In a population of gerbils in Hardy-Weinberg equilibrium, the frequency of homozygous recessive individuals is 0.33. What is the frequency of the dominant phenotype?

Question

BlackTom AI · Accepted Answer

Hardy-Weinberg relates genotype frequencies by p^2 + 2pq + q^2 = 1; here q^2 (homozygous recessive) = 0.33.

1) Relevant knowledge points and concepts
- In Hardy-Weinberg equilibrium p = frequency of the dominant allele, q = frequency of the recessive allele.
- Genotype frequencies are p^2 (homozygous dominant), 2pq (heterozygous), and q^2 (homozygous recessive).
- The dominant phenotype is expressed by both p^2 and 2pq, so its frequency = p^2 + 2pq = 1 − q^2.

2) Step-by-step reasoning
- Start from the given q^2 and compute q (allele frequency).
- Compute p = 1 − q.
- Compute dominant phenotype frequency as 1 − q^2 (or as p^2 + 2pq) and round appropriately.

3) Calculations with intermediate steps
- q^2 = 0.33.
- q = sqrt(0.33) = 0.574456... (approx).
- p = 1 − q = 1 − 0.574456... = 0.425544... (approx).
- p^2 = (0.425544...)^2 ≈ 0.181086 (homozygous dominant).
- 2pq = 2 × 0.425544... × 0.574456... ≈ 0.488826 (heterozygous).
- Dominant phenotype = p^2 + 2pq = 0.181086 + 0.488826 ≈ 0.669912 ≈ 0.67.
- Alternatively, 1 − q^2 = 1 − 0.33 = 0.67 directly.

4) Why the correct answer is correct
- Because individuals showing the dominant phenotype include both homozygous dominant and heterozygous genotypes; using Hardy-Weinberg identity yields dominant frequency = 1 − q^2 = 0.67. The direct subtraction avoids rounding error from intermediate sqrt.

5) Why the other options are incorrect
- b. 0.18 is approximately p^2 (homozygous dominant only), not the full dominant phenotype frequency.
- c. 0.43 is approximately p (the allele frequency of the dominant allele), which is not a phenotype frequency.
- d. 0.49 is approximately 2pq (heterozygotes only), not the combined dominant phenotype frequency.

6) Conclusion
- The frequency of the dominant phenotype is 0.67, which matches the provided correct answer (a. 0.67).

In a population of gerbils in Hardy-Weinberg equilibrium, the frequency of homozygous recessive individuals is 0.33. What is the frequency of the dominant phenotype?单项选择题

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