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4.4.7Unit 4: Energy, Environment, Microbiology and Immunity

Hardy-Weinberg Equation — IAL Edexcel Linear Revision Notes & Topical Questions

5 min read 5 parts Lesson 27 of 28 Unit quiz

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Part 1 of 5Principle and Conditions

4.4.7 Hardy-Weinberg Equation

If certain conditions hold, the allele frequencies of a gene in a population stay the same from one generation to the next.

Random mating
  • Individuals must mate at random with respect to the gene in question.
Large population
  • The population must be very large so that chance has little effect on allele frequencies.
No change
  • There must be no migration, no mutation and no natural selection.
Interpretation
  • If allele frequencies do change, then migration, mutation or selection has probably occurred.

Part 2 of 5Equations

For a gene with two alleles, a dominant (B) and a recessive (b), the population has genotypes BB, Bb and bb.

1
The frequency of the dominant allele is p and of the recessive allele is q, so p + q = 1.
2
The frequency of homozygous dominant individuals is p², and of homozygous recessive individuals is q².
3
The frequency of heterozygotes is 2pq, because the b and B can be inherited from either parent.
4
All genotypes together make the whole population, so p² + 2pq + q² = 1.
5
Start with the recessive phenotype, because it must be homozygous recessive and so gives q² directly.

Part 3 of 5Why Allele Frequencies Change

Why Allele Frequencies Change
Mutation
  • Creates new alleles, which are the primary source of genetic variation.
Natural selection
  • Selection pressures favour some phenotypes, so favoured alleles increase in frequency over generations.
Population bottleneck
  • A sudden fall in numbers shrinks the gene pool and can remove alleles, as in cheetahs.
Founder effect
  • A small group starting a new population carries only part of the variation, so rare alleles can become common.

Part 4 of 5Worked Example

Question

  • A recessive condition affects 1 in 400 people (q² = 0.0025).
  • Calculate q, p, the frequency of carriers (2pq), and the number of carriers in a population of 2000.

  1. q = √0.0025 = 0.05.
  2. p = 1 − q = 1 − 0.05 = 0.95.
  3. 2pq = 2 × 0.95 × 0.05 = 0.095, and p² = 0.9025 (check: 0.9025 + 0.095 + 0.0025 = 1).
  4. Carriers in 2000 people = 0.095 × 2000 = 190.

Answer q = 0.05, p = 0.95, carrier frequency 0.095, so 190 carriers.

Part 5 of 5Exam Checklist & Tips

4.4.7 – Key Points for the Exam

  • Allele frequency The proportion of all the alleles of a gene in a population that are one particular allele.
  • Hardy-Weinberg principle Allele frequencies stay constant between generations if no evolutionary forces act.
  • Gene pool All the alleles of all the genes in a population.
  • Founder effect Loss of variation when a new population is started by a few individuals.

Common Mistakes

  • Taking q² as the frequency of the recessive allele, when q² is the frequency of recessive homozygotes and q is the allele frequency.
  • Forgetting the factor of 2 in the heterozygote term 2pq.
  • Assuming that all individuals showing the dominant phenotype are homozygous.
  • Not checking that the three genotype frequencies add up to 1.

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