Question

A population has a gene with 2 alleles, G and g. The frequency of the G allele is 0.8. The frequency of the g allele is 0.2. This is all that you know. What is the frequency of the GG genotype?

Answer 1

Answer: The frequency of GG is 0.64

Explanation: using Hardy-weinberg equation

g^2 + 2Gg + G^2 =1 ................(1)

And the sum of the alleles at the locus must be 1.

Therefore:

G + g = 1 ..............................(2)

Since

G=0.8

g= 0.2

G^2 =GG (Homozygous G gene)

g^2 = gg (Homozygous g gene)

Using equation 1

GG+ (2×0.8×0.2) + gg =1

Therefore

GG + 0.32 + gg = 1

GG + gg = 0.68...............(3)

Solving equation 2

G + g = 1

g = 1 - G

Square both side

g^2 = (1 - G)^2 ...............4

Where g^2 = gg

Therefore gg = (1 - G)^2.............(5)

Substitute equation 5 into equation 3

GG + (1 - G)^2 = 0.68

Therefore

GG = 0.68 - (1 - G)^2

GG = 0.68 - (1 - 0.8)^2

GG = 0.68 - 0.04

GG = 0.64