Effect of Harvest on MTE Calculated by Single Step Process for Stochastic Population Model Under Allee Effect
arXiv:1910.06217 · doi:10.1063/1.5135465
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.
arXiv comment5 pages
References in corpus (7)
- Extinction of metastable stochastic populations
- WKB theory of large deviations in stochastic populations
- Switching rates of multi-step reactions
- Extinction of oscillating populations
- Demographic stochasticity and extinction in populations with Allee effect
- Impact of Colored Environmental Noise on the Extinction of a Long-Lived Stochastic Population: Role of the Allee Effect
- Applications of WKB and Fokker-Planck methods in analyzing population extinction driven by weak demographic fluctuations