We’ve used Hardy-Weinberg equilibria to determine phenotype frequencies in a population. The Hardy-Weinberg equations assume that a population is stable. In other words, allele frequencies are not changing—there’s no selection pressure.
But what happens when selection is acting upon a population? Theoretically, we understand that selection will favor certain alleles or allele combinations over others. This will shift the balance of alleles toward a new equilibrium. If we know the magnitude of the selection pressure, we can calculate the effect of selection on allele frequencies.
Let’s work through a sample problem to unpack this set of questions.
You and your medical team are summoned to Capitol City, where a strange epidemic has rendered 9% of the population sterile. Working rapidly, you discover that there’s a strong correlation between Factor G, a protein found in blood, and the fertile residents: all the fertile residents test positive for Factor G, but all the infertile residents test negative for Factor G. Later genetic and biochemical tests reveal that the population of Capitol City carries two alleles for a gene that is necessary for the production of Factor G such that G is dominant to g. All the fertile residents are genotypically GG or Gg. All gg individuals are now sterile. The original frequencies of G and g were as follows:
G = 0.7
g = 0.3
After the epidemic, what are the allele frequencies of G and g in the next generation?
Let’s define a new term first.
* Fitness, W. Fitness is a measure of reproductive success and should be a value between 0 and 1. If there is no selection pressure reducing the reproductive success of a genotype, then W = 1. If a genotype cannot reproduce (as in our sample problem above, where gg individuals are sterile), then W = 0.
So for our sample problem:
For GG, W = 1
For Gg, W = 1
For gg, W = 0.
We’ll make use of these values below.
Now we need to dive deeper into the math to connect s to Hardy-Weinberg equilibria.
We could have predicted that if q2 = 0, then p2 + 2pq = 1. So that set of calculations confirms our prediction, but we still have no idea what p and q are after selection. We need another set of equations for that task.
And there you have it! Now it’s your turn: what if the epidemic, rather than making gg individuals sterile, reduced their fertility by 50% What would the frequency of G and g be after one round of selection pressure? (I’ll provide or confirm the answer in the comments when someone asks for it.)
References:
Comprehensive Genetics coursepack, 2014 version, published by Dr. John Ellison, Texas A&M University
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