Hardy-Weinberg Law

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The 'Hardy-Weinberg Law describes the distribution of genotypes of populations of diploid, sexually reproducing organisms under a certain set of conditions, as was first formulated by G.H. Hardy and W. Weinberg.

Hardy-Weinberg Equilibrium

A population is in Hardy-Weinberg equilibrium for a given gene whenever the following conditions are met:

• The alleles for the gene in question are neither adaptive nor maladaptive, i.e. there is no selection pressure on that gene.
• Mating occurs randomly with respect to the distribution of the alleles for the gene in question, i.e. an organism with a given allele is not more or less likely to mate with an organism with any other particular variation of this gene.
• The population is self-contained, i.e. there is no influx or outflux of new alleles.
• The mutation rate of this gene is negligible.

When these conditions are met, the Hardy-Weinberg Law dictates that the frequency of each genotype in the whole population is constrained by the frequency of each allele within the population, and is constant over time.

Departures from Hardy-Weinberg Equilibrium in a population indicate that one or more of these conditions is not met, and hence may indicate selection for or against a particular allele in that population if it is known to be self-contained. It is less likely that it indicates a high mutation rate for a particular gene as mutation rates tend to be relatively low compared to the timescales on which most experiments are carried out.

Distribution of genotypes

The Hardy-Weinberg law dictates that given that a population contains two alleles, A and a, for a particular gene such that is the proportion of alleles that are of the first type, A, and is the proportion that are of the second type, a, the following equation holds true:

Where represents the fraction of the population with the genotype, AA, represents the fraction of the population with the genotype, Aa, and represents the fraction of the population with the genotype, aa.

This is actually a special case of the Hardy-Weinberg Law used to describe a population with only two alleles for a given gene. The generalized form that describes a population with n alleles for a given gene is:

Where is the proportion of the ith allele in the population, and each term of the series (after simplification by combining like terms) is the proportion of organisms with the genotype Ai Aj where Ai is the allele with frequency and Aj is the allele with frequency .