A stochastic metapopulation model accounting for habitat dynamics

Ross, JV (2006) A stochastic metapopulation model accounting for habitat dynamics. Journal of Mathematical Biology, 52 6: 788-806. doi:10.1007/s00285-006-0372-8


Author Ross, JV
Title A stochastic metapopulation model accounting for habitat dynamics
Journal name Journal of Mathematical Biology   Check publisher's open access policy
ISSN 0303-6812
Publication date 2006
Sub-type Article (original research)
DOI 10.1007/s00285-006-0372-8
Volume 52
Issue 6
Start page 788
End page 806
Total pages 19
Editor O Diekmann and A Hastings
Place of publication New York
Publisher Springer
Collection year 2006
Language eng
Subject C1
230202 Stochastic Analysis and Modelling
780101 Mathematical sciences
Abstract A stochastic metapopulation model accounting for habitat dynamics is presented. This is the stochastic SIS logistic model with the novel aspect that it incorporates varying carrying capacity. We present results of Kurtz and Barbour, that provide deterministic and diffusion approximations for a wide class of stochastic models, in a form that most easily allows their direct application to population models. These results are used to show that a suitably scaled version of the metapopulation model converges, uniformly in probability over finite time intervals, to a deterministic model previously studied in the ecological literature. Additionally, they allow us to establish a bivariate normal approximation to the quasi-stationary distribution of the process. This allows us to consider the effects of habitat dynamics on metapopulation modelling through a comparison with the stochastic SIS logistic model and provides an effective means for modelling metapopulations inhabiting dynamic landscapes.
Keyword Diffusion Approximations
Habitat Dynamics
Markov Chains
Metapopulations
Stochastic Logistic Model
Stochastic Models
Mathematics, Interdisciplinary Applications
Biology
Quasi-stationary Distributions
Markov Population Processes
Persistence
Extinction
Landscapes
Q-Index Code C1

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
2007 Higher Education Research Data Collection
 
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Created: Wed, 15 Aug 2007, 08:19:07 EST