Deuterostomes comprise three phyla with radically different body plans. Phylogenetic bracketing of the living deuterostome clades suggests the latest common ancestor of echinoderms, hemichordates and chordates was a bilaterally symmetrical worm with pharyngeal openings, with these characters lost in echinoderms. Early fossil echinoderms with pharyngeal openings have been described, but their interpretation is highly controversial. Here, we critically evaluate the evidence for pharyngeal structures (gill bars) in the extinct stylophoran echinoderms Lagynocystis pyramidalis and Jaekelocarpus oklahomensis using virtual models based on high-resolution X-ray tomography scans of three-dimensionally preserved fossil specimens. Multivariate analyses of the size, spacing and arrangement of the internal bars in these fossils indicate they are substantially more similar to gill bars in modern enteropneust hemichordates and cephalochordates than to other internal bar-like structures in fossil blastozoan echinoderms. The close similarity between the internal bars of the stylophorans L. pyramidalis and J. oklahomensis and the gill bars of extant chordates and hemichordates is strong evidence for their homology. Differences between these internal bars and bar-like elements of the respiratory systems in blastozoans suggest these structures might have arisen through parallel evolution across deuterostomes, perhaps underpinned by a common developmental genetic mechanism.

X- ray tomography

Specimens were imaged with X-ray micro-tomography and synchrotron tomography. Details of scan settings are provided in Supplementary Table 1. Raw files can be found under the specimen's name. 

Three-dimensional reconstructions

Tomographic datasets for the specimens were digitally reconstructed using the SPIERS software suite. See electronic supplementary information and Supplementary Figure 1 for details. Measurements of length were standardised against the total length of the pharynx or internal thecal cavity for each model, whereas measurements of width, depth and spacing were standardised against the diameter of the pharynx or internal thecal cavity. Finalised versions of the reconstructions in .spv and .spvf files can be found under the specimen's name.

Data analysis

Raw dataset can be found on internal_bar_data.csv. Standardised measurements of the structures of interest were analysed quantitatively in R 3.6.3 using principal component analysis (PCA) and linear discriminant analysis (LDA). The analyses were conducted using the stats (v3.6.3) and MASS (v7.3.51.5) packages. LDA results were further interrogated via partition plots for every combination of two variables using the klaR (v0.6.15) package. In addition, the normalised data were analysed using MANOVA, ANOVA at 95% confidence and post-hoc testing (Holm-Bonferroni and Tukey 95% confidence tests) using the stats (v3.6.3) package. Further methodological details and R scripts are provided as electronic supplementary information.

- raw data scan file

I- reconstruction .spv file. This is a finalised version of the reconstruction with possibility of alteration.

II- reconstruction .spvf file. This is a finalised version of the reconstruction without possibility of alteration, older versions of SPIERSview might not be able to process it.

III- measurement acquisition (reconstruction file + final.csv). For instructions see supplementary files (electronic_material.pdf).

IV- multivariate analysis (final.csv + final_rcode.R).

All raw scan files have the scan info and settings included in the uploaded folder except Jaekelocarpus oklahomensis where the settings can be found at the original data source http://digimorph.org/specimens/Jaeckelocarpus_oklahomensis/