## What is Hardy Weinberg Equilibrium and why it is important?

The frequencies of allele and genotype were maintained constant from one generation to another due to the absence of other evolutionary forces. It is otherwise called the Hardy Weinberg principle the field of population genetics.

## History

In the year of 1908, a German physician named Wilhelm Weinberg and a British mathematician named G.H.Hardy independently discovered the concept of Hardy Weinberg Equilibrium. The paper presented by Hardy mainly focuses on expressing the falseness of a concept that a dominant allele would tend to get increased in frequency automatically. The scientists used mathematical models to conclude that gene pool frequencies are maintained in a fundamentally stable manner but then they have mentioned that evolution should be expected in every population at all the time virtually.

## Hardy Weinberg Equilibrium Assumptions

Based on the understanding of the concept proposed by Hardy and Weinberg, all the geneticists concluded that the evolution mechanism is not possible in a population if certain assumptions are satisfied. The assumptions are as follows:

• Every organism in a population is diploid.
• Reproduction can occur only in the sexual method.
• The generations in a population must not be overlapping.
• Mating is assumed to be random.
• The size of the population is immensely large.
• The frequencies of alleles tend to be equal in the sexes.
• Natural selection, migration, mutation, gene flow is absent.

It is stated that no ideal population is capable of satisfying these assumptions as these principles act as a fundamental line against which scientists measure the evolution of genes in a particular population. Thus, the Hardy Weinberg equilibrium exists as a helpful model to compare the actual modifications in the population.

Random mating

This states that the probability for mating two genotypes is the product of the population’s genotype frequencies. The deviation from random mating exists when the mating occurs in a population that is genetically closely related or more distantly related than an individual that is chosen randomly from the given population. As a result of mating in a non-random manner, frequencies of genotype get modified, not the frequencies of alleles.

Large population size

When the size of the population is large, it results in successful gametes in a large sample. When the gametes are large enough, it creates a state where the probability for the representation of the offspring allelic frequencies to that of its parental population is greater. In contrast, in the case of a small population size, modifications in the frequencies of alleles occur only by chance. These kinds of modifications are otherwise named random genetic drift.

Absence of mutation

It exerts only very little effect on the alleles’ frequencies. The rate of mutation is of the order 10-4 to 10-8. The modifications of the alleles’ frequencies are mostly in the same order. The mutation that is occurring recurrently maintains the population’s alleles even if a strong selection process exists against them.

Absence of migration

The modifications in the frequencies of alleles and genotype occur via the addition or loss of alleles which results from the migration of individuals into or from a population. Thus, in case of no migration, the alleles’ frequency is not modified and it tends to become more homozygous. The Hardy Weinberg proportions are typically not correct for some migration models that represent the Wahlund effect.

Absence of natural selection

This particular assumption states that the reproductive advantage is not focused on any individual over other individuals based on the genotype. This assumption takes place in the absence of natural selection. Only when selection occurs, modifications in the frequencies of alleles take place.

## Hardy Weinberg Law

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

The law explains the interlink between the frequencies of genotype and alleles. The genotype’s frequency is the square expansion of those frequencies of alleles. This is also stated differently as in given population, the estimation of frequencies of the genotype that is expected is possible under specific limited assumptions or conditions. It can occur if the different allelic frequency in a population is already familiar.

## Hardy Weinberg Equation and Analysis

The modifications in the frequency of alleles in a given population over generations are termed evolution. In contrast, the population in Hardy Weinberg is defined as not evolving. The equation derived based on the Hardy Weinberg equilibrium concept is called the Hardy Weinberg equation. In this particular equation, p is represented as the dominant allele’s frequency and q is the representation of the recessive allele’s frequency. This is explained with an example to conclude a Hardy Weinberg equation. Consider a single locus with the presence of only two alleles namely A and a. The A’s frequency is represented as ‘p’ and the a’s frequency is represented as ‘q’. Thus, the expected frequency of genotype in random mating under limited conditions are:

f(aa) = aa homozygotes are q2

f(AA)= AA homozygotes are p2

f(Aa) = heterozygotes are 2pq

From the above, the Hardy Weinberg equation is represented as p2 + q2 + 2pq = 1. The frequencies of alleles p and q remain constant without any influence such as migration, genetic drift, mutation, natural selection. These steady conditions help in attaining the equilibrium state.

## Applications of the Hardy Weinberg Equilibrium

The natural selection process consistently determines the variation in genetics due to migration, genetic drift, mutation, sexual and natural selection. This particular Hardy Weinberg law gives an equation for a non-evolving population. The law can be used to compare with the population that is evolving. The major application of these principles is multiple alleles, complete dominance, frequencies of recessive alleles that are harmful, sex-linked loci, and linkage disequilibrium.

• Complete dominance: This is when the equilibrium of Hardy-Weinberg prevails in a population, the alleles’ frequencies can be estimated in the existence of complete dominance but it cannot differentiate between two genotypes.
• Multiple alleles: The Hardy Weinberg principle allows for the calculation of the genotype’s frequencies at particular loci which has more than two alleles, for example the ABO blood group.
• Linkage disequilibrium: Consider two-locus in the same chromosome in which both have two or more alleles. The recombination that results in genetic exchange, which occurs regularly over a certain period can facilitate the frequencies of alleles at two syntonic loci to attain equilibrium.
• Frequencies of recessive alleles that are harmful: The Hardy Weinberg principle is used to determine the frequencies of heterozygous carriers of recessive genes that are harmful.
• Sex-linked loci: The Hardy Weinberg principle can also be applied to estimate the gene’s frequency in the case of loci that are sex-linked in both females and males.

## Practice Problems

In a class, there are 100 students. Among them, 91 performed well in the course and 9 blew it by receiving a grade of F. In the case of the greatly unlikely event that these traits are genetic instead of environmental if these traits include recessive and dominant alleles, and if the 9% represent the homozygous recessive condition’s frequency, determine the following:

• The recessive allele’s frequency.
• The dominant allele’s frequency.
• The heterozygous individual's frequency.

Solution

• The recessive allele’s frequency: Let us consider that the homozygous recessive for this gene q2 represents 9% (i.e., = 0.09), the square root of q2 is 0.3 (i.e., =30%).
• The dominant allele’s frequency: As we know, q = 0.3, and p + q = 1, then p = 0.7 (i.e., =70%).
• The heterozygous individual's frequency: In this case, the frequency is represented as 2pq. In this problem, 2pq equals 0.42, which states that the homologous individual’s frequency for this gene is 42% (i.e., 2 (0.7)(0.3) = 0.42).

## Context and Applications

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for

• Bachelors in Biology
• Masters in Biology

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