Correct Answer -Option b
Explanation- Ruling out the impossible pedigrees
Consider pedigree d :- Founding parents are not affected, therefore, they must be carriers so as to pass on the disease. If we consider dominant allele for the disease, then founding parents would have been afeected ones. Thus the recessive allele is responsible for the disease. With both parents as carriers, it is possible to get affected offspring -F1 (probability of 1/4). When affected F1 marries and produces offspring (F2), it must not be affected. The F2 offspring can be carrier or entirely unaffected (as the disease is mentioned as rare, the individuals marrying into the family are assumed to have no allele disease). But in the pedigree d it is shown that F2 also shows diesease condition. This is not possible, hence option d is wrong.
Consider pedigree c:- One of the founding parent is affected and the other one is carrier (If another parent is considered unaffected, all offsprings will be carrier, but this is not shown in pedigree c). Here the recessive allele is responsible for disease.The offsprings of founding parent are either affected or carrier. When affected F1 marries and produces offspring (F2), it must not be affected. The F2 offspring can be carrier (as the disease is mentioned as rare, the individuals marrying into the family are assumed to have no allele disease). Similarly, When carrier F1 marries and produces offspring (F2), it must not be affected, it must be a carrier. But in pedigree c carrier F1 is shown to produce affected offspring. Thus pedigree c is not a correct option.
Consider pedigree a:- To have all affected offsprings of founding parents, it is necessary that the allele responsible must be dominant. Here it is the female of founding parent who is affected, thus the alllele ia autosomal and not X-linked. Now though the pedigree inheritence pattern in pedigree a is possible, the population with dominant autosomal allele propagates abundantly. Since the disease is rare, this pedigree wont fit into the category. Thus pedigree a is wrong option for the given condition.
Now,
Consider pedigree b.- In pedigree b, the male of founding parent is shown affected, and all the female offsprins of founding parent are shown affected, therefore, the allele responsible is dominant and X-linked (Since females have two X chromosome, the single X-linked allele inherited from father wont be able to produce affected offspring, but it will produce a carrier, since all females are affected, the allele responsible is dominant.
See image for further clarification.
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