What you need to know
- 4.20(i)Hardy–WeinbergEquations p + q = 1 and p² + 2pq + q² = 1 that predict allele and genotype frequencies in a large population that is not evolving. equation to see whether allele frequencyHow common an allele is in a gene pool, as a proportion of all the alleles of that gene. is changing over time.
- 4.20(ii)Allele-frequency change from mutationA change in the sequence of bases in DNA. and natural selectionIndividuals with alleles that give an advantage are more likely to survive and reproduce, so those alleles become more common over generations..
Hardy–Weinberg is a null model. Genetic drift, migration and non-random mating also change frequencies; mention them as reasons the model can fail, but the required drivers in 4.20(ii) are mutation and natural selection. Speciation from isolation is the next lesson. Heterozygosity H (4.17) is a sample statistic; 2pq is a Hardy–Weinberg prediction.
By the end, you should be able to…
- Define a gene poolAll the alleles of all the genes in a population. and genetic diversityThe variety of alleles in a population or species..
- Calculate p, q and expected genotypeThe alleles an organism has for a gene. frequencies.
- Explain how mutation and selection change allele frequency.
Build your understanding
The gene pool is the stock of alleles
A gene poolAll the alleles of all the genes in a population. is all the alleleA different version of the same gene, found at the same locus. in a reproducing populationAll the individuals of one species living in one area at the same time. or speciesA group of organisms that can interbreed to produce fertile offspring.. genetic diversityThe variety of alleles in a population or species. is the variety of those alleles. A large, outbreeding population usually holds more diversity than a tiny captive group. Diversity matters because some alleles may prove useful if the environment changes; it is not automatically “better geneA sequence of DNA bases that codes for a polypeptide or a functional RNA.”.
The heterozygosityA measure of genetic diversity: H = number of heterozygotes ÷ number of individuals, for one gene locus. index from 4C 2 estimates diversity at a scored marker. Hardy–WeinbergEquations p + q = 1 and p² + 2pq + q² = 1 that predict allele and genotype frequencies in a large population that is not evolving., below, is a different tool: it predicts genotypeThe alleles an organism has for a gene. frequencies from allele frequencyHow common an allele is in a gene pool, as a proportion of all the alleles of that gene. if several assumptions hold.
The Hardy–Weinberg null model
For two alleles, p + q = 1. If mating is random and other assumptions hold, genotype frequencies are p² (homozygousHaving two identical alleles of a gene. p), 2pq (heterozygousHaving two different alleles of a gene.) and q² (homozygous q), and p² + 2pq + q² = 1. You can estimate q from the frequency of a recessiveAn allele that is expressed in the phenotype only when no dominant allele is present (when homozygous). phenotypeThe observable characteristics of an organism, produced by its genotype interacting with the environment. as √(q²), then find p = 1 − q, then expected heterozygotes as 2pq.
The Hardy–Weinberg null model (continued)
Fictional example: 16 of 100 diploidHaving two sets of chromosomes (2n), one from each parent. organisms show a recessive phenotype, so q² = 0.16, q = 0.40, p = 0.60. Expected heterozygote frequency is 2 × 0.60 × 0.40 = 0.48, so 48 individuals. If you later measure p = 0.45 in the same population, allele frequency has changed and Hardy–Weinberg is not describing a static pool.
Mutation and selection move p and q
Mutation introduces new alleles, or extra copies of an allele, so it can change p and q. Most mutationA change in the sequence of bases in DNA. are not advantageous; the specification still requires mutation as a source of change. natural selectionIndividuals with alleles that give an advantage are more likely to survive and reproduce, so those alleles become more common over generations. then changes frequency when genotypes differ in survival or reproduction. Alleles that improve success become more common in the next generation.
Assumptions behind Hardy–Weinberg include no selection, no mutation, no migration, random mating and a large population (so drift is negligible). Real populations often break them. The equation is still useful: it is the pattern you would see if nothing were changing, so a mismatch is evidence that something is.
NOT: selection does not create the allele. Mutation does not, by itself, make it common.
- Frequency is a proportion of the pool, not a count of species
- Hardy–Weinberg assumes no selection and no mutation
- Drift and migration can also change frequencies
- The required drivers to name are mutation and selection
Two traps this diagram blocks
- Do not say selection produces the mutation it then favours.
- Do not treat a Hardy–Weinberg calculation as proof that selection is happening. Agreement with the model suggests those forces are not currently detectable.
From the diagram alone
Question
Explain the different roles of mutation and natural selection in changing a gene pool. [3]
Show a model answer
Mutation can add a new allele to the gene pool. Natural selection then changes how common alleles are, because individuals with an advantageous allele are more likely to survive and reproduce. Selection does not create the new base sequence.
| Quantity | What it is | Typical use |
|---|---|---|
| Heterozygosity index H | Counted heterozygotes / N at a marker | Measure diversity in a sample (4.17) |
| 2pq | Hardy–Weinberg expected heterozygote frequency | Predict genotypes from p and q (4.20) |
| Change in p or q over time | Allele frequency not constant | Evidence that mutation, selection or another process is acting |
Make your reasoning visible
Start from the recessive phenotype if that is what you can see
q² is the recessiveAn allele that is expressed in the phenotype only when no dominant allele is present (when homozygous). frequency only if the alleleA different version of the same gene, found at the same locus. is recessive. State that assumption.
