Hostname: page-component-77c89778f8-fv566 Total loading time: 0 Render date: 2024-07-23T19:19:34.724Z Has data issue: false hasContentIssue false
  • English
  • Français

Velocities of propagation for stepping-stone models of population growth

Published online by Cambridge University Press:  14 July 2016

Eric Renshaw
Eric Renshaw*
Affiliation:
University of Edinburgh
Get access Rights & Permissions [Opens in a new window]

Abstract

A population is composed of an infinite number of colonies situated at the integer points of a single co-ordinate axis. Each colony develops according to a simple birth and death process and migration is allowed between nearest neighbours only. Exact expressions are derived for both the asymptotic velocity of propagation and the shape of the wave profile as the population spreads along the axis, and it is shown that they are identical with the saddle point approximations developed by Daniels.

Keywords

BIRTHDEATHMIGRATIONSPATIAL POPULATION PROCESSSTEPPING-STONE MODELVELOCITY OF PROPAGATIONBESSEL FUNCTIONSADDLE POINT APPROXIMATIONCONTACT DISTRIBUTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 14 , Issue 3 , September 1977 , pp. 591 - 597
Copyright
Copyright © Applied Probability Trust 1977 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramowitz, M. and Stegun, I. A. (1965) Handbook of Mathematical Functions , Dover, New York.Google Scholar
Bailey, N. T. J. (1968) Stochastic birth, death and migration processes for spatially distributed populations. Biometrika 55, 189–198.Google Scholar
Daniels, H. E. (1975) The deterministic spread of a simple epidemic. In Perspectives in Probability and Statistics: Papers in Honour of M. S. Bartlett , ed. Gani, J., Applied Probability Trust, Sheffield; Academic Press, London, 373–386.Google Scholar
Kendall, D. G. (1965) Mathematical models of the spread of infection. In Mathematics and Computer Science in Biology and Medicine. H.M.S.O., London, 213–225.Google Scholar
Mollison, D. (1972a) The rate of spatial propagation of simple epidemics. Proc. 6th Berkeley Symp. Math. Statist. Prob. 3, 579–614.Google Scholar
Mollison, D. (1972b) Possible velocities for a simple epidemic. Adv. Appl. Prob. 4, 233–257.Google Scholar
Renshaw, E. (1972) Birth, death and migration processes. Biometrika 59, 49–60.Google Scholar
Renshaw, E. (1974) Stepping-stone models for population growth. J. Appl. Prob. 11, 16–31.Google Scholar