# How to use the Hardy Weinberg Equation? Why is the Hardy Weinberg Equation used? And More to Know

## (EXPLAINED) – What actually is the Hardy Weinberg Equation?

The Hardy Weinberg Equation states that the allele and the genotype frequency in a population is stable when the population is not evolving.

Meaning that the allele and the genotype frequency remain constant from generation after generation when the population is not evolving and so the population is stable.

So, until and unless there are some evolutionary forces acting upon the population, there won’t be any change in the allele or the genotypic frequencies.

Mathematically,

• The Hardy Weinberg Equation for allele frequency is p+q=1, because the total frequency of both alleles will be 100% when the population is not evolving.
• The Hardy Weinberg Equation for genotype frequency is (p+q)2=1 or p2+2pq+q2=1, because the total frequency of the genotypes consisting of two alleles will also be 100% when the population is not evolving.

Here, p is the frequency of the dominant allele (A), and q is the frequency of the recessive allele (a) while taking the case that only the two allele frequencies p and q are there for the particular genotype.

Here, p2 stands for the frequency of the Homozygous dominant genotype (AA), pq stands for the frequency of the Heterozygous genotype (Aa), and q2 stands for the frequency of the Homozygous recessive genotype (aa).

It is also to be noted that the Hardy Weinberg Equation is also termed as the Genetic Equilibrium condition because the gene pool (i.e. the total genes and their alleles in a population) remains constant when there’s no evolution.

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Using this equilibrium, mathematically it is possible to predict and calculate the frequency of two alternate alleles within a population.

The principle is named after the English mathematician Godfrey Hardy and German physician Wilhelm Weinberg, to know if the population is evolving or not, and also to calculate or predict the allele and genotype frequency within the population.

## How to use the Hardy Weinberg Equation? How do you calculate p, q, and 2pq? – (Explained with an Example)

To use the Hardy Weinberg Equation we must always remember the two formulas, viz

• To calculate allele frequency, it is p+q=1
• To calculate genotype frequency, it is p2+2pq+q2=1

Example

We have a population of 1000 plants, of which 16% are dwarf (tt) plants. So, in such a case, the genotypes for the height of the plant are TT (tall), Tt (tall), Tt (tall), and tt (dwarf) in the population. So, How to find the frequencies and the number of individuals in the population with different genotypes. Let’s Know!

Here according to the genotype

• TT (tall plant genotype) is Homozygous dominant.
• Tt (tall plant genotype) is Heterozygous.
• tt (dwarf plant genotype) is Homozygous recessive.

Here according to the Hardy Weinberg Equation formulas

• p is the allele frequency of the allele T
• p2 is the genotype frequency of the genotype TT
• q is the allele frequency of the allele t
• q2 is the genotype frequency of the genotype tt
• pq is the genotype frequency of the genotype Tt

Calculations: To calculate p, q, and 2pq

• So, the frequency of the tt (dwarf plant genotype) is 0.16 i.e. q2=0.16. So, the allele frequency of t is 0.4 i.e. q=0.4 (Since, q2=0.16 ⇒ q= √(0.16) ⇒ q=0.4)
• So if, q=0.4 then, p=0.6  (Since, p+0.4 =1 ⇒ p=1-0.4 ⇒ p=0.6)
• So if, p=0.6 then, p2=0.36 (Since, p2=(0.6)2=0.36)
• So now, 2pq=0.48 (Since, 2pq=2×0.6×0.4=0.48)

Substituting these numbers for frequencies and applying them to the original population shows that

• 36% of the plants are Homozygous dominant (TT), which is 360 individual plants (Since, 0.36×1000=180).
• 16% of the plants are Homozygous recessive (tt), which is 160 individual plants (Since, 0.16×1000=160).
• 48% of the plants are Heterozygous (Tt), which is 480 individual plants (Since, 0.48×1000=480).

Results

• So, 360 plants are Tall plants with genotype TT.
• So, 160 plants are Dwarf plants with genotype tt.
• So, 480 plants are Tall plants with genotype Tt.

## Why is the Hardy Weinberg Equation used?

Here are some of the Uses & Applications of the Hardy Weinberg Equation. Let’s Know:

1. This is used to calculate the genetic variation of a population at equilibrium.

2. This is used to determine the allele and genotype frequencies in a population.

3. This is used to determine the number of individuals in a population with the same allele and genotype in the particular locus of the chromosome.

4. This equilibrium is used in population genetical studies as it indicates the unchanging frequency of alleles and genotypes in a stable, idealized population which is not evolving.

5. This can also be used in determining the complete dominance of the genotype when the two alleles in the genotype cannot be distinguished.

6. This can also be used to calculate the frequency of heterozygous carriers of harmful recessive genes.

7. This is also helpful in calculating the frequency of the genotype with more than two alleles. In such cases, the equation changes a bit. Just for three alleles, the equation will be (p+q+r)2=1, for four alleles the equation will be (p+q+r+s)2=1, and so on.

8. This equilibrium can also be used for calculating the gene frequencies in case of sex-linked loci in both males and females.

9. This can also be used to determine the linkage disequilibrium if linkage equilibrium is not reached in a gene pool (i.e. the total genes and their alleles in a population). Linkage equilibrium is the state of genetic equilibrium in a population that can be reached due to genetic exchange by recombination with two or more alleles at one locus and another locus on the same chromosome with two or more alleles.

