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 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.
Keywords
Cite
@article{arxiv.1412.3857,
title = {Analysis and control of pre-extinction dynamics in stochastic populations},
author = {Garrett Nieddu and Lora Billings and Eric Forgoston},
journal= {arXiv preprint arXiv:1412.3857},
year = {2014}
}
Comments
17 pages, 9 figures. Final version to appear in Bulletin of Mathematical Biology