Hagfish from the Cretaceous Tethys Sea and a reconciliation of the morphological–molecular conflict in early vertebrate phylogeny

Significance Jawless, boneless, and virtually without fossil record, hagfish have long escaped systematists’ grip on their place among other fish. Yet their systematic resolution is critical to define vertebrates as a clade. Here we report an unequivocal fossil hagfish from the Cretaceous Mediterranean. Using this fossil to calibrate the evolutionary history of the group, our analysis supports hagfish and lampreys as sister groups, which likely diverged from one another in early Paleozoic times. As a result, vertebrates have a deep dichotomy, where some fossil jawless vertebrates sit closer to hagfish and lampreys than to jawed vertebrates. We showed that morphology-based analysis converged onto molecular inferences when characters are coded nonindependently, providing a case study for morphological–molecular conflicts in animal phylogeny.


A1. Taphonomy and Paleoecological Implications
Holotype of Tethymyxine tapirostrum (BHI 6445) is exquisitely preserved. The preservation of branchial pouches suggests the early stage of decay when buried (1,2). In comparison to a decay series of a modern hagfish (Myxine glutinosa) under controlled conditions, the organs preserved in BHI 6445 include the intestine (onset of loss in M. glutinosa: 2 days post-mortem), slime glands (4 days), heart (6 days), branchial pouches (15 days), barbels and liver (48 days), myomeres and caudal fin (63 days), chondrocranium and keratinous tooth plates (200 days) (1,2). Among them, the gut is preserved in BHI 6445, and the slime glands are represented by α-keratin infillings. Some other organs are not preserved, even though they are expected to be present in the slab of BHI 6445, including: nasopharyngeal duct, pharyngocutaneous duct, and mouth (4 days) and inflection of myomeres (11 days) (1,2). On the basis of this combination, BHI 6445 may be best compared to decay stage 2 of modern hagfish, between the onset of loss of heart and of branchial pouches (1,2).
The mode of preservation is similar to the specimens of Mesomyzon mengae from the Lower Cretaceous Jehol Group of China (3,4). Compared to the modern river lamprey Lampetra fluviatilis, the organs prone to rapid disintegration but preserved in the specimens of Mesomyzon include: branchial cartilages (11 days), pericardiac cartilage (135 days), branchial lamellae, chondrocranium, and otic capsules (207 days) (1,2). This combination would place the adult specimens of Mesomyzon between the decay stage 1 (loss of branchial cartilages) and 2 (loss of kidney) (1,2). In specimens of Mesomyzon, the external organs such as the epidermis and myomeres are preserved so well that they obscure internal structures. Therefore, it is difficult to constrain the morphology of the skeletons and visceral tissues in this taxon. This is not the case in BHI 6445. Like in typical vertebrate fossils from the Cenomanian limestone of Hâdjula (5,6), the soft integument is only discerned at the outline, perhaps within a decay halo, which allows delineation of internal structures. These observations based on decay sequences of modern relatives cannot be assumed to replicate the taphonomy of fossil taxa precisely (7). However, these comparisons indicate: (a) the tissues that tend to be lost relatively early post-mortem are non-equivocally preserved in BHI 6445 (e.g., intestine, branchial pouches, keratin); and thus (b) taphonomic artifacts are unlikely to explain the presence of myxinoid synapomorphies (e.g., posteriorly displaced branchial pouches) in BHI 6445 or the absence of characters diagnostic to other known vertebrate lineages.
Paleoecological implications remain unclear for the occurrence of a hagfish in Hâdjula. The Cenomanian limestone of the locality has been interpreted as a mass-death assemblage of shallow, coastal, marine fauna of an inter-reef basin on the carbonate platform (5,6,8) -seemingly an unexpected environment in which to find a hagfish. Living hagfish generally inhabit deep (> 400 m), high-salinity (> 30 ppt), low-temperature (< 20 ºC) regimes, especially at low latitudes (9). However, they may transiently occupy benthic habitats shallower than 50 m (9). If similar ecological constraints applied to Tethymyxine, it would suggest that the type specimen of Tethymyxine does not represent a resident population in the Cenomanian of Hâdjula. However, it is difficult to compare the occurrence of Tethymyxine with the ecology of modern hagfish in the absence of precise paleoclimatic estimates or geochemical indicators for local environmental conditions.

A2. Provenance
Holotype of Tethymyxine tapirostrum (BHI 6445) was discovered in the Cenomanian strata ( keV (flux ~10 9 photons s -1 ) and a beam diameter of 50 µm defined by a pinhole. Fluoresced x-rays were detected using a single element Vortex silicon drift detector. SRS-XRF maps from SSRL were processed from the raw detector count raster files using a custom MATLAB script that converted the data array into 8 bit tiff images clipped at various contrast percentiles. Image subtraction was performed using ImageJ (13), and the image correlation was completed using the CorrelationJ plugin.
Energy dispersive spectra for quantification were obtained from single spot locations (50 µm spot size) for 100 live seconds. All EDS spectra were fitted using PyMCA (14) from fundamental parameters of the experiment using a Durango apatite (fluoroapatite) mineral standard with known element concentrations for calibration. 2σ errors on concentration were calculated using the standard deviation of peak area for each element output by PyMCA. The concentrations of each element are an average of 3 individual EDS spectra taken within a few hundred microns of each other on the same specimen.
The results from SRS-XRF were analyzed primarily through spatial distribution of trace elements (Figs. S3, S4) (15). Several elements have similar concentrations in the fossil and the matrix.
The Ca signal appears relatively reduced throughout the fossil tissue compared to the high Ca content of the embedding limestone matrix. Thus, absolute Ca contents may be high in the tissues, but it is difficult to contrast specific tissues against the background on the basis of distributions alone. In the case of S, the spectrum is clearly different between the preserved tissues and the glue that shows only inorganic S (Fig. S4). The inorganic S and other organic S species (with peak energies equivalent to theoretical values for methionine sulphoxide, sulphonate, and cysteine) in the matrix are oxidation products diffused away from BHI 6445. Higher S levels in the tissues relative to the matrix (Table S1) imply that mass transfer of S was from the fossil outwards. However, spectroscopy shows relatively high levels of organic S in the matrix as well, which is a function of the biogenic nature of the Hâdjula limestones. The XANES spectroscopy confirms that the organic S species present in both the matrix and fossil are different and requires further detailed study via this method to quantify the compositional variance.
The curatorial artifacts (glue and paint) can be easily identified in SRS-XRF, highlighting potential advantage of applying this method to fossils. An 'N-shaped' repair in the center of the specimen is highlighted by the glue, which showed elevated levels of Ti, V, Mn, and Fe. The distributions of Ni, Cu, Zn, P, S, As and Hg were predominantly controlled by soft tissues. These results are consistent with the observation that Cu, As, Fe and Hg naturally accumulate in the tissues of extant hagfish (16). In particular, hagfish are predisposed to hyperacumulate Hg. As for Ni, the living hagfish Eptatretus stoutii takes up this element via a high affinity-low capacity transport pathway, which mainly accumulates the element in the brain, gills, and heart (17). The high levels of P and S in BHI 6445 may be attributed to the presence of polysulphate peptides in the skin (18). Thus, the levels of these elements observed in BHI 6445 are expected for a myxinoid. Although the concentrations of Hg were below detection limits on a single point, the SRS-XRF maps indicate the presence of this element. A cadaver decay island appears to surround BHI 6445. This decay halo may be due to the mass-transfer of elements from the organism to the embedding matrix. The fossil still has elevated levels of several elements (P, S, As, Cl, Zn and Cu) relative to the matrix. Fe distributions also indicate a small decay halo. Data from SRS-XRF are deposited at DOI: 10.6084/m9.figshare.7545002
A treatment of miRNAs as discrete characters (presence/absence) favors cyclostome monophyly over paraphyly, as hagfish and lampreys share at least four miRNA families unique to them (34). However, the phylogenetic utility of presence/absence of miRNA families has since been questioned (42). In the analysis by Heimberg and colleagues (34), sampling errors were not considered because non-detection of expression in samples was interpreted as the absence of the miRNA family altogether. Furthermore, secondary loss of miRNA is common across the metazoan tree. Heimberg and colleagues (34) presented a tree in which all secondary losses of miRNA were mapped outside the stems of cyclostomes, gnathostomes, and vertebrates. The models incorporating sampling errors and secondary losses did not corroborate such miRNA-based trees (42). Therefore, cyclostome monophyly remains under question when the datasets contain standard presence/absence data.
In comparison to phenotypic data, molecular datasets have almost always supported monophyly of cyclostomes (41,(43)(44)(45)(46)(47)(48)(49)(50)(51)(52). Cyclostome monophyly is a topology predicted for long branch attraction, so this is an expected result of a molecular-based analysis (41). The consistency of molecular inferences is not to be confused with additive reinforcement of the topology (41). Nevertheless, cyclostome monophyly has gained wide acceptance to the extent that recent phenotype-based analyses use monophyletic cyclostomes as a topological constraint (23,28,32,33,35). Such a constraint imposes serious theoretical implications to interpreting the resulting trees. For these reasons, cyclostome paraphyly has not been ruled out entirely (53).
For the new attempt including Tethymyxine in the dataset, both parsimony and Bayesian analyses were performed. The morphological dataset is common among all analyses. It contains 52 taxa (Table S2) and 168 characters (Part E. List of Characters). Rationales for taxon and character sampling are discussed in detail in Part D. Character and Taxon Sampling. The purpose of combining parsimony and Bayesian analyses is to identify robustly supported clades. Parsimony and probabilistic methods often result in trees of different shapes and resolutions even using the same morphological datasets (54,55). The debate is ongoing about which method outperforms others, and which method should be favored (56)(57)(58)(59)(60)(61)(62)(63). For our analyses, it is critical to avoid confusing those two questions. Bayesian methods tend to be more accurate than parsimony, but parsimony appears to be more precise (greater resolution) (58,59). Probabilistic methods require proper estimates of parameters or priors (54,64), which remains challenging in cyclostomes.
The factors to consider for our dataset are: (a) it contains a large proportion of taxa that are highly incomplete (Table S2) in morphological datasets impact the performance of probabilistic methods remains unclear (54,65).
Under parsimony, however, contingency coding has predictable outcomes (66). Therefore, we used maximum parsimony as a primary line of phylogenetic analyses, and ran Bayesian analyses to highlight areas of agreement and disagreement with the results of the parsimony analysis.

