The random-walk problem is adopted as a starting point for the analytical study of dispersal in living organisms. The solution is used as a basis for the study of the expanson of a growing population, and illustrative examples are given. The law of diffusion is deduced and applied to the understanding of the spatial distribution of population density in both linear and two-dimensional habitats on various assumptions as to the mode of population growth or decline. For the numerical solution of certain cases an iterative process is described and a short table of a new function is given. The equilibrium states of the various analytical models are considered in relation to the size of the habitat, and questions of stability are investigated. A mode of population growth resulting from the random scattering of the reproductive units in a population discrete in time, is deduced and used as a basis for study on interspecific competition. The extent to which the present analytical formulation is applicable to biological situations, and some of the more important biological implications are briefly considered.
%0 Journal Article
%1 skellam1951random
%A Skellam, J. G.
%D 1951
%I Oxford University Press, Biometrika Trust
%J Biometrika
%K Fisher-KPP density_dependence dispersal invasions seed_dispersal spatial_heterogeneity travelling_wave
%N 1/2
%P 196--218
%T Random Dispersal in Theoretical Populations
%U http://www.jstor.org/stable/2332328
%V 38
%X The random-walk problem is adopted as a starting point for the analytical study of dispersal in living organisms. The solution is used as a basis for the study of the expanson of a growing population, and illustrative examples are given. The law of diffusion is deduced and applied to the understanding of the spatial distribution of population density in both linear and two-dimensional habitats on various assumptions as to the mode of population growth or decline. For the numerical solution of certain cases an iterative process is described and a short table of a new function is given. The equilibrium states of the various analytical models are considered in relation to the size of the habitat, and questions of stability are investigated. A mode of population growth resulting from the random scattering of the reproductive units in a population discrete in time, is deduced and used as a basis for study on interspecific competition. The extent to which the present analytical formulation is applicable to biological situations, and some of the more important biological implications are briefly considered.
@article{skellam1951random,
abstract = {The random-walk problem is adopted as a starting point for the analytical study of dispersal in living organisms. The solution is used as a basis for the study of the expanson of a growing population, and illustrative examples are given. The law of diffusion is deduced and applied to the understanding of the spatial distribution of population density in both linear and two-dimensional habitats on various assumptions as to the mode of population growth or decline. For the numerical solution of certain cases an iterative process is described and a short table of a new function is given. The equilibrium states of the various analytical models are considered in relation to the size of the habitat, and questions of stability are investigated. A mode of population growth resulting from the random scattering of the reproductive units in a population discrete in time, is deduced and used as a basis for study on interspecific competition. The extent to which the present analytical formulation is applicable to biological situations, and some of the more important biological implications are briefly considered.},
added-at = {2024-01-21T18:15:38.000+0100},
author = {Skellam, J. G.},
biburl = {https://www.bibsonomy.org/bibtex/24ec3d827cf4dce4967f881231e151e2e/peter.ralph},
interhash = {199840a3dbdad1319a10bdd8ed211315},
intrahash = {4ec3d827cf4dce4967f881231e151e2e},
issn = {00063444},
journal = {Biometrika},
keywords = {Fisher-KPP density_dependence dispersal invasions seed_dispersal spatial_heterogeneity travelling_wave},
number = {1/2},
pages = {196--218},
publisher = {Oxford University Press, Biometrika Trust},
timestamp = {2024-01-21T18:15:38.000+0100},
title = {Random Dispersal in Theoretical Populations},
url = {http://www.jstor.org/stable/2332328},
urldate = {2024-01-21},
volume = 38,
year = 1951
}