Topic 7.5 Notes – Hardy–Weinberg Equilibrium

1. What Hardy-Weinberg Equilibrium Is

Hardy-Weinberg equilibrium (HWE) describes a population where:

• Allele frequencies stay constant from one generation to the next.
• Genotype frequencies follow a predictable pattern based on those allele frequencies.

It’s a model of a non-evolving population. That matters because in AP Bio, evolution is defined very specifically as:

Evolution = change in allele frequencies over time.

So if allele frequencies do not change, the population is not evolving at that gene.

HWE works as a null hypothesis:

• If observed genotype frequencies match HWE predictions → no evidence of evolution.
• If they differ → something is disrupting equilibrium.

You are basically asking: Is this population behaving like it’s not evolving?

2. The Five Conditions Required for Hardy-Weinberg Equilibrium

All five conditions must be met for equilibrium. In real life, they never are perfectly met. That’s why evolution happens.

1. Large population size

Prevents genetic drift.
In small populations, allele frequencies can change just by chance.

2. No migration

Also called no gene flow.
If individuals enter or leave, they bring or remove alleles.

3. No mutations

Mutation creates new alleles.
New alleles change allele frequencies.

4. Random mating

Individuals mate without preference for genotype or phenotype.
If mating is nonrandom, genotype frequencies shift.

5. No natural selection

All genotypes have equal survival and reproductive success.
If one genotype leaves more offspring, its alleles increase.

Here’s a clean way to see how each condition connects to evolution:

Any violation can cause allele frequencies to change.

3. The Hardy-Weinberg Equations

These equations let you predict genotype frequencies from allele frequencies.

Allele Frequency Equation

$$p + q = 1$$

• $p$ = frequency of one allele
• $q$ = frequency of the other allele
• Only works for two alleles at one gene

Genotype Frequency Equation

$$p^{2} + 2pq + q^{2} = 1$$

• $p^{2}$ = homozygous dominant
• $2pq$ = heterozygous
• $q^{2}$ = homozygous recessive

These represent proportions of the whole population.

You can picture this as a Punnett square built from allele frequencies:

Hardy-Weinberg equations shown as a Punnett square

The sides are labeled $p$ and $q$, and the four boxes give you $pp$, $pq$, $pq$, and $qq$. When you combine the two heterozygous boxes, you get $2pq$.

The key idea is that allele frequencies determine genotype frequencies in a predictable way.

4. How to Solve Hardy-Weinberg Problems

On tests, you are usually given phenotype data.

Let’s walk through the logic.

Step 1: Identify the recessive phenotype

Only the recessive phenotype guarantees genotype (aa).
So its frequency = $q^{2}$.

Step 2: Solve for $q$

$$q = \sqrt{q^{2}}$$

Step 3: Solve for $p$

$$p = 1 - q$$

Step 4: Find genotype frequencies

• Homozygous dominant = $p^{2}$
• Heterozygous = $2pq$
• Homozygous recessive = $q^{2}$

Step 5: Compare expected vs observed

If expected genotype frequencies do not match actual data, at least one HWE condition is violated.

A common AP move is giving you observed counts and asking whether evolution is occurring. That question is really asking whether the data fit HWE predictions.

5. When and Why Allele Frequencies Change

If allele frequencies change, evolution is happening.

Here’s how each force disrupts equilibrium:

• Genetic drift
  Random changes, strongest in small populations.
• Gene flow
  Migration moves alleles between populations, often reducing differences between them.
• Mutation
  Introduces new alleles into the gene pool.
• Natural selection
  Increases frequency of alleles that improve survival or reproduction.
• Nonrandom mating
  Changes genotype frequencies immediately. By itself it may not change allele frequencies, but it can set the stage for selection to act.

Hardy-Weinberg gives you the mathematical expectation for stability. Real populations almost always deviate, and those deviations are evidence of evolution.