Hardy-Weinberg Equilibrium
The Hardy-Weinberg Equilibrium (HWE) is a principle stating that allele and genotype frequencies in an ideal, infinitely large, randomly mating population will remain constant from generation to generation in the absence of evolutionary influences such as mutation, selection, gene flow, and genetic drift. It provides a mathematical null hypothesis against which real populations can be compared to detect evolutionary change. The principle was independently formulated by Godfrey Hardy and Wilhelm Weinberg in 1908.
Key Formula
p² + 2pq + q² = 1 and p + q = 1
LaTeX: p^2 + 2pq + q^2 = 1 \quad \text{and} \quad p + q = 1
| Symbol | Meaning | Unit |
|---|---|---|
| p | Frequency of the dominant allele (A) | dimensionless (0–1) |
| q | Frequency of the recessive allele (a) | dimensionless (0–1) |
| p² | Frequency of homozygous dominant genotype (AA) | proportion |
| 2pq | Frequency of heterozygous genotype (Aa) | proportion |
| q² | Frequency of homozygous recessive genotype (aa) | proportion |
Worked Example
Problem
In a population of 10,000 individuals, 900 have the recessive homozygous genotype (aa) for albinism. Assuming Hardy-Weinberg equilibrium, calculate the allele frequencies and the expected number of carriers (Aa).
Solution
Step 1: Find q². Frequency of aa = 900/10,000 = 0.09, so q² = 0.09. Step 2: Find q. q = √0.09 = 0.3. Step 3: Find p. p = 1 – q = 1 – 0.3 = 0.7. Step 4: Find frequency of carriers (Aa). 2pq = 2 × 0.7 × 0.3 = 0.42. Step 5: Calculate number of carriers. 0.42 × 10,000 = 4,200 individuals.
Answer
p = 0.7 (dominant allele), q = 0.3 (recessive allele), 4,200 carriers (Aa)
Conditions Required for Hardy-Weinberg Equilibrium
| Condition | Requirement | Violation Causes |
|---|---|---|
| Large population | Effectively infinite population size | Genetic drift |
| Random mating | No mate selection based on genotype | Sexual selection or assortative mating |
| No mutation | Allele frequencies unchanged by mutation | Point mutations, insertions, deletions |
| No gene flow | No migration in or out of population | Immigration or emigration |
| No natural selection | All genotypes equally fit | Differential survival or reproduction |
Interactive Tools
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Related Terms
Genetic Drift
Genetic drift is a mechanism of evolution referring to random changes in allele frequencies in a population due to chance sampling events rather than natural selection, most pronounced in small populations. Unlike natural selection, genetic drift is non-directional and can lead to the fixation (frequency = 1) or loss (frequency = 0) of alleles regardless of their adaptive value. Two important forms are the bottleneck effect (sudden population reduction) and the founder effect (small group establishes a new population), both of which reduce genetic diversity.
Genetic Linkage
Genetic linkage refers to the tendency of genes located close together on the same chromosome to be inherited together during meiosis, rather than independently assort as predicted by Mendel's Law of Independent Assortment. The degree of linkage between two genes is inversely proportional to the physical distance between them; closely linked genes rarely recombine, while distantly located genes recombine more frequently and approach independent assortment. Linkage mapping uses recombination frequencies to construct genetic maps that estimate distances between genes in centimorgans (cM).
Non-disjunction
Non-disjunction is the failure of homologous chromosomes or sister chromatids to separate properly during meiosis I, meiosis II, or mitosis, resulting in daughter cells with an abnormal number of chromosomes (aneuploidy). When non-disjunction occurs during meiosis, the resulting gametes may have one extra chromosome (n+1, called trisomy after fertilisation) or one fewer chromosome (n-1, called monosomy after fertilisation). Non-disjunction is the most common cause of chromosomal abnormalities in humans, with its frequency increasing with maternal age.
Named after Godfrey Harold Hardy (1877–1947), an English mathematician, and Wilhelm Weinberg (1862–1937), a German physician. Both independently derived the equilibrium equations in 1908. Hardy reportedly considered the problem trivial from a mathematician's perspective, having been asked about it by biologist Reginald Punnett.