David Marjanović
email: david.marjanovic@gmx.at

Hillary C Maddin
email: hillary.maddin@carleton.ca

Jennifer C Olori
email: jennifer.olori@oswego.edu

Michel Laurin
email: michel.laurin@mnhn.fr

The new problem of Chinlestegophis and the origin of caecilians (Amphibia

Keywords: phylogeny, phylogenetics, majority-rule consensus, Amphibia, Lissamphibia, Gymnophionomorpha, Gymnophiona, Chinlestegophis, Rileymillerus, Funcusvermis most parsimonious tree. MRC: majority-rule consensus. OTU Matrices, Methodologies, and Missteps

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Chinlestegophis jenkinsi was named and described by Pardo et al. (2017a) as a Late Triassic stem-caecilian. Although we agree that C. jenkinsi presents an interesting mix of characters, we wish to respond to claims Pardo et al. (2017a) made about Chinlestegophis that were incompletely tested, and are in some cases weakened by underlying problems with character construction and taxon sampling. Taken together, those basic issues raise doubts about the main claim of Pardo et al. (2017a)-that Chinlestegophis is a stem-caecilian.

Caecilians have a scanty fossil record [START_REF] Santos | A review of the fossil record of caecilians (Lissamphibia; Gymnophionomorpha) with comments on its use to calibrate molecular timetrees[END_REF][START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF], with the earliest well-supported stem members, Funcusvermis gilmorei [START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF], and Eocaecilia micropodia Jenkins and Walsh, 1993[START_REF] Jenkins Fa | An Early Jurassic caecilian with limbs[END_REF], dating from the Late Triassic and the Early Jurassic. Eocaecilia retains limbs and some cranial bones that are absent in the caecilian crown group (Gymnophiona; see Wake 2020); partial femora were also assigned to Funcusvermis and the Early Cretaceous or, more likely, Late Jurassic [START_REF] Lasseron | New data on the microvertebrate fauna from the Upper Jurassic or lowest Cretaceous of Ksar Metlili (Anoual Syncline, eastern Morocco)[END_REF]) Rubricacaecilia monbaroni Evans and[START_REF] Evans | A stem-group caecilian (Lissamphibia: Gymnophiona) from the Lower Cretaceous of North Africa[END_REF][START_REF] Evans | A stem-group caecilian (Lissamphibia: Gymnophiona) from the Lower Cretaceous of North Africa[END_REF][START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF]. Since Eocaecilia was named, a more thorough anatomical study [START_REF] Jenkins Fa | Anatomy of Eocaecilia micropodia, a limbed caecilian of the Early Jurassic[END_REF]) and many phylogenetic analyses confirmed its position along the caecilian stem [START_REF] Laurin | The importance of global parsimony and historical bias in understanding tetrapod evolution. Part I. Systematics, middle ear evolution, and jaw suspension[END_REF][START_REF] Vallin | Cranial morphology and affinities of Microbrachis, and a reappraisal of the phylogeny and lifestyle of the first amphibians[END_REF]Maddin et al. 2012a;Pardo et al. 2017a: fig. S6). However, despite the absence of serious doubts about the status of Eocaecilia in the literature [START_REF] Evans | A stem-group caecilian (Lissamphibia: Gymnophiona) from the Lower Cretaceous of North Africa[END_REF]Carroll 2007: 54;Sigurdsen andBolt 2010: 1373; further corroborated by [START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF], Pardo et al. (2017a: abstract) stated: "The position of Eocaecilia within tetrapod phylogeny is controversial, as it already acquired the specialized morphology that characterizes modern caecilians by the Jurassic." That statement is misleading: all phylogenetic analyses that included Eocaecilia support its placement as a stem-caecilian; it is the position of caecilians as a group in the context of its ancestry among extinct tetrapods that remained controversial.

In contrast, the interpretation of Chinlestegophis jenkinsi (slightly younger than Funcusvermis: [START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF]) as a stem-caecilian (Pardo et al. 2017a) has less anatomical and phylogenetic support. Without a more comprehensive analysis based on a substantially revised matrix, Chinlestegophis currently cannot be supported as a stemcaecilian and should not be treated as one in secondary analyses, such as molecular estimates of divergence times (as previously stated by [START_REF] Santos | A review of the fossil record of caecilians (Lissamphibia; Gymnophionomorpha) with comments on its use to calibrate molecular timetrees[END_REF][START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF]). The problem is not merely one of narrow paleontological interest, but also carries broader implications for understanding the tempo and sequence of amphibian evolution. The analyses by Pardo et al. (2017a) surprisingly appeared to anchor the caecilians (through Chinlestegophis) within the stereospondyl temnospondyls, whereas frogs and salamanders (i.e., batrachians) remained in a more common placement as dissorophoid temnospondyls, producing a novel and immediately controversial hypothesis of lissamphibian origins.

Therefore, reassessing the position of Chinlestegophis among other tetrapods (including Eocaecilia) may have major implications for understanding the ancestry of all extant amphibians. Indeed, the captivating notion of the problem of amphibian origins and the evolution of specialized caecilian traits having been "solved" with the discovery of Chinlestegophis has already permeated popular zoology textbooks (Pough et al. 2022, figs. 9.2 and 9.5).

Here we show that the original phylogenetic analyses (Pardo et al. 2017a) fall short in supporting the placement of Chinlestegophis as a stem-caecilian because of 1) problems with the matrices used, including narrow taxon sampling, errors and oversights in character construction and modification, and incorrect scores within the original data sets underpinning the resulting matrices; 2) a suboptimal methodology, including reliance on a majority-rule consensus tree and incomplete reporting of tree statistics; and 3) qualitative problems with the diagnostic features linking Chinlestegophis (and in some cases Rileymillerus) to caecilians. Our objective is to review and evaluate the problematic aspects of the original analyses in order to facilitate future emendations and expansions, so that a clearer picture of the affinities of Chinlestegophis may emerge.

Although [START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF] supplementary information parts 3-4) published their reevaluation of one of the matrices and the characters that Pardo et al. (2017a) had used to tie caecilians to Chinlestegophis and other stereospondyls while our work was still in progress, their work complements ours, as we expand upon the matrix corrections, character treatments and parameters used for analyses, and discussion of character construction.

Nomenclature

Our usage of the clade names Gymnophiona, Amphibia and Lissamphibia follows Wake (2020) and Laurin et al. (2020a, b); temnospondyl nomenclature follows [START_REF] Schoch | The evolution of major temnospondyl clades: an inclusive phylogenetic analysis[END_REF][START_REF] Schoch | The putative lissamphibian stem-group: phylogeny and evolution of the dissorophoid temnospondyls[END_REF], except for the name Temnospondyli, whose definition by [START_REF] Schoch | The evolution of major temnospondyl clades: an inclusive phylogenetic analysis[END_REF] excludes important groups of animals universally considered temnospondyls when applied to our trees; instead, we use the definition by [START_REF] Yates | The phylogeny of the 'higher' temnospondyls (Vertebrata: Choanata) and its implications for the monophyly and origins of the Stereospondyli[END_REF]. Whenever possible we applied the same set of names to all figures. Junior synonyms are shown in parentheses, and names that cannot be applied to a particular tree (because of qualifying clauses or definitions that restrict their applicability to certain phylogenetic contexts) are not shown on that tree; by chance, [START_REF] Schoch | The evolution of major temnospondyl clades: an inclusive phylogenetic analysis[END_REF] Eutemnospondyli cannot be applied in any of our figures. [START_REF] Schoch | The evolution of major temnospondyl clades: an inclusive phylogenetic analysis[END_REF] gave identical definitions for Stereospondyli and Stereospondylomorpha; it is obvious that that is an accident and that the intended definition for Stereospondyli can be recovered by replacing "most" by "least". Misspellings of genus and species names in the matrices and figures of Pardo et al. (2017a) were silently corrected by us. See Marjanović and Laurin (2019: 13) for discussion of the correction of "Albanerpetontidae" to Albanerpetidae.

