There are four alleles of gene G in a HW population The freq

There are four alleles of gene G in a H-W population. The frequencies of alleles G1, G2, G3, and G4 are represented by variables p, q, r, and s respectively. Use basic algebra to derive a general expression using variables for of each of the following...

a. the proportion of individuals that do not carry any G1 alleles:

b. the proportion of the heterozygotes that do not carry any G2 alleles:

Solution

allele frequency equation

p + q + r + s = 1

Genotype frequencies equation

p2 + 2pq + 2pr + 2ps + q2 + 2qr + 2qs + r2 + 2rs + s2 = 1

The number of genotypes with 2 alleles is 1 + 2 = 3

with 3 alleles 1 + 2 + 3 = 6

with 4 alleles 1 + 2 + 3 + 4 = 10

The proportion of individuals that do not carry G1 alleles is 0.25

The proportion of heterozygotes that do not carry any G2 alleles 0.5