Calculator Form
Example Data Table
| Scenario | μ | ν | s | h | q0 | Approximate q̂ |
|---|---|---|---|---|---|---|
| Recessive deleterious allele | 0.00001 | 0 | 0.10 | 0 | 0.01 | 0.01 |
| Partial dominance case | 0.00001 | 0 | 0.20 | 0.50 | 0.01 | 0.0001 |
| Dominant deleterious allele | 0.00001 | 0 | 0.10 | 1 | 0.01 | 0.0001 |
Formula Used
The calculator tracks a deleterious allele with mutant frequency q and normal allele frequency p = 1 − q.
Genotype fitness values are AA = 1, Aa = 1 − hs, and aa = 1 − s.
Mean fitness is W̄ = p² + 2pq(1 − hs) + q²(1 − s).
After selection, the mutant allele becomes q′ = [pq(1 − hs) + q²(1 − s)] / W̄.
After forward and back mutation, the next generation is q(next) = q′(1 − ν) + (1 − q′)μ.
For standard approximations without back mutation, a fully recessive deleterious allele uses q̂ ≈ √(μ/s), while dominant or partially dominant selection uses q̂ ≈ μ/(hs).
Carrier frequency is 2pq. Affected homozygote frequency is q². Mutation load is L = 1 − W̄.
How to Use This Calculator
Enter the forward mutation rate μ for the harmful allele. Add a back mutation rate ν only if you want reversions included.
Set the selection coefficient s to describe fitness reduction in aa individuals. Use h to describe how strongly heterozygotes are selected.
Choose the starting allele frequency q0, the number of generations to simulate, and a population size for expected counts.
Press the calculate button. The result block appears below the header and above the form. Review the summary, graph, and generation table.
Use the CSV button to save the summary and trajectory rows. Use the PDF button to save a compact report.
Mutation Selection Balance in Population Genetics
Mutation-selection balance describes a stable compromise between two opposing evolutionary forces. Mutation introduces new deleterious alleles into a population. Selection removes those alleles because they reduce fitness. When both pressures offset one another, the harmful allele settles near an equilibrium frequency.
This balance depends on three main inputs. The first is mutation rate. Higher mutation rates keep feeding the deleterious allele into the population. The second is selection strength. Stronger selection removes the allele more efficiently. The third is dominance. If the deleterious effect is recessive, heterozygotes hide the allele from strong selection, so it can persist longer.
That is why recessive cases often use the square-root approximation q̂ ≈ √(μ/s). In contrast, dominant or partially dominant alleles are exposed to selection even in heterozygotes, so equilibrium is usually much lower and follows q̂ ≈ μ/(hs) when the allele remains rare.
This calculator also simulates the full generation-by-generation recurrence. That matters because real parameter choices may include back mutation, partial dominance, or starting frequencies far from equilibrium. The numeric path shows how quickly the system stabilizes and how carrier burden changes over time.
The summary table reports equilibrium allele frequency, carrier rate, expected affected individuals, mean fitness, and mutation load. These outputs can support genetics teaching, mathematical biology exercises, and quick scenario testing when comparing assumptions.
FAQs
1. What is mutation-selection balance?
Mutation-selection balance is the point where new deleterious alleles enter through mutation as quickly as selection removes them. The equilibrium depends mainly on mutation rate, selection strength, and dominance.
2. Why does the recessive case use a square root?
For a fully recessive harmful allele, selection only acts strongly on homozygotes. That makes the equilibrium depend on a square root, giving q ≈ √(μ/s) under standard assumptions.
3. What does the dominance coefficient h mean?
The dominance coefficient h measures how much selection acts on heterozygotes. Zero means recessive, one means dominant, and intermediate values represent partial dominance.
4. What happens when selection is weak?
When selection is weak, harmful alleles can persist at higher frequencies. Small s values usually increase equilibrium q, carrier frequency, and expected mutation load.
5. Why include back mutation?
Back mutation lets the deleterious allele revert to the original allele. It is often tiny, but including it gives a more flexible recurrence model.
6. Does this model include genetic drift?
No. This page uses deterministic allele-frequency recursion, not random genetic drift. It works best for large populations where chance fluctuations are comparatively small.
7. What is mutation load?
Mutation load is the reduction in mean fitness caused by deleterious alleles. Here it is reported as L = 1 − W̄ using the selected equilibrium frequency.
8. Does starting frequency change the final answer?
Initial frequency changes the short-run trajectory, but a stable system usually converges toward the same equilibrium. The number of generations needed depends on the starting point and parameters.