Question

Tay–Sachs disease is an autosomal recessive disorder. Homozygous recessive individuals lack a key enzyme called hexosaminidase A, which presents as progressive mental and motor deterioration until death occurs around age 5. Heterozygous individuals, called Tay–Sachs carriers, develop no symptoms of the disease. Tay–Sachs disease was historically more prevalent within populations of Ashkenazi Jews, Pennsylvania Dutch, southern Louisiana Cajuns, and eastern Quebec French Canadians. Today, individuals descended from these populations are more likely to be Tay–Sachs carriers, but genetic testing within these populations has largely eliminated the occurrence of Tay–Sachs disease. For a randomly mating population, calculate the Tay–Sachs carrier frequency to three decimal points if 1 in 3600 individuals develops Tay–Sachs disease.

Answer 1

Answer:

0.033

Explanation:

Tay–Sachs disease is an autosomal recessive disorder. The possible genotypes and phenotypes are:

• TT = normal
• Tt = carrier
• tt = Tay-Sachs disease

I will use p to call the frequency of the dominant T allele, and q the frequency of the recessive t allele.

If the population is in equilibrium, the frequency of the tt genotype is q².

$q^2 = 1/3600\\\\q=\sqrt{1/3600} \\\\q=1/60=0.017\\\\and\\p + q = 1\\p=1-q\\p=0.983$

The frequency of the Tt genotype is 2pq.

$2pq= 2*0.983*0.017\\2pq=0.033$

The Tay–Sachs carrier frequency will be 0.033