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Remarks on the spatial distribution of a reproducing population

Published online by Cambridge University Press:  14 July 2016

J. F. C. Kingman
J. F. C. Kingman*
Affiliation:
University of Oxford
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Abstract

Several authors have noted that simple models for the evolution of a reproducing and spatially distributed population have no limiting distribution, although a Poisson process in statistical equilibrium has sometimes been implicitly assumed. It is shown that, even when a mechanism for restricting population density is postulated, a Poisson process is usually impossible to achieve, essentially because of an assumption of independent displacements. When this assumption is abandoned, a Poisson process is possible, at least for some highly idealised models.

Keywords

POISSON PROCESSBRANCHING RANDOM WALKCOX PROCESSISOLATION BY DISTANCECLUSTER PROCESS
Type
Short Communications
Information
Journal of Applied Probability , Volume 14 , Issue 3 , September 1977 , pp. 577 - 583
Copyright
Copyright © Applied Probability Trust 1977 

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