Analysis and Control of Pre-extinction Dynamics in Stochastic Populations

Garrett Nieddu, Lora Billings, Eric Forgoston

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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.

Original languageEnglish
Pages (from-to)3122-3137
Number of pages16
JournalBulletin of Mathematical Biology
Issue number12
Publication statusPublished - 6 Dec 2014



  • Master equation
  • Mean time to extinction
  • Pre-extinction dynamics
  • Stochastic population models
  • WKB approximation

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