A devastating new disease called UofM Disease is found to occur in 1 out of every 17,500 births. What would be the predicted percentage of carriers for this homozygous recessive disease in the population?

Question

BlackTom AI · Accepted Answer

Hardy-Weinberg equilibrium gives the relationship between allele and genotype frequencies: q^2 = frequency of the homozygous recessive phenotype, q = frequency of the recessive allele, p = frequency of the dominant allele, and 2pq = carrier (heterozygote) frequency.

1) Relevant concepts
- For an autosomal recessive disease, observed disease incidence = q^2.
- Solve q = sqrt(q^2), then carrier frequency ≈ 2pq (and when q is small, p ≈ 1 so 2pq ≈ 2q).

2) Step-by-step reasoning and calculations
- Given disease incidence = 1/17,500.
- q^2 = 1/17,500 = 0.00005714285714285714.
- q = sqrt(0.00005714285714285714) ≈ 0.0075598 (allele frequency, as a proportion).
  - Intermediates: sqrt(1/17,500) = 1 / sqrt(17,500) ≈ 1 / 132.28756555322954 ≈ 0.0075598.
- p = 1 − q ≈ 1 − 0.0075598 = 0.9924402.
- Carrier frequency = 2pq = 2 × 0.9924402 × 0.0075598.
  - Compute 0.9924402 × 0.0075598 ≈ 0.0075026.
  - Then 2 × 0.0075026 ≈ 0.0150052 as a proportion.
- Convert to percent: 0.0150052 × 100 ≈ 1.50052%, which rounds to 1.5%.

3) Why this is correct
Because the disease incidence directly gives q^2, taking the square root yields q and using 2pq yields the heterozygote (carrier) frequency. With q small, p ≈ 1 so carrier frequency is essentially 2q ≈ 1.51%, matching 1.5%.

4) Why other options are incorrect
- A (0.000114%) and B (0.0114%) are far too small; they do not correspond to q, q^2, or 2q for this incidence.
- C (0.015%) is two orders of magnitude too small (0.015% = 0.00015 proportion, not ~0.015).
- E (7.55%) is roughly 10× the allele frequency in percent (q ≈ 0.756%), not the carrier frequency.
- Option D (1.5%) matches the calculated carrier frequency ≈ 1.5005%.

Conclusion: The predicted percentage of carriers is 1.5%, which matches the provided correct answer.

A devastating new disease called UofM Disease is found to occur in 1 out of every 17,500 births. What would be the predicted percentage of carriers for this homozygous recessive disease in the population?Single choice

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