Abstract
Evolution of mutation rate controlled by a neutral modifier is studied for a locus with two alleles under temporally fluctuating selection pressure. A general formula is derived to calculate the evolutionarily stable mutation rate μ(ess) in an infinitely large haploid population, and following results are obtained. (I) For any fluctuation, periodic or random: (1) if the recombination rate r per generation between the modifier and the main locus is 0, μ(ess) is the same as the optimal mutation rate μ(op) which maximizes the long-term geometric average of population fitness; and (2) for any r, if the strength s of selection per generation is very large, μ(ess) is equal to the reciprocal of the average number T of generations (duration time) during which one allele is persistently favored than the other. (II) For a periodic fluctuation in the limit of small s and r, μ(ess)T is a function of sT and rT with properties: (1) for a given sT, μ(ess)T decreases with increasing rT; (2) for sT </= 1, μ(ess)T is almost independent of sT, and depends on rT as μ(ess)T & 1.6 for rT << 1 and μ(ess)T & 6/rT for rT >> 1; and (3) for sT >/= 1, and for a given rT, μ(ess)T decreases with increasing sT to a certain minimum less than 1, and then increases to 1 asymptotically in the limit of large sT. (III) For a fluctuation consisting of multiple Fourier components (i.e., sine wave components), the component with the longest period is the most effective in determining μ(ess) (low pass filter effect). (IV) When the cost c of preventing mutation is positive, the modifier is nonneutral, and μ(ess) becomes larger than in the case of neutral modifier under the same selection pressure acting at the main locus. The value of c which makes μ(ess) equal to μ(op) of the neutral modifier case is calculated. It is argued that this value gives a critical cost such that, so long as the actual cost exceeds this value, the evolution rate at the main locus must be smaller than its mutation rate μ(ess).
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Selected References
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- Darnell J. E., Jr Variety in the level of gene control in eukaryotic cells. Nature. 1982 Jun 3;297(5865):365–371. doi: 10.1038/297365a0. [DOI] [PubMed] [Google Scholar]
- Ishii K., Matsuda H. Extension of the Haldane-Muller principle of mutation load with application for estimating a possible range of relative evolution rate. Genet Res. 1985 Aug;46(1):75–84. doi: 10.1017/s0016672300022461. [DOI] [PubMed] [Google Scholar]
- Ishii K., Matsuda H., Ogita N. A mathematical model of biological evolution. J Math Biol. 1982;14(3):327–353. doi: 10.1007/BF00275397. [DOI] [PubMed] [Google Scholar]
- Levins R. Theory of fitness in a heterogeneous environment. VI. The adaptive significance of mutation. Genetics. 1967 May;56(1):163–178. doi: 10.1093/genetics/56.1.163. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Matsuda H., Ishii K. Stationary gene frequency distribution in the environment fluctuating between two distinct states. J Math Biol. 1981 Feb;11(2):119–141. doi: 10.1007/BF00275437. [DOI] [PubMed] [Google Scholar]
- Takahata N., Ishii K., Matsuda H. Effect of temporal fluctuation of selection coefficient on gene frequency in a population. Proc Natl Acad Sci U S A. 1975 Nov;72(11):4541–4545. doi: 10.1073/pnas.72.11.4541. [DOI] [PMC free article] [PubMed] [Google Scholar]