A recessive deleterious allele has mutation rate μ = 10⁻⁵ and selection coefficient s = 0.01. What is the approximate equilibrium frequency of this allele?
A10⁻⁵ — the equilibrium frequency equals the mutation rate
B0.032 — approximately √(μ/s) = √(10⁻³) ≈ 0.032
C10⁻³ — the equilibrium frequency is μ/s for recessive alleles
D0.1 — the allele frequency is dominated by drift in most populations
For a recessive deleterious allele, q̂ ≈ √(μ/s) = √(10⁻⁵/0.01) = √(10⁻³) ≈ 0.032. The square root formula applies to recessives because heterozygotes are nearly unaffected; selection acts mainly on rare homozygotes, making removal inefficient. Option C (μ/s) is the formula for dominant deleterious alleles. Option A (μ alone) ignores the role of selection entirely.
Question 2 Multiple Choice
In a large population, researchers measure a recessive deleterious allele at carrier frequency 1 in 25 — far higher than the ~1 in 1,000 predicted by mutation-selection balance. What is the most parsimonious explanation?
AThe population is too small for selection to act effectively, so drift has inflated the allele
BThe mutation rate for this allele is unusually high, approximately 10⁻³
CAn additional evolutionary force such as heterozygote advantage is maintaining the allele above the mutation-selection equilibrium
DThe selection coefficient has been overestimated; the allele is actually nearly neutral
Deviations from predicted q̂ are diagnostically valuable: they signal that factors beyond simple mutation-selection balance are operating. A 40-fold excess (1/25 vs 1/1000) is hard to explain by uncertainty in μ or s alone. Heterozygote advantage (heterozygotes have higher fitness than either homozygote) can stably maintain alleles well above mutation-selection equilibrium — this is the leading explanation for cystic fibrosis allele frequencies in European populations. Option A (drift) is plausible only in small populations; option B would require a mutation rate ~1,000× typical.
Question 3 True / False
Strong natural selection against a deleterious allele will eventually eliminate it mostly from a large population.
TTrue
FFalse
Answer: False
This is the core misconception mutation-selection balance corrects. Even with selection coefficient s = 1 (lethal), mutation constantly reintroduces the allele at rate μ each generation. The equilibrium frequency q̂ ≈ √(μ/s) for recessives is never zero as long as μ > 0. Selection cannot drain a pool that is continuously refilled. The equilibrium exists precisely because removal (by selection) and introduction (by mutation) balance — stronger selection lowers the equilibrium frequency but never reaches zero.
Question 4 True / False
At mutation-selection balance, the rate at which selection removes deleterious alleles from the population equals the rate at which new mutations introduce them.
TTrue
FFalse
Answer: True
This is the definition of the equilibrium. The 'balance' in mutation-selection balance is a dynamic steady state: every generation, selection removes a fraction s·q² (approximately) of the allele copies (for a recessive), and mutation introduces approximately μ new copies. When these rates are equal, q stops changing. This is analogous to a chemical equilibrium — not static, but a balance of opposing fluxes. The equilibrium frequency formulas are derived by setting Δq(selection) = −Δq(mutation) and solving for q.
Question 5 Short Answer
Why can't natural selection eliminate a deleterious allele entirely from a population, even if selection against it is very strong?
Think about your answer, then reveal below.
Model answer: Because mutation continuously reintroduces the allele. Each generation, a small fraction μ of the relevant alleles mutates from the wild-type to the deleterious form. No matter how efficiently selection removes existing copies, it cannot prevent new ones from arising by mutation. The equilibrium is reached when the rate of introduction (μ per allele per generation) exactly balances the rate of removal (a function of s and the current allele frequency). As long as μ > 0, the equilibrium frequency is positive — selection can lower the frequency but not reach zero.
This insight also predicts that genetic diseases with high mutation rates will be more prevalent than those with low mutation rates, even when selection against them is equally strong. It explains why eliminating genetic diseases by selective pressure alone is futile — the mutation process acts as a constant source. It also explains why the equilibrium formula q̂ ≈ √(μ/s) improves as s increases (stronger selection means lower equilibrium) but never reaches q̂ = 0.