Hardy Weinberg Law

The Hardy Weinberg law, also called as the Hardy Weinberg equilibrium or Hardy Weinberg Principle, is a concept that says in a large, non evolving & randomly mating population, allele frequencies or gene frequencies remain constant from generation to generation. There is no genetic drift, no migration, no mutation and no natural selection, which maintain the gene frequency constant.

1.0Hardy Weinberg Statement

This principle provide a mathematical formula to express a population is evolving or not :-

p + q = 1 (No change, Evolution absent)

p → frequency of dominant allele (A)

q → frequency of recessive allele (a)

Squaring at both the sides (Binomial expansion) of equation & expression will become :

(p + q)² = 1

p² + 2pq + q² = 1

where p² = frequency of individual with genotype AA

q² = frequency of individual with genotype aa

2pq = frequency of individual with genotype Aa

Note : If p+ q ≠ 1 [Evolution present]

2.0Who proposed Hardy Weinberg Law

In the twentieth century Godfrey Harold (G.H.) Hardy, a British mathematician and Wilhelm Weinberg, a German physician in 1908, each published paper describing a mathematical expression between genotype frequencies and allelic frequencies. This equation/expression, now known as Hardy Weinberg equilibrium, law or principle.

The law resolved the puzzle related to the proportions of recessive & dominant traits in a large mixed population and how mutation, gene flow, genetic drift , natural selection can alter  the genetic variation.

3.0Assumptions of Hardy Weinberg Law

Key assumptions for this law are listed below :-

• Random mating : Members of a population must mate randomly to produce the zygote of the next generation.
• No natural selection : All individuals must have equal chance for survival & reproduction.
• No mutation : It means no evolution in a population, because mutation can  leads to variation in DNA,  change allele frequencies.
• No migration : When migration of a section of population, to another place & population not occurs, migration can introduce new genes/alleles to population & disturb the Hardy Weinberg Law.
• No genetic drift : Random change of gene/allelic frequencies in a population merely by chance do not occur.
• Genetic drift operates rapidly in small population.
• Large population size : population must be large to reduce the risk of genetic drift.

4.0Infringement of Hardy Weinberg Law

• Non-random mating : Individuate mate with each other non-randomly because they are genetically or phenotypically similar, this can change the genotype frequencies & deviate Hardy Weinberg principle.
• Selection (Artificial or Natural) : Selection of a particular genotype either naturally or artificially leads to change in allele frequencies generation after generation.
• Mutation : Sudden changes of genetic material (DNA), introduce variation into a population & change the existing allele frequencies.
• Migration : When migration of a section of population to another place and population occurs, gene frequencies change in the original as well as in the new population. New genes/alleles are added to the new population and these are lost from the old population. There would be a gene flow if this gene migration, happens multiple times.
• Genetic drift : If the change in gene frequency occurs by chance, it is called genetic drift.

5.0Applications of Hardy Weinberg Law

It provide a mathematical equation to estimate the frequency of allele in a population that is constant (non-evolving).

Multiple Alleles : More than 2 alternative forms of same gene are called multiple alleles.

Example : 

ABO blood group system are determined by three alleles I^A, I^B and i                                

I^A = dominant    

I^B = dominant   

i = recessive

Possible phenotypes - A, B, AB, O

Possible number of genotypes = $\frac{3(3+1)}{2}$ = 6 genotypes.

Complete Dominance : In this Dominant allele completely masks the effect of recessive allele.

For haploid pathogens, Hardy Weinberg model is not valid.

6.0Importance of Hardy Weinberg Law

Hardy Weinberg Law has following significance :-

• It indicates evolutionary forces like genetic drift ,mutation, non-random mating, migration and natural selection which helps in changes the allelic frequencies.
• It connects allele frequencies to genotype frequencies.
• We would predict if the population was in genetic equilibrium with Hardy Weinberg law.
• Measured frequency differ from expected values, then the direction (difference) indicates the extent of evolutionary changes.

7.0Solved Questions

Question 1. For the MN-blood group system, the frequencies of A & B alleles are 0.6 & 0.4 respectively. The expected frequency of MN-blood group bearing organisms is likely to be ?

Solution: (p + q)² = p² + 2pq + q² = 1

(0.6 + 0.4)² = (0.6)² + 2pq + (0.4)²

1 = 0.36 + 2pq + 0.16

2pq = 0.48 = 48%

Question 2. In Hardy Weinberg equation, the frequency of heterozygous individual is represented by-

Solution: Binomial expansion of (p + q) = 1

(p + q)² = 1

p² + 2pq + q² = 1

where, 2pq = The frequency of heterozygous individuals with genotype Aa.