Biology for AP Courses · The Evolution of Populations

Population Genetics

8 min read

Safety note: educational content only — the cystic fibrosis carrier figures are commonly taught reference values to verify against current texts; the worked example is a constructed teaching scenario. No clinical guidance or fabricated data are given.

On this page 9 sections

In 30 seconds
Why this matters
The college version
Eli explains
Worked example
Key takeaway
Check yourself
Study tools
Sources & references

In 30 seconds

is the study of how allele and genotype frequencies change — or stay the same — in populations. Its cornerstone is the , developed independently around 1908 by mathematician G. H. Hardy and physician Wilhelm Weinberg. The principle states that allele and genotype frequencies in a population remain constant from generation to generation if five conditions are met: no mutations, , no natural selection, an extremely large population size (so chance, or , is negligible), and no gene flow. When those conditions hold, the population is in — and, by definition, it is not evolving. Two equations describe the equilibrium. For a locus with two alleles, A (frequency p) and a (frequency q): p + q = 1, and the genotype frequencies are p² + 2pq + q² = 1, where p² = AA, 2pq = Aa, and q² = aa. The power of the principle is that it provides a : if observed frequencies deviate from these predictions, one or more of the five conditions is being violated — and that violation tells you which evolutionary force is at work.

Why this matters

The Hardy-Weinberg principle is the mathematical baseline for all of population genetics. In practice, real populations almost never satisfy all five conditions, which is exactly the point: the equations are a yardstick against which evolution is measured. Clinically, the same math is used to estimate frequencies for recessive genetic conditions — the classic example is cystic fibrosis, where the frequency of affected individuals in some populations is commonly taught as roughly 1 in 2500, giving a carrier frequency (2pq) of about 1 in 25 (reference figures to verify against current texts). Conservation geneticists use Hardy-Weinberg logic to detect inbreeding or population bottlenecks, and forensic scientists use allele-frequency statistics to evaluate the significance of DNA-profile matches. On the AP® exam, Hardy-Weinberg calculation problems are among the most predictable free-response items.

The college version

Core Concepts

The two equations and what they mean

At a locus with two alleles, A and a:

p = frequency of allele A; q = frequency of allele a; p + q = 1. Because every gene copy in the population is either A or a, the two allele frequencies must add to 1.
p² + 2pq + q² = 1 gives the genotype frequencies predicted at equilibrium: p² = AA, 2pq = Aa, q² = aa. This follows from the allele frequencies behaving like probabilities: the chance that two A gametes meet is p × p = p², and so on (the Hardy-Weinberg assumption of random mating).

Check with numbers: if p = 0.7 and q = 0.3, then AA = 0.49, Aa = 2(0.7)(0.3) = 0.42, and aa = 0.09 — and 0.49 + 0.42 + 0.09 = 1.

The five conditions: a checklist for "no evolution"

Each condition is the absence of an evolutionary mechanism:

No mutations — mutation would introduce new alleles (change p and q).
Random mating — mate choice or inbreeding changes genotype frequencies.
No natural selection — differential survival or reproduction shifts allele frequencies.
Extremely large population size — in small populations, random sampling effects (genetic drift) move allele frequencies by chance.
No gene flow — migrants add or remove alleles.

If all five hold, allele frequencies stay constant and the population does not evolve. Note a subtle point about condition 2: nonrandom mating (like inbreeding) changes genotype frequencies but not allele frequencies — so by itself it does not cause evolution, though it alters the population's genotype distribution.

Using the equations: the standard problem-solving path

The classic exam setup gives you the frequency of a recessive phenotype and asks for allele and carrier frequencies. Because heterozygotes (Aa) and homozygous dominants (AA) often look identical, you cannot read p² or 2pq directly from phenotypes — but you can read q², because only aa individuals show the recessive trait. The route:

q² = frequency of affected (aa) individuals.
Take the square root: q = √q².
p = 1 − q.
Then p² = homozygous dominant frequency, and 2pq = carrier (heterozygous) frequency.

Worked example (commonly taught reference figures): if q² = 1/2500 = 0.0004, then q = 0.02, p = 0.98, and carrier frequency 2pq = 2 × 0.98 × 0.02 ≈ 0.039 — about 1 in 25 people. The same method works for any recessive trait with known affected frequency.

Deviations from equilibrium = evolution in progress

Compare observed genotype frequencies to Hardy-Weinberg predictions. If they match, the population appears to be at equilibrium for that locus. If they differ, one of the conditions is violated — and the pattern of the deviation points to the cause: a deficit of heterozygotes may suggest inbreeding or population subdivision; an excess may suggest heterozygote advantage or nonrandom mating; allele-frequency shifts over time implicate selection, drift, mutation, or gene flow. This "diagnostic" use of the principle is what makes it a working tool rather than a curiosity.