B2c. Bayesian analyses
For Bayesian analyses, we used MrBayes ver. 3 (Fig. S6) using tree priors. Some of these nodes were given strong priors on the basis of (a) consensus of molecular clock estimates and (b) other constraints (e.g., Northern and Southern Hemispheric clades of lampreys were encouraged to diverge from one another before the complete separation of Laurasia and Gondwana). The BEAST analysis was run over 10 million generations, and MCC tree was selected for median heights.
The position and membership of the anaspid clade is unconventional in this analysis. Anaspids have been placed on the stem of gnathostomes in most previous analyses (23, 26-28, 32, 33, 35, 36). In this analysis, euphaneropids -or 'naked' anaspids -(Euphanerops and Jamoytius) are nested within the clade of 'armoured' anaspids (Birkenia, Rhyncholepis, and Lasanius). Achanarella, Ciderius, and Cornovichthys were often compared with euphaneropids anatomically but found in a polytomy at the base of vertebrates in the previous analysis (32). These potential euphaneropids form outgroups of that clade. It takes five additional steps to move the clade (preserving all other topologies) to either the stem of gnathostomes or that of vertebrates. However, it is two steps away to have one or more of these anaspid taxa outside cyclostomes. This instability is expected given that many of these taxa are incompletely preserved. The stem cyclostome status of euconodonts is consistent with some of the recent analyses (28,33).
Mature chondrocytes that are hypertrophied to the diameter of approximately 50 µm (101:1) and organized in pairs (102:1) unite myxinoids and petromyzontiforms, but these two states also occur in Euphanerops (77). With Euphanerops nested among anaspids on the cyclostome stem, these two characters are constrained to the total cyclostome node (Table S3).

C2. Bayesian Inferences
MCMC search of the morphological dataset including 52 core taxa (retained + new;

C3. Morphological Support for Cyclostome Monophyly
Cyclostome monophyly has never been supported parsimoniously by morphological data before this analysis. This topological change is attributed to enhancement of contingency coding and maximum inclusion of putative fossil cyclostomes (both detailed in Part D. Character and Taxon Sampling).
When the matrix was re-scored without considering character contingency, cyclostomes formed a grade where myxinoids ((myxinoid crown + euconodonts) + Gilpichthys) became nested outside the clade of petromyzontiforms and gnathostomes under strict consensus of 3198 most parsimonious trees (Fig.   S8a). This is a classical position of myxinoids in the previous phenotype-based cladistic analyses.
Under contingency coding, the consensus trees from the parsimony and Bayesian analyses (Figs. S6 and S7) corroborated phylogenetic inferences based on molecular data. In addition, they provide topological resolution for some controversial fossil taxa. Unexpectedly, unambiguous character changes at the total and crown nodes of Cyclostomi did not include many structures considered synapomorphic to cyclostomes such as lingual apparatus and velum (37,38) unless optimized under ACCTRAN (Table S3: Cyclostomi). These structures have relatively low preservation potentials in fossils (1,2,78), and the characters are uninformative to parsimony as they cannot be compared outside cyclostomes (discussed in Part D. Character and Taxon Sampling). The contingency coding ruled most characters related to biomineralization inapplicable among crown cyclostomes, and redefined characters previously considered simply absent in hagfish. Thus it prevented myxinoids from slipping stemward, and the presence of several characters with relatively high consistency index (e.g., 161:1: anterior shift of postotic myomeres; CI=1.00) united them with petromyzontiforms.
The stem cyclostome status of anaspids and euconodonts implies that living cyclostomes lost the ability to mineralize their skeletons secondarily. When character contingency was not considered (thus biomineralization was implicitly weighted), these topologies were not recovered (Fig. S8a).  (80). If this line of inference is correct, the innate potential to mineralize skeletal matrix may have existed as a crown-vertebrate trait.

C4a. Analysis of characters for crown cyclostomes
The parsimony and Bayesian analyses suggest Tethymyxine is a crown myxinoid, sister to Rubicundus.
It still remains possible that the barbels were misidentified. Anatomically, the connection with the anterior tentacular cartilage (Fig. S1) makes a compelling case that the identified barbels are real.

C4b. Analysis of characters for conodonts
Several characters scored for conodonts may be interpreted differently (detailed discussion in Part E. Conodont apparati were once compared to hagfish tooth plates based on detection of amelogenin in the latter (82). No morphological evidence was presented, and a histological comparison reveals no similarity between the two structures (83). A spectroscopic analysis recently suggested keratinous residues in conodont elements (84). However, nothing is known about morphology of the structure that consisted of keratin. Therefore, the character for keratinous teeth is coded as absent in conodonts conservatively (141:0). Conodont feeding mechanics has been compared to the lingual apparatus of living cyclostomes (85,86). In the absence of evidence for skeletal and muscular components of the lingual apparatus, however, this comparison could be interpreted as an implicit resurrection of a comparison between conodont elements and hagfish keratinous teeth.

List of Characters
For interpretations of the preserved structures that were questioned originally in this analysis, reversing these character scores ( S8c). Under this scheme, euconodonts and Gilpichthys remained on the myxinoid stem. Therefore, any particular assessment of individual character scores does not seem to impact the topology of euconodonts greatly.

C4c. Analysis of characters for Pipiscius
Pipiscius is another taxon that we coded conservatively. Although consistently reconstructed as a lamprey-like animal (87)(88)(89)(90), an alternative view compared the taxon with Xidazoon, a Cambrian vetulicolian (91). A survey of the list of synapomorphies ( with Pipiscius nested in that polytomy (Fig. S8d). Gilpichthys was resolved in a polytomy with myxinoids and petromyzontiforms at the crown cyclostome node. In anaspids, 'naked' anaspids formed a clade to which an immediate outgroup is Lasanius, followed by the clade of Birkenia and Rhyncholepis. This secondary analysis predict that further evidence for the characters coded conservatively in our analyses would resolve Pipiscius as a stem petromyzontiform.

C4d. Analysis of characters for Gilpichthys
The petromyzonform position of Gilpichthys (Fig. S6) is also intriguing, as this taxon has always been compared to hagfish (87)(88)(89). However, the myxinoid affinity is based on the lack of lamprey-like characters and not on the presence of characters diagnostic to myxinoids (Table S3). The parallel anterior structures were interpreted as keratinous tooth plates (141:1), but this occurs among petromyzontiforms. In addition, Gilpichthys can be scored for only a small proportion of characters (22.6%). Therefore, the position is more sensitive to the inclusion/exclusion of the characters coded for Gilpichthys than to interpretations of the characters preserved.

C4e. Analysis of characters for euphaneropids
Similar arguments can be made about Achanarella, Ciderius, and Cornovichthys. These taxa contain missing or inapplicable entries for 76.2-79.8% of characters. We provide justification for individual character scoring in Part E. List of Characters. As for the first three (Table S3), character states are similar to Euphanerops and Jamoytius for unambiguous and optimized synapomorphies at the major nodes (Table S3). Recently, an assessment of taphonomy at the type localities suggested Achanarella and Cornovichthys as different ontogenetic stages of an euphaneropid (92). Merging these two taxa, strict consensus of the most parsimonious trees (n=28435) collapsed all internal nodes within anaspids except for the clade of the composite euphaneropid and Ciderius, and most internal nodes of petromyzontiforms to collapse into a polytomy at the crown cyclostome node (Fig. S8e). When Achanarella, Ciderius, and Cornovichthys were deleted from the dataset, other anaspid taxa were nested in a polytomy (Fig. S8f).
The overall morphology suggests that Achanarella, Ciderius, and Cornovichthys are closely related to Euphanerops and perhaps to Jamoytius. Nested outside the clade birkeniids + euphaneropids However, the gut trace above this fin suggests that the anus was behind the ventral fin. share several important characters with crown vertebrates, including the well-developed sensory capsules, overall head configurations, and pharyngeal and axial skeletons (Table S3). They consistently lack most other diagnostic character states at the internal nodes within the crown group of vertebrates, or are not preserved with them (Table S3). One exception is Haikouella, which was coded as lacking neural crest-derived skeleton (1:0) and endoskeletal fin supports (83:0). Haikouichthys and Metaspriggina have skeletal bars in the pharynx, but were not coded for neural crest-derived skeletons (1:?) in the absence of other correlates of neural crest (e.g., 3:1, distinct prechordal head) and with the mesodermally derived pharyngeal cartilages in cephalochordates (93). The pharyngeal region of Myllokunmingia is not preserved well enough to assess this character. Haikouella -coeval with Haikouichthys and known from numerous well-preserved specimens (94) -still has no evidence for these elements, or any other skeletal elements known to be derived from neural crest in modern vertebrates. The character 'fin supports' was coded following the same logic. Changing these character scores in Haikouella to unknown (1:?, 83:?) resulted in an identical topology of strict consensus tree with Fig. S6.

