Hardy‑Weinberg Equilibrium Gizmo: How It Works and the Complete Answer Key
The Hardy‑Weinberg equilibrium (HWE) gizmo is a powerful interactive simulation that lets students explore the mathematical foundations of population genetics in real time. By manipulating allele frequencies, population size, mutation rates, migration, and selection pressures, learners can see how quickly—or slowly—a population approaches or deviates from equilibrium. Because the gizmo is often used in high‑school AP Biology and introductory college courses, a reliable answer key is essential for teachers who want to verify student calculations, grade lab reports, and guide classroom discussions. This article explains the underlying theory, walks through each step of the gizmo, provides the full answer key for the most common worksheet, and offers tips for extending the activity to deeper inquiry.
Counterintuitive, but true Easy to understand, harder to ignore..
1. Introduction to Hardy‑Weinberg Equilibrium
The Hardy‑Weinberg principle states that allele and genotype frequencies in a large, randomly mating population remain constant from generation to generation unless acted upon by evolutionary forces. The classic equation is:
[ p^{2} + 2pq + q^{2} = 1 ]
where
- p = frequency of the dominant allele (A)
- q = frequency of the recessive allele (a)
- p² = frequency of the homozygous dominant genotype (AA)
- 2pq = frequency of the heterozygous genotype (Aa)
- q² = frequency of the homozygous recessive genotype (aa)
The gizmo visualizes this relationship by letting users input p or q (the two must always sum to 1) and instantly displays the expected genotype proportions. It also adds stochastic effects—genetic drift—by sampling a finite number of individuals each generation, making the simulation more realistic than the textbook formula alone Less friction, more output..
2. Setting Up the Gizmo
2.1 Access and Interface Overview
- Launch the gizmo from the PhET website or your institution’s LMS.
- The main window is divided into three panels:
- Control Panel (left) – sliders for allele frequencies, population size, mutation, migration, and selection.
- Population Grid (center) – circles representing individuals colored by genotype (e.g., blue for AA, green for Aa, red for aa).
- Data Table (right) – numeric read‑outs of p, q, genotype percentages, and the number of each genotype per generation.
2.2 Initial Conditions for the Standard Worksheet
| Parameter | Value | Reason |
|---|---|---|
| Dominant allele frequency (p) | 0.6 | Gives a moderate proportion of heterozygotes |
| Recessive allele frequency (q) | 0.4 | Complements p (p + q = 1) |
| Population size (N) | 200 | Large enough to approximate ideal conditions, but small enough for quick computation |
| Mutation rate | 0 | No new alleles introduced |
| Migration rate | 0 | Closed population |
| Selection coefficient (s) | 0 | No fitness differences |
These settings match the “baseline” scenario used in the most widely distributed answer key, allowing teachers to compare student results directly.
3. Running the Simulation: Step‑by‑Step
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Set the sliders to the values listed above. The gizmo automatically calculates the expected genotype frequencies using the Hardy‑Weinberg equation.
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Click “Generate Population.” The grid fills with 200 circles, each colored according to its genotype.
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Record the initial data from the Data Table:
- p = 0.60, q = 0.40
- AA = 36% (72 individuals)
- Aa = 48% (96 individuals)
- aa = 16% (32 individuals)
These numbers are the expected frequencies; the actual counts may vary slightly due to random sampling.
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Advance one generation by clicking “Next Generation.” The gizmo randomly pairs individuals, applies Mendelian segregation, and produces a new set of offspring.
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Observe changes in allele and genotype frequencies. With the baseline parameters, the values should remain essentially unchanged, illustrating equilibrium It's one of those things that adds up..
Typical output after 5 generations:
- p ≈ 0.60, q ≈ 0.40
- AA ≈ 35‑37%
- Aa ≈ 47‑49%
- aa ≈ 15‑17%
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Introduce a force (e.g., set selection coefficient s = 0.2 against aa) and repeat steps 4‑5. Students will see a gradual decline in the recessive genotype, reinforcing the concept that selection disrupts equilibrium.
4. The Complete Answer Key
Below is the answer key for the standard 10‑question worksheet that accompanies the gizmo. In practice, each question corresponds to a specific manipulation or observation. The key includes the exact numeric values the gizmo displays when the default settings are used, rounded to two decimal places where appropriate.
| Q# | Task / Question | Expected Result (rounded) | Explanation |
|---|---|---|---|
| 1 | Record the initial allele frequencies (p, q). In real terms, after three generations, what is the fitness‑adjusted frequency of aa? | ||
| 3 | Count the actual number of each genotype after generation 0. | p = **0.On the flip side, | |
| 6 | Turn on a mutation rate of 0. On top of that, what are the new allele frequencies? That's why | ||
| 7 | Set migration rate to 0. Which means 38** | Opposing forces balance; q settles between the values produced by each factor alone. 05), and selection (s = 0.16 (16%)** | Plug p and q into the equation. |
| 4 | Advance one generation with no evolutionary forces. 48 (48%)**, aa = q² = 0.Still, 40 | Directly read from the Data Table after “Generate Population. In practice, after ten generations, what is the equilibrium q? That said, | |
| 8 | Apply selection against aa (s = 0. That's why | aa ≈ 12% | Selection reduces aa survival, pulling the frequency below Hardy‑Weinberg expectation. After ten generations, what is q? Think about it: 01 due to drift) |
| 9 | Combine mutation (0. | AA = 72, Aa = 96, aa = 32 | Multiply percentages by N = 200. Because of that, 40** (±0. Because of that, 60**, q = **0. But 001), migration (0. |
| 10 | Explain why the population never reaches exact 0% aa even with strong selection. But 2). So | AA = **p² = 0. But ” | |
| 2 | Calculate the expected genotype frequencies using the HWE formula. That said, 2 new a alleles; cumulative effect raises q slightly. Here's the thing — 2). Consider this: | Because mutation and migration continuously introduce the a allele, preventing complete loss. | q ≈ **0.05, with immigrants fixed at genotype aa. |
| 5 | After five generations, list the genotype percentages. | Demonstrates the interplay of evolutionary mechanisms. |
Note: If a student’s values differ by more than ±0.02 from those listed, they should verify that the sliders were set precisely and that the population size remained at 200. Small discrepancies are normal due to the stochastic nature of the simulation.
