FSI (Fluctuating Selection among Individuals) Reduces the Mean Fixation Time (Generations) of a Mutation

A common assumption in molecular evolution is the fixed selection nature of a mutation, for instance, a neutral mutation is selectively neutral for all individuals who carry the mutation, and so forth a deleterious or beneficial mutation. Our recent work challenged this presumption, postulating that individuals with a specific mutation exhibit a fluctuation in fitness, short for FSI (fluctuating selection among individuals). Moreover, an intriguing phenomenon called selection-duality emerges, that is, a slightly beneficial mutation could be a negative selection (the substitution rate less than the mutation rate). It appears that selection-duality is bounded: the low-bound is the generic neutrality where the mutation is neutral by the means of fitness on average, while the up-bound is the substitution neutrality where the substitution rate equals to the mutation rate. In this paper, we conducted a thorough theoretical analysis to evaluate how many generations needed for a selection-duality mutation to be fixed in a finite population. A striking finding is that the mean fixation time of a selection-duality mutant, including the generic neutrality and the substitution neutrality, is approximately identical, which is considerably shorter than the case of strict neutrality without FSI. One may further envisage that the fast-fixation nature of selection-duality mutations could result in a considerable genetic reduction at linked sites.