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

    In a single-locus model with two alleles A₁ and A₂, initial p = f(A₁) = 0.001. The three curves trace f(A₁) over time for three modes of dominance relationships. The Blue curve shows the case of dominance of A₁ to A₂, such that W₁₁ = W₁₂ = 1.0 and W₂₂ = 0.2. The Red curve shows the additive (semi-dominance) model, in which each A₂ allele decreases dW = 0.4, such that W₁₁ = 1.0, W₁₂ = (1.0 - 0.4) = 0.6, and W₂₂ = 1.0 - (0.4 + 0.4) = 0.2. The Green curve shows the case where A₁ is recessive to A₂ , such that W₁₁ = 1.0 and W₁₂ = W₂₂ = 0.2. The difference between the shapes of the curves reflects how mean population fitness () varies as f(A₁)  1.0 (SR2019 4.2).

    The dominance relationships of any two alleles at a locus are fixed genetically. The graph can also illustrate the fate of a common allele under negative directional selection: invert the Y-axis values top to bottom (1  0) and label it f(A₂) = q. That is, the mathematical behaviors of advantageous and disadvantageous alleles are complementary for any particular dominance model.

    The principles presented in this graph will be explored in greater depth in the laboratory exercises for Natural Selection.

HOMEWORK: Demonstrate that these same curves can be obtained for f(B) = q, from appropriate values entered in the Hardy- Weinberg program GSM in Excel.