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.
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References
Anderson DF (2007) A modified next reaction method for simulating chemical systems with time dependent propensities and delays. J Chem Phys 127:214107
Baillie JEM, Hilton-Taylor C, Stuart SN (eds) (2004) IUCN Red List of threatened species: a global species assessment. Gland, Switzerland, and Cambridge, UK
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
Drake JM, Griffen BD (2010) Early warning signals of extinction in deteriorating environments. Nature 467(7314):456–459. doi:10.1038/nature09389
Gardiner C (2009) Stochastic methods: a handbook for the natural and social sciences, 4th edn. Springer, Berlin
Gibson MA, Bruck J (2000) Efficient exact stochastic simulation of chemical systems with many species and many channels. J Phys Chem 104(9):1876–1889
Gillespie DT (2001) Approximate accelerated stochastic simulation of chemically reacting systems. J Chem Phys 115(4):1716–1711
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
Haugen A (1942) Life history studies of the cottontail rabbit in southwestern Michigan. Am Mid Nat 28(1):204–244. doi:10.2307/2420701
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
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
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
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
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
Johnson P (2014) Adaptivetau: Tau-leaping stochastic simulation. R package version 2.1. https://CRAN.R-project.org/package=adaptivetau.
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
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
Lande R (1988) Demographic models of the northern spotted owl (Strix occidentalis caurina). Oecologia 75(4):601–607
Lindborg R, Eriksson O (2004) Historical landscpare connectivity affects present plant species diversity. Ecol 85(7):1840–1845
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
Loehle C, Li BL (1996) Habitat destruction and the extinction debt revisited. Ecol App 6(3):784–789. doi:10.2307/2269483
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
Ovaskainen O, Hanski I (2002) Transient dynamics in metapopulation response to perturbation. Theor Popul Biol 61:285–295
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):1770–1774
Tilman D, May RM, Lehman CL, Nowak MA (1994) Habitat destruction and the extinction debt. Nature 371(6492):65–66. doi:10.1038/371065a0
Vitousek PM, D’Antonio CM, Loope LL, Westbrooks R (1996) Biological invasions as global environmental change. Am Sci 84(5):468–478
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
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
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Zarada, K., Drake, J.M. Time to extinction in deteriorating environments. Theor Ecol 10, 65–71 (2017). https://doi.org/10.1007/s12080-016-0311-2
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DOI: https://doi.org/10.1007/s12080-016-0311-2