Analysis and Control of Pre-extinction Dynamics in Stochastic Populations

Garrett Nieddu, Lora Billings, Eric Forgoston

Research output: Contribution to journalArticle

6 Scopus citations

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.

Original languageEnglish
Pages (from-to)3122-3137
Number of pages16
JournalBulletin of Mathematical Biology
Volume76
Issue number12
DOIs
StatePublished - 6 Dec 2014

Keywords

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

Fingerprint Dive into the research topics of 'Analysis and Control of Pre-extinction Dynamics in Stochastic Populations'. Together they form a unique fingerprint.

  • Cite this