Compare two times
4.20(i) is about change over time. One snapshot can fit Hardy–WeinbergEquations p + q = 1 and p² + 2pq + q² = 1 that predict allele and genotype frequencies in a large population that is not evolving. and still not prove the populationAll the individuals of one species living in one area at the same time. never changes.
Key explanations
- The gene poolAll the alleles of all the genes in a population. is the complete set of alleles in a population.
- mutationA change in the sequence of bases in DNA. can introduce a new allele. Until then selection cannot increase that allele.
- natural selectionIndividuals with alleles that give an advantage are more likely to survive and reproduce, so those alleles become more common over generations. increases the frequency of an allele that makes survival or reproduction more likely in that environment.
Avoid this misconception
The claim: If a population matches Hardy–Weinberg this year, evolution has stopped for ever.
The correction: It is a null model for those conditions. Selection, mutation, migration or drift can still change frequencies later.
Is this population changing? Use Hardy–Weinberg to find out
A gene pool is all the alleles in a population. The Hardy–Weinberg equation predicts what the gene pool looks like if nothing is changing it. In the model below you can switch on the things that do change it and watch what happens.
What the model shows
A made-up population with one gene that has two alleles: A, which is dominant, and a, which is recessive. Each circle is one individual carrying two alleles. The graph tracks how common each allele is (p for A, q for a), generation after generation.
What to look for
Whether the lines on the graph stay flat or move. Then change one thing at a time (selection, mutation, migration or a small population) and see which ones make p and q change.
What it tells us
In a large population with no selection, mutation or migration, allele frequencies stay the same: that is the Hardy–Weinberg prediction (p² + 2pq + q² = 1). When the frequencies change over time, something such as selection or mutation is acting.
Be careful what you claim
One snapshot that fits Hardy–Weinberg does not prove a population never changes; you need to compare two times. Real populations have many genes and overlapping generations. The mutation and migration rates here are far bigger than real ones, so changes show up within minutes.
Try it in the model: start with the lesson’s numbers (16 in 100 show the recessive trait), work out q and the expected number of carriers, then press Step 10 with nothing acting.
Gene pools and Hardy–Weinberg
A fictional population starts with the lesson’s numbers (16 of 100 recessive, q = 0.40). Run generations with nothing acting, then add selection, mutation, migration or a small population, and watch whether p and q stay put.
What you see
- A population of individuals, each drawn with two alleles: dark blue A and amber a. aa individuals show the recessive phenotype.
- A graph of allele frequencies p (A) and q (a) over generations.
- Genotype bars this generation, with outlines for the Hardy–Weinberg expectation p², 2pq, q² from the same q.
How to use it
- Step or run generations. Choose the population size: small populations drift.
- Change the fitness of aa (selection), the mutation rate A → a and migration from a neighbouring population.
- Split into two isolated populations with their own selection to watch gene pools diverge.
What it shows
- Hardy–Weinberg as a null model: with no forces and a large population, p and q do not change.
- How selection and mutation (4.20 ii) change allele frequencies, and how drift and migration break the assumptions.
- Why comparing two times, not one snapshot, is the test of change.
Limits of the model
- Fictional population. One gene with two alleles, discrete generations, random mating and selection on survival only.
- Mutation and migration rates are exaggerated so changes appear within tens of generations.
- A “very large” population is calculated exactly (no drift) and drawn as 100 individuals.
Guided tour · step 1 of 8
- The population starts as the lesson’s example: 16 of 100 show the recessive phenotype.
- In Lesson dataset below the simulator, enter q and Expected heterozygotes in 100.
- Press Check.
q² = 0.16, so q = √0.16 = 0.40 and p = 0.60. Expected heterozygotes 2pq = 2 × 0.60 × 0.40 = 0.48, so 48 of 100.
Run generations
Forces
Is Hardy–Weinberg holding?
Expected from q now: AA 36 %, Aa 48 %, aa 16 %. Very large population: frequencies are exact, so any gap between bars and outlines is real (for example selection removing aa).
Lesson dataset
Fictional example: 16 of 100 diploid organisms show the recessive phenotype.
Stretch: a later sample of 100 has 36 recessive phenotypes. What is q now?
Explain
Assumptions
Hardy–Weinberg proportions and constant p and q need: no selection, no mutation, no migration, random mating and a large population. The required drivers of change in 4.20(ii) are mutation and natural selection; drift, migration and isolation show other ways the model fails.
Check your understanding
Try each question before opening the suggested answer.
