Genotype Frequencies & Hardy Weinberg

Genotype Frequency Operations are performed together with a Hardy-Weinberg QA test. Only Markers and Samples that have passed the basic Matrix QA, filtered by specified missingness thresholds as well as non-mismatching markers status will be considered in the Genotype Frequency count & Hardy Weinberg Operation.

Genotype Frequency count

A recount of Genotypes is done, and a 3×3 contingency table is created for each marker as in the following example:

AA Aa aa
Case 110 85 15
Control 90 72 48
All 200 157 63


Similarly to what’s exposed above, an alternate genotype frequency count is performed on the control population to calculate the Hardy-Weinberg test. This is necessary for non-autosomal chromosomes, where only the female samples in the control population are taken in account to calculate the Hardy-Weinberg test.

The Hardy-Weinberg test is calculated through the Chi-Square value, as in the following contingency table example:

AA Aa aa
Observed 90 72 48
Expected 75.6 100.8 33.6

To arrive at this table, first we calculate the frequency of every observed allele:

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

Having the equation for genotype frequencies:

pAA = freq A²
pAa = 2 × freq A × freq a
paa = freq a²

The expected frequencies are:

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

Once this contingency table is built for every marker, the X² (Chi-Square) is calculated as follows:

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.


The last test to be calculated in this Operation is the Observed and Expected Heterozygosity:

Observed Heterozygosity = obsAa / total genotypes count
Expected Heterozygosity = pAa

See Genotype Frequency & Hardy-Weinberg section for details on table displays.