Difficulty: Introductory | Prerequisites: Basic understanding of alleles, genotypes, and Mendelian inheritance.
Evolutionary biology needs a baseline: a way to say "nothing is happening" so that when something does happen, you can spot it. Hardy-Weinberg equilibrium is that baseline. It describes a hypothetical population where allele frequencies never change, generation after generation. In practice, real populations almost never meet every HWE condition, and that is precisely the point. By comparing observed genotype frequencies to the frequencies HWE predicts, biologists can detect which evolutionary forces (drift, selection, mutation, gene flow, non-random mating) are at work.
You should already be comfortable with alleles, genotypes, and basic probability before diving in here.
The Hardy-Weinberg principle says that allele and genotype frequencies in a population stay constant across generations unless an evolutionary force (drift, selection, mutation, gene flow, or non-random mating) acts on them. It works as a null hypothesis: plug in allele frequencies, calculate expected genotype frequencies, and compare to what you observe. A mismatch means evolution is happening.
Alleles
Alternative versions of a gene that arise by mutation and are found at the same locus on homologous chromosomes. Think of alleles as different flavours of the same gene.
Genotype
The combination of alleles an individual carries at a given locus (e.g. AA, Aa, or aa). In simple terms, it is the genetic recipe behind a trait.
Gene pool
The complete set of alleles present in a population at a given time. Imagine scooping every copy of every allele from every individual into one big collection.
Allele frequency
The proportion of a specific allele relative to all alleles at that locus in the gene pool. Calculated as: (number of copies of the allele) / (total number of alleles in the population).
p and q
Conventional symbols for the frequencies of two alleles at a single locus. p typically represents the dominant allele frequency, q the recessive. They must sum to 1: p + q = 1.
Hardy-Weinberg principle (HWE)
The principle stating that allele and genotype frequencies in a population remain constant from generation to generation in the absence of evolutionary forces. It serves as the null model in population genetics.
Law of AND (multiplication rule)
The probability of two independent events both occurring equals the product of their individual probabilities. In HWE, the probability of drawing allele A and then allele A again is p x p = p².
Law of OR (addition rule)
The probability that one event or another occurs equals the sum of their individual probabilities (for mutually exclusive events). In HWE, heterozygotes can form as Aa or aA, so their combined frequency is pq + pq = 2pq.
Genotypic frequencies
The proportions of each genotype (AA, Aa, aa) in the population. Under HWE these are p², 2pq, and q² respectively.
Genetic drift
Random changes in allele frequencies from one generation to the next, caused by chance sampling of alleles rather than by selection. Think of it as statistical noise in small populations.
Random mating
Mating without regard to genotype. One of the conditions required for HWE. If individuals choose mates based on phenotype or relatedness, allele frequencies can shift.
Mutation
A heritable change in DNA sequence. Mutations introduce new alleles into the gene pool and, if occurring at different rates, can shift allele frequencies over time.
Natural selection
Differential survival and reproduction of individuals due to differences in phenotype. The alleles behind advantageous traits increase in frequency; those behind harmful traits decrease.
Genetic bottleneck
A sharp reduction in population size (due to a disaster, for instance) that randomly eliminates alleles from the gene pool. The surviving population may have very different allele frequencies from the original.
Founder effect
A form of genetic drift that occurs when a small group of individuals colonises a new area. The new population's gene pool reflects only the alleles those founders happened to carry.
HWE as a null model
Hardy-Weinberg equilibrium is the "nothing is happening" scenario in population genetics. It predicts what genotype frequencies should look like if no evolution is occurring.
If observed frequencies match HWE predictions, there is no evidence that evolutionary forces are acting at that locus.
If observed frequencies deviate from HWE predictions, one or more evolutionary agents must be at work: natural selection, genetic drift, mutation, gene flow, or non-random mating.
Five conditions for HWE to hold
No natural selection (all genotypes have equal fitness)
No genetic drift (the population is infinitely large)
No mutation (no new alleles appear)
No gene flow (no migration in or out of the population)
Random mating (individuals do not choose mates based on genotype)
All five must hold simultaneously. Violating even one means allele frequencies can change across generations.
Calculating allele frequencies from the gene pool
Count every copy of each allele in the population.
Divide by the total number of alleles (for a diploid organism with N individuals, total alleles = 2N).
For two alleles A and a: p = frequency of A, q = frequency of a, and p + q = 1.
Predicting genotype frequencies
Once you know p and q, genotype frequencies follow from probability:
Frequency of AA = p² (probability of drawing A twice)
Frequency of Aa = 2pq (A then a, or a then A)
Frequency of aa = q²
These must also sum to 1: p² + 2pq + q² = 1.
