Dayhoff and JTT distances (Gamma rates)

The PAM and JTT distances correct for multiple substitutions based on a model of amino acid substitution described as substitution-rate matrices. The PAM distance uses PAM 001 matrix (p. 348 in Dayhoff 1979) and the JTT distance uses JTT matrix (Jones et al. 1992). The matrix (F) uses a substitution-rate matrix (Q) and the gamma distribution with parameter a for the rate variation among sites. It consists of the observed proportions of amino acid pairs with their divergence time t, 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 computed iteratively 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.