Genetics: Punnett squares and Hardy–Weinberg

Punnett square — write each parent as allele pairs: Aa, AaBb, AaBbCc. Upper case is dominant. Genes are assumed to assort independently (unlinked). Choose complete dominance, incomplete dominance (the heterozygote is intermediate), or codominance (both expressed) per gene. Ratios are reduced to whole numbers — the dihybrid AaBb × AaBb gives the classic 9 : 3 : 3 : 1.

X-linked — write the mother as XAXa and the father as XAY or XaY. Sons inherit their X from their mother.

Hardy–Weinberg — from genotype counts, p = (2·AA + Aa)/2N; expected counts are p²N, 2pqN, q²N, and χ² = Σ(O − E)²/E with 1 degree of freedom (3 classes − 1 − 1 estimated parameter). From a recessive disease incidence, q = √incidence and the carrier frequency is 2pq.

Pedigree risk — for an autosomal recessive trait, each parent passes the allele with probability P(carrier) × ½; an unaffected sibling of an affected person has a 2/3 carrier probability.

Map distance — Haldane d = −½ ln(1 − 2r) (no interference) and Kosambi d = ¼ ln1 + 2r)/(1 − 2r, in centimorgans.