Question

In a population of plants, the allele for red flowers (R) is dominant over the allele for white flowers (r). If 36\% of the population has white flowers, what is the frequency of the recessive allele (r) in the population?

• A. 0.6
• B. 0.4
• C. 0.36
• D. 0.64

Hint:

In Hardy-Weinberg problems, the frequency of the recessive phenotype directly gives \( q^2 \). Take the square root to find the recessive allele frequency (\( q \)), and use \( p + q = 1 \) to find the dominant allele frequency if needed.

Answer 1

The Correct Option is A

The white flower phenotype occurs in plants with the homozygous recessive genotype (rr). Under Hardy-Weinberg equilibrium, the frequency of the recessive genotype (rr) is denoted as \( q^2 \), where \( q \) represents the frequency of the recessive allele (r).
Given that 36% of the population exhibits white flowers: - The frequency of the rr genotype is 0.36, hence \( q^2 = 0.36 \). To determine the frequency of the recessive allele (r), calculate \( q \): \[ q^2 = 0.36 \] \[ q = \sqrt{0.36} = 0.6 \] Therefore, the frequency of the recessive allele (r) in the population is 0.6.
As a verification, the Hardy-Weinberg equation for genotype frequencies is: \[ p^2 + 2pq + q^2 = 1 \] Where \( p \) is the frequency of the dominant allele (R). With \( q = 0.6 \): \[ p = 1 - q = 1 - 0.6 = 0.4 \] The calculated frequency of the rr genotype (\( q^2 = (0.6)^2 = 0.36 \)) aligns with the provided 36%, confirming the result.