HardyWeinberg Principle/Equation/Equilibrium/Law
Introduction & Principles
The HardyWeinberg principle states that in any population allele and genotype frequencies remain constant i.e. they are in equilibrium. In order for the equilibrium to continue the following conditions require to be met:
1. No mutations must occur so that new alleles do not enter the population.
2. No gene flow can occur
3. Random mating must occur
4. The population must be sufficiently large so that no genetic drift (random chance) can cause the allele frequencies to change.
5. No selection can occur so that certain alleles are preferentially selected or not selected
If we consider two individuals that are heterozygous for a specific trait which we will designate [Aa] then during meiosis and the creation of gametes, 50% will contain the [A] allele and 50% the [a] allele. Of their offspring 25% will be homozygous [AA], 25% will be homozygous [aa] and 50% will be heterozygous [Aa] as shown in the probability table below:
A 
a 


A 
AA 
Aa 
a 
aA 
aa 
If we denote the frequency of the [A] allele as p and the frequency of the [a] allele as q, then we can denote the frequencies as: p^{2} + q^{2} + 2pq = 1.
For a three allele system: p, q and r, the frequencies can be denoted as:
p^{2} + q^{2} + r^{2} + 2pq + 2pr + 2qr = 1.
It is possible to display the data for a biallelic locus within a population graphically using a de Fitetti diagram. This graphical display is often referred to as the HardyWeinberg parabola. The curve represents the point where the alleles are in a state of HardyWeinberg equilibrium.
Data Interpretation
Consider the case of homozygous Protein C deficiency. This is a rare disorder but for this example let us assume that it affects 1/2500 births in the UK. From this we can calculate the frequency of heterozygous and homozygous [normal] individuals. We will designate the normal allele p as [PCn] and the mutant allele q as [pcm]
If we remember that p^{2} + q^{2} + 2pq = 1 and in this case p is the frequency of the [PCn] allele and q the frequency of the [pcm] allele, then:
1. q^{2} = 1/2500 = 0.0004. The square root of 0.0004 = 0.02. This is the frequency of the recessive [pcm] allele in the general population
2. The frequency of p must be 10.02 which is 0.98 and so this is the frequency of the normal [PCn] allele in the general population.
3. The frequency of heterozygotes is derived from 2pq = 2 x 0.02 x 0.98 = 0.04. So in this example 1/25 of the population are heterozygous for the PC allele and would have potentially low PC levels. In reality Homozygous PC deficiency is exceptionally rare although more frequent in countries where consanguineous marriage is common.