Common Confusions

Do not confuse	With	Difference
p²	p	p² is the homozygous dominant genotype frequency; p is the allele frequency — never substitute one for the other
Dominant allele	Most common allele	Dominance is about phenotype expression, not abundance (e.g., a dominant trait can be rare)
Hardy-Weinberg equilibrium	A description of real populations	Real populations rarely meet all five conditions; equilibrium is a baseline, not an observation
Nonrandom mating	Evolution	Inbreeding changes genotype frequencies but leaves allele frequencies (p, q) unchanged
q²	Frequency of the disease/trait	q² is the homozygous recessive genotype frequency; affected individuals are aa, but carriers (2pq) are far more numerous for rare recessives
Genetic drift	Natural selection	Drift is random chance in small populations; selection is nonrandom differential reproduction
"In equilibrium"	"All conditions met"	Equilibrium means frequencies are constant given the conditions — if conditions change, frequencies change

Eli explains

The same idea, in plain words

Explain it like I’m 10

Imagine a huge bowl of red and white jelly beans, and every year you mix them and count. If the bowl never changes — no one adds jelly beans, no one eats the red ones, and the bowl is so big that luck doesn't matter — the red-to-white ratio stays the same forever. That's Hardy-Weinberg equilibrium: a recipe for "nothing changes." If the ratio does change, something broke the recipe, and that something is evolution.

Worked example

Is this population evolving? Researchers count genotypes at a flower-color locus in 100 plants: 60 AA, 30 Aa, 10 aa. First compute observed allele frequencies: A = 60 × 2 + 30 = 150 of 200 → p = 0.75; a = 30 + 20 = 50 of 200 → q = 0.25. Now predict equilibrium genotype frequencies: AA = 0.75² = 0.5625 → 56.25 plants; Aa = 2(0.75)(0.25) = 0.375 → 37.5 plants; aa = 0.25² = 0.0625 → 6.25 plants. Observed (60, 30, 10) versus predicted (56.25, 37.5, 6.25): there is a deficit of heterozygotes and an excess of both homozygotes. That pattern is the classic signature of inbreeding or population subdivision — nonrandom mating — rather than selection. The population is not in Hardy-Weinberg equilibrium, and the deviation tells the researchers which condition to investigate.

Key takeaways

p + q = 1 (allele frequencies) and p² + 2pq + q² = 1 (genotype frequencies).
p = dominant allele frequency, q = recessive allele frequency, as commonly labeled.
Five conditions: no mutation, random mating, no selection, huge population (no drift), no gene flow.
Equilibrium = no evolution; any violation signals an evolutionary mechanism at work.
Solve problems starting from q² = affected (recessive homozygous) frequency, then q = √q², p = 1 − q, carriers = 2pq.
Dominance and frequency are unrelated: a dominant allele can be rare.
Nonrandom mating changes genotype frequencies but not allele frequencies.

Check yourself

6 review questions from the chapter. Try each one, then open the answer.

State the Hardy-Weinberg equations and define every symbol.
Show answer
p + q = 1, where p and q are the frequencies of alleles A and a; p² + 2pq + q² = 1, where p² = AA, 2pq = Aa, and q² = aa genotype frequencies.
List the five conditions required for Hardy-Weinberg equilibrium.
Show answer
No mutations; random mating; no natural selection; an extremely large population (negligible genetic drift); no gene flow.
In a population where q² = 0.0004, what are q, p, and the carrier frequency 2pq?
Show answer
q = √0.0004 = 0.02; p = 1 − 0.02 = 0.98; carrier frequency 2pq = 2 × 0.98 × 0.02 ≈ 0.039 (roughly 1 in 25).
Why can't you read p² directly from the number of dominant-phenotype individuals?
Show answer
Because AA and Aa individuals usually have the same phenotype under complete dominance, you cannot distinguish p² from 2pq by counting dominant-phenotype individuals — only q² (the recessive homozygotes) is directly observable.
What does a heterozygote deficit relative to Hardy-Weinberg predictions suggest?
Show answer
A heterozygote deficit relative to predictions suggests nonrandom mating (e.g., inbreeding) or population subdivision — mating is not random with respect to genotype.
Does nonrandom mating alone cause evolution? Explain.
Show answer
No — nonrandom mating changes genotype frequencies but leaves allele frequencies (p and q) unchanged, and evolution is defined as a change in allele frequencies.

Keep learning

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Study toolsKey vocabulary

Key vocabulary

Population genetics: The study of allele and genotype frequencies in populations
Hardy-Weinberg principle: Allele and genotype frequencies stay constant if five conditions hold
Hardy-Weinberg equilibrium: A population whose frequencies match predictions and are not changing
Genetic drift: Random changes in allele frequencies due to chance in small populations
Null hypothesis: The default expectation (no change) that data are tested against
Carrier: A heterozygote (Aa) carrying a recessive allele without showing the trait
Random mating: Mating that is independent of genotype

Sources & references

openstax.org — Biology Ap Courses

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