Hardy-Weinberg: p + q = 1, where p = freq(A) = 0.1, q = freq(a) = 0.9
Frequency of AA = p² = (0.1)² = 0.01
Aa = 2pq = 2(0.1)(0.9) = 0.18 | aa = q² = (0.9)² = 0.81
Answer: 0.01
Cornerstone of population genetics: allele and genotype frequencies remain stable in large, non-evolving populations. Mathematical statement: (p+q)² = p²+2pq+q² = 1 where p=freq(A), q=freq(a). This means nature alone (simple Mendelian inheritance) does not change allele frequencies — evolutionary forces are needed.
Useful for genetic counselling. Example: albinism (aa) frequency = 1/10,000 = 0.0001 = q². Therefore q = 0.01, p = 0.99. Carrier (Aa) frequency = 2pq = 2(0.99)(0.01) = 0.0198 ≈ 1/50. So approximately 1 in 50 people are carriers even when only 1 in 10,000 show the condition.
Detecting evolution: compare observed vs H-W expected genotype frequencies. Deviations indicate: selection (non-random survival/reproduction), mutation (new alleles appearing), genetic drift (random frequency changes in small populations), gene flow (migration adding/removing alleles), non-random mating (assortative mating, inbreeding).
Natural selection: differential survival/reproduction based on genotype. Genetic drift: random sampling error more significant in small populations — can fix or eliminate alleles. Bottleneck effect: population crash → loss of genetic diversity. Founder effect: small founding population → allele frequencies differ from source. Gene flow: migration introduces new alleles or changes existing frequencies.
Allele frequencies stay constant only if the population is large, mating is random, and there is no mutation, no gene flow (migration) and no natural selection. Real populations violate at least one of these, which is precisely why evolution happens. The principle is therefore a null model: any measured departure from $p^2 + 2pq + q^2 = 1$ is evidence that one of the five factors is operating.
In a small population, allele frequencies can change by chance alone rather than by selection — this is genetic drift, and its effect is stronger the smaller the population. The founder effect occurs when a few individuals start a new colony and carry an unrepresentative sample of the original gene pool. A bottleneck has the same result through a sudden population crash. Both explain why small isolated populations often show unusual allele frequencies and reduced variation.
Stabilising selection favours the average and reduces variation, as with human birth weight. Directional selection favours one extreme and shifts the mean, as with peppered moths during industrialisation. Disruptive selection favours both extremes over the mean and can eventually split one population into two. Graph questions on this topic are asking you to identify which of these three the curve shows.
Forgetting to square-root q². The observed recessive phenotype frequency is q², not q. Skipping the square root is the single commonest error here.
Thinking Hardy-Weinberg describes evolution. It describes a population that is NOT evolving. Departure from it is what signals evolution.