Phylogenetic Distance Calculator
Calculate Jukes-Cantor, Kimura 2-parameter, and other evolutionary distances.
Why Observed Differences Understate Divergence
Counting differing sites underestimates the substitutions that actually occurred, because a site can change more than once. A second change may revert the site or produce a different base, but either way only one difference is counted.
| Observed p | JC distance d | Underestimate |
|---|---|---|
| 0.05 | 0.052 | 4% |
| 0.15 | 0.167 | 11% |
| 0.25 | 0.304 | 22% |
| 0.50 | 0.824 | 65% |
| 0.75 | undefined | Saturation limit |
At p = 0.75 the sequences are statistically indistinguishable from random, since four bases chosen at random match a quarter of the time. The correction becomes unreliable well before that, typically above p ≈ 0.5.
Why K2P Usually Fits Better
Jukes–Cantor assumes all substitution types are equally likely. In reality transitions outnumber transversions roughly two to one, because purine-to-purine and pyrimidine-to-pyrimidine changes are chemically easier and often synonymous in the third codon position.
| Model | Assumes | Parameters |
|---|---|---|
| Jukes–Cantor | All substitutions equal, equal base frequencies | 1 |
| Kimura 2-parameter | Transitions ≠ transversions | 2 |
| HKY85 | Plus unequal base frequencies | 5 |
| GTR | All six substitution types differ | 9 |
More parameters fit better but need more data to estimate reliably. Model selection tools such as jModelTest use information criteria to balance fit against overparameterisation, rather than simply choosing the most complex option.
Rate Heterogeneity Across Sites
All these models assume every site evolves at the same rate, which is badly false. Third codon positions change freely while first and second are constrained, and structural or catalytic residues barely change at all.
Adding a gamma distribution of rates across sites usually improves fit more than any additional substitution parameter, which is why models are commonly written as GTR+Γ rather than GTR alone.
Worked Examples
Common Mistakes
Multiple substitutions at one site are invisible. The underestimate is 22% at p = 0.25 and 65% at p = 0.50.
Transitions typically outnumber transversions twofold. K2P separates them and generally fits real sequence data better.
More parameters need more data. Model selection should balance fit against overparameterisation using information criteria.
Third codon positions evolve far faster than first and second. Adding a gamma distribution usually improves fit more than extra substitution parameters.