• Motoo Kimura

Articles written in Journal of Genetics

• Optimum mutation rate and degree of dominance as determined by the principle of minimum genetic load

It is demonstrated that by introducing what may be called the principle of minimum genetic load, the spontaneous mutation rate and the average degree of dominance of deleterious mutant genes may be derived theoretically from the total genetic damage and the rate of substitution of genes in horotelic evolution. The relations connecting these quantities may be expressed by a pair of equations:$$\left. \begin{gathered} \Sigma _\mu = \frac{{0 \cdot 3419E}}{{\bar h}}\left( {1 + 1 \cdot 720\bar h + ...} \right) \hfill \\ \bar h = 0 \cdot 6838\sqrt {\frac{E}{{2D}}} \left( {1 + 1 \cdot 018 \sqrt {\frac{E}{{2D}}} + ...} \right) \hfill \\ \end{gathered} \right\}$$, where Σμ is the spontaneous mutation rate per gamete per generation,h is the average degree of dominance in fitness of deleterious mutant genes,D is the total mutational damage or approximately the rate of inbreeding depression in fitness per unit increase in the inbreeding coefficient andE is the rate of substitution of genes in horotelic evolution. The above formulae are sufficiently simple to be checked by observational data now available. The present result offers, as a byproduct, a new theory of dominance which can account for the partial dominance in fitness of the normal alleles of “recessive” deleterious genes.

The implication of the principle of minimum genetic load for a cyclical change in environmental condition is also discussed.

• The role of compensatory neutral mutations in molecular evolution

A pair of mutations at different loci (or sites) which are singly deleterious but restore normal fitness in combination may be called compensatory neutral mutations. Population dynamics concerning evolutionary substitutions of such mutants was developed by making use of the diffusion equation method. Based on this theory and, also, by the help of Monte Carlo simulation experiments, a remarkable phenomenon was disclosed that the double mutants can easily become fixed in the population by random drift under continued mutation pressure if the loci arc tightly linked, even when the single mutants are definitely deleterious. More specifically, I consider two loci with allelesA andA’ in the first locus, and allelesB andB’in the second locus, and assign relative fitnesses 1, 1-s’, 1-s’ and 1 respectively to the four gene combinationsAB, A’B, AB’ andA’B’, wheres’ is the selection coefficient against the single mutants (s’ &gt; 0). Letv be the mutation rate per locus per generation and assume that mutation occurs irreversibly fromA toA’ at the first locus, and fromB toB’ at the second locus, whereA andB are wild type genes, andA’ andB’ are their mutant alleles. In a diploid population of effective size Ne (or a haploid population of 2Ne breeding individuals), it was shown that the average time (T) until joint fixation of the double mutant (A’B’) starting from the state in which the population consists exclusively of the wild type genes (AB) is not excessively long even for large 4Nes’ values. In fact, assuming2Nev = 1 we have -T = 54Ne for 4Nes’ = 400, and -T = 128Ne for 4Nes’ = 1000. These values are not unrealistically long as compared with -T~ 5Ne obtained for 4Nes’ = 0. The approximate analytical treatment has also been extended to estimate the effect of low rate crossing over in retarding fixation. The bearing of these findings on molecular evolution is discussed with special reference to coupled substitutions at interacting amino acid (or nucleotide) sites within a folded protein (orrna) molecule. It is concluded that compensatory neutral mutants may play an important role in molecular evolution.

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019