# Variations in Populations

> AP Biology · AP Biology CED Unit 7: Natural Selection
> Source: https://www.owlsprep.com/study/ap-biology-u7-variations-in-populations/

This study guide covers genetic variation sources, allele/genotype frequency calculation, Hardy-Weinberg equilibrium, and how evolutionary forces shape variation in populations, aligned to AP Biology CED Unit 7.

**Prerequisites:** [Basic Mendelian genetics for diploid organisms](https://www.owlsprep.com/study/ap-biology-mendelian-genetics/); [Core principles of natural selection](https://www.owlsprep.com/study/ap-biology-u7-natural-selection-intro/)

## Learning objectives

- Identify sources of genetic variation within populations
- Calculate allele and genotype frequencies for diploid populations
- Apply the Hardy-Weinberg equilibrium model to test for evolution
- Predict how different evolutionary forces alter population genetic variation

## What Are Variations in Populations?

Variation in populations refers to differences in heritable nucleotide sequences (alleles) and resulting phenotypes among individuals within a single interbreeding population, defined as a group of the same species living in the same geographic area that can interbreed.

This topic is core to Unit 7: Natural Selection, which makes up 13–25% of the total AP Biology exam score per the official CED. It appears on both multiple-choice (MCQ) and free-response (FRQ) sections.

Genetic variation is the raw material for natural selection: without differences in heritable traits, natural selection cannot change the prevalence of adaptive traits over time. Variation is quantified using allele frequencies and genotype frequencies. Within-population variation drives microevolution, small-scale changes in allele frequency over generations that lead to macroevolutionary change over longer time scales.

**Population Variation** — Differences in heritable alleles and phenotypes among individuals within a single interbreeding population of the same species

*Example:* Variation in root depth among sunflowers in a single coastal population

## Sources of Genetic Variation

Genetic variation originates and is maintained in populations through multiple mechanisms, with mutation as the ultimate source of all new variation. Only germline mutations (occurring in gamete-producing cells) are passed to offspring and contribute to population-level variation. Most mutations are neutral or harmful, but rare beneficial mutations create new adaptive traits for natural selection to act on.

1. **Sexual reproduction**: Crossing over in meiosis I, independent assortment of homologous chromosomes, and random fertilization generate new combinations of existing alleles, creating phenotypic variation without new mutation.
2. **Gene flow**: Movement of individuals and their alleles between populations, which can introduce new alleles into a population.
3. **Standing cryptic variation**: Most populations carry rare, existing alleles that are not expressed under typical environmental conditions, which can become visible when the environment changes.
4. **Balancing selection**: Natural selection that maintains multiple alleles in a population, such as heterozygote advantage in sickle cell anemia.

**Worked example:** A population of wild coastal sunflowers has no new mutations detected for a root depth locus over 10 generations. Researchers measure a significant increase in phenotypic variation for root depth after a multi-year drought. Propose two explanations for this increase that do not invoke new mutation, and justify each.

1. 1. First explanation: Cryptic standing genetic variation is now expressed after environmental change.
2. Reasoning: Before the drought, the soil was consistently moist, so existing rare alleles for deep root growth did not produce a measurable change in phenotype. After the drought, deep root growth is now required to reach water, so the cryptic alleles are expressed, increasing observable phenotypic variation.
3. 2. Second explanation: Gene flow from a neighboring inland population.
4. Reasoning: Drought may have forced inland sunflower plants with deeper roots to migrate into the coastal population. Interbreeding introduces new alleles for deep root growth from the existing inland gene pool, increasing variation in the coastal population without new mutation.
5. A third valid explanation is disruptive selection: drought favors both shallow and deep root depths over intermediate depths, increasing the range of variation from existing alleles.

> **Exam tip:** When asked for sources of variation on an FRQ, always explicitly distinguish between ultimate sources (mutation) and proximate sources that reshuffle existing variation (gene flow, sexual recombination) to earn full points.

## Allele and Genotype Frequency Calculation

To quantify variation in populations, biologists calculate allele and genotype frequencies. By convention, $p$ is the frequency of the dominant allele, and $q$ is the frequency of the recessive allele for a biallelic (two-allele) locus in a diploid population. For any population, the sum of allele frequencies for a locus equals 1, so $p + q = 1$ always holds, regardless of whether the population is evolving.

$$p = \frac{(2 \times \text{number of AA individuals}) + (\text{number of Aa individuals})}{2N}$$

Genotype frequencies also sum to 1: $f(AA) + f(Aa) + f(aa) = 1$. This calculation works for any population, evolving or not, and is the foundation for detecting microevolution (any change in allele frequency over generations).

