The Hardy-Weinberg Principle

Population Genetics

A gene pool is the complete set of all alleles present in a population at a given time. Population genetics studies how allele frequencies change (or remain stable) over generations and is fundamental to understanding evolution.

The Hardy-Weinberg Principle

The Hardy-Weinberg principle states that allele frequencies and genotype frequencies in a population will remain constant from generation to generation, provided that certain conditions are met. A population meeting these conditions is said to be in Hardy-Weinberg equilibrium.

Conditions for Equilibrium

1. No mutation — no new alleles are created

2. No natural selection — all genotypes are equally fit (no selective advantage or disadvantage)

3. No migration (gene flow) — no individuals enter or leave the population

4. Random mating — individuals do not choose mates based on genotype

5. Large population size — no genetic drift (random changes in allele frequency due to chance events in small populations)

In reality, no natural population meets all these conditions perfectly. The Hardy-Weinberg principle serves as a null model — a baseline against which real populations can be compared. If observed genotype frequencies deviate significantly from Hardy-Weinberg predictions, one or more of the conditions is being violated, indicating that evolution is occurring.

The Hardy-Weinberg Equations

For a gene with two alleles, the dominant allele is designated A (frequency = p) and the recessive allele a (frequency = q).

Equation 1: Allele Frequencies

p + q = 1

Since there are only two alleles, their frequencies must sum to 1 (100% of all copies of that gene in the population).

Equation 2: Genotype Frequencies

p² + 2pq + q² = 1

This equation gives the expected frequencies of the three genotypes:

Genotype	Frequency	Phenotype
AA (homozygous dominant)	p²	Dominant phenotype
Aa (heterozygous)	2pq	Dominant phenotype
aa (homozygous recessive)	q²	Recessive phenotype

The equation is derived from the binomial expansion of (p + q)², which represents the random combination of alleles during sexual reproduction.

Using the Hardy-Weinberg Equations

Worked Example 1

In a population of 10,000 people, 64 have phenylketonuria (PKU), an autosomal recessive condition.

Step 1: PKU is recessive, so affected individuals have genotype aa. The frequency of aa is:

q² = 64/10,000 = 0.0064

Step 2: Find q (frequency of the recessive allele):

q = √0.0064 = 0.08

Step 3: Find p (frequency of the dominant allele):

p = 1 - q = 1 - 0.08 = 0.92

Step 4: Find the carrier frequency (heterozygotes, Aa):

2pq = 2 × 0.92 × 0.08 = 0.1472 (14.72%)

Step 5: In a population of 10,000, the expected number of carriers is:

0.1472 × 10,000 = 1,472 carriers

Worked Example 2

In a population, the frequency of the recessive allele for cystic fibrosis is 0.04.

• q = 0.04, so p = 0.96
• Frequency of affected individuals (aa): q² = 0.0016 (1.6 per 1,000)
• Frequency of carriers (Aa): 2pq = 2 × 0.96 × 0.04 = 0.0768 (about 1 in 13)
• Frequency of homozygous dominant (AA): p² = 0.9216

Check: p² + 2pq + q² = 0.9216 + 0.0768 + 0.0016 = 1.0000 ✓

Why Populations Deviate from Equilibrium

When allele frequencies change over generations, evolution is occurring. The forces that cause deviation from Hardy-Weinberg equilibrium are:

1. Natural Selection

Individuals with certain alleles/genotypes have higher fitness (survival and reproductive success) than others. Over time, beneficial alleles increase in frequency and harmful alleles decrease.

• Directional selection — one extreme phenotype is favoured (e.g. antibiotic resistance in bacteria)
• Stabilising selection — the intermediate phenotype is favoured (e.g. human birth weight)
• Disruptive selection — both extremes are favoured over the intermediate

2. Genetic Drift

In small populations, allele frequencies can change randomly from generation to generation simply by chance — which gametes happen to form the next generation. This is called genetic drift.

• Bottleneck effect — a sudden reduction in population size (e.g. natural disaster) randomly eliminates alleles, reducing genetic diversity. The surviving population may have very different allele frequencies from the original.
• Founder effect — a small group colonises a new area, carrying only a subset of the original population's alleles. The new population has reduced genetic diversity and potentially different allele frequencies. Example: Ellis-van Creveld syndrome has a high frequency among the Amish, descended from a small founding group.

3. Gene Flow (Migration)

Movement of individuals (and their alleles) between populations can change allele frequencies. Immigration introduces new alleles; emigration removes them.

4. Mutation

New mutations introduce new alleles. While individual mutations are rare, they are the ultimate source of all genetic variation.

5. Non-Random Mating

If individuals preferentially mate with others of similar (or different) phenotype, genotype frequencies shift from Hardy-Weinberg predictions, though allele frequencies may remain unchanged.

Testing for Hardy-Weinberg Equilibrium

To test whether a population is in equilibrium:

1. Observe the number of individuals of each phenotype/genotype

2. Calculate expected genotype frequencies using the Hardy-Weinberg equations

3. Compare observed and expected values using a chi-squared (χ²) test

4. If the difference is not significant (p > 0.05), the population is consistent with equilibrium

5. If the difference is significant (p ≤ 0.05), one or more equilibrium conditions are being violated

Codominance and Multiple Alleles

The Hardy-Weinberg principle can be extended to systems with more than two alleles. For example, the ABO blood group system has three alleles: Iᴬ, Iᴮ, and i. With frequencies p, q, and r:

p + q + r = 1

(p + q + r)² = p² + q² + r² + 2pq + 2pr + 2qr = 1

Where p² = IᴬIᴬ, 2pr = Iᴬi (both type A), q² = IᴮIᴮ, 2qr = Iᴮi (both type B), 2pq = IᴬIᴮ (type AB), r² = ii (type O).

Exam Tips

• AQA always provides the Hardy-Weinberg equations on the formula sheet — you need to know how to USE them, not memorise them
• The key entry point is usually q² — the frequency of the homozygous recessive phenotype, because this is the genotype you can identify directly from the phenotype
• Always show your working clearly and state what each symbol represents
• Remember that carriers (2pq) are usually far more common than affected individuals (q²) — this is a common calculation
• When asked why real populations deviate from equilibrium, name specific factors and explain how they change allele frequencies