= Transition-transversion ratio
An observed <transition-transversion ratio> compares the number of <nucleotide transitions> with the number of <nucleotide transversions> in a specified set of <sequence alignment> differences:
$$
R=\frac{N_{\mathrm{transition}}}{N_{\mathrm{transversion}}}.
$$
Six transition differences and two transversion differences give $R=3$. If no transversion is observed, this ordinary finite ratio is undefined; the raw counts should remain explicit.
The instantaneous rate parameter can use a different convention. In the <Kimura two-parameter model>, let $\alpha$ be the rate to the one transition target and $\beta$ the rate to each of the two transversion targets from a base. Then
$$
\kappa=\frac{\alpha}{\beta},\qquad R_{\mathrm{instantaneous}}=\frac{\alpha}{2\beta}=\frac{\kappa}{2}.
$$
Thus $\kappa=4$ corresponds to twice as many instantaneous transition events as total transversion events, not four times as many.<A simple method for estimating evolutionary rates of base substitutions through comparative studies of nucleotide sequences by Motoo Kimura>[Two-rate substitution model; per-target transition and transversion definitions]{ref}
Observed endpoint differences can hide repeated <nucleotide substitutions>. Under independent uniform endpoint bases, the four directed transition mismatches and eight transversion mismatches give a limiting ratio $1/2$, even when short-time event rates differ. Always state whether the ratio describes scored differences, total events or rates per possible target.
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