The limiting behaviour of a mainland-island metapopulation

McVinish, R. and Pollett, P. K. (2012) The limiting behaviour of a mainland-island metapopulation. Journal of Mathematical Biology, 64 5: 775-801. doi:10.1007/s00285-011-0429-1

Author McVinish, R.
Pollett, P. K.
Title The limiting behaviour of a mainland-island metapopulation
Journal name Journal of Mathematical Biology   Check publisher's open access policy
ISSN 0303-6812
Publication date 2012-04
Year available 2011
Sub-type Article (original research)
DOI 10.1007/s00285-011-0429-1
Volume 64
Issue 5
Start page 775
End page 801
Total pages 27
Place of publication Heidelberg, Germany
Publisher Springer
Collection year 2012
Language eng
Abstract Stochastic patch occupancy models (SPOMs) are a class of discrete time Markov chains used to model the presence/absence of a population in a collection of habitat patches. This class of model is popular with ecologists due to its ability to incorporate important factors of the habitat patch network such as connectivity and distance between patches as well as heterogeneity in patch characteristics. We present an asymptotic examination of a simple type of SPOM called the mainland-island model. In this model a single patch called the mainland is connected to a large number of smaller patches called islands and each island is only connected to the mainland. We discuss the limiting behaviour of the SPOM as the number of islands increases and the size of the islands decrease relative to the mainland. We demonstrate that a variety of limiting behaviours is possible depending on the scaling of the island size and on the heterogeneity of habitat quality.
Keyword Limit theorem
Markov chain
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Published online: 28 May 2011

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2012 Collection
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Citation counts: TR Web of Science Citation Count  Cited 5 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 6 times in Scopus Article | Citations
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Created: Thu, 10 May 2012, 09:32:03 EST by Dr Ross Mcvinish on behalf of Mathematics