Testing for Hardy Weinberg Proportions

If a population is in equilibrium, then it is randomly mating for the locus in question, and selection, migration, mutation, and small population size have not significantly influenced the genotypic frequencies since random mating last took place. To determine whether these conditions are met, the genotypic proportions expected under the Hardy-Weinberg law must be compared with the observed genotypic frequencies. To do so, we first calculate the allelic frequencies, then find the expected genotypic frequencies by using the square of the allelic frequencies, and finally compare the observed and expected genotypic frequencies by using a chi-square test.

2pq = f(A1A2) q2 = f(A2A2) 2pr = f(AA3) 2qr = f(A2A3) r2 = f(A3A3)

The square of the allelic frequencies can also be used to calculate the expected genotypic frequencies for loci with four or more alleles.

Worked Problem

Jeffrey Mitton and his colleagues found three genotypes (R2R2, R2R3, and R3R3) at a locus encoding the enzyme peroxidase in ponderosa pine trees growing in Colorado. The observed numbers of these genotypes at Glacier Lake, Colorado, were:

Genotypes

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