Hardy and Weinberg are two scientists who gave a law that tells about gene and the frequency of genotypes in particular gene pool. In elaborated way, in an ideal population, i.e. the condition where population is not changing in any respect, like no migration, no mutation and no selection. Overall, when no evolutionary force acts on the given population, there will be no change in gene frequency.

The above explanation can be better understood with an example. This example is mathematically illustrated so as to make a better understand on Hardy-Weinberg equation and the overall concept of gene frequency. Let’s imagine two allele of a single locus. One allele is named ‘A’ and the other can be named ‘a’. Here, let’s take a hypothetical value i.e. frequency of A to be 0.6 and that of a is 0.4. Now as per the Hardy-Weinberg rule the probability that the zygote will have A only is 0.6*0.6= 0.36. Likewise, the probability the zygote that will have Aa is 0.6*0.4= 0.24 and that of aA is 0.4*0.6= 0.24. Now finally, the probability of having aa in a zygote is 0.4*0.4= 0.16. If we see the complete procedure we can figure out that the genotype AA will occur 12 times whereas Aa will occur 24 times. Same is the case with aA and finally aa will occur 8 times. As per the Hardy-Weinberg law the distribution of genotypes among the zygotes will come to be: a_{2} + 2ab + b_{2} i.e. 0.36+ 0.48+ 0.16=1.

This calculation clearly tells us that if the population is ideal or the data we looked on are hypothetical and hence no change in frequency is noticed and genotype frequency can easily be predicted after one generation of random mating.

When the given population meets all the assumption set by Hardy-Weinberg, and no change in frequency of gene occur than equilibrium is established and hence is called Hardy-Weinberg equilibrium. To get the answer to Hardy-Weinberg equilibrium, frequency of genotype is first determine, then allelic frequency is calculated from genotypic frequency and this allelic frequency is used to predict next generation’s genotypic frequency. Finally, in the given equation, if the genotypic frequency does not fit the given equation of Hardy-Weinberg, i.e. a2+2ab+b2, then it can be said that the assumption of Hardy-Weinberg cannot be applied to the real world because all the evolutionary forces comes into play. Migration means the people who travel from one place to the other and this bring changes in the population, likewise, mutation, random mating are all the natural forces that takes place, so when real world forces is applied population changes and hence the gene frequency also changes.

Hardy-Weinberg equation and the law not only tell about the changes that take place in the genotypic frequency rather it also highlights many other important things. It tells that dominant traits do not increase after each generation. Variations also occur in the population if the change in genetic frequency takes place and finally information about many neutral genes can be figured out.

This way Hardy-Weinberg equation provides lots of information on gene and gene frequency that have helped researches to take on further studies and make the genetics at much more higher level. hardy-Weinberg has bought advancement in the genetics. The mathematical proofs have helped scientist discover much more about on genetics and work on many more of the information.

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