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2) Tay-Sachs disease is an autosomal recessive neurological disorder that is fatal in infancy. Despite its...

2) Tay-Sachs disease is an autosomal recessive neurological disorder that is fatal in infancy. Despite its invariably lethal effect, Tay-Sachs disease occurs at very high frequency in some Central and Eastern European (Ashkenazi) Jewish populations. In certain Ashkenazi populations, 1 in 1000 infants has Tay-Sachs disease. Population biologists believe the high frequency is a consequence of genetic bottlenecks caused by pogroms (genocide) that have reduced the population multiple times in the last several hundred years.

a) In the population described, what is the frequency of the recessive allele that produces Tay-Sachs disease?

b) Assuming mating occurs at random in this population, what is the probability a couple are both carriers of Tay-Sachs disease?

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Answer #1

Normal allele = T

Tay sach allele = t

Frequency of population with this disease = 1/1000

Genotypic frequency = tt = 1/1000 = 0.001

Allelic frequency of t = √0.001 = 0.0316

Allelic frequency of T = 1 - 0.0316 = 0.9684

Frequency of carriers = Tt = 2 × 0.0316 × 0.9684 = 0.0612

Probability that both individuals of a couple are carriers = 0.0612 × 0.0612 = 0.00374

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