16.1 Hardy-Weinberg Equilibrium

Hardy-Weinberg Equilibrium

The Hardy-Weinberg equilibrium describes a theoretical state where allele and genotype frequencies in a population remain constant from generation to generation. It serves as a null model in population genetics: if a real population deviates from Hardy-Weinberg expectations, something evolutionary must be happening. That makes it the baseline you compare everything else against.

The core equation is $p^2 + 2pq + q^2 = 1$. It lets you calculate expected genotype frequencies from allele frequencies and then compare those expectations to what you actually observe in a population. Deviations point toward evolutionary forces like mutation, migration, drift, or natural selection.

Assumptions of Hardy-Weinberg Equilibrium

For a population to stay in Hardy-Weinberg equilibrium, five conditions must all hold simultaneously. In reality, no natural population meets every one of these perfectly, which is exactly the point. They define the "no evolution" scenario.

• No mutation — Allele frequencies stay constant because no new alleles are created and no existing alleles are changed or removed.
• No migration (gene flow) — No individuals enter or leave the population, so no alleles are added or lost through movement.
• Large population size — The population must be large enough that genetic drift (random fluctuations in allele frequency due to chance) is negligible. Small populations are far more vulnerable to drift.
• Random mating (panmixia) — Individuals pair up without regard to genotype or phenotype. No one preferentially mates with similar or dissimilar partners.
• No natural selection — All genotypes survive and reproduce equally well. No genotype has a fitness advantage over another.

If even one of these assumptions is violated, allele frequencies can shift across generations, meaning the population is evolving.

Application of the Hardy-Weinberg Equation

The equation relates allele frequencies to genotype frequencies for a locus with two alleles:

$p + q = 1$

where $p$ is the frequency of one allele (often called the dominant allele, A) and $q$ is the frequency of the other allele (often the recessive allele, a). Squaring the allele-frequency expression gives the genotype frequencies:

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

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

Worked example: Suppose 1 in 2,500 individuals in a population shows a recessive phenotype (aa).

1. Set $q^2 = \frac{1}{2500} = 0.0004$.

2. Solve for $q$: $q = \sqrt{0.0004} = 0.02$.

3. Solve for $p$: $p = 1 - q = 1 - 0.02 = 0.98$.

4. Calculate genotype frequencies:

   • AA: $p^2 = (0.98)^2 = 0.9604$
   • Aa: $2pq = 2(0.98)(0.02) = 0.0392$
   • aa: $q^2 = 0.0004$

Notice that heterozygous carriers (about 3.9% of the population) are far more common than affected homozygotes (0.04%). This is a key insight: for rare recessive conditions, most copies of the recessive allele are hidden in carriers.

Calculating allele frequencies from genotype counts: If you know the actual number of each genotype in a population, you can count alleles directly:

• $p = \frac{2(\text{number of AA}) + (\text{number of Aa})}{2(\text{total individuals})}$
• $q = \frac{2(\text{number of aa}) + (\text{number of Aa})}{2(\text{total individuals})}$

This allele-counting method is more accurate than taking the square root of a genotype frequency, because it doesn't assume the population is already in equilibrium.

Determination of Equilibrium Status

To test whether a population is in Hardy-Weinberg equilibrium:

1. Count observed genotypes in the population (AA, Aa, aa).
2. Calculate observed allele frequencies using the allele-counting method above.
3. Calculate expected genotype frequencies by plugging $p$ and $q$ into the Hardy-Weinberg equation.
4. Compare observed vs. expected genotype counts. A chi-square ($\chi^2$) goodness-of-fit test is the standard statistical tool here. With two alleles, there is 1 degree of freedom (3 genotype classes minus 2 estimated parameters).
5. If the $\chi^2$ value is not significant (p > 0.05), the population is consistent with Hardy-Weinberg equilibrium. A significant result means something is likely driving the population away from equilibrium.

Factors Disrupting Hardy-Weinberg Equilibrium

Each violated assumption corresponds to a specific evolutionary mechanism.

• Mutation introduces new alleles or converts one allele into another, gradually shifting allele frequencies. Mutation rates are typically low per generation, so mutation alone changes frequencies slowly. Example: the sickle cell allele (HbS) arose by a point mutation in the $\beta$-globin gene.
• Migration (gene flow) occurs when individuals move between populations carrying different allele frequencies. Immigration adds alleles; emigration removes them. This can homogenize allele frequencies between populations over time. (Note: the founder effect is actually a form of genetic drift, not gene flow, because it involves a small group starting a new population with a non-representative sample of alleles.)
• Small population size (genetic drift) causes random, unpredictable changes in allele frequency. Two classic scenarios:
  • Bottleneck effect — A sharp reduction in population size (disease, disaster) randomly eliminates alleles, reducing genetic diversity.
  • Founder effect — A small group colonizes a new area, carrying only a subset of the original population's alleles.
• Non-random mating changes genotype frequencies without directly changing allele frequencies.
  • Assortative mating (preferring similar phenotypes) increases homozygosity.
  • Disassortative mating (preferring dissimilar phenotypes) increases heterozygosity.
  • Inbreeding is an extreme form of non-random mating that increases homozygosity across the entire genome.
• Natural selection occurs when genotypes differ in fitness (survival and/or reproductive success). Alleles associated with higher fitness increase in frequency over generations. Example: bacteria carrying antibiotic-resistance alleles survive treatment and pass those alleles to the next generation, increasing the resistance allele's frequency.