no Poisson or Jukes-Cantor correction is needed. That is true only if all sites are variable. For example, if only 12 of 100 sites are variable, observing 10 differences implies 23.9 replacements [r = -12(19/20) ln[1 - (20/19)(10/12)], which is more than double the 10.6 replacements [r = -100(19/20)ln[1 - (20/19)(20/100)] calculated on the assumption that all 100 sites were variable. The example may well be somewhat extreme, but any minor problem gets amplified as the ancestor becomes increasingly distant.

We do not assert that the parameters used to get the fit in Figure 3 and Table 1 are necessarily correct, but we want to make five observations.

The first observation is that the implications of the parameter values are likely to be correct. These implications are (i) there are about 28 covarions that (ii) tend to turn over fairly often, although (iii ) the number of allowable alternatives at a variable position is, on average, limited (two to four alternatives), and (iv) that there is a sizeable number of positions (40) that cannot fix a replacement even though the covarions fix them (v) with a reasonable rate of approximately six replacements per 10 Myr.

The second observation follows from the pattern seen in Figure 3 (and Table 1) that the simulated values are consistently lower than the observed ones during the first 100 Myr but consistently higher in the intermediate years (200–600 Mya). This pattern is expected if a sizeable fraction of the potentially variable codons has a significantly lower probability of becoming variable than the rest. This is biologically reasonable, although an alternative possibility is that the paleontological dates are either systematically underestimated for the early dates or overestimated for the intermediate dates. This would make it easier to obtain a better fit for both regions, simply by assuming a somewhat larger or smaller replacement rate respectively.

The third observation is that while we know of no good estimates of the divergence time of S. cerevisiae and N. crassa, our data, based simply on differences and not on covarions, place their divergence around 380 ± 40 Mya.

Fourth, we have tried a correction for superimposed replacements of the Jukes-Cantor type where b = 19/20 for the fungi–metazoan divergence. The value obtained is r = -162 × (0.95)ln[1 - 67/(0.95 × 162)] = 88 replacements, a 31% increase over the 67 observed differences, whereas the number of replacements required to obtain 67 differences in the simulations is 600, which is a 796% increase. Thus, corrections of the Jukes-Cantor type may still yield divergences that are gross underestimates if a covarion model is operating.

Fifth, the rate of amino acid replacement that fits our data is 6 × 10-7 replacements per year for the entire gene. This is the same as

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