There are 15 unrooted trees linking the 5 major spiralian phyla and each has been supported in at least one publication (table S1).

Tree numbering throughout this study refers to the trees in this figure. For all 105 rooted trees, the rooting scheme follows that depicted in unrooted T1.

Branches linking spiralian phyla are shorter that the short, disputed deuterostome branch.

A and B are data from MARL. C and D are data from SERR. Compared to the site-homogeneous model (A, C), internal branches (orange) become shorter under the site-heterogeneous model while the long branches leading to Platyhelminthes (blue) and Mollusca (dark green) become even longer (B, D). Scales are identical on either side of the y-axis breaks.

Relative median RELL pseudo-bootstraps (AD) and randomised taxon-jackknives (EH) log-likelihood ranks for all rooted trees, see tables S2 and S4 for all ranks.

Highest- and lowest- ranked topologies labelled for all analyses, along with every seventh topology from highest- to lowest-ranked, Topologies ranked by their difference in log-likelihood to the mean log-likelihood of each RELL or jackknife distribution. The RELL analyses of both datasets under the site-homogeneous LG+F+G4 model (A, B) occupy the widest ranges of log-likelihoods, which is consistent with the statistically significant differences found by the KW test. The RELL analyses under the site-heterogeneous EDM+F+G4 model (C, D) occupy a much narrower range of log-likelihoods. The jackknife analyses show a similar trend, wider range of median log-likelihood scores under LG+F+G4 (E, F) than under EDM+F+G4 (G, H); however, the log-likelihood ranges of the jackknives under LG+F+G4 are very similar to that occupied by RELL under EDM+F+G4, consistent with the lack of statistically significant differences between topologies in the jackknife analyses.

With simulated data inadequate models incorrectly support platyhelminth root.

Using data simulated on an unresolved Spiralia, tree we ranked rooted spiralian topologies by difference to mean log-likelihood score. Highest- and lowest- ranked topologies labelled for all analyses, along with every seventh-topology from highest- to lowest-ranked. For datasets simulated under EDM (complex) but scored under LG (simple) the 15 topologies with Spiralia rooted on Platyhelminthes are highest ranked (A, B). The plots for the ‘correctly’ specified models (C, D) show the expected approximately equal log-likelihood scores for all 105 rooted topologies. See table S6 for complete topology rankings.

Most fixed-taxon RELL bootstrap and randomised taxon-jackknife replicates, under both site-homogeneous (LG) and site-heterogeneous (EDM) models, recover unrooted T4 as the best-scoring topology.

Heights of bars correspond to the number of replicates where each topology had the highest log-likelihood score.

With simulated data, misspecified models recover unrooted T4 within the set of highest-scoring topologies.

Using data simulated on an unresolved Spiralia tree we ranked unrooted spiralian topologies by difference to mean log-likelihood score. For datasets simulated under EDM (complex) but scored under LG (simple), three topologies (T4, T5 and T14) are within the highest-ranked topologies for both empirical datasets (A, B). The plots for the ‘correctly’ specified models (C, D) show the expected approximately equal log-likelihood scores for all 15 unrooted topologies.