C4g. Questionable myxinoid affinity of Palaeospondylus
Palaeospondylus was only included in secondary analyses. This problematic taxon has been posited as a stem myxinoid, stem petromyzontiform, jawless stem gnathostome, placoderm, chondrichthyan, teleost, or dipnoan/amphibian larva -but no hypothesis has been tested in a rigorous cladistic analysis (95)(96)(97)(98)(99). A recent reconstruction of Palaeospondylus as a stem myxinoid (95) is certainly provocative but contains some internal inconsistencies (100). The comparison is tenuous for some of the characters, such as: (a) the purported nasal capsule basket fused to the main palatal element; (b) the purported velar cartilages as mineralized, displaced elements; (c) the purported lingual apparatus being a bilaterally paired structure; and (d) otic capsule, which has three semicircular canals like jawed gnathostomes (100,101). Like many other problematic taxa, even the coarsest classification is difficult because Palaeospondylus does not exhibit multiple characters that clearly falsify alternatives. As such, we used two coding schemes. (A) The cyclostome model was coded on the assumption that Palaeospondylus was a cyclostome (but not necessarily a myxinoid; excluding internal inconsistencies from character coding). (B) The gnathostome model was coded on the assumption that it was a gnathostome (but not necessarily jawless or jawed, nor specifically as placoderm, chondrichthyan, actinopterygian, or dipnoan).
When Palaeospondylus was coded on the assumption that it is a cyclostome, internal nodes of gnathostomes were collapsed into a polytomy at the crown vertebrate node (Fig. S8g). Other 'ostracoderms' were found in the cyclostome stem. Palaeospondylus was nested within anaspids in a polytomy with Euphanerops. When Palaeospondylus was coded on the assumption that it is a gnathostome, the taxon was still found as a sister taxon to Euphanerops. Under strict consensus, anaspids migrated to the gnathostome stem as a basal grade, whereas cyclostomes formed a clade (Fig.   S8h).
However, Euphanerops and Palaeopondylus are disparate from each other in suites of characters except for the combination of two characters (101:1, 102:1) -which code for large size and paired organization of chondrocytes. So these trees alone do not support or reject any of the multiple hypotheses proposed for the affinity of Palaeospondylus. In the very least, the quantitative analyses failed to corroborate the myxinoid hypothesis.

C4h. Exclusion of Tullimonstrum
Tullimonstrum is another problematic taxon recently reconstructed as a stem petromyzontiform (36) or as a vertebrate (102). For this taxon, a reanalysis questioned its membership as a petromyzontiform and the coding responsible for the placement (103). That reanalysis highlights the need for critical evaluation of the petromyzontiform or vertebrate hypotheses of Tullimonstrum against its alternative positions in protostomes (such as arthropods and molluscs). Soft tissue traits in Tullimunstrum have been interpreted variably to align with its proposed affinity, but rarely has evidence been presented to falsify particular hypotheses. Characters used to support the vertebrate or petromyzontiform affinity (36) can be interpreted differently (100,103). These include those interpreted as arcualia, myomeres, or branchial pouches, proposed organization of the feeding apparatus, and number and arrangement of the structures interpreted as tectal cartilages.
Coding Tullimonstrum in our dataset similarly to the scheme B of Sallan and colleagues (103) (see Supplementary Data File 3), our preliminary parsimony analysis found it on the petromyzontiform stem, collapsing the total petromyzontiform node with Gilpichthys. This analysis did not test sensitivity of the character coding or sampling. Rather than supporting the petromyzontiform or vertebrate affinity, the preliminary result highlights the degree of care that it must take to set a comparative framework for such a puzzling animal. A hypothesis cannot be falsified with a dataset sampling only one of the potential groups, and a resolved topology does not justify that choice of comparative framework. At this time, no single cladistic dataset available can test the full range of possible affinities for Tullimonstrum. So the taxon is not considered further in this paper.

C4i. Concluding statements for secondary analyses
Based on a number of primary and secondary analyses, the topology presented in Fig. S6  The fossil taxa tended to be coded conservatively in this analysis. However, modifications to individual character scores did not impact the overall topology significantly. A review of justifications for the chosen character scores indicates that no one measure fits all when multiple conflicting interpretations exist for the characters. Sometimes one interpretation was favored, whereas other times the character coding was compromised into equivocal state as unknown or inapplicable. One taxon may be coded using different standards of evidence from one character to another, and standards of evidence may differ from a taxon to another in the same character. These decisions were made on case-by-case basis, and are discussed in individual character descriptions (Part E. List of Characters).

D1. Sampling Strategies, Overview
The character list and data matrix used for this study were mainly derived from previous analyses (19-21, 23-29, 32-36, 105). Primary purposes of our analysis are to resolve the phylogenetic position of Tethymyxine and to test cyclostome relationships. Secondarily, those of putative stem cyclostomes and stem vertebrates may be affected by addition of new characters and taxa or re-interpretation of the existing characters. With these intentions, we constructed the dataset to (a) synthesize datasets from the recent analyses (32,33,35,36) in character and taxon sampling and (b) increase character and taxon sampling as necessary. information. All characters included in the CMC, MSL, GDS, and/or KD datasets were considered. As a general rule, coding in this dataset reflects the latest scoring so that the GDS and KD coding supersedes the MSL or CMC wherever they disagree. We supplemented this initial dataset with (a) characters from other past analyses (27,29,34) and (b) wholly new characters. Each character in the list is denoted by the latest authority that defined it.
We edited the compiled character list extensively to: (1) revise character definitions; (2) revise character coding; and (3) eliminate parsimony-uninformative characters such that at least two states provide grouping information within a character. Each of these decisions is accounted for in 4.3 Character Sampling and in the notes added to each modified character description (Part E. List of Characters: these characters are indicated as definition modified or coding modified). Most revisions to character definitions and coding were made to reorganize hierarchically related character states through non-additive binary coding and contingency coding (66). The CMC dataset (35) and its subsequent revisions (32,33,36) already consist mostly of binary characters and contain contingency coding for 6-9% of all scores (Fig. S5A) Following these previous efforts, we enhanced the coding strategies (1)(2)(3) further. An enforcement of the reductive and contingency coding strategies is necessary as phenotype-based cladistic analysis of cyclostomes and gnathostomes has been criticized for favoring absence of derived states over loss or degeneracy of characters (22,34,37,41,88,89,(106)(107)(108).
We followed the GDS analysis in using maximum parsimony as a primary method of phylogenetic reconstruction and using Bayesian analysis as secondary. Parsimony has predictable outcomes for optimization of non-binary additive and contingency coding strategies (66). On the other hand, these coding methods may affect Bayesian inferences computationally, but precise impacts are unknown. Although parsimony-uninformative characters are known to contribute to Bayesian inferences, such characters were still eliminated from the dataset to simplify the analytical pipeline, because: (a) non-additive and contingency coding strategies would require re-coding the existing characters that are contingent upon or related to the uninformative characters added back in; and (b) it is beyond the scope of the present study to sample unique character states exhaustively among these deep chordate lineages, at which point the character sets will no longer be reciprocal between parsimony and Bayesian analyses. Therefore, we optimized the dataset for a maximum parsimony analysis first to generate the shortest primary phylogenetic hypothesis, and then subjected the same dataset to a Bayesian analysis to test for congruence and robustness of phylogenetic inferences supported by parsimony. and locality-specific trends in taphonomic bias (26,28,32,103) to reduce stemward slippage of softbodied taxa (78,109,110), conforming the analytical strategy in the recent analyses.

