# AP Biology Population Genetics

> AP Biology · Unit 7: Natural Selection
> Source: https://www.owlsprep.com/study/ap-biology-u7-population-genetics/

This study guide covers core population genetics concepts for AP Biology Unit 7, including allele and genotype frequency calculation, Hardy-Weinberg Equilibrium, evolutionary mechanisms, and genetic drift, with worked examples and exam tips.

**Prerequisites:** [Basic Mendelian inheritance for diploid organisms](https://www.owlsprep.com/study/ap-biology-u4-mendelian-genetics/); Core definitions of alleles, genotypes, and biological populations

## Learning objectives

- Calculate allele and genotype frequencies in diploid populations
- Apply the Hardy-Weinberg Equilibrium model to test for evolution
- Distinguish between the 5 mechanisms of evolution that violate HWE assumptions
- Differentiate between founder effect and bottleneck effect (types of genetic drift)
- Calculate relative fitness and post-selection allele frequencies

## Core Concepts and Standard Notation

Population genetics is the quantitative study of the distribution and change in allele and genotype frequencies within biological populations, forming the core mathematical foundation for the study of evolution in AP Biology. It frames evolution as a measurable change in allele frequency over generations, rather than just a qualitative change in trait distribution, allowing researchers to test hypotheses about evolutionary forces. This topic accounts for ~15% of Unit 7 exam weight, appearing regularly on both multiple-choice and free-response sections.

- $p$ = frequency of the dominant allele in the population
- $q$ = frequency of the recessive allele in the population
- $p^2$ = frequency of the homozygous dominant genotype
- $2pq$ = frequency of the heterozygous genotype
- $q^2$ = frequency of the homozygous recessive genotype

## Hardy-Weinberg Equilibrium (HWE)

The Hardy-Weinberg Equilibrium is a null model that describes a population that is *not evolving*, meaning allele and genotype frequencies remain constant from generation to generation. For a biallelic autosomal locus, the model is derived from probability rules for independent allele sampling from a gene pool, giving two core equations:

$$p + q = 1$$

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

**Hardy-Weinberg Equilibrium** — A null model of non-evolving populations that requires five key assumptions to hold: no new mutations, random mating, no natural selection, large population size, and no gene flow. Any violation indicates evolution is occurring.

**Worked example:** A population of 500 wildflowers has 120 red-flowered (RR), 280 pink-flowered (Rr), and 100 white-flowered (rr) individuals. Calculate allele frequencies for R and r, then determine if the population is in HWE for this locus.

1. Count total alleles for this diploid population:
2. $$500 \text{ individuals} \times 2 = 1000 \text{ total alleles}$$
3. Count R and r alleles and calculate frequencies: R alleles = $(120 \times 2) + 280 = 520$, so $p = 520/1000 = 0.52$. r alleles = $(100 \times 2) + 280 = 480$, so $q = 480/1000 = 0.48$. $p + q = 1$, which checks out.
4. Calculate expected HWE genotype frequencies: $p^2 = (0.52)^2 = 0.2704$, $2pq = 2(0.52)(0.48) = 0.4992$, $q^2 = (0.48)^2 = 0.2304$, which sum to 1 as expected.
5. Compare to observed frequencies: Observed $RR = 0.24$, $Rr = 0.56$, $rr = 0.20$. Observed and expected differ significantly, so the population is not in HWE.

> **Exam tip:** Always count alleles correctly for diploid organisms: multiply the number of homozygotes by 2 before adding heterozygotes to get the total allele count. Never use individual counts directly for $p$ and $q$.

