Evolution by gene duplication and compensatory advantageous mutations.

Relaxation of selective constraint is thought to play an important role for evolution by gene duplication, in connection with compensatory advantageous mutant substitutions. Models were investigated by incorporating gene duplication by unequal crossing over, selection, mutation and random genetic drift into Monte Carlo simulations. Compensatory advantageous mutations were introduced, and simulations were carried out with and without relaxation, when genes are redundant on chromosomes. Relaxation was introduced by assuming that deleterious mutants have no effect on fitness, so long as one or more genes free of such mutations remain in the array. Compensatory mutations are characterized by the intermediate deleterious step of their substitutions, and therefore relaxation by gene redundancy is important. Through extensive Monte Carlo simulations, it was found that compensatory mutant substitutions require relaxation in addition to gene duplication, when mutant effects are large. However when mutant effects are small, such that the product of selection coefficient and population size is around unity, evolution by compensatory mutation is enhanced by gene duplication even without relaxation.