Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-23T05:21:01.494Z Has data issue: false hasContentIssue false
  • English
  • Français

Looking backwards in time in the Moran model in population genetics

Published online by Cambridge University Press:  14 July 2016

Peter Clifford  and
Aidan Sudbury
Peter Clifford*
Affiliation:
University of Oxford
Aidan Sudbury*
Affiliation:
Monash University
*
∗Postal address: Mathematical Institute, 24–29 St. Giles, Oxford, OX1 3LB, England.
∗∗Postal address: Department of Mathematics, Monash University, Clayton, Vic 3168, Australia.
Get access Rights & Permissions [Opens in a new window]

Abstract

The Moran model in population genetics may also be regarded as an invasion process (or voter model) on the complete n-graph. Tracing lines of ancestry is equivalent to studying the dual process. Using this technique certain results concerning lines of ancestry can be derived very rapidly.

Keywords

INVASION PROCESSVOTER MODEL
Type
Short Communications
Information
Journal of Applied Probability , Volume 22 , Issue 2 , June 1985 , pp. 437 - 442
Copyright
Copyright © Applied Probability Trust 1985 

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

Clifford, P. D. and Sudbury, A. W. (1973) A model for spatial conflict. Biometrika 60, 581–588.Google Scholar
Donnelly, P. (1983) Ph.D. Thesis, Oxford University.Google Scholar
Donnelly, P. (1984) The transient behaviour of the Moran model in population genetics. Math. Proc. Camb. Phil. Soc. 95, 349–358.Google Scholar
Donnelly, P. and Welsh, D. J. A. (1983) Finite particle systems and infection models. Math. Proc. Camb. Phil. Soc. 94, 167–182.Google Scholar
Felsenstein, J. (1971) The rate of loss of multiple alleles in finite haploid populations. Theoret. Popn. Biol. 2, 391–403.Google Scholar
Griffiths, R. C. (1980) Lines of descent in the diffusion approximation of neutral Wright–Fisher models. Theoret. Popn. Biol. 17, 37–50.Google Scholar
Holley, R. and Liggett, T. M. (1975) Ergodic theorems for weakly interacting infinite systems and the voter model. Ann. Prob. 3, 643–663.Google Scholar
Karlin, S. (1968) Equilibrium behaviour of population genetics models with non-random mating II. J. Appl. Prob. 5, 487–566.CrossRefGoogle Scholar
Littler, R. A. (1975) Loss of variability in a finite population. Math. Biosci. 25, 151–163.Google Scholar
Sawyer, S. (1977) On the past history of an allele now known to have frequency p. J. Appl. Prob. 14, 439–450.Google Scholar
Watterson, G. A. (1983) Allele frequencies after a bottleneck. Monash University Statistics Research Report No. 83.Google Scholar
Watterson, G. A. (1984) Lines of descent and the coalescent. Theoret. Popn. Biol. 25.CrossRefGoogle Scholar