Chapter 20, Problem 22P

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 $750$ 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. What is a genetic bottleneck?

b. Explain how a genetic bottleneck and its aftermath could result in a population that carries a lethal allele in high frequency

c. In the population described, what is the frequency of the recessive allele that produces Tay $-$ Sachs disease?

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