8.1 Hardy-Weinberg equilibrium and its assumptions

Hardy-Weinberg Equilibrium Fundamentals

Hardy-Weinberg equilibrium (HWE) predicts that allele and genotype frequencies in a population will stay constant from generation to generation, as long as no evolutionary forces are acting on that population. It serves as the null hypothesis in population genetics: if a population isn't in HWE, something interesting is happening evolutionarily.

By comparing real populations against this idealized baseline, researchers can pinpoint which forces (mutation, selection, migration, drift) are driving genetic change.

Assumptions of Hardy-Weinberg Equilibrium

HWE only holds when five strict conditions are met. In reality, natural populations almost never satisfy all five, which is exactly why the model is useful: violations point you toward the evolutionary forces at work.

• Large population size — Minimizes genetic drift, the random fluctuation of allele frequencies that hits small populations hardest. In a population of 50 individuals, chance alone can shift allele frequencies dramatically; in a population of 500,000, those random effects average out.
• Random mating — Every individual is equally likely to mate with any other, regardless of genotype. No sexual selection, no assortative mating (where similar phenotypes preferentially pair up), and no inbreeding.
• No mutation — No new alleles are introduced, and existing alleles aren't converted into different forms. This keeps the allele pool unchanged between generations.
• No migration (gene flow) — No individuals enter or leave the population. Immigration brings in new alleles; emigration removes them. Either disrupts equilibrium.
• No natural selection — All genotypes survive and reproduce equally well. No genotype has a fitness advantage or disadvantage.

Calculations with Hardy-Weinberg Equations

Two equations form the core of HWE calculations.

Allele frequency equation:

$p + q = 1$

Here, p is the frequency of the dominant allele (e.g., A) and q is the frequency of the recessive allele (e.g., a) in a two-allele system. Since these are the only two options, their frequencies must add to 1.

Genotype frequency equation:

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

• $p^2$ = frequency of homozygous dominant individuals (AA)
• $2pq$ = frequency of heterozygous individuals (Aa)
• $q^2$ = frequency of homozygous recessive individuals (aa)

This equation is just the binomial expansion of $(p + q)^2$, which makes sense because each individual receives one allele from each parent independently.

Typical problem-solving steps:

1. Identify what you know. Usually you're given the frequency of the recessive phenotype, since that's the only genotype you can identify directly from phenotype alone.

2. Set $q^2$ equal to the recessive phenotype frequency.

3. Take the square root to find $q$.

4. Calculate $p = 1 - q$.

5. Plug $p$ and $q$ into the genotype equation to find $p^2$, $2pq$, and $q^2$.

Example: Suppose 16% of a population shows the recessive phenotype.

1. $q^2 = 0.16$

2. $q = \sqrt{0.16} = 0.4$

3. $p = 1 - 0.4 = 0.6$

4. Genotype frequencies: $p^2 = 0.36$ (AA), $2pq = 0.48$ (Aa), $q^2 = 0.16$ (aa)

So 48% of the population are carriers (heterozygotes), which is a result you can't observe directly from phenotype but can estimate using HWE.

You can also calculate allele frequencies from genotype counts:

• $p = p^2 + \frac{1}{2}(2pq)$
• $q = q^2 + \frac{1}{2}(2pq)$

These formulas count up all copies of each allele: homozygotes contribute two copies, heterozygotes contribute one.

Interpretation of Hardy-Weinberg Results

When observed genotype frequencies match HWE predictions, the population is in equilibrium for that locus, and there's no evidence of evolutionary forces acting on it.

When observed and expected frequencies don't match, one or more assumptions are being violated. For instance, an excess of homozygotes compared to HWE expectations can signal inbreeding, while a deficit of one homozygous class might indicate selection against that genotype.

Common applications:

• Estimating carrier frequencies for recessive genetic disorders (e.g., cystic fibrosis, where roughly 1 in 25 individuals of European descent is a carrier)
• Detecting selection pressure by comparing observed vs. expected genotype frequencies over time
• Establishing a baseline before testing for specific evolutionary mechanisms

Keep in mind that HWE is a theoretical model. Its power comes not from perfectly describing real populations, but from giving you a precise expectation to test against. When reality departs from the model, that departure tells you something about evolution in action.