Change in frequency of a rare allele under Positive Directional Selection
Dominant, Additive Semi-Dominant, & Recessive cases

    In a single-locus model with two alleles A₁ and A₂, let  initial q = f(A₂) = 0.001. The three curves trace f(A₂) over time for three modes of dominance. The Blue curve shows the case where A₂ is dominant to A₁ (W₂₂ = W₁₂ W₁₁). The Red curve shows an additive (semi-dominance) model, in which each A₂ allele decreases fitness by the same amount, such that W₂₂ W₁₂   W₁₁. The Green curve shows the case where A₂ is recessive to A₁ (W₁₁ = W₁₂ W₂₂). The differences between the shapes of the curves reflect how mean population fitness () varies as q = f(A₂)  1.0.

    Remember: the dominance relationships of the two alleles with respect to fitness are fixed genetically, according to whether the A₁A₂ heterozygote is more similar to the A₁A₁ or A₂A₂ homozygotes. It is not determined by the phenotypic values themselves.

    The information in the graph also shows the fate of a common allele under negative directional selection, IF the Y-axis values were inverted top to bottom (1  0) and labelled f(A₁) = p. That is, the behavior of the two alleles at a locus are complementary for any particular dominance model.

HOMEWORK: (1) As part of the lab exercises, show that these curves can be obtained with the appropriate selection coefficients (s) in the Hardy - Weinberg selection programs GSM in Excel, or natsel in Python. (2) Prove the complementarity of the behavior of the dominant and recessive alleles.