likelihood values are calculated using the true topology, and caution is needed when the
phylogeny is uncertain (Yang et al. 1995). This problem is attenuated taking into account
that relationships which are not well established (e.g. the branching order of animal phyla)
are set as polytomies in the tree of Figure 1.1. The JTT-F+dG model is used to calculate
the likelihood values with and without the clock assumption. We focus on GPDH, SOD,
and XDH because they are more extensively represented in our study than the other
proteins. The JTT-F+dG clock model is rejected only for the case of XDH (−2logΛ=42.
7, P<10−^6 , 33^ d.f.). For GPDH and SOD, relaxation of the clock assumption does not
improve significantly the likelihood (−2logΛ=42.7, P>0.01, 29 d.f.; and −2logΛ=69.3,
P>0.01, 60 d.f., respectively). As we have seen (see Figures 1.2, 1.3) XDH is the most
clock-like of the three proteins. Yet, its conspicuously greater length (599 residues versus
241 and 107, for XDH versus GPDH and SOD, respectively) yields the molecular clock
test for XDH more sensitive to departures from the rate constancy assumption.
Whither the clock?The theoretical foundation originally proposed for the clock, namely the neutrality theory
of molecular evolution, is untenable. The variance of molecular rates of evolution has
contributed much to invalidating the theory. Supplementary hypotheses have been
proposed, such as those enunciated in the introduction of this chapter. These hypotheses
invoke parameters or processes that might be ascertained, at least in favourable cases, and
thus lead to predictive inferences. The tests that we have designed rely on the prediction
made by several hypotheses that all genes of a given lineage will be equally affected,
because they postulate attributes that are equally shared by all genes of a species, such as
population size, generation time, polymerases, or some other (defined or not) biological
characteristic of the species. The evidence brought forward in this chapter makes these
remediating hypotheses untenable. The rate variation pattern is erratic. Figures 2 and 3
make it graphically obvious that some lineages, such as Fungi (see Figure 1.3), evolve
fastest for some genes (GPDH and TPI), slowest for other genes (SOD and XDH), and
intermediately for the remaining two genes (G6PD and GPD). These vagaries may be a
consequence of natural selection, whether in response to the fickleness of the biotic and
physical external environment, or to complex interactions within or between the
organisms of the species. But, at the present state of knowledge, there seems to be no way
to make predictions as to how molecular evolutionary rates would be impacted, so that
we could derive precise inferences about phylogenetic relationships or the timing of past
events. One might expect, for example, that functionally related proteins might evolve in
similar patterns across lineages. But our results do not favour this conclusion. G6PD is
metabolically adjacent to PGD, and so are GPDH and TPI, and all four enzymes are
involved in central cell metabolism, but the members of each pair do not exhibit
consistent patterns of molecular evolution across lineages, much less all four enzymes (see
Figure 1.3).
There are, nevertheless, genes and proteins for which the molecular clock seems to
hold with fair accuracy, at least for certain groups of organisms and/or time intervals
(Kimura 1983; Nei 1987; Li 1997). Even in these cases caution should be exercised
before accepting observed rate variation as insignificant. The molecular clock tests used to
MOLECULAR CLOCKS: WHENCE AND WHITHER? 21