We use "caecilians" for crown-group caecilians (Gymnophiona: Wake 2020) and their uncontroversial relatives like Eocaecilia and Funcusvermis. This may be, depending on the phylogenetic hypothesis, a smaller grouping than Gymnophionomorpha under either the original definition of that name [START_REF] Marjanović | A reevaluation of the evidence supporting an unorthodox hypothesis on the origin of extant amphibians[END_REF] or the potentially much wider one by [START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF]. The problem of how best to define Gymnophionomorpha is beyond the scope of this paper.

The names Lepospondyli and Microsauria are used here informally for traditional groupings of taxa; the likely para-or polyphyly of these groupings (see [START_REF] Marjanović | Phylogeny of Paleozoic limbed vertebrates reassessed through revision and expansion of the largest published relevant data matrix[END_REF] for discussion and references, especially but not only Pardo et al. [2017b]) is beyond the scope of this work. For simplicity we present these names without quotation marks throughout. Pardo et al. (2017a) analyzed two matrices: a taxonomically broader, unpublished dataset, and an expanded, published matrix focused on the position of Chinlestegophis and Rileymillerus within temnospondyls. The originally unpublished matrix (see Supplementary File 1 for a NEXUS file), which generated the trees shown in Pardo et al. (2017a: fig. S6), contains 319 characters (27 of them parsimony-uninformative, including five constant ones) and 71 OTUs; it is based on the matrix of Maddin et al. (2012a), with additions of characters and taxa from [START_REF] Huttenlocker | Cranial morphology of recumbirostrans (Lepospondyli) from the Permian of Kansas and Nebraska, and early morphological evolution inferred by micro-computed tomography[END_REF] and several new ones. Those earlier matrices are based on that of Anderson et al. (2008a), but subsequently proposed corrections to that matrix [START_REF] Marjanović | The origin(s) of modern amphibians: a commentary[END_REF][START_REF] Skutschas | Cranial anatomy of the stem salamander Kokartus honorarius (Amphibia: Caudata) from the Middle Jurassic of Kyrgyzstan[END_REF][START_REF] Sigurdsen | The origin of modern amphibians: a re-evaluation[END_REF] were neither included in the resulting composite matrix nor addressed in the text by Pardo et al. (2017a) or any of the references therein. Those changes have considerable influence on the resulting tree topology, as exemplified in Figure 1. et al. (2008a), who had found extant amphibians to be diphyletic, with the stem-caecilian Eocaecilia among lepospondyls but Albanerpetidae, Caudata, Triadobatrachus and Anura among temnospondyls, Lissamphibia (cyan rectangle) is recovered and placed among "lepospondyls" (orange rectangle). The temnospondyl Gerobatrachus, interpreted as a member of the batrachian stem by Anderson et al. (2008a(Anderson et al. 2008b); i.e., closest to frogs and salamanders), is marked with a purple rectangle and white font. The names of extant taxa are in boldface; "frogs" and "salamanders" are composites. The application of the name Amphibamiformes is unclear due to the absence of Dissorophus.

Matrix history and taxon sampling

Numbers below internodes are bootstrap percentages (in bold if 50 or higher; "-" indicates clades contradicted by the bootstrap tree, always by clades with bootstrap percentages of 40 or less), numbers above internodes are Bremer values. Some or all of the Bremer values shown as "≥ 5" might actually be 5, because Marjanović and[START_REF] Marjanović | The origin(s) of modern amphibians: a commentary[END_REF][START_REF] Marjanović | The origin(s) of modern amphibians: a commentary[END_REF])) were unable to find all trees that were up to 5 steps longer than the MPTs, although the fact that an earlier iteration of this analysis, with a dataset that differed only in two cells, found the same results makes this possibility unlikely. Note that "Asaphestera" as used here is a chimera of the amniote Asaphestera, the "microsaur" Steenerpeton and an indeterminate lower jaw; most of the material belongs to Steenerpeton, however [START_REF] Mann | Reassessment of historic 'microsaurs' from Joggins, Nova Scotia, reveals hidden diversity in the earliest amniote ecosystem[END_REF]. The Dendrerpetidae OTU was originally called "Dendrerpeton" but is mostly based on its apparently close relative Dendrysekos. It is of course common practice to modify and expand existing data sets, and underlying errors are frequently perpetuated into later generations of matrices when first-hand reassessment of specimens is infeasible, detailed comparison to the literature is deemed too time-consuming, or the full history of characters becomes obscured over time, leading to different meanings of the same character for different taxa that were added or revised at different times [START_REF] Marjanović | Phylogeny of Paleozoic limbed vertebrates reassessed through revision and expansion of the largest published relevant data matrix[END_REF][START_REF] Gee | Returning to the roots: resolution, reproducibility, and robusticity in the phylogenetic inference of Dissorophidae (Amphibia: Temnospondyli)[END_REF][START_REF] Gee | The disadvantage of derivation: conserved systematic flaws in primary data have repeatedly biased the phylogenetic inference of Temnospondyli (Tetrapoda, Amphibia)[END_REF]. In those cases, conservative practice is to accept that preexisting descriptions and scores are reliable. However, over many iterations of matrices, substantial errors can and do accumulate-this is a known and pervasive problem with large data matrices that are recycled in consecutive studies [START_REF] Simões | Giant taxon-character matrices: quality of character constructions remains critical regardless of size[END_REF][START_REF] Laurin | Response: Commentary: A reassessment of the taxonomic position of mesosaurs, and a surprising phylogeny of early amniotes[END_REF][START_REF] Marjanović | Phylogeny of Paleozoic limbed vertebrates reassessed through revision and expansion of the largest published relevant data matrix[END_REF][START_REF] Gee | Returning to the roots: resolution, reproducibility, and robusticity in the phylogenetic inference of Dissorophidae (Amphibia: Temnospondyli)[END_REF][START_REF] Gee | The disadvantage of derivation: conserved systematic flaws in primary data have repeatedly biased the phylogenetic inference of Temnospondyli (Tetrapoda, Amphibia)[END_REF]Kligman et al. 2023: supp. inf. part 4; and see our Discussion section).

The merging of existing matrices also can generate additional problems related to redundant characters and states. As an example, multiple characters related to the lower jaw in the published matrix of Pardo et al. (2017a) carry redundancy (in particular characters 147, 148, 146, 272, 273, 322, 344; see full evaluation below), and because each is strongly associated with specialized morphologies mainly observed in caecilians, even when correctly scored, these may generate bias by inflating support for the purported relationship between Chinlestegophis and caecilians. Moreover, as characters are merged, moved, modified, and added, it becomes increasingly easy to overlook simple mechanical errors, such as state 26 (2) being mentioned neither in the list of state labels within the matrix file nor in the character list despite all three states being scored for numerous taxa in the matrix (Pardo et al. 2017a:

SI appendix parts C, D).
Robust analyses also may be thwarted by constraints related to the original taxon sampling of the underlying matrices; in other words, matrices compiled by other authors were (implicitly or explicitly) constructed with the intent to apply them to specific problems, and thus any clade may be densely or sparsely sampled depending on the question that was originally addressed, rather than on questions of later interest. Inserting new taxa may be difficult if additional variation is not easily accommodated without major character revisions, and this may limit which taxa can be speedily added. The matrix of Anderson et al. (2008a) is slightly modified from that of [START_REF] Anderson | Incorporating ontogeny into the matrix: a phylogenetic evaluation of developmental evidence for the origin of modern amphibians[END_REF], which is a merger of a matrix that sampled lepospondyls [START_REF] Anderson | The phylogenetic trunk: maximal inclusion of taxa with missing data in an analysis of the Lepospondyli (Vertebrata, Tetrapoda)[END_REF]) and a matrix that sampled amphibamiform temnospondyls (Anderson et al. 2008b). As a result, all descendants of the matrix of Anderson et al. (2008a), including the unpublished matrix of Pardo et al. (2017a), sample lepospondyls, amphibamiforms, and very little in between; in the case of Pardo et al. (2017a: fig. S6), other than the amphibamiforms and the added taxa Chinlestegophis and Rileymillerus, taxa include only seven other temnospondyl OTUs (some composite), the colosteid Greererpeton, lepospondyls, the diadectomorph pan-amniote Limnoscelis, the seymouriamorph Seymouria and the anthracosaur Proterogyrinus. The taxon sample is completed by the designated outgroup Acanthostega, the earliest well-understood limbed vertebrate.

