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Spatial dynamics of biological populations

Published online by Cambridge University Press:  01 July 2016

Eric Renshaw
Eric Renshaw*
Affiliation:
University of Edinburgh
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Extract

Considerable interest has recently been shown in the spatial spread of infection between static individuals. A different approach yielding similar types of processes is to allow the individuals themselves to migrate from site to site. This movement may be physical migration, mutation from one type of organism to another, or it may even represent an approximation to the initial development of a spatial epidemic. We shall consider the population to be distributed amongst either a finite number of sites (model A), or an infinite number situated at the nodes of a lattice (model B). In this latter situation individuals are only allowed to migrate between sites which are nearest neighbours, and the transition rates are assumed to be spatially homogeneous. Individuals at each site undertake a simple birth-death-migration-immigration process.

Type
Stochastic Modelling
Information
Advances in Applied Probability , Volume 7 , Issue 3 , September 1975 , pp. 459 - 460
Copyright
Copyright © Applied Probability Trust 1975 

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References

Bailey, N. T. J. (1968) Stochastic birth, death and migration processes for spatially distributed populations. Biometrika 55, 189–198.CrossRefGoogle Scholar
Renshaw, E. (1972) Birth, death and migration processes. Biometrika 59, 49–60.Google Scholar
Renshaw, E. (1973) Interconnected population processes. J. Appl. Prob. 10, 1–14.CrossRefGoogle Scholar
Renshaw, E. (1974) Stepping stone models for population growth. J. Appl. Prob. 11, 16–31.CrossRefGoogle Scholar