# What is Hardy Weinberg Equilibrium?

Hardy Weinberg equilibrium explains the genetic variation among the populations which remains constant from one generation to the next without disturbing factors.

In a large random mating population, the allele and the genotype frequencies stay constants in the absence of evolutionary influences from one generation to the preceding generations.

Influences occurring are inclusive of the choices of mating, natural selection, gene flow, genetic hitchhiking, founder effect, meiotic drive, population bottleneck, inbreeding and assortative mating.

Genotype and the allele frequencies are related to each. This law also conveys the genetic drift in a population has been known already.

Taking a gene of a single locus which consists of only two alleles, indicated by A which has its corresponding frequencies and it is termed as f(A) =p and f(a)-1 respectively, then the corresponding genotype frequencies are expected under a limited condition where random mating is;

f(AA)=p^{2} for the homozygotes AA.

f(aa)=q^{2} for homozygotes aa.

f(Aa)=2pq for the heterozygotes

The equation of Hardy Weinberg principle can be represented as;

P^{2}+q^{2}+2pq=1

Here the allele frequencies p and q remain constant in absence of all kind of influences, such as mutation, natural selection, genetic drift, etc. from one generation to the another. Thus equilibrium can be reached.

## History of Hardy Weinberg Equilibrium

Hardy Weinberg Equilibrium was proposed by two researchers namely G.H Hardy and Wilhelm Weinberg. These two members were actually the pioneers in mathematics, and they illustrated this principle scientifically.

So, this law is commonly referred to as Hardy Weinberg equilibrium, theory or law. Hardy’s thesis paid a central attention to debunk the view which prevailed at the times when dominant allele has a capability to increase in frequency automatically.

Now a days the uncertainty on selection and dominance is not remarkable. In recent times, Hardy Weinberg s frequencies in the genotype tests are applied to evaluate population which stratifies and sorts the random-mating.

### Interference of Hardy Weinberg Equilibrium

There are few deductions according to this principle and they are listed below:

Only sexual reproductions take place

Mating occurs randomly

Size of population is indefinitely large

Diploid entities occur

Overlapping of generations do not occur

There will be an equality of frequencies between the alleles in terms of sexes

There will be no trace of gene flow, selection, mutation, migration or admixture.

If there are any changes with regard to the above-mentioned assumptions, it leads to discrepancies from expected outcomes.

The consequences occurring are dependent on the deduction which has been digressed.

The law mentioned in the population have the Hardy Weinberg proportions when the single generation of random mating is carried out in a population.

In some cases, the assumption of random mating is breached, and the particular population will not possess the proportions of Hardy Weinberg’s law.

The most common source of non-random mating is considered as breeding, which leads to a rise in homozygosity of the genes.

#### Four's of Hardy Weinberg Equilibrium

Breaching of any one of these four assumptions causes the populations to possess a proportions of Hardy Weinberg principle.

However, with time there will be an alteration in a given frequencies.

##### I. Mutation

Mutation has a mild impact in the frequency of the allele. The rate of mutation occurs in the order of 10^{-4} to 10^{-8}.

Mostly the modifications in the frequencies of the alleles occurs in this order, even if there is any sturdy selection against the alleles in the given population, recurrent mutation will take care of it.

###### II. Selection

Selection typically leads to a change in the frequency of the alle and it occurs rapidly. In some kind of selections, the selected one results in equilibrium where is no loss of alleles, which is also said to be as balancing selection, where as in other kind of selections, such as directional selection there will be a gradual loss of the alleles.

###### III. Size of The Population

If the size of a population is small it leads to the random alteration in the frequencies of the alleles which attributes the sampling effect, commonly known as genetic drift. If the alleles are found in a fewer copy, sampling effects are considered to be significant.

###### IV. Migration

Migration in two or more population helps in associating the alleles genetically together. Here among the populations, the frequency of allele has the tendency to become more homozygous.

Significantly, a few models of migration in the non-random mating are said to be as Wahlund effect. Hardy Weinberg proportions are invalid in some cases.

###### Application of Hardy Weinberg Equilibrium

Generally natural populations depict the genetic variations continuously and leads to the alterations in the form of mutations, migration, genetic drift, natural or in sexual selection.

However, Hardy Weinberg Equilibrium provides a mathematical criterion of the population which is non-evolving and that can be compared among the evolving populations.

Over-time if the frequencies of the alleles are noted and estimated for the excepted frequencies, depending upon the values of the Hardy Weinberg law, then the evolution of the population which are driven can be hypothesized.

This law offers a protype, which can be used as a point of organization order to study the population of the genetics in the diploid entities, which also fulfills the assumption of the random mattings, large populations, no mutations, selection or migration, Apart from this Hardy Weinberg model is not applicable to haploid pathogens, in the event of a population which are not found in an equilibrium, one of the assumptions related to this law gets violated.

This suggests that selection non-random mating or migration influences the population, where the case experiments are done and the hypothesis are advanced in order to understand the reason behind the non-equilibrium of the population.

###### Hardy Weinberg Equilibrium Citations

- A century of Hardy-Weinberg equilibrium. Twin Res Hum Genet . 2008 Jun;11(3):249-56.
- Hardy Weinberg Equilibrium Disturbances in Case-Control Studies Lead to Non-Conclusive Results. Cell J . 2021 Jan;22(4):572-574.
- A note on exact tests of Hardy-Weinberg equilibrium. Am J Hum Genet . 2005 May;76(5):887-93.

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