%0 Journal Article %1 kingman1977remarks %A Kingman, J. F. C. %D 1977 %I Applied Probability Trust %J Journal of Applied Probability %K Poisson_process density_dependence point_processes spatial_branching spatial_coalescent %N 3 %P pp. 577-583 %T Remarks on the Spatial Distribution of a Reproducing Population %U http://www.jstor.org/stable/3213460 %V 14 %X 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.

@article{kingman1977remarks, 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.}, added-at = {2015-08-04T03:00:30.000+0200}, author = {Kingman, J. F. C.}, biburl = {https://www.bibsonomy.org/bibtex/2f8e902d998ab5ef25dfde156f379b67f/peter.ralph}, interhash = {81b4109bc87f516a27f7bd794523dde9}, intrahash = {f8e902d998ab5ef25dfde156f379b67f}, issn = {00219002}, journal = {Journal of Applied Probability}, keywords = {Poisson_process density_dependence point_processes spatial_branching spatial_coalescent}, language = {English}, number = 3, pages = {pp. 577-583}, publisher = {Applied Probability Trust}, timestamp = {2015-08-04T03:00:30.000+0200}, title = {Remarks on the Spatial Distribution of a Reproducing Population}, url = {http://www.jstor.org/stable/3213460}, volume = 14, year = 1977 }