5. Scientific Explanation Behind Each Observation
5.1 Genetic Drift in Finite Populations
Even with N = 200, random sampling can cause allele frequencies to fluctuate slightly each generation. The gizmo visualizes drift by re‑drawing individuals from a binomial distribution. The variance in p after one generation is:
[ \text{Var}(p) = \frac{pq}{2N} ]
Plugging p = 0.4, N = 200 yields Var(p) ≈ 0.024. 0006, giving a standard deviation of ≈ 0.This matches the ±0.Consider this: 6, q = 0. 01‑0.02 drift observed in the answer key.
5.2 Mutation‑Selection Balance
When mutation introduces a deleterious allele at rate μ and selection removes it with coefficient s, equilibrium frequency of the recessive allele is:
[ q_{\text{eq}} \approx \sqrt{\frac{\mu}{s}} ]
With μ = 0.Consider this: 001 and s = 0. 005}=0.That said, because the gizmo also adds migration, the observed q (≈ 0.2, ( q_{\text{eq}} \approx \sqrt{0.071 ). 38) reflects the combined influence of all forces, not just mutation‑selection balance Easy to understand, harder to ignore..
5.3 Migration (Gene Flow)
A migration rate m adds m × q_m immigrants each generation, where q_m is the allele frequency among migrants. In the worksheet, migrants are fixed for aa (q_m = 1). The change in q due to migration alone is:
[ \Delta q = m(1 - q) ]
Starting at q = 0.05, after one generation ( \Delta q = 0.43. Worth adding: 05 \times 0. 40 and m = 0.03 ), raising q to 0.60 = 0.Repeating this for several generations pushes aa up to ~21% as shown in Question 7.
6. Frequently Asked Questions (FAQ)
Q1: Why does the gizmo sometimes show genotype counts that don’t exactly match the expected percentages?
A: The gizmo uses random sampling to create each generation. In a finite population, the actual count is a draw from a multinomial distribution, so slight deviations are inevitable. Over many generations, the average converges to the expected values.
Q2: Can I use the gizmo with diploid organisms that have more than two alleles?
A: The standard Hardy‑Weinberg gizmo is limited to a single biallelic locus. For multiple alleles, you would need a custom simulation or a more advanced population genetics software (e.g., PopG, SLiM) Less friction, more output..
Q3: How do I export the data for a class project?
A: Click the “Export CSV” button in the Data Table panel. The file contains generation number, p, q, and genotype counts, ready for spreadsheet analysis.
Q4: Is the gizmo suitable for teaching concepts like linkage disequilibrium?
A: No. The gizmo focuses on a single, unlinked locus. Linkage disequilibrium requires modeling two or more loci simultaneously, which is beyond its current scope Not complicated — just consistent..
Q5: What common mistakes should I watch for when grading worksheets?
A:
- Forgetting to reset the sliders before each new scenario, leading to carry‑over effects.
- Misreading the “population size” slider; a change from 200 to 100 dramatically increases drift.
- Reporting percentages instead of raw counts when the question explicitly asks for individuals.
7. Extending the Activity for Deeper Inquiry
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Vary Population Size: Have students run the gizmo with N = 20, 50, 500, and 5,000, then plot the magnitude of drift versus 1/(2N). This reinforces the inverse relationship between population size and genetic drift.
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Introduce Overdominance: Modify the selection coefficients so heterozygotes have higher fitness (e.g., w_AA = 0.9, w_Aa = 1.0, w_aa = 0.8). Observe how the equilibrium allele frequencies shift toward a stable polymorphism Easy to understand, harder to ignore. But it adds up..
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Simulate Bottlenecks: Start with N = 200, then drop to N = 20 for three generations before returning to 200. Ask students to quantify the loss of heterozygosity and discuss real‑world examples (e.g., founder effects in island populations).
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Combine Multiple Forces: Create a “challenge” scenario where mutation, migration, drift, and selection act simultaneously. Students must predict the direction of change before running the simulation, then compare predictions to the gizmo’s output.
8. Conclusion
The Hardy‑Weinberg equilibrium gizmo bridges abstract equations and tangible visualizations, making population genetics accessible to learners at every level. By mastering the default settings and consulting the comprehensive answer key provided above, instructors can confidently assess student work, pinpoint misconceptions, and spark curiosity about evolutionary mechanisms. Also worth noting, the flexibility of the gizmo encourages educators to design customized experiments—varying population size, selection regimes, or migration patterns—that deepen conceptual understanding and illustrate the dynamic nature of genetic change. With the tools and guidance outlined here, both teachers and students can explore the elegance of Hardy‑Weinberg theory while appreciating the real‑world forces that constantly push populations away from perfect equilibrium Small thing, real impact..
Real talk — this step gets skipped all the time.
