Hardy-Weinberg Principle

This lesson covers: 

  1. The assumptions of the Hardy-Weinberg principle
  2. The Hardy-Weinberg equation
  3. Applying the principle to calculate allele frequencies

What is the Hardy-Weinberg principle?

The Hardy-Weinberg principle involves a mathematical equation that helps calculate the frequencies of alleles for a particular gene within a population. Allele frequency refers to how often an allele appears in a population.


In this context, a population is defined as a group of organisms of the same species living in a specific area at a certain time, with the potential to interbreed.

The assumptions of the Hardy-Weinberg principle

The Hardy-Weinberg principle states that allele frequencies in a population will remain constant across generations if certain conditions are fulfilled.


The key assumptions are:

  • No mutations occur.
  • There is no migration into or out of the population.
  • Mating is random.
  • The population size is large.
  • There are no natural selection pressures.


In essence, the gene pool, which comprises all alleles of all genes in all individuals of a population at a given time, stays consistent over time. This concept of genetic equilibrium is crucial for analysing changes in gene frequencies over time.

The Hardy-Weinberg equation

The Hardy-Weinberg equation models the relationship between allele frequencies.


The variables it includes are as follows:

  • p - The frequency of the dominant allele.
  • q - The frequency of the recessive allele.
  • p2 - The frequency of homozygous dominant individuals (derived as if the genotype were pp).
  • 2pq - The frequency of heterozygous individuals (derived as the genotype could be either pq or qp).
  • q2 - The frequency of homozygous recessive individuals (derived as if the genotype were qq).


The total of all possible allele combinations must equal 1:

p2+2pq+q2=1

This equation links genotype frequencies directly to allele frequencies.


The sum of all alleles for this gene in the population must also equal 1:

p+q=1

These two equations can be rearranged to calculate allele frequencies.

Worked example - Calculating allele frequencies in a population

Imagine a scenario where a recessive allele a causes a rare genetic disorder in 1 out of 40,000 people in a large population. Calculate the frequency of the dominant allele A and the heterozygous genotype Aa.


Step 1: Equations

p2+2pq+q2=1

p+q=1

q2= frequency of homozygous recessives (aa)


Step 2: Identify q2 and calculate q

as 1 in 40,000 individuals are homozygous recessive (aa), we can calculate q2

q2=40,0001​=0.000025

q= frequency of recessive allele (a) =√q2​=√0.000025=0.005


Step 3: Rearrangement to find p

p=1−q

p= frequency of dominant allele (A) =1−0.005=0.995


Step 4: Substitution and correct evaluation

2pq= frequency of heterozygotes (Aa)

2pq=2×0.995×0.005=0.00995


therefore, the frequency of the heterozygous genotype Aa is 0.00995, or 0.995%, within the population