Answer:
- The frequency of the dominant allele, p = 0.542
- The proportion of black moths that are heterozygous 2pq = 0.496
Explanation:
According to Hardy-Weinberg, the allelic frequencies in a locus are represented as p and q, referring to the allelic dominant or recessive forms. The genotypic frequencies after one generation are p² (Homozygous dominant), 2pq (Heterozygous), q² (Homozygous recessive). Populations in H-W equilibrium will get the same allelic frequencies generation after generation. The sum of these allelic frequencies equals 1, this is p + q = 1.
In the same way, the sum of genotypic frequencies equals 1, this is
p² + 2pq + q² = 1
Being
- p the dominant allelic frequency,
- q the recessive allelic frequency,
- p² the homozygous dominant genotypic frequency
- q² the homozygous recessive genotypic frequency
- 2pq the heterozygous genotypic frequency
In the exposed example, 79% of the moths of the species Biston betularia were black due to the presence of a dominant gene for melanism.
If the genotypic frequency of back moths is 0.79, then, by performing the following equation we can get the not-black moths genotypic frequency:
p² + 2pq + q² = 1
where p² is the homozygous dominant genotypic frequency, q² the homozygous recessive genotypic frequency, and 2pq is the heterozygous genotypic frequency.
As 0.79 is the phenotypic frequency of black moths, then this frequency equals p²+2pq.
Clearing the equation:
p² + 2pq + q² = 1
0.79 + q² = 1
q² = 1 - 0.79
q² = 0.21
The genotypic frequency of non-black moths is 0.21. So, from here we can calculate the allelic frequency:
q² = 0.21
q= v 0.21
q = 0.458
If 0.46 is the allelic frequency of non-black moths, then by clearing the equation p + q = 1, we can get the p allelic frequency:
p + q = 1
p + 0.458 = 1
p = 1 - 0.458
p = 0.542
- The genotypic frequency p² = (0.542)² = 0.294
- The heterozygote genotypic frequency
2 x p x q = 2 x 0.542 x 0.458 = 0.496
Finally, we can check this answer by clearing the following equation:
p² + 2pq + q² = 1
0.294 + 0.496 + 0.21 = 1
