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Population
Genetics

Explore how allele frequencies change across generations, the conditions for Hardy-Weinberg equilibrium, and the forces that drive evolution in populations.

AP Biology

What Is a Population?

A population is a group of individuals of the same species living in the same area at the same time and capable of interbreeding. In genetics, we focus on the population's gene pool: the total collection of all alleles present in the population.

Allele and Genotype Frequencies

Allele Frequency
How common a specific allele is in the gene pool. For allele \(A\): \(p = \frac{\text{copies of } A}{\text{total allele copies}}\)
Genotype Frequency
The proportion of individuals with a specific genotype (e.g., \(AA\), \(Aa\), or \(aa\)) in the population.

Why Does This Matter?

Population genetics bridges Mendelian genetics (inheritance in individuals) with Darwinian evolution (change in populations). By tracking allele frequencies over time, we can detect whether evolution is occurring and identify which forces are driving it.

Medicine
Predicting genetic disease prevalence (e.g., sickle-cell carrier frequency)
Conservation
Monitoring genetic diversity in endangered species
Forensics
Estimating probability of DNA profile matches in a population

The Hardy-Weinberg Principle

The Hardy-Weinberg principle states that in a non-evolving population, allele and genotype frequencies remain constant from generation to generation. It gives us two foundational equations:

Visualizing Equilibrium

Frequency of allele A (p) Genotype Frequency 0 0.25 0.50 0.75 1.0 0 0.25 0.50 0.75 1.0 Frequency of allele A (p) Genotype Freq 0 0.25 0.50 0.75 1.0 0 0.25 0.50 0.75 1.0 \(p^2\) (AA) \(q^2\) (aa) \(2pq\) (Aa)

Five Conditions for Equilibrium

1
No mutations: no new alleles are created or altered.
2
Random mating: individuals pair by chance, not by genotype or phenotype.
3
No natural selection: all genotypes survive and reproduce equally well.
4
Very large population size: no genetic drift (random fluctuations are negligible).
5
No gene flow: no immigration or emigration of alleles.

Microevolution vs. Macroevolution

Microevolution Macroevolution
Scale Within a single population Above the species level
Timeframe Generations to centuries Thousands to millions of years
Measurable? Yes: allele frequency changes Inferred from fossil/molecular data
Example Pesticide resistance in insects Origin of new phyla (Cambrian explosion)
HW connection Detected by deviations from HW Cumulative result of microevolution

Forces That Disrupt Equilibrium

Natural Selection
Differential survival and reproduction based on phenotype. Directional, stabilizing, or disruptive.
Genetic Drift
Random changes in allele frequency, strongest in small populations. Includes bottleneck and founder effects.
Gene Flow
Movement of alleles between populations via migration. Tends to reduce differences between populations.
Mutation
Creates new alleles. Rare per locus per generation, but the ultimate source of all genetic variation.
Ten genotypes and founder sample
Ten genotypes and founder sample
A beetle habitat accompanies a hypothetical source-to-founder comparison. An authored companion lists ten genotypes and highlights founders 1 AA and 4 Aa.
A founder event can change allele frequencies through sampling without a fitness advantage. In this synthetic example, 10 source diploids carry 10 A and 10 a copies; founders 1 and 4 carry 3 A and 1 a. The habitat image is contextual, not a measured sample.

Types of Natural Selection

Directional Phenotype Stabilizing Phenotype Disruptive Phenotype

How to Apply Hardy-Weinberg

1
Identify the known value. Usually you are given the frequency of the homozygous recessive phenotype, which equals \(q^2\).
2
Calculate \(q\). Take the square root: \(q = \sqrt{q^2}\).
3
Calculate \(p\). Since \(p + q = 1\), we get \(p = 1 - q\).
4
Find genotype frequencies. Compute \(p^2\) (homozygous dominant), \(2pq\) (heterozygous), and \(q^2\) (homozygous recessive).
5
Verify. Check that \(p^2 + 2pq + q^2 = 1\). If the problem asks about phenotypes, combine dominant genotypes.

Example 1: Albinism

In a population, 1 in 10,000 individuals is albino (homozygous recessive \(aa\)). Assuming Hardy-Weinberg equilibrium, find the frequency of carriers (\(Aa\)).

Example 2: Sickle-Cell Allele

In a West African population, 9% of individuals have sickle-cell disease (\(ss\)). What percentage are heterozygous carriers (\(Ss\))?

Example 3: Testing for Evolution

A population of 500 wildflowers shows: 320 red (\(RR\)), 160 pink (\(Rr\)), and 20 white (\(rr\)). Is this population in Hardy-Weinberg equilibrium?

Common Mistakes

✕ Forgetting the Square Root
Students use \(q^2\) directly instead of taking \(q = \sqrt{q^2}\) before calculating \(p\).
✕ Confusing Phenotype with Genotype
The dominant phenotype includes both \(p^2\) and \(2pq\). Only \(q^2\) maps directly to the recessive phenotype.
✕ Applying HW When Conditions Fail
HW is a null model. If the population is small, non-random mating occurs, or selection is present, the equations give inaccurate results.

Summary of Evolutionary Forces

Force Effect on Variation Random or Directed?
Natural Selection Can increase or decrease Directed (adaptive)
Genetic Drift Decreases Random
Gene Flow Increases within; decreases between Random (non-adaptive)
Mutation Increases Random
Non-random Mating Alters genotype ratios (not allele freq) Directed

Question 1 of 5

In a population in Hardy-Weinberg equilibrium, the frequency of the recessive allele \(q = 0.3\). What is the expected frequency of heterozygous individuals?

Question 2 of 5

Which of the following is NOT a condition required for Hardy-Weinberg equilibrium?

Question 3 of 5

A population of 1,000 beetles has 360 green (\(GG\)), 480 brown (\(Gg\)), and 160 tan (\(gg\)). What is the frequency of the \(G\) allele?

Question 4 of 5

A hurricane reduces a large island bird population from 10,000 to 50 individuals. Which evolutionary force is most likely to change allele frequencies in the surviving population?

Question 5 of 5

In a region where malaria is prevalent, individuals heterozygous for the sickle-cell allele (\(Ss\)) have higher fitness than either homozygote. This is an example of: