Population Genetics

Hardy-Weinberg Equilibrium

• A non-evolving population obeys $p + q = 1 \qquad p^2 + 2pq + q^2 = 1$ where $p^2$ is homozygous dominant, $2pq$ heterozygous carriers, and $q^2$ homozygous recessive.
• Five required conditions: no mutation, no migration, no selection, large population (no drift), and random mating. Violate any one and the population is evolving.

The Standard Calculation

• Start from the affected (recessive) frequency: it equals $q^2$. Take the square root for $q$, then $p = 1 - q$, then compute carriers as $2pq$.
• Cystic fibrosis example: $q^2 = 1/2500$ gives $q = 0.02$, $p = 0.98$, and carrier frequency $2pq \approx 0.04$ — about 1 in 25, roughly 100 times more common than the disease. Rare recessive alleles hide mostly in heterozygotes.
• X-linked recessive traits: affected males occur at frequency $q$ (hemizygous), affected females at $q^2$, explaining the male excess.

When Equilibrium Breaks

• Genetic drift dominates small populations: allele frequencies swing randomly regardless of fitness. Migration (gene flow) homogenizes populations; nonrandom mating shifts genotype frequencies; selection changes allele frequencies directionally.

Key Takeaways

• Always enter the math through $q^2$, the observable recessive phenotype.
• Carriers vastly outnumber affected individuals for rare alleles.
• Males show X-linked recessive traits at frequency $q$, not $q^2$.
• Small population plus shifting frequencies with constant selection points to drift.