The more narrowly focused published matrix of Pardo et al. (2017a) omits almost all taxa not sampled by [START_REF] Schoch | The evolution of major temnospondyl clades: an inclusive phylogenetic analysis[END_REF], retaining only temnospondyls, lissamphibians, and the same two outgroups as [START_REF] Schoch | The evolution of major temnospondyl clades: an inclusive phylogenetic analysis[END_REF], Proterogyrinus and Greererpeton. The stated reason for this drastic omission of taxa, which eliminated all lepospondyls, Seymouria and Limnoscelis, was to reduce calculation time for the Bayesian analysis (Pardo et al. 2017a: E5394), after analysis of the unpublished matrix suggested that Chinlestegophis and lissamphibians nested within Temnospondyli.

In short, Pardo et al. (2017a) first tested the phylogenetic position of Chinlestegophis and the similar Rileymillerus [START_REF] Bolt | A new Temnospondyl Amphibian from the Late Triassic of Texas[END_REF] "coarsely" by adding them to a matrix that sampled lepospondyls, amphibamiforms, a few other extinct taxa, and lissamphibians.

Chinlestegophis and Rileymillerus were found as temnospondyls close to, but outside, Amphibamiformes (Pardo et al. 2017a: fig. S6). Accepting the result that Chinlestegophis, Rileymillerus and lissamphibians were temnospondyls, Pardo et al. (2017a) zoomed in by adding them to a matrix that sampled temnospondyls (and temnospondyl-related characters) more broadly, but omitted most other extinct clades. The question of whether caecilians are lepospondyls or stereospondyl temnospondyls was never adequately tested; the unpublished matrix lacks stereospondyls and uses unrevised scores for lepospondyls that were previously criticized [START_REF] Marjanović | The origin(s) of modern amphibians: a commentary[END_REF][START_REF] Skutschas | Cranial anatomy of the stem salamander Kokartus honorarius (Amphibia: Caudata) from the Middle Jurassic of Kyrgyzstan[END_REF][START_REF] Sigurdsen | The origin of modern amphibians: a re-evaluation[END_REF], whereas the published one lacks lepospondyls altogether.

The published matrix further lacks representation of Albanerpetidae (a member or the sister group of Lissamphibia), despite their presence in the unpublished matrix and their undoubted affinities with lissamphibians (see below). [START_REF] Daza | Enigmatic amphibians in mid-Cretaceous amber were chameleonlike ballistic feeders[END_REF] added Albanerpetidae (as a composite taxon with new data) back into the published matrix of Pardo et al. (2017a) and analyzed the result by implied weighting. They found caecilians and batrachians as sister taxa, followed by Karauridae as the next more distant relative, then Albanerpetidae, then the branchiosaurid Apateon and then the rest of Amphibamiformes. Chinlestegophis and Rileymillerus instead formed the sister-group of Brachyopoidea within Stereospondyli (Daza et al. 2020: fig. 4E, S14). Clearly, omitting even the poorly known Albanerpetidae had a large effect on the resulting relationships among extinct taxa and living amphibians.

Phylogeny inferred from parsimony

The original parsimony analysis of the published matrix yielded 882 shortest trees (Pardo et al. 2017a; and see below). As often occurs, the strict consensus was poorly resolved. To remedy this, Pardo et al. (2017a: fig. S7B) produced a majority-rule consensus (MRC) tree and used it as the basis for comparison with the tree resulting from a Bayesian analysis of the same matrix (their fig. 2C = S7A). Both the MRC and Bayesian trees showed batrachians as amphibamiforms, but caecilians as stereospondyls closest to Chinlestegophis, and Rileymillerus as sister to caecilians + Chinlestegophis. However, none of the 28 nodes that separate caecilians and (batrachians + karaurids) have 50% or higher bootstrap support, and none (even the basal caecilian node) occur in 100% of the shortest trees (Pardo et al. 2017a: fig. S7B). We stress that the percentage of MPTs in which a given node occurs, as long as it is not 0 or 100, is not a support measure in a parsimony analysis (references in Serra Silva and Wilkinson 2021; also stressed by [START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF] in a longer discussion: supp. inf.

part 3); all MPTs are equally most parsimonious, and therefore equally optimal by the sole criterion the analysis used. Therefore, the MRC tree provides an incomplete picture of the results of any parsimony analysis, even if there is only a single island of MPTs (see below). Indeed, a fully resolved MRC is not even necessarily identical to any MPT (J. Felsenstein, pers. comm. to D. M. 2017).

Investigating that problem specifically, Serra [START_REF] Silva | On defining and finding islands of trees and mitigating large island bias[END_REF] reevaluated the full diversity of MPTs supported by the published matrix of Pardo et al. (2017a), noting in their introductory paragraph that " [d]espite concerns that summarizing MPTs with the majorityrule consensus is potentially misleading […], some workers still use the majority-rule method as if it were unproblematic (e.g. […] Pardo et al. 2017[a])." After briefly describing reanalysis by Marjanović and Laurin (2018: 57-58;2019: 144, fig. 30I-K), they demonstrated why the MRC is misleading in the specific case of Pardo et al. (2017a), and why it is important to inspect individual trees when the strict consensus is unsatisfactorily resolved: the 882 trees form islands which are each highly congruent internally, but very different from each other. Over half of the MPTs belong to a single island; therefore, the overall MRC (Pardo et al. 2017a nests inside Amphibamiformes, close to Gerobatrachus [START_REF] Atkins | Braincase simplification and the origin of lissamphibians[END_REF][START_REF] Schoch | A Triassic stem-salamander from Kyrgyzstan and the origin of salamanders[END_REF]Daza et al. 2020: fig. 4D/S13;[START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF]. It further differs from the largest island in that the karaurids occupy their usual position as stem-salamanders (corroborated by [START_REF] Jones | Middle Jurassic fossils document an early stage in salamander evolution[END_REF], not the entirely novel one as stem-batrachians found on the largest island.

Moreover, on the stereospondyl side of the tree, Chinlestegophis and Rileymillerus form the sister-group of Brachyopoidea, rather than being nested in it as on the largest island.

Another island (Marjanović and Laurin 2019: fig. 30K;Serra Silva and Wilkinson 2021: fig. 3b) shows Lissamphibia as the sister-group of Chinlestegophis + Rileymillerus. Together, they are nested within Stereospondyli, next to Brachyopoidea. Within Lissamphibia, Karauridae and Batrachia are sister-groups as on the largest island.

Yet another island (Marjanović and Laurin 2019: fig. 30I;Serra Silva and Wilkinson 2021: fig. 3a) positions Lissamphibia next to Gerobatrachus within Amphibamiformes, and Chinlestegophis is nested within the caecilians as the sister-group of Eocaecilia, while Rileymillerus is placed among the stereospondyls as the sister-group of Brachyopoidea.

