perhaps some positions can never tolerate a replacement (Fitch and Markowitz, 1970). Thus multiple replacements at a site may occur more frequently than would be the estimate when the whole sequence is considered to be variable. However, as replacements are accepted, those very changes may affect and change the sites that are covariable. Thus the sites that have changed across very different taxa may be considerably greater than the number that are covariable in any given species. It seemed possible that the unrecognized presence of covarions could hide the extent of multiple replacements, thus causing the deeper (older) portions of the tree to appear as if evolving too slowly. As the other of us (F.J.A.) has embarked on a program of extensive SOD sequencing, it seems a propitious time to collaborate on a deeper evaluation of this problem.

From this collaboration, we have determined the number of covarions in SOD (28 in Drosophila) and shown that the molecular clock could be working fairly well. This is done by showing, by simulation, that the observed amino acid differences could have arisen if, among the fungi and metazoans, SOD had 44 of its codons permanently invariable and there was a high rate of exchange between codons that are covarions and those that are not variable at any particular time.


The data analyzed were 67 SOD sequences, aligned by eye. The sequences are from GenBank (see Figure 1 for sequence numbers), except for most of the flies, which came from the lab of F.J.A. The tree was obtained using the ANCESTOR program (Fitch, 1971; Fitch and Farris, 1974). The number of covarions was determined by the method of Fitch and Markowitz (1970).

Simulations were performed (Fitch and Ye, 1991) using a program for which the user prescribes five parameters: (i), the length of the sequence; (ii), the number of covarions; (iii), the persistence of the covarion set (the probability that no covarion will be exchanged for a presently invariable codon; if an exchange does occur, only one of the covarions is exchanged; the possibility of an exchange exists after each replacement); (iv), the number of alternative amino acids allowed at a site, and (v) the times at which the number of amino acid differences are to be determined. The times are in units of amino acid replacements and hence the clock is perfect in the simulations.

The divergence times can have any value but, to test the possibility that the SOD data can arise by the simulated clock, the replacements must be in the same proportion as the paleontological time estimates. The time estimates we used are given in Table 1.

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