Theoretical Ecology

, Volume 10, Issue 1, pp 65–71 | Cite as

Time to extinction in deteriorating environments

ORIGINAL PAPER

Abstract

Habitat degradation and destruction are the predominant drivers of population extinction, but there is little theory to guide the analysis of population viability in deteriorating environments. To address this gap, we investigated extinction times in time-varying, demographically stochastic versions of the logistic model for population dynamics. A property of these models is the “extinction delay,” a quantitative measure of the time lag in extinction created by species-specific extinction debt. For completeness, three models were constructed to represent the different demographic routes by which deterioration may affect population dynamics. Numerical analysis for two notional life histories indicated that the demographic response to environmental deterioration had a large effect on extinction delay, but a third analysis showed that the trajectory of the decline in carrying capacity ultimately characterized its magnitude. A concave decline in carrying capacity produced a large extinction delay while a small delay occurred with a convex decline. Furthermore, our results explore the non-monotonicity of extinction debt with respect to the speed of deterioration. A peak is present at low levels of deterioration, and the height of the peak and the asymptote of delay are affected by both life history parameterizations and the rate of change of the carrying capacity. The results suggest that population viability analyses must consider not only environmental deterioration, but also the effects of deterioration on the trajectory of the decline in carrying capacity.

Keywords

Environmental deterioration Time to extinction Extinction debt Bifurcation delay 

References

  1. Anderson DF (2007) A modified next reaction method for simulating chemical systems with time dependent propensities and delays. J Chem Phys 127:214107CrossRefPubMedGoogle Scholar
  2. Baillie JEM, Hilton-Taylor C, Stuart SN (eds) (2004) IUCN Red List of threatened species: a global species assessment. Gland, Switzerland, and Cambridge, UKGoogle Scholar
  3. Corlett RT (2015) The Anthropocene concept in ecology and conservation. Trends in Ecol Evol 30(1):36–41. doi: 10.1016/j.tree.2014.10.007 CrossRefGoogle Scholar
  4. Drake JM, Griffen BD (2010) Early warning signals of extinction in deteriorating environments. Nature 467(7314):456–459. doi: 10.1038/nature09389 CrossRefPubMedGoogle Scholar
  5. Gardiner C (2009) Stochastic methods: a handbook for the natural and social sciences, 4th edn. Springer, BerlinGoogle Scholar
  6. Gibson MA, Bruck J (2000) Efficient exact stochastic simulation of chemical systems with many species and many channels. J Phys Chem 104(9):1876–1889CrossRefGoogle Scholar
  7. Gillespie DT (2001) Approximate accelerated stochastic simulation of chemically reacting systems. J Chem Phys 115(4):1716–1711CrossRefGoogle Scholar
  8. Hallam TG, Clark CE (1981) Non-autonomous logistic equations as models of populations in deteriorating environment. J Theor Biol 93(2):303–311. doi: 10.1016/0022-5193(81)90106-5 CrossRefGoogle Scholar
  9. Haugen A (1942) Life history studies of the cottontail rabbit in southwestern Michigan. Am Mid Nat 28(1):204–244. doi: 10.2307/2420701 CrossRefGoogle Scholar
  10. Helm A, Hanski I, Pärtel M (2006) Slow response of plant species richness to habitat loss and fragmentation. Ecol Lett 9:72–77. doi: 10.1111/j.1461-0248.2005.00841.x PubMedGoogle Scholar
