Mutation-Selection Balance Calculator
Calculate equilibrium allele frequency under mutation-selection balance.
Why Recessive and Dominant Differ So Much
At equilibrium, new mutations exactly replace those removed by selection. The equilibrium frequency depends critically on whether selection can see the allele in heterozygotes.
| Mode | Equilibrium frequency | Reason |
|---|---|---|
| Recessive (h = 0) | q = √(μ/s) | Hidden in heterozygotes |
| Dominant (h = 1) | q = μ/s | Exposed every generation |
| Partial (0 < h < 1) | q ≈ μ/(hs) | Partly exposed |
The square root makes an enormous difference. At μ = 10−5 and s = 1, a recessive allele sits at frequency 0.0032 while a dominant one sits at 10−5 — over three hundred times rarer. Recessive alleles hide from selection in heterozygotes, so far more copies persist.
Note how small a dominance coefficient is needed to change the picture. Even h = 0.02 makes the allele behave far more like a dominant, because selection acting on the many heterozygotes outweighs selection on the rare homozygotes.
Why Some Diseases Are Commoner Than Predicted
Cystic fibrosis carrier frequency in European populations is around 1 in 25, which is higher than mutation–selection balance alone predicts. Several explanations are proposed:
| Explanation | Mechanism |
|---|---|
| Heterozygote advantage | Proposed resistance to cholera or typhoid — debated |
| Founder effects | Ancestral population bottleneck |
| Genetic drift | Small historical population sizes |
| Relaxed selection | Modern medicine reduces s |
The heterozygote advantage hypothesis remains unproven for CF, though it is well established for sickle cell and malaria. Where it does operate, the equilibrium is set by balancing selection rather than mutation–selection balance, and frequencies can be far higher.
Genetic Load
The mutational load is the fitness reduction a population carries from deleterious alleles at equilibrium. A striking result is that load depends on mutation rate, not on selection coefficient — a strongly deleterious allele is rarer but each occurrence costs more, and the two effects cancel exactly.
Worked Examples
Common Mistakes
Recessives are hidden in heterozygotes, so equilibrium frequency is the square root of μ/s — far higher than the dominant expression gives.
Most so-called recessive alleles have small but non-zero dominance. Even h = 0.02 shifts behaviour substantially toward the dominant case.
Founder effects, drift and relaxed selection also raise frequencies. Heterozygote advantage is established for sickle cell but unproven for cystic fibrosis.
Mutational load depends on mutation rate, not selection coefficient. Stronger selection makes alleles rarer but each costs proportionally more.