The Estimation of Genetic Divergence

We have independently repeated the computer simulations on which Nei and Tateno (1978) base their criticism of REH theory and have extended the analysis to include mRNAs as well as proteins. The simulation data confirm the correctness of the REH method. The high average value of the fixation intensity mu 2 found by Nei and Tateno is due to two factors: 1) they reported only the five replications in which mu 2 was high, excluding the forty-five replications containing the more representative data; and 2) the lack of information, inherent to protein sequence data, about fixed mutations at the third nucleotide position within codons, as the values are lower when the estimate is made from the mRNAs that code for the proteins. REH values calculated from protein or nucleic acid data on the basis of the equiprobability of genetic events underestimate, not overestimate, the total fixed mutations. In REH theory the experimental data determine the estimate T2 of the time average number of codons that have been free to fix mutations during a given period of divergence. In the method of Nei and Tateno it is assumed, despite evidence to the contrary, that every amino acid position may fix a mutation. Under the latter assumption, the measure X2 of genetic divergence suggested by Nei and Tateno is not tenable: values of X2 for a alpha hemoglobin divergences are less than the minimum number of fixed substitutions known to have occurred. Within the context of REH theory, a paradox, first posed by Zuckerkandl, with respect to the high rate of covarion turnover and the nature of general function sites in proteins is resolved.