Early warning signals of extinction in deteriorating environments.
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.
Drake
John M
JM
Odum School of Ecology, University of Georgia, Athens, Georgia 30602, USA. jdrake@uga.edu
Griffen
Blaine D
BD
D000818:Animals; D003621:Daphnia / Q000254:growth & development / Q000502:physiology*; D017753:Ecosystem; D053476:Extinction, Biological; D005544:Forecasting; D008954:Models, Biological; D011156:Population Density; D011157:Population Dynamics
Science. 2000 Nov 17;290(5495):1358-60
11082063
Ecology. 2006 Sep;87(9):2215-20
16995621
Am Nat. 2007 Jun;169(6):738-47
17479460
Nature. 2005 Jun 30;435(7046):1226-9
15988524
Trends Ecol Evol. 2008 Aug;23(8):453-60
18582986
Nature. 2009 Sep 3;461(7260):53-9
19727193
Ecol Lett. 2010 Apr;13(4):464-72
20148928
Ecol Lett. 2006 Jan;9(1):51-60
16958868
Nature. 2008 Jul 3;454(7200):100-3
18596809
Nat Med. 2003 Mar;9(3):241-2; author reply 242
12612550
PLoS Biol. 2005 Jul;3(7):e222
15934788
Proc Natl Acad Sci U S A. 2009 Jan 20;106(3):826-31
19124774
Proc Natl Acad Sci U S A. 2008 Feb 12;105(6):1786-93
18258748
Ecol Lett. 2008 May;11(5):450-60
18279354
Ecol Lett. 2006 Mar;9(3):311-8
16958897
Proc Natl Acad Sci U S A. 2008 Sep 23;105(38):14308-12
18787119
Nature. 2007 Sep 13;449(7159):213-7
17851524