Evolutionary Distance Calculators

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Evolutionary distance is a measure of the amount of molecular sequence divergence between two biological sequences (DNA, RNA, or protein) since their common ancestor. It is expressed as the number of substitutions per site (d), corrected for multiple hits at the same position (which would cause underestimation of true divergence). The simplest model is Jukes-Cantor (JC69), which assumes equal rates among all nucleotide substitutions. More complex models (Kimura 2-parameter, HKY85, GTR) account for different substitution types and base frequencies. Evolutionary distances are used to build phylogenetic trees by neighbor-joining and distance-based methods.

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Observed and Corrected Divergence

Observed divergence: p = number of different positions / total aligned positions. Problem: multiple hits at the same site are invisible → p underestimates true divergence at high divergence. Jukes-Cantor correction: d_JC = −(3/4) × ln(1 − 4p/3). Example: p = 0.15: d_JC = −(3/4) × ln(1 − 4×0.15/3) = −(3/4) × ln(0.80) = −0.75 × (−0.223) = 0.167 substitutions/site.

Common Substitution Models

  • Jukes-Cantor (JC69): simplest; equal rates for all 12 nucleotide substitutions; equal base frequencies
  • Kimura 2-parameter (K2P): two rates — transitions (Ts) and transversions (Tv); equal base frequencies; κ = Ts/Tv ratio
  • HKY85: K2P + unequal base frequencies
  • GTR (General Time Reversible): 6 rate parameters + 4 base frequencies; most general; widely used

Neighbor-Joining (NJ) Tree

Build tree from pairwise distance matrix: start with star topology; iteratively join two sequences that minimize total tree length; fast and approximate; used for initial exploratory analysis or when number of taxa is large.

Model Selection

jModelTest or ModelTest-NG: calculate AIC/BIC for all models → select best-fitting model. Important: using too simple a model underestimates long distances; too complex a model may overfit.

Glossary

Evolutionary Distance (d)
Number of substitutions per site between two sequences since divergence; corrected for multiple hits by substitution models; d_JC = −(3/4)ln(1−4p/3); used for neighbor-joining trees and molecular clocks.
Jukes-Cantor (JC69) Model
The simplest nucleotide substitution model; equal rates for all 12 substitution types; equal base frequencies; d_JC = −(3/4)ln(1−4p/3); underestimates distance when rates are unequal.
Neighbor-Joining (NJ)
Distance-based phylogenetic tree construction; creates tree from pairwise distance matrix by iteratively joining closest sequences; fast for large datasets; approximate; less accurate than ML or Bayesian methods.

Frequently Asked Questions

Evolutionary distance (d) = the estimated number of substitutions per site that have occurred since two sequences shared a common ancestor. Observed divergence (p) = fraction of different positions in an alignment. Problem: at high divergence, some sites mutate multiple times (multiple hits) — back-mutations restore the original nucleotide, and parallel mutations produce the same change in both lineages. Both make sequences look more similar than they are → p underestimates true evolutionary distance. Correction: substitution models (Jukes-Cantor, Kimura 2-parameter, GTR) mathematically correct for multiple hits. The correction becomes increasingly important at divergence > 15–20%.

The Jukes-Cantor (1969) model is the simplest nucleotide substitution model: assumes equal rates for all 12 possible nucleotide substitutions; assumes equal base frequencies (0.25 each). JC distance: d_JC = −(3/4) × ln(1 − 4p/3). Where p = observed proportion of different sites. Example: p = 0.20: d_JC = −0.75 × ln(1 − 0.2667) = −0.75 × ln(0.7333) = −0.75 × (−0.310) = 0.232 subs/site. Compared to observed p = 0.20, the JC model corrects upward to 0.232 — accounting for multiple hits. Limitation: the JC model is an oversimplification — transitions are more common than transversions; base frequencies are usually not equal. More realistic models (K2P, HKY, GTR) provide better fits.

Distance-based phylogenetics: calculate pairwise evolutionary distances for all pairs of sequences → construct a distance matrix → build a tree. Neighbor-joining (NJ) method: starts with a 'star topology' (all sequences connected to one central node); iteratively joins the pair of sequences that minimizes the total tree length; continues until all sequences are joined in a bifurcating tree. NJ is fast (handles thousands of sequences) and appropriate for initial analysis. Limitations: NJ only uses pairwise distances; loses information about shared derived characters (synapomorphies); less powerful than maximum likelihood or Bayesian methods for well-resolved trees. NJ is commonly used for: rapidly processing large datasets (barcoding); constructing reference trees; quality-checking sequence alignments.

Model selection uses information criteria (AIC: Akaike; BIC: Bayesian) to choose the model that best fits the data without overfitting. Tools: jModelTest (free, standalone), ModelTest-NG (fast, command-line), IQ-TREE (built-in model selection via -m TEST). Steps: (1) Align sequences. (2) Run model selection tool — tests all available models. (3) Select model with lowest AIC or BIC. (4) Use selected model for distance calculations or phylogenetic analysis. Common best-fit models: GTR+G (general time reversible + gamma rate variation): most commonly selected for protein-coding genes and 16S rRNA. HKY+G: good intermediate model for many datasets. TIM, TVMef, TVM: specialized rate matrix models. Importance: using JC69 for data that fits GTR can cause systematic errors in tree topology and distance estimates at high divergence.