Analysis and control of pre-extinction dynamics in stochastic populations

2014/12/11 by Garrett Nieddu, Nieddu, Garrett, Lora Billings +3
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #FOS: Biological sciences #FOS: Physical sciences #Populations and Evolution (q-bio.PE) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #q-bio.PE

paper · pdf · doi:10.48550/arxiv.1412.3857

17 pages, 9 figures. Final version to appear in Bulletin of Mathematical Biology

arxiv created 2014/12/11 · arxiv updated 2014/12/16

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 WKB (Wentzel-Kramers-Brillouin) 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.

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