Skip to main content Accesibility Help

Clone-selection and optimal rates of mutation

  • Ilan Eshel (a1)

The paper employs methods of multitype branching processes to evaluate the probability of survival of mutable clones under environmental conditions which are unfavorable to the original parent of the clone. When other factors are taken to be constant, the long-term survival probability of a clone is implicitly demonstrated as a function of the intrinsic rate of mutation carried by this clone. The existence of a mutation rate which maximizes clone survival probability is shown and the effects of environmental deterioration on this optimal rate are studied. Finally, rigorous quantitative results are obtained for the classical situation of a Poisson distribution of offspring numbers. These results are then applied to the biological problem of indirect selection (Eshel (1972)).

Hide All
[1] Nei, M. (1967) Modification of linkage intensity by natural selection. Genetics 57, 625626.
[2] Nei, M. (1969) Linkage modification and sex difference in recombination. Genetics 63, 681699.
[3] Feldman, W. M. (1972) Selection for linkage modification I: random mating populations. Theor. Pop. Biol. 3, 324346.
[4] Karlin, S. and Mcgregor, J. (1973) Toward a theory of modifier genes. Theor. Pop. Biol. To appear.
[5] Karlin, S. and Mcgregor, J. (1972) The evolutionary development of modifier genes. Proc. Nat. Acad. Sci. U.S.A. 69, 36113614.
[6] Fisher, R. A. (1958) The Genetical Theory of Natural Selection. Dover, New York.
[7] Eshel, I. (1973) Clone selection and the evolution of modifier genes. Theor. Pop. Biol. To appear.
[8] Kimura, M. (1960) Optimum mutation rate and degree of dominance as determined by the principle of minimum genetic load. J. Genetics 57, 2134.
[9] Kimura, M. (1967) On the evolutionary adjustment of spontaneous mutation rates. Genet. Res. 9, 2334.
[10] Karlin, S. and Mcgregor, J. (1968) The role of the Poisson progeny distribution in population genetics models. Math. Biosci. 2, 1117.
[11] Harris, T. (1963) The Theory of Branching Processes. Springer-Verlag, Berlin.
[12] Dwass, M. (1969) The total progeny in a branching process and a related random walk. J. Appl. Prob. 6, 682686.
[13] Karlin, S. (1966) A First Course in Stochastic Processes. Academic Press, New York.
[14] Crow, J. F. and Kimura, M. (1970) An Introduction to Population Genetics Theory. Harper and Row, New York.
[15] Moran, P. A. P. (1962) The Statistical Processes of Evolutionary Theory. Clarendon Press, Oxford.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed