Hardy weinberg equilibrium

Hardy Weinberg law or Equilibrium by G. H. Hardy (a mathematician) and Wilhelm Weinberg (a physician).

 “The relative frequencies of genes and alleles in a large and randomly mating (panmictic) population tend to remain constant from generation to generation without  mutation, selection, migration and genetic drift.” Acc.to the law the population is not undergoing evolutionary changes.

1.The evolutionary forces are absent (mutation, selection, drift) in the population.

2. The sizeof the population is large.

3. Its individuals are in random mating. The gametes produced by the mates combine at random and the gene frequency remains constant. 

4. There is no evolution in the population.

5. All the genotypes in a population reproduce equally successfully.

6.No emigration or immigration (no gene flow).

 Example-

Suppose a Mendelian population  allele ‘A’ and ‘a’  is on one locus. the frequency of gametes with gene ‘A’ will be same as the frequency of ‘A’ gene. Similarly the frequency of gametes with ‘a’ will be same as the frequency of ‘a’ gene.

Let the numerical proportion of different genes in this population is as follows:

                           AA                     Aa                  aa

                          36%                   48%                 16%
‘AA’ will contribute approximately 36% of all gametes in the population. ‘aa’ individuals will produce 16% of all the gametes. Gametes from ‘Aa’ individuals will contribute 48% with gene ‘A’ and with gene ‘a’ roughly in equal proportion.

If the frequency of ‘A’ is represented as ‘p’ and the frequency of ‘a’ is represented by ‘q’ and if there is random mating of gametes with genes ‘A’ and ‘a’ at the equilibrium state, the population will contain following frequencies of the genes ‘A’ and ‘a’ generation after generation:

AA + 2Aa + aa as genotype frequency

p2 + 2pq + q2 as gene frequency

In a population of large size the probability of receiving the gene ‘A’ from both parents will be p X p = p2

Similarly the probability of receiving the gene ‘a’ from both the parents will be q X q = q2

The probability of being heterozygous will be  pq + pq = 2pq

The relationship between gene frequency and genotype frequency can be expressed as:          

p2 + 2pq + q2 = 1    

or   (p + q)2 = 1

This relation is known as Hardy-Weinberg formula of binomial expression.

From this equation, it is clear that in a large random mating population not only gene frequencies but also genotype frequencies will remain constant.

                                                              Image source-http://bioap.wikispaces.com/Ch23+Collaboration

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