Tree shape and branch length
Not all topologies are equally difficult to recover accurately. The pectinate topology (Fig. 5A), which shows the longest terminal branches (when its internal branches are all of about the same lengths), is most difficult, followed by the equiprobable (Fig. 5C) and the symmetrical topology (although this may be linked with the fact that internal branch lengths of that tree were roughly proportional with the number of descendant taxa, except for the branch below the ingroup; Fig. 5B; Fig. 6; Table 1). This confirms our second hypothesis. Modifying the distribution of branch lengths yielded results that are more difficult to interpret (S5). Our first assumption was that the results would improve (i.e., the resolving power would be greater and the artefactual resolution lower) as the terminal/internal branch length ratio decreases. This assumption is corroborated for the trees D, E and F (Fig. 5) for resolving power under ordered parsimony and 3ta, but only for trees D and E for unordered parsimony. Tree G yielded worse results, perhaps because some internal branches are shorter. Results on artefactual resolution are more complicated to interpret. Along with the branch lengths of a tree, the 3ts content of clades is another important parameter to consider when performance is assessed using the ITRI. It is directly connected to tree shape, i.e. the number of terminal taxa inside and outside each clade (Nelson and Ladiges, 1992). As a consequence, some clades and characters they support will affect more the ITRI than others. More specifically, clades with few taxa within them or with few taxa outside them have less 3ts content than clades containing an intermediate number of taxa (in our trees, clades with the maximal 3ts content have ten taxa inside and eleven taxa outside). These imbalanced clades will impact results only slightly compared to balanced clades. This may explain partly why tree shape influences phylogenetic reconstruction.
Comparisons of results between an ultrametric tree (Fig. 5C) and a paleontological tree of the same topology (Fig. 5D) show that the latter features better resolving power and less artifactual resolution for ordered parsimony and 3ta. This result is congruent with the claim that adding extinct taxa breaks long branches, which results in important improvement on the resolution of the optimal trees. This claim is supported both on empirical data (Gauthier et al., 1988) and simulations (Huelsenbeck, 1991).