Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-30T00:24:19.252Z Has data issue: false hasContentIssue false
  • English
  • Français

Global stability of genetic systems governed by mutation and selection. II

Published online by Cambridge University Press:  24 October 2008

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

Abstract

An infinite genetic population of haploid particles is considered in which selection is controlled by a single locus at which there are an infinite number of possible alleles. These alleles are arranged in an infinite sequence and mutation occurs only to nearest neighbours. This is the ‘ladder model’ of Ohta and Kimura which was put forward as a possible explanation of the distributions of electromorphs in electrophoretic observations. Following an earlier paper, conditions are obtained on the selection coefficients which ensure that a stationary stable state exists. One such model is solved explicitly. The problem, important in evolutionary theory, of the rate of approach to such stationary states starting from some other state, is also discussed briefly.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 81 , Issue 3 , May 1977 , pp. 435 - 441
Copyright
Copyright © Cambridge Philosophical Society 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

REFERENCES

(1)Kingman, J. F. C.Coherent random walks arising in some genetic models. Proc. Roy. Soc. Ser. A 351 (1976), 19–31.Google Scholar
(2)Mirsky, L.An introduction to linear algebra (Oxford, Clarendon Press, 1955).Google Scholar
(3)Moran, P. A. P.Wandering distributions and the electrophoretic profile. Theoret. Populn. Biology 8 (1975), 318–330.CrossRefGoogle ScholarPubMed
(4)Moran, P. A. P.Global stability of genetic systems governed by mutation and selection. Math. Proc. Cambridge Philos. Soc. 80 (1976), 331–336.CrossRefGoogle Scholar
(5)Ohta, T. and Kimura, M.A model of mutation appropriate to estimate the number of electrophoretically detectable alleles in a finite population. Genetical Research 22 (1973), 201–204.CrossRefGoogle Scholar
(6)Ohta, T. and Kimura, M.Theoretical analysis of electrophoretically detectable alleles: models of very slightly deleterious mutations. Amer. Naturalist 109 (1975), 137–145.CrossRefGoogle Scholar
(7)Seneta, E.Non-negative Matrices (London, George Allen and Unwin, 1973).Google Scholar
(8)Vere-Jones, D.Ergodic properties of non-negative matrices. Pacific J. Math. 22 (1967), 361–386.CrossRefGoogle Scholar