Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-24T10:54:20.198Z Has data issue: false hasContentIssue false
  • English
  • Français

Clumping effects in models of isolation by distance

Published online by Cambridge University Press:  14 July 2016

Aidan Sudbury
Aidan Sudbury*
Affiliation:
Monash University, Clayton, Victoria
Get access Rights & Permissions [Opens in a new window]

Abstract

Individuals situated on the infinite line breed and produce offspring that independently migrate a distance that is a random variable depending on the number in each family. It is shown that under very general conditions the individuals in the nth generation will tend to form clumps.

Keywords

MIGRATIONBRANCHING RANDOM WALKCLUSTER PROCESSCONSANGUINITYINBREEDING COEFFICIENT
Type
Short Communications
Information
Journal of Applied Probability , Volume 14 , Issue 2 , June 1977 , pp. 391 - 395
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

[1] Malecot, G. (1969) The Mathematics of Heredity. Freeman, San Francisco.Google Scholar
[2] Felsenstein, J. (1975) A pain in the torus: some difficulties with models of isolation by distance. Amer. Natur. 109, 359–368.CrossRefGoogle Scholar
[3] Asmussen, S. and Kaplan, N. (1976) Branching random walks. Stoch. Proc. Appl. 4, 1–33.CrossRefGoogle Scholar
[4] Clifford, P. and Sudbury, A. W. (1973) A model for spatial conflict. Biometrika 60, 581–588.CrossRefGoogle Scholar
[5] Moran, P. A. P. (1975) Wandering distributions and the electrophoretic profile. Theoret. Pop. Biol. 8, 318–331.Google Scholar
[6] Kingman, J. F. C. (1976) Coherent random walks arising in some genetical models. Proc. R. Soc. London A 351, 19–31.Google Scholar