The equations of the Hardy-Weinberg equilibrium are useful to get allelic and genotypic frequencies. In the example q = 0.538 ≅ 0.54 . Option D. 0.54
What is the Hardy-Weinberg Equilibrium?
The Hardy-Weinberg equilibrium theory states that allelic and genotypic frequencies remain the same through generations in a population that is in equilibrium.
Assuming a diallelic gene,
The allelic frequencies in a locus are represented as
- The frequency of the dominant allele f(X) is p
- The frequency of the recessive allele f(x) is q
The genotypic frequencies after one generation are
- p² (H0m0zyg0us dominant genotypic frequency),
- 2pq (Heter0zyg0us genotypic frequency),
- q² (H0m0zyg0us recessive genotypic frequency).
The addition of the allelic frequencies equals 1
p + q = 1.
The sum of genotypic frequencies equals 1
p² + 2pq + q² = 1
In the exposed example, the gene coding for eye color is diallelic.
- B is dominant and codes for blue
- b is recessive and codes for green
N = 100 individuals
Green eyed individuals = 29
Blue eyed individuals = 71
- The frequency of green eyed individuals is 29/100 = 0.29 ⇒ q²
- The frequency of blue eyed individuals is 71/100 = 0.71 ⇒ p² + 2pq
If q² = 0.29, then
q = √0.29
q = 0.538
If q = 0.538, then the value of p can be calculated by clearing the following equation
p + q = 1
p + 0.538 = 1
p = 1 - 0.538
p = 0.462
We can use the p value to calculate p²
If p = 0.462, then
p² = 0.462²
p² = 0.2134
And the frequency of the heter0zyg0us genotype is
2pq = 2 x 0.462 x 0.538
2pq = 0.497
p² + 2pq + q² = 1
0.213 + 0.497 + 0.29 = 1
The frequency of the recessive allele is q = 0.538.
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