7.5 Hardy-Weinberg Equilibrium

Hardy-Weinberg equilibrium is a mathematical model that describes allele and genotype frequencies in a non-evolving population. It assumes five conditions: large population size, no migration (gene flow), no new mutations, random mating, and no natural selection. Those conditions are never fully met in nature, so H–W serves as the null hypothesis: if observed frequencies differ from expectations (using p + q = 1 and p^2 + 2pq + q^2 = 1), evolution is occurring. You need to know it because it gives a baseline to detect evolutionary forces (genetic drift, gene flow, mutation, nonrandom mating, selection). On the AP exam you’ll be asked to calculate allele/genotype frequencies, state the null hypothesis, and interpret deviations—skills tied to LO 7.5.A and EK 7.5.A. Review the CED keywords (p, q, p^2, 2pq, q^2, founder/bottleneck effects) and practice problems on Fiveable (topic study guide: https://library.fiveable.me/ap-biology/unit-7/hardy-weinberg-equilibrium/study-guide/DQK5SLWcKmZatpBgPXmV; unit overview: https://library.fiveable.me/ap-biology/unit-7; practice: https://library.fiveable.me/practice/ap-biology).

Hardy-Weinberg gives you a quick way to get allele frequencies from genotype counts when a population is (hypothetically) not evolving. Use p for one allele frequency and q for the other, with p + q = 1 and p² + 2pq + q² = 1. Steps: 1. If you have genotype counts, convert to frequencies by dividing by total individuals. Example: 100 individuals: 36 AA, 48 Aa, 16 aa → f(AA)=0.36, f(Aa)=0.48, f(aa)=0.16. 2. Use p² = f(AA) and q² = f(aa) if the population is in H-W. Here p = sqrt(0.36)=0.6, q = sqrt(0.16)=0.4. 3. Or calculate directly from genotypes: p = [2(AA) + (Aa)] / (2N). From counts above: p = [2·36 + 48]/200 = 120/200 = 0.6; q = 1 − p = 0.4. 4. Check: p² (0.36) + 2pq (0.48) + q² (0.16) = 1. On the AP exam you may be asked to compute p or q from genotype data or to test if a population is in Hardy-Weinberg equilibrium (compare observed vs expected genotype frequencies). For extra practice, see the Topic 7.5 study guide (https://library.fiveable.me/ap-biology/unit-7/hardy-weinberg-equilibrium/study-guide/DQK5SLWcKmZatpBgPXmV) and lots of practice problems (https://library.fiveable.me/practice/ap-biology).

p and q are just labels for the two alleles at a single gene. By definition in the CED: p = frequency of allele 1 and q = frequency of allele 2, and p + q = 1. In the Hardy-Weinberg genotype model those allele frequencies predict genotype frequencies: p² = frequency of the homozygote for allele 1 (AA), 2pq = frequency of heterozygotes (Aa), and q² = frequency of the homozygote for allele 2 (aa). Important points: - Which allele you call p vs. q is arbitrary—pick the allele you care about (e.g., a disease allele) and call its frequency p. - If you know genotype counts you can calculate allele frequencies (EK 7.5.A.2). - Use the equations as a null model to test for evolution (EK 7.5.A.1). For a clear walk-through and practice problems, see the Topic 7.5 study guide (https://library.fiveable.me/ap-biology/unit-7/hardy-weinberg-equilibrium/study-guide/DQK5SLWcKmZatpBgPXmV) and more practice questions (https://library.fiveable.me/practice/ap-biology).

Hardy-Weinberg needs five conditions: (1) very large population size (no genetic drift), (2) no migration/gene flow, (3) no new mutations, (4) random mating, and (5) no natural selection. These matter because if any are broken allele/genotype frequencies change over generations—so HW gives a null hypothesis (a non-evolving population) you can test with p + q = 1 and p² + 2pq + q² = 1. Practically, HW lets you spot processes like drift (small populations), gene flow (migration), mutation, nonrandom mating (inbreeding or assortative mating), or selection when observed frequencies deviate from expected. On the AP exam you’ll often state these conditions and use HW as a model to calculate allele frequencies or justify why a population is evolving (LO 7.5.A; EK 7.5.A.1). For extra review and practice problems tied to Topic 7.5, see the Fiveable study guide (https://library.fiveable.me/ap-biology/unit-7/hardy-weinberg-equilibrium/study-guide/DQK5SLWcKmZatpBgPXmV) and the Unit 7 overview (https://library.fiveable.me/ap-biology/unit-7).

