Mutation–Selection Balance for a Recessive Allele

For a rare allele q, the frequency of recessive homozygotes is approximately q². Selection removes roughly s·q² alleles per generation, while mutation introduces variants at rate μ. At equilibrium, μ≈s·q², giving q̂≈√(μ/s). The square root appears because the allele is selected mainly when homozygous in this recessive model. This is an approximation for small q and μ, not a universal population prediction. μ and s must refer to the same generation and fitness definition. Equilibrium and complete recessivity require separate checks in observed data. Slow environmental change can further shift an apparent equilibrium.

Only if the allele is fully recessive and genotype frequencies approximately follow Hardy–Weinberg is the frequency of affected homozygotes q̂². With μ=10⁻⁶ and s=0.01, q̂≈0.01 and q̂²≈0.0001, or 0.01%. This is not a direct prevalence estimate: diagnosis, penetrance, genetic heterogeneity, population structure and carrier fitness can change observed frequency. Allele frequency and disease rate must not be confused. μ and s must refer to the same generation and fitness definition. Equilibrium and complete recessivity require separate checks in observed data. Slow environmental change can further shift an apparent equilibrium.

It assumes complete recessivity, constant mutation and selection rates, a large deterministic population, random mating and a simple diploid one-locus system. With incomplete dominance, heterozygotes are selected and equilibrium depends differently on μ and s. Drift matters at small effective population size; migration, multiple mutation pathways and changing environments also move populations away from equilibrium. Use the equation as a transparent baseline model, not as a clinical or population prediction without checking assumptions. μ and s must refer to the same generation and fitness definition. Equilibrium and complete recessivity require separate checks in observed data. Slow environmental change can further shift an apparent equilibrium.

Reproduce the example calculation: For mu=10⁻⁶ per generation and s=0.01, qhat≈sqrt(10⁻⁶/10⁻²)=sqrt(10⁻⁴)=0.01. Mutation–Selection Balance for a Recessive Allele uses q̂ ≈ √(μ/s). In plain terms, for a rare, fully recessive deleterious allele, a simple model balances mutation input against loss through selection. Unit check: q, mutation rate mu per allele per generation, and selection coefficient s are dimensionless. Approximation for a rare, fully recessive deleterious allele, low forward mutation, random mating and a large deterministic population. Values are comparable only when their definitions, denominators and periods match. Record these details next to the result so the reference group is clear. If the direction is implausible, check data preparation and the calculation basis before discussing biological causes.

A key limit of Mutation–Selection Balance for a Recessive Allele is this: Approximation for a rare, fully recessive deleterious allele, low forward mutation, random mating and a large deterministic population. Do not use the metric without its reference; it is useful for Interpreting idealized equilibrium frequencies of rare recessive variants in evolutionary and population genetics. For a rare, fully recessive deleterious allele, a simple model balances mutation input against loss through selection. When comparing populations or experiments, check whether definitions, denominators and observation periods match. If the assumption is implausible, the result shows only what the simplified model calculates from its inputs; it is not a reliable estimate for the target population. State this limitation in the report, and do not infer a causal effect from the formula alone.