Exam code:8BN0
Hardy-Weinberg Equation
Hardy-Weinberg Principle
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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
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There are several conditions or assumptions that must be met for the Hardy-Weinberg principle to hold true:
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Mating must be random between individuals
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The population is infinitely large
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There is no migration, mutation or natural selection
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The Hardy-Weinberg equation allows for the calculation of allele and genotype frequencies within populations
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It also allows for predictions to be made about how these frequencies will change in future generations
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If the allele frequencies in a population change over time, then it means that migration, mutation or natural selection has happened
Hardy-Weinberg calculations
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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:
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Homozygous dominant (BB)
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Heterozygous (Bb)
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Homozygous recessive (bb)
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When using the Hardy-Weinberg equation, the frequency of a genotype is represented as a proportion of the population
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For example, the BB genotype could be 0.40
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Whole population = 1
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The letter p represents the frequency of the dominant allele (B)
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The letter q represents the frequency of the recessive allele (b)
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As there are only two alleles at a single gene locus for this phenotypic trait in the population:
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p + q = 1
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The chance of an individual being homozygous dominant is p2
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In this instance, the offspring would inherit dominant alleles from both parents ( p x p = p2 )
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The chance of an individual being heterozygous is 2pq
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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
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The chance of an individual being homozygous recessive is q2
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In this instance, the offspring would inherit recessive alleles from both parents ( q x q = q2 )
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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.
Answer:
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We will use F / f to represent dominant and recessive alleles for feather colour
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Those with the recessive phenotype must have the homozygous recessive genotype, ff
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Therefore q2 = 0.10 (as 10% of the individuals have the recessive phenotype and q2 represents this)
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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:
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Allele frequencies:
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p = F = 0.68
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q = f = 0.32
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Genotype frequencies:
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p2 = FF = 0.46
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q2 = ff = 0.10
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2pq = Ff = 0.44
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Examiner Tips and Tricks
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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