Two Families and a Recessive Disorder
A couple, both unaffected, have a child with an autosomal recessive disorder. Genetic testing shows both parents are heterozygous carriers. The mother is pregnant again. Separately, the mother's brother, who is also unaffected, is planning children with a woman from a population where the carrier frequency for this disorder is 1 in 50. The family wants to know the risk for the new baby and whether the brother should be tested. A counselor notes that the disorder allele is rare and that the parents' first affected child changes the probability calculations for relatives.
1. Calculate the probability that the new baby will be affected and the probability it will be an unaffected carrier.
Read the worked answer
Both parents are carriers (Aa × Aa). The Punnett square gives 1 AA : 2 Aa : 1 aa. The probability the baby is affected (aa) is 1/4, or 25%. The probability the baby is an unaffected carrier (Aa) is 2/4 = 1/2, or 50%. The probability of being unaffected is 3/4. Note that among unaffected children, the chance of being a carrier is 2/3, which matters when counseling the child later. These probabilities are independent for each pregnancy; the previous affected child does not change the 25% risk for this pregnancy.
2. Estimate the risk that the mother's unaffected brother has a child with the disorder, and explain why testing him would change the estimate.
Read the worked answer
The brother's parents must both be carriers because they had an affected child (the mother's affected nephew is not relevant here - the affected child is the mother's child, so the grandparents' status must be inferred). Actually the affected child belongs to the mother, so the mother is a known carrier. Her brother's carrier probability comes from their parents: if both grandparents are carriers, an unaffected sibling has a 2/3 chance of being a carrier. But we do not know the grandparents are carriers unless the disorder appeared in their children. The mother is a carrier, so at minimum one grandparent contributed the allele; the brother's risk is 1/2 if one parent is a carrier, or 2/3 if both are. Using the standard assumption that both parents are carriers, the brother's carrier probability is 2/3. His partner's carrier probability is 1/50. The chance both are carriers is (2/3)(1/50) = 2/150 ≈ 1.3%. If both are carriers, the chance of an affected child is 1/4, so the overall risk is about 1.3% × 25% ≈ 0.33%, roughly 1 in 300. Testing the brother would replace the 2/3 estimate with certainty: if he is not a carrier, the risk drops to essentially zero (barring new mutations); if he is a carrier, the risk becomes 1/4 × 1/50 = 1/200.