Selection Coefficient Calculator

Calculate the selection coefficient (s) and relative fitness of genotypes. Model how natural selection changes allele frequencies over generations in diploid populations.

🧬 Population Genetics📐 Δp = sp²q/(1-sq²) (against aa)🧬 Biology
Initial recessive allele frequency q
Selection coefficient s (against aa)
Number of generations t
Please enter valid values.

Formula & Reference

VariableSymbolFormulaUnits
Selection Coefficient Calculator—Δp = sp²q/(1-sq²) (against aa)per generation

Step-by-Step Examples

Example 1
Mild Selection

q=0.50, s=0.10, t=10 generations. Mildly disadvantageous recessive.

  • After 10 gen: q decreases from 0.50
  • Rate of decrease slows as q drops (recessives hidden in heterozygotes)
  • Significant time needed to eliminate recessive allele
✓ q drops noticeably in 10 generations under mild selection
Example 2
Strong Selection

Lethal recessive (s=1.0): aa dies. q0=0.5, t=10.

  • After 10 gen: q decreases substantially
  • But elimination of recessive allele is slow as it becomes rare (hidden in Aa heterozygotes)
  • q=0.5 to ~0.09 in 10 gen for s=1
✓ Even lethal recessives are eliminated slowly
Example 3
Sickle Cell Balanced Selection

In malaria regions: s(SS)=0.9 (sickle cell anemia), but HbS allele maintained by heterozygote advantage.

  • Balanced polymorphism: q_equilibrium = s1/(s1+s2)
  • Heterozygotes (Aa=HbAHbS) have highest fitness
  • Allele maintained at intermediate frequency
✓ Balanced polymorphism maintains both alleles

Real-World Applications

🦧
Conservation
Selection coefficients help predict if deleterious alleles will be purged in managed populations.
💊
Drug Resistance
Antibiotic resistance: s against drug-sensitive bacteria in presence of antibiotic drives rapid allele frequency change.
🧬
Evolutionary Genomics
Detect genes under selection by measuring allele frequency changes faster than neutral expectation.
🌿
Artificial Selection
Crop breeding: selection coefficient quantifies intensity of selection on desired traits.

Common Mistakes to Avoid

⚠️
Recessives respond slowly to selection

When q is small, most recessive alleles are hidden in Aa heterozygotes (unaffected by selection). Elimination is very slow at low frequencies.

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s=1 means lethal, s=0 means neutral

s ranges from 0 (no selection against genotype) to 1 (lethal, leaves no offspring). Intermediate s is partially deleterious.

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Selection favors dominant alleles faster

Dominant deleterious alleles are exposed to selection even in heterozygotes. Purged much faster than recessive deleterious alleles.

Frequently Asked Questions

What is the selection coefficient? ▾
s = 1 - (relative fitness of selected genotype). s=0: no selection. s=0.1: 10% fewer offspring than most fit. s=1: lethal. Measures intensity of selection against a genotype.
What is relative fitness? ▾
w = reproductive success relative to most fit genotype (w=1). If AA and Aa have w=1 and aa has w=0.9, then s=0.1 against aa.
Why do recessives persist despite selection? ▾
When rare, recessive alleles are mostly in heterozygotes (Aa), which are not selected against. Selection is very inefficient at eliminating rare recessives. Even at s=1: needs ~100 generations to go from q=0.1 to q=0.01.
What is heterozygote advantage? ▾
When Aa (heterozygote) has HIGHER fitness than both AA and aa. Maintains a stable polymorphism. Example: sickle cell trait protects against malaria.
What drives allele fixation vs polymorphism? ▾
Strong directional selection: one allele fixes. Heterozygote advantage: stable polymorphism. Frequency-dependent selection: polymorphism. Genetic drift: random fixation.

Related Biology Calculators

🧬 Hardy-Weinberg🧬 Genetic Drift🧬 Effective Pop Size🧬 Allele Frequency🧬 Fixation Index Fst