**Worked example:** In a population of 200 diploid clover plants, 72 are homozygous dominant (TT) for trifoliate leaves, 96 are heterozygous (Tt), and 32 are homozygous recessive (tt) for quadrifoliate leaves. Calculate the frequency of the recessive $t$ allele.

1. 1. Calculate total alleles: Total individuals = 200, so total alleles =
2. $$2 \times 200 = 400$$
3. 2. Count $t$ alleles: Homozygous $tt$ contribute 2 $t$ each, heterozygous $Tt$ contribute 1 $t$ each. Total $t$ alleles =
4. $$(2 \times 32) + (1 \times 96) = 64 + 96 = 160$$
5. 3. Calculate frequency:
6. $$q = \frac{160}{400} = 0.4$$
7. 4. Verify: $p = [(2 \times 72) + 96]/400 = 240/400 = 0.6$, so $p + q = 0.6 + 0.4 = 1$, confirming the calculation is correct.

> **Exam tip:** Always write 'total alleles = 2 × number of diploid individuals' at the start of every calculation to avoid the most common student mistake of using the number of individuals as the total allele count.

## Hardy-Weinberg Equilibrium

Hardy-Weinberg equilibrium (HWE) is a null model that describes the expected allele and genotype frequencies for a population that is NOT evolving. If all five HWE assumptions are met, allele and genotype frequencies will remain constant from generation to generation. The five assumptions are: (1) no new mutation, (2) no gene flow, (3) random mating, (4) no genetic drift (very large population size), (5) no natural selection. HWE is used to test for evolution: if observed genotype frequencies differ significantly from HWE expectations, one or more assumptions are violated, meaning evolution is occurring.

$$p^2 + 2pq + q^2 = 1$$

Where $p^2$ is the expected frequency of homozygous dominant (AA), $2pq$ is the expected frequency of heterozygous (Aa), and $q^2$ is the expected frequency of homozygous recessive (aa).

**Worked example:** A recessive allele for black coat color occurs such that 4% of a deer population in HWE has black coats (the rest are brown). What is the frequency of heterozygous brown-coated deer that carry the black allele?

1. 1. Let $q$ = frequency of the recessive black allele, $p$ = frequency of the dominant brown allele. Only homozygous recessive individuals have black coats, so
2. $$q^2 = 0.04$$
3. 2. Solve for $q$:
4. $$q = \sqrt{0.04} = 0.2$$
5. 3. Solve for $p$:
6. $$p = 1 - q = 1 - 0.2 = 0.8$$
7. 4. Heterozygotes have frequency $2pq = 2(0.8)(0.2) = 0.32$, so 32% of the population are heterozygous carriers.

> **Exam tip:** You will almost always start HWE calculations with $q^2$, because only homozygous recessive phenotypes can be directly distinguished from other phenotypes; dominant phenotypes include both homozygotes and heterozygotes that cannot be separated by observation.

## Effects of Evolutionary Forces on Variation

Different evolutionary forces alter the amount of genetic variation in a population in predictable ways. Mutation increases variation by adding new alleles. Genetic drift (random changes in allele frequency due to chance events) almost always reduces variation, because rare alleles are much more likely to be lost by chance, especially in small populations. Two common forms of drift that reduce variation are the bottleneck effect (when a large population crashes to a small size due to a disturbance) and the founder effect (when a small group founds a new population with only a subset of the original variation).

Gene flow typically increases variation within a population, because it introduces new alleles from other populations. Natural selection has variable effects: directional selection (favoring one extreme phenotype) reduces variation; disruptive selection (favoring both extreme phenotypes) increases variation; stabilizing selection (favoring the intermediate phenotype) reduces variation; and balancing selection maintains multiple alleles, preserving variation.

**Worked example:** A large population of tropical butterflies is split into two small isolated populations by deforestation. After 30 generations, one small population has 75% less genetic variation than the original large population. Name the most likely evolutionary force causing this change, and explain why.

