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Analysis and Control of Pre-extinction Dynamics in Stochastic Populations

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Abstract

We consider a stochastic population model, where the intrinsic or demographic noise causes cycling between states before the population eventually goes extinct. A master equation approach coupled with a (Wentzel–Kramers–Brillouin) WKB approximation is used to construct the optimal path to extinction. In addition, a probabilistic argument is used to understand the pre-extinction dynamics and approximate the mean time to extinction. Analytical results agree well with numerical Monte Carlo simulations. A control method is implemented to decrease the mean time to extinction. Analytical results quantify the effectiveness of the control and agree well with numerical simulations.

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Acknowledgments

We gratefully acknowledge support from the National Science Foundation. G.N., L.B., and E.F. were supported by the National Science Foundation awards CMMI-1233397 and DMS-0959461. This material is based upon work while L.B. was serving at the National Science Foundation. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. We also gratefully acknowledge Dirk Vanderklein and Andrew McDougall for helpful discussions.

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Authors and Affiliations

  1. Department of Earth and Environmental Sciences, Montclair State University, 1 Normal Avenue, Montclair, NJ, 07043, USA

    Garrett Nieddu

  2. Department of Mathematical Sciences, Montclair State University, 1 Normal Avenue, Montclair, NJ, 07043, USA

    Lora Billings & Eric Forgoston

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  1. Garrett Nieddu
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  2. Lora Billings
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  3. Eric Forgoston
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Correspondence to Eric Forgoston.

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Nieddu, G., Billings, L. & Forgoston, E. Analysis and Control of Pre-extinction Dynamics in Stochastic Populations. Bull Math Biol 76, 3122–3137 (2014). https://doi.org/10.1007/s11538-014-0047-3

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  • DOI: https://doi.org/10.1007/s11538-014-0047-3

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