Article
Analysis and Control of Pre-extinction Dynamics in Stochastic Populations
Bulletin of Math Biology
(2014)
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
- Stochastic population models,
- Pre-extinction dynamics,
- Mean time to extinction,
- · Master equation,
- WKB approximation
Disciplines
Publication Date
Fall November 26, 2014
DOI
10.1007/s11538-014-0047-3
Citation Information
Garrett T Nieddu, Lora Billings and Eric Forgoston. "Analysis and Control of Pre-extinction Dynamics in Stochastic Populations" Bulletin of Math Biology (2014) ISSN: 1522-9602 Available at: http://works.bepress.com/lora-billings/5/