Selection and Mutation

Abstract

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

$$p = \mathop p\nolimits^* = {{\mathop w\nolimits_{12} - \mathop w\nolimits_{22} } \over {\left( {\mathop w\nolimits_{12} - \mathop w\nolimits_{22} } \right) + \left( {\mathop w\nolimits_{12} - \mathop w\nolimits_{11} } \right)}}.$$