Question

What would be the probability that a mating between first cousins would produce a child with Tay-Sachs disease? What, then, is the relative risk of having a child with Tay-Sachs disease for first-cousin vs. random mating?

Answer 1

Tay-Sachs disease is a rare inherited disorder that progressively destroys the nerve cells in brain and spinal cord. It is very rare in general population and genetic mutations causes this disease,

If all the people who marry into the family are homozygous normal then the probability that a mating between first cousins would produce a child with Tay-Sachs disease is 1/144.

If the marraige takes place between first cousins, lets consider the risk of having a child affected with disease condition that has gene frequency q. If we have no knowledge about genes of male there is a chance 2pq that he is the carrier of this condition. If he is carrier there is 1 in 8 chance that his cousin is also carrier due to comon ancestry. The overall risk of an affected child is, 2pq x 1/8 x 1/4 = pq/16

If the marriage takes place between unrelated people i.e random mating, the risk would have been q2, the ratio of risk is, pq/16:q2 = p:16q

As it is a rare recessive condition, q will be small and p will therefore be almost 1 and the ratio simplifies to 1:16q

Regardless of any approximations it remains true that consanguineous marriages increases the chances of homozygosity and thus increases the risk of expression of Tay-Sachs disease.