  11. Hicks LL, Herter DR, Early RJ (2003) Clines in life history characteristics of the spotted owl in Washington. Northwestern Nat 84(2):57–67. doi: 10.2307/3536730 CrossRefGoogle Scholar
  12. Highland S, Jones J (2014) Extinction debt in naturally contracting mountain meadows in the Pacific Northwest, USA: varying responses of plants and feeding guilds of nocturnal moths. Biodivers Conserv 23(10):2529–2544. doi: 10.1007/s10531-014-0737-z CrossRefGoogle Scholar
  13. Huang SL, Hao Y, Mei Z, Turvey ST, Wang D (2012) Common pattern of population decline for freshwater cetacean species in deteriorating habitats. Freshw Biol 57(6):1266–1276. doi: 10.1111/j.1365-2427.2012.02772.x CrossRefGoogle Scholar
  14. Hylander K, Ehrlén J (2013) The mechanisms causing extinction debts. Trends Ecol Evol 28(6):341–346. doi: 10.1016/j.tree.2013.01.010 CrossRefPubMedGoogle Scholar
  15. Johnson P (2014) Adaptivetau: Tau-leaping stochastic simulation. R package version 2.1. https://CRAN.R-project.org/package=adaptivetau.
  16. Kindsvater HK, Mangel M, Reynolds JD, Dulvy NK (2016) Ten principles from evolutionary ecology essential for effective marine conservation. Ecol Evol 6(7):2125–2138. doi: 10.1002/ece2.2012 CrossRefPubMedPubMedCentralGoogle Scholar
  17. Kuussaari M, Bommarco R, Heikkinen RK, Helm A, Krauss J, Lindborg R, Öckinger E, Pärtel M, Pino J, Rodá F (2009) Extinction debt: a challenge for biodiversity conservation. Trends Ecol Evol 24(10):564–571. doi: 10.1016/j.tree.2009.04.011 CrossRefPubMedGoogle Scholar
  18. Lande R (1988) Demographic models of the northern spotted owl (Strix occidentalis caurina). Oecologia 75(4):601–607CrossRefPubMedGoogle Scholar
  19. Lindborg R, Eriksson O (2004) Historical landscpare connectivity affects present plant species diversity. Ecol 85(7):1840–1845CrossRefGoogle Scholar
  20. Lira PK, Ewers RM, Banks-Leite C, Pardini R, Metzger JP (2012) Evaluating the legacy of landscape history: extinction debt and species credit in bird and small mammal assemblages in the Brazilian Atlantic forest. J Appl Ecol 49:1325–1333. doi: 10.1111/j.1365-2664.2012.02214.x CrossRefGoogle Scholar
  21. Loehle C, Li BL (1996) Habitat destruction and the extinction debt revisited. Ecol App 6(3):784–789. doi: 10.2307/2269483 CrossRefGoogle Scholar
  22. McGill BJ, Dornelas M, Gotelli NJ, Magurran AE (2015) Fifteen forms of biodiversity trend in the Anthropocene. Trends Ecol Evol 30(2):104–113. doi: 10.1016/j.tree.2014.11.006 CrossRefPubMedGoogle Scholar
  23. Ovaskainen O, Hanski I (2002) Transient dynamics in metapopulation response to perturbation. Theor Popul Biol 61:285–295CrossRefPubMedGoogle Scholar
  24. Sala OE, Chapin FS, Armesto JJ, Berlow E, Bloomfield J, Dirzo R, Huber-Sanwald E, Huenneke LF, Jackson RB, Kinzig A et al (2000) Global biodiversity scenarios for the year 2100. Science 287(5459):1770–1774CrossRefPubMedGoogle Scholar
  25. Tilman D, May RM, Lehman CL, Nowak MA (1994) Habitat destruction and the extinction debt. Nature 371(6492):65–66. doi: 10.1038/371065a0 CrossRefGoogle Scholar
  26. Vitousek PM, D’Antonio CM, Loope LL, Westbrooks R (1996) Biological invasions as global environmental change. Am Sci 84(5):468–478Google Scholar
  27. Griffen BD, Drake JM (2008) Effects of habitat quality and size on extinction in experimental populations. Proc R Soc B 275(1648):2251-2256. doi: 10.1098/rspb.2008.0518
  28. Hanski I, Ovaskainen O (2002) Extinction Debt at Extinction Threshold. Conserv Biol 16 (3):666-673. doi: 10.1046/j.1523-1739.2002.00342.x

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Odum School of EcologyUniversity of GeorgiaAthensUSA

Personalised recommendations