Variations in Populations — AP Biology Study Guide

For: AP Biology candidates sitting AP Biology.

Covers: Sources of genetic variation in populations, allele and genotype frequency calculation, Hardy-Weinberg equilibrium, impacts of evolutionary forces on variation, and the role of variation in natural selection, aligned to AP Biology CED Unit 7.

You should already know: Basic Mendelian genetics for diploid organisms, evolution is defined as change in allele frequency over time, core principles of natural selection.

A note on the practice questions: All worked questions in the "Practice Questions" section below are original problems written by us in the AP Biology style for educational use. They are not reproductions of past College Board / Cambridge / IB papers and may differ in wording, numerical values, or context. Use them to practise the technique; cross-check with official mark schemes for grading conventions.

1. What Is 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. Variations in populations appears on both multiple-choice (MCQ) and free-response (FRQ) sections, most often as a 3–4 point part of a longer FRQ or 1–2 standalone MCQs.

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 (the proportion of a specific allele at a given locus in the population) and genotype frequencies (the proportion of each allele combination in the population). Unlike variation between species, within-population variation drives microevolution, small-scale changes in allele frequency over generations that lead to macroevolutionary change over longer time scales.

2. Sources of Genetic Variation

Genetic variation originates and is maintained in populations through a hierarchy of mechanisms, with mutation as the ultimate source of all new variation. Random mutation describes heritable changes to an organism’s nucleotide sequence that create new alleles; 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.

Beyond new mutation, existing variation is reshuffled and maintained through four key mechanisms: (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, where heterozygotes have malaria resistance, keeping both alleles in malaria-endemic regions.

Worked Example

Problem: 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.

Solution:

1. First explanation: Cryptic standing genetic variation is now expressed after environmental change. 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.
2. Second explanation: Gene flow from a neighboring inland population. 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.
3. 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.

3. 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.

To calculate allele frequency from genotype counts: each diploid individual carries two alleles per locus, so the total number of alleles in a population of $N$ individuals is $2N$. Homozygous individuals carry two copies of their allele, while heterozygotes carry one copy of each allele. The formula for the frequency of the dominant $A$ allele is: $$p=\frac{(2\times \text{number of AA individuals})+(\text{number of Aa individuals})}{2N}$$ 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

Problem: 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.

Solution steps:

1. Calculate total alleles: Total individuals = 200, so total alleles = $2\times 200=400$.
2. Count $t$ alleles: Homozygous $tt$ contribute 2 $t$ each, heterozygous $Tt$ contribute 1 $t$ each. Total $t$ alleles = $(2\times 32)+(1\times 96)=64+96=160$.
3. Calculate frequency: $q=\frac{160}{400}=0.4$.
4. Verify: $p=[(2\times 72)+96]/400=(144+96)/400=240/400=0.6$, 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.

4. 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.

When these assumptions are met, the relationship between allele and genotype frequencies is given by the Hardy-Weinberg equation: $$p^2+2pq+q^2=1$$ 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). 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.

Worked Example

Problem: 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?

Solution steps:

1. Let $q$ = frequency of the recessive black allele, $p$ = frequency of the dominant brown allele. Only homozygous recessive individuals have black coats, so $q^2=0.04$.
2. Solve for $q$: $q=\sqrt{0.04}=0.2$.
3. Solve for $p$: $p=1-q=1-0.2=0.8$.
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.

5. 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

Problem: 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.

Solution steps:

1. Identify the force: Genetic drift via the bottleneck effect.
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. 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. 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.

6. Common Pitfalls (and how to avoid them)

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

7. Practice Questions (AP Biology Style)

Question 1 (Multiple Choice)

In a population of 100 diploid daisies, 49 plants are homozygous dominant (PP) for purple petals, 42 are heterozygous (Pp), and 9 are homozygous recessive (pp) for white petals. What is the allele frequency of $p$ in this population? A) 0.09 B) 0.3 C) 0.42 D) 0.7

Worked Solution: First, total alleles for 100 diploid individuals is $2\times 100=200$. Count the number of $p$ alleles: homozygous $pp$ contribute 2 $p$ each, heterozygous $Pp$ contribute 1 $p$ each. Total $p$ alleles = $(2\times 9)+42=18+42=60$. Allele frequency = $60/200=0.3$. Check: Frequency of $P$ is $(2\times 49+42)/200=140/200=0.7$, so $p+P=1$, which confirms the calculation. The correct answer is B.

Question 2 (Free Response)

Tay-Sachs disease is a recessive genetic disorder that occurs in approximately 1 out of every 3600 births in a large human population. Assume the population is in Hardy-Weinberg equilibrium for this locus. (a) Calculate the frequency of the recessive Tay-Sachs allele in the population. Show your work. (b) Calculate the frequency of heterozygous carriers for the Tay-Sachs allele in the population. Show your work. (c) Explain one reason this population might deviate from Hardy-Weinberg equilibrium for this locus, and predict the effect of the deviation on the recessive allele frequency over time.

Worked Solution: (a) Only homozygous recessive individuals have Tay-Sachs, so frequency of homozygous recessive is $q^2=1/3600\approx 0.000278$. Solve for $q$: $q=\sqrt{0.000278}\approx 0.0167$. The frequency of the recessive allele is ~0.017. (b) The frequency of the dominant normal allele is $p=1-q=1-0.0167=0.9833$. Carrier frequency is $2pq=2(0.9833)(0.0167)\approx 0.0328$, or ~3.3% of the population. (c) One common deviation is natural selection: individuals with Tay-Sachs have reduced survival and do not reproduce, so the assumption of no selection is violated. Because selection removes homozygous recessive individuals from the breeding population, the frequency of the recessive Tay-Sachs allele will decrease gradually over time.

Question 3 (Application / Real-World Style)

Conservation biologists studied an endangered population of 30 black rhinos in a South African game reserve after poaching reduced the population from 500 individuals in 1970 to 30 in 1990. Researchers measured extremely low genetic variation in the 1990 population compared to the 1970 population. In 1995, 10 black rhinos from a large wild population in Namibia were introduced into the South African reserve. By 2023, the population had grown to 120 individuals, and genetic variation had increased by 40% compared to 1990. Explain the mechanism that caused the increase in genetic variation, and connect the increase to the population's ability to adapt to future climate change.

Worked Solution: The original 1990 South African population experienced a genetic bottleneck: poaching reduced the large 1970 population to 30 individuals, so most of the original genetic variation was lost when rare alleles were eliminated by genetic drift. The mechanism that increased variation in 2023 is gene flow from the Namibian population: the introduction of 10 new rhinos added new alleles that were lost from the bottlenecked South African population, increasing overall genetic variation. In context: Higher genetic variation means the population has a larger pool of heritable traits available for natural selection. If climate change brings new stressors like higher temperatures or new diseases, there is a higher chance some individuals will have adaptive alleles that allow them to survive and reproduce, making the population less likely to go extinct.

8. Quick Reference Cheatsheet

9. What's Next

Variations in populations is the foundation for all further study of microevolution and macroevolution in AP Biology Unit 7. Next, you will study how different patterns of selection and speciation arise from changes in variation over time; without a solid understanding of how to calculate allele frequencies and what drives changes in variation, you will not be able to connect microevolutionary changes to the origin of new species. This topic also feeds into broader topics across the course, including population ecology and conservation biology, where reduced genetic variation in endangered species is a key threat to biodiversity.

• Hardy-Weinberg Equilibrium
• Evolutionary Forces
• Speciation
• Biodiversity Conservation