Core concept1 exam ›
```
p + q = 1
p^2 + 2pq + q^2 = 1
```
- p = normal allele frequency, q = mutant allele frequency
- q^2 = disease incidence (AR homozygotes)
- 2pq = carrier frequency ~ 2q when the disease is rare (p ~ 1)
The one-line method
- Disease incidence 1 in N -> q = 1/sqrt(N) -> carrier frequency ~ 2/sqrt(N)
- CF 1 in 2500 -> q = 1/50 -> carrier ~1 in 25
- PKU 1 in 10,000 -> q = 1/100 -> carrier ~1 in 50
- Note the carrier frequency is always far higher than intuition suggests
Key detail
Assumptions (violation = the exam's second question)
- Large population, random mating (violated by consanguinity, which inc homozygotes)
- No migration, no new mutation, no selection
- Violated in practice by founder effects and genetic drift - which is why ethnicity-specific carrier frequencies are used
- Tay-Sachs ~1/30 Ashkenazi Jewish; sickle trait up to 1/4 in parts of West Africa (heterozygote advantage against falciparum malaria)
- Alpha- and beta-thalassaemia in Mediterranean, SE Asian, Middle Eastern populations
Worked risks
- Affected (q/q) x unaffected general-population partner
- risk child affected = P(partner is a carrier) x 1/2
- CF: 1/25 x 1/2 = 1 in 50
- Two unaffected general-population partners
- 2q x 2q x 1/4
- CF: 1/25 x 1/25 x 1/4 = 1 in 2500 (returns you to the population incidence - the consistency check)
- Unaffected sib of an affected child x general-population partner
- 2/3 (Bayesian: AA excluded) x 1/25 x 1/4 = 1 in 150
- X-linked: disease frequency in males = q; female carrier frequency ~2q; so q is read straight off the male incidence (G6PD, haemophilia)
Clinical relevance
- Reproductive carrier screening in Australia is Medicare-funded for CF, SMA and fragile X for couples planning or in early pregnancy; expanded panels are available privately
- Partner testing after a positive carrier result is what converts an individual result into a couple risk
- A negative carrier test reduces but does not abolish risk - residual risk depends on panel detection rate; it must be quoted
- Consanguinity counselling: first cousins share 1/8 of genes -> absolute risk of a serious birth defect ~5-6% vs ~3% background
- If the partner is from the same founder population, use the population-specific carrier frequency, not the general one
Correlations
- Pedigree analysis; Punnett square recurrence risk
- Autosomal recessive inheritance with incomplete penetrance
- Cystic fibrosis, thalassaemia, sickle cell disease
- Complex/polygenic disease genetics
4 of 4 sections written · drafted 2026-09-04