D2. Excluded Characters
Characters were excluded on the following basis: (a) definition is unclear; (b) character is parsimonyuninformative, or does not contribute to resolving hagfishes or lampreys (if each was treated as a natural clade) in a parsimony analysis; and (c) characters duplicate the same phenotypic variations.
Characters in category (b) may have been typically coded in previous analyses as primitive ('0)' for chordates and hagfish, and derived ('1') for lampreys and gnathostomes. Instead, many of these characters were coded for contingency as inapplicable ('-') for chordates, 0 for hagfish, and 1 for lampreys and gnathostomes. In the latter coding scheme, the character does not contribute to resolving cyclostomes parsimoniously as a clade or a grade.
CMC (Conway Morris and Caron, 2014) #5 (adenohypophysis, simple versus complex): definitions are unclear. This character is parsimony-uninformative unless coded for invertebrate chordates, which lack the system at anatomical levels.
Therefore, the outgroups would be coded as inapplicable, whereas all living vertebrate taxa would be scored as present. This distribution does not inform cyclostomes.
CMC #20 (semicircular canals, absent or present): cannot be coded for the outgroups that lack an otic capsule (=parsimony-uninformative).
CMC #33 (endodermal branchial lamellae, absent or present): parsimony-uninformative when coding for hagfish is revised from absent to present.
CMC #34 (branchial lamellae with filaments, absent or present): parsimony-uninformative when the taxa lacking branchial lamellae are coded as inapplicable for this character.
CMC #36 (oral hood, absent or present): this character is redundant with the oral funnel/disc after re-coding. Cephalochordates do not have an oral hood readily comparable to lampreys. The prominent hood-like snout in lampreys arises from the posthypophyseal process anterior to the nasohypophyseal canal. The developmental attribute of this morphology is described in another character (#66, this analysis).
CMC #63 (midline retractor muscle and paired protoractor muscles, absent or present): the definition does not provide accurate description of the morphology. This character applies to both hagfish and lampreys (although the former was originally coded as absent), but in both lineages there are multiple retractors (38,111). The character is inapplicable to those without a cyclostome-like lingual apparatus because the 'protractors' and 'retractors' cannot be compared with any other oropharyngeal structures outside cyclostomes. Once they are coded as such, the character is invariable.
CMC #68 (neurocranium entirely closed dorsally, absent or present): parsimony-uninformative when re-coded. In the extant gnathostomes, the neurocranium is closed by: (a) dermal skull roof (cranial vault; derived from neural crest and mesoderm in various combinations) and/or (b) extension of chondral elements (occipitals). These two states cannot be confused.
CMC #85 (scales/denticles/teeth composed of odontodes, absent or present): this character is constant after re-coding. Odontodes assume mineralized dermal skeleton, dentine, and pulp cavity, but these attributes are already described in the existing characters. Therefore, the taxa lacking dentine or mineralized dermal skeleton altogether cannot be scored for this character and are inapplicable. All known taxa with mineralized dermal skeleton and dentine have odontodes by definition (coded as present). So no taxon can be coded as absent. In this analysis, character #115 describes monodontodes versus polyodontodes as contingent on the presence of dentine (and therefore of odontodes).
With respect to ambient salinity that differs among taxa (e.g., freshwater lampreys versus marine hagfish), the character may be modified to contrast osmoregulator against osmoconformer, those with kidneys against those without, or those with particular ion channels against those without. However, it is difficult to formulate specific characters on different modes of osmosis because comparative studies emphasized the lack of physiological traits in hagfish that are otherwise shared across gnathostomes (19). Hagfish may be truly primitive in physiology or secondarily specialized, but this cannot be meaningfully assessed in a cladistic context without sufficient character-by-character comparison with anadromous lampreys and invertebrate chordates. because neither the notochord nor axial musculature is retained post-metamorphosis.

D3. Included Characters
The characters encoding presence/absence of placode-derived structures (adenohypophysis, nasal capsules, eyes, otic capsules, lateral line) in vertebrates cannot be decoupled from the presence of ectodermal placodes. Assigning the inapplicable status to taxa lacking neurogenic ectodermal placodes (hemichordates and cephalochordates) forces all such characters to become parsimony-uninformative.
Nevertheless, these characters are coded as absent for both outgroups and retained in the present dataset. This is because: (a) functional or anatomical homologues of these sensory/secretory structures have been proposed in vertebrate outgroups independent of the presence/absence of placodes (119-124); (b) the emergence of neurogenic ectodermal placodes is not necessarily coupled to the evolution of one particular sensory capsule (e.g., tunicates have placodes but none of vertebrate-like sensory capsules) (125)(126)(127)(128), so these characters vary independently from one another; and (c) some putative stem vertebrates may be argued to possess or lack one or more of these sensory capsules that are decay resistant in the living analogues (1, 2, 78).
As discussed in the rationale for deleted characters, those that can be coded only for several extant taxa under our scheme tend to be parsimony-uninformative (constant, or non-polarized). One exception to this tendency is the presence of internal taste buds (#43, this analysis) -oropharyngeal chemoreceptive structures innervated by gustatory nerves (facial, glossopharyngeal, and vagus nerves) (129,130). Coding for presence/absence of the internal taste buds (HSM #27), hagfish, invertebrate chordates, and hemichordates would be scored as absent (34). However, these taxa are not equivalent in the state of absence. Hagfish have a unique chemosensory structure called Schreiner organ, which resembles internal taste buds. The organ is innervated by the trigeminal nerve and not contingent on the purinergic signaling (130,131). So this character may be modified to accommodate two states (internal taste buds; Schreiner organs). As Schreiner organs are identified in two hagfish species (Eptatretus stoutii and Myxine glutinosa) (131), the character state may be useful as a myxinoid synapomorphy even if it does not contribute to the resolution of cyclostome mono-/paraphyly.

Part E. List of Characters
See Abbreviations for previous datasets above for the identitites of datasets abbreviated here.
The original definition has been modified from the presence of neural crest to that of the occur as a mesodermal derivative in cephalochordates (93). Tunicates were originally coded as having neural crest (35), but they lack such typical neural crest derivatives (140). Although evidence points to the presence of neural crest-like cell lineages in tunicates (141,142), the multi-potent differentiation of neural crest including skeletal derivatives is still unique to vertebrates.
The presence of neurogenic ectodermal placodes in tunicates (122,(125)(126)(127)(128)143) suggests that the sensory fates of these ectodermal thickenings constitute a synapomorphy of olfactores (and the constituent cell types and gene expressions may have their evolutionary origins deeper still).
For fossil taxa and those for which embryos are not known, the presence of sensory capsules was used as an indicator.
One important prediction of the New Head Hypothesis is that the evolution of neural crest gave rise to the prechordal cranium (119,144,145). Indeed, all living vertebrates exhibit a prominent prechordal cranium to house the nasal and adenohypophyseal organs and encapsulate the forebrain. On the other hand, Haikouichthys and Metaspriggina have a notochord extending well frontally, and the nasal capsules are tucked between the eyes, whereas the mouth sits at a more posterior level (35). The character cannot be scored in hemichordates (no notochord) or

