Martin Pontz, Remus Stana, Yoav Ram

When the mutation rate is high and/or the population size is large, recurrent mutation can lead to multiple, independently generated copies of the same beneficial allele spreading through the population. However, classical analyses of fixation probability and time assume that the mutation rate is low and therefore, that fixation and extinction of a beneficial allele occur faster than the appearance of additional copies. We developed a diffusion equation approximation for the fixation probability and time that accounts for recurrent mutation, incomplete fixation, and fixation from standing genetic variation. Our results show that when the number of new beneficial alleles per generation in the population is greater than one, fixation is guaranteed, and fixation time is significantly lower than expected by the standard approximation. Moreover, we show that fixation time is significantly shorter if the initial allele frequency is greater than 0, or if fixation is defined for an allele frequency lower than 1.