Question

14. Describe how you can test the hypothesis of Hardy-Weinberg equilibrium if all you know is observed genotype frequencies. Use complete sentences.

Answer 1

Let A be the dominant allele and a be recessive allele.

Observed Genotypes : AA, Aa, aa

p=freq A = ((observed AA count × 2) + observed Aa count) / (total genotypes count × 2)
q=freq a = ((observed aa count × 2) + observed Aa count) / (total genotypes count × 2)

The equation for genotype frequencies are

pAA = freq A² = p²
pAa = 2 × freq A × freq a = 2pq
paa = freq a² = q²

The expected frequencies are calculated as:

expAA = pAA × total genotypes count
expAa = pAa × total genotypes count
expaa = paa × total genotypes count

Using the above formula,  The Hardy-Weinberg equation is checked as:

p² + 2pq + q² = 1; p+q=1

Build a contingency table and calculate $\chi 2$ table using the formula

X² = (obsAA-expAA)²/(expAA) + (obsaa-expaa)²/(expaa) + (obsAa-expAa)²/(expAa)

From this X² value, a p-value can be calculated for a X² distribution with 1 degree of freedom.