Early warning signals of extinction in deteriorating environments

Abstract

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.

Factors Influencing the Detectability of Early Warning Signals of Population Collapse

“…Populations approaching certain kinds of thresholds have been shown to exhibit generic early warning signals-leading indicators-prior to a transition, a function of a population's diminishing ability to return to its prior state after environmental perturbation, known as critical slowing down (Contamin and Ellison 2009;Drake and Griffen 2010a;Carpenter et al 2011;Dakos et al 2011Dakos et al , 2012b. Such early warning signals include an increase in the standard deviation of a population's size, a decrease in the return rate of a population to its mean after a perturbation, and an increase in the autocorrelation of a population's demographic fluctuations (Dakos et al 2012a).…”

“…Drake and Griffen (2010a) used a long-term experiment (approximately 60 generations; Ebert 2005) in small-scale aquatic microcosms to show that leading indicators of population collapse could be identified several generations before populations became extinct. Field tests of such signals have been provided by, among others, Carpenter et al (2011), whose whole-lake manipulation demonstrated that statistical signals of a regime shift were detectable more than a year before the shift occurred.…”

Recent advances and future directions in soils and sediments research

“…Terrestrial ecosystems respond non-linearly to climate change with multiple factors over long periods (Scheffer et al 2009;Dillon et al 2010;Doak and Morris 2010;Drake and Griffen 2010;Sun et al 2010), and can have tipping points or critical boundaries at which a sudden shift to a contrasting dynamic regime might occur (Rockström et al 2009;Scheffer et al 2009;Dillon et al 2010;Doak and Morris 2010;Drake and Griffen 2010). Significantly, more C is stored in the world's soils than in the above-ground biomass and atmosphere (Davidson and Janssens 2006;Fontaine et al 2007;Gruber and Galloway 2008;Heimann and Reichstein 2008;Piao et al 2009).…”

On damping in the vicinity of critical points

“…One well-known indicator of an approaching bifurcation is critical slowing down, where a system responds sluggishly to external perturbations [1]. This phenomenon has been observed in biological systems as an early warning sign of extinction in species [2]. It has also been used to forecast climate shifts [3,4] and to predict phase transitions in statistical mechanics [5,6].…”

“…The equilibrium paths for this system are given by 2) and hence for a given control parameter λ we obtain corresponding equilibria,…”