Edexcel International A Level Biology

Revision Notes

4.20 Hardy-Weinberg Equation

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Changes in Allele Frequency

Hardy-Weinberg Principle

  • The Hardy-Weinberg principle states that if certain conditions are met, the allele frequencies of a gene within a population will not change from one generation to the next
  • There are several conditions or assumptions that must be met for the Hardy-Weinberg principle to hold true:
    • Mating must be random between individuals
    • The population is infinitely large
    • There is no migration, mutation or natural selection
  • The Hardy-Weinberg equation allows for the calculation of allele and genotype frequencies within populations
  • It also allows for predictions to be made about how these frequencies will change in future generations
  • If the allele frequencies in a population change over time, then it means that migration, mutation or natural selection has happened

Hardy-Weinberg calculations

  • If the phenotype of a trait in a population is determined by a single gene with only two alleles (we will use B / b as examples throughout this section), then the population will consist of individuals with three possible genotypes:
    • Homozygous dominant (BB)
    • Heterozygous (Bb)
    • Homozygous recessive (bb)
  •  When using the Hardy-Weinberg equation, the frequency of a genotype is represented as a proportion of the population
    • For example, the BB genotype could be 0.40
    • Whole population = 1
    • The letter p represents the frequency of the dominant allele (B)
    • The letter q represents the frequency of the recessive allele (b)
    • As there are only two alleles at a single gene locus for this phenotypic trait in the population:

p + q = 1

  • The chance of an individual being homozygous dominant is p2
    • In this instance, the offspring would inherit dominant alleles from both parents ( p x p = p2 )
  •  The chance of an individual being heterozygous is 2pq
    • Offspring could inherit a dominant allele from the father and a recessive allele from the mother ( p x q ) or offspring could inherit a dominant allele from the mother and a recessive allele from the father ( p x q ) = 2pq
  • The chance of an individual being homozygous recessive is q2 
    •  In this instance, the offspring would inherit recessive alleles from both parents ( q x q = q2 )
  • As these are all the possible genotypes of individuals in the population, the following equation can be constructed:

p2 + q2 + 2pq = 1

Worked example

In a population of birds, 10% of the individuals exhibit the recessive phenotype of white feathers. Calculate the frequencies of all genotypes.


    • We will use F / f to represent dominant and recessive alleles for feather colour
    • Those with the recessive phenotype must have the homozygous recessive genotype, ff
    • Therefore q2 = 0.10 (as 10% of the individuals have the recessive phenotype and q2 represents this)

To calculate the frequencies of the homozygous dominant ( p2 ) and heterozygous ( 2pq ):

Step 1: Find q

square root of q squared end root equals square root of 0.1 end root equals 0.32

Step 2: Find p (the frequency of the dominant allele F). If q = 0.32, and p + q = 1

p + q = 1

p = 1 - 0.32

p = 0.68

Step 3: Find p2 (the frequency of homozygous dominant genotype)

0.682 = 0.46

p2 = 0.46

Step 4: Find 2pq = 2 x (p) x (q)

2 x (0.68) x (0.32)

= 0.44

Step 5: Check calculations by substituting the values for the three frequencies into the equation; they should add up to 1

p2 + 2pq + q2 = 1

0.46 + 0.44 + 0.10 = 1

In summary:

  • Allele frequencies:
    • p = F = 0.68
    • q = f = 0.32
  • Genotype frequencies:
    • p2 = FF = 0.46
    • q2 = ff = 0.10
    • 2pq = Ff = 0.44

Exam Tip

When you are using Hardy-Weinberg equations, start your calculations by determining the proportion of individuals that display the recessive phenotype - you will always know the genotype for this: homozygous recessive. Remember that the dominant phenotype is seen in both homozygous dominant, and heterozygous individuals.  Also, don’t mix up the Hardy-Weinberg equations with the Hardy-Weinberg principle. The equations are used to estimate the allele and genotype frequencies in a population. The principle suggests that there is an equilibrium between allele frequencies and there is no change in this between generations.

Reasons for Changes in Allele Frequency


  • Organisms of the same species will have very similar genotypes, but two individuals (even twins) will have differences between their DNA base sequences
  • Considering the size of genomes, these differences are small between individuals of the same species
  • The small differences in DNA base sequences between individual organisms within a species population is called genetic variation
  • Genetic variation is transferred from one generation to the next and it generates phenotypic variation within a species population
  • The primary source of genetic variation is mutation (changes in the DNA base sequence)
  • Mutation results in the generation of new alleles
    • The new allele may be advantageous, disadvantageous or have no apparent effect on phenotype
    • New alleles are not always seen in the individual that they first occur in
    • They can remain hidden (not expressed) within a population for several generations before they contribute to phenotypic variation

Natural selection

  • Variation exists within a species population
  • This means that some individuals within the population possess different phenotypes (due to genetic variation in the alleles they possess; remember members of the same species will have the same genes)
  • Environmental factors affect the chance of survival of an organism; they, therefore, act as a selection pressure
  • Selection pressures increase the chance of individuals with a specific phenotype surviving and reproducing over others
  • The individuals with the favoured phenotypes are described as having a higher fitness
    • The fitness of an organism is defined as its ability to survive and pass on its alleles to offspring
    • Organisms with higher fitness possess adaptations that make them better suited to their environment
  • When selection pressures act over several generations of a species, they can cause a change in the allele frequency and the phenotype frequency in a population through natural selection
    • Natural selection is the process by which individuals with a fitter phenotype are more likely to survive and pass on their alleles to their offspring so that the advantageous alleles increase in frequency over time and generations

