Hardy-Weinberg Equation (Edexcel A (SNAB) A Level Biology)

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Hardy-Weinberg Equation

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.

Solution:

    • 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

Natural Selection Hardy-Weinberg Principle Worked Example equation

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

Examiner 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.

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Marlene

Author: Marlene

Expertise: Biology

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.