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 whereas 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 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 general.