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4.1.6Topic 4 · Biodiversity and Natural Resources

Hardy-Weinberg Equation — Edexcel A Level Biology A (SNAB) 9BI0 Revision Notes & Topical Questions

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📚 Edexcel A Level Biology A (SNAB) 9BI0 Hub / Topical Revision
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4.1.6 Hardy-Weinberg Equation — Edexcel A Level Biology A (SNAB) 9BI0 notes: Use the Hardy-Weinberg equations to calculate allele and genotype frequencies and to test whether a population is evolving.The gene pool is the set of all alleles in a population.The allele frequency is …

  • What the symbols mean
  • p2 + 2pq + q2 = 1
  • Exam-style question 1
  • Exam-style question 2
  • Exam-style question 3
  • Genetic drift

Section 1 of 9Gene pools and frequencies

The gene pool is the set of all alleles in a population.

Allele frequency
The allele frequency is the proportion of all the alleles of a gene that are of a given type.
For a gene with two alleles, dominant A and recessive a, we use p for the frequency of A and q for the frequency of a.
Because there are only two alleles:

p + q = 1

What the symbols mean: p = frequency of the dominant allele · q = frequency of the recessive allele · p2 = homozygous dominant · 2pq = heterozygous · q2 = homozygous recessive

Evolution can be defined as a change in allele frequencies in a population over generations.

Section 2 of 9The Hardy-Weinberg principle

The Hardy-Weinberg principle states that in a large population in which certain conditions are met, allele frequencies and genotype frequencies stay constant from one generation to the next. The conditions are:

1
The population is very large, so chance effects (genetic drift) are negligible.
2
Mating is random.
3
There is no mutation.
4
There is no migration (gene flow) into or out of the population.
5
There is no natural selection: all genotypes are equally likely to survive and reproduce.

No real population meets all these conditions, but the equation gives a useful baseline and a way to measure how far a population differs from it.

Section 3 of 9The equations

When random mating occurs, the genotype frequencies are given by the expansion of (p + q)2:

p2 + 2pq + q2 = 1

TermMeaning
p2Frequency of homozygous dominant (AA)
2pqFrequency of heterozygous (Aa)
q2Frequency of homozygous recessive (aa)

Frequencies are given as decimals between 0 and 1, so a percentage must be divided by 100.

Section 4 of 9Worked method

1
Identify the group you can count exactly. This is usually the homozygous recessive phenotype, whose genotype is aa, so its frequency is q2.
2
Take the square root to find q.
3
Calculate p = 1 - q.
4
Calculate p2 and 2pq to find the other genotype frequencies.
5
To find a number of individuals, multiply the frequency by the population size.

Example

  • cystic fibrosis affects about 1 in 2500 people in a population, so q2 = 0.0004, giving q = 0.02, p = 0.98, and the carrier frequency 2pq = 2 x 0.98 x 0.02 = 0.0392, or about 1 in 25.
  • This shows that many more people carry the recessive allele than show the condition, because the allele is hidden in heterozygotes.

Section 5 of 9Using the equation to detect evolution

If the observed genotype frequencies in a population differ from those predicted by the Hardy-Weinberg equation, or if allele frequencies change between generations, then one or more of the conditions is not being met and evolution is occurring.

Using the equation to detect evolution
For example, if antibiotic resistance in bacteria is increasing, the frequency of the resistance allele is rising due to natural selection.
A sudden fall in numbers (a population bottleneck) or the founding of a new population by a few individuals (founder effect) changes allele frequencies by chance.
The method can be used to study populations of humans, to find carrier frequency of genetic diseases such as sickle cell anaemia or phenylketonuria,
  • which helps in planning healthcare screening.

Section 6 of 9Limitations and exam tips

Only two alleles are assumed, and the equation applies to one gene at a time.

Limitations and exam tips
A calculated value is only as accurate as the assumptions.
Dominance is needed so that the recessive homozygote can be identified from the phenotype,
  • so for codominant alleles the three genotypes can be counted directly.
Always show each step, give answers to the appropriate number of decimal places, and check that p2 + 2pq + q2 adds to 1.
  • A frequent error is to treat the dominant phenotype frequency as p2;
    • it is actually p2 + 2pq, because both AA and Aa show the dominant phenotype.

A second worked example uses a codominant or counted system.

1
In a sample of 200 people, 98 are MM, 84 are MN and 18 are NN.
2
The number of M alleles is (2 x 98) + 84 = 280 out of 400 alleles, so the frequency of M is 0.7 and of N is 0.3.
  • The Hardy-Weinberg expected numbers are p2 x 200 = 98, 2pq x 200 = 84 and q2 x 200 = 18,
  • so the observed and expected values match and the population is in equilibrium for this gene.
3
A chi-squared test can be used to judge whether any difference between observed and expected numbers is significant.
4
The Hardy-Weinberg model is also used in public health to estimate how common a recessive disease allele is,
  • and how the frequency of carriers changes if selection acts against affected homozygotes.
5
Because selection against a rare recessive allele removes it only from homozygotes, the allele falls in frequency very slowly,
  • since most copies are hidden in heterozygous carriers.

Section 7 of 9Exam-style questions

  1. In a population of 1000 beetles, 90 have a recessive phenotype of yellow wing cases. Calculate the frequency of the dominant allele and the number of heterozygotes. [4]4 marks

  2. State three conditions necessary for the Hardy-Weinberg principle to apply. [3]3 marks

  3. In a population the frequency of allele A is 0.6 in one generation and 0.5 in the next. Explain what this shows. [2]2 marks

Section 8 of 9Key terms

TermMeaning
Allele frequencyThe proportion of a particular allele among all the alleles of a gene in a population.
Gene poolAll the alleles of all the genes in a population.
Genetic driftRandom change in allele frequency, especially in small populations.
Founder effectReduced genetic variation when a new population is founded by few individuals.
BottleneckA sharp fall in population size that reduces genetic variation.
Hardy-Weinberg principleThe prediction that allele frequencies stay constant under specified conditions.

Section 9 of 9Exam technique

1
Assuming that q2 is the frequency of the recessive allele. q is the allele frequency; q2 is the frequency of the recessive genotype.
2
Using percentages rather than decimals in the equation.
3
Treating the dominant phenotype frequency as p2 alone.
4
Forgetting that the equation assumes no selection, so it cannot be used when selection is acting.
5
Not square-rooting q2 to get q.

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