tunicates (no distinct cephalization). Euphanerops is superficially similar to the condition in
Metaspriggina, but the presence of midline cartilages anterior to the notochord indicates a prechordal cranium (77). Arandaspids have the eyes exposed at the anterior end, with the nasohypophyseal canals tucked between them (146). However, it is more plausible to interpret the position in light of heterostracan anatomy, where the optic tectum extends anteriorly.
Heterostracans tend to have the eyes exposed in anterior positions, but internal casts indicate that they had a prominent prechordal cranium (88,(147)(148)(149). Hemichordates are coded as inapplicable because they lack a fully closed, axially elongate neural tube. Gene expression patterns indicate cyclostomes do have the rhombic lip and medial ganglionic eminence (150). Previously, a cerebellar primordium has been considered present in lampreys but absent in hagfish (151), but new evidence (150) reveals that (a) brain development in hagfish parallels that of gnathostomes in gene expression patterns more closely than that of lampreys; and (b) cyclostomes do exihibit similar brain regionalization patterns at the level of gene expression. Cyclostomes still lack a clearly demarcated cerebellum with corpus cerebelli, so the original definition was modified in accordance with the analysis by Khonsari and colleagues (29). Non-vertebrates lack a tripartite brain (#4, this analysis). They are coded as inapplicable (-) for this character. This character is contingent on having a vertebrate brain and cranial nerves (#4, this analysis).
In the galeaspid Shuyu, the roots for V1+0 and V2+3 are well separated (152) so the ganglia were likely independent as well. In osteostracans, these nerves share a narrow root under the myodome of the orbital cavity (153,154) so the ganglia were likely fused. One conspicuous example is seen in Belonaspis (MNHN SVD 1005). It is difficult to assess this character in arthrodires, but the size and shape of the trigeminal canal are comparable to those in chondrichthyans (155)(156)(157)(158)(159), and they are tentatively coded as separated. This character is contingent on having a vertebrate brain and cranial nerves (#4, this analysis). The original definition in the CMC dataset concerned the presence of pretrematic branch in branchial nerves, where jawless vertebrates were coded as lacking the branch. Cyclostomes clearly have pretrematic branch in the glossopharyngeal and vagus nerves (160). The facial nerve, however, lacks the bipartite organization of pre-and post-trematic branches being separated by the hyomandibular pouch (29,161). What appears to correspond to a pretrematic branch is a split of the postrematic branch. The lack of the pretrematic branch in the facial nerve is also consistent with the lack of pseudobranch (gill-like folded epithelium in hyomandibular position) in cyclostomes, suggesting that the structure represents a derived state acquired in the stem of gnathostomes (115). 8. Spinal cord in cross section: 0, round; 1, flattened (CMC #9: definition modified).
Shape description was modified for clarity. This character supplements character #9 (ventral and dorsal roots united). Indeed, hagfish and gnathostomes are similar to each other for having the dorsal and ventral roots united (they are separate in lampreys). However, both roots originate at the intra-segmental level (medial to myomeres) in lampreys and gnathostomes, whereas the origin is at the inter-segmental level (medial to myosepta) in hagfish (162). To capture the full range of this variation, this addition to CMC #10 is required.
The Mauthner fibers are identified primarily by their position at rhombomere 4. Therefore, the character is inapplicable ('-') for outgroups without a tripartite brain (#4, this analysis).
The character is inapplicable to taxa lacking a pineal organ (#12, this analysis) and/or a skull (#3, this analysis).
This character is compound, as the state 2 assumes coverage by the dermis as well. However, the character is included in the current form as the state 2 only applies to a nested ingroup within the crown group Myxinoidea, which is the only group of taxa with covered eyes in this dataset. The character is contingent on character #26 (presence of eye).
The character is contingent on the presence of eyes (#26, this analysis). Euconodonts are typically coded as having extraocular muscles on the basis of the fibrous soft tissues preserved in the Carboniferous euconodont Promissum (172). This observation constitutes one of the prominent inferences for the vertebrate affinity of conodonts, but also has attracted controversy (27). Certainly, the extraocular muscles are a collection of individual bundles of muscles, whereas the supposed structure in Promissum shows no such organization. Two lines of evidence consistent with the original interpretation are the position close to the posited eye and the fibrous texture unlike typical cartilages (172). Alternatively, the tissues may be preserved in a more advanced stage of decay than assumed originally (22). In that case, it would be difficult to identify the tissue as anything more specific than remnants of cranial musculature.
Another possible interpretation is that the 'extraocular muscles' of Promissum represent a patch of mucocartilage-like supporting tissue. Mucocartilages in modern larval lampreys  This character explicitly refers only to the numbers of elements so as not to assume any one of multiple possible schemes of homology among these muscles a priori. A reference to number of elements (and not to interpretations of homology for the individual components) allows placoderms to be scored for this character.
Depending on the identification schemes, additional characters may be formulated to resolve ingroup relationships among gnathostomes, but this is beyond the schope of this analysis. In a brief summary, correspondence with the counterparts in crown gnathostomes is unclear for the four muscles innervated by the oculomotor nerve in placoderms. The anterior oblique (corresponding to inferior oblique in crown gnathostomes) is undisputed. The rectus inserting dorsally appears to correspond superior rectus topographically and probably received innervation from the dorsal ramus, but has been identified as internal rectus on the basis of its insertion dorsally to the anterior oblique (178). Problematically, identification of this muscle as internal rectus assumes either: (a) the superior rectus was lost and one additional muscle added in placoderms; or (b) the superior rectus independently evolved in lampreys and gnathostomes.
Transposition of the extraocular muscles is necessary no matter which assignment is followed -the internal rectus passes below the anterior oblique in lampreys, whereas it typically inserts dorsal to the inferior oblique in crown gnathostomes. Therefore, it appears most parsimonious to recognize the four muscles in placoderms as homologous to those of crown gnathostomes (anterior oblique [inferior oblique], internal rectus, inferior rectus, and superior rectus; the last probably being the only muscle innervated by the dorsal ramus). This character is contingent on the presence of extraocular muscles (#28, this analysis).
This shift of the oblique muscle correlates with the shift of another oblique muscle from anterior to inferior. This character is contingent on the presence of extraocular muscles (#28, this analysis).
Lampreys have an external and posterior rectus -only the external rectus persists in crown gnathostomes (retractor bulbi are tetrapod-specific condition). On the basis of the insertion scars, placoderms likely had two muscles innervated by the abducens nerve, although the homology of the second muscle to the posterior rectus remains unresolved (178). In osteostracans, a single myodome sits in the corresponding position, and it remains unclear whether one or two muscles attached here despite reconstructions typically depict two (179). It is scored as unknown ('?') in the present analysis. This character is contingent on the presence of extraocular muscles (#28, this analysis).
32. Eyes: 0, laterally placed (interorbital distance equal to width of head at that position); 1, close together near midline (interorbital distance substantially less than width of head at that position); 2, on prominent eyestalk (new character).
This character is contingent on the presence of eyes (#26, this analysis All characters concerning the inner ear anatomy are inapplicable to taxa that lack an otic capsule (#33, this analysis).  The absence of internal taste buds in hagfish should not be confused with that in non-vertebrate chordates and hemichordates, as the function is replaced by the unique epidermal structure Schreiner organs (innervated by the non-gustatory trigeminal nerve; not requiring purinergic signaling) (130,131). This is a specialization unique to hagfish and reported in multiple extant species. The implication is that internal taste buds and Schreiner organs are mutually exclusive, so these are treated as separate states in a single character. Alternatively, this character may be coded in two characters: (a) end chemosensory organs innervated by cranial nerves in head: 0, absent; 1, present; and contingent on the presence, (b) end chemosensory organs: 0, internal taste buds; 1, Schreiner organs. However, the character (a) will be constant because the character cannot be coded for outgroups that lack cranial nerves.
This character potentially correlates with the presence/absence of the prechordal cranium and the posthypophsyeal/internasohypophyseal distance (#3 and #17, this analysis). However, states vary for this character primarily among those with a distinct prechordal cranium, and independently from the distance between the nostril and mouth. This character is inapplicable outside vertebrates as the preoptic head cannot be recognized in the outgroups. This character applies only to those taxa that score for anteriorly displaced branchial apparatus in the previous character (state 1 of character #45).
47. Branchial apparatus, displaced posteriorly such that prebranchial length is: 0, less than a quarter; 1, approximately quarter; 1, greater than a third of body length (new character).
This character applies only to those taxa that score for posteriorly displaced branchial apparatus in the previous character (state 2 of character #45). The original definition (branchial bars, external or internal) was modified to allow identification of states with respect to anatomical correlates. This character is inapplicable for those taxa lacking branchial lamellae (character #48, this analysis), and for Haikouella and Pikaia in which the branchial structures appear to have been exposed externally (183). Although the adorbital opening has been interpreted as spiracular in amphiaspidiform heterostracans and pituriaspids (115,186,187), this character is conservatively coded as unknown in both taxa. Beyond its position beside the orbit and otic capsule, little evidence exists for the hyomandibular identity of this opening. An alternative interpretation for this opening is a nasohypophyseal aperture (149). The amphiaspidiform condition is likely an independent derivation within heterostracans (88,115) because this clade is nested within the Heterostraci (188)(189)(190)(191)(192), and because the general condition among heterostracans is blind (0) for this character. Modifying the scores for heterostracans (0/1) and pituriaspids (1) did not affect the topology presented in Fig. S6. This character was evaluated with respect to dimensions of branchial pouches to ensure some independence from the previous character (#54, this analysis). For example, osteostracans have excurrent ducts extending posteriorly, but the space between the ducts remains roughly consistent with dimensions of the pouches. This is not the case in some taxa of hagfish, which score for both excurrent ducts extending posteriorly and their openings closely packed together (194). Multiple rows of external branchial openings occur in species of "Paramyxine" that are now considered as an ingroup nested within Eptatretus (70,194). The coding for euconodonts This character is contingent on the previous one (#56) and therefore inapplicable for those constrained to five arches supporting branchial lamellae. Among jawless vertebrates, the number of branchial pouches varies within and between lineages. In hagfish, the number is anywhere between four to fourteen (197). The range is similar among birkeniids (198). The range is greater among galeaspids from five to 45 plus (196). It is difficult to count the number of arches precisely in Euphanerops, but the number is at least 30 (77). Galeaspids and Euphanerops are unique among vertebrates in having substantially more than twenty branchial arches. So this number is used arbitrarily to distinguish the capacity to develop an exceptionally large number of branchial arches, and composite taxa were coded for the largest number that occurs within that lineage.
The previous two characters (#56, 57) described whether or not the number of branchial arches (pouches) is constrained at five and whether or not the number of the arches can exceed the count normally observed in the development of living vertebrates, respectively. These characters do not describe most variations in the number of branchial arches among jawless vertebrate lineages in which the number is not constant or tightly controlled (196). Among these lineages, five and ten each breaks the distribution into discrete ranges. Few (some hagfish species) have only four branchial pouches, whereas several have five (197). Several lineages have more than ten branchial openings, including arandaspids, some anaspids (Jamoytius and Pharyngolepis), and probably Cornovichthys and Achanarella (196,199,200). Living lampreys all have seven (76). A reexamination of the holotype of Priscomyzon (AM 5750) revealed at least eight and as many as nine branchial arches. The count in Hardistiella is based on Lund and Janvier (201). Hagfish fall anywhere in this range from four to fourteen although most have six to eight (197). The character is inapplicable to taxa that score for either a constant number (five) (#56, this analysis) or an exceedingly large number (>20) of branchial pouches/arches (#57).  The character is inapplicable for those with a highly depressiform profile (#82, this analysis) or those with parabranchial cavities (#52, this analysis). 61. Opercular flaps associated with branchial openings: 0, absent; 1, present (CMC #32).
Coding has been revised according to Gabbott and colleagues (32).