In other words, parsimony analysis of the published matrix of Pardo et al. (2017a) supports positions within Amphibamiformes or Stereospondyli equally strongly for Chinlestegophis, the undoubted caecilians, and Batrachia (including Karauridae).

Bayesian inference of phylogeny

With the result of the parsimony analysis of the published matrix wholly inconclusive, any argument from that matrix that the topology shown in fig. S7B of Pardo et al. (2017a) should be preferred over the equally parsimonious alternatives must come from the congruence of that topology with the result of the Bayesian analysis of the same matrix, which is the only result figured in the main paper (Pardo et al. 2017a: figs. 2B, C, 3, S7A). However, we do not think that Bayesian inference is automatically superior to parsimony as a method of phylogenetic analysis of paleontological matrices.

The supposed problem of common branch lengths for all characters in previous simulations, pointed out by [START_REF] Goloboff | Weighted parsimony outperforms other methods of phylogenetic inference under models appropriate for morphology[END_REF]Goloboff et al. ( , 2018) ) and given great weight by Marjanović and Laurin (2019: 98), was fully accounted for by the two latest treatments of the question of how best to analyze morphological data [START_REF] Puttick | Probabilistic methods outperform parsimony in the phylogenetic analysis of data simulated without a probabilistic model[END_REF][START_REF] Keating | Morphological phylogenetics evaluated using novel evolutionary simulations[END_REF]) and found to be irrelevant. Yet, those two studies did not simulate any missing data, and the misuse of the MRC to represent the results of parsimony analyses by [START_REF] Puttick | Probabilistic methods outperform parsimony in the phylogenetic analysis of data simulated without a probabilistic model[END_REF] will overestimate the precision but underestimate the accuracy of parsimony, as Keating et al. (2020: fig. 5) demonstrated. Furthermore, the homoplasy distributions in the matrices simulated by [START_REF] Puttick | Probabilistic methods outperform parsimony in the phylogenetic analysis of data simulated without a probabilistic model[END_REF], and probably [START_REF] Keating | Morphological phylogenetics evaluated using novel evolutionary simulations[END_REF] as well, do not encompass cases like the matrix of [START_REF] Marjanović | Phylogeny of Paleozoic limbed vertebrates reassessed through revision and expansion of the largest published relevant data matrix[END_REF] at the very least, and evidently not the matrix of Pardo et al. (2017a) either-given the multiple starkly different topologies that it supports as equally parsimonious.

Even more importantly, as paleontological matrices generally do (contrary to the implication by King [2020]), the matrix of Pardo et al. (2017a) contains multiple conflicting signals as well as large amounts of missing data. That combination is known to present a major problem for parametric methods in phylogenetics, including Bayesian inference, whereas parsimony (as a non-parametric method) is immune to that particular issue [START_REF] Simmons | A confounding effect of missing data on character conflict in maximum likelihood and Bayesian MCMC phylogenetic analyses[END_REF][START_REF] King | Which morphological characters are influential in a Bayesian phylogenetic analysis? Examples from the earliest osteichthyans[END_REF]. Specifically, when character conflict is present (and at least one terminal branch has a positive length), parametric methods give much greater weight to the signal present in characters that are sampled for all taxa than to the signal present in incompletely sampled characters, even if very little information is missing [START_REF] Simmons | A confounding effect of missing data on character conflict in maximum likelihood and Bayesian MCMC phylogenetic analyses[END_REF][START_REF] King | Which morphological characters are influential in a Bayesian phylogenetic analysis? Examples from the earliest osteichthyans[END_REF]. Given that there is no reason to assume a correlation between homoplasy and preservation, we regard this as a flaw of parametric methods for paleontological applications.

We also would like to draw attention to figure 1 of Mongiardino [START_REF] Koch | Fossils improve phylogenetic analyses of morphological characters[END_REF], in which the proportion of quartets in a simulation study that are accurately resolved by undated Bayesian inference (as used by Pardo et al. 2017a) increases when the amount of missing data also increases, or in other words decreases when accurate data are added. Although this startling result is not statistically significant, it seems that undated Bayesian inference was, in that case, right for the wrong reasons, and is likely to be wrong for the same reasons in other circumstances.

Finally, by default, parsimony is somewhat less vulnerable than parametric methods to the long-known problem of heterotachy (Crotty et al. 2019, and references therein). That problem was solved, but currently the solution is implemented in only one program, which only performs maximum-likelihood analysis and cannot deal with most features of morphological data [START_REF] Crotty | GHOST: recovering historical signal from heterotachously evolved sequence alignments[END_REF]); a solution remains unavailable for Bayesian inference. On the empirical side, [START_REF] Palci | The homologies and evolutionary reduction of the pelvis and hindlimbs in snakes, with the first report of ossified pelvic vestiges in an anomalepidid (Liotyphlops beui)[END_REF] recovered a plausible topology of total-group snakes when they analyzed their dataset with parsimony, but a highly implausible one, requiring ecologically unmotivated reversals, by Bayesian inference. Thus, we strongly emphasize the conclusion of Marjanović and Laurin (2019: 96-99) that the accuracy of the matrix is much more important than the method of analysis, because no method can compensate for misscoring or miscoding of morphological data, a major issue we document for the matrix published and relied upon by Pardo et al. (2017a).

Material and Methods

As noted above, Pardo et al. (2017a) performed analyses of two matrices (one published, one unpublished) with similar character samples but different taxon samples. The originally unpublished matrix was kindly shared with us by J. Pardo and A. Huttenlocker, and we publish it here: Supplementary File 1 contains the unaltered matrix in a NEXUS file, with an added PAUP command block that replicates our analyses of it (called a1 and a2 below) when the file is executed in PAUP*. All of our analyses (Table 1) were run in PAUP* 4.0a169 [START_REF] Swofford | PAUP* (*Phylogenetic Analysis Using PAUP)[END_REF] for Windows. This includes bootstrap analyses to test the results of selected phylogenetic analyses for robustness; we have relied on not only the bootstrap trees, which we present as figures, but also on the lists of bipartitions in the PAUP* output (Supplementary Tables 1234, contained in Supplementary File 2). The published matrix was modified in Mesquite versions up to 3.70 [START_REF] Maddison | Mesquite: a modular system for evolutionary analysis[END_REF]. The Kishino/Hasegawa, Templeton and winning-sites tests were employed to assess whether constrained and unconstrained trees resulting from the previously unpublished matrix are significantly different; all three tests are available in PAUP*. ), not compatible with bootstrap tree inf. char. = number of parsimony-informative characters; LH = "lepospondyl hypothesis" on lissamphibian origins (Eocaecilia closer to Carrolla 382 than to Doleserpeton); SF = Supplementary File that contains the matrix and the settings for the analysis in question.

As described below, for some of our analyses of the published matrix, we added Albanerpetidae from Daza et al. (2020, based mainly on Yaksha) rather than from Schoch et al. (2020, based on Celtedens ibericus McGowan and[START_REF] Mcgowan | Albanerpetontid amphibians from the Cretaceous of Spain[END_REF], with a few additions from Shirerpeton). We have not added Funcusvermis for any analyses; we consider the effects of adding Funcusvermis sufficiently tested by [START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF], who added it to their revision of the matrix of [START_REF] Schoch | A Triassic stem-salamander from Kyrgyzstan and the origin of salamanders[END_REF], which was itself an expansion and slight revision of the published matrix of Pardo et al. (2017a). Pardo et al. (2017a) We reanalyzed the originally unpublished matrix (associated with figure S6 of Pardo et al. 2017a) to determine how many steps are needed to change the results. Two analyses were performed: one (a1) unconstrained, to replicate the original results, and one (a2) constrained to find Eocaecilia closer to the lepospondyl Carrolla than to the temnospondyl Doleserpeton, de facto enforcing the "lepospondyl hypothesis" of lissamphibian origins (but not any particular version of it) to enable us to compare the number of necessary extra steps. (The constraint also allows the "polyphyly hypothesis" that was supported by earlier versions of that matrix, most recently [START_REF] Huttenlocker | Cranial morphology of recumbirostrans (Lepospondyli) from the Permian of Kansas and Nebraska, and early morphological evolution inferred by micro-computed tomography[END_REF].)

