Pedigree with an Unexpected Affected Daughter
A couple seeks genetic counseling. The husband is unaffected; the wife is unaffected. They have one affected daughter and one unaffected son. The wife's father was affected by the same rare condition; her mother was unaffected. The husband's family has no history of the condition. The condition is known to be caused by a single gene. The counselor notes that the couple is consanguineous: the husband and wife are first cousins through their shared grandmother, who was unaffected. The wife is now pregnant and asks about the risk. Assume the condition is fully penetrant and the disease allele is rare in the general population.
1. Determine the most likely mode of inheritance. Consider autosomal recessive, autosomal dominant, X-linked recessive, and X-linked dominant, and explain which fits all observations.
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Autosomal recessive fits best. The wife's father is affected (aa) and her mother unaffected, so the wife must be a carrier (Aa) - she is unaffected, consistent. The husband is unaffected but is a first cousin; through the shared grandmother he may also carry the allele. Two carrier parents can have an affected daughter (aa) and an unaffected son (A_). X-linked recessive fails: an affected daughter would need an affected father (she would inherit Xᵃ from him), but the husband is unaffected. X-linked dominant fails because the wife is unaffected yet has an affected daughter - an affected daughter must inherit the dominant allele from a parent, and neither parent is affected. Autosomal dominant also fails for the same reason: an affected child needs an affected parent, and both parents are unaffected. Autosomal recessive is the only model consistent with unaffected parents having an affected child, and the consanguinity raises the prior probability that the husband carries the same rare allele.
2. The wife's carrier status is certain. Estimate the husband's probability of being a carrier and the risk that the next child is affected, showing your reasoning about the pedigree.
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The wife is certainly Aa (her father was aa). The husband's carrier probability depends on the pedigree. His grandmother is the shared ancestor. If the grandmother was a carrier (Aa), each of her children has a 1/2 chance of being a carrier. The husband's parent (the grandmother's child) has probability 1/2 of being Aa; if that parent is Aa and the other parent is AA (population assumption), the husband has 1/2 chance of inheriting a. So P(husband Aa | grandmother Aa) = 1/2 × 1/2 = 1/4. Since the grandmother is unaffected but has an affected grandchild through the wife's line, the grandmother must be at least a carrier - indeed she passed the allele to the wife's father. So treat P(grandmother Aa) as effectively 1 given the pedigree. Then P(husband Aa) ≈ 1/4. Risk to the next child = P(husband Aa) × 1/4 = 1/4 × 1/4 = 1/16 ≈ 6.25%. If the husband is tested and found not to carry the allele, the risk falls to near the population carrier frequency.