title: A model for a spatially structured metapopulation accounting for within patch dynamics.
abstract: We develop a stochastic metapopulation model that accounts for spatial structure as well as within patch dynamics. Using a deterministic approximation derived from a functional law of large numbers, we develop conditions for extinction and persistence of the metapopulation in terms of the birth, death and migration parameters. Interestingly, we observe the Allee effect in a metapopulation comprising two patches of greatly different sizes, despite there being decreasing patch specific per-capita birth rates. We show that the Allee effect is due to the way the migration rates depend on the population density of the patches.
authors.affiliation: School of Mathematics and Physics, University of Queensland, St Lucia 4072, Queensland. Electronic address: a.smith23@uq.edu.au.
authors.forename: Andrew G
authors.initials: AG
authors.lastname: Smith
authors.affiliation: School of Mathematics and Physics, University of Queensland, St Lucia 4072, Queensland.
authors.forename: Ross
authors.initials: R
authors.lastname: McVinish
authors.affiliation: School of Mathematics and Physics, University of Queensland, St Lucia 4072, Queensland.
authors.forename: Philip K
authors.initials: PK
authors.lastname: Pollett
mesh_terms: D003198:Computer Simulation; D053476:Extinction, Biological; D008390:Markov Chains; D008962:Models, Theoretical; D011157:Population Dynamics
keywords: Extinction; Markov process; Metapopulation; Partially ordered flow; Spatially structured