Question

A large population of moths contains 35% white moths caused by the double recessive genotype, bb. What are all the allelic and genotypic frequencies for this population?

Answer 1

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