Waiting for a compensatory mutation: Phase zero of the shifting-balance process

In highly integrated genetic systems, changes in any one component may have a deleterious effect on fitness, but coordinated, or compensatory, change in these components could lead to an overall increase in fitness compared with the current state. Wright designed his shifting-balance theory to account for evolutionary change in such systems, since natural selection alone can not lead to the new optimal state. A largely untreated aspect of the shifting-balance theory, that of the limiting impact of waiting for the production of new mutations, is analysed here. It is shown that the average time to double fixation of compensatory mutations is extremely long (of the order of tens or hundreds of thousands of generations), because selection is too effective in large populations, and mutations are too rare in small populations. Further, the probability that a new mutant will arise and undergo fixation quickly is extremely small. Tight linkage can reduce the time to fixation somewhat, but only in models in which the double heterozygote does not have reduced fitness. It is argued that the only reasonable way for compensatory mutations to become fixed in a population is if the new mutants are first allowed to achieve a moderate frequency through the relaxation of selection. Under these conditions, the time required to reach fixation is reasonably low, although the probability of being fixed is still small when the initial allele frequencies are low. It is likely that the waiting time for fixation of new mutants, which is here called phase zero, is the major limiting factor for the success of the shifting-balance process.