Question

If you know that a population is 75% the dominant phenotype and 25% is the recessive phenotype, can you determine approximately how many of the dominant phenotype are homozygous dominant and how many are heterozygous dominant? Try this mathematically

Answer 1

If dominant allele = p, and recessive allele = q,
and p+q = 1, then:

`{(p + q)}^(2) = {p}^(2) + 2pq + {q}^(2) \\ where \: {p}^(2) \: is \: homozygous \: domin \\ {q}^(2) \: is \: homozygous \: recessive \\ and \: 2pq = heterozygous`
So if 75% have the p, then p^2 = homozygous dominant

`{p}^(2) = {(.75)}^(2) = .5625`
And if the other 25% have the q, the q^2 = homozygous recessive

`{q}^(2) = {(.25)}^(2) = .0625`
Now those remaining MUST be the heterozygous, thus 2pq are those:
2pq = 2(.75)(.25) = .375

Therefore homozygous dominant are 56.3% and heterozygous are 37.5%