Analyses of the unpublished matrix of

In both analyses, all characters were unordered, and no changes were made to the matrix. The search parameters were as follows: 10,000 random addition sequence replicates (far more than proved necessary) were performed holding one tree at each step, followed by branch swapping using TBR (tree bisection and reconnection) with a reconnection limit of 8 and a limit of 50 million rearrangements per replicate (which was never hit); steepest descent was not in effect; unlimited automatic increases on the Maxtrees setting; branches collapsed if maximum branch length was 0.

Analyses of the unmodified previously published matrix

We reanalyzed (analysis b) an unrevised version of the published matrix of Pardo et al.

(2017a: supporting information part D; basis for their figures 2, 3 and S7) to verify its replicability and to further inspect the results. We computed consensus trees for each island, rather than for the entire sample of MPTs; unlike Serra [START_REF] Silva | On defining and finding islands of trees and mitigating large island bias[END_REF], who computed the MRC of each island, we used the strict consensus. The search settings were as above, except for the use of only 1000 unlimited replicates.

We also present a bootstrap analysis of this matrix (200 bootstrap replicates, each with 500 addition sequence replicates limited to 10 million rearrangements) to enable a better understanding of its support for various hypotheses. Most bootstrap values returned by Pardo et al. (2017a: fig. S7B) were below 50% and not originally published; however, clades supported by moderate bootstrap values (e.g., 45%) may still be better supported than any single alternative. Yaksha, the new albanerpetid they described-to the published matrix of Pardo et al. (2017a) and analyzed the resulting matrix with implied weighting, using concavity values (k) ranging from 10 to 200 in increments of 10. The MRC of the results of all twenty analyses pooled together was presented in Daza et al. (2020: fig. S14); numbers of optimal trees, tree lengths or indices were not published. Although most nodes occur in 100% of the trees (a number that may, however, result from rounding up to the nearest unit in some cases), and although the analysis at k = 200 was practically unweighted (the lower the value of k, the more strongly are homoplastic characters downweighted), we ran our single analysis (c) unweighted to be sure which trees the matrix supports at face value. [START_REF] Keating | Morphological phylogenetics evaluated using novel evolutionary simulations[END_REF] demonstrated that unweighted parsimony is more accurate than implied-weights parsimony under certain realistic conditions; in addition, a basic assumption of implied weighting-an exponential distribution in which homoplasy-free characters are more common than those with any other number of extra steps-is not likely to be met for this matrix, and the performance of implied weights when that assumption is not met has not been studied [START_REF] Marjanović | Phylogeny of Paleozoic limbed vertebrates reassessed through revision and expansion of the largest published relevant data matrix[END_REF].

Addition of Albanerpetidae to the previously published matrix

Instead of publishing matrix files, [START_REF] Daza | Enigmatic amphibians in mid-Cretaceous amber were chameleonlike ballistic feeders[END_REF] published only the scores of the albanerpetid OTUs they revised in, or added to, the previously published matrix files they used. They confused the scores they added to the matrix of Pardo et al. (2017a;their reference 22) with the scores of Albanerpetidae they revised in the matrix of Pardo et al. (2017b;their reference 21) and presented these scores for the wrong matrix on pp. 16 and 17 of their supplementary text; this is easy to determine because the matrix of Pardo et al. (2017a) has 345 characters whereas that of Pardo et al. (2017b) has 370. Unable to add a string of 370 scores to a matrix of 345 characters, we added the string of 345 scores to the matrix of Pardo et al. (2017a) without any changes. The resulting NEXUS file, including a PAUP block that repeats analysis c when executed, is published here as Supplementary File 3. The search settings were as above.

Ordering continuous characters

In the analyses of both matrices performed by Pardo et al. (2017a), as well as that by [START_REF] Daza | Enigmatic amphibians in mid-Cretaceous amber were chameleonlike ballistic feeders[END_REF], all multistate characters were unordered, even though some represent continuous or meristic morphoclines, which are more appropriately treated as ordered characters [START_REF] Grand | Phylogenetic inference using discrete characters: performance of ordered and unordered parsimony and of threeitem statements[END_REF][START_REF] Rineau | Experimental systematics: sensitivity of cladistic methods to polarization and character ordering schemes[END_REF][START_REF] Rineau | Impact of errors on cladistic inference: simulation-based comparison between parsimony and three-taxon analysis[END_REF][START_REF] Marjanović | Phylogeny of Paleozoic limbed vertebrates reassessed through revision and expansion of the largest published relevant data matrix[END_REF]; and references therein).

Many characters used for phylogenetic analysis represent discretizations of intrinsically continuous variables that represent sizes, shapes and ratios, and the rationale for lumping similar values into a single state to produce discrete states follows the same logic as ordering the resulting states linearly [START_REF] Wiens | Character analysis in morphological phylogenetics: problems and solutions[END_REF]. Simulations showed that ordering such states increases resolving power (the ability to recover clades) and reduces the occurrence of erroneous topologies [START_REF] Grand | Phylogenetic inference using discrete characters: performance of ordered and unordered parsimony and of threeitem statements[END_REF][START_REF] Rineau | Experimental systematics: sensitivity of cladistic methods to polarization and character ordering schemes[END_REF][START_REF] Rineau | Impact of errors on cladistic inference: simulation-based comparison between parsimony and three-taxon analysis[END_REF].

In the process of ordering all such clines in the unmodified published matrix, we discovered (like Kligman et al., 2023: supp. inf. part 4) that state 2 of character 9 is missing from the character list of Pardo et al. (2017a: part C of the supplementary text). In the "charstatelabels" block of the NEXUS file published as part D of the supplementary text, state 2 does occur, but in the matrix it is scored exclusively for Ichthyophis. J. Pardo (pers. comm. 2021) explained that state 2, absent from Schoch's (2013) matrix, was intended to be introduced into the matrix, but this was implemented incompletely and accidentally omitted from the published character list. For characters 3, 26 and 201, the implementation of state 2 as published in part D seems complete even though it is likewise missing from part C in all three cases. Conversely, character 292 has three states in part C, of which state 1 does not occur in the matrix. Characters 301 and 318 have three states in part C as well, of which the matrix lacks state 2.

We performed two parsimony and two bootstrap analyses-without (d1) and with (d2) Albanerpetidae as in analyses b and c-ordering the following clinal characters of the published matrix: 9, 67, 75, 110, 143, 145, 158, 163, 170, 182, 187, 191, 201, 205, 209, 213, 214, 221, 226, 229, 242, 243, 262, 264, 266, 269, 271, 273, 279, 298, 300, 302, 304, 327, 328, and 334 (36 ordered out of 345 total characters; 10.4%). We first reordered the states of characters 9, 205, 221, 327 and 328 to allow linear ordering because the original order did not follow the cline. The states of character 9 (preorbital region length) originally were: 0, less than twice the length of posterior skull table; 1, more; 2, equal in length. That character discretizes a continuous variable, so we ordered the character after changing the numbering of the states to: 0, less than twice the length of posterior skull table; 1, equal in length; 2, more (longer). Likewise, states 0 and 1 of characters 205 and 221 had to be exchanged, as well as states 1 and 2 of characters 327 and 328. The resulting data matrix (and PAUP block) is available as Supplementary File 4.

