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.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Reference20 articles.
1. Spatial interaction and the statistical analysis of spatial pattern;Besag;J. R. Statist. Soc. B,1974
2. Model building and the analysis of spatial pattern in human geography;Cliff;J. R. Statist. Soc. B,1975
3. Some statistical methods connected with series of events;Cox;J. R. Statist. Soc. B,1955
4. Sawyer S. (1977) Asymptotic properties of the probability of identity in a geographically structured population. Adv. Appl. Prob. 9,
5. On Poisson laws for distributions of particles in space;Dobrushin;Ukrain. Mat. Z.,1956
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