is again contingent upon tree balance such that perfectly balanced trees will have a SCI of
0.50, while fully pectinate trees yield the full range of SCI scores (Wills 1999). The effect
of tree balance on the RCI is more complex. A perfect RCI score of 100 per cent is possible
only if the first appearance of all taxa is contemporaneous and fully pectinate trees
fulfilling these stratigraphic requirements will always acheive this score. However, other
topologies may not be able to achieve a perfect RCI score even if the component taxa meet
these stratigraphic requirements (Wills 1999). The GER controls for the distribution of
range data and is also sensitive to tree balance. However, by randomly reassigning the
stratigraphic range data over the tree it is possible to assess whether stratigraphy-
cladogram congruence is significantly better than random, while holding the potential
biases (stratigraphy, taxon number, tree balance) constant (Wills 1999). Permutation
tests can also be applied to SCI calculation and the degree to which these metrics deviate
from random provides a measure of confidence in their significance (Wills 1999).
The SCI, RCI, and GER (as well as permutation tests for significance of these indices)
were calculated for the overall tree and for the internal record of each of the plesions in
the overall tree, using Ghosts 2.3 (Wills 1999) and the results are presented in
Table 10.2. Dates for chronostratigraphic boundaries used in the stratigraphy file for the
program were obtained from Tucker and McKerrow (1995), Gradstein and Ogg (1996),
Saylor et al. (1998), Tucker et al. (1998), Cooper (1999), Encarnación et al. (1999),
Figure 10.4 Cladogram from Figure 10.2 calibrated to time to reveal inferred ghost lineages;
observed stratigraphic range data represented by thick black bars and large gaps represented by thick
dashed bars.
204 THE ORIGIN AND EARLY EVOLUTION OF CHORDATES