Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-26T13:30:12.065Z Has data issue: false hasContentIssue false
  • English
  • Français

The survival of a mutant under general conditions

Published online by Cambridge University Press:  24 October 2008

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

Extract

In genetics it is of considerable interest to be able to calculate the probabilities that a mutant gene will either be lost to the population or that its allele will be lost, since, in general, if no further mutation occurs, one of these two events must ultimately take place in any finite population. A good deal of research has been done on this problem by Fisher (l) and Kimura (3) and the purpose of this paper is to extend their results to more general situations and to discuss the validity of their approximations.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 2 , April 1961 , pp. 304 - 314
Copyright
Copyright © Cambridge Philosophical Society 1961

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)Fisher, R. A., The genetical theory of natural selection (Oxford, 1930).CrossRefGoogle Scholar
(2)Harris, T. E., Some mathematical models for branching processes. Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (Berkeley and Los Angeles, 1951), 305–28.Google Scholar
(3)Kimura, M., Some problems of stochastic processes in Genetics. Ann. Math. Stat. 28 (1957), 882–901.CrossRefGoogle Scholar
(4)Moran, P. A. P., The survival of a mutant gene under selection. J. Aust. Math. Soc. 1 (1959), 121–6.CrossRefGoogle Scholar
(5)Moran, P. A. P., The survival of a mutant gene under selection, II. J. Aust. Math. Soc. 1 (1960), 485–91.CrossRefGoogle Scholar
(6)Moran, P. A. P., and Watterson, G. A., The genetic effects of family structure in natural populations. Aust. J. Biol. Sci. 12 (1958), 1–15.CrossRefGoogle Scholar
(7)Terrill, H. M. and Sweeny, L., An extension of Dawson's table of the integral of ex2. J. Franklin Inst. 237 (1944), 495–7;Google Scholar
Terrill, H. M. and Sweeny, L., An extension of Dawson's table of the integral of ex2. J. Franklin Inst. 238 (1944), 220–2.Google Scholar
(8)Watterson, G. A., On the relationship between a discrete and continuous diffusion process, with application to genetic populations. I. Theoretical aspects. II. Some finite populations models (to appear).Google Scholar
(9)Fisher, R. A., Stage of development as a factor influencing the variation in numbers of offspring, frequency of mutants and related quantities. Ann. Eugen., Lond., 9 (1939), 406–8.CrossRefGoogle Scholar
(10)Haldane, J. B. S., The equilibrium between selection and random extinction. Ann. Eugen., Lond., 9 (1939), 400–5.CrossRefGoogle Scholar