The reh theory of protein and nucleic acid divergence: A retrospective update

Over half a decade has passed since the quantitative REH theory of evolutionary divergence in nucleic acids and proteins was published. The principle tenant of this theory is that natural selection and stochastic processes interact, the main effect of the former being to restrict those codon sites which may fix mutations. At the time it was published the theory predicted a magnitude for the total number of fixed nucleotide replacements that was appreciably larger than estimates then current. 'In the last two years these predictions have been confirmed in those protein families for which the experimental data base is large: cytochromec, α-hemoglobin,β-hemoglobin, and myoglobin. It has come to our attention, chiefly through private correspondance, but also in one published review, that certain aspects of the REH theory have caused confusion among some users. This paper discusses these particular aspects in some detail, restates the theory in a manner which emphasizes its essential simplicity, analyzes the magnitude of possible sources of errors, and considers some important statistical matters not dealt with elsewhere. The calculational methodology is simplified by replacing tables and graphs by polynomial expressions, and deriving a more simple expression for calculating the number of codons which have been free to fix mutations during some part of the period of divergence of two species. A statistical bias in the estimation of the fixation intensity is corrected. It is hoped these changes will make the method more accessible to those without extensive computing facilities.