Population Genetics and Risk Calculation
Core concepts
Understand Hardy-Weinberg equilibrium: p + q = 1 and p^2 + 2pq + q^2 = 1, where p and q are allele frequencies. Know how to calculate carrier frequency from disease incidence for autosomal recessive conditions (carrier frequency ~2 x sqrt(incidence)). Understand the effect of consanguinity, founder effects, genetic drift, and selection on allele frequencies.
Be able to apply Bayesian analysis to carrier risk after a negative test, incorporating prior probability and test sensitivity. Know the recurrence risks for autosomal dominant (50%), autosomal recessive (25% affected, 50% carrier), X-linked (affected males from carrier mothers; 50% of sons affected), and mitochondrial inheritance (variable, maternal).
Traps
Examiners test the difference between allele frequency and genotype frequency, and the assumption of Hardy-Weinberg (large population, random mating, no selection/mutation/migration). A common trap is forgetting to multiply by 2 for the carrier frequency (2pq). Another is misapplying recurrence risk when the genotype of a parent is unknown; use Bayes to update.
Rule of thumb
For a rare autosomal recessive disease with incidence 1/N, q ~ sqrt(1/N) and carrier frequency ~ 2/sqrt(N). For a 1/10,000 incidence, q = 1/100 and carrier frequency ~ 1/50.
Worked example
Incidence 1/40,000: q = 1/200, p ~ 1, carrier frequency = 2pq ~ 1/100. If a sibling of an affected child tests negative with 90% sensitivity, the residual carrier risk is the prior (2/3) times the false-negative rate (0.10) divided by the total probability of a negative test, illustrating Bayesian updating.