## Mechanisms of Evolution (HWE Violations)

HWE acts as a null model: when we observe deviations from HWE predictions, we can infer that one or more evolutionary mechanisms are acting on the population. Each deviation corresponds to a violation of one of the five HWE assumptions, and each mechanism alters allele and genotype frequencies in predictable ways:

- **Mutation**: Creates new alleles, changes frequency very slowly over time; it is the ultimate source of genetic variation.
- **Non-random mating (e.g., inbreeding)**: Increases homozygosity by genotype, but does not change overall allele frequency on its own.
- **Natural selection**: Differential survival and reproduction based on phenotype causes consistent, adaptive changes in allele frequency, modeled using relative fitness.
- **Genetic drift**: Random change in allele frequency due to sampling error in small populations; changes are non-adaptive.
- **Gene flow**: Movement of alleles between populations reduces genetic differentiation between groups.

**Worked example:** A population of lizards has three genotypes for body size: $BB$ (large), $Bb$ (medium), $bb$ (small). Survival rates for each genotype are: $BB$: 60%, $Bb$: 80%, $bb$: 40%. Current allele frequencies are $p = 0.5$, $q = 0.5$. Calculate relative fitness for each genotype, and find the new frequency of $b$ after selection.

1. Calculate relative fitness by dividing each survival rate by the highest survival rate (80% for $Bb$):
2. $$w_{BB} = 0.6/0.8 = 0.75, \quad w_{Bb} = 0.8/0.8 = 1.0, \quad w_{bb} = 0.4/0.8 = 0.5$$
3. Pre-selection genotype frequencies are $p^2 = 0.25$ ($BB$), $2pq = 0.5$ ($Bb$), $q^2 = 0.25$ ($bb$).
4. Calculate unnormalized post-selection frequencies by multiplying pre-selection frequency by relative fitness, then sum to get mean fitness $\bar{w}$: $BB = 0.1875$, $Bb = 0.5$, $bb = 0.125$, so $\bar{w} = 0.8125$.
5. Normalize to get post-selection frequencies, then calculate new $q$: $BB \approx 0.231$, $Bb \approx 0.615$, $bb \approx 0.154$. New $q = f(bb) + 0.5f(Bb) \approx 0.46$.

> **Exam tip:** When calculating relative fitness, always divide by the highest survival rate, not the sum of survival rates. This scales all fitness values between 0 and 1 for easy comparison.

## Genetic Drift: Founder and Bottleneck Effects

Genetic drift is random fluctuation in allele frequency caused by sampling error in small populations, and it is a frequently tested HWE violation on the AP exam. Unlike natural selection, genetic drift causes non-adaptive changes: allele frequency shifts are random and unrelated to the fitness of the allele. Two commonly tested scenarios are:

- **Founder effect**: Occurs when a small subset of a larger population founds a new, isolated population. The founder group is not genetically representative of the original population, so allele frequencies change randomly.
- **Bottleneck effect**: Occurs when a large population is drastically reduced in size by a random event (e.g., natural disaster, habitat destruction). The surviving population has reduced genetic diversity and altered allele frequencies due to random sampling.

**Worked example:** A main population of bats has an allele frequency of $p = 0.8$ for the dominant $A$ allele (fog echo-location ability) and $q = 0.2$ for the recessive $a$ allele. A small group of 10 bats is blown off course to a new isolated island, and by chance 1 bat is $aa$, 8 are $AA$, and 1 is $Aa$. Is this founder effect or bottleneck effect? What is the new frequency of $a$?

1. Classify the event: This is founder effect, not bottleneck. A new isolated population is founded by a small subset of the original population, which matches the definition of founder effect. Bottleneck refers to reduction of an existing population, not founding a new one.
2. Calculate total alleles for 10 diploid bats:
3. $$10 \times 2 = 20 \text{ total alleles}$$
4. Count $a$ alleles: 1 $aa$ contributes 2 $a$ alleles, 1 $Aa$ contributes 1 $a$ allele, so total $a = 3$. New frequency is $q = 3/20 = 0.15$, a random change from the original $q = 0.2$.

> **Exam tip:** The most common AP exam question distinction: founder effect = new population, bottleneck effect = existing population reduced. Both are types of genetic drift.

