Homework Answers
Ans : Tay-sachs is a recessive disorder and is found in 1 in 3000 individuals every generation. Therefore this condition is in Hardy - Weinberg equilibrium.
Hardy-Weinberg equilibrium equation is,
p2 + 2pq + q2 = 1 and p + q = 1
where,
p2 = frequency of homozygous dominant genotype ("AA")
2pq = frequency of heterozygous genotype ("Aa")
q2 = frequency of homozygous recessive genotype ("aa")
p = frequency of dominant allele ("A")
q = frequency of recessive allele ("a")
a) Frequency of "aa" genotype = homozygous recessive genotype
Total individuals = 3000
Since Tay-Sachs disease is a recessive disorder (aa), the frequency of (aa) is represented as q2
Therefore,
q2 = 1 / 3000
q2 = 0.00033
b) Frequency of the q allele
We have calculated q2 = 0.00033
Therefore,
q = √0.00033
q = 0.0182
c) Frequency of p allele
We have equation ,
p + q = 1
Substituting q = 0.0182 in equation , we get
p + 0.0182 = 1
p = 1 - 0.0182
p = 0.9818
d) Carriers means the individuals have both the allele 'A' and 'a' in their genotype but is not expressing as it is a recessive disorder,
Therefore,
Frequency of individuals who are carriers for Tay-Sachs disorder = Frequency of heterozygous genotype (Aa)
Frequency of heterozygous genotype (Aa) = 2pq
We have p = 0.9818 and q = 0.0182
Substituting,
2pq = 2 x 0.9818 x 0.0182
= 0.0357
e) Frequency of homozygous dominant (AA) = p2
We have p = 0.9818
Therefore,
p2 = (0.9818)2
p2 = 0.9639
Final answer :
a) Frequency of "aa" genotype = q2 = 0.00033
b) Frequency of "q" allele = 0.0182
c) Frequency of "p" allele = 0.9818
d) Frequency of individuals who are "carriers" for Tay-Sachs = "2pq" = 0.0357
e) Frequency of "homozygous dominant (AA)" = " p2 " = 0.9639
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1. Tay Sachs disease is an inherited disorder. Children who are born with Tay Sachs have progressive neurological problems and typically die before age 4. It is inherited in an autosomal recessive manner Below are pedigrees from two families where some members of a family have Tay Sachs disease. Neither Hillary nor Justin have Tay Sachs disease. If Hillary and Justin have a child, what is the chance this child will have...
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