Hardy-Weinberg Equilibrium
Hardy-Weinberg equilibrium is the null model of evolution — a description of what a population's genetics look like when nothing is changing them. It is not a prediction that populations stay still; it is the baseline you compare a real population against so you can tell whether it is evolving at all. If the observed frequencies drift away from what the model predicts, something — selection, drift, migration, mutation, non-random mating — is at work. Topic 7.5 is where you learn to run that comparison and read what the deviation means.
Two equations carry the whole idea. For a gene with two alleles, the allele frequencies sum to one: p + q = 1. From those, the genotype frequencies follow by expanding the square: p² + 2pq + q² = 1, where p² is the homozygous-dominant share, 2pq the heterozygous share, and q² the homozygous-recessive share. The move students miss is that these are two different layers — an allele frequency is not a genotype frequency, and a dominant allele is not automatically the common one. Dominance is about which phenotype shows; frequency is about how often the allele appears. A rare dominant allele stays rare unless some force pushes it.
Interactive · Hardy-Weinberg
Set the allele frequency p, then watch the genotype frequencies p², 2pq, and q² fall out of the square. Break one condition at a time — add selection, shrink the population, bias the mating — and see the frequencies walk away from the equilibrium prediction, which is exactly the signal that a population is evolving.
Hardy-Weinberg · Open the full sandbox →The five conditions are where the misreadings cluster, and they are not an arbitrary checklist: each one switches off one specific evolutionary force. No mutation keeps new alleles from appearing, no gene flow keeps alleles from migrating in or out, no natural selection keeps every genotype reproducing equally, random mating keeps genotypes from pairing off non-randomly, and a large population keeps genetic drift from swinging frequencies by chance. Students treat the conditions as five hoops to memorize rather than five forces held at zero (U7-BIO10). And when they run the math they slip between the layers — reading a dominant allele as the common one, or squaring a phenotype rather than an allele frequency (U7-BIO11). Every scenario in this topic asks you to keep p + q = 1 and p² + 2pq + q² = 1 straight, and to treat each condition as a force you have deliberately turned off.
The work
3 ways in · any order
Lesson
Hardy-Weinberg Equilibrium
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Hardy-Weinberg is the null model: allele frequencies obey p + q = 1, genotype frequencies obey p² + 2pq + q² = 1, and the five conditions each hold one evolutionary force at zero. The lesson walks the ways students misread that — squaring a phenotype instead of an allele frequency, assuming a dominant allele must be the common one, and treating the five conditions as an arbitrary checklist rather than five forces switched off. It closes with a ten-scenario applet that asks you to keep the allele and genotype layers straight and to read every deviation as evolution at work.
Diagnostic
10-item topic check
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Ten items on the Hardy-Weinberg model — that the five conditions are not an arbitrary checklist but five evolutionary forces (mutation, gene flow, selection, non-random mating, drift) each held at zero (U7-BIO10); and that allele frequencies (p + q = 1) and genotype frequencies (p² + 2pq + q² = 1) are separate layers, so a dominant allele is not automatically the common one and you square an allele frequency, not a phenotype (U7-BIO11). Take it cold to surface which of these are still tangled, or after the lesson to confirm they hold.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears the misconception and moves you to the next.