10. Hardy-Weinberg principle provides a mathematical baseline for studying non-evolving populations by comparing them with the evolving populations and thereby to come with various analysis, predictions, and conclusions about what evolutionary forces might be at play in the evolution of the population.

## Why does the Hardy Weinberg equation equal 1?

The Hardy Weinberg equilibrium equation is always equal to 1 because it indicates that the population is not evolving, and so, is stable.

The reason that the combined frequencies of p and q must equal 1, since together they represent all the alleles for that trait in the population at the same locus of the same chromosome.

In a more clear statement, the Hardy Weinberg equilibrium equation is always equal to 1, because the total frequency of both alleles will be 100% when the population is not evolving.

So, p+q=1, or you can say, (p + q)²=1. Here, 1 represents that the total frequency of both alleles (p & q) will be 100%.

This statement that the population is not evolving is not true at all in the real world scenario, as no population on the earth remains stable for generations. So, in the real world, there will be changes in the allele and genotype frequency.

But, while calculating the particular allele or genotype frequency in a population we always consider that population to be not evolving at all so that we can calculate the frequency clearly and predict the availability of the alleles and genes.

So, for that reason, we equal the sum total of all of the alleles or genes to be always equal to 1. This indicates that the equation is constant and so the population is stable without evolution.

And, if the Hardy Weinberg Equilibrium equation doesn’t equal 1, then this would clearly indicate that the population is surely evolving and that would make the meaning of the equaltion wrong and so it wouldn’t have been so easily possible to mathematically calculate or predict the allele and gene frequency.

## Why is there a 2 in 2pq in the Hardy Weinberg Equilibrium equation?

There is 2 in 2pq in the Hardy Weinberg Equilibrium equation because it represents the frequency of the Heterozygous genotype (Aa), if we want to calculate the genotype frequency of the population.

We know that the Hardy Weinberg Equation for allele frequency is p+q=1, where p and q are the two different alleles of the same gene at the same locus of the same chromosome.

And, the Hardy Weinberg Equation for genotype frequency is (p+q)(p+q)=1, where there are two p and two q respectively in the genotype. So, it’s (p+q)2=1 or p2+2pq+q2=1.

So, in algebra, we know that the formula for (a+b)2 is a2+2ab+b2. So, for that reason, equating p2+2pq+q2 for (p+q)2 in the Hardy Weinberg Equation gives us 2 in 2pq. This allows the proper calculation of the genotype frequency of the population.

In the equation, p2 represents the frequency of the homozygous genotype AA, q2 represents the frequency of the homozygous genotype aa, and 2pq represents the frequency of the heterozygous genotype Aa.

In addition, the sum of the allele and genotype frequencies for all of the alleles at the locus must be 1, so p+q=1 and p2+2pq+q2=1.

So, if you want to calculate the allele frequency, 2pq isn’t required. Whereas, if you want to calculate the genotype frequency, then the value of 2pq needs to be evaluated to predict the genotype frequency in the given population.

## What are the factors that affect the Hardy Weinberg equilibrium?

The factors that can affect the Hardy Weinberg equilibrium equation are Genetic Recombination, Mutation, Gene drift, Gene flow, and Natural selection.

1. Genetic recombination during sexual reproduction leads to diversity in the genotype and phenotype of different organisms causing evolution. This causes the production of offspring with combinations of traits that differ from those found in either parent.
2. Mutations are permanent changes in the gene sequence of DNA that alter genes and alleles leading to genetic variation in a population.
3. Genetic drift causes a small group of the population to separate from the larger population. This causes the less availability of all the alleles in the small group thus causing a change in the frequencies of certain genes. This causes evolution.
4. Gene flow is the migration of new members in the population from another population. This positively results in the addition of new alleles into the existing gene pool causing changes in the allele frequencies.
5. Natural Selection is a process where the organisms that are better adapted to an environment will survive and reproduce. This means that the advantageous alleles of an adapted organism are passed on to the offspring and the unadapted ones get extinct.

We know that the Hardy Weinberg equilibrium indicates no evolution in the population, but due to the above-mentioned factors affecting the population evolution do occur in the real world that doesn’t allow the establishment of the equilibrium in the real practical world.

In other words, the Hardy-Weinberg principle just assumes conditions with no mutations, migration, or natural selective pressure for or against genotype in a large population.

In the real world, however, no population can satisfy these conditions, as this principle only offers a useful model to compare real population changes.

## What happens if the Hardy Weinberg Equilibrium is violated?

If the Hardy Weinberg equilibrium is violated due to the various factors of evolution then the allele frequency will change. Simply meaning that the allele frequencies may change from one generation to the next.

This mainly happens as a result of natural selection over the long run when individuals with certain genotypes survive better than others, then the allele frequencies may change from one generation to the next.

Over the small run, when the various evolutionary forces add up together then mutation, genetic drift, gene flow, genetic recombination alters the allele frequencies from one generation to the next.

But times like when inbreeding occurs in a small population for some generations, then the number of heterozygotes (Aa) will decrease because the individuals that are mating have the same alleles. This won’t violate the equilibrium a lot as the chances of evolution are very very low if the other evolutionary forces don’t act upon it.

Cases like when the population is large enough so that accident of sampling may be ignored, or when mating takes place at random, or when mutation takes place at the rate which is same in both directions, or when all of the members of the population survive and have equal reproduction rates. During such cases, the Hardy Weinberg equilibrium is less likely to be violated.