Red hair ( rr = autosomal recessive) is found in approximately 4 percent of the
ID: 173924 • Letter: R
Question
Red hair (rr = autosomal recessive) is found in approximately 4 percent of the people in Norway. If we assume that the Norwegian population is in Hardy-Weinberg equilibrium with respect to hair color, what percentage of all marriages could potentially have a child with red hair?
Calculate p and q first, then calulate the frequency of the homozygotes and heterozygotes. In the population, there will be 2 homozygote types and one heterozygote.Only 3 out of the 4 possible matings will give red haired children. Use these data to calculate the probabilities of the 3 different matings that can result in red haired offspring and total them. Refer to the ‘Punnet Square’ on slide 13 of lecture 35 when you’re doing this.
10.24
25.92
100
2.56
12.96
10.24
25.92
100
2.56
12.96
Explanation / Answer
'rr' is found in 4% people. So, frequency of recessive genotype = 0.04 = q^2
q = 0.2; p = 1-0.2 = 0.8
Frequency of 'RR' = 0.8*0.8 = 0.64
Frequency of 'Rr' = 2pq = 2*0.8*0.2 = 0.32
Now, if there is a cross between 'rr' and 'rr', then all children will have red hair 0.04 * 0.04 = 0.0016
If there is a cross between 'RR' and 'rr', no children will have red hair.
If there is a cross between 'Rr' and 'Rr' then 1/4 children will have red hair. 1/4 * 0.32 * 0.32 = 0.0256
If there is a cross between 'Rr' and 'rr', then 1/2 children will have red hair = 1/2 * 0.32 * 0.04 = 0.0064
So, total frequency of population having 'rr' = 0.0016+0.0256+0.0064 = 0.0336 i.e. 3.36% of the population will have red hair.
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