Effect of harvest on MTE calculated by single step process for stochastic population model under Allee effect

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.

Deterministic and Stochastic Research of Cubic Population Model with Harvesting

“…Although there are various approaches to describe the model including stochastic properties with noise, two approaches are basically in the foreground [21,22]. Master equation can be solved by using transition rates representing the transition of a population from n individuals to n + r individuals [23][24][25]. Although there is no general solution of the master equation, a mean field equation can be obtained [26].…”