Dayhoff and JTT Models

The PAM and JTT distances correct for multiple substitutions based on the model of amino acid substitution described as substitution-rate matrices. The PAM distance uses the PAM 001 matrix (p. 348 in Dayhoff 1979) and the JTT distance uses the JTT matrix (Jones et al. 1992). Using a substitution-rate matrix (Q), the matrix (F), which consists of the observed proportions of amino acid pairs between a pair of sequences with their divergence time t, is given by the following equation

where A denotes the diagonal matrix of the equilibrium amino acid frequencies for Q. From this equation, the evolutionary distance d = 2tQ can be iteratively computed by a maximum-likelihood method. The eigen values for the PAM and JTT matrices required in this computation were obtained from the program source code of PHYLIP version 3.6 (Felsenstein et al. 1993-2001).

MEGA provides facilities for computing the following quantities:

The variance of d can be estimated by the bootstrap method.