6.1.2(f) - Hardy-Weinberg allele-frequency calculations

Model And Symbols

An allele frequency is the proportion of all copies of a gene in a population that are a particular allele. In a diploid population, each individual has two alleles for a gene, so the gene pool contains twice as many allele copies as there are individuals.

For a simple two-allele locus, use:

• $p$ for the frequency of one allele, often the dominant allele in simple examples
• $q$ for the frequency of the other allele, often the recessive allele in simple examples

Because those two alleles make up all the alleles at that locus:

The identity p + q = 1 holds for a two-allele locus even outside equilibrium. Under the Hardy–Weinberg model, random union of gametes predicts the following genotype frequencies:

For alleles A and a, the terms mean:

[DIAGRAM: hardy_weinberg_equation_map: Lesson 146: Hardy-Weinberg allele-frequency calculations - diagram 01; asset_slug: 146_m06_1_2_hardy_weinberg_allele_frequency_calculations__diagram_01; recommended_method: drawn_biology; description: A deterministic 16:9 flow diagram mapping allele frequencies p and q to genotype frequencies p^2, 2pq and q^2, with the two OCR-provided equations and labels for AA, Aa and aa.]

An Aa offspring can arise from A in the egg and a in the sperm (probability pq), or a in the egg and A in the sperm (qp). Adding these mutually exclusive outcomes gives 2pq. AA requires two A gametes, giving p², and aa requires two a gametes, giving q².

When genotypes are counted directly, count allele copies: the frequency of A is (2 × number of AA + number of Aa)/(2 × total individuals). Taking the square root of a recessive phenotype frequency instead requires the equilibrium model.

A frequency is a proportion, so it is usually written as a decimal between 0 and 1. A percentage is found by multiplying the frequency by 100. For example, a frequency of 0.04 is 4%.

Before using an equation, decide whether the information describes an allele frequency or an expected genotype frequency.

From Recessive Phenotype

Many Hardy-Weinberg questions start with the frequency of a recessive phenotype. In a simple dominant/recessive example, individuals with the recessive phenotype must be homozygous recessive, such as aa. That means the recessive phenotype frequency is $q^2$, not $q$.

The safe route is:

1. Convert the recessive phenotype frequency into a decimal.
2. Set this equal to $q^2$.
3. Take the square root to find $q$.
4. Use $p + q = 1$ to find $p$.
5. Use the requested term, such as $2pq$, and convert to a percentage if needed.

The biggest trap is treating the recessive phenotype frequency as $q$. If 9 in 10 000 show the recessive phenotype, 0.0009 is $q^2$. The allele frequency $q$ is the square root of that value.