# 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.

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?
asked Nov 18, 2013 in Genetics

+1 vote

A)

where,
p = dominant allele frequency
q = recessive allele frequency
p^2 = frequency of the homozygous dominant individuals
2pq = frequency of the heterozygous individuals
q^2 = frequency of the homozygous recessive individuals

also,

p+q=1
p^2 + 2pq + q^2 = 1

Since 1 in 1000 are born with Tay-Sachs that is the frequency of aa, the homozygous recessive.

We also need to find q the recessive allele frequency,

since

q^2 = 1/1000

q = 0.0316

B)

The probability is equal to

2pq

since we know q, we can find p,

p=1-q = 0.968

so

2pq=0.0612

0.0612 is the proportion of the population that is heterozygous.  Therefore, to find the probability that two people both have it we just square this number.

0.0612^2 =0.003745

answered Nov 20, 2013 by ~Expert~ (464 points)