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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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.
The authors declare no competing financial interests.
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). https://doi.org/10.1038/nature09389
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