Question

Question #bcc40

Answer 1

Alleles:
Dominant alleles: `0.02%`
Recessive alleles: `99.98%`

Genotypes:
Homozygous dominant: `99.96%`
Heterozygous: `0.04%`
Homozygous recessive: `0.00000004%`, or, basically `0%`

Explanation:

This is 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"`

The frequency of the dominant phenotype, being born with cleft palate, is `1/2500` or `0.0004`. This number represents both the homozygous dominant and heterozygous genotypes (both `p^2` and`2pq`).

Thus, just the the frequency of homozygous recessive genotypes and recessive (people who don't have cleft palate) phenotype, is equal to `q^2`, which is also

`1-"frequency of people with cleft palate"=1-0.0004=0.9996`

If `color(blue)(q^2=0.9996`, take the square root of both sides find that `color(red)(q=0.9998`.

Since `p+q=1`,

`p+0.9998=1`, so `color(red)(p=0.0002)`.

Find `p^2` and `2pq`:

`color(blue)(p^2)=(0.0002)^2color(blue)(=0.00000004`

`color(blue)(2pq)=2(0.0002)(0.9998)color(blue)(=0.0004`

Alleles:
Dominant alleles: `0.02%`
Recessive alleles: `99.98%`

Genotypes:
Homozygous dominant: `99.96%`
Heterozygous: `0.04%`
Homozygous recessive: `0.00000004%`, or, basically `0%`

Notice that rounding makes the percentages added up to slightly more than `100%`.

Also, the Hardy-Weinberg equilibrium is only true when the following conditions are met, which in reality is never:

• organisms are diploid.
• only sexual reproduction occurs.
• generations are non overlapping.
• mating is random.
• population size is infinitely large.
• allele frequencies are equal in the sexes.
• there is no migration, mutation or selection.