AP Biology · Unit 7 · Topic 7.5

Hardy-Weinberg Equilibrium

The lesson3 min read

The recessive phenotype's frequency is q², never q. Take the square root before anything else.

Hardy-Weinberg is the 'nothing is happening' baseline for one gene in a population. When real counts miss that baseline, some force is at work, and the shape of the miss hints at which one.

Key terms

  • Allele frequency — the share of all copies of a gene that are one allele. With two alleles, p + q = 1.
  • Genotype frequency — the share of individuals with each genotype. The baseline predicts p² AA, 2pq Aa, and q² aa.
  • Hardy-Weinberg equilibrium — allele frequencies holding steady from one generation to the next. A population in equilibrium is not evolving at that gene.
  • Carrier — a heterozygote (Aa). It holds one recessive allele but shows the dominant trait.
  • Inbreeding — mating with relatives. It makes homozygotes more common and heterozygotes rarer. On its own, it leaves allele frequencies unchanged.

How to run the numbers

  1. Given genotype counts, count alleles. Each AA holds two A's and each Aa holds one. p = A copies ÷ (2 × individuals), and q = 1 − p.
  2. Given only phenotypes, start with the recessive one. Only aa individuals show it, so its frequency is q². Take the square root to get q.
  3. Predict genotypes: p² AA, 2pq Aa, q² aa, which add up to 1. Multiply each by the population size for expected counts.
  4. Compare observed with expected. If the gap is too big to be chance (a chi-square test decides), at least one condition is broken.
  5. The conditions: a large population, random mating, no gene flow, no mutation, and no selection. Break any one, and the prediction can fail.

Why it matters

Hardy-Weinberg is the baseline for the rest of this unit. Selection, drift, gene flow, and mutation are each a way to break a condition. Exam questions hand you counts, ask you to compute frequencies, then ask what broke. It also explains why harmful recessive alleles linger. When q is small, 2pq dwarfs q², so almost every copy sits in a healthy carrier, where selection can't reach it.

Exam traps

TrapActually
4% of people show the recessive trait, so q = 0.04.That 4% is q², since only aa individuals show it. The square root gives q = 0.2.
The dominant allele is the common one, or it will become common.Dominance decides which allele shows, not how many copies exist. Under Hardy-Weinberg conditions, a rare dominant allele stays rare.
Equilibrium means the two alleles are equally common.Any p and q can be at equilibrium. What matters is that they hold steady and genotypes match p², 2pq, q².
Too few heterozygotes means selection is favoring one allele.A symmetric pattern, with both homozygotes inflated, is the classic sign of inbreeding. It regroups alleles into homozygotes without changing their frequencies.
Worked example

A large wildflower population is at Hardy-Weinberg equilibrium. Red (R) is dominant to white (r), and 9% of the plants are white. A gardener pulls up every white-flowered plant before it can shed pollen or set seed. The remaining plants mate at random. About what percent of the next generation will be white?

  1. White plants are rr, so q² = 0.09. That gives q = 0.3 and p = 0.7.
  2. Picture 100 plants: 49 RR, 42 Rr, 9 rr. Pull the 9 white ones. 91 plants remain, carrying 182 alleles.
  3. Only the 42 Rr plants carry r, one copy each. New q = 42 ÷ 182 ≈ 0.23.
  4. Random mating again: white = q² ≈ 0.23 × 0.23 ≈ 0.05.

About 5% white: down from 9%, but nowhere near zero.

Pulling white plants removes only the r alleles sitting in rr plants. The 42 red Rr plants still pass r to half their gametes, and two carriers can produce a white seedling. The near miss is 0%, which assumes the allele lived only in the plants you could see. Selection against a recessive trait slows down as the allele gets rarer, because more of its copies hide in carriers.

Now try it on real exam-style questions

Ten questions on Hardy-Weinberg Equilibrium, each with a ten-second explanation. Free, no account.

Three questions to check yourself

Question 1 · 7.5 Hardy-Weinberg Equilibrium

Errors in DNA copying that create new alleles break which Hardy-Weinberg condition?

  1. A No gene flow
  2. B No new mutations
  3. C Random mating
  4. D No natural selection
Show the answer

B — A copying error that changes a gene's sequence is a mutation, and the Hardy-Weinberg model assumes no new mutations add or change alleles. Gene flow also brings in alleles, but by moving them from another population rather than creating them.

Question 2 · 7.5 Hardy-Weinberg Equilibrium

Each spring, storms carry adult butterflies from a large mainland population onto an island, where the arrivals breed with island residents. Over decades, island allele frequencies at many loci shift toward mainland values. Which Hardy-Weinberg condition does this scenario violate?

  1. A Mating occurs at random with respect to genotype
  2. B The population is closed to migration from elsewhere
  3. C The population is large enough that chance has little effect
  4. D Mutation is rare enough to be ignored at these loci
Show the answer

B — Gene flow is the movement of alleles between populations, and it pulls the receiving gene pool toward the donor's composition. Here the island receives breeding immigrants year after year, so its frequencies drift steadily toward mainland values at many loci at once. That simultaneous, directional, genome-wide shift is the fingerprint of gene flow rather than of selection, which would act on particular loci, or of drift, which has no consistent direction.

Question 3 · 7.5 Hardy-Weinberg Equilibrium

A population in Hardy-Weinberg equilibrium at a locus shows which pattern across generations?

  1. A Allele frequencies stay the same each generation
  2. B The dominant allele becomes more common each generation
  3. C Each genotype is present at an equal frequency
  4. D The recessive allele slowly disappears from the population
Show the answer

A — Equilibrium means the population is not evolving at that locus, so allele frequencies (and the genotype frequencies they predict) hold steady from one generation to the next. Being dominant or recessive has no effect on how common an allele becomes; that depends on processes such as selection or drift.