The equation representing the Hardy-Weinberg equilibrium is derived for a gene w
ID: 41370 • Letter: T
Question
The equation representing the Hardy-Weinberg equilibrium is derived for a gene with only two alleles.
a) Derive a similar equation describing the equilibrium proportions of genotypes for a gene with three alleles. [Hint: The Hardy-Weinberg equation above is just the binomial, (p+q), squared.]
b) A single gene with three alleles (IA, IB, and i) is responsible for the ABO blood groups. IAIA, or IAi is type A, IBIB, or IBi is type B, IAIB is type AB and ii is type O. Among Armenians, the frequency of IA is 0.360, the frequency of IB is 0.104, and the frequency of i is 0.536. Using your equation from part a above, calculate the frequencies of the three blood types [Hint: There are multiple genotypes with the same phenotype].
Explanation / Answer
a)for three allele: trinimial equation = (p+q+r)2= p2+q2+r+2qr+2pr+pq=1
b)
Blood type
O
A
B
AB
Frequency
r(ii)
p2 + 2pr (IA , iIA)
q2 +2qr (IB , iIB)
2pq(IAIB)
Allelic frequency:
IA = p =0.360
IB = q =0.104
i = r =0.536
Thus,
Blood group A= p2 + 2pr= (0.36)2 + 2(0.36X0.536)
=0.1296 + 0.386
= 0.516
Blood group B= q2 +2qr = (0.104)2 +2(0.104 + 0.563)
= 0.0108 + 0.111
=0.122
Blood group AB= 2pq = 2X 0.36X0.104= 0.074
Blood group O= r2 = 0.536X0.536= 0.287 ?0.29
Blood type
O
A
B
AB
Frequency
r(ii)
p2 + 2pr (IA , iIA)
q2 +2qr (IB , iIB)
2pq(IAIB)
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