Analysis and control of pre-extinction dynamics in stochastic populations

TL;DR

This paper analyzes the pre-extinction dynamics in stochastic populations using a master equation and WKB approximation, and proposes a control method to influence extinction times, validated by simulations.

Contribution

It introduces an analytical framework combining master equations and WKB approximation to understand pre-extinction dynamics and control in stochastic populations.

Findings

Analytical expressions for pre-extinction cycling behavior.

Effective control strategies to modify mean extinction time.

Good agreement between analytical results and simulations.

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.