Hardy-Weinberg equilibrium

**Equations** - Allele frequencies: p + q = 1 (p = dominant allele, q = recessive allele). - Genotype frequencies: p² (homozygous dominant) + 2pq (heterozygous) + q² (homozygous recessive) = 1.

**Assumptions (all must hold)** 1. No new mutations. 2. No natural selection. 3. Random mating (no assortative mating or inbreeding). 4. No gene flow (no migration). 5. Very large population (no genetic drift). Violations: selection, mutation, nonrandom mating, migration, and small population size (drift, founder effect, bottleneck) shift allele frequencies. Inbreeding and assortative mating change genotype frequencies (more homozygotes) but not allele frequencies by themselves.

**Autosomal recessive disease (classic USMLE calculation)** - Disease incidence = q², so q = √incidence. - p = 1 − q. - Carrier frequency = 2pq. When q is small, p ≈ 1, so 2pq ≈ 2q. - Example: cystic fibrosis incidence is 1/2500. q² = 1/2500, q = 1/50 (0.02), p = 0.98, carrier frequency = 2(0.98)(0.02) ≈ 1/25 (about 4%). - Carriers greatly outnumber affected individuals. Most mutant alleles are "hidden" in heterozygotes.

**Autosomal dominant disease** - Affected frequency = p² + 2pq. Often approximated as 2pq when the disease is rare. - Use q² for the unaffected, then work backward to find q and p.

**X-linked recessive disease** - In males, disease incidence = q (males have one X). - In females, disease incidence = q², and carrier frequency = 2pq. - Example: if 1/100 males are affected, q = 0.01, so about 1/10,000 females are affected and about 2% are carriers.

**Clinical and exam pearls** - Pitfall: the question may give carrier frequency or allele frequency instead of disease incidence. Identify what the given number represents (q², q, 2pq) before calculating. - Heterozygote advantage maintains deleterious alleles (sickle cell trait protects against malaria; CF carriers may have protection against cholera or typhoid). - Founder effect and genetic drift explain a high allele frequency in isolated groups (e.g., Tay-Sachs in Ashkenazi Jews, Amish populations). - Use the equation only if the population is at equilibrium. Questions often state this explicitly ("assume the population is in Hardy-Weinberg equilibrium"). - Equilibrium is reached after one generation of random mating. - Applications include estimating carrier risk for genetic counseling and detecting evolutionary forces acting on a population. A deviation from expected genotype frequencies (for example, an excess of homozygotes) suggests inbreeding or selection. In genetic association studies, it is also used as a quality-control check for genotyping errors.