Hardy-Weinberg Equilibrium | AP Bio Unit 7 Study Guide

Getting Started

At the heart of evolutionary biology is the study of how life changes over time. To understand this change, we must first establish a baseline for what a non-changing, or non-evolving, population looks like at the genetic level. This chapter explores the Hardy-Weinberg equilibrium, a foundational principle in population genetics that provides a mathematical model for a population's gene pool—the total collection of all the genes and their different versions, or alleles, in that population. By understanding the strict conditions required to maintain this genetic stasis, we can identify the forces that drive evolutionary change in the real world.

What You Should Be Able to Do

After completing this section, you should be able to:

Describe the five conditions required for a population to remain in Hardy-Weinberg equilibrium.
Explain how the violation of any of these conditions can cause allele and genotype frequencies to change over time.
Use the Hardy-Weinberg equations to calculate the frequencies of alleles and genotypes within a population.
Compare the genetic structure of a hypothetical, non-evolving population with that of a population undergoing evolutionary change.

Key Concepts & Mechanisms

The Hardy-Weinberg principle is best understood through the lens of change and continuity over time. It establishes a baseline condition of genetic continuity and then highlights the key changes, or evolutionary mechanisms, that disrupt this equilibrium.

Baseline Condition: The Hardy-Weinberg Principle

The Hardy-Weinberg principle states that in a population that is not evolving, the frequencies of alleles and genotypes will remain constant from generation to generation. This state of genetic stasis is called Hardy-Weinberg equilibrium. It serves as a "null hypothesis" for evolution; if a population's frequencies deviate from the predictions of this model, it is evidence that evolution is occurring.

For a gene with two alleles, a dominant allele (e.g., A) and a recessive allele (e.g., a), we can represent their frequencies with variables:

The frequency of the dominant allele (A) is denoted by p.
The frequency of the recessive allele (a) is denoted by q.

Since these are the only two alleles for this gene in the population, their frequencies must sum to 1 (or 100%).

Allele Frequency Equation:p + q = 1

From these allele frequencies, we can predict the frequencies of the three possible genotypes (AA, Aa, and aa) if the population is in equilibrium. This is based on the probability of drawing two alleles at random from the gene pool:

The frequency of the homozygous dominant genotype (AA) is p².
The frequency of the heterozygous genotype (Aa) is 2pq.
The frequency of the homozygous recessive genotype (aa) is q².

These genotype frequencies must also sum to 1.

Genotype Frequency Equation:p² + 2pq + q² = 1

A population is in equilibrium only if it meets five strict conditions.

Key Changes: The Five Agents of Evolutionary Change

The true power of the Hardy-Weinberg model is in what it reveals when its conditions are not met. The violation of any of the five conditions is a mechanism of evolutionary change, causing allele or genotype frequencies to shift.

No Mutations: Mutations are changes in the DNA sequence and are the ultimate source of new alleles. If mutations occur, they introduce new genetic information into the gene pool, directly altering the values of p and q.
Random Mating: Mating must be random with respect to the trait being studied. If individuals choose mates based on their genotype (e.g., mating only with similar-looking individuals), it leads to non-random mating. This can alter genotype frequencies (e.g., increasing homozygotes) but does not, by itself, change allele frequencies.
No Natural Selection: All genotypes must have equal survival and reproductive rates. If a particular genotype confers a fitness advantage or disadvantage, natural selection will occur. Alleles that increase fitness will become more common in subsequent generations, while those that decrease fitness will become rarer, causing p and q to change.
Extremely Large Population Size: The model assumes an infinitely large population to negate the effects of random chance. In small populations, random fluctuations in allele frequencies can occur from one generation to the next, a process called genetic drift. For example, by pure chance, a few individuals might leave more offspring than others, and the alleles they carry will increase in frequency, regardless of their adaptive value.
No Gene Flow: There can be no migration of individuals into or out of the population. Gene flow is the movement of alleles between populations. When individuals migrate, they introduce their alleles into the new population and remove them from the old one, changing allele frequencies in both.

Key Continuities: The Persistence of Alleles

If all five conditions are met, the model predicts perfect continuity. The allele frequencies p and q will not change from one generation to the next. The shuffling of alleles during meiosis and random fertilization does not, by itself, alter the overall frequencies in the gene pool. This demonstrates that inheritance itself is not a mechanism of evolution; rather, evolution requires one of the "key change" agents to be active.

Key Models & Diagrams

The relationship between the conditions for equilibrium and the agents of evolution can be summarized in a matrix.

Condition for Equilibrium	Violation (Agent of Evolution)	Effect on Allele & Genotype Frequencies
No Natural Selection	Natural Selection	Allele and genotype frequencies change in a directional, adaptive way.
No Mutation	Mutation	New alleles are introduced, slowly changing allele frequencies over time.
No Gene Flow	Migration / Gene Flow	Allele frequencies change as alleles are transferred between populations.
Large Population	Genetic Drift	Allele frequencies change randomly and unpredictably, especially in small populations.
Random Mating	Non-random Mating	Genotype frequencies change (e.g., more homozygotes), but allele frequencies may not.

