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A survey of stepping-stone models in population dynamics

Published online by Cambridge University Press:  01 July 2016

Eric Renshaw
Eric Renshaw*
Affiliation:
University of Edinburgh
*
∗Postal address: Department of Statistics, University of Edinburgh, King&s Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK.
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Abstract

A survey is presented of stochastic and deterministic developments in the study of the effects of nearest-neighbour ‘migration’ between spatially separated ‘colonies’. Such processes are of general applicability, and are relevant to any vector process X(t) = (X 1(t), · ··, XN (t)) in which the arrival, departure and transfer rates for the states {X(t) = n} may be written in the form α i (ni ), βi (ni ) and γ ij (ni , nj ), respectively, where n = (n 1, · ··, nN ). Whilst the main body of results are described in terms of birth-death, genetic and epidemic situations, the final section examines within colony interaction in the context of spatial predator-prey processes.

Keywords

BIRTH, DEATH, MIGRATIONDIFFUSIONSPATIAL PROCESSESEPIDEMICSGENETICSPREDATOR-PREYCONTACT DISTRIBUTIONSSADDLEPOINT APPROXIMATIONSVELOCITIES OF PROPAGATION

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Type
Research Article
Information
Advances in Applied Probability , Volume 18 , Issue 3 , September 1986 , pp. 581 - 627
Copyright
Copyright © Applied Probability Trust 1986 

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