Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-26T01:10:07.906Z Has data issue: false hasContentIssue false
  • English
  • Français

Global stability of genetic systems governed by mutation and selection

Published online by Cambridge University Press:  24 October 2008

P. A. P. Moran
P. A. P. Moran
Affiliation:
The Australian National University, Canberra
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper considers the behaviour of infinite haploid genetic populations under the influence of mutation and selection depending on a single locus. Under wide conditions the Perron–Frobenius theory of non-negative matrices and its generalization by Vere-Jones are used to prove that there is a single globally stable state of the population when there is a finite or, under more restrictive conditions, an infinite set of possible alleles.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 80 , Issue 2 , September 1976 , pp. 331 - 336
Copyright
Copyright © Cambridge Philosophical Society 1976

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

REFERENCES

(1)Edwards, R. E.Functional Analysis (New York, Holt, Rinehart and Winston, 1965).Google Scholar
(2)Moran, P. A. P.Wandering distributions and the electrophoretic profile. Theoretical Population Biology 8 (1975), 318–330.Google Scholar
(3)Moran, P. A. P. Wandering distributions and the electrophoretic profile. H. (To appear.)Google Scholar
(4)Ohta, T. and Kimura, M.A model of mutation appropriate to estimate the number of electrophoretically detectable alleles in a finite population. Genet. Rea. 22 (1973), 201–204.Google Scholar
(5)Ohta, T. and Kimura, M.Theoretical analysis of electrophoretically detectable alleles: models of very slightly deleterious mutations. American Naturalist 109 (1975), 137–145.Google Scholar
(6)Seneta, E.Non-negative Matrices (London, George Allen and Unwin, 1973).Google Scholar
(7)Vere-Jones, D.Ergodic properties of non-negative matrices. I. Pacific Journal of Mathematics 22 (1967), 361–386.Google Scholar
(8)Wright, S.Evolution in Mendelian populations. Genetics 16 (1931), 97–159.Google Scholar