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In this essay we will discuss about the Hardy-Weinberg law of population genetics.

The formula (p + q)^{2} = p^{2} + 2pq + q^{2} is expressing the genotypic expectations of progeny in terms of gametic or allelic frequencies of the parental gene pool and is originally formulated by a British mathematician Hardy and a German physician Weinberg (1908) independently.

Both forwarded the idea, called Hardy-Weinberg law or equilibrium after their names. That both gene frequencies and genotype frequencies will remain constant from generation to generation in an infinitely large interbreeding population in which mating is at random and no selection, migration or mutation occur.

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Should a population initially be in disequilibrium, one generation or random mating is sufficient to bring it into genetic equilibrium and thereafter the population will remain in equilibrium (unchanged in gametic and zygotic frequencies) as long as Hardy-Weinberg condition persists.

**Assumptions of Hardy-Weinberg Equilibrium****: **

We will consider a population of diploid, sexually reproducing organisms with a single autosomal locus segregating two alleles (i.e., every individual is one of three genotypes – MM, MN and AW).

**The following major assumptions are necessary for the Hardy-Weinberg equilibrium to hold: **

1. Random Mating,

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2. Large Population Size,

3. No Mutation or Migration, and

4. No Natural Selection.

**1. Random Mating: **

The first assumption of Hardy-Weinberg equilibrium is random mating which means that the probability that two genotypes will mate is the product of the frequencies (or probabilities) of the genotypes in the population.

If an MM genotypes makes up 90% of a population, then any individual has a 90% chance (probability = 0.9) of mating with a person with an MM genotype. The probability of an MM by MM mating is (0.9) (0.9), or 0.81.

Any deviation from random mating comes about for two reasons: choice or circumstance. If members of a population choose individuals of a particular phenotype as mates more or less often than at random, the population is engaged in assortative mating.

If individuals with similar phenotypes are mating more often than at random, positive assortative mating is in force; if matings occur between individuals with dissimilar phenotypes more often than at random, negative assortative mating or disassortative mating is at work.

Further, deviation from random mating also arise when mating individuals are either more closely related genetically or more distantly related than individuals chosen at random from the population.

Inbreeding is the mating of related individuals, and outbreeding is the mating of genetically unrelated individuals. Inbreeding is a consequence of pedigree relatedness (e.g., cousins) and small population size.

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One of the first distinct observations of population genetics is that deviation from random mating alter genotypic frequencies but not allelic frequencies. Imagine a population in which every individual is the parent of two children on the average, each individual will pass on one copy of each of his or her alleles.

Assortative mating and inbreeding will change the zygotic (genotypic) combinations from one generation to the next, but will not change which alleles are passed into the next generation. Thus, genotypic, but not allelic frequencies change under non-random mating.

**2. ****Large Population Size: **

Although an extremely large number of gametes are produced in each generation, each successive generation is the result of a sampling of a relatively small portion of the gametes of the previous generation. A sample may not be an accurate representation of a population, especially if the sample is small.

Thus, the second assumption of the Hardy-Weinberg equilibrium is that the population is infinitely large. A large population produces a large sample of successful gametes. The larger the sample of successful gametes, the greater the probability that the allelic frequencies of the offspring will accurately represent the allelic frequencies in the parental population.

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When populations are small or when alleles are rare, changes in allelic frequencies take place due to chance alone. These changes are referred to as random genetic drift or just genetic drift.

**3. ****No Mutation or Migration: **

Allelic and genotypic frequencies may change through the loss or addition of alleles through mutation or migration (immigration or emigration) of individuals from or into a population, ne third and fourth assumptions of the Hardy-Weinberg equilibrium are that neither mutation nor migration causes such allelic loss or addition in the population.

**4. ****No Natural Selection: **

The final assumption necessary to the Hardy-Weinberg equilibrium is that no individual will have a reproductive advantage over another individual because of its genotype. In other words, no natural selection in occurring. (Note. Artificial selection, as practised by animal and plant breeders, will also perturb the Hardy-Weinberg equilibrium of captive population).

The significance of Hardy-Weinberg equilibrium was not immediately appreciated. A rebirth of biometrical genetics was later brought about with the classical papers of R.A. Fisher, beginning in 1918 and those of Sewall Wright, beginning in 1920.

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Under the leadership of these mathematicians, emphasis was placed on the population rather than on the individual or family group, which had previously occupied the attention of most Mendelian geneticists. In about 1935, T. Dobzhansky and others started to interpret and to popularize the mathematical approach for studies of genetics and evolution.

**Genetic Equilibrium****: **

As shown by Hardy and Weinberg, alleles segregating in a population tend to establish an equilibrium with reference to each other. Thus, if two alleles should occur in equal proportion in a large, isolated breeding population and neither had a selective or mutational advantage over the other, they would be expected to remain in equal proportion generation after generation. This would be a special case because alleles in natural populations seldom if ever, occur in equal frequency.

They may, however, be expected to maintain their relative frequency, whatever it is, subject only to such factors as chance, natural selection, differential mutation rates or mutation pressure, meiotic drive and migration pressure, all of which alter the level of the allele frequencies. A genetic equilibrium is maintained through random mating.