Analysis and Control of Pre-extinction Dynamics in Stochastic Populations

Garrett Nieddu, Lora Billings, Eric Forgoston

Research output: Contribution to journalArticleResearchpeer-review

5 Citations (Scopus)

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

Fingerprint

Extinction
extinction
Population
Noise
Demography
WKB Approximation
Numerical Simulation
Optimal Path
Computer simulation
Cycling
Population Model
Master Equation
simulation
Stochastic Model
control methods
Quantify
demographic statistics
Monte Carlo Simulation
Decrease
analysis

Keywords

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

Cite this

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Analysis and Control of Pre-extinction Dynamics in Stochastic Populations. / Nieddu, Garrett; Billings, Lora; Forgoston, Eric.

In: Bulletin of Mathematical Biology, Vol. 76, No. 12, 06.12.2014, p. 3122-3137.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Billings, Lora

AU - Forgoston, Eric

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