The search settings were as above. 200 bootstrap replicates were performed, each using 500 random addition sequences. Instead of presenting the bootstrap values on consensus trees, we present the bootstrap trees (those including the clades with greater frequencies than their alternatives) with their bootstrap values.

Evaluation of potential synapomorphies and revisions to the published matrix

Throughout the main text and the supplementary material, Pardo et al. (2017a) suggested various features as synapomorphies of caecilians with either Chinlestegophis alone or Chinlestegophis and other stereospondyls. Many correspond to characters in the published matrix. Here we evaluate all proposed synapomorphies and explain, where applicable, our revisions of scores in the matrix. To facilitate retrieval and ensure nothing is overlooked, we quote and discuss them below in the order in which they appeared in Pardo et al. (2017a).

Our intention is not to fully revise the matrix (see Gee 2022), but to demonstrate the strong influence exerted by incorrect scores and compounding errors.

The resulting modified matrix is presented in Supplementary Files 5 and 6 and was analyzed (analyses e1-e4: Table 1) using the same parameters applied in our analyses b-d, both without ordering characters (e1, e3; Supplementary File 5) and with the same character ordering used in analysis d (e2, e4; Supplementary File 6), and both without (e1, e2) and with Albanerpetidae as in analyses c and d2 (e3, e4). Analysis e4 was bootstrapped using the same parameters as for the bootstraps of analyses b, d1 and d2.

The diagnosis of Chinlestegophis (which is repeated in part B of the supplementary information of Pardo et al. 2017a) states on p. E5389: "A shared feature with stereospondyls and caecilians is opisthotics fused to exoccipitals." As pointed out by [START_REF] Santos | A review of the fossil record of caecilians (Lissamphibia; Gymnophionomorpha) with comments on its use to calibrate molecular timetrees[END_REF], that feature is universal among lissamphibians except larval and some neotenic salamanders (e.g., [START_REF] Duellman | Biology of Amphibians[END_REF][START_REF] Jones | Middle Jurassic fossils document an early stage in salamander evolution[END_REF]. It further occurs in the amphibamiform temnospondyl Doleserpeton [START_REF] Sigurdsen | The Lower Permian amphibamid Doleserpeton (Temnospondyli: Dissorophoidea), the interrelationships of amphibamids, and the origin of modern amphibians[END_REF], a few lepospondyls (e.g., [START_REF] Pardo | Cranial morphology of the brachystelechid 'microsaur' Quasicaecilia texana Carroll provides new insights into the diversity and evolution of braincase morphology in recumbirostran 'microsaurs[END_REF] and some [START_REF] Maddin | Micro-computed tomography study of a three-dimensionally preserved neurocranium of Albanerpeton (Lissamphibia, Albanerpetontidae) from the Pliocene of Hungary[END_REF][START_REF] Daza | Enigmatic amphibians in mid-Cretaceous amber were chameleonlike ballistic feeders[END_REF] though apparently not all albanerpetids [START_REF] Matsumoto | The first record of albanerpetontid amphibians (Amphibia: Albanerpetontidae) from East Asia[END_REF]). Among stereospondyls, conversely, it seems to be limited to extremely large and correspondingly unusually highly ossified adults of Mastodonsaurus giganteus (Jaeger, 1828) (Kligman et al. 2023: supp. inf. part 3). There is no corresponding character in the published matrix of Pardo et al. (2017a).

"Shared features with brachyopoids and caecilians" were proposed to (p. E5389) "include lacrimal fused to maxilla". This hypothesis is difficult to evaluate. The maxillopalatine of Funcusvermis does not contain the nasolacrimal duct, so there is no evidence that it contains the lacrimal bone [START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF]. In Chinlestegophis, a separate lacrimal is absent, and the nasolacrimal duct lies entirely in what would otherwise be called the maxilla (Pardo et al. 2017a); however, the maxilla is dorsoventrally much narrower than what is expected for a fusion product. (The maxilla is taller, but not conspicuously so, in the closely related Rileymillerus [Bolt and Chatterjee 2000: fig. 1.3]; however, Kligman et al. [2023: supp. inf. part 3] suggested quite plausibly that the fragmentary supposed nasal of Rileymillerus is actually a separate lacrimal.) As a result, fusion of the lacrimal to the maxilla cannot be distinguished from wholesale absence of the lacrimal in the currently known material of Chinlestegophis. Similarly, the cause of the absence of a separate lacrimal (loss or fusion) in most brachyopoids and a few other stereospondyls is unknown; even the nasolacrimal canal has not been traced in any of them (see Kligman et al. 2023: supp. inf. part 3 for details).

Only in a few gymnophionans, as pointed out by [START_REF] Santos | A review of the fossil record of caecilians (Lissamphibia; Gymnophionomorpha) with comments on its use to calibrate molecular timetrees[END_REF] Hanken 1982), although it has generally been hard in gymnophionans to tell the prefrontal, the lacrimal, and even the septomaxilla apart, and it is not clear whether the lacrimal ever forms in most gymnophionans [START_REF] Theska | Musculoskeletal development of the Central African caecilian Idiocranium russeli (Amphibia: Gymnophiona: Indotyphlidae) and its bearing on the re-evolution of larvae in caecilian amphibians[END_REF]. It is wholly unknown if the two extant species scored in the matrix, Epicrionops bicolor Boulenger, 1883, and Ichthyophis bannanicus Yang, 1984, let alone the Early Jurassic Eocaecilia, possess(ed) a discrete lacrimal bone during development or not. However, character 21 of the published matrix only describes presence or absence of the lacrimal, without mentioning the causes of such absence (such as fusion to the maxilla). We interpret this as describing the observed presence or absence of a separate bone in adults and have therefore not changed the scores of these taxa (all "absent", state 1).

The sentence quoted above continues (onto the next page): "and two small posterior processes ('horns') on the occipital exposure of the tabular, just posterior to the otic notch (as in chigutisaurids)." Part B of the supplementary information in Pardo et al. (2017a) expressed some uncertainty about this: "two modest protuberances project from the occipital face of the tabular [of Chinlestegophis]. These processes may correspond to a rudimentary tabular horn, but their size and unusual topological relationship to the otic notch makes this homology uncertain. However, it is similar in position to the 'tabular horn' of some brachyopoids, particularly Batrachosuchus and Vigilius" (both of which are brachyopids, not chigutisaurids). Intriguingly, Batrachosuchus was scored as lacking "tabular horns" (pointed out by Gee 2022: app. 2.4.2), and see Kligman et al. (2023: supp. inf. part 3) for the doubtful homology of the "tabular horns" of Chinlestegophis and any brachyopoids. Later on p. E5390, Pardo et al. (2017a) made clear that tabular 'horns' are not known in any caecilians.

Indeed, for character 65-"Tabular (horn). Present in some form (0), or entirely absent (1)"-Eocaecilia was scored as unknown (?), and Epicrionops and Ichthyophis were scored as inapplicable (-) because they unambiguously lack tabulars (presence/absence of tabulars is coded by character 239, and absence of the bone predicts absence of its horn). This means that this character does not hold Chinlestegophis and caecilians together in the published matrix. We have kept the scores for the caecilians and only changed the scores of the extant salamanders Cryptobranchus and Hynobius from unknown to inapplicable because they clearly lack tabulars; this change has no impact on any calculations of relationships.