Branchial epithelium: 0, internal; 1, external (new character).
The suggestion of externally exposed branchial structures in Haikouella and Pikaia (183)  This character is contingent on the presence of mineralized integumentary skeleton (#113, this analysis). Even though inapplicable status ('-') is assigned accordingly, these character states necessarily correlate with micro-/macromeric integumentary skeletons. Nevertheless, the character is included because some variations do exist within and among lineages (e.g., anaspids). It is defined as an unordered and compound multistate character because each state is discrete from one another and because no two states can be reasonably grouped in exclusion of others. For example, birkeniids exhibit both states 0 and 3 (198). The order of character states does not reflect any discernible trend or logic of progression.

Position of mouth: 0, terminal; 1, subterminal (CMC #35; definition modified).
Mouth orientation is correlated partly with overall body profile (#82, this analysis), but position of mouth with respect to other cranial landmarks (e.g., nasohypophyseal canal) can vary independently of the overall body profile. 65. Epidermal oral cirri: 0, absent; 1, present (new character). 66. Postoptically derived ectomsenchyme anterior to mandibular arch gives rise to palatal structures that: 0, meet at midline under nasal/nasohypophyseal organs; 1, meet at dorsal midline anterior to nasohypophyseal organs and form a prominent oral roof (new character).
In vertebrates, three streams of neural crest cells populate the premandibular and mandibular regions (37,39,115,164,166). Among them, the postoptic stream gives rise to a posthypophyseal process (upper lip) in cyclostomes (39,164), whereas it forms the trabecular cartilage anterior to the adenohypophysis in crown gnathostomes (165,166,202). Although these structures differ in topology between cyclostomes and crown gnathostomes (due to a tripartite organization of the nasohypophyseal placode in the latter), the postoptic streams still If Tullimonstrum were to be included, the taxon cannot be scored for this character for a similar reason. The identity of putative tectal cartilages in this animal has been since questioned (103), and no unambiguous nasohypophyseal opening has been identified (36).
However, Haikouichthys and Metaspriggina may be scored provisionally for the character on the basis of the position of the nasal capsules, eyes, and mouth (35,163). Coding these taxa for this character potentially conflicts with the assessment for the characters about This character only applies to petromyzontiforms. The coding follows Gill and colleagues (72) and Renaud and colleagues (73). 71. Velar tentacles, papillae or tubercles: 0, absent; 1, present (new character).
This character only applies to petromyzontiforms. The coding follows Gill and colleagues (72) and Renaud and colleagues (73).

E3. Circulatory System
72. Multi-chamber heart: 0, absent; 1, present (CMC #38; coding modified). The original character (high blood pressure, absent or present) was vaguely defined. In that form, the character is redundant with the closed/open circulatory system (#74) and with the absence/presence of a multichambered heart (#72). The character was modified to refer to the specialized subcutaneous blood sinus present in hagfish. As the sinus extends the entire body length (collected both from the head and tail), the presence of this sinus can be ruled out for stem gnathostomes with a dermal head skeleton with internal impressions.

It is unknown ('?') whether the heart has multiple chambers in
Smooth internal surfaces of the dermal plates in heterostracans may be used as an inference for subcutaneous sinus underneath the dermal skeleton (88). This interpretation, however, is inconsistent with the role in epidermal intake and output that the sinus plays in living hagfish (206,207). A massive subcutaneous sinus is correlated with low blood pressure The character is inapplicable to those that lack lymphocytes (#78, this analysis). 80. Subaponeurotic vascular plexus: 0, absent; 1, present (CMC #44; coding modified).
The character is inapplicable to non-vertebrate outgroups.

E4. Fins and Fin-folds
81. Body forms, relative length: 0, less than five times the next largest dimension (height or width); 1, greater than five but less than ten times; 2, greater than ten times (new character).
To be conservative with effects of taphonomy and decay, maximum dimension is interpreted at the plane of preservation (so it is more likely to underestimate relative length than to overestimate). Admittedly, body profile is a poorly defined composite character but also constitutes one of few biologically informative composite traits that can be observed in poorly preserved early vertebrates.
The original character (fin ray support, absent or present) is modified to distinguish endoskeletal and exoskeletal (dermal) components of the fin skeleton from one another. In the original dataset, fin rays (exoskeleton) and radials (endoskeleton) appear to have been confused.
Contrary to the original coding, endoskeletal fin radials are present in hagfish ('1') (20,211,212). Haikouella is coded as absent ('0'). The exoskeletal component of the fin skeleton (rays) is parsimoniously uninformative when coded with contingency to mineralized exoskeleton. 84. Distinct dorsal fin: 0, absent; 1, present (CMC #45; coding modified). In comparison to Euphanerops (77,(213)(214)(215), Achanarella is coded for the presence of an anal fin because of the pronounced epidermal ridge anterior to the caudal fin (199). Cornovichthys -a larger euphaneropid from the same locality -has a prominent ventral midline fin. The gut trace above the fin suggests that it sat anterior to the anus, hence not an anal fin (200). See the description of secondary analyses (C4e. Analysis of characters for euphaneropids) for the impact of this and other character scores on the anaspid topologies. As for osteostracans, it is debatable whether the ventral lobe of the terminal fin represents a modified anal fin or constitutes a part of the caudal fin. This is reminiscent of the abnormal anal fin reported for a female of Petromyzon marinus (216). In this analysis, they are coded conservatively as absence of the anal fin.  coding modified).
The following changes were made to the MSL dataset based on personal observations of specimens: Euconodonta, Haikouella, hagfish, lampreys ('0'); euphaneropids and thelodonts ('1'); arandaspids ('2'). Tullimonstrum was not considered in this analysis, but it has no distinct lobe in this region ('0'). The character is contingent on the presence of bone (#96, this analysis). Two alternative coding strategies exist for this and the following character: (a) formulate one character distinguishing acellular against cellular bone or (b) formulate one character each for the presence/absence of acellular and cellular bone. The alternative (a) may be preferable in principle to not weight either of the characters; however, in many taxa acellular and cellular bones coexist (231,232), and both acellular and cellular bones distribute widely among stem chondrichthyans (acanthodians) and osteichthyans (134,(233)(234)(235). So these two tissue types should be treated separately as in the alternative (b). To make the character for acellular bone more specific, and to distinguish types of plywood-like bone in osteichthyans, the following character for the presence/absence of acellular bone is edited to refer specifically to lamellar acellular bone seen in fossil jawless vertebrates.  (77,97,180). This condition also occurs in soft cartilages of hagfish (111). Although such pairing organization broadly occurs in growing cartilages within and outside vertebrates (93,111,231), This character is contingent on the presence of mineralized skeleton (#95, this analysis). The identification of dentine in anaspids (33) is accepted tentatively in this analysis, although some inferences used by Keating and Donoghue (33) are insufficiently justified. For example, they refer to Smith and Hall (135) (237)(238)(239)(240)(241), and partly because little evidence justifies the assumption that two different types of dermal bone should not coexist in the same element. The association of enamel/oid and dentine would be a valid argument if the thin superficial layer is not an artifact of scanning but represents a true enamel/oid layer (230).

