Population Genetics: The Hardy-Weinberg Equilibrium

The Hardy-Weinberg equilibrium is a model that proposes allele (variations of a gene) and genotype (genetic makeup) frequencies within a population remain constant when the population is in equilibrium. If in equilibrium, were are able to calculate the allele and genotype frequencies for these populations. For a population to be defined as being in “Hardy-Weinberg equilibrium,” the population must meet a 5-point criteria:

1. No mutations are taking place.
2. No migration is occurring.
3. Random mating is occurring (no sexual selection).
4. No natural selection occurring (therefore no evolution).
5. The population is extremely large with equal opportunities for mating.

When we take a step back to think of this model, no real populations will ever meet the points of this criteria! However, this model has become very useful to make predictions of allele and genotype frequencies of populations based on population samples. It is important to note that this equilibrium principle only considers the gene(s) of interest and not all genes simultaneously!

The Hardy-Weinberg equilibrium uses the following formula: p² + 2pq + q² = 1, where:

p = frequency of the dominant allele
q = frequency of the recessive allele
p + q = 1

Therefore:
p² = frequency of the homozygous dominant genotype
2pq = frequency of the heterozygous genotype
q²= frequency of the homozygous recessive genotype

Example

 If 64% of a population have the homozygous dominant genotype BB, what percentage of the population are of the genotype Bb? Are of the genotype bb?

The frequency of BB = 64% = 0.64 = p²
This means that the frequency of the B allele =  p = √0.64= 0.80

Knowing that p + q = 1, this means that 1–p = q,  therefore:
q = 1 – 0.80 = 0.2

With both p and q now known, we can calculate the frequencies of both the Bb and bb genotypes using the Hardy-Weinberg equilibrium equation:

Bb = 2pq = 2(0.8)(0.2) = 0.32
Bb = q² = (0.2) = 0.04

Therefore the percentages of the other two genotypes within the population are 32% Bb and 4% bb.

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