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 is expressed in plants with the homozygous recessive genotype (rr). According to the Hardy-Weinberg principle, which describes allele and genotype frequencies in a population in equilibrium, the frequency of the recessive genotype (rr) is represented as \( q^2 \), where \( q \) is the frequency of the recessive allele (r).
Given that 36\% of the population has white flowers: - The frequency of the rr genotype is 36\%, or \( q^2 = 0.36 \). To find the frequency of the recessive allele (r), calculate \( q \): \[ q^2 = 0.36 \] \[ q = \sqrt{0.36} = 0.6 \] Thus, the frequency of the recessive allele (r) in the population is 0.6.
To verify, note that the Hardy-Weinberg equation for genotype frequencies is: \[ p^2 + 2pq + q^2 = 1 \] Where \( p \) is the frequency of the dominant allele (R). Since \( q = 0.6 \): \[ p = 1 - q = 1 - 0.6 = 0.4 \] The frequency of the rr genotype (\( q^2 = (0.6)^2 = 0.36 \)) matches the given 36\%, confirming the calculation.