Hardy-Weinberg Equilibrium

What is Hardy-Weinberg Equilibrium?

The Hardy-Weinberg principle is a mathematical baseline that describes allele and genotype frequencies in a population that is not evolving. If a population meets five conditions — no mutation, no migration, random mating, no natural selection, and a large enough population to avoid genetic drift — allele frequencies p and q remain constant generation after generation, and genotype frequencies are always p² (AA) + 2pq (Aa) + q² (aa) = 1. No real population is perfectly static, but the principle is useful precisely because deviations from it reveal which evolutionary force is operating. A population of sickle-cell carriers that has more heterozygotes than 2pq predicts is showing balancing selection. A small island population whose allele frequencies jump erratically from year to year is showing genetic drift. This simulation lets you set starting conditions and then introduce selection, mutation, and population size to watch the equilibrium break — or hold.

Parameters explained

Allele Frequency p

Allele Frequency p sets the starting proportion of the A allele in the gene pool. Because p + q = 1, every change to p also changes q, then the expected genotype frequencies: AA = p², Aa = 2pq, and aa = q². In AP Biology Big Idea 7, this is the quantitative baseline students use before arguing that evolution is happening. For HS-LS4-3, pFreq lets students connect mathematical evidence to how heritable variation is distributed before selection, drift, mutation, or gene flow changes that distribution.

Selection Coefficient s

Selection Coefficient s controls how strongly natural selection acts against the aa genotype. At s = 0, aa individuals have the same modeled fitness as AA and Aa, so the no-selection Hardy-Weinberg assumption is preserved. Raising s gives aa lower reproductive success, so allele frequencies shift as the recessive allele is exposed in homozygotes. This supports AP Biology Big Idea 7 by showing that evolution is a change in allele frequencies, not simply a trait appearing. It also supports HS-LS4-3 because students can use graph evidence to explain how advantageous traits become more common.

Mutation Rate μ

Mutation Rate μ adds a recurring source of new allele copies in the model. Hardy-Weinberg assumes no mutation, so μ = 0 belongs to the equilibrium baseline. Increasing μ shows mutation pressure: allele frequencies can change even when selection, migration, and drift are absent. The effect is usually slower than selection, which is a useful AP Biology Big Idea 7 comparison because mutation creates variation while selection sorts variation. For HS-LS4-3, students can describe mutation as one source of heritable variation that may later affect survival and reproduction depending on the environment.

Migration Rate

Migration Rate models gene flow, the movement of alleles into the population from outside. Hardy-Weinberg assumes no migration, so a nonzero value intentionally breaks that condition. In the Gene Flow preset, students can see allele frequencies shift even without selection or mutation because incoming individuals or gametes change the gene pool. This aligns with AP Biology Big Idea 7 by separating gene flow from natural selection as a distinct evolutionary mechanism. It also supports HS-LS4-3 discussions about how populations change when environments and population connections alter which heritable variants are present.

Population Size N

Population Size N controls the strength of genetic drift, the random sampling effect that is strongest in small populations. Hardy-Weinberg assumes an effectively infinite population, so large N keeps random fluctuation small while N = 10 makes allele frequencies jump unpredictably. This is essential for AP Biology Big Idea 7 because students often expect only selection to cause evolution; drift can change allele frequencies without improving adaptation. For HS-LS4-3, popSize helps students evaluate when a population pattern is evidence of chance sampling rather than a trait increasing because it improves survival or reproduction.

Common misconceptions

• MisconceptionA dominant allele automatically becomes more common over time.

  CorrectDominance describes how an allele is expressed, not how common it is. Hardy-Weinberg equilibrium holds allele frequencies constant regardless of dominance — frequency change only happens when one of the five equilibrium conditions is violated. Note that under selection, dominance does affect dynamics: a deleterious dominant allele is exposed to selection in every heterozygote, whereas a deleterious recessive can persist hidden in carriers, so the two decline at very different rates.

• MisconceptionIf a trait is rare, the allele must be recessive.

  CorrectTrait rarity and allele dominance are unrelated. A dominant allele can be rare (frequency near 0) if it has recently arisen by mutation or causes low fitness. Huntington's disease is caused by a dominant allele that remains rare because its fitness effects appear after reproductive age.

• MisconceptionHardy-Weinberg equilibrium means allele frequencies are always 50/50.

  CorrectHardy-Weinberg equilibrium preserves whatever starting frequencies are set — it does not push them toward 0.5. If p = 0.9 at generation 0 and all five conditions are met, p stays at 0.9 indefinitely. The principle is about stability, not about a specific value.

• MisconceptionIn a population of 50, the Hardy-Weinberg equation still gives accurate predictions.

  CorrectHardy-Weinberg assumes effectively infinite population size. In a population of 50, genetic drift — random sampling error in allele transmission — is large enough to shift frequencies by several percent per generation. The equation can still be applied as a reference expectation, but deviations from it are expected and do not necessarily indicate selection.

How teachers use this lab

1. Baseline calculation exercise: use the 1 HW Equilibrium preset or set pFreq = 0.7, selectionCoeff = 0, mutationRate = 0, migrationRate = 0, and popSize = 1000. Have students calculate p², 2pq, and q², then confirm that the model matches the no-selection, no-mutation, no-migration, no-drift baseline.
2. Selection evidence investigation: use 2 Selection vs aa, then compare it with 1 HW Equilibrium. Students explain how changing only selectionCoeff alters allele frequencies and connect the result to HS-LS4-3 evidence for differential survival and reproduction.
3. Genetic drift comparison: use 3 Genetic Drift N=10, then raise popSize to 1000 while keeping selectionCoeff, mutationRate, and migrationRate at 0. Students identify why random sampling causes much larger allele-frequency change in small populations.
4. Mutation versus migration contrast: compare 4 Mutation Pressure with 5 Gene Flow. Students cite mutationRate and migrationRate values to distinguish new allele formation from allele movement between populations.
5. AP-style claim-evidence-reasoning: assign groups one preset, hide the label, and ask them to infer whether selection, mutation, migration, or drift is disrupting Hardy-Weinberg equilibrium using pFreq trends, popSize, and the active parameter values.