Chordal disposition
Furthermore, it is odd that tubules are lacking in the proposed dentine in birkeniids. Accepting their observations preliminarily, however, dentine is coded as present in birkeniids. Lasanius is coded as unknown for the lack of information.
It is possible to consider dentine to be tubular by definition. However, this typological issue is less of a concern than whether anaspids have a component of dermal skeleton laid out by odontoblasts or not. This character may be modified to "mineralized matrix of odontoblasts" with the same distribution of character states, and would still be open to the same discussion outlined in the previous paragraph. Deleting this character did not affect tree topology.
This character is contingent on the presence of dentine (#103). Spherical/globular dentine occurs in anaspids and conodonts among jawless vertebrates (23,33,242,243). Spherical mineralization similar to that in anaspids also occurs in galeaspids (237,238), but there is no further support that this tissue represents true dentine. The condition in arandaspids (244) is interpreted as tubular. As in the characters describing different types of bones, two alternatives exist for this and the following character: (a) formulate one character distinguishing tubular versus spherical dentines or (b) formulate one character each for the presence/absence of tubular and spherical dentines. The alternative (a) does not weight either of the characters; however, the two types coexist in conodonts and some crown gnathostomes. So these two tissue types should be treated separately as in alternative (b).
The original definition is modified to refer specifically to tubular dentine. Taxa lacking dentine are coded as inapplicable.
Given the diversity of dentinous tissues among early vertebrates, the original definition (mesodentine or orthodentine) is modified into three independent characters (#106-108, this analysis) that describe histological differences in multiple types of dentine at the level of odontoblasts. All of these three characters are contingent on the presence of tubular dentine (#105, this analysis; inapplicable to the globular/spherical dentine in anaspids). The present character distinguishes mesodentine and semidentine from other types of dentine. Different types of dentine may coexist in the same animal or within a lineage. Thus, they are coded on the basis of typical histological characteristics identified in that taxonomic unit. The character is contingent on the presence of dentine (#103, this analysis).
Conodonts are coded as having a dentine type somewhat comparable to mesodentine (23,242,245). Astraspis is considered having the grade of meta-to orthodentine (134) (coded as 0), although this assessment is at odds with interpretations of the canals invading from the pulp cavity (246,247). Thelodonts exhibit a diversity of dentine histology (88,134,217). In general, however, the canaliculi show polarized but irregular branching and spacing as in Turinia in the grade of meta-to orthodentine. Loganellia is coded as having the grade of mesodentine.
As in other characters coding for skeletal tissues, the original character is split into two so that one only refers to the presence/absence and the other describes monotypic versus bitypic. The presence of enameloid is accepted preliminarily in anaspids (33) and heterostracans (248).
Although thyestidians form a nested ingroup within osteostracans (250,251), it is more plausible to consider that the potential to secrete enamel/oid is conserved within osteostracans than to assume that enamel evolved secondarily. In a similar vein, euconodonts evolved enameloid independently from the rest of vertebrates (243) but this lineage is coded as present.
Although enamel as a tissue likely evolved convergently, it also remains unclear how many times enamel, enameloid, and enamel-like tissues evolved within vertebrates. As this analysis does not heavily sample taxa at lower taxonomic levels, this character should be coded as the potential to secrete enamel or enamel-like tissues rather than the distribution of the tissue within each lineage. Alternatively, the character may be defined more finely to differentiate the known types of enamel and enamel-like tissues, but this is beyond the scope of this analysis as these characters will be parsimony-uninformative in the taxon sampling of this dataset. The present character is contingent on the presence of dentine (odontodes) (#103, this analysis).
Given variations and overlaps in cell lineages and modes of mineralization to give rise to hard skeletal elements (135,137,139,231,233,253,254), it is difficult to formulate a character to distinguish skeletal elements by either of the criteria and score fossil OTUs on the basis of The character is contingent on the previous character (#112, this analysis) and is intended to discriminate the condition in taxa such as Lasanius and placoderms, which only have partial coverage of the trunk with mineralized scales/plates. 114. Odontodes: 0, monodontodes; 1, polyodontodes (CMC #108; coding modified).
In addition to contingency on the presence of odontodes (nested in the presence of dentine Euconodonts may be coded for this character (#114) and its contingent character (#127).
Tissues that compose the conodont 'teeth' (e.g., crown tissue, spheritic mineralization) appear to have evolved in stepwise fashion within the lineage (243). Perhaps for this reason, they were coded inapplicable for this character by Gabbott and colleagues (32). Nevertheless, the presence of these mineralized tissues and the pulp cavity qualify these elements morphologically as odontodes. Euconodonts are inapplicable for characters describing micro-/macromery (e.g., #129, this analysis) because they lack mineralized integumentary skeleton. Coding this character (#114) and its contingent character (#127) uncertain for euconodonts did not affect the strict consensus topology presented in Fig. S6. All taxa that lack dentine (#103, this analysis) were scored as inapplicable. Anaspids, thelodonts, and chondrichthyans lack the middle cancellar layer, but the latter two differ from anaspids in having the base as attachment and having a non-growing crown (88,134,198,217). These two variants should not be confused in a single state of the absence of the three-layerd exoskeleton. The calcium signature in the dermis of Jamoytius (28) is tentatively interpreted as a degenerate form of a typical anaspid condition of having a single tissue type forming a basal lamella and a superficial layer, but the specific morphology has not been described. This taxon is therefore coded as inapplicable. Galeaspids are also interpreted as having a basal lamella and a superficial layer (variably invaded by sensory canals), regarding calcified cartilages as secondary endoskeletal lining (237,238). The tubercles in this lineage consist of spherical mineralization that superficially resembles 'spherical dentine' of anaspids.
This character partly correlates with dentine characters (#104, #108, this analysis) but distributions do not overlap completely. This character only codes for the integumentary skeleton so that teeth and other exoskeletal elements are excluded. Furthermore, the superficial layer does not always consist of dentine. For example, galeaspids are not coded as having 'spherical dentine' (#104, this analysis), but the similarity with anaspids is accepted for this character as having a superficial layer of spherical mineralization (237,238). The coding for placoderms is based on a survey of previous works (134,(239)(240)(241)255). This character is contingent on the presence of mineralized exoskeletons (#112, this analysis).
As in the superficial layer, the original definition by Keating and Donoghue (33)  This character only applies to those that score for having a middle cancellar layer.
This character is contingent on the presence of a mineralized integumentary skeleton (#112, this analysis).
Shape of tubercles likely reflects mode of growth, whereas shape of scales may be influenced by other spatial factors (such as arrangement and density). This character is contingent on the presence of a mineralized integumentary skeleton (#112, this analysis). This character refers to calcified or ossified endoskeletal cartilages lining the dermal elements (entirely or partially), which occur in galeaspids, osteostracans, and most jawed gnathostomes.
Antiarchs have some endoskeletal components to the mainly dermal skeleton at the exoendoskeletal interface in the jaws, pectoral joints, and rhinocapsular element (221,257), although in general the dermal plates consist of exoskeletal components (240). The character coding does not discriminate macromery versus micromery, but is contingent on having a mineralized dermal skull and endoskeleton (#111, 129, this analysis). Thelodonts are coded as inapplicable, as no bones or calcified cartilages are known from these taxa.  (35,163). Myxinikela has the cartilaginous elements in the branchial region, which is connected to the neurocranial region by what appears to be collagenous structures (71,263). In hemichordates and tunicates this character is inapplicable.
The original definition of 'circumoral teeth' does not distinguish variants properly. For example, lampreys have multicuspidate piston tooth plates within the buccal cavity and radial circumoral teeth in the oral funnel, whereas hagfish have two pairs of multicuspidate tooth plates. Both were coded originally for the presence of circumoral teeth, but these variations should not be confused. Therefore, the criterion is whether the structures are housed within the buccal cavity or exposed periorally. Absence in jawless stem gnathostomes was evaluated on the basis of whether or not the perioral morphology would allow such structures. The ring of cuspidate plates in Pipiscius is interpreted as a perioral structure outside the buccal cavity, so the coding for this taxon is presence in the perioral region ('1') for this character but absence This character is contingent on the presence of perioral feeding structures (character #137).
Perioral plates and lip scales are present broadly among stem gnathostomes, but they are continuous epidermal structures. In contrast, the perioral teeth of lampreys are discontinuous.
The original character ('circumoral' teeth, present or absent) was split into two characters, one describing perioral structures (#137) and this character describing buccal structures.
The coding as present in Mayomyzon is based on FMNH FR5687. Myxineidus is coded as present for this character given recent evidence (264). This character is contingent on the presence of buccal feeding elements, which is described by the foregoing character (#139, this analysis). 141. Perioral/buccal feeding structure consisting of keratin: 0, absent; 1, present (CMC #57; definition modified).
Invertebrate outgroups are coded as inapplicable for this character. Gilpichthys and Pipiscius are coded conservatively as unknown ('?'). Geochemical comparison (36) suggests the proposed feeding apparatus in these taxa had a similar composition. This assessment also applies to Tullimonstrum, which was the subject of that paper (36). However, the comparison did not have a reference tissue that is clearly keratin from the same locality. Alternative coding and its effects are discussed in C4c. Analysis of characters for Pipiscius and C4d. Analysis of characters for Gilpichthys.
The original character (piston cartilage and apical plate, absent or present) only applies to lampreys. It was therefore redefined to include the lingual and dental apparatus of hagfish, as compared by Yalden (38). The character is inapplicable to those taxa in which no clear homologue of mandibular arch can be identified. Pipiscius is coded as absent, as its funnel-like arrangement of the circumoral teeth precludes a structure resembling the cyclostome lingual apparatus. Euconodonts have been suggested to have a cyclostome-like lingual apparatus (86), and this is functionally consistent. However, there is no anatomical evidence to indicate such a structure in a conodont. A potential piston cartilage is preserved in Euphanerops, but other components of the lingual apparatus are not (77). These taxa are coded conservatively as unknown ('?').
This character is not contingent on the presence of buccal tooth plates for two reasons: This character is incompatible with the character #140 because the transversely and vertically biting apparatus cannot coexist. Therefore, those taxa scored as present for the transverse biting apparatus are scored as inapplicable for this character. This character only applies to potential myxinoids. Euconodonts are inapplicable.

