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The Jukes–Cantor correction estimates substitutions per site from the observed fraction of differing bases and accounts for multiple changes at a site.
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Formula
p is the fraction of different homologous sites, 0≤p<0.75 · dJC is substitutions per site, dimensionless
| Symbol | Meaning | Unit |
|---|---|---|
| Model-corrected evolutionary distance per site | substitutions/site | |
| Observed fraction of unequal aligned homologous nucleotide positions | fraction from 0 to 1 |
d_{JC}=-\frac{3}{4}\ln\left(1-\frac{4p}{3}\right)JC69 assumes four equally frequent nucleotides and equal rates for every substitution type. It partially corrects for unobserved multiple substitutions; distance grows sharply as p approaches 0.75 and is undefined for p≥0.75. Gaps, poorly aligned regions and unequal base composition violate this simple model. dJC is a model-dependent expected number of substitutions per site, not an observed percent difference and not a time without a clock model.
Homologous bases are aligned reliably and JC69 equal-frequency and equal-rate assumptions are plausible.
The raw fraction of differing sites is corrected for hidden multiple changes under a symmetric substitution model.
Rearrange for observed distance
This gives expected p-distance under JC69 assumptions.
p=0.10. Calculate dJC to three places.
dJC=−0.75 ln(1−4·0.10/3)≈0.107 substitutions/site.
Reading dJC as an observed percentage or direct evolutionary time.
dJC is a model-based distance per site; time requires a mutation rate or clock assumption.
Formula cluster
the corrected distance exceeds p-distance because reversals can be hidden.
For p=0.10, dJC=−0.75·ln(1−0.1333)=−0.75·ln(0.8667)≈0.107 substitutions per site. Check: dJC is slightly above the raw distance 0.10 because the model accounts for hidden multiple changes. At p=0.75, the logarithm argument tends to zero.
Correct simple pairwise DNA distances for phylogenetic comparisons under an explicit model
Here is how to work through a typical Jukes–Cantor Distance Correction (dJC = −¾ ln(1 − 4p/3)) task step by step:
Task
p=0.10. Calculate dJC to three places.
Solution path
dJC=−0.75 ln(1−4·0.10/3)≈0.107 substitutions/site.
a model correction to observed base differences for possible multiple substitutions. Its output is expected nucleotide substitutions per homologous site.. the corrected distance exceeds p-distance because reversals can be hidden. The quantity answers a specific biological or statistical question, not automatically the full cause of an observed pattern. Tie it to the population, sample or model level from which inputs came. A number without that reference can be misleading across studies. Keep description separate from explanation: the metric summarizes data but does not by itself establish the underlying mechanism.
Use p is raw difference proportion and dJC is corrected model distance. The units are both values are dimensionless per site; dJC is read as substitutions per position.. Check that numerator and denominator refer to the same time interval, target population and scale. Proportions entered as percentages usually need conversion to values between zero and one. Write units and definitions beside the observations. This helps catch swapped groups, mismatched age intervals or a wrong denominator before they distort the result. Also document measurement definitions and preprocessing, because studies can operationalize the same symbols differently.
The central assumption is: JC69 assumes equal base frequencies and equal rates between bases. p remains below 0.75 and alignment gaps or misassignments are handled. If base composition is strongly biased or substitution pathways differ., interpretation changes or the formula no longer fits. State sampling, measurement method and biological scale. A model is useful because it simplifies a question, but its limits belong in the report. Do not automatically transfer parameters to different species, populations, laboratories or sampling conditions. Report these assumptions with the result so readers can judge which populations and conditions the conclusion can cover.
In the example, p=0.10 gives about 0.107 substitutions per site. The check is: back-transforming dJC returns approximately p=0.10. Substitute calculated values back into the original relation and check whether ranges and units are biologically plausible. Rounded data can create a small discrepancy, but should not change direction or order of magnitude. Also test a simple limiting case, such as zero, complete detection or equal groups. This separates arithmetic errors from model limitations. Round intermediate values only at the end, and check the order of magnitude against the biological question.
A nearby quantity is the uncorrected p-distance between two aligned sequences. The substantive distinction is that p-distance counts observed differences; JC69 also models unobserved multiple substitutions. Both can appear in the same biological analysis, but they use different inputs and answer different questions. Choose by the requested output and verify the data definition before comparing values. A related name does not imply identical units or interchangeable interpretation. This matters when a descriptive statistic is reported alongside a model parameter. Before comparing values, align definitions, populations, observation periods and analysis rules; otherwise the difference may be methodological.
Quanta exam set
Curated exam set for "Jukes–Cantor Distance Correction":
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Which formula describes Jukes–Cantor Distance Correction?
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How do you rearrange Jukes–Cantor Distance Correction for Rearrange for observed distance?
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Which common mistake happens with Jukes–Cantor Distance Correction?
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