Hardy-Weinberg almost never happens because its five strict conditions are basically impossible in nature: a very large population, no migration (no gene flow), no new mutations, random mating, and no natural selection. Real populations are finite (so genetic drift and bottlenecks matter), individuals move between populations (gene flow), mutations constantly introduce new alleles, mates are often chosen nonrandomly, and selection acts all the time. The CED calls H-W a “null hypothesis” for this reason—it’s a baseline model you use to detect evolution. If observed genotype frequencies deviate from p² + 2pq + q², one or more evolutionary forces (genetic drift, gene flow, mutation, nonrandom mating, or selection) are acting. On the AP exam you’ll use H-W to calculate allele frequencies and test the null (often with chi-square)—practice those calculations and interpretations. Review the Topic 7.5 study guide (https://library.fiveable.me/ap-biology/unit-7/hardy-weinberg-equilibrium/study-guide/DQK5SLWcKmZatpBgPXmV) and drill practice problems (https://library.fiveable.me/practice/ap-biology) to get fast at spotting which condition is broken.

Step-by-step for AP-style Hardy-Weinberg problems (straightforward method you can use on the exam): 1. Check assumptions: state that H-W models a non-evolving population (large size, no migration, no mutation, random mating, no selection)—this is your null hypothesis (EK 7.5.A.1). 2. Identify what you’re given (genotype counts, phenotype % or one allele freq). If you have counts, convert to frequencies by dividing by total N. 3. If you’re given genotype frequencies, get allele frequencies: p = freq(AA) + ½ freq(Aa); q = 1 − p (EK 7.5.A.2). If you’re given p or q directly, use p + q = 1. 4. Use p and q in p² + 2pq + q² = 1 to predict genotype frequencies or expected counts (multiply by N). 5. If problem asks whether population is in equilibrium, compare observed vs expected (use chi-square if asked—AP allows calculators). State which H-W condition might be violated (selection, drift, gene flow, nonrandom mating). 6. Always label p and q and show substitution steps (AP graders want clear math and reasoning). For more examples and practice, check the Topic 7.5 study guide (https://library.fiveable.me/ap-biology/unit-7/hardy-weinberg-equilibrium/study-guide/DQK5SLWcKmZatpBgPXmV) and hit practice questions (https://library.fiveable.me/practice/ap-biology).

Allele frequency = how common a single version (allele) of a gene is in the whole population (p and q). For a two-allele locus p + q = 1 (e.g., p = frequency of A, q = frequency of a). Genotype frequency = how common a genotype is (AA, Aa, aa) among individuals. In Hardy-Weinberg equilibrium genotype frequencies are predicted from allele frequencies: p² (AA) + 2pq (Aa) + q² (aa) = 1. So allele freq is about single copies in the gene pool; genotype freq is about combinations in individuals. Important AP point: you can calculate allele frequencies from observed genotype counts (EK 7.5.A.2) and use H-W as a null hypothesis to test for evolution (EK 7.5.A.1). For more practice and examples that match the CED, check the Topic 7.5 study guide (https://library.fiveable.me/ap-biology/unit-7/hardy-weinberg-equilibrium/study-guide/DQK5SLWcKmZatpBgPXmV) and the practice bank (https://library.fiveable.me/practice/ap-biology).

