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:
[tex]p+q=1[/tex]
[tex]p^{2}+2pq+q^{2}=1[/tex]
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:
[tex]p^{2}=\frac{37}{13+37}[/tex]
[tex]p^{2}=\frac{37}{50}[/tex]
[tex]p^{2}=0.74[/tex]
[tex]p=\sqrt{0.74}[/tex]
p = 0.86
For the black allele:
[tex]p+q=1[/tex]
[tex]q=1-p[/tex]
[tex]q=1-0.86[/tex]
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.
