Selection and Mutation

One of the conclusions of the previous chapter was that the existence of selective differences among genotypes generally leads to changes in gene frequencies. Assuming Hardy-Weinberg proportions, the frequency p’ of A1 in any generation is related to its frequency p in the previous generation by $$p' = {{\mathop w\nolimits_{11} \mathop p\nolimits^2 + \mathop w\nolimits_{12} pq} \over {\mathop w\nolimits_{11} \mathop p\nolimits^2 + 2\mathop w\nolimits_{12} pq + \mathop w\nolimits_{22} \mathop q\nolimits^2 }},$$ where the w ij are defined in Section 1.6. The change Δp in the frequency of A1 is thus $$\Delta p = pq{{\mathop w\nolimits_{11} p + \mathop w\nolimits_{12} \left( {1 - 2p} \right) - \mathop w\nolimits_{22} q} \over {\mathop w\nolimits_{11} \mathop p\nolimits^2 + 2\mathop w\nolimits_{12} pq + \mathop w\nolimits_{22} \mathop q\nolimits^2 }}.$$ Clearly Δp=0 whenever p=0 or p=1, corresponding to fixation of A2 or A1. Δp is also zero when $$p = \mathop p\nolimits^* = {{\mathop w\nolimits_{12} - \mathop w\nolimits_{22} } \over {\left( {\mathop w\nolimits_{12} - \mathop w\nolimits_{22} } \right) + \left( {\mathop w\nolimits_{12} - \mathop w\nolimits_{11} } \right)}}.$$