In a population of red recessive and black beetles in HW equ

In a population of red (recessive) and black beetles in HW equilibrium, the frequency of black beetles is 91%. What is the frequency of the black allele? If the frequency of red beetles is 91%, what are the phenotype frequencies? The genotype frequencies? The allele frequencies? How many of each genotype in a population of 10000 beetles? Assume HW equilibrium.

Solution

If B is the dominant black allele and b is the red recessive allele such that frequency of dominant allele is represented by P and frequency of recessive allele is q.

If frequency of black beetles is 91%, then frequency of recessive red beetles (bb) is 9%.

Recessive red beetles (bb) = q2 = 9%.

ie q2 = 0.09.

Therefore frequency of red allele, q = 0.3.

As per HW Law, P + q = 1, P = 1 - q

P = 1 - 0.3 = 0.7.

Therefore allele frequency of black allele (B) = 0.7.

If frequency of red (bb) is 91%.

ie bb = q2 = 91.

q2 = 91%,

Therefore q = 0.91.

Allele frequency of recessive red allele (b) = 0.91

P+ q = 1, P = 1- q

P = 1- 0.91 = 0.09.

Therefore allele frequency of black allele (B) = 0.09.

Genotypic frequency of;

BB = (P2) = (0.09)2 = 0.008.

bb = (q2) = (0.91)2 = 0.83.

Bb = 2Pq = 2× 0.09 × 0.91 =0.162.

Number of individuals in population of 10000 beetles

BB = 0.008 × 10,000 = 80.

bb = 0.83 × 10,000 = 8300.

Bb = 0.162 × 10,000 =1620.