A stochastic metapopulation model accounting for habitat dynamics

Journal of Mathematical Biology
J V Ross

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.

References

Jun 22, 1999·Journal of Theoretical Biology·S BrachetP H Gouyon
Apr 21, 2001·Journal of Theoretical Biology·P Amarasekare, H Possingham
Nov 1, 2000·The American Naturalist·Juan E KeymerSimon A Levin

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Citations

Jul 20, 2007·Journal of the Royal Society, Interface·M J Keeling, J V Ross
Nov 1, 2008·Journal of the Royal Society, Interface·C E DangerfieldM J Keeling
May 21, 2008·Ecological Applications : a Publication of the Ecological Society of America·Joshua V RossHugh P Possingham
Nov 28, 2013·Mathematical Biosciences·Andrew G SmithPhilip K Pollett
May 2, 2013·Journal of Mathematical Biology·Matthew Graham, Thomas House
Nov 26, 2009·Mathematical Biosciences·P K PollettJ V Ross
Aug 12, 2008·Theoretical Population Biology·Stephen J Cornell, Otso Ovaskainen
Feb 6, 2007·Theoretical Population Biology·Séverine VuilleumierHugh P Possingham
Sep 21, 2006·Theoretical Population Biology·J V RossP K Pollett
Sep 7, 2016·Theoretical Population Biology·R McVinishY S Chan
Oct 4, 2012·Physical Review Letters·Michael KhasinLeonard M Sander
Dec 4, 2015·Conservation Biology : the Journal of the Society for Conservation Biology·Karlo HockPeter J Mumby
Jul 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Marifi Güler

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