Key Components & Evidence

Population: A localized group of individuals of the same species that are capable of interbreeding and producing fertile offspring. This is the fundamental unit of evolution.
Gene Pool: The aggregate of all copies of every type of allele at all loci in every individual in a population.
Allele Frequency: The proportion of a specific allele within a population. It is calculated as the number of copies of that allele divided by the total number of alleles for that gene in the population.
Genotype Frequency: The proportion of a specific genotype within a population. It is calculated as the number of individuals with that genotype divided by the total number of individuals in the population.
p + q = 1: The mathematical model for calculating allele frequencies for a gene with two alleles.
p² + 2pq + q² = 1: The mathematical model for calculating the expected genotype frequencies in a population at equilibrium.
Genetic Drift: A mechanism of evolution in which allele frequencies of a population change over generations due to chance events. It is most pronounced in small populations.
Gene Flow: The transfer of alleles into or out of a population due to the movement of fertile individuals or their gametes. It can reduce genetic differences between populations.
Natural Selection: The process in which individuals with certain inherited traits tend to survive and reproduce at higher rates than other individuals because of those traits. It is the only mechanism that consistently causes adaptive evolution.

Skill Snapshots

Causation

Cause: A sudden environmental change makes a previously neutral allele advantageous. Effect: Natural selection acts on the population, increasing the frequency of the advantageous allele over generations.
Cause: A small group of individuals colonizes a new island. Effect: The new population's gene pool is subject to strong genetic drift and may have different allele frequencies than the source population (the founder effect).
Cause: Two previously isolated populations of plants begin to be cross-pollinated by a new insect species. Effect: Gene flow occurs between the two populations, making their gene pools more similar over time.

Comparison

Hardy-Weinberg Equilibrium vs. Evolution: Equilibrium is a static state where allele frequencies do not change, whereas evolution is a dynamic process defined by changes in allele frequencies over generations.
Genetic Drift vs. Natural Selection: Genetic drift causes random, non-adaptive changes in allele frequencies, while natural selection causes directional, adaptive changes that increase a population's fitness in its environment.
Allele Frequency vs. Genotype Frequency: Allele frequency (p, q) refers to the proportion of individual alleles in the gene pool, while genotype frequency (p², 2pq, q²) refers to the proportion of individuals with a specific combination of two alleles.

Change & Continuity Over Time (CCOT)

Baseline: A large, isolated population of moths has a stable frequency of 90% for the dark-wing allele (p=0.9) and 10% for the light-wing allele (q=0.1).
Change 1 (Selection): A new predator arrives that can easily spot dark-winged moths. Over many generations, the frequency of the dark-wing allele decreases, and the light-wing allele increases.
Change 2 (Drift): A wildfire randomly eliminates 95% of the moth population. The surviving moths, by chance, have an allele frequency of p=0.5 and q=0.5, a drastic change not related to adaptation.
Continuity: If the population remained large and isolated, with no predators and random mating, the allele frequencies would be expected to remain at p=0.9 and q=0.1 indefinitely.

Common Misconceptions & Clarifications

Misconception: The Hardy-Weinberg equilibrium is a common state for natural populations.
- Clarification: The opposite is true. The five conditions are almost never met in nature. The model's value is not in describing reality, but in providing a baseline to measure how much a real population is evolving and which forces are likely responsible.
Misconception: Dominant alleles are always more common than recessive alleles.
- Clarification: An allele's frequency is independent of its dominance. A dominant allele can be very rare (e.g., the allele for Huntington's disease), and a recessive allele can be very common (e.g., the allele for O-type blood). Frequencies are determined by evolutionary pressures, not by the allele's expression.
Misconception: Any change in a population is evolution.
- Clarification: Evolution is specifically defined as a change in the allele frequencies in a population over generations. For example, non-random mating can change genotype frequencies, but if allele frequencies p and q remain the same, it is not considered evolution in the strictest sense.
Misconception: Individuals evolve.
- Clarification: Individuals are subject to natural selection, but only populations can evolve. An individual's genetic makeup is fixed at birth; evolution is the change in the genetic composition of the entire population across generations.

One-Paragraph Summary

The Hardy-Weinberg equilibrium principle is a fundamental concept that acts as a mathematical null hypothesis for evolution. It describes a hypothetical, non-evolving population where allele and genotype frequencies remain constant across generations, a state that requires five specific conditions: no mutation, random mating, no natural selection, a large population size, and no gene flow. The violation of these conditions represents the primary mechanisms of evolutionary change, such as natural selection and genetic drift. By using the equations p + q = 1 and p² + 2pq + q² = 1, scientists can calculate expected frequencies and compare them to observed data from real populations. This comparison allows them to determine whether a population is evolving and to form hypotheses about the forces driving that change.

Hardy-Weinberg Equilibrium - AP Biology Study Guide