Confidence intervalsDivergence times of lineages cannot be dated precisely (Figures 3.3, 3.5). Confidence
intervals are an essential part of any molecular dating technique and grow in size as errors
are introduced to these analyses at a number of levels. Statements such as ‘the divergence
time between Drosophila and vertebrates was about 830 million years ago’ (Gu 1998) impart
a spurious level of confidence. In an attempt to reduce confidence intervals a number of
studies have removed so-called ‘outliers’ before averaging divergence times across the genes
(e.g. Kumar and Hedges 1998; Wang et al. 1998). In contrast, the estimates of Bromham
et al. (1998) and Cutler (2000) are very large yet more accurately reflect the genetic
variability of the sample.
FossilsAlong with the problems of using only one or a few calibration points, by far the majority
of metazoan divergence time studies use absolute dates for calibration points. Marshall
(1990) presented a method for calculating confidence intervals on divergence times based
on the notion that the better the fossil record, the smaller the gap will be between the earliest
known fossil and the time of origin of the group. These methods were improved to allow
predicted collecting and/or preservation biases to be combined into the calculation of
confidence intervals (Marshall 1997; Foote and Sepkoski Jr 1999). More recently work by
Tavaré et al. (2002) has combined both molecular and palaeontological approaches to
divergence estimation and shows that good agreement between the two can be achieved.
Their calculations took into account data on the number of extant species, the mean species
lifetime, the age of the bases of the stratigraphic intervals (and the number of fossils found
in these), and the relative size of the sampling intensity at each interval.
Standard error of the meanThe standard error of the mean is often used to provide confidence intervals around
molecular dating estimates (e.g. Hedges et al. 1996). However the standard error only
provides an indication of the certainty of the mean of the population from which the sample
was taken. It does not provide a confidence interval for the single true date of divergence
(Cooper et al. 2001) and provides error intervals that are unrealistically narrow.
Stochiosticity of the molecular clockMolecular clocks do not tick at regular intervals, but instead at random points in time. In
order to characterize these, ‘point processes’ must be applied—statistical models that
describe events occurring at random times (Gillespie 1991). Generally, the ‘ticking’ of the
molecular clock is assumed to follow a simple Poisson distribution of substitution
occurrences (Zuckerkandl and Pauling 1965). Most methods assume that the clock adheres
strictly to this process. However, confidence intervals calculated for divergence time
estimates often ignore the Poisson variance of this distribution, taking instead the standard
error of the mean divergence estimates as the total estimate error (Wang et al. 1998). For
deeper divergences the ‘cumulative’ errors are greater and so pose a particular problem
52 RICHARD A.FORTEY ET AL.