Effect of Harvest on MTE Calculated by Single Step Process for Stochastic Population Model Under Allee Effect

TL;DR

This paper models the impact of harvesting on the mean time to extinction in a stochastic population under Allee effect, using a single step process and WKB approximation to connect micro-interactions with macro outcomes.

Contribution

It introduces a quadratic harvest function into the cubic population model under Allee effect and derives MTE using a novel single step process approach.

Findings

Harvest reduces the mean time to extinction.

Micro-macro parameter relationship established.

WKB approximation effectively predicts extinction times.

Abstract

In this study, first we expand the cubic population model under Allee effect with a quadratic harvest function that represents harvest effect. Then, using four reaction equations representing the micro-interactions within the population under the influence of demographic noise and harvest, we obtain the mean field equations containing the effect of the harvest from the solution of the master equation. In this way, a relationship is established between the micro and macro parameters of the population. As a result, we calculate Mean Time to Extinction (MTE) by using WKB approximation for single step processes and observe the effect of harvesting.