Think of p and q as the two allele frequencies in a population (p + q = 1). The equation p² + 2pq + q² = 1 just breaks the population’s genotypes into proportions you’d expect in a non-evolving (Hardy-Weinberg) population: - p² = frequency of homozygote for allele 1 (AA) - 2pq = frequency of heterozygotes (Aa) - q² = frequency of homozygote for allele 2 (aa) So if p = 0.6 and q = 0.4, expect 0.36 AA, 0.48 Aa, 0.16 aa. Those numbers are predictions only when the five H-W conditions hold: large population, no migration, no new mutations, random mating, and no natural selection (CED EK 7.5.A.1). On the AP exam you’ll use this model as a null hypothesis: compare observed genotype counts to H-W expectations (often with chi-square) to decide if evolution (allele frequencies changing) is happening. For more practice and a focused study guide, check the Topic 7.5 Hardy-Weinberg study guide (https://library.fiveable.me/ap-biology/unit-7/hardy-weinberg-equilibrium/study-guide/DQK5SLWcKmZatpBgPXmV) and the Unit 7 overview (https://library.fiveable.me/ap-biology/unit-7). For drills, use Fiveable practice problems (https://library.fiveable.me/practice/ap-biology).

Because Hardy-Weinberg (H–W) gives a precise, testable prediction for a non-evolving population, it’s used as the null hypothesis: “allele frequencies won't change; genotype frequencies = p² + 2pq + q².” The CED even lists the five perfect conditions (large population, no migration, no mutations, random mating, no selection)—which, in nature, are never fully met. That doesn’t make the model useless. Instead, it gives you a baseline expectation. If your observed genotype frequencies differ significantly from p²:2pq:q² (you’d often use a chi-square on the AP exam), you reject the null and infer one or more evolutionary forces (genetic drift, gene flow, mutation, nonrandom mating, or selection) are acting. On AP tasks you’ll sometimes be asked to “state the null hypothesis” or use H–W to calculate expected frequencies (p + q = 1), so treat H–W as the clear “no evolution” claim you test against. For a quick review and practice problems, see the Topic 7.5 study guide (https://library.fiveable.me/ap-biology/unit-7/hardy-weinberg-equilibrium/study-guide/DQK5SLWcKmZatpBgPXmV) and more practice at (https://library.fiveable.me/practice/ap-biology).

Population size matters because one Hardy-Weinberg condition is “a large population size.” In small populations random sampling causes allele frequencies to wander (genetic drift) so the HW null model breaks down. That’s why founder effects and bottlenecks can rapidly change p and q and shift genotype frequencies away from p²+2pq+q². In contrast, very large populations make random fluctuations negligible, so allele frequencies stay near HW expectations unless other forces (selection, migration, mutation, nonrandom mating) act. There’s no single magic cutoff in the CED—“large” means large enough that drift is negligible. Practically, populations with effective size (Ne) in the low hundreds or less show noticeable drift; Ne in the thousands makes drift much weaker. Remember HW is a null hypothesis on the exam: if you detect changes in frequencies, one cause could be small population size (drift) rather than selection. For review and practice, see the Topic 7.5 study guide (https://library.fiveable.me/ap-biology/unit-7/hardy-weinberg-equilibrium/study-guide/DQK5SLWcKmZatpBgPXmV) and Unit 7 overview (https://library.fiveable.me/ap-biology/unit-7); practice questions are at (https://library.fiveable.me/practice/ap-biology).

Hardy-Weinberg is the null model: if i) large population, ii) no migration, iii) no new mutations, iv) random mating, and v) no natural selection hold, allele frequencies stay constant. If any condition is violated, allele frequencies change. - Genetic drift (small population, bottleneck, founder effect): frequencies change randomly from generation to generation; rare alleles can be lost or fixed. - Gene flow (migration): alleles move between populations, making them more similar. - Mutation: creates new alleles and slowly shifts frequencies. - Nonrandom mating (inbreeding, assortative mating): changes genotype frequencies (and can expose recessive alleles), which can alter effective allele frequencies over time. - Natural selection: alleles linked to higher fitness increase directionally. On the AP, treat HW as a null hypothesis: if observed frequencies deviate from p² + 2pq + q², one of those forces is acting. For a focused review, see the Topic 7 study guide (https://library.fiveable.me/ap-biology/unit-7/hardy-weinberg-equilibrium/study-guide/DQK5SLWcKmZatpBgPXmV) and try practice problems (https://library.fiveable.me/practice/ap-biology).

