AICvalues of the present models without and with the selective constraints on amino acids, which are based on mean energy increments due to an amino acid substitution (EI), the Miyata's and the Grantham's physico-chemical distances, for the 1-PAM amino acid substitution matrices of JTT, WAG, cpREV,

a #parameters with for JTT, for WAG, for cpREV, and for mtREV; see text for details.
bML parameters in each model are specified by the parameter id numbers in the parenthesis, and other parameters are fixed at , , , , , and . Each id number corresponds to the parameter id number listed in Table 3.