title: Approximating the Critical Domain Size of Integrodifference Equations.
abstract: Integrodifference (IDE) models can be used to determine the critical domain size required for persistence of populations with distinct dispersal and growth phases. Using this modelling framework, we develop a novel spatially implicit approximation to the proportion of individuals lost to unfavourable habitat outside of a finite domain of favourable habitat, which consistently outperforms the most common approximations. We explore how results using this approximation compare to the existing IDE results on the critical domain size for populations in a single patch of good habitat, in a network of patches, in the presence of advection, and in structured populations. We find that the approximation consistently provides results which are in close agreement with those of an IDE model except in the face of strong advective forces, with the advantage of requiring fewer numerical approximations while providing insights into the significance of disperser retention in determining the critical domain size of an IDE.
authors.affiliation: Mathematical and Statistical Sciences, 632 Central Academic Building, University of Alberta, Edmonton, AB, T6G 2G1, Canada. jrreimer@ualberta.ca.
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.identifier: http://orcid.org/0000-0003-0250-0423
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: D000818:Animals; D017753:Ecosystem; D055641:Mathematical Concepts; D008954:Models, Biological; D011157:Population Dynamics / Q000706:statistics & numerical data*
keywords: Approximation; Bifurcation point; Critical domain size; Integrodifference equations