For a recessive deleterious allele with selection coefficient s against aa and mutation rate μ, the approximate equilibrium allele frequency q is:

• A. μ/s
• B. sqrt(s/μ)
• C. sqrt(μ/s)
• D. μ^2 / s

Answer: (C)

Mutation–selection balance for a recessive deleterious allele works by balancing new mutations against selection removing the deleterious homozygotes. When the allele is rare, most copies reside in heterozygotes that aren’t affected by selection, so the strength of selection against the allele is governed by the frequency of homozygotes, which is q^2. The input of new deleterious alleles per generation is μ. At equilibrium, the mutation inflow roughly equals the selective removal: μ ≈ s q^2. Solving for q gives q ≈ sqrt(μ/s). This is the reason the correct result is the square root form. This approximation assumes μ is small and the allele is indeed rare, so q is much less than 1.