Concise Notes on Hardy-Weinberg Equilibrium

Hardy-Weinberg Principle

The Hardy-Weinberg principle describes the relationship between allele frequencies and genotype frequencies in a randomly mating population. It posits that after one generation of random mating, genotype frequencies will stabilize at p^2, 2pq, and q^2, where p and q represent the frequencies of two alleles (A and B) at a single locus.

Assumptions

The principle relies on several key assumptions:

  1. Random mating
  2. Absence of natural selection
  3. Large population size (negligible genetic drift)
  4. No gene flow or migration
  5. No mutation
  6. Autosomal locus

Violations of these assumptions can lead to deviations from Hardy-Weinberg equilibrium.

Implications

  • Genetic variation is conserved in large, randomly mating populations.
  • It allows the determination of the proportion of carriers for a recessive allele.
  • Dominant alleles are not necessarily the most common.
  • Rare alleles are more likely to be found in heterozygotes.

Generalizations

The principle can be extended to polyploid organisms and genes with multiple segregating alleles, using the multinomial expansion (p1 + … + pk)^n, where n is the number of chromosome sets and k is the number of segregating alleles. It can also be applied to sex-linked genes, though equilibrium may take multiple generations.

Testing Hardy-Weinberg Proportions

A Chi-square (\chi^2) test with one degree of freedom can assess whether a population is in Hardy-Weinberg equilibrium. This involves comparing observed genotype counts with expected counts derived from allele frequencies, using the formula \chi^2 = \frac{(observed - expected)^2}{expected}. A significant \chi^2 value (e.g., greater than 3.84 with a p-value < 0.05) indicates a departure from Hardy-Weinberg equilibrium.

Departures from Hardy-Weinberg Proportions

Deviations from Hardy-Weinberg equilibrium can arise from:

  • Genotyping Error: Inaccurate genotype calls due to DNA quality, artifacts, or human error.
  • Non-Random Mating & Population Structure: Inbreeding, assortative mating, and population structure (Wahlund effect) can cause an excess of homozygotes or heterozygotes.
  • Natural Selection: Selection pressures alter allele and genotype frequencies, especially when genotypic fitnesses are non-multiplicative (w{AB}^2 \neq w{AA} \cdot w_{BB}). Overdominance leads to excess heterozygotes, while underdominance leads to excess homozygotes. Strong directional selection also causes marked departures.
  • Other Causes: Genetic drift (in small populations) and mutation can also lead to deviations, though the effects of mutation are usually small due to low mutation rates.