Interpreting a Family Pedigree for a Recessive Disorder
A couple, Amal and Karim, seek genetic counselling. Amal's brother has an autosomal recessive disorder caused by mutations in a single gene. Neither Amal nor her parents are affected. Karim is unaffected, but his maternal uncle has the same disorder. The population carrier frequency for this disorder is estimated at 1 in 25. Amal is pregnant with their first child. The couple wants to know the probability that their child will be affected, assuming no consanguinity and using the population carrier frequency for Karim. Assume Amal's parents are both carriers (obligate carriers, since they have an affected son).
1. Calculate the probability that Amal is a carrier, and the probability that Karim is a carrier, justifying each from the pedigree.
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Amal's carrier probability: Amal's parents are both obligate carriers (they have an affected child, so each must carry one mutant allele). For an unaffected child of two carriers, the possible genotypes are AA (1/4), Aa (2/4), aa (1/4). Since Amal is unaffected, she cannot be aa. Conditional on being unaffected, P(Aa) = (2/4) / (3/4) = 2/3.
Karim's carrier probability: Karim's maternal uncle is affected (aa), so Karim's maternal grandparents must each have contributed an 'a' - they are both carriers (or one is affected, but the problem states the uncle is the affected one; the standard assumption is both grandparents are carriers). Karim's mother is an unaffected child of two carriers, so P(mother is Aa) = 2/3. Karim is unaffected; his father is assumed unrelated with population carrier frequency 1/25. For Karim to be a carrier, he must inherit 'a' from his mother. P(Karim is Aa | mother Aa) = 1/2.
So P(Karim is Aa) = P(mother Aa) × P(Karim inherits a | mother Aa) = (2/3) × (1/2) = 1/3.
(Note: the population frequency 1/25 applies to Karim's father, not to Karim directly, because Karim has a known family history through his mother. Using 1/25 for Karim would ignore the pedigree information and underestimate his risk.)
2. Using the carrier probabilities, compute the probability that the child is affected, and explain how the counselling would change if Amal's carrier status were confirmed by testing.
Read the worked answer
Probability child is affected: Both parents must be carriers, and both must pass the mutant allele. P(child aa) = P(Amal Aa) × P(Karim Aa) × (1/4) = (2/3) × (1/3) × (1/4) = 2/36 = 1/18 ≈ 5.6%
If Amal's carrier status is confirmed (P = 1): P(child aa) = 1 × (1/3) × (1/4) = 1/12 ≈ 8.3%.
If Amal is confirmed NOT to be a carrier (P = 0): The child cannot be affected (0%), assuming Karim's allele is the only source and the disorder is fully recessive.
Counselling implication: Genetic testing converts a probabilistic estimate into near-certainty and can sharply change the couple's risk. If Amal is a carrier, the risk rises to ~8.3% and prenatal or preimplantation testing options can be discussed. If she is not a carrier, the couple can be strongly reassured. This illustrates why confirming carrier status by molecular testing is more informative than relying on pedigree probabilities alone.