A population is in H-W equilibrium if through generations, the sum of the allelic frequencies equals 1, as well as the sum of the genotypic frequencies equals 1. p = 0.3676 and q = 0.6324.
In a population that is in H-W equilibrium, the allelic frequencies in a locus are represented as p and q. Assuming a diallelic gene,
The allelic frequencies in a population are
• p is the dominant allele frequency,
• q is the recessive allele frequency.
The genotypic frequencies after one generation are
• p² (H0m0zyg0us dominant genotypic frequency),
• 2pq (Heter0zyg0us genotypic frequency),
• q² (H0m0zyg0us recessive genotypic frequency).
If a population is in H-W equilibrium, it gets the same allelic and genotypic frequencies generation after generation.
p + q = 1.
p² + 2pq + q² = 1
According to this framework, and following the problem statement, the frequency of individuals with sickle-cell disease is 0.40.
Sickle-cell disease is a recessive trait.
People with the disorder has two copies of the recessive allele.
F(ss) = q² = 0.40
To get the allelic frequency q, we just eed to take the square root of the q² value.
q² = 0.40
q = √0.40
q = 0.6324
Now, if you want to get the dominant allele frequency, p, you just need to clear the following equation,
p + q = 1
p = 1 - q
p = 1 - 0.6324
p = 0.3676
So, the frequency of the dominant allele is f(S) = p = 0.3676 and the frequency of the recessive allele is f(s) = q = 0.6324.
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