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Stochastic matrix models for conservation and management: a comparative review of methods

Authors

  • John Fieberg,

    1. Biomathematics Graduate Prorgram Department of Statistics, North Carolina State University, Raleigh, NC 27695-8203, U.S.A. Current address: Department of Ecology and Evolutionary Biology, Cornell University, Ithaca NY 14853-2701, U.S.A.
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  • Stephen P. Ellner

    1. Biomathematics Graduate Prorgram Department of Statistics, North Carolina State University, Raleigh, NC 27695-8203, U.S.A. Current address: Department of Ecology and Evolutionary Biology, Cornell University, Ithaca NY 14853-2701, U.S.A.
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John Fieberg E-mail: jfieberg@nwifc.wa.gov

Abstract

Stochastic matrix models are frequently used by conservation biologists to measure the viability of species and to explore various management actions. Models are typically parameterized using two or more sets of estimated transition rates between age/size/stage classes. While standard methods exist for analyzing a single set of transition rates, a variety of methods have been employed to analyze multiple sets of transition rates. We review applications of stochastic matrix models to problems in conservation and use simulation studies to compare the performance of different analytic methods currently in use. We find that model conclusions are likely to be robust to the choice of parametric distribution used to model vital rate fluctuations over time. However, conclusions can be highly sensitive to the within-year correlation structure among vital rates, and therefore we suggest using analytical methods that provide a means of conducting a sensitivity analysis with respect to correlation parameters. Our simulation results also suggest that the precision of population viability estimates can be improved by using matrix models that incorporate environmental covariates in conjunction with experiments to estimate transition rates under a range of environmental conditions.

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