Practice question
Retrieval and explanation · suggested answer
What is a gene pool?
Show suggested answer
All the alleles present in a reproducing population or species.
Practice question
Retrieval and explanation · suggested answer
Write the Hardy–Weinberg expressions for two alleles.
Show suggested answer
p + q = 1 and p² + 2pq + q² = 1, where 2pq is the expected heterozygote frequency.
Practice question
Retrieval and explanation · suggested answer
How can natural selection change allele frequency?
Show suggested answer
If genotypes differ in survival or reproduction, some alleles are passed on more often, so p and q in the next generation differ from the last.
Take the idea further
Apply the same specification knowledge to an unfamiliar problem. Any extra assumptions are supplied in the question.
Stretch question
In the fictional sample above, q² = 0.16 so q = 0.40. A later sample of 100 has 36 recessive phenotypes. Has allele frequency changed, and what must you still be careful about?
Show a hint
Recalculate q, then think about sampling error.
Explore the reasoning
New q² = 0.36, q = 0.60, so the point estimate of q has risen. You should still treat sampling variation, scoring errors and whether the phenotype is truly recessive as uncertainties; a larger sample or a direct genotype count would strengthen the claim that selection or mutation has acted.
Recall this lesson
Lesson recall questions
Question 1 of 5: How can you tell allele frequency is changing in a population?
Hardy–Weinberg, selection and isolation
Practice question
Retrieval and explanation · suggested answer
How can you tell allele frequency is changing in a population?
Lesson: 4C 4: Gene Pool and Genetic Diversity
Build the sequence from memory first. Then reveal the model order.
Tap the steps in the order you recall. Tap a placed step to send it back.
- 01Next step
- 02Waiting
- 03Waiting
Tap to place
Put your biology to work
Explore where these ideas appear in the world. Enrichment, not extra required recall.
Why a “no change” equation is still biology
4C · Gene Pool and Genetic DiversityNature Education’s Scitable account treats Hardy–Weinberg as the genotype frequencies expected in a diploid population that is not evolving. If observed frequencies differ, at least one assumption has…Specification 4.20(i)Read & use the scienceClose article
Why this matters
Nature Education’s Scitable account treats Hardy–Weinberg as the genotype frequencies expected in a diploid population that is not evolving. If observed frequencies differ, at least one assumption has failed. That is exactly how 4.20(i) uses the equation: as a test for change, not as a promise that wild populations are ideal. Hardy–Weinberg predicts genotype frequencies from allele frequencies under specified assumptions, including random mating and no selection, migration or mutation. If measured data do not fit, a biologist investigates which assumption or sampling issue matters. One count cannot establish the cause of change. Researchers often repeat sampling across generations and compare loci. In an exam calculation, define p and q, apply p² + 2pq + q² = 1, and then interpret what the comparison actually permits you to conclude.
Back to the specification
Pearson Edexcel IAL Biology · Issue 2, February 2021 · Unit 2, pp. 21–24. The application extends beyond required recall.
- 4.20(i) understand how the Hardy-Weinberg equation can be used to see whether a change in allele frequency is occurring in a population over time
Use the science
Why does one generation of classroom data not “prove Hardy–Weinberg forever”?
Explore a possible response
It tests those students, that locus, that time. Selection or mutation can still act in later generations or at other loci.
Explore the source
- Scitable: the Hardy–Weinberg principleNature Education
Genetic rescue has limits
4C · Gene Pool and Genetic DiversityThe US Fish and Wildlife Service describes a programme that introduced Texas panthers into the small Florida panther population to increase genetic diversity. This is an intervention in…Specification 4.20(i) · 4.20(ii)Read & use the scienceClose article
Why this matters
The US Fish and Wildlife Service describes a programme that introduced Texas panthers into the small Florida panther population to increase genetic diversity. This is an intervention in a gene pool, not a proof that every allele automatically becomes common. Researchers monitor breeding, survival and genetic measures over generations. Hardy–Weinberg provides a baseline for thinking about allele frequencies, while actual populations can violate its assumptions through migration, selection and small size. The programme connects a syllabus equation to conservation decisions. Habitat loss and other threats still need separate attention; adding genes alone cannot solve every ecological problem.
Back to the specification
Pearson Edexcel IAL Biology · Issue 2, February 2021 · Unit 2, pp. 21–24. The application extends beyond required recall.
- 4.20(i) understand how the Hardy-Weinberg equation can be used to see whether a change in allele frequency is occurring in a population over time
- 4.20(ii) understand that changes in allele frequency can come about as a result of mutation and natural selection
Use the science
Why would introduction of new individuals make a Hardy–Weinberg no-migration assumption inappropriate?
Explore a possible response
Incoming panthers bring alleles from another population. Migration can change allele frequencies, so the no-migration model no longer describes the intervention.
Explore the source
- Florida panther genetic restoration programmeUS Fish and Wildlife Service