## Common pitfalls

- **Wrong:** Counting individuals instead of alleles when calculating $p$ and $q$, e.g., using 100 recessive individuals out of 500 total as $q = 0.2$
  - Why it fails: Students confuse genotype frequency (count of individuals) with allele frequency (count of alleles) for diploid organisms
  - Correct: Always multiply the number of homozygous individuals by 2, add the number of heterozygous individuals, then divide by twice the total number of individuals to get allele frequency
- **Wrong:** Assuming $q^2$ equals the frequency of the recessive allele
  - Why it fails: Students mix up notation for allele frequency ($q$) and homozygous recessive genotype frequency ($q^2$), leading to algebra errors
  - Correct: Always label variables first; $q = \sqrt{q^2}$ only when the only observed data is the number of recessive phenotypes in a HWE population
- **Wrong:** Claiming non-random mating (like inbreeding) changes allele frequencies
  - Why it fails: Students confuse genotype frequency change with allele frequency change
  - Correct: Non-random mating changes how alleles are arranged into genotypes, not total allele counts. Do not list it as a mechanism that changes overall allele frequency unless selection is also acting
- **Wrong:** Calling genetic drift 'natural selection that happens in small populations'
  - Why it fails: Students mix up adaptive (selection) and non-adaptive (drift) evolutionary change
  - Correct: Always note that genetic drift causes random changes in allele frequency that are not tied to allele fitness, unlike natural selection
- **Wrong:** Claiming a population is in HWE because most assumptions are met
  - Why it fails: Students memorize the assumptions but forget all must hold for no evolution
  - Correct: If any one HWE assumption is violated, the population is evolving, so allele frequencies will change between generations

## Cheatsheet

| Category | Formula / Rule | Notes |
| --- | --- | --- |
| Sum of allele frequencies | $p + q = 1$ | Applies to any 2-allele locus, regardless of HWE |
| HWE Genotype Frequencies | $p^2 + 2pq + q^2 = 1$ | Only applies if all 5 HWE assumptions are met |
| Recessive allele from recessive phenotype | $q = \sqrt{q^2}$ | Only valid for HWE populations with recessive phenotypes only in homozygotes |
| Carrier (heterozygote) frequency | $2pq$ | Always 2 times the product of the two allele frequencies |
| Relative Fitness | $w = \frac{\text{Genotype survival rate}}{\text{Highest survival rate}}$ | Scales fitness between 0 and 1 for selection modeling |
| New allele frequency after selection | $q_{\text{new}} = f(bb) + 0.5 \times f(Bb)$ | Same calculation as any allele frequency, after normalizing post-selection frequencies |
| Total allele count (diploid) | $\text{Total alleles} = 2 \times \text{number of individuals}$ | Always multiply individual count by 2 for diploid organisms |
| HWE Assumptions | 1. No mutation 2. Random mating 3. No selection 4. Large population 5. No gene flow | Any violation = evolution is occurring |
| Founder Effect | Genetic drift in a new population | New population founded by a small subset of the original population |
| Bottleneck Effect | Genetic drift in a reduced existing population | Random population crash causes loss of genetic diversity |

## What's next

Population genetics provides the quantitative framework for all subsequent study of evolution in AP Biology Unit 7. Next, you will apply the core concepts of allele frequency change and the null model of HWE to analyze patterns of natural selection (directional, stabilizing, disruptive) and the process of speciation. Without mastering the material in this sub-topic, you will not be able to correctly interpret experimental data on evolutionary change, which is a regularly tested skill in both MCQ and FRQ sections of the AP exam. This topic also connects back to Mendelian genetics and molecular genetics, and feeds into the big idea that evolution is a measurable change in genetic variation over time.

- [Hardy-Weinberg Equilibrium](https://www.owlsprep.com/study/ap-biology-u7-hardy-weinberg-equilibrium/)
- [Evidence of Evolution](https://www.owlsprep.com/study/ap-biology-u7-evidence-of-evolution/)
- [Common Ancestry and Speciation](https://www.owlsprep.com/study/ap-biology-u7-common-ancestry-and-speciation/)

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