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Genomics

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Description

The Hardy-Weinberg principle (HWP) (also Hardy-Weinberg equilibrium (HWE), or Hardy-Weinberg law), named after G. H. Hardy and Wilhelm Weinberg, states that, under certain conditions, after one generation of random mating, the genotype frequencies at a single gene? locus will become fixed at a particular equilibrium value. It also specifies that those equilibrium frequencies can be represented as a simple function of the allele frequencies at that locus.

In the simplest case of a single locus? with two alleles A and a with allele frequencies of p and q, respectively, the HWP predicts that the genotypic frequencies for the AA homozygote to be p2, the Aa heterozygote to be 2pq and the other aa homozygote to be q2. The Hardy-Weinberg principle is an expression of the notion of a population in "genetic equilibrium" and is a basic principle of population genetics.

Assumptions

The original assumptions for Hardy–Weinberg equilibrium (HWE) were that the organism under consideration is:

  • Diploid, and the trait under consideration is not on a chromosome that has different copy numbers for different sexes, such as the X chromosome in humans
  • Sexually reproducing, either monoecious or dioecious
  • Discrete generations

In addition, the population under consideration is idealised, that is:

  • Random mating within a single population
  • Infinite population size (or sufficiently large so as to minimize the effect of [genetic drift]?)

and experiences:

  • No selection
  • No mutation?
  • No migration (gene flow)

The first group of assumptions are required for the mathematics involved. It is relatively easy to expand the definition of HWE to include modifications of these, such as for sex-linked traits. The other assumptions are inherent in the Hardy-Weinberg principle.

A 'Hardy-Weinberg population' is used as a reference population when discussing various factors. It is not surprising that these populations are static.

Derivation

A better, but equivalent, probabilistic description for the HWP is that the alleles for the next generation for any given individual are chosen randomly and independent of each other. Consider two alleles, A and a, with frequencies p and q, respectively, in the population. The different ways to form new [Genotype? genotypes] can be derived using a Punnett square, where the fraction in each cell is equal to the product of the row and column probabilities.

Females
A (p)a (q)
MalesA (p)AA (p2)Aa (pq)
a (q)Aa (pq)aa (q2)

These frequencies are called Hardy-Weinberg frequencies (or Hardy-Weinberg proportions). This is achieved in one generation, and only requires the assumption of random mating with an infinite population size.

Sometimes, a population is created by bringing together males and females with different allele frequencies. In this case, the assumption of a single population is violated until after the first generation, so the first generation will not have Hardy-Weinberg equilibrium. Successive generations will have Hardy-Weinberg equilibrium.

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