Hardy-Weinberg equilibrium describes a state in which genotype frequencies are constant from generation to generation and in which genotype frequencies are a product of allele frequencies. This condition prevails in situations in which there are an absence of mutations, migrations, non-random mating and environmental factors favoring particular genotypes. In a paper published in 1908, G. H. Hardy sought to disprove the Mendelian idea that dominant genetic characteristics would tend to appear in the whole population, while recessive characteristics would tend to disappear. In that same year, Dr. Wilhelm Weinberg published a paper proving the same idea. Later, he went a step further to be the first one to apply it to human populations.

Figure. Hardy-Weinberg Equilibrium (HWE) plot

HelixTree includes a feature that allows you to determine how closely the respective genotypes in your data approximate a state of Hardy-Weinberg equilibrium. Pictured is a data set with 200 markers. By clicking in a location, the white table at the lower left is updated, showing the number of alleles the marker has, the p-value for the Hardy-Weinberg equilibrium correlation, the negative log of the p-value, and the Hardy-Weinberg equilibrium correlation R. You can zoom in on any point in the plot by Right-Clicking and diagonally dragging a rectangular region. You can also summarize all data for each marker and export HWE values into a separate spreadsheet.

Sometimes genotypes deviate from Hardy-Weinberg equilibrium due to genotyping errors. It may be beneficial to exclude such genotypes before performing association analysis. In the case of genome-wide association studies where several thousand genotypes might deviate from Hardy-Weinberg equilibrium, an efficient means for excluding these genotypes is needed.

HelixTree includes a HWE clean up script that rapidly filters genotypes that deviate from Hardy-Weinberg equilibrium according to a user-specified threshold. This script can be run on cases and controls simultaneously or on each separately. After running this script, genotypes that deviate from Hardy-Weinberg equilibrium are grayed-out in the spreadsheet and excluded from further analysis.