definition modified).
This character describes externally exposed, radially organized circumoral teeth. This character cannot be scored for taxa with oral plates or jaws. Pipiscius is coded as unknown for this character. Although the circumoral ring of cuspidate plates in this taxon superficially resembles the circumoral teeth of lampreys, it is organized in annular fashion (not radial) and embedded deeply within the oral hood as an externally open funnel. Each cuspidate plate is elongate and its basal tissue was probably unlike those of lampreys and hagfishes -which are organized as a cone and a cap (82,111,(265)(266)(267). 146. Circumoral keratinous teeth, number of tooth rows in lateral field: 0, three; 1, four; 2, five or greater (new character).
This character applies to lampreys only. For the terminology of the circumoral field, see Hubbs and Potter (74).
The original character (arcualia, absent or present) does not capture the diversity of sclerotomederived axial skeletons in vertebrates because the distribution of arcualia can be variably interpreted (268). Neural arches, centra, and haemal arches are the midline elements of the axial skeleton, and the centra consist of basidorsal, basiventral, interdorsal, and interventral ossification centers (162). These elements are distributed taxonomically as mosaics -lampreys have neural arches, whereas hagfish have the elements that can be interpreted as a haemal archlike structure anatomically (53), or as vestigial vertebrae (269). Euphanerops appears to have all elements as calcified cartilages (77). Therefore, this character is more broadly defined and followed by three characters that describe contingent conditions of the axial skeletons. These subsequent characters are inapplicable to those in which the axial skeleton is absent. The character definition has been modified to allow assessment based on the outline. The cartilages supporting the barbels in living hagfish are susceptible to decay (2). The barbels in Myxinikela have been interpreted differently because the outline is not exactly well delineated in the holotype (FMNH PR15373) (71,89,90,263,271). The second specimen (FMNH PR8472) is currently studied, and it appears to have nasohypophyseal barbels.
This character is only applicable to those in which the posthypophyseal processes meet at the midline. The presence/absence of subnasal cartilage is treated conservatively as a separate character from the presence/absence of tectal cartilages. It could be argued that the posthypophyseal processes forming a prominent oral roof in lampreys precludes rod-like cartilages supporting sensory structures in principle, and the processes forming the floor of the nasohypophyseal canal in hagfish also precludes tectal cartilages. However, this reasoning is based solely on the two living forms of cyclostomes and is therefore circular.
This character is contingent on the presence of a posthypophyseal process meeting at the midline (cyclostome upper lip) (#66, this analysis).
Hagfish are coded as present for this character. The taxa lacking myomeres or having simple myomeres are designated as inapplicable.
Haikouella is coded as Z-shaped myomeres ('0') for having a gentle inflection (94,117 In adult stages of lampreys, the digestive tract separates from the branchial passage and passes over the branchial region. Such separation or loop of the digestive tract dorsal to a branchial apparatus occurs in osteostracans (153,154). Two conflicting interpretations have been proposed for the digestive tract of Euphanerops, but each reconstruction suggests either passing or looping of the tract over the branchial apparatus (77). In furcacaudiforms, the gut trace (interpreted as stomach) extends onto the dorsal side of the branchial openings, again suggesting either passing or looping of the digestive tract over the branchial apparatus (272,273). This feature is ambiguously represented in Turinia (coded as unknown) (274). 164. Anus, with respect to distribution of mesoderm: 0, terminal or subterminal; 1, non-terminal (new character).
Slime glands are susceptible to decay relative to other soft tissue structures (1,2), but Tethymyxine shows that the mechanically strong, tightly coiled, high-performance fibres of slime (α-keratin and mucin) (276)(277)(278)(279)(280)(281)(282) are resistant to decay relative to other proteins. Given the high keratin composition, this character can be coded for the taxa from the localities that readily preserve keratin -structurally or chemically (283). This character is applicable only to lampreys.

EXPLANATION OF DATA SUPPLEMENTS
These data supplements are also available in original file format at DOI: 10     Non-vertebrate outgroups scored most highly for inapplicable states because many characters in the dataset describe vertebrate-specific morphology. Cyclostomes contain more inapplicable coding than gnathostomes, due mainly to the lack of mineralized skeletons. (C) In addition to inapplicable coding, information may be missing for characters. Overall, the taxa with uncertain affinity are less complete than other taxonomic categories in our dataset. (D) Inapplicable codings occur in higher frequencies among skeletal characters than in other character categories in our dataset. This is because a substantial portion of the skeletal characters describes morphology of mineralized skeletons. (E) In contrast, skeletal characters contain lesser amount of missing entries than other character categories in our dataset, because of higher preservation potentials of mineralized skeletons. Whiskers on box plots indicate 95% confidence intervals of standard errors, and transverse lines indicate means. The GDS dataset does not distinguish inapplicable scores ('-') and missing entries ('?'); so it was not included in comparisons of inapplicable and missing character values. Percentiles were computed by interpolation.  Table S4 for the list of synapomorphies based on this strict consensus tree.  The bar at each node shows 95% HPD interval for node age, indicated in MY (million years) by red font. The nodes are set at median of the frequency distribution for node-age estimates. Node ages are estimated based on the molecular clock of 16S-COI sequences calibrated with fossil occurrences in the birthdeath model. Therefore, HPD is not available for nodes that: (a) collapse into a polytomy consisting of terminal, fossil taxa only in the maximum parsimony analysis (Fig. S6) Fig. S2): C = cyclostomes; G = gnathostomes; I = non-vertebrate outgroups; O = ostracoderms; U = uncertain affinity. Sources used to code the taxa include: S = first hand observation of specimens; L = information derived from literature or second-hand data (including photographs provided by colleagues); C = digital data derived from CT scan and other radiation or histological methods; U = information derived from unpublished specimens. *Additional taxa included only in a subset of analyses.  Table S3. List of synapomorphies for major nodes in a strict consensus of the most parsimonious trees generated in a maximum parsimony analysis (Fig. S6) with character states for selected taxa. Parsimony-based character optimization methods cannot distinguish missing information ('?') from inapplicable state ("-"). Thus, ACCTRAN and DELTRAN are both blind to contingency between characters. Some character changes are optimized to nodes more inclusive than those to which their parent characters are optimized. This is particularly problematic for ACCTRAN because it places a character change to the most inclusive node possible. These spuriously optimized changes are denoted by asterisk (*). Furthermore, additional character changes may not be optimized if an internal clade entirely consists of taxa with inapplicable scores due to contingency to another character. These character changes with parsimoniously silent transformations are denoted by diesis ( ‡).

Taxonomic unit
These are known problems with the method of character optimization.         Table S4. Comparison of character support for cyclostomes in morphological cladistic datasets. Left column lists unambiguous, ACCTRAN-, or DELTRAN-optimized synapomorphies of total-and crown-group cyclostomes under maximum parsimony. Bold, italic typeface indicates synapomorphies supported in the analysis presented in this paper. Each remaining column represents a dataset. All datasets except our own were given a topological constraint to produce the cyclostome clade.
Key insights provided by this comparison are: (a) much of the character support for cyclostomes as recovered in our analysis exists in previous datasets; and (b) this support -hence the clade -is recovered in our analysis after treatment of non-independent character coding. Our analysis did not find congruence for many character transformations optimized as cyclostome synapomorphies in the constrained analyses of previous datasets. Most of these transformations fall into one of the following categories: symplesiomorphic to cyclostomes in our analysis ( §); optimized to internal nodes within cyclostomes in our analysis (°); optimized to a reverse character polarity in our analysis (**); not included in our analysis due to uninformative nature ( ‡). These categories are consequences of increased sampling and increased inapplicable coding (to accommodate character non-independence) (see Part D for detailed discussion).
Methods: Tree constraint was used to enforce the cyclostome topology. For each dataset, a heuristic search was run (per original analysis) to obtain strict consensus of most parsimonious trees. From this, tree constraint designated: (i) hagfish and lampreys to form a clade; (ii) any taxon resolved on the hagfish or lamprey stem in the unconstrained strict consensus tree to fall within the cyclostome crown; (iii) any taxon resolved on the cyclostome stem in the unconstrained strict consensus tree to be unconstrained topologically. A heuristic search was run again under this constraint, and most parsimonious character changes were mapped onto strict consensus of the topologically constrained shortest trees under both ACCTRAN and DELTRAN. Character coding or taxonomic composition was not altered. All analyses were conducted in PAUP.

Table annotations:
+=Transformation is optimized as a synapomorphy of the crown or total group Cyclostomi. ++= Transformation is optimized as a synapomorphy of the crown or total group Cyclostomi, but is coded by more than one character in the original source. ±=Transformation is optimized as a synapomorphy of the crown or total group Cyclostomi, but the character is a composite in that analysis (coded by more than one character in our analysis). *=Character is included in our new dataset, but a specific transformation is optimized to a different node. **=Character is included in our new dataset, and a specific transformation is optimized to a different node in reverse direction due to correction of non-independent coding. Example: Cerebellum with corpus cerebelli is absent in hagfish and lampreys and present in crown-group gnathostomes (the character was coded as inapplicable to non-vertebrate outgroups). Most parsimonious transformation is from absence to presence on the gnathostome stem, not from presence to absence in the cyclostome stem. °=Character transformation is optimized to an internal node within the cyclostome crown (or subject to artifacts of non-independent coding; see the legend for Table S3) §=Symplesiomorphies to cyclostomes in our analysis (a specific transformation is optimized somewhere between the root of the tree and the crown vertebrate node). †=Character is modified in our dataset. ‡=Character is not included in our dataset. N =New character in our analysis.