title: Analysis and control of pre-extinction dynamics in stochastic populations.
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 (Wentzel-Kramers-Brillouin) WKB 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.
authors.affiliation: Department of Earth and Environmental Sciences, Montclair State University, 1 Normal Avenue, Montclair, NJ, 07043, USA, nieddug1@mail.montclair.edu.
authors.forename: Garrett
authors.initials: G
authors.lastname: Nieddu
authors.forename: Lora
authors.initials: L
authors.lastname: Billings
authors.forename: Eric
authors.initials: E
authors.lastname: Forgoston
mesh_terms: D000818:Animals; D003198:Computer Simulation; D053476:Extinction, Biological; D055641:Mathematical Concepts; D008954:Models, Biological; D009010:Monte Carlo Method; D011157:Population Dynamics; D013269:Stochastic Processes; D013997:Time Factors