Question

A population of Muscovy ducks contains 13 birds with black masks and 37 birds with red masks. Red masks are the dominant trait. What is the frequency of the black allele? What is the frequency of the red allele? What is the frequency of heterozygotes?

Answer 1

Answer: Black allele has frequency of 0.14.

              Red allele has frequency of 0.86.

             The frequency of heterozygotes is 0.241

Explanation: Hardy-Weinberg model states the frequency of alleles in a population will stay in equilibrium as long as there are external influences. It is also used to determine alleles frequencies using the following equations:

$p+q=1$

$p^{2}+2pq+q^{2}=1$

p represents frequency of dominant allele;

q represents frequency of recessive allele;

2pq is frequency of heterozygotes;

For the frequency of red allele, which is dominant, we can use:

$p^{2}=\frac{37}{13+37}$

$p^{2}=\frac{37}{50}$

$p^{2}=0.74$

$p=\sqrt{0.74}$

p = 0.86

For the black allele:

$p+q=1$

$q=1-p$

$q=1-0.86$

q = 0.14

Frequency of heterozygotes is

2pq = 2(0.86)(0.14)

2pq = 0.241

Frequencies for a population of Muscovy ducks are 0.86 for red allele, 0.14 for black allele and 0.241 for heterozygote.