Question

Brown hair (H) is dominant to blonde hair (h). If there are 168 brown haired people in a population of 200, what are the allele frequencies for brown and blonde hair?

Answer 1

Brown hair H- dominant

Blonde hair h- recessive

There is a 200 population

168 of it are brown hair -homozygous (HH), heterozygous (Hh)

32 are blonde hair -hh

Using the Hardy-Weinberg equation,

p² + 2pq + q² = 1

Whereas:

p²= homozygous dominant (HH)

2pq= heterozygous dominant (Hh)

q²= recessive (hh)

Blonde hair (hh)= 200 (total population) - 168 (brown hair, HH, Hh)= 32

So, the blonde hair of the total population is = 16% or 0.16. This is equal to q².

q²= frequency of homozygous recessive (hh) = 0.16

q = √0.16 which is = 0.4

The sum of both frequencies is = 100% = p+q =1

Sum of both frequencies = 100% = p + q = 1

In turn, p = 1-q

p= 1- 0.4

p= 0.6

p² = the frequency of homozygous dominant (HH)

=pXp = 0.6 X 0.6

=0.36

2pq = the frequency of heterozygous brown hair

= 2 (0.6) (0.4) = 0.48

2pq= frequency of heterozygous dominant (Hh) = 0.48

0.36+ 0.48+ 0.16 = 1

Brown hair- 0.84

Blonde hair- 0.16