Populations and the Hardy-Weinberg Principle

Populations and the gene pool

A population is all the organisms of one species in a particular area that can interbreed. The gene pool is all the alleles of all the genes in that population. Allele frequency is how common an allele is in the gene pool.

The Hardy-Weinberg principle

The Hardy-Weinberg principle predicts that allele and genotype frequencies stay constant from generation to generation — provided certain conditions are met:

• no mutations, no natural selection, no migration;
• a large population;
• random mating.

If these hold, the frequencies don't change. Where they do change, it shows evolution is occurring.

The equations

For a gene with two alleles, let:

• p = frequency of the dominant allele;
• q = frequency of the recessive allele.

Allele frequencies:

p + q = 1

Genotype frequencies:

p² + 2pq + q² = 1

where p² = homozygous dominant, 2pq = heterozygous, q² = homozygous recessive.

Using the equations

The recessive phenotype is the easiest starting point, because only q² individuals show it:

1. q² = frequency of the recessive phenotype (given).

2. q = √q².

3. p = 1 − q.

4. Then find any genotype frequency (e.g. carriers = 2pq).

Worked example

In a population, 16% show the recessive phenotype (aa). Find the frequency of carriers (Aa).

1. q² = 0.16 → q = √0.16 = 0.4.

2. p = 1 − 0.4 = 0.6.

3. Carriers = 2pq = 2 × 0.6 × 0.4 = 0.48 (48%). ✓

Factors that change allele frequencies

• Natural selection (directional/stabilising) — the main driver.
• Genetic drift — random changes, especially in small populations.
• Gene flow (migration), and mutation introducing new alleles.

Over time these can lead to speciation when populations become reproductively isolated (allopatric = geographical; sympatric = same area).

Common mistakes

• Forgetting to square-root q² to get q (a very common slip).
• Mixing up which term is which: q² = recessive phenotype, 2pq = heterozygotes.
• Applying Hardy-Weinberg when its conditions clearly don't hold.

Exam tips

• Start from q² (the recessive phenotype) and work back to q, then p.
• Learn both equations and what each genotype term represents.
• State the assumptions of Hardy-Weinberg when asked why it may not apply.

Key facts to remember

• p + q = 1 and p² + 2pq + q² = 1; q² = homozygous recessive, 2pq = heterozygous carriers, p² = homozygous dominant.
• Assumes a large population, no selection/mutation/migration, random mating; deviation indicates evolution.
• Allele frequencies change through natural selection, genetic drift, gene flow and mutation, potentially leading to speciation.