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Clone-Selection and Optimal Rates of Mutation

Ilan Eshel
Journal of Applied Probability
Vol. 10, No. 4 (Dec., 1973), pp. 728-738
DOI: 10.2307/3212376
Stable URL: http://www.jstor.org/stable/3212376
Page Count: 11
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Clone-Selection and Optimal Rates of Mutation
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Abstract

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)).

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