JC69

JC69, short for Jukes-Cantor 1969, is a simple nucleotide substitution model used in molecular evolution and phylogenetics. It assumes four nucleotides (A, C, G, T) with equal base frequencies and identical substitution rates among all nucleotides, and it treats sites as evolving independently under a Poisson process.

In the JC69 model, the substitution rate matrix Q has off-diagonal entries μ/3 for any replacement from one base to any other, with diagonal entries set so that each row sums to zero. The probability that a nucleotide remains the same after time t is P_same(t) = 1/4 + 3/4 e^{-4μt/3} and the probability of a difference is P_diff(t) = 3/4 (1 - e^{-4μt/3}). The expected proportion of observed differences p relates to evolutionary time t by p = 3/4 (1 - e^{-4μt/3}). A simple distance estimator is d = -3/4 ln(1 - 4p/3).

Historical impact and usage: The JC69 model provides the baseline for correcting observed differences to infer evolutionary distance between sequences. It is widely used as a teaching tool and for quick, rough distance estimates, especially when data are limited or as an initial step in analyses.

Limitations: The model assumes equal base composition and equal substitution rates among all nucleotide pairs, neglects transition/transversion biases, and does not accommodate rate variation among sites. For longer sequences, multiple substitutions at the same site lead to underestimation of distances. More complex models, such as Kimura 2-parameter (K2P), HKY, and general time-reversible (GTR), address these limitations.

See also: Nucleotide substitution model; Kimura 2-parameter; HKY85; GTR; molecular evolution.