On the same page, "[s]hared features with Rileymillerus and caecilians include the following: orbits small and laterally directed." Orbit size, not coded in the published matrix, should be quantified before it can be evaluated, but is expected to be convergent among animals that live in low-light conditions. Indeed the orbits of Funcusvermis appear to have been considerably larger than those of other caecilians, Chinlestegophis or Rileymillerus [START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF]. Orbit location was included as character 26: "Orbit location. Medial, framed by wide jugals laterally (0), or lateral emplacement, framed by very slender jugals [START_REF] Wake | Gymnophiona[END_REF]." [START_REF] Dilkes | for 2014) Carpus and tarsus of Temnospondyli[END_REF] revised the definition of character 26, but focused on the width of the jugal in his modifications. We interpret the intention of character 26 to be the location of the orbit and instead suggest rewording this character. Additionally, although three states are scored in the original matrix, only two are given in the character definition. The third state refers to particularly large orbits framed by relatively slender jugals and slender frontals (J. Pardo pers. comm. 2021; Kligman et al. 2023: supp. inf. part 4), but it is scored for batrachians that lack jugals. In order to keep the scores, we have reinterpreted it as referring to the size of the orbit or orbitotemporal fenestra rather than the jugal explicitly. Therefore, like [START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF], we have only changed the score of Eocaecilia from 2 to 1. We have further followed [START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF] in changing the scores of two amphibamiforms: Platyrhinops from 2 to 1, Apateon from 0 to 2.

"Shared features with caecilians include double tooth row on mandible" is stated in the next sentence of Pardo et al. (2017a). This feature is represented in the published matrix as no less than seven separate characters: 146, 147, 148, 272, 273, 322 and 344. Character 146 reads: "Symphyseal teeth. No accessory teeth posterior to symphyseal tusks (0), or a transverse row of such teeth [START_REF] Wake | Gymnophiona[END_REF]." State 1 is found in some stereospondyl taxa.

Despite the absence of symphyseal tusks, state 1 also was scored for Chinlestegophis, Eocaecilia and the two extant caecilians (Pardo et al., 2017a). We changed the score of Chinlestegophis to 0 because the lingual toothrow of the holotype and the referred specimens is restricted to the coronoids, and the coronoids do not participate in the symphyseal region of this animal (Pardo et al. 2017: fig. S3, movies S4 and S7). The lingual toothrow of Eocaecilia, Epicrionops and Ichthyophis does reach all the way to the symphysis, so we retained a score of 1 for those, but caution that this likely duplicates character scores for the coronoid dentition characters as explained in the Discussion (contra [START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF].

Characters 147 and 148 describe presence/absence of teeth on specific coronoids and are thus redundant with character 272, which describes presence/absence of coronoid teeth in general (Pardo et al. 2017a). Characters 147 and 148 contain potentially important, non-overlapping variation, so we opted to keep that variation over retaining the more general variation captured by character 272, which we have excluded from our analyses. Because it is difficult to identify which coronoid is tooth-bearing in some taxa (i.e., where fewer than three distinguishable coronoids are present), Doleserpeton and caecilians in particular, we have, unlike Kligman et al. (2023: supp. inf. part 4), modified the definition of characters 147 and 148 as follows, which allowed us to keep all of the original scores: 147. Dentition lingual of distal half of labial toothrow. Present (0), or absent [START_REF] Wake | Gymnophiona[END_REF].

148. Dentition lingual of mesial half of labial toothrow. Present (0), or absent [START_REF] Wake | Gymnophiona[END_REF].

Character 322, "Splenial teeth. Present (0), absent (1)", was scored 0 exclusively for Ichthyophis, Epicrionops and the dvinosaurian temnospondyl Trimerorhachis insignis Cope, 1878. The scores for the former two refer to the fact that the lingual toothrow of caecilians has historically been thought to be borne on the splenial (references in Müller 2006;

"splenial" was still used in quotation marks by [START_REF] Wilkinson | A new genus and species of rhinatrematid caecilian (Amphibia: Gymnophiona: Rhinatrematidae) from Ecuador[END_REF]). However, the bone that bears this toothrow is not in the ventral position of a splenial, but the dorsolingual one of a coronoid, in the three extant caecilians whose development is well enough understood to tell [START_REF] Müller | Skeletal development of the direct-developing caecilian Gegeneophis ramaswamii (Amphibia: Gymnophiona: Caeciliidae)[END_REF][START_REF] Müller | Ontogeny of the skull, lower jaw, and hyobranchial skeleton of Hypogeophis rostratus (Amphibia: Gymnophiona: Caeciliidae) revisited[END_REF][START_REF] Theska | Musculoskeletal development of the Central African caecilian Idiocranium russeli (Amphibia: Gymnophiona: Indotyphlidae) and its bearing on the re-evolution of larvae in caecilian amphibians[END_REF]; a splenial has never been positively identified in any caecilian-or any other lissamphibian. In other words, the scores of 1 for Triadobatrachus, Cryptobranchus, Hynobius, Ambystoma and Leptodactylus are not correct either; we have followed [START_REF] Gee | The disadvantage of derivation: conserved systematic flaws in primary data have repeatedly biased the phylogenetic inference of Temnospondyli (Tetrapoda, Amphibia)[END_REF] in changing the scores of all lissamphibians that were not already scored as unknown to inapplicable (-). Moreover, the existence of teeth (including found teeth to be absent there in personal observation of AMNH FARB 4565 (type specimen of T. insignis) and AMNH FARB 4572 (referred to the same species). We changed this score to 1. Only one certain and one possible case of tooth-bearing splenials are known in all of Tetrapodomorpha, if not Gnathostomata, and neither is sampled in any of the matrices we mention here: Caerorhachis, in which a "denticle" field extends from the coronoids and the prearticular onto the splenial [START_REF] Ruta | The tetrapod Caerorhachis bairdi Holmes and Caroll from the Lower Carboniferous of Scotland[END_REF], and the unnamed "Parrsboro jaw", where the same may or may not be the case [START_REF] Sookias | Redescription and phylogenetic analysis of the mandible of an enigmatic Pennsylvanian (Late Carboniferous) tetrapod from Nova Scotia, and the lability of Meckelian jaw ossification[END_REF]. In short, state 0 does not occur in the revised matrix at all; the character is constant and therefore useless in a parsimony analysis. This is contrary to the main text, in which they erroneously [START_REF] Müller | Ontogeny of the skull, lower jaw, and hyobranchial skeleton of Hypogeophis rostratus (Amphibia: Gymnophiona: Caeciliidae) revisited[END_REF][START_REF] Theska | Musculoskeletal development of the Central African caecilian Idiocranium russeli (Amphibia: Gymnophiona: Indotyphlidae) and its bearing on the re-evolution of larvae in caecilian amphibians[END_REF] described the pseudodentary as "comprising the dentary, coronoid, splenial, and anterior Meckel's cartilage" (p. E5391).

Character 344 also appears to target the presence of a lingual row of dentition on the mandible as seen in gymnophionans and taxa like Chinlestegophis. The character is defined as: "Dentary marginal dentition. Single row (0), multiple rows [START_REF] Wake | Gymnophiona[END_REF]." The three caecilian OTUs and Chinlestegophis, and no other OTUs, were scored as having multiple rows (1); however, Chinlestegophis has only one dentary toothrow as described and illustrated by Pardo et al. (2017a), and in caecilians, as discussed above, the lingual row of teeth is borne on a coronoid rather than on the dentary. Thus, we rescored those taxa as having a single row of dentary teeth (0), meaning that state 1 does not occur in the revised matrix and this character, too, is uninformative.

