 In the first generation, the genotypic frequencies at the zygotic stage are \(p^2 , 2pq\) and \(q^2\) for \(A_1 A_1,\) \(A_1 A_2,\) \(A_2 A_2\) respectively, by the Hardy-Weinberg principle. The three genotypes produce successful gametes in proportion to their fitnesses, i.e., in the ratio \(w_{11}:w_{12}:w_{22}\).  The average fitness in the population is \(w = p^2 w_{11} + 2pq w_{12} + q^2 w_{22}\). Assuming there is no mutation, and that Mendel’s law of segregation holds, then an \(A_1 A_1\) organism will produce only \(A_1\) gametes, an \(A_2 A_2\) organism will produce only \(A_2\) gametes, and an \(A_1 A_2\) organism will produce \(A_1\) and \(A_2\) gametes in equal proportion (on average). Therefore, the proportion of \(A_1\) gametes, and thus the frequency of the \(A_1\) allele in the second generation at the zygotic stage, is: