Molecular Clock Calculator

Calculate divergence time between species from molecular data and substitution rates.

Number of nucleotide differences

Sequence length (bp) (bp)

Substitution rate (substitutions/site/year) (sub/site/yr)

mtDNA: 2.3×10⁻⁸, Nuclear: 10⁻⁹

Calibration point (Mya) if known (Mya)

0 = use rate directly

Please check your inputs and try again.

Why Raw Divergence Needs Correcting

Counting observed differences underestimates true divergence, because a site that has changed twice may look unchanged, and a site that changed to a different base still counts as one difference. Multiple hits hide substitutions.

Jukes–Cantor: K = −¾ ln(1 − ⅔p) T = K / 2r

Observed p	Corrected K	Underestimate
0.05	0.0517	3%
0.10	0.1073	7%
0.25	0.3041	22%
0.50	0.8240	65%

The correction is negligible for closely related sequences and enormous for distant ones. Beyond about 0.5 observed divergence the correction becomes unreliable and eventually undefined — at p = 0.75 the sequences are indistinguishable from random.

Jukes–Cantor assumes all substitutions are equally likely, which is false. Transitions outnumber transversions roughly twofold, so Kimura's two-parameter model, which separates them, generally fits real data better.

Why Divide by Two

Divergence accumulates along both lineages since their common ancestor. Two species that split 10 million years ago have each been changing for 10 million years, so the total path is 20 million years of evolution. Omitting the factor of two doubles every date.

Choosing a Rate

Sequence	Approximate rate (per site per year)	Suitable for
Mitochondrial D-loop	10⁻⁷	Within-species, recent
Mitochondrial coding	2–3 × 10⁻⁸	Recent divergences
Nuclear synonymous	~5 × 10⁻⁹	Species-level
Nuclear non-synonymous	~1 × 10⁻⁹	Deep divergences

Mitochondrial DNA evolves roughly an order of magnitude faster than nuclear, which is why it suits recent divergences but saturates quickly for deep ones. Matching the rate to the timescale is the single most important choice in the calculation.

Rates are also lineage-specific — generation time and metabolic rate both affect them — so modern studies use relaxed clock models with fossil calibration rather than a single global rate.

Worked Examples

Example 1: Mitochondrial DNA: 30 diff in 1000bp, rate=2.3e-8

K=0.0306, T=K/(2×2.3e-8)

Result: T=0.665 Mya = 665,000 years divergence

Human-Neanderthal mtDNA divergence ~500-700 kya

Example 2: Nuclear gene: 30 diff/1000bp, rate=1e-9

Same K, slower rate

Result: T=15.3 Mya

Much more ancient divergence with slower nuclear rate

Example 3: When correction matters most

Observed divergence 0.25 versus 0.05

Result: 22% versus 3% underestimate

At low divergence the correction is negligible. At high divergence, ignoring it substantially understates the true number of substitutions.

Example 4: Why mitochondrial DNA saturates

p approaching 0.5 in mtDNA

Result: Correction becomes unreliable

Fast-evolving sequence reaches saturation quickly. Beyond about 0.5 observed divergence, dates from mtDNA should not be trusted.

Common Mistakes

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Skipping the multiple-hit correction

Observed divergence underestimates true divergence, by 22% at p = 0.25 and 65% at p = 0.50. Jukes–Cantor or a richer model is essential.

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Forgetting to divide by two

Divergence accumulates along both lineages. Using T = K/r rather than K/2r doubles every estimated date.

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Using a mitochondrial rate for deep divergences

Mitochondrial DNA saturates quickly. Beyond a few million years nuclear sequences give more reliable estimates.

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Applying one global rate across lineages

Generation time and metabolic rate cause substantial variation. Relaxed clock models with fossil calibration are the current standard.

Frequently Asked Questions

Why divide by 2?

Both lineages accumulate substitutions since divergence. 20 differences = 10 accumulated in each lineage. T = K/(2r) accounts for this. Factor of 2 is for divergence time from common ancestor.

Molecular clock controversies?

Rate heterogeneity between lineages (generation time effect, metabolic rate). Rate variation between loci (neutral vs selected). Calibration points from fossils are uncertain. Relaxed clock models allow rate variation. BEAST, PAML, MrBayes implement sophisticated models.

Why correct observed divergence?

Because multiple substitutions at the same site hide one another. Observed differences underestimate true divergence, severely for distant sequences.

Why divide by two?

Because both lineages have accumulated substitutions since they diverged, so the total evolutionary path is twice the divergence time.

Which substitution rate should I use?

Match it to the timescale. Mitochondrial rates suit recent divergences; nuclear synonymous sites suit species-level and deeper comparisons.

Why is Kimura's model preferred over Jukes–Cantor?

Because transitions occur roughly twice as often as transversions. Kimura's two-parameter model accounts for that bias and fits real data better.