Time for spreading of compensatory mutations under gene duplication.

Evolution by compensatory mutations is accelerated by gene duplication because selective constraint is relaxed by gene redundancy. A mutation is called compensatory if it corrects the effect of an earlier deleterious mutation. Without duplication, Kimura has shown that the time for spreading of compensatory mutations is much reduced by tight linkage between the two chromosomal sites of mutations. In this report, the time for spreading with gene duplication was studied by using the diffusion equation method of Kimura, together with computer simulations. It was shown that, when 2Nv- is much less than unity, the time for spreading is greatly shortened by gene duplication as compared with the case of complete linkage between the two sites of mutations, where 2N is the effective population size (haploid) and v- is the rate of compensatory mutations. However, if 2Nv- greater than 1, gene duplication is not effective for accelerating the evolution by such mutations.