Hardy-Weinberg (H-W) is the “null” model: if a population meets five conditions (large size, no migration, no new mutations, random mating, no natural selection) allele frequencies don’t change. To test whether a population is evolving, do this: 1) Get genotype counts (AA, Aa, aa). 2) Calculate allele frequencies: p = freq(A) = (2·AA + Aa) / (2·N); q = 1 − p. 3) Use p and q to get expected genotype frequencies: p² (AA), 2pq (Aa), q² (aa), multiply by N for expected counts. 4) Compare observed vs expected. Small differences → population might be in H-W (not evolving). Big differences → evolution is occurring. Use a chi-square test or qualitatively note which H-W assumptions are violated (drift, gene flow, selection, nonrandom mating, mutation). On the AP exam you’ll often be asked to calculate p and q, give expected genotype frequencies (p²+2pq+q²=1), and state H-W as a null hypothesis. For a quick refresher and practice problems, check the Topic 7.5 study guide (https://library.fiveable.me/ap-biology/unit-7/hardy-weinberg-equilibrium/study-guide/DQK5SLWcKmZatpBgPXmV) and the practice problem bank (https://library.fiveable.me/practice/ap-biology).

Hardy-Weinberg assumes no migration and no new mutations (CED EK 7.5.A.1). Migration (gene flow) changes allele frequencies by adding or removing alleles when individuals move between populations—immigrants can raise the frequency of alleles that were rare (or bring in alleles that were absent), so p and q no longer sum to the same values generation-to-generation. Mutation creates new alleles (or converts one allele to another), so it directly changes p and q as well. Even though mutation rates are usually low, over many generations new alleles can spread or provide raw material for selection. Both processes therefore violate the Hardy-Weinberg conditions (ii and iii), so genotype frequencies (p², 2pq, q²) will deviate from expected values and the null model fails. On the AP exam you’ll be asked to identify these violations and predict direction of allele-frequency change—practice with the Topic 7.5 study guide (https://library.fiveable.me/ap-biology/unit-7/hardy-weinberg-equilibrium/study-guide/DQK5SLWcKmZatpBgPXmV) and more problems at (https://library.fiveable.me/practice/ap-biology).

Hardy-Weinberg (HW) is the “null model” for a non-evolving population: if p + q = 1 and p² + 2pq + q² hold, allele frequencies don’t change. One of the five HW conditions is “no natural selection” (CED EK 7.5.A.1.v). So natural selection directly breaks HW: when certain genotypes have higher fitness, their allele frequencies change (directional, stabilizing, or disruptive selection), and the population moves away from HW expectations. Practically, you calculate expected genotype frequencies from p and q, compare to observed (using chi-square on the AP exam), and a significant difference suggests evolution—often selection. HW is a useful null hypothesis for spotting selection, drift, migration, nonrandom mating, or mutation (CED EK 7.5.A.1). For a focused review, see the Topic 7.5 study guide (https://library.fiveable.me/ap-biology/unit-7/hardy-weinberg-equilibrium/study-guide/DQK5SLWcKmZatpBgPXmV) and unit practice problems (https://library.fiveable.me/practice/ap-biology).

Good question—we assume random mating in Hardy-Weinberg because the model is a simplified null hypothesis, not because it’s realistic. By listing five strict conditions (large population, no migration, no mutation, random mating, no selection—EK 7.5.A.1), the Hardy-Weinberg model gives a baseline expectation: if none of those forces act, allele frequencies (p and q) stay constant and genotype frequencies follow p² + 2pq + q². That makes it easy to detect evolution: when real populations deviate from HW, you can point to which assumption(s) are broken (e.g., assortative mating or inbreeding changes genotype frequencies; selection or migration changes allele frequencies). So random mating is an assumption because it isolates other causes of change and gives you a testable null hypothesis for AP exam questions (LO 7.5.A). For a quick review and practice with problems, see the Topic 7.5 study guide (https://library.fiveable.me/ap-biology/unit-7/hardy-weinberg-equilibrium/study-guide/DQK5SLWcKmZatpBgPXmV) or the Unit 7 page (https://library.fiveable.me/ap-biology/unit-7).