Question

How to calculate the frequency of heterozygous (Mm) in a random mating population if the total frequency of dominant phenotype is 0.19?

Answer 1

`0.18`, or `18%`

Explanation:

Use the Hardy-Weinberg equilibrium.

Alleles: `p+q=1`

`p="frequency of the dominant allele"`
`q="frequency of the recessive allele"`

Genotypes: `p^2+2pq+p^2=1`

`p^2="frequency of homozygous dominant genotype"`
`2pq="frequency of heterozygous genotype"`
`q^2="frequency of homozygous recessive genotype"`

In your scenario, the dominant phenotype has a frequency of `0.19`.

This is misleading, since both the `p^2` and `2pq` terms represent the dominant phenotype. The `2pq` term, while genotypically heterozygous, still displays the dominant phenotype.

On the other hand, just the `q^2` term represents all the recessive phenotypes in the population.

We can rearrange the second equation to see that:

`q^2=1-(p^2+2pq)`

and `p^2+2pq=0.19`, so `q^2=1-0.19=0.81`.

If `q^2=0.81`, we can determine `q`.

`q=sqrt(q^2)=sqrt(0.81)=0.9`

If `q=0.9`, use the allele equation to determine that `p=1-0.9=0.1`.

We now have all the information we need to find the heterozygous frequency, which equals `2pq`.

`2pq=2(0.9)(0.1)=color(red)(0.18`.