error of the estimate. Likelihood-based estimation methods that incorporate this error have
been developed (Rambaut and Bromham 1998; Cutler 2000).
In reality, the molecular clock often appears to violate the assumptions of a Poisson
process, suggesting that this may not always be an appropriate model to use. Two cases in
which this becomes clear are in the observation of lineage-specific rate variation and in the
over-dispersion of the actual calculated substitution variance relative to the Poisson-assumed
variance. This latter problem has been analysed by Cutler (2000) who replaced the Poisson
process with a more general stationary process (using a central limit theorem
approximation). It was found that for mitochondrial genes reconstructing metazoan
evolution, the stationary process provides a significantly better fit to the data than the
Poisson. It was suggested that this may be a better process to use when both the dataset and
the number of substitutions per branch is large.
Non-independence of comparisonsIn many studies, the clock is calibrated by averaging all pairwise comparisons among taxa
within a group (e.g. Wray et al. 1996; Wang et al. 1998). However, it is sometimes
overlooked that these values are not independent (Felsenstein 1981) because they are based
on shared regions of a tree. This lack of independence leads to unrealistic confidence in the
correlation between time and divergence and confounds error calculations. Where possible,
calibrations should be based on independent lineages. Non-independent comparisons are
often a problem when using pairwise distance methods, but processes that incorporate the
whole phylogeny, such as maximum parsimony (MP) and ML, can circumvent this problem
(Lewis 2001).
Rate variationMolecular evolutionary rates can differ between taxa and lineages. For example Ayala (1999)
reported that the superoxide dismutase gene evolved five times faster within Drosophila
groups than it did in multicellular organisms in general. Additionally, Rodríguez-Trelles et
al. (2001) applied divergence time estimation techniques to three variable-rate genes (SOD,
GPDH, and XDH) and retrieved a very large range of divergence estimates, illustrating the
effects of rate variation on such tests. Friedrich and Tautz (1997) also showed that the
substitution rate in the 28S rRNA dipteran stem-lineage underwent marked acceleration in
comparison with other insect groups prior to the diversification of the major dipteran
subgroups.
Relative rate testsRelative rate tests compare the amount of change in each of two ingroup sequences with
respect to an outgroup. These are commonly used to identify data that do not conform to
rate uniformity, which are then removed from the analysis (e.g. Gu 1998). These tests are
nearly as old as the molecular clock hypothesis. They first came into use in immunological
cross-reaction studies, which utilized the molecular clock hypothesis to date the origin of
the hominoids (Sarich and Wilson 1967).
54 RICHARD A.FORTEY ET AL.