Hardy-Weinberg equilibrium describes what happens to allele and genotype frequencies in a population when evolution is not occurring. This cheat sheet helps students organize the equations, assumptions, and reasoning used in population genetics problems. It is useful for connecting Punnett square ideas to real populations and for deciding whether a population is evolving.
The core formulas are p + q = 1 and p^2 + 2pq + q^2 = 1, where p and q are allele frequencies. The terms p^2, 2pq, and q^2 represent genotype frequencies for homozygous dominant, heterozygous, and homozygous recessive individuals. A population is in Hardy-Weinberg equilibrium only if there is no mutation, random mating, no natural selection, very large population size, and no gene flow.
Key Facts
- For a gene with two alleles, the allele frequency equation is p + q = 1.
- The genotype frequency equation is p^2 + 2pq + q^2 = 1.
- In Hardy-Weinberg notation, p is the frequency of one allele and q is the frequency of the other allele.
- The genotype frequency p^2 represents homozygous dominant individuals, 2pq represents heterozygous individuals, and q^2 represents homozygous recessive individuals.
- If the recessive phenotype is visible, its frequency is q^2, so q = square root of q^2.
- Allele frequencies and genotype frequencies are proportions, so they must be between 0 and 1.
- Hardy-Weinberg equilibrium requires no mutation, random mating, no natural selection, a very large population, and no migration.
- If observed genotype frequencies are very different from expected Hardy-Weinberg frequencies, the population may be evolving.
Vocabulary
- Allele frequency
- The proportion of a specific allele among all copies of that gene in a population.
- Genotype frequency
- The proportion of individuals in a population that have a specific genotype.
- Hardy-Weinberg equilibrium
- A condition in which allele and genotype frequencies stay constant across generations because no evolutionary forces are acting.
- Homozygous
- Having two identical alleles for a gene, such as AA or aa.
- Heterozygous
- Having two different alleles for a gene, such as Aa.
- Gene flow
- The movement of alleles into or out of a population through migration and reproduction.
Common Mistakes to Avoid
- Using q instead of q^2 for the recessive phenotype is wrong because the recessive phenotype usually represents homozygous recessive individuals, not the recessive allele frequency.
- Forgetting to take the square root of q^2 is wrong because q^2 is a genotype frequency, while q is an allele frequency.
- Treating percentages as whole numbers is wrong because Hardy-Weinberg equations use proportions, so 36% must be written as 0.36.
- Assuming every population is in equilibrium is wrong because Hardy-Weinberg equilibrium depends on strict conditions that are often not met in nature.
- Mixing up 2pq and p^2 is wrong because 2pq represents heterozygotes, while p^2 represents homozygous dominant individuals.
Practice Questions
- 1 In a population, 16% of individuals show the recessive phenotype. Find q, p, and the expected heterozygote frequency 2pq.
- 2 A population has p = 0.7 and q = 0.3. Calculate the expected frequencies of AA, Aa, and aa.
- 3 In a sample of 500 individuals, the expected aa frequency is 0.09. How many individuals are expected to have the aa genotype?
- 4 A small island population loses many individuals after a storm. Explain why this population may no longer meet Hardy-Weinberg equilibrium conditions.
Understanding Hardy-Weinberg Equilibrium Reference
Hardy-Weinberg calculations begin with a clear description of the trait. First decide which phenotype reveals a genotype. A recessive phenotype is especially useful because every individual showing it has two recessive alleles.
If 9 out of 100 people show that phenotype, the recessive genotype frequency is 0.09. The square root of 0.09 is 0.3, which gives the recessive allele frequency. The other allele frequency is found by subtracting 0.3 from 1.
From there, students can predict the expected frequencies of all three genotypes. Multiplying each predicted frequency by the population size changes a proportion into an expected number of individuals.
A dominant phenotype needs more care. An individual with the dominant appearance may have two dominant alleles or one dominant allele plus one recessive allele. Looking at appearance alone cannot separate those groups.
This is why the dominant phenotype frequency is not simply the dominant homozygous genotype frequency. In real genetics, some traits do not follow simple dominant and recessive patterns at all.
Codominance, incomplete dominance, multiple alleles, and environmental effects can make a basic two-allele model less suitable. Before using the equations, check whether the problem states that one allele is fully dominant and whether the population is being treated as a simple model.
The assumptions matter because each one blocks a process that can change frequencies. Mutation creates new DNA versions, though it usually acts slowly. Migration brings alleles into a population or removes them from it.
Natural selection changes reproductive success when some inherited traits help organisms survive or reproduce. Small populations can change by chance alone. This chance effect is called genetic drift.
A storm, disease outbreak, or small group founding a new population can make drift strong. Nonrandom mating does not always change allele frequencies immediately, but it changes how alleles are paired into genotypes. Inbreeding, for example, often increases homozygous genotypes and reduces heterozygous genotypes.
Expected values are a comparison point, not proof that a population has no evolution. A small sample can differ from the prediction just by chance. Scientists collect genotype data, calculate expected counts, then use statistical tests to judge whether the difference is larger than random sampling would reasonably produce.
In class problems, compare observed and expected values carefully. Keep frequencies as decimals until the final step, and check that genotype frequencies add to 1. Remember that allele frequencies count copies of alleles, not people.
Each diploid individual carries two copies of a gene, so a population of 50 individuals contains 100 allele copies at that gene. This distinction prevents many common errors.