1. 1. Identify the force: Genetic drift via the bottleneck effect.
2. 2. Reasoning: Deforestation reduced the large original population to a small size, so the new small population only has a subset of the genetic variation present in the original population.
3. 3. In small populations, random chance has a large effect on allele frequencies: rare alleles are quickly lost over generations because they are unlikely to be passed to offspring by chance.
4. 4. Other forces (e.g., natural selection) are not the best fit here, because the change is caused by population size reduction from habitat fragmentation, not selection for specific traits.

> **Exam tip:** Always match the scenario to the effect: population isolation or size reduction = genetic drift, new individuals entering = gene flow, new trait = mutation.

## Common pitfalls

- **Wrong:** Counting alleles as equal to the number of individuals when calculating allele frequency for diploid organisms, e.g., using 100 as the total allele count for 100 individuals.
  - Why it fails: Students confuse number of individuals with number of alleles, forgetting most organisms discussed in AP Bio are diploid.
  - Correct: Always write `total alleles = 2 × number of diploid individuals` at the start of any calculation, then check that $p + q = 1$ to confirm.
- **Wrong:** Calculating $p$ as the square root of the frequency of dominant phenotypes in HWE.
  - Why it fails: Students memorize the rule for $q$ and incorrectly apply it to $p$.
  - Correct: Always start HWE by assigning $q^2$ to the homozygous recessive phenotype, solve for $q$, then calculate $p = 1 - q$.
- **Wrong:** Claiming Hardy-Weinberg equilibrium describes actual evolving populations, rather than being a null model.
  - Why it fails: Courses focus on HWE calculation, so students forget its core purpose.
  - Correct: Always frame HWE as a null expectation for non-evolving populations; deviations from HWE indicate evolution is occurring.
- **Wrong:** Stating mutation is the only source of genetic variation in populations.
  - Why it fails: Students memorize that mutation is the ultimate source and forget other mechanisms.
  - Correct: Distinguish between ultimate sources (mutation) and proximate sources (gene flow, sexual recombination) that increase variation without new mutation.
- **Wrong:** Claiming genetic drift only occurs in small populations.
  - Why it fails: Students learn drift is strongest in small populations and incorrectly generalize that it does not occur in large populations.
  - Correct: State genetic drift occurs in all populations, but its effects on reducing variation are only pronounced in small populations.
- **Wrong:** Attributing all changes in variation to natural selection.
  - Why it fails: Students associate evolution with natural selection and forget neutral processes.
  - Correct: Always consider genetic drift, gene flow, and mutation before defaulting to natural selection as an explanation.

## Cheatsheet

| Concept | Key Rule/Formula | Exam Notes |
| --- | --- | --- |
| Allele Frequency (diploid) | $p = \frac{2AA + Aa}{2N}, \quad p+q=1$ | Always multiply individuals by 2 |
| Hardy-Weinberg Equilibrium | $p^2 + 2pq + q^2 = 1$ | Null model for non-evolving populations |
| HWE Calculation Start | q² = frequency of recessive phenotype | Only recessives can be directly observed |
| Mutation Effect on Variation | Increases variation | Ultimate source of new alleles |
| Genetic Drift Effect on Variation | Usually decreases variation | Strongest effect in small populations |
| Gene Flow Effect on Variation | Usually increases variation | Adds new alleles from other populations |
| Directional/Stabilizing Selection | Decreases variation | Favors one or intermediate phenotype |
| Disruptive/Balancing Selection | Maintains/increases variation | Preserves multiple alleles/phenotypes |

## What's next

Variations in populations is the foundation for understanding microevolution, which connects directly to broader topics in AP Biology Unit 7. Understanding how genetic variation arises and is maintained allows you to predict how populations will adapt to environmental change, such as climate change or the evolution of antibiotic resistance in bacteria. After mastering this sub-topic, you are ready to explore how speciation occurs from accumulated changes in population variation over time, and how evidence for evolution is drawn from patterns of variation within and between populations. Build out your Unit 7 knowledge with the following related topics to prepare for exam day.

- [Unit 7 Overview](https://www.owlsprep.com/study/ap-biology-u7-overview/)
- [Origins of Life on Earth](https://www.owlsprep.com/study/ap-biology-u7-origins-of-life-on-earth/)
- [Ecology Overview](https://www.owlsprep.com/study/ap-biology-u8-overview/)

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