## Table of Contents

- What Is Hardy Weinberg Law?
- Who Proposed The Hardy Weinberg Law?
- Assumptions for the Hardy Weinberg Principle
- Infringement of the Hardy Weinberg Equilibrium
- Applications of the Hardy Weinberg Principle
- Summary
- Frequently Asked Questions on Hardy Weinberg Law

## 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 a with corresponding frequencies f(A) = p and f(a) = q respectively, then the genotype frequencies that can be expected under limited condition being random mating is

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

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

f(Aa) = 2pq for heterozygotes

The Hardy Weinberg Equation can be represented by

p^{2} + q^{2} + 2pq = 1 |

The allele frequencies p and q 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.

**Also Check: ****MCQs on Hardy Weinberg Law**

## Who Proposed The Hardy Weinberg Law?

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

Hardy’s thesis centrally paid attention to debunking 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 frequency tests are applied to evaluate population stratification and other sorts of non-random mating.

## Assumptions for the Hardy Weinberg Principle

Listed below are a few assumptions for 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 regard to the above-mentioned assumptions, it can lead to discrepancies from the expected outcome. The consequences are completely dependent on the deduction that has been digressed.

The law mentions that a population shall have Hardy Weinberg proportions (given genotypic frequencies) once a single generation of random mating is carried out. In case the assumption of random mating is breached, this population will not possess 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.

## Infringement of the Hardy Weinberg Equilibrium

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

**Mutation –** it has a mild impact on the allele frequencies. The rate of mutation is in this 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 have the tendency to become more homozygous. Essentially, a few migration models are the Wahlund effect (non-random mating). Hardy–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 equilibrium provides a mathematical criterion 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 based on the values of Hardy-Weinberg principle, then workings that drive the evolution of the population can be hypothesised.

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 equilibrium 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.

Also Check: Incomplete Dominance

### II. Multiple Alleles

Calculation of genotypic frequencies at a locus with more than two alleles is allowed in the Hardy Weinberg principle, for instance in the ABO blood groups. Three alleles are present in IA, IB, IC 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 of 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, 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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## Frequently Asked Questions on Hardy Weinberg Law

### What are the 5 assumptions of the Hardy Weinberg equilibrium?

The five assumptions of Hardy Weinberg equilibrium are:

- Random mating
- No mutation
- No natural selection
- No gene flow or migration
- A very large population size (no genetic drift)

### What does the Hardy Weinberg law mean?

Hardy Weinberg law states that genetic variations remain constant in a large, randomly mating population. The frequency of alleles and genotypes remains constant from generation to generation and the population exists in a genetic equilibrium if there are no disturbances such as mutation, migration, natural selection, etc.

### How do you use the Hardy Weinberg equation?

The Hardy Weinberg equation is used to calculate the genetic variation in a population, which is in genetic equilibrium. If ‘p’ is a frequency of the allele ‘A’ and ‘q’ is the frequency of the allele ‘a’ of a single locus and sum of the allelic frequencies is 1, i.e. p + q = 1, then according to Hardy Weinberg equation p^{2} + q^{2} + 2pq = 1, where p^{2 }is a frequency of dominant homozygotes (AA), q^{2 }is a frequency of recessive homozygotes (aa) and 2pq is a frequency of heterozygotes (Aa). This equation can be used to determine and predict the frequencies of different genotypes if allele frequencies are known and analyse if there exist any variation in calculated and observed frequencies.

### Why is the Hardy Weinberg principle important?

The Hardy Weinberg principle is important in analysing the genetic variation existing in a population and comparing the actual variation to the calculated value from Hardy Weinberg law if the population was in equilibrium. If the actual frequency in a population differs from the expected value then it is an indication of disturbance and violation of one or more assumptions, which can further be investigated. It also helps in estimating the frequency of the heterozygous carriers of a harmful recessive gene.

### What do p and q stand for in the Hardy Weinberg equation?

In the Hardy Weinberg equation (p^{2} + q^{2 }+ 2pq = 1), p is the frequency of the dominant allele and q is the frequency of the recessive allele for a gene controlled by a pair of alleles.