An example of natural selection in rabbits

  • Variation in fur colour exists within rabbit populations
  • At a single gene locus, normal brown fur is produced by a dominant allele whereas white fur is produced by a recessive allele in a homozygous individual 
  • Rabbits have natural predators like foxes which act as a selection pressure
  • Rabbits with a white coat do not camouflage as well as rabbits with brown fur, meaning predators are more likely to see white rabbits when hunting
  • As a result, rabbits with white fur are less likely to survive than rabbits with brown fur
  • The rabbits with brown fur have a selection advantage, so they are more likely to survive to reproductive age and be able to pass on their alleles to their offspring
  • Over many generations, the frequency of alleles for brown fur will increase and the frequency of alleles for white fur will decrease

White and brown rabbits natural selection

Selective pressure acting on a rabbit population for one generation. Predation by foxes causes the frequency of brown fur alleles in rabbits to increase and the frequency of white fur alleles in rabbits to decrease

Reproductive Isolation

  • Organisms that belong to the same species share the same characteristics and are able to produce fertile offspring
  • Reproductive isolation occurs when changes in the alleles and phenotypes of some individuals in a population prevent them from successfully breeding with other individuals in the population that don't have these changed alleles or phenotypes
  • Examples of allele or phenotype changes that can lead to reproductive isolation include:
    • Seasonal changes - some individuals in a population may develop different mating or flowering seasons (becoming sexually active at different times of the year) to the rest of the population (i.e their reproductive timings no longer match up)
    • Mechanical changes - some individuals in a population may develop changes in their genitalia that prevent them from mating successfully with individuals of the opposite sex (i.e. their reproductive body parts no longer match up)
    • Behavioural changes - some individuals in a population may develop changes in their courtship behaviours, meaning they can no longer attract individuals of the opposite sex for mating (i.e. their methods of attracting a mate are no longer effective)
  • These changes could be brought about due to geographical barriers isolating populations or random mutations producing new, different alleles in a population


  • Speciation can occur when populations of a species become separated from each other by geographical barriers
    • The barrier could be natural like a body of water, or a mountain range
    • It can also be man-made, like a motorway
  • This creates two populations of the same species who are reproductively isolated from each other, and as a result, no genetic exchange can occur between them
  • If there are sufficient selection pressures acting to change the gene pools (and allele frequencies) within both populations then eventually these populations will diverge and form separate species 
    • The changes in the alleles/genes of each population will affect the phenotypes present in both populations
    • Random mutations within each population will also change allele frequencies in each
    • Over time, the two populations may begin to differ physiologically, behaviourally and anatomically (structurally)
  • This type of speciation is known as allopatric speciation


Allopatric speciation occurring due to geographical isolation of two populations of the same species

  • Sometimes populations of the same species live in the same geographical area but they become separated from each other by ecological or behavioural means
    • An example of ecological separation is populations that live in different environments within the same area e.g. plants growing in soil with different pH levels may flower at different times from each other causing reproductive isolation
  • This type of speciation that occurs without the presence of a geographical barrier is known as sympatric speciation

Reproductive separation leading to speciation

Reproductive separation due to behavioural changes that resulted in sympatric speciation occurring

Population bottlenecks

  • A large population is required for the maintenance of a diverse gene pool
  • Sometimes dramatic events occur (such as natural disasters or disease) that decrease the size of a population dramatically
  • This is known as a population bottleneck
  • It can lead to a significant decrease in the size of the gene pool of the population and will have a dramatic effect on the allele frequencies as a result thereof
  • The remaining population will be more susceptible to the loss of alleles and the effects of mutations will be magnified in the new population
    • An example is the cheetah which survived a near-extinction event in the past
    • Only a few individuals remained and as a result the genetic diversity of all living cheetahs are very low
    • This makes them very vulnerable to disease or environmental changes

Bottleneck effect in cheetahs_2

A population bottleneck in the past has dramatically decreased the genetic variation in cheetahs populations

The Founder effect

  • This refers to the loss of genetic variation if a new population is formed by a small number of individuals that left the main population
  • Since the initial gene pool is small, it is unlikely that it will contain the genetic variation of the original population that the individuals came from
  • Should any of these individuals carry unusual mutations in their genome, these will appear more frequently in the new population
    • An example of this is the unusually high occurrence of Ellis-van Creveld syndrome (a type of dwarfism) among the Amish community in the USA
    • This was the result of a few individuals that were heterozygous for the recessive allele that formed part of the founding Amish population

The founder effect in lizards

The Founder effect can amplify the occurrence of genetic mutations in a population due to the small gene pool of the founding members

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Author: Marlene

Marlene graduated from Stellenbosch University, South Africa, in 2002 with a degree in Biodiversity and Ecology. After completing a PGCE (Postgraduate certificate in education) in 2003 she taught high school Biology for over 10 years at various schools across South Africa before returning to Stellenbosch University in 2014 to obtain an Honours degree in Biological Sciences. With over 16 years of teaching experience, of which the past 3 years were spent teaching IGCSE and A level Biology, Marlene is passionate about Biology and making it more approachable to her students.