Last week we derived a formula for calculating change in gene frequencies, given the initial gene frequency, the degree of dominance (if any), and the difference in fitness values (if any) of the various genotypes.

This week we’ll use that formula as it could apply in real-life.

Let’s revisit the following graph from Effectiveness of Selection: Initial Gene Frequency and Fitness Differences:

Assume that the ‘A₂‘ allele is undesired at the ‘A’ locus, and has a gene frequency q of 0.3. Assume too that the ‘A₂‘ allele is completely dominant, and with respect to fitness, that the A₁A₂ and A₂A₂ genotypes produce half as many offspring relative to the A₁A₁ genotype. Thus:

s₁ = 0
s₂ = 0.5
s₃ = 0.5

and

Let’s now assume that there is no dominance at the ‘A’ locus. With respect to fitness, the A₁A₂ genotype produces 25% fewer offspring relative to the A₁A₁ genotype, while the A₂A₂ genotype produces half as many offspring relative to the A₁A₁ genotype.

s₁ = 0
s₂ = 0.25
s₃ = 0.5

and

But what if ‘A₂‘ was completely recessive? Assume that the A₁A₂ genotype produces as many offspring relative to the A₁A₁ genotype, while the A₂A₂ genotype produces half as many offspring relative to the A₁A₁ genotype.

s₁ = 0
s₂ = 0
s₃ = 0.5

and

We have shown how, in one generation of selection, that the frequency q of the ‘A₂‘ allele drops noticeably from 0.3 to 0.2 if completely dominant. This is less marked if there is no dominance at the ‘A’ locus, where the frequency drops slightly from 0.3 to 0.24. The change in frequency is even less if the allele is completely recessive, from 0.3 to 0.27. These values can be seen graphically — below is the same graph as above, but with the inital gene frequency q = 0.3 marked with a red line. You can see how the steepness (change in frequency) differs for each line between where each begins at q = 0.3 (read this as generation 0) and one generation later (further to the right along the x-axis).

This concludes the Selection Strategies: Simply Inherited Traits section.