title: Extinction times and size of the surviving species in a two-species competition process.
abstract: We investigate a stochastic model for the competition between two species. Based on percentiles of the maximum number of individuals in the ecosystem, we present an approximating model for which the extinction time can be thought of as a phase-type random variable. We determine formulae for the probabilities of extinction and the moments of the extinction time. We discuss the use of several quasi-stationary assumptions. We include a comparative study between existing asymptotic results, results obtained from a simulation of the process, and our solution.
authors.affiliation: Faculty of Mathematics, Complutense University of Madrid, 28040 Madrid, Spain. antonio_gomez@mat.ucm.es
authors.forename: A
authors.initials: A
authors.lastname: Gómez-Corral
authors.forename: M López
authors.initials: ML
authors.lastname: García
mesh_terms: D001723:Birth Rate; D003163:Competitive Behavior; D003198:Computer Simulation; D053476:Extinction, Biological; D015233:Models, Statistical; D009026:Mortality; D011157:Population Dynamics