Kimura two-parameter model

The Kimura two-parameter model is a nucleotide substitution model that allows one instantaneous rate for nucleotide transitions and another for nucleotide transversions. A transition exchanges two purines or two pyrimidines; a transversion exchanges a purine with a pyrimidine. In the model's symmetric form, each base has one transition neighbor with rate $\alpha$ and two transversion neighbors, each with rate $\beta$. Equal equilibrium base frequencies and constant rates across sites are important assumptions.^[ref]

For aligned sequences let $P$ be the fraction of sites differing by a transition and $Q$ the fraction differing by a transversion. The estimated pairwise molecular divergence, measured in substitutions per site, isFor 1,000 comparable sites with 40 transition differences and 20 transversion differences, $P=0.04$, $Q=0.02$ and $\hat{d}\approx 0.06289$, compared with an observed mismatch fraction $0.06$. The excess accounts for multiple changes that can be hidden at the endpoints under the model.^[ref]

The logarithms require $1-2P-Q>0$ and $1-2Q>0$. Near their boundaries, small sampling changes can produce large distance changes; beyond them this finite real-valued correction is unavailable. The formula is a model-based inference, not a universal correction for arbitrarily divergent sequences. Unequal base composition or strong variation among sites can violate its assumptions.

The name refers to the two substitution-rate classes, not to two observed substitutions or two species. When rates are expressed per unit time, the total instantaneous departure rate from a base is $\alpha +2\beta$. Converting a fitted distance to elapsed time further requires a molecular clock rate calibration.