Neutral Evolution Rate Calculator

Calculate neutral substitution rate, synonymous site divergence, and test neutral theory.

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The Molecular Clock and Why Divergence Is Doubled

Kimura's neutral theory holds that most substitutions that fix are selectively neutral, so they accumulate at the underlying mutation rate. That gives a clock — but the divergence between two sequences counts changes along both lineages since their common ancestor.

r = K / (2T)

The factor of two is the commonest error in the calculation. Two species that split 10 million years ago have each accumulated substitutions for 10 million years, so the total path length is 20 million years of evolution.

Sequence classApproximate rate (per site per year)
Synonymous sites≈ 5 × 10−9 — near neutral
Pseudogenes≈ 5 × 10−9
Non-synonymous sites≈ 1 × 10−9 — constrained
Histone genes< 10−10 — extremely conserved

The spread across that table is the evidence for the theory. Sites where changes have no phenotypic consequence evolve fastest; sites under functional constraint evolve slowest. Rate variation between classes reflects selection, not mutation.

Why the Clock Is Not Strictly Constant

FactorEffect on rate
Generation timeShorter generations, faster clock per year
Metabolic rateHigher rate, more oxidative damage
DNA repair efficiencyVaries between lineages
Effective population sizeAffects fixation of nearly neutral variants

The generation time effect is substantial: rodents accumulate substitutions per year several times faster than primates, because replication errors arise per generation rather than per year. This is why modern dating uses relaxed clock models that allow rates to vary across a phylogeny rather than assuming one global rate.

Saturation limits the method at long timescales. Once multiple substitutions have occurred at the same site, observed divergence underestimates true divergence, and correction models such as Jukes–Cantor or Kimura two-parameter become necessary.

Worked Examples

Example 1: Mammalian genes: Ks=0.15, T=10Mya
r=0.15/20=0.0075 sub/site/Mya
Result: 7.5×10⁻⁹/site/yr — typical mammalian rate
~1 neutral sub/150 sites/10Mya
Example 2: Ka=0.02, Ks=0.15: Ka/Ks=0.133
Strong purifying selection
Result: Most genes: Ka/Ks<<1 (conserved)
Average mammalian protein: Ka/Ks ~0.15
Example 3: Why rodents evolve faster per year
Mouse and human lineages compared
Result: Rodent rate several-fold higher
Substitutions arise per replication, and shorter generations mean more replications per year. Per-generation rates are far more similar than per-year rates.
Example 4: Saturation at deep divergence
Two sequences 500 million years apart
Result: Observed divergence underestimates true
Multiple substitutions have occurred at many sites, some reverting. Correction models estimate the hidden changes but reliability degrades with depth.

Common Mistakes

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Forgetting to divide by 2T

Divergence accumulates along both lineages since the common ancestor. Using T rather than 2T doubles the calculated rate.

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Assuming one clock rate across all lineages

Generation time and metabolic rate differ substantially. Rodents evolve several times faster per year than primates.

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Ignoring saturation in deep comparisons

Multiple hits at the same site cause observed divergence to underestimate true divergence. Jukes–Cantor or similar correction is needed.

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Using non-synonymous sites for clock calibration

They are under selection and evolve more slowly and less regularly. Synonymous sites and pseudogenes approximate neutrality far better.

Frequently Asked Questions

Kimura's neutral theory?
Most nucleotide substitutions are selectively neutral, fixed by genetic drift. Rate of neutral substitution = mutation rate (independent of Ne). Provides molecular clock. Prediction: synonymous > nonsynonymous rates (confirms neutral evolution predominates).
Neutral substitution rate constancy?
Rate varies by: DNA repair efficiency, generation time, metabolic rate. Rodents evolve 10× faster than primates per year (shorter generation). Per-generation rates more similar. This complicates molecular clock calibration across taxa with different life histories.
Why divide by 2T rather than T?
Because both lineages have been accumulating substitutions since they diverged. The total evolutionary path between them is twice the divergence time.
Why are synonymous sites used for clock calibration?
They change the DNA without changing the protein, so selection is largely blind to them and they accumulate at close to the neutral mutation rate.
Is the molecular clock constant?
Not strictly. Generation time, metabolic rate and repair efficiency all vary between lineages, which is why relaxed clock models are now standard.
What is substitution saturation?
Multiple changes at the same site over long timescales, so observed divergence underestimates the true number. Correction models partially compensate.