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, initial p = f(A₁) = 0.001. The three curves trace f(A₁) over time for three modes of dominance. The Blue curve shows the case of dominance of W₁₁ to W₁₂ (W₁₁ = W₁₂ = 1.0). The Red curve shows an additive (semi-dominance) model, in which each W₂ allele decreases dW = 0.4, such that W₁₂ = 1.0 - 0.4 = 0.6., and  W₂₂ = 1.0 - (0.4+0.4) = 0.2. The Green curve shows the case where W₂₂ is recessive to W₁₂ (W₁₂ = 0.2). The difference between the shapes of the curves reflects how mean population fitness () varies as f(A₁)  1.0.

    NB: The dominance relationships of any two alleles at a locus are fixed genetically. The graph also shows the fate of a common allele under negative directional selection, IF Y-axis values are inverted top to bottom (1  0) and labelled f(A₂) = q. That is, the 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 curves can be obtained from similar selection coefficient values in the Hardy - Weinberg selection programs GSM in Excel, or natsel in Python. Important Note: REMEMBER that this is a graph of p, rather than q as elsewhere in these notes, or in the two programs.