Jukes-Cantor Model Calculators

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The Jukes-Cantor (JC69) model is the simplest model of DNA sequence evolution, proposed by Jukes and Cantor in 1969. It assumes that all four nucleotides (A, T, G, C) occur in equal frequencies, all substitution types occur at equal rates, and substitutions at different sites are independent. The JC correction converts observed proportion of differences (p-distance) to an estimate of the true evolutionary distance by correcting for multiple substitutions at the same site — a critical correction for divergent sequences. JC69 is foundational to phylogenetics despite its simplifying assumptions.

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Jukes-Cantor Formula

d_JC = −(3/4) × ln(1 − (4/3) × p)

p = observed proportion of different nucleotides (p-distance); d_JC = estimated evolutionary distance (substitutions per site). The correction is necessary because at high divergence, multiple substitutions at the same site cause p-distance to underestimate the true evolutionary distance.

Why Correction Is Needed

If a site mutates multiple times (A→G→A), only one change is visible from sequence comparison but two actually occurred. At high p-distances (> 0.20), the uncorrected p-distance substantially underestimates true divergence. The JC correction accounts for this by assuming substitutions follow a Poisson process with equal rates. As p approaches 0.75 (the maximum for 4 equally probable bases), d_JC approaches infinity.

Worked Example

Two DNA sequences differ at 15% of sites (p = 0.15): d_JC = −0.75 × ln(1 − (4/3 × 0.15)) = −0.75 × ln(1 − 0.20) = −0.75 × ln(0.80) = −0.75 × (−0.2231) = 0.1673 substitutions per site.

Limitations and More Complex Models

JC69 assumes: equal base frequencies; equal substitution rates; rate homogeneity across sites. Real DNA evolution violates all these. More realistic models: Kimura 2-parameter (K2P) — different rates for transitions vs. transversions; HKY85 — unequal base frequencies; GTR — all substitution rates free to vary; GTR+Γ — adds rate variation across sites. Despite its simplicity, JC69 is still used for rapid analysis and educational purposes.

Glossary

Jukes-Cantor (JC69) Model
The simplest DNA evolution model; assumes equal base frequencies and equal substitution rates; corrects p-distance for multiple hits: d_JC = −(3/4)ln(1 − 4p/3).
p-Distance
The observed proportion of different nucleotides between two aligned sequences; underestimates true evolutionary distance at high divergence due to multiple substitutions; corrected by models like JC69.
Transition/Transversion Ratio (Ts/Tv)
The ratio of transitions (purine↔purine or pyrimidine↔pyrimidine) to transversions (purine↔pyrimidine); typically 2–10× in real DNA; accounted for by the Kimura 2-parameter model but not JC69.

Frequently Asked Questions

The Jukes-Cantor correction estimates true evolutionary distance from observed sequence differences. Raw p-distance (proportion of differing sites) underestimates true divergence at higher values because multiple substitutions at the same site are invisible — a site can mutate back to its original state or change multiple times between two sequences. The JC formula d_JC = −(3/4) ln(1 − (4p/3)) corrects for this multiple-hit problem, giving a better estimate of the total substitutions per site that have actually occurred.

Step 1: Calculate p-distance (proportion of differing sites). Step 2: Apply JC formula: d_JC = −(3/4) × ln(1 − (4/3 × p)). Example: two 100 bp sequences differ at 20 sites: p = 20/100 = 0.20. d_JC = −0.75 × ln(1 − (4/3 × 0.20)) = −0.75 × ln(0.733) = −0.75 × (−0.311) = 0.233 substitutions/site. This is 0.233 vs. 0.20 raw — the correction adds ~17% to the estimate at this divergence level.

JC69 assumes all substitution types (transitions A↔G, C↔T; transversions A↔C, A↔T, etc.) occur at equal rates. In reality, transitions (purine-to-purine or pyrimidine-to-pyrimidine) occur 2–10× more frequently than transversions due to the chemistry of base changes. Kimura 2-parameter (K2P) model has two separate rate parameters: α for transitions and β for transversions. K2P is more accurate for most DNA sequence datasets. Both are much simpler than the General Time Reversible (GTR) model used in modern maximum likelihood phylogenetics.

The JC correction becomes unreliable as p approaches 0.75 (the theoretical maximum for 4 equally probable bases — at full randomness, 3/4 of sites differ). As p approaches 0.75, the term inside the logarithm approaches zero and d_JC approaches infinity. In practice, the JC correction is considered unreliable above p ≈ 0.50–0.60 because the model assumptions (equal base frequencies, equal rates) are increasingly violated at high divergence. For highly divergent sequences, more complex models (GTR+Γ) and profile-based methods are preferred.