Question

Assuming that a diploid genomic locus has 3-alleles, A, C and G, in a population of N individuals, in generation “t”, such that the frequency of each of these alleles are p, q, and r respectively, derive the two tenets of Hardy Weinberg Equilibrium after one generation of random mating.

Answer 1

Let's first examine the tenets for two alleles;

Two tenets of Hardy Weinberg equilibrium for two alleles are

• p+q = 1, where p and q are gene frequencies for Dominant allele say A and recessive allele, say B respectively
• square the above to obtain p²+q² +2pq=1, where p²=genotypic frequency of individuals with homozygous A, q²=genotypic frequency of individuals with homozygous B, and 2pq = genotypic frequency of individuals with heterozygous AB

Two tenets of Hardy Weinberg equilibrium for three alleles are

• p+q+r = 1, where p, q and r are gene frequencies for alleles A,B, and C respectively.
• square the above to obtain p²+q² + r²+2pq + 2pr + 2 qr =1, where p²=genotypic frequency of individuals with homozygous A, q²=genotypic frequency of individuals with homozygous B,r²=genotypic frequency of individuals with homozygous Cand 2pq +2pr +2qr = genotypic frequency of individuals with heterozygous condition