosystems. Ecol. Lett. 11, 450–460 (2008)

    Article  Google Scholar 

  24. Dakos, V., van 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 

  25. McSharry, P. E., Smith, L. A. & Tarassenko, L. Prediction of epileptic seizures: are nonlinear methods relevant? Nature Med. 9, 241–242 (2003)

    CAS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  27. Lenton, T. M. et al. Tipping elements in the Earth’s climate system. Proc. Natl Acad. Sci. USA 105, 1786–1793 (2008)

    ADS  CAS  Article  Google Scholar 

  28. Hastings, A. & Wysham, D. Regime shifts in ecological systems can occur with no warning. Ecol. Lett. 13, 464–472 (2010)

    Article  Google Scholar 

  29. Drake, J. M. Extinction times in experimental populations. Ecology 87, 2215–2220 (2006)

    Article  Google Scholar 

  30. Biggs, R., Carpenter, S. R. & Brock, W. A. Turning back from the brink: detecting an impending regime shift in time to avert it. Proc. Natl Acad. Sci. USA 106, 826–831 (2009)

    ADS  CAS  Article  Google Scholar 

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G. Fussman, A. Hastings, A. Kramer, R. Hall, A. Park and T. Stratmann provided comments on earlier versions of this paper. A. Silletti assisted with the preparation of the manuscript. This research was supported by funding from the Odum School of Ecology, a University of Georgia Faculty Research Grant and funding from the University of South Carolina.

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J.M.D. and B.D.G. jointly conceived the study. B.D.G. performed the experiment. J.M.D. performed the analysis and wrote the paper.

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Correspondence to John M. Drake.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Information comprising Appendix I: Experimental and analytical methods, Appendix II: Extinction time distribution including Supplementary Figure 1 with legend and Appendix III: Critical slowing down and early warning signals in single population trajectories including Supplementary Figures 1-11 with legends. Additional references are also included. (PDF 2125 kb)

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

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