Hardy-Weinberg?

Question

A population of butterflies shows the following frequencies for wing coloration: 27 individuals with spotted wings and 973 with solid wings. Spotted is recessive, and the population is in hardy-weinberg equilibrium. How many of those with solid wings are expected to be homozygous for the dominant allele?

Can someone please help me understand how to do a problem like this. Thanks a lot.

Answer 1

The Hardy-Weinberg equation is based on the fact that the sum of the frequencies of the two alleles for a gene equals one.  So, in order to do this problem, first you have to determine the homozygous recessive frequency, then the frequency of the recessive allele and then from that you can determine the frequency of the dominant allele.  Here is how.

The number of individuals in the population is 27 + 973 = 1000.

If the frequency of the recessive allele is given by q, then the frequency of the homozygous recessives is given by q^2, so:

q^2 = 27/1000 = 0.027

q = 0.1643

So, if p is the frequency of the dominant allele, then:

p + q = 1

p = 1 - q

p = 1 - 0.1643

p = 0.8357

Since the frequency of the homozygous dominant is p^2, then:

p^2 = (0.8357)^2 = 0.698

Further, the frequency of the heterozygotes is:

2pq = 2 x 0.8357 x 0.1643 = 0.275

To check the answer:

p^2 + 2pq + q^2 = 1

0.698 + 0.275 + 0.027 = 1, yes it is correct.

Just as a side note, we had to assume there were only two alleles for the gene because the problem did not state specifically how many alleles.

So, since the frequency of the homozygous dominant is 0.698 and there are 1000 individuals, then 698 individuals would be expected to be homozygous dominant.  You would also expect 275 to be heterozygous and you already know that 27 are homozygous recessive (spotted wings).