Analysis and control of pre-extinction dynamics in stochastic populations

Garrett Nieddu; Lora Billings; Eric Forgoston

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arXiv · 1412.3857

Analysis and control of pre-extinction dynamics in stochastic populations

Garrett Nieddu·Lora Billings·Eric Forgoston

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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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Garrett Nieddu, Lora Billings, Eric Forgoston. 2014-12-11. Analysis and control of pre-extinction dynamics in stochastic populations. https://arxiv.org/abs/1412.3857

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