Analysis and Control of Pre-extinction Dynamics in Stochastic Populations

Garrett Nieddu; Lora Billings; Eric Forgoston

doi:10.1007/s11538-014-0047-3

Analysis and Control of Pre-extinction Dynamics in Stochastic Populations

Garrett Nieddu, Lora Billings, Eric Forgoston

Research output: Contribution to journal › Article › peer-review

10 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 language	English
Pages (from-to)	3122-3137
Number of pages	16
Journal	Bulletin of Mathematical Biology
Volume	76
Issue number	12
DOIs	https://doi.org/10.1007/s11538-014-0047-3
State	Published - 6 Dec 2014

Keywords

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

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10.1007/s11538-014-0047-3

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title = "Analysis and Control of Pre-extinction Dynamics in Stochastic Populations",

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.",

keywords = "Master equation, Mean time to extinction, Pre-extinction dynamics, Stochastic population models, WKB approximation",

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T1 - Analysis and Control of Pre-extinction Dynamics in Stochastic Populations

AU - Nieddu, Garrett

AU - Billings, Lora

AU - Forgoston, Eric

PY - 2014/12/6

Y1 - 2014/12/6

N2 - 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.

AB - 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.

KW - Master equation

KW - Mean time to extinction

KW - Pre-extinction dynamics

KW - Stochastic population models

KW - WKB approximation

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SP - 3122

EP - 3137

JO - Bulletin of Mathematical Biology

JF - Bulletin of Mathematical Biology

IS - 12

ER -

Analysis and Control of Pre-extinction Dynamics in Stochastic Populations

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