Extinction times and moment closure in the stochastic logistic process

Newman, T. J., Ferdy, Jean Baptiste and Quince, C. (2004) Extinction times and moment closure in the stochastic logistic process. Theoretical Population Biology, 65 (2). pp. 115-126. ISSN 0040-5809

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We investigate the statistics of extinction times for an isolated population, with an initially modest number M of individuals, whose dynamics are controlled by a stochastic logistic process (SLP). The coefficient of variation in the extinction time V is found to have a maximum value when the death and birth rates are close in value. For large habitat size K we find that Vmax is of order K1/4/M1/2, which is much larger than unity so long as M is small compared to K1/2. We also present a study of the SLP using the moment closure approximation (MCA), and discuss the successes and failures of this method. Regarding the former, the MCA yields a steady-state distribution for the population when the death rate is low. Although not correct for the SLP model, the first three moments of this distribution coincide with those calculated exactly for an adjusted SLP in which extinction is forbidden. These exact calculations also pinpoint the breakdown of the MCA as the death rate is increased.

Item Type: Article
Additional Information: Funding Information: T.J.N. is grateful to the Jeffress Foundation and the NSF (Division of Environmental Biology and Division of Applied Mathematics) under Grant DEB-0328267 for financial support. J.-B.F. has been supported by NSF Grant DEB-9527986 to Jane Molofsky.
Uncontrolled Keywords: conservation,demographic stochasticity,fluctuations,moment closure approximation,quasi-stationary distribution,time to extinction,ecology, evolution, behavior and systematics ,/dk/atira/pure/subjectarea/asjc/1100/1105
Faculty \ School: Faculty of Science > School of Biological Sciences
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Depositing User: LivePure Connector
Date Deposited: 12 Sep 2022 11:31
Last Modified: 21 Oct 2022 01:40
URI: https://ueaeprints.uea.ac.uk/id/eprint/88136
DOI: 10.1016/j.tpb.2003.10.003

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