Interpreting a Family Pedigree for a Recessive Trait
In a family, a recessive condition (affected = aa) appears in some members. Two unaffected parents (generation I) have three children: an affected son, an unaffected daughter, and an unaffected son. The unaffected daughter marries an unaffected man whose father was affected. They are planning children and want to know their risk. Assume the trait is autosomal recessive, both parents in generation I are carriers, and no new mutations occur. The family is confused because neither grandparent couple showed the condition, yet a child is affected.
1. Explain how two unaffected parents can have an affected child, and give the genotype of each generation-I parent and the affected son.
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An autosomal recessive condition only shows when both copies are recessive (aa). An unaffected person may be a carrier (Aa) and show no symptoms because the dominant allele A masks a.
Generation-I parents must both be Aa (carriers). Each passes 'a' with probability 1/2, so a child has 1/4 chance of aa (affected), 1/2 chance of Aa (carrier, unaffected), 1/4 chance of AA (unaffected, non-carrier).
The affected son is aa. This is why the condition can 'skip' a generation - the parents carried it silently.
2. Determine the probability that the unaffected daughter is a carrier, and then the probability that her first child with her unaffected husband will be affected.
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Daughter's carrier probability: she is unaffected, so she is either AA or Aa (aa excluded). Among unaffected offspring the ratio AA : Aa is 1 : 2, so P(she is Aa) = 2/3.
Husband's genotype: he is unaffected but his father was affected (aa), so he must have inherited one 'a' → he is definitely Aa (probability 1).
Child affected (aa): requires mother to pass 'a' AND father to pass 'a'.
- P(mother passes a) = P(she is Aa) × 1/2 = (2/3)(1/2) = 1/3.
- P(father passes a) = 1/2.
- P(child aa) = 1/3 × 1/2 = 1/6 ≈ 17%.
3. If their first child is affected, what does that reveal about the daughter's genotype, and what is then the risk for each subsequent child?
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An affected child (aa) must receive 'a' from both parents. Since the husband is Aa, the daughter must also carry 'a' - so she is confirmed Aa. (The 2/3 prior probability is now resolved to certainty.)
With both parents Aa × Aa, each subsequent child independently has a 1/4 (25%) chance of being affected, 1/2 chance of being a carrier, and 1/4 chance of being AA. Each pregnancy is independent, so previous outcomes do not change the 1/4 risk.