Question

Allozyme phenotypes of alcohol dehydrogenase in the flowering plant Phox drummondii are determined by three co-dominant alleles of a single gene. In one sample of 70 plants the following data were obtained:

Genotype	A1A1	A2A2	A3A3	A1A2	A1A3	A2A3
Number	4	24	10	10	2	20

What is the frequency of the A2 allele in this sample?

0.628

0.238

0.557

0.432

0.337

Answer 1

For genes with three alleles such as A1, A2, and A3 with population frequencies are p, q, and r, the expected frequencies for the genotypes A1A1, A1A2, A2A2, A2A3, A3A3, and A1A3A are

A1A1 = p²,     A1A2 = 2pq, A2A2 = q²
A2A3 = 2qr, A3A3 = r², A1A3 = 2pr

Thus, the expected frequency of A2 allele = 2A2+ A1A2 + A2A3/ 2*70

= 48 + 10 + 20/ 140 = 0.5571

Answer 2

Consider A1, A2 and A3 are the three alleles of a particular gene and their frequencies are p, q, and r.

If we apply Hardy-Weinberg equilibriym, p + q + r = 1. Thus, (p + q + r)² = 1

If we expand this we get p²,  2pq,  q²,  2qr,  r²,  2pr = 1. In which p = A1, q = A2 and r = A3.

The formula to calculate the expected frequency of A2 allele is = 2*A2+ A1A2 + A2A3 / 2*70 = = 48 + 10 + 20/ 140 = 0.557