The Mathematical Institute, University of Oxford, Eprints Archive

Approximating the critical domain size of integrodifference equations

Reimer, J R and Bonsall, M B and Maini, P. K. (2016) Approximating the critical domain size of integrodifference equations. Bulletin of Mathematical Biology, 78 (1). pp. 72-109.

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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.

Item Type:Article
Uncontrolled Keywords:Integrodifference equations Approximation Critical domain size Bifurcation point
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:1923
Deposited By: Philip Maini
Deposited On:29 Jan 2016 07:29
Last Modified:29 Jan 2016 07:29

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