Hardy-Weinberg: equilibrium, the test, and the Wahlund effect

Genotype frequencies

Allele frequency p

Frequency of allele A. The other allele, a, has frequency q = 1 - p.

Sample size

People genotyped, so 2n alleles.

Inbreeding F

Fraction of heterozygotes missing relative to 2pq. Negative F is a heterozygote excess.

Test

PLINK runs the exact test. The chi-square is unreliable when expected counts are small.

Sampling panel

Seed

500 samples of size n are drawn from a population truly in equilibrium at this p.

Why 1 degree of freedom: three genotype classes give 2 degrees of freedom, but the allele frequency used for the expected counts is estimated from the same data, and that costs one more. Using 2 df here is a common mistake.

Wahlund tab

Subpopulations

Allele frequencyWeight

Weights are the share of the pooled sample each subpopulation contributes. The pooled sample has n people.

Equilibrium

AA-

Aa-

aa-

Equilibrium

The same thing in R Copy

The same thing in R