title: The critical domain size of stochastic population models.
abstract: Identifying the critical domain size necessary for a population to persist is an important question in ecology. Both demographic and environmental stochasticity impact a population's ability to persist. Here we explore ways of including this variability. We study populations with distinct dispersal and sedentary stages, which have traditionally been modelled using a deterministic integrodifference equation (IDE) framework. Individual-based models (IBMs) are the most intuitive stochastic analogues to IDEs but yield few analytic insights. We explore two alternate approaches; one is a scaling up to the population level using the Central Limit Theorem, and the other a variation on both Galton-Watson branching processes and branching processes in random environments. These branching process models closely approximate the IBM and yield insight into the factors determining the critical domain size for a given population subject to stochasticity.
authors.affiliation: Mathematical and Statistical Sciences, 632 Central Academic Building, University of Alberta, Edmonton, AB, T6G 2G1, Canada.
authors.forename: Jody R
authors.initials: JR
authors.lastname: Reimer
authors.affiliation: Mathematical Ecology Research Group, Department of Zoology, University of Oxford, Tinbergen Building, South Parks Road, Oxford, OX1 3PS, UK. michael.bonsall@zoo.ox.ac.uk.
authors.forename: Michael B
authors.initials: MB
authors.lastname: Bonsall
authors.affiliation: Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK.
authors.forename: Philip K
authors.initials: PK
authors.lastname: Maini
mesh_terms: D004463:Ecology; D004777:Environment; D008954:Models, Biological; D011157:Population Dynamics; D013269:Stochastic Processes
keywords: Branching processes; Critical domain size; Individual-based model; Integrodifference equation; Stochasticity