 Continuing with our one locus, two allele model, suppose that the \(A_1\) allele is selectively superior to \(A_2\), but recurrent mutation from \(A_1\) to \(A_2\) prevents \(A_1\) from spreading to fixation. The rate of mutation from \(A_1\) to \(A_2\) per generation, i.e., the proportion of \(A_1\) alleles that mutate every generation, is denoted \(u\). (Empirical estimates of mutation rates are typically in the region of \(10^{-6}\).) Back mutation from \(A_2\) to \(A_1\) can be ignored, because we are assuming that the \(A_2\) allele is at a very low frequency in the population, thanks to natural selection. What happens to the gene frequency dynamics under these assumptions? Recall equation (1) above, which expresses the frequency of the \(A_1\) allele in terms of its frequency in the previous generation. Since a certain fraction \((u)\) of the \(A_1\) alleles will have mutated to \(A_2\), this recurrence equation must be modified to: