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Limits of large metapopulations with patch-dependent extinction probabilities

Part of: Limit theorems Stochastic processes Markov processes

Published online by Cambridge University Press:  01 July 2016

R. McVinish  and
P. K. Pollett
R. McVinish*
Affiliation:
University of Queensland
P. K. Pollett*
Affiliation:
University of Queensland
*
∗ Postal address: Department of Mathematics, University of Queensland, Brisbane, QLD 4072, Australia.
∗ Postal address: Department of Mathematics, University of Queensland, Brisbane, QLD 4072, Australia.
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Abstract

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We propose a model for the presence/absence of a population in a collection of habitat patches. This model assumes that colonisation and extinction of the patches occur as distinct phases. Importantly, the local extinction probabilities are allowed to vary between patches. This permits an investigation of the effect of habitat degradation on the persistence of the population. The limiting behaviour of the model is examined as the number of habitat patches increases to ∞. This is done in the case where the number of patches and the initial number of occupied patches increase at the same rate, and for the case where the initial number of occupied patches remains fixed.

Keywords

Chain binomial modelfixed pointweak convergencepoint process

MSC classification

Primary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
Secondary: 60G55: Point processes 60F05: Central limit and other weak theorems
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 42 , Issue 4 , December 2010 , pp. 1172 - 1186
Copyright
Copyright © Applied Probability Trust 2010 

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