4.1.6 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

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

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