Hardy-Weinberg Law

Hardy Weinberg Law of Equilibrium:

The most fundamental idea in a population genetics was proposed by English-man G.H. Hardy and German W. Weinberg simultaneously in the year 1908. Later in 1929-30, the mathematical treatment of the distribution of gene and genotype frequencies in a population was developed principally by R.A. Fischer, JR. Haldane and Sewall Wright. The Hardy-Weinberg Law is the foundation of population genetics and of modem evolutionary theory.

This law can be defined as ‘The relative frequencies oi various kinds of genes in a large and randomly mating sexual panmictic population tend to remain constant from generation to generation in the absence of mutation, selection and gene flow”.

 

Hardy-weinberg’s law describes a theoretical situation in which a population Is undergoing no evolutionary change. It explains that if the evolutionary forces are absent, the population is large and its individuals have random mating. Thus each parent produces equal number of gametes. Such gametes combine at random and the gene frequency remains constant. Finally the genetic equilibrium of the genes is maintained and the variability present in the population is preserved.

For example, suppose there is a panmictic population with gene ‘A’ will be the same is the frequency of gene ‘A’: Similarly the frequency of gametes with ‘a’ will be equal to the frequency of the gene ‘a’.

 

If the gametes unite at random, the total number of different genotypes will be

 

There is a random union of the gametes with gene ‘A’ and ‘a’ at the

Equilibrium state, the population will contain the following frequencies of the genotypes and genes ‘A’ and ‘a’ generation after generation.

AA + 2 Aa + aa (or) p2 + pq + 42 genotype frequency. in population of large size, the probability of receiving.

i) The gent ‘A’ from both this parents will be p c p = p2, ii) for gene ‘a’ will be q x q = q2

iii) the probability of being heterozygote will be pq + pq = 2 pq.

As such the relationship between gene frequency and genotype frequency can be expressed as

2

p +2pq+q =1

2

(p+q)

- It is known as Hardy-Weinberg formula or binomial expression. it is clear that in a large and randomly mating population not only gene frequency but also the genotype frequencies will remain constant.

According to Hardy-Weinberg’ law:

i) The gene and genotype frequencies of each allele in a population remain at an equilibrium generation after generation. -

ii) in a- population, the mating is a completely random- manner.

iii) The equilibrium in the genotype and gene frequencies occurs on in large sized populations. But in small sized population gene frequencies may be un predict table.

iv) MI the genotypes in a population reproduce equally and successfully,

Example In human populations, persons with gene T find weak solution of PTC (Phenyl -thio-carbamide) to be bitter in taste. But the homozygous ‘ft persons, the PTC is tasteless, Moreover, persons are unaware of their reaction to PTC and nobody selects his mate according to whether he or she can or cannot taste this substance. As such the marriages take place at random. Suppose, in a particular island or in a town the number of homozygous tasters (17) and of homozygous non tasters is equal, the probable marriages could occur as follows.

 

Therefore, the geno type frequency in the first generation will be TT-25% Tt = 50% and It = 25%. The homgous tasters (Ti’) and heterozygous tasters (Tt) are phenotypic ally alike. So the populations possess 75% tasters and 25% are non-tasters. The same results can be obtained if we consider the union of gametes at the time of fertilization.

 

There the genotype frequencies according to Hardy-Weinberg’s equation.

0.25 TT + 0.50 Tt.+ 0.25 ft (p - is frequency for gene 1)
p2 ÷2pq+q2 =l(q isfrequency for t )

 

This law provides a situation, where the genes in the population have reached the equilibrium and the gene pool is constant In such case, there will be no evolution. In nature, the mutations, natural selection, Non- random mating, genetic drifts and differential migration operate to change the genetic equilibrium actually can bring about organic evolution.