Question

The allele for the hair pattern widow's peak is dominant. In a population of 1000 individuals, 510 show the dominant phenotype. How many individuals would you expect of each of the possible 3 genotypes for this trait? How do you answer this?

Answer 1

For the homozygous dominant genotype there will be `90` individuals. For the heterozygous genotype there will be `420` individuals and for the homozygous recessive genotype there will be `490` individuals.

Explanation:

You answer this by using Hardy-Weinberg Equation.

From the `1000` individuals, we know that `510` show dominant phenotype but we don't know how many of those individuals are homozygous dominant or heterozygous because both show dominant trait.

But we can infer that the remaining `490` individuals show recessive trait and therefore have homozygous recessive genotype.

`490/1000 = 0.49 = q^2`

`0.7 = q`

`p + q = 1`

`p = 1 - q`

`p = 0.3`

Then

`p^2 = 0.09`

`q^2 = 0.49`

`2pq = 2(0.7)(0.3) = 0.42`

Double Check:

`p^2 + 2pq + q^2 = 1`

`0.09 + 0.42 + 0.49 = 1`

You thus have

`0.09(1000) = 90 ->` with homozygous dominant genotype

`0.42(1000) = 420 ->` with heterozygous genotype

`0.49(1000) = 490 ->` with homozygous recessive genotype

Double Check:

`90 + 420 + 490 = "1000 individuals"`

`90 + 420 = "510 individuals " ->` with dominant phenotype