Additionally, character 273 is: "Coronoid teeth. Larger than marginal (0), equal to marginal The next feature listed as shared between Chinlestegophis and caecilians is "quadrate completely anterior to ear", possibly meaning the otic capsules. If so, this character statewhich is not coded in the matrix-is standard among brachystelechid and lysorophian lepospondyls [START_REF] Maddin | A redescription of Carrolla craddocki (Lepospondyli: Brachystelechidae) based on high-resolution CT, and the impacts of miniaturization and fossoriality on morphology[END_REF][START_REF] Glienke | A taxonomic revision of Batropetes (Amphibia, Microsauria) from the Rotliegend (basal Permian) of Germany[END_REF][START_REF] Glienke | Two new species of the genus Batropetes (Tetrapoda, Lepospondyli) from the Central European Rotliegend (basal Permian) in Germany[END_REF][START_REF] Pardo | Cranial morphology of the brachystelechid 'microsaur' Quasicaecilia texana Carroll provides new insights into the diversity and evolution of braincase morphology in recumbirostran 'microsaurs[END_REF][START_REF] Pardo | Cranial morphology of the Carboniferous-Permian tetrapod Brachydectes newberryi (Lepospondyli, Lysorophia): new data from µCT[END_REF]) and widespread among lissamphibians as well. For present purposes it is only interesting if caecilians are temnospondyls, which this matrix cannot test.

Next is "broad, parallel-sided parasphenoid cultriform process >20% skull width". Three characters in the published matrix (112,114,343) attempt to capture variation in parasphenoid shape, particularly that of the cultriform process, but "broad" and "parallelsided" have different distributions. Although the cultriform process of Chinlestegophis is even broader than that of Eocaecilia, this condition is more or less universal among lissamphibians (references in Marjanović and Laurin 2008: 185-189), occurs prominently in lysorophians [START_REF] Pardo | Cranial morphology of the Carboniferous-Permian tetrapod Brachydectes newberryi (Lepospondyli, Lysorophia): new data from µCT[END_REF], and also is found in the morphologically most immature dissorophoid temnospondyls (e.g., Nyranerpeton: Werneburg 2012).

Character 112 is presented in the character list as having two states: "Cultriform process (width). Base not wider than rest, clearly set off from basal plate (0), or merging continuously into plate ( 1)" (Pardo et al. 2017a: part C of the supplementary text). In the matrix, however, three states are scored; the first two are as given in the list, and the third (state 2) is called "flaring anteriorly" in the "charstatelabels" block, as in [START_REF] Schoch | The evolution of major temnospondyl clades: an inclusive phylogenetic analysis[END_REF]. We followed Gee (2022) and [START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF] in transferring state 2 to character 343, which originally described whether the cultriform process is "[n]arrow, tapering anteriorly (0)" or "spatulate and parallel-sided (1)". In other words, character 112 now describes the shape of the caudal end of the cultriform process in two states, and character 343 now describes the shape of the rostral end in three states that form a continuum of widths; character 343 is therefore ordered in our analyses with ordered characters (e2, e4). Our scores for both characters follow those of Gee ( 2022), which represents an update on [START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF]. In addition, we scored Chinlestegophis as unknown for character 343; it was reconstructed as having state 1 (Pardo et al. 2017a: fig. 1H) and scored accordingly, but the entire rostral half of the cultriform process appears to be unknown (Pardo et al. 2017a: fig. 1B).

Character 114 is: "Cultriform process (outline). Of similar width throughout (0), or posteriorly expanding abruptly to about twice the width [START_REF] Wake | Gymnophiona[END_REF]." State 1 was scored only for the two extant caecilian OTUs and for the temnospondyls Rileymillerus, Eryops and Onchiodon.

We are not sure if the conditions of those taxa should be considered homologous; the two eryopids have a bulbous expansion near the base of the cultriform process, followed caudally by a constriction and then the basal plate along with its contacts to the pterygoids [START_REF] Sawin | The cranial anatomy of Eryops megacephalus[END_REF][START_REF] Boy | Über einige Vertreter der Eryopoidea (Amphibia: Temnospondyli) aus dem europäischen Rotliegend (? höchstes Karbon -Perm) 3. Onchiodon[END_REF]); Rileymillerus has a strongly biconcave cultriform process that gradually expands caudally until it reaches five times its narrowest width where it merges into the basal plate (Bolt and ). This includes Eocaecilia, despite its retention of postparietal and probable tabular bones (Pardo et al. 2017a: fig. 3;[START_REF] Jenkins Fa | Anatomy of Eocaecilia micropodia, a limbed caecilian of the Early Jurassic[END_REF]). Conversely, milder examples of the stereospondyl condition exist in various lepospondyls (Santos et al. 2020, and references therein). Therefore, Eocaecilia should not receive the same score as Chinlestegophis; we reinterpreted the character as referring to condyle elongation instead of the skull table, limiting state 1 to condyles with a stalked base, and consequently revised the scores of Eocaecilia, Cryptobranchus and Ambystoma to 0.

The last character state proposed to be shared by Chinlestegophis and caecilians (Pardo et al. 2017a: E5390) is presence of a "pterygoquadrate", referring to fusion of the pterygoid and the quadrate bones (as observed in the ontogeny of some extant caecilians: [START_REF] Wake | Development of the skull of Dermophis mexicanus (Amphibia: Gymnophiona), with comments on skull kinesis and amphibian relationships[END_REF][START_REF] Müller | Skeletal development of the direct-developing caecilian Gegeneophis ramaswamii (Amphibia: Gymnophiona: Caeciliidae)[END_REF][START_REF] Müller | Ontogeny of the skull, lower jaw, and hyobranchial skeleton of Hypogeophis rostratus (Amphibia: Gymnophiona: Caeciliidae) revisited[END_REF]Theska et al. 2018: fig. 1c). On the next page, however, Chinlestegophis is more cautiously stated to possess, "perhaps, an incipient pterygoquadrate based on the structure of the suspensorium and apparent absence of the quadratojugal." The full description of the skull (Pardo et al. 2017a: part B of the supplementary text) states the matter in a similarly limited way: "A separate quadrate is not evident in either side of the skull, but it is likely that the saddle-shaped posterolateral face of the pterygoid represents the articular glenoid, and we hypothesize that this therefore represents a fused pterygoid-quadrate element (pterygoquadrate)." Thus, a pterygoquadrate is not observed in Chinlestegophis, and cannot be used to link it to caecilians. The issue is further complicated by Eocaecilia, in which the quadrate appears to be fused to the stapes and not to the pterygoid [START_REF] Jenkins Fa | Anatomy of Eocaecilia micropodia, a limbed caecilian of the Early Jurassic[END_REF]). Additionally, a pterygoquadrate is not universal in Gymnophiona, being absent in non-teresomatans like Ichthyophis, Epicrionops and Amazops (Jenkins et al. 2007: fig. 6B, D;Wilkinson et al. 2021: fig. 3) and the teresomatan Chikila ("pterygoid process of the quadrate", separated from the quadrate by a suture and meeting the maxillopalatine, in Kamei et al. 2012: fig. S2(b)). If the fused pterygoquadrate is not only real in Chinlestegophis, but also homologous between Chinlestegophis and Teresomata or a subset thereof, it must have been independently lost three successive times in Eocaecilia, Rhinatrematidae and Ichthyophiidae, and at least once more in Chikila.

The pterygoquadrate may be coded as state 2 of character 318: "Quadrate-maxilla separated by.

[sic] Pterygoid (0), small pterygoid and pterygoid process of quadrate [START_REF] Wake | Gymnophiona[END_REF], by pterygoid process of quadrate only (pterygoid absent) (2)." In agreement with the discussion above, state 2 does not occur in the matrix, which lacks teresomatans.

Pardo et al. (2017a: E5390

) also stressed that "[i]n the temporal region, there is a small, round supratemporal that is only loosely articulated to its surrounding calvarial elements. This bone is morphologically and topologically identical to an element identified as the 'tabular' in Eocaecilia". As pointed out by Marjanović and Laurin (2019: 151, app 1A), make clear that the morphology and topology of the