Principe de Hardy-Weinberg

The Hardy-Weinberg Principle states that in a large, randomly mating population, allele frequencies remain constant over time if the population is not evolving. When two alleles exist at a locus, their frequencies—represented by p and q—always add up to one. This principle provides a null model for studying evolution and detecting when populations deviate from genetic equilibrium.

The Hardy-Weinberg equation (p² + 2pq + q² = 1) relates allele frequencies to genotype frequencies. Homozygous individuals have frequencies of p² and q², representing the probability of inheriting the same allele from both parents. Heterozygous individuals occur with frequency 2pq because the dominant allele can come from either parent, creating two possible crosses.

Hardy-Weinberg equilibrium requires an infinite population size, random mating, and an absence of genetic mutations, natural selection, and gene flow. When these conditions are met, allele frequencies remain constant and the population does not evolve. Most natural populations violate at least one condition, making true equilibrium rare in nature.

The Hardy-Weinberg Principle requires an infinite or very large population size because random events can strongly change allele frequencies in small populations. In large populations, random sampling errors are negligible, so allele frequencies remain stable across generations. Small populations experience unpredictable fluctuations that violate equilibrium assumptions.

Random mating ensures that alleles combine by chance alone, without preference for particular genotypes. This produces predictable genotype frequencies based on allele frequencies. When mating is non-random or selective, genotype frequencies deviate from Hardy-Weinberg predictions, indicating the population is evolving or under different genetic conditions.

The Hardy-Weinberg Principle serves as a null model or baseline for population genetics studies. By comparing observed genotype frequencies to Hardy-Weinberg predictions, scientists can identify which evolutionary forces—such as mutation, gene flow, and genetic drift—are acting on a population. This helps detect genetic associations and genotyping errors in research.

In the early 20th century, scientists wondered why rarely-observed dominant traits did not increase in frequency across generations in randomly-mating populations. For example, polydactyly (extra fingers or toes) remained rare despite being dominant. In 1908, Wilhelm Weinberg and G. H. Hardy independently demonstrated that genetic variation could remain unchanged, establishing the principle of Hardy-Weinberg equilibrium.