Jukes-Cantor JC69: dP/dt = Q·P; p(t) = 3/4·(1−e^{−4αt}); first-order Markov substitution model

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Jukes-Cantor 1969 (JC69) model — the foundational molecular-evolution substitution framework. Physical setup: DNA sites evolve independently under a continuous-time Markov chain on the 4 nucleotides {A, C, G, T} with uniform rate α for…

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Linear ODE
JC69: p(t)=3/4·(1−exp(−4αt)); d(p)=−3/4·ln(1−4p/3); p_∞=3/4; dp/dt|₀=3α; d(p=3/8)=(3/4)ln2

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