Hardy- Weinberg law is an interesting topic in population genetics that tells about the relationship of allele in gene pool and the frequency of genotype. Hence, it is a mathematical calculation on alleles and genotypes that defines evolution and the changes that takes place over a period of time. This law was intelligently developed by two great people, one a famous mathematician Godfrey H. Hardy and the other, a physician William Weinberg. Therefore, this law is named these scientists. Hardy- Weinberg clearly tells the condition of allele and the genotype in ideal case. Here, ideal condition refers to some of the important points, such as: the population when infinitely large and it is not affected due to any of the events like mutation, migration, selection and hence random mating takes place. Hardy- Weinberg law makes two different predictions when the above mentioned criteria is accurately fulfilled and the predictions are: allele frequency does not change with time and on the other hand if there are two alleles A and a in a single locus, after one generation of random mating, the overall population can be mathematically represented by a formula, A^{2}+2ab+B^{2}= c. Therefore, as per this law, evolution will not take place if these factors does not comes in play or if there is no migration, mutation, natural selection etc, but in the real world, it is not possible that all these factor remain stable, at one or the other point these factors will affect the population. Therefore, evolution is sure to happen and it cannot be neglected.

One equation developed by Godfrey Hardy and William Weinberg to describe the genotype in a population or its condition in upcoming generation is mathematically explained below:

A locus with two alleles A and a, among these two alleles, the frequency of A can be considered p and that of a can be considered q, now after random mating, the probability that a zygote will have allele A is p*p= p^{2}, likewise, the probability that a zygote will have allele a is q*q=q^{2}. Similarly, the probability that zygote will have both allele A and a is A*a=Aa and allele a*A=aA. Therefore, the distribution of alleles in a zygote received from male and the female is: p2+2pq+q2 that equals to one. Therefore the final equation becomes: p2+2pq+q2=1. Hence this equations very well describes the predictions made by Hardy- Weinberg law.

Hardy- Weinberg equilibrium means the stage where all the assumption and criteria on gene pool are met and the frequency of two allele of a particular locus results in predicted genotypic frequency. This is done by determining genotypic frequency and from that allelic frequency is calculated and then with the obtained result, next generation genotypic frequency is calculated. This way, if the final result fits the Hardy- Weinberg law then the equilibrium is established but alternatively if the genotype frequency does not comes out as expected then the assumptions is not acceptable or becomes invalid.

- Firstly, it helps to identify the forces that bring changes in the allele frequency.
- It helps to find out neutral alleles in the gene pool.
- It also clarifies that dominant trait does not change always generation after generation.
- From the hardy- Weinberg law or assumptions, it becomes easy for us to calculate genotype of the entire locus.
- Helps to find out about the genetic disorder in an individual.

It’s not only on the alleles and genotypes where Hardy- Weinberg law holes a major priority, instead in many cases such as: in the study of multiple alleles, ex- linked trait and heterozygote frequency also; this law can be brilliantly applied. In case of multiple allele, the best example can be blood group ABO in which multiple allele are present in the single locus. There are three alleles in this locus, IA, IB, and IO that gives six allelic combinations among which only four combinations are acceptable or noticeable. Therefore, if variables p, q, and r becomes: p+q+r=1. Thus, as per Hardy- Weinberg law, genotypic frequency becomes: (p+q+r)^{2}= p^{2}+q^{2}+r^{2}+2pq+2pr+2qr=1. . Likewise, in case of X- linked trait, where female have XY and male have XX, the frequency of male expressing the X linked traits is same as that of X- linked allele in the gene pool. Beside these two important functions: this law also helps to find out the frequency of heterozygote’s by calculating homozygous recessive in the population and hence knowing the allele and the genotype.

This way Hardy- Weinberg law plays an important role in providing different genetic information and hence clarifying the reasons for evolution at different steps.

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