The old REH theory remains unsatisfactory and the new REH theory is problematical - a reply to holmquist and jukes

Summary In response to criticism of REH theory (Fitch 1980), Holmquist and Jukes (1981) have mostly avoided the criticism or misunderstood it. Since they themselves state in their response that Amino acid sequence data alone cannot be used to estimate total nucleotide substitutions, they agree with the criticism. Most of their paper treats the newer theory (here designated as the REHN theory) which attempts to use the nucleotide sequences encoding proteins to better estimate total nucleotide substitutions (Holmquist and Pearl 1980). Since I made no criticism of REHN theory, their comments are frequently beside the point of my original criticism of REH theory. Nevertheless, it is shown here that REHN theory is also unsatisfactory in that: One, the varions are now more clearly defined but in such a way as to preclude the same codon from suffering a nucleotide substitution in more than one evolutionary interval. Two, the set of codons that accepts silent substitutions is identical to the set that accepts amino acid changing nucleotide substitutions. Three, the uncertainty in the REH estimate is considerable in that alternative excellent fits to the same observatuonal data may give alternative REH values that differ significantly even before stochastic variation and selective bias are considered. Four, the fit of their model to data is an irrelevancy where there are zero degrees of freedom.