## What Is Hardy Weinberg Law?

**Statement Of Hardy Weinberg Law **

“In a large, random-mating population, the genotype and allele frequencies remain constant in the absence of any evolutionary influences from one to another generation. Influences are inclusive of a choice of mate, natural selection, genetic drift, mutation, sexual selection, gene flow, genetic hitchhiking, founder effect, meiotic drive, population bottleneck, inbreeding and assortative mating.”

Genotype frequencies and allele frequencies are related to each other in a way that it is the square expansion of such allele frequencies. In other words, the law conveys that in a population, it is possible to estimate the expected frequencies of genotypes under a certain limited set of assumptions, provided the frequency of different alleles in a population is already known.

Take a case of a single locus with only two alleles indicated by A and B with corresponding frequencies f(A) = x and f(B) = y respectively, then the genotype frequencies that can be expected under limited condition being random mating is

f(AA)= x^{2} for AA homozygotes

f(BB) = y^{2} for BB homozygotes

f(AB) = 2xy for heterozygotes

The allele frequencies x and y remain constant in the absence of any kind of influences such as mutation, natural selection, genetic drift, etc from one to another generation. This is how the equilibrium can be reached. If there were a third allele, say C, with a frequency z, then the expected genotypic proportion could be (x+y+z)^{2}_{. }

### Who Proposed The Law?

The law is named after G.H. Hardy and Wilhelm Weinberg. They were pioneers in mathematically illustrating this principle also referred to as Hardyâ€“Weinberg equilibrium, theorem, law or model.

Hardy’s thesis centrally paid attention to debunk the view that prevailed in those times that a dominant allele has the tendency to increase in frequency automatically. In today’s times, the uncertainty on selection and dominance is not very remarkable. In the current times, the Hardy-Weinberg genotype frequencies tests are applied to evaluate population stratification and other sorts of non-random mating.

## Inferences From Hardyâ€“Weinberg Law

Listed below are a few deductions from the law:

- Only sexual reproduction can take place
- Process of mating is random
- The size of the population is indefinitely large
- Entities are diploid
- Generations do not overlap
- Equality of allele frequencies in terms of sexes
- No traces of gene flow, selection, mutation, migration or admixture

In case there is any breach with regards to the above-mentioned assumptions, it can lead to discrepancies from the expected outcome. The consequences, as a result, is completely dependent on the deduction that has been digressed.

The law mentions that the population shall have the Hardy Weinberg proportions (given genotypic frequencies) once a single generation of random mating is carried out in a population. In case the assumption of random mating is breached, this population will not possess the Hardy Weinberg proportions. The most common source of a non-random mating is inbreeding. It leads to the rise in the homozygosity of all genes.

Breaching any one of these 4 assumptions can cause the population at each generation to still possess the Hardyâ€“Weinberg proportions, however, with time, there will be a change in the allele frequencies.

**Mutation –** it has a mild impact on the allele frequencies. Rate of mutation is in this o order 10^{-4} to 10^{-8}. Mostly, modifications to the allele frequencies are of this order. Even if there persists a sturdy selection against the alleles in the population, recurrent mutations will conserve it.

**Selection –** typically this leads to a change in the allele frequencies and is a rapid one. Few types of selections, the selected ones can result in equilibrium with no loss of alleles, namely balancing selection, while some other selections such as directional selection can gradually result in the loss of alleles.

**Size of the population** being small can lead to a random alteration in the allele frequencies which can be attributed to the sampling effect known as genetic drift. When alleles are found in a fewer copy, sampling effects are significant.

**Migration** – two or more than two populations can be associated together, genetically with migration. Here, amongst the populations, the allele frequencies has the tendency to become more homozygous. Essentially, a few migration models are the Wahlund effect (non-random mating). Hardyâ€“Weinberg proportions typically are invalid for such models.

## Applications of the Hardy-Weinberg Principle

Natural populations persistently depict genetic variation altering from mutation, genetic drift, migration, sexual selection and natural selection. The Hardy-Weinberg law provides a mathematical criterion of that of a population that is non-evolving which can be compared to evolving populations. Over time, if the allele frequencies are noted and estimated for the expected frequencies basis the values of Hardy-Weinberg law, then workings that drive the evolution of the population can be hypothesized.

The law offers a prototype which is typically used as a point of origination to study the population genetics of diploid entities, which fulfil the fundamental assumption of random mating, large population, no mutation, migration or selection.

However, the Hardy-Weinberg model is not applicable to haploid pathogens. In the event of a population not being found in Hardy-Weinberg equilibrium, one of the assumptions in this law then gets violated. This conveys that selection, non-random mating or migration has influenced the population, in which case experiments are carried out and hypotheses are advanced in order to understand the reasons behind the non-equilibrium of the population.

**I. Complete Dominance**

Allele frequencies can be detected in the presence of complete dominance when Hardy-Weinberg equilibrium prevails wherein it is not possible to differentiate between two genotypes. Two genotypes AA and Aa having the same phenotype as a result of complete dominance of A over a, can help determine the allele frequencies from frequencies of the individuals indicating recessive phenotype aa. Here, the frequency of aa individual should be equivalent to the square of the frequency of the recessive allele.

**II. Multiple Alleles **

Calculation of genotypic frequencies at a loci with more than two alleles is allowed in the Hardy-Weinberg principle, for instance in the ABO blood groups. Three alleles are present in I^{A}, I^{B}, I^{C} with p,q and r frequencies respectively where p + q + r = 1. With random mating, the genotype of a population will be given by (p + q + r)^{2}

**III. Linkage Disequilibrium **

Take, for instance, two or more alleles on the same chromosome, at two different loci with 2 or more alleles. As a result of genetic exchange by recombination taking place at regular time intervals, at two syntenic loci, the frequency of allelic combinations attains equilibrium.

In the event of not being able to attain an equilibrium, alleles are known to be in a linkage disequilibrium, which is as a result of two or more linked alleles to be inherited jointly, more frequently than expected. Such gene groups are also known as supergenes.

**IV. Frequencies If Harmful recessive Alleles**

The law can also be applied to estimate the frequency of heterozygous carriers of recessive genes that are harmful. In a population, two alleles, A and a are at an autosomal locus with p and q frequencies, respectively and p + q = 1, then AA, Aa and aa genotypes will have the following frequency will be p^{2} + q^{2} + 2pq. In case, the aa genotype tends to express a phenotype that is harmful, such as cystic fibrosis, then in the population, the proportion of the affected individuals shall be q^{2}, the recessive allele frequency of the heterozygous carrier shall be 2pq.

## Summary

- In a given population, the Hardy-Weinberg principle assumes that the population is indefinite and not influenced by sexual, natural selection, mutation and migration.
- Frequency of alleles can be calculated by the frequency of recessive genotypes. Then estimate the square root of this frequency to find the frequency of the recessive allele
- In a population, the frequency of alleles can be indicated by p + q = 1, with p = frequency of the dominant allele and q = frequency of the recessive allele.
- In a population, the frequency of alleles can be indicated by p
^{2}+ q^{2}+ 2pq = 1, where p^{2}_{ }is the frequency of homozygous dominant genotype, q^{2}_{ }^{ }is the frequency of recessive genotype and 2pq is the frequency of heterozygous genotype.

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