During the decline to extinction, animal populations may present dynamical phenomena not exhibited by robust populations. Some of these phenomena, such as the scaling of demographic variance, are related to small size, while others result from density dependent nonlinearities. Although understanding the causes of population extinction has been a central problem in theoretical biology for decades, the ability to anticipate extinction has remained elusive. 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 signaled by critical slowing down (CSD). We conducted an experiment with replicate laboratory populations of Daphnia magna to test this hypothesis. Here we show that populations crossing a transcritical bifurcation, experimentally induced by the controlled degradation of environmental conditions, exhibit statistical signatures of CSD after the onset of environmental deterioration and prior to the critical transition.
Results/Conclusions
Populations in constant environments did not show these patterns. Four statistical indicators all showed evidence of CSD as early as 110 days (~7.9 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 prior to 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 general.
