BiologyMeasuring Evolution With Allele Frequencies
Lumi stands at a holographic population map showing hundreds of glowing beetle icons scattered across a forest floor, each beetle colored either brown or green, pointing to frequency graphs updating in real time as beetles are selected or removed.
- Explain what the Hardy-Weinberg equilibrium model predicts about allele frequencies in a non-evolving population.
- Identify the five conditions required for a population to remain in Hardy-Weinberg equilibrium.
- Calculate allele frequencies and expected genotype frequencies using the Hardy-Weinberg equations p + q = 1 and p² + 2pq + q² = 1.
- Predict how violating one Hardy-Weinberg condition shifts allele frequencies and constitutes evidence of evolution.
- Compare observed genotype frequencies to Hardy-Weinberg expectations to determine whether evolution is occurring.
Key terms
- Hardy-Weinberg equilibrium
- The condition where allele frequencies stay constant across generations without evolution
- Allele frequency
- The proportion of a particular allele among all alleles for a gene in a population
- Genotype frequency
- The proportion of individuals carrying a particular genotype in a population
- Null model
- A baseline prediction of no change against which observed data are compared
- Genetic drift
- Random change in allele frequencies, strongest in small populations
A Baseline for Detecting Change
Evolution at the population level means allele frequencies change over time, but to detect change you first need a prediction for no change. The Hardy-Weinberg model provides that baseline, showing that under idealized conditions allele frequencies remain constant generation after generation. It is a null model: when real genotype frequencies deviate significantly from its predictions, you have evidence that an evolutionary force is at work.
The Two Equations
The model uses p for the frequency of one allele and q for the other, and because there are only two alleles, p plus q equals 1. Expanding the square of that sum gives the genotype predictions: p squared is the frequency of dominant homozygotes, 2pq is the frequency of heterozygotes, and q squared is the frequency of recessive homozygotes, with p squared plus 2pq plus q squared equal to 1. The recessive homozygote frequency q squared is especially useful because it is directly observable.
The Five Conditions
Equilibrium holds only when all five conditions are met: a very large population so drift is negligible, random mating, no mutation, no gene flow, and no natural selection. These conditions rarely hold in nature, which is the point. When any one is violated, allele frequencies shift, so detecting a deviation from Hardy-Weinberg expectations identifies which evolutionary force, such as selection or drift, is acting on the population.
Worked examples
In a population at equilibrium, q squared for aa individuals is 0.04. Find p.
- Recognize that q squared is the genotype frequency, so take the square root to recover the allele frequency q.
- Compute the square root: the square root of 0.04 is 0.20, so q equals 0.20.
- Use p plus q equals 1: p equals 1 minus 0.20, which is 0.80. Do not subtract q squared directly, which would wrongly give 0.96.
Answer: p = 0.80.
Activity
A beetle population has allele frequencies p = 0.6 and q = 0.4. Drag each label to the correct Hardy-Weinberg expected genotype frequency box.
Practice
If q equals 0.3 in an equilibrium population, calculate the expected AA, Aa, and aa frequencies.
Given observed genotype frequencies that differ from predictions, identify which condition is likely violated.
Common mistakes to avoid
- The dominant allele is the most commonAllele frequency is unrelated to dominance; a recessive allele can be far more common than the dominant one in a population.
- p equals 1 minus q squaredYou must take the square root of q squared to get q first, then compute p as 1 minus q, not 1 minus q squared.
Check your understanding
A population biologist finds that the frequency of homozygous recessive individuals (aa) in a large beetle population is 0.04. Assuming Hardy-Weinberg equilibrium, what is the frequency of the dominant allele A (p)?
A researcher monitors a small, isolated island bird population over 20 generations and finds that allele frequencies shift substantially each generation even though the birds mate randomly and there is no selection, mutation, or migration. Which Hardy-Weinberg condition is most likely violated?
Why is Hardy-Weinberg equilibrium described as a null model for evolution?
Recap
Hardy-Weinberg is a null model predicting constant allele frequencies under five idealized conditions, using p plus q equal to 1 and p squared plus 2pq plus q squared equal to 1. Because those conditions rarely hold, observed deviations from the predicted genotype frequencies reveal that an evolutionary force is driving change.
Reflect
Why is a model built on conditions that rarely occur still one of the most useful tools in evolution?