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

Layer 3 — Biologyin the computational-biology subtree

Sympy-exact symbolic witness of the Jukes-Cantor 1969 (JC69) transition-probability formula, its inverse distance estimator, the 3/4 saturation limit, and the initial-rate anchor. Setup: α (substitution rate per site per unit time), t…

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

Explore 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 on the interactive knowledge graph →