3.7.2Genetics, Evolution and EcosystemsCore

Hardy–Weinberg and Allele Frequencies

The Hardy–Weinberg model links allele frequencies to expected genotype frequencies under specified conditions. Distinguish an allele’s frequency from the frequency of a recessive phenotype.

35 min Inheritance and Gene Pools

What you'll be able to do

Calculate allele frequencies from genotype counts
Use p+q=1 and p²+2pq+q²=1
Evaluate equilibrium assumptions and departures

Count gene copies rather than just individuals

For a diploid population at a two-allele locus, there are two allele copies per individual. If p is the frequency of A and q the frequency of a, p+q=1. Count A copies as twice the number of AA individuals plus the number of Aa individuals, divided by twice the population size.

An individual carries a genotype, while allele frequency describes a population’s gene pool. A frequency is not the same as a raw count, and a change in population size need not change allele frequency if genotype proportions remain the same.

Apply the equilibrium prediction

With random mating and the relevant model assumptions, expected genotype frequencies are p² for AA, 2pq for Aa and q² for aa. Their sum is one. The heterozygote term includes two possible parental combinations, which is why it is 2pq rather than pq.

For a fully recessive phenotype in the simple complete-dominance model, its frequency can represent q². Take a square root to find q before finding p or 2pq. The dominant phenotype frequency is p²+2pq, not simply p.

p+q=1,\qquad p^2+2pq+q^2=1

Evaluate the assumptions and evidence

The simplified model assumes a large population, random mating and no relevant selection, mutation or migration changing the allele frequencies. Genetic drift is negligible in the ideal large-population limit. These conditions create a useful null model against which real populations can be compared.

A departure from expected genotype frequencies does not identify one unique cause automatically. Non-random mating, selection, population structure, sampling and measurement can all matter. Use data and context to support a specific explanation; the equations are a model, not a rule that every natural population must obey exactly.

Apply the biology

Try each question before opening the worked response. Use precise biological terms, connect each cause to its effect, and check units and assumptions when interpreting data.

Example 1A recessive phenotype occurs in 9% of a population assumed to meet the model. Find q, p and heterozygote frequency.

q^2=0.09

, so q=0.30.

2p=0.70 and

2pq=2(0.70)(0.30)=0.42

Answerq=0.30, p=0.70 and 42% heterozygotes.

Example 2A sample contains 20 AA, 50 Aa and 30 aa individuals. Calculate the A allele frequency without assuming equilibrium.

1There are 200 allele copies.

2A copies =2×20+50=90.

3p=90/200=0.45.

Answer0.45; direct allele counting does not require assuming the genotype frequencies are at equilibrium.

Equation recap

p+q=1,\qquad p^2+2pq+q^2=1

Relationship recap

Common mistakes to avoid

Using a recessive phenotype frequency as q rather than q².

Take the appropriate square root.

Claiming a departure proves natural selection alone.

Evaluate alternative causes and the evidence.

Key takeaways

Allele and genotype frequencies describe different quantities.
Equilibrium equations generate conditional predictions.
Departures require interpretation rather than an automatic causal label.

Test yourself

Answer a few questions, then review anything you missed.

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Keep practising

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