Hardy-Weinberg (AQA A Level Biology): Revision Note
Exam code: 7402
Natural selection: Hardy-Weinberg principle
The Hardy-Weinberg principle states that allele frequencies in a population will remain constant from one generation to the next if specific conditions are met
The equation can be used to:
Calculate allele and genotype frequencies
Predict how these frequencies will change across generations
Conditions for the Hardy-Weinberg principle
For the Hardy-Weinberg principle to be correctly applied to a population a series of conditions, or assumptions, need to be met
Organisms are diploid
Organisms reproduce by sexual reproduction only
There is no overlap between generations (parents do not mate with offspring)
Mating is random
The population is large
There is no migration, mutation, or selection
This would mean no individuals entering the population (immigration) or leaving (emigration)
Selection refers to both natural and artificial selection
Allele frequencies are equal in both sexes
The Hardy-Weinberg principle can be useful when building models and making predictions, but the assumptions listed are very rarely, if ever, all present in nature
Hardy-Weinberg equations
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)
All frequencies are expressed as proportions (values between 0 and 1)
For example:
if every individual in the population has the homozygous dominant genotype (BB), its frequency will be 1
if half of the population show this genotype, then the frequency will be 0.5
Allele frequencies
For a gene with two alleles (B and b):
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 for this gene:
p + q = 1
For example:
In a population of 100 individuals, there are 200 alleles
If there are 120 dominant (B) alleles, the frequency of the dominant allele = 120/200
Therefore:
p = 120 ÷ 200 = 0.6
q = 1 - 0.6 = 0.4
Genotype frequencies
Frequency of genotypes can also be represented; this is the proportion of all of the individuals with a particular genotype
For a gene with two alleles (B and b):
The homozygous dominant (BB) genotype is represented by p2
The heterozygous genotype (Bb) is represented by 2pq
The homozygous recessive genotype (bb) is represented by 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
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 Tips and Tricks
Tips for approaching a Hardy-Weinberg calculation question
Start with q²: Always begin by identifying the frequency of the recessive phenotype
This is the only genotype you can determine directly (must be homozygous recessive, bb)
Identify known and unknown values:
Check what the question gives you (e.g. q² or p)
Work out what it asks for (e.g. 2pq)
Use the appropriate equation(s) to connect them
Don’t confuse the equations with the principle:
The equations estimate allele and genotype frequencies
The principle assumes no change in allele frequencies between generations (i.e. genetic equilibrium)
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