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The Limiting Behaviour of Hanski's Incidence Function Metapopulation Model

Part of: Limit theorems Markov processes

Published online by Cambridge University Press:  19 February 2016

R. McVinish  and
P. K. Pollett
R. McVinish*
Affiliation:
University of Queensland
P. K. Pollett*
Affiliation:
University of Queensland
*
∗ Postal address: School of Mathematics and Physics, University of Queensland, Brisbane, QLD 4072, Australia. Email address: r.mcvinish@uq.edu.au.
∗∗ Email address: pkp@maths.uq.edu.au.
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Abstract

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Hanski's incidence function model is one of the most widely used metapopulation models in ecology. It models the presence/absence of a species at spatially distinct habitat patches as a discrete-time Markov chain whose transition probabilities are determined by the physical landscape. In this analysis, the limiting behaviour of the model is studied as the number of patches increases and the size of the patches decreases. Two different limiting cases are identified depending on whether or not the metapopulation is initially near extinction. Basic properties of the limiting models are derived.

Keywords

Extinction thresholdpoint processstochastic patch occupancy modelSPOMweak convergence

MSC classification

Primary: 92D40: Ecology
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) 60F05: Central limit and other weak theorems
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 2 , June 2014 , pp. 297 - 316
Copyright
© Applied Probability Trust 

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