Early warning signals of extinction in deteriorating environments

Journal name:
Nature
Volume:
467,
Pages:
456–459
Date published:
DOI:
doi:10.1038/nature09389
Received
Accepted
Published online

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.

At a glance

Figures

  1. Dynamics of representative populations from an experiment in which extinction was observed under deteriorating and constant conditions.
    Figure 1: Dynamics of representative populations from an experiment in which extinction was observed under deteriorating and constant conditions.

    In all populations, a transient phase (grey regions) was observed during which an initial population explosion (‘baby boom’) was followed by a decline and smaller peak (‘echo boom’). Inspection shows this transient period to have ceased by around day 100 in all populations. On day 154, populations in the deteriorating-environment treatment group began to undergo a slow decline in the availability of food while populations in the control group were maintained at the initial level of food supply. Accordingly, in constant-food environments populations settled to a regime of stationary fluctuations, whereas in deteriorating environments the transient phase was followed by a virtually continuous decline. The difference between the stationary fluctuations of the constant-food environments and the continuous decline in deteriorating environments is most evident in the inset panels, where the abundance is plotted on a logarithmic scale and where the continual decline of the population in the deteriorating environment is unmistakable in contrast to the fluctuations in the constant environment.

  2. Estimated growth rate versus time for deteriorating-environment and control populations.
    Figure 2: Estimated growth rate versus time for deteriorating-environment and control populations.

    Deteriorating environmental conditions led to growth rates less than replacement (black line) and eventual extinction. Points are individual estimates corresponding to a pair of successive observations of a particular population. Lines are Loess smooth curves (span, 0.75; thick grey and blue lines) plus/minus standard error (thin grey and blue lines). Results are insensitive to the choice of span in the range [0.6, 1.0]. The inset plot shows the same points over a reduced range to accentuate the downturn in deteriorating environments after day 271, when food levels were 95μl. The stair plot, corresponding to the secondary y axis, shows actual food supply rate (microlitres of suspended food medium) over time.

  3. Coefficient of variation, skewness, autocorrelation, and spatial correlation in population size are leading indicators of extinction.
    Figure 3: Coefficient of variation, skewness, autocorrelation, and spatial correlation in population size are leading indicators of extinction.

    a, Coefficient of variation; b, skewness; c, autocorrelation; d, spatial correlation. The lines show the changes in each measure among populations over time, by treatment, for the duration of the experiment. The hatched regions show the difference between treatment and control populations. The dashed vertical line shows the estimated time at which the transcritical bifurcation occurred and the extinction equilibrium and upper equilibrium switched stability, that is, the critical transition. The period immediately preceding this transition was one of CSD, manifested by increases in each indicator in deteriorating environments relative to control populations. Days on which the feeding regime was changed are indicated by inverted triangles along the x axis. Insets in c and d illustrate changes in spatial and temporal correlations over time; ρ denotes the correlation coefficient for the designated interval.

  4. A composite early warning index comprising all four indicators is highly sensitive to the onset of critical slowing down.
    Figure 4: A composite early warning index comprising all four indicators is highly sensitive to the onset of critical slowing down.

    a, Time-specific calculations of W1 when plotted against time show that non-stationary behaviour in population dynamics may be detected within three weeks (where dashed lines change from black to grey) if a 2σ standard is used to trigger a warning and within two weeks if a 1σ standard is used to trigger a warning. The solid line shows the running average of W1, which will be zero for stationary systems. The index W1 is based on the standardized mean difference between deteriorating environments and constant reference environments. b, For comparison, we also investigated a composite early warning index that depends only on the data stream resulting from chambers in the deteriorating environment treatment (W2). This index was highly sensitive to fluctuations in the period before the onset of environmental deterioration and never clearly departed from 2σ region. When optimized, however, this index detected critical slowing down as early as one week after the onset of environmental deterioration.

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Author information

Affiliations

  1. Odum School of Ecology, University of Georgia, Athens, Georgia 30602, USA

    • John M. Drake
  2. Department of Biological Sciences, University of South Carolina, Columbia, South Carolina 29208, USA

    • Blaine D. Griffen

Contributions

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.

Competing financial interests

The authors declare no competing financial interests.

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Supplementary information

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  1. Supplementary Information (2M)

    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.

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