You are studying a population of
100 people and discover that 36
of these people are ss for a
genetic condition. use the hardy-
weinberg equation to figure out
the frequencies of the s and s
alleles. what are the frequencies
of the ss, ss, and ss genotypes?

The frequency of the s allele is 0.6, the frequency of the S allele is 0.4

SS frequency = 0.16 (16%)

Ss frequency = 0.48 (48%)

ss frequency = 0.36 (36%)

Explanation:

When there are two alleles of a gene in a population, the frequency of each allele = 1. That means that the sum of the frequencies of both alleles is 100%

p + q = 1

For our alleles, that means S + s = 1

For the 3 possible genotypes from 3 alleles,

p² + 2pq + q² = 1

For our genotypes, that means S² + 2 x S x s + s² = 1

Since we know that 36 people have the genotype ss, we can add that into our equation:

S² + 2 x S x s + 36 = 1

Therefore, to work out the value of s, we take the square root of 36 () = 6.

Therefore s = 6, which we convert to 0.6 (because we are talking about frequencies not percentages)

Back to our initial equation

p + q = 1, so S + s = 1

We know s = 0.6, so

S + 0.6 = 1,

so S = 0.4

For the genotype frequencies

p² + 2pq + q² = 1

0.4² + 2 x 0.4 x 0.6 + 0.6² =1

0.16 + 0.48 + 0.36 = 1

p² is the SS frequency = 0.16

2pq is Ss frequency = 0.48

q² is ss frequency = 0.36

oxygen +1 most likely