Jukes-Cantor model ($P_{ii}(t)=\frac{1}{4}+\frac{3}{4}{e}^{-4qt}$)

The Jukes-Cantor model is a symmetric four-state continuous-time Markov chain for DNA evolution. Each change to a specified different base has rate $q$, so the total rate of actual changes is $3q$. Its same-base probability is $1/4+(3/4)e^{-4qt}$ and its probability for one specified different base is $(1/4)(1-e^{-4qt})$. The probability of any mismatch is three times the latter, tending to $3/4$ at long times. Distinguish the exponent parameter $4q$ from the actual per-site mutation rate $3q$ when fitting this model.