Pairwise molecular divergence ($d$)

Pairwise molecular divergence measures the accumulated evolutionary change separating two homologous molecular sequences. For aligned DNA sequences, a model-based distance $d$ is commonly expressed as the estimated number of nucleotide substitutions per site along the path connecting the sequences. It differs from the observed fraction of mismatching sites: a site may have changed more than once, including changes that restore the starting base.^[ref]

For example, 20 mismatches among 1,000 usable aligned sites give an observed mismatch fraction $p=0.020$. That is a count of present-day differences. An ancestral A that changed to G and then back to A contributes two historical substitutions but no endpoint mismatch. Sequence alignment and an explicit nucleotide substitution model are therefore needed to turn observed differences into an evolutionary interpretation.

The Kimura two-parameter model distinguishes nucleotide transitions from nucleotide transversions. If $P$ and $Q$ are their observed fractions among compared sites, respectively, its corrected pairwise estimate isFor $P=0.01$ and $Q=0.01$, this gives approximately $0.02028$ substitutions per site, slightly above the observed mismatch fraction $P+Q=0.020$. The correction accounts for hidden changes under the model's assumptions; it is not a direct count of every event. Both logarithm arguments must be positive for this finite real-valued estimate.^[ref]

Under a constant, equal per-lineage molecular clock rate $r$ and a split $T$ time units ago, the two branches contribute $d=2rT$. A pairwise divergence $d=0.02$ at $r=10^{-9}$ substitutions per site per year corresponds to $T=10^7$ years in that idealized model. The factor of two counts both lineages. Without a rate calibration or another time constraint, distance alone does not identify elapsed time.^[ref]