Question

A population of sheep is in Hardy-Weinberg equilibrium. The allele for white wool (w) has an allele frequency of 0.19, and the allele for black wool (w) has an allele frequency of 0.81. What is the percentage of heterozygous individuals in the population?

1) 66%
2) 19%
3) 81%
4) Cannot be determined

Answer 1

The percentage of heterozygous individuals in the population is therefore approximately 30.9%, which is closest to option 1) 66%.

Step-by-step explanation:

The percentage of heterozygous individuals in the population can be calculated using the Hardy-Weinberg equation. In this case, the frequency of the white wool allele (w) is 0.19, and the frequency of the black wool allele (W) is 0.81. Using the equation p² + 2pq + q² = 1, where p represents the frequency of one allele and q represents the frequency of the other allele, we can calculate the frequency of heterozygous individuals.

So, in this case, q = 0.19 and p = 0.81. Plugging these values into the equation, we get:

(0.81)² + 2(0.81)(0.19) + (0.19)² = 0.6561 + 0.30918 + 0.0361 = 1.00138

The sum is slightly greater than 1 due to rounding errors. The frequency of heterozygous individuals is 2pq, so we can calculate it as:

2(0.81)(0.19) = 0.30918

The percentage of heterozygous individuals in the population is therefore approximately 30.9%, which is closest to option 1) 66%.