Using HWE to detect evolution
Observe the actual genotype counts in a population.
Calculate allele frequencies from those counts.
Use p and q to predict expected genotype frequencies under HWE.
Compare observed vs expected. A statistically significant difference means the population is not in Hardy-Weinberg equilibrium, so at least one evolutionary force is acting.
p + q = 1Allele frequencies for a two-allele system must sum to 1.
p^2 + 2pq + q^2 = 1Genotype frequencies under HWE. This is simply the expansion of (p + q)².
Probability rules in context
Law of AND (multiplication): P(AA) = p x p = p². The chance of inheriting allele A from both parents.
Law of OR (addition): P(Aa) = P(Aa) + P(aA) = pq + qp = 2pq. The heterozygote can form two ways.
Genetic counsellors use HWE to estimate the carrier frequency of recessive genetic disorders. If 1 in 10,000 individuals is affected (aa), then q² = 0.0001, q = 0.01, and the carrier frequency (2pq) is roughly 2%. Conservation biologists compare observed genotype frequencies to HWE predictions to assess whether small populations are losing genetic diversity through drift or inbreeding.
Students often think HWE describes how evolution works. It does the opposite: it describes what happens when evolution is absent. It is a null model.
Students sometimes assume that if a population is not in HWE, natural selection must be the cause. Drift, gene flow, mutation, and non-random mating can all produce deviations.
A common mistake is forgetting that heterozygotes can form two ways (Aa and aA), leading students to write pq instead of 2pq.
Some students confuse allele frequencies with genotype frequencies. Allele frequencies are p and q. Genotype frequencies are p², 2pq, and q². They are related but not the same thing.
Be ready to calculate allele frequencies from genotype counts and vice versa. This is the bread-and-butter HWE exam question.
Know all five conditions for HWE and be able to explain what happens when each is violated.
Understand why HWE is called a null hypothesis. Exams often ask you to explain its role rather than just plug numbers into the formula.
Genetic drift, bottlenecks, and founder effects are frequently tested alongside HWE. Expect a question asking why drift hits small populations harder than large ones.
True or false: If a population is in Hardy-Weinberg equilibrium, evolution is occurring.
Answer: False. HWE means no evolution is occurring.
Fill in the blank: The frequency of heterozygotes in a population under HWE is ______.
Answer: 2pq.
True or false: Genetic drift is more powerful in large populations than in small ones.
Answer: False. Drift has a stronger effect on small populations because random sampling errors are proportionally larger.
Fill in the blank: p + q = 1 describes the relationship between ______ frequencies.
Answer: Allele.
True or false: Non-random mating alone can cause allele frequencies to change.
Answer: False. Non-random mating changes genotype frequencies but does not by itself change allele frequencies.
Q: Why is the Hardy-Weinberg principle useful to biologists?
A: It provides a null model. By comparing a population's observed genotype frequencies to HWE expectations, biologists can detect whether evolutionary forces are acting. Without this baseline, there would be no principled way to demonstrate that evolution is occurring at a given locus.
Q: A population has 160 AA individuals, 480 Aa individuals, and 360 aa individuals. Is this population in Hardy-Weinberg equilibrium?
A: Total = 1,000 individuals = 2,000 alleles. Count of A alleles = (160 x 2) + 480 = 800. p = 800/2000 = 0.4. q = 1 - 0.4 = 0.6. Expected under HWE: AA = p² x 1000 = 160, Aa = 2pq x 1000 = 480, aa = q² x 1000 = 360. Observed matches expected exactly, so yes, this population is in HWE.
Q: Why does genetic drift affect small populations more than large populations?
A: In small populations, each individual represents a larger fraction of the total gene pool. Random events (who survives, who mates) can shift allele frequencies substantially in a single generation. In large populations, these random fluctuations average out and have little effect on overall frequencies.
Q: A recessive allele causes a condition found in 1 in 2,500 individuals. What is the carrier frequency?
A: q² = 1/2500 = 0.0004. q = 0.02. p = 0.98. Carrier frequency (2pq) = 2 x 0.98 x 0.02 = 0.0392, or about 3.9%.
Hardy-Weinberg is the foundation for the natural selection unit that follows. The modes of selection (directional, stabilising, disruptive) are all ways HWE can be violated. Genetic drift connects directly to the population-size themes in conservation biology. The concept of allele frequency reappears in discussions of speciation and gene flow between populations.
Hardy-Weinberg equilibrium, HWE, null model, population genetics, allele frequency, genotype frequency, p squared plus 2pq plus q squared, gene pool, genetic drift, bottleneck effect, founder effect, random mating, evolutionary agents, five conditions for HWE, BBIO 180, intro biology, University of Washington