Let's assume that there are only two alleles for this gene, B and b. Since the double recessive genotype (bb) results in white moths, we know that the frequency of the b allele is 0.35^(1/2) = 0.59 (since b is homozygous recessive in all white moths). The frequency of the other allele (B) can be calculated as 1 - 0.59 = 0.41.
To calculate the genotypic frequencies, we can use the Hardy-Weinberg equation:
p^2 + 2pq + q^2 = 1
where p is the frequency of the B allele and q is the frequency of the b allele.
Substituting in our values, we get:
(0.41)^2 + 2(0.41)(0.59) + (0.59)^2 = 1
This simplifies to:
0.1681 + 0.4862 + 0.3481 = 1
So the genotypic frequencies are:
BB = 0.1681
Bb = 0.4862
bb = 0.3481
To summarize:
Allele frequencies:
B = 0.41
b = 0.59
Genotypic frequencies:
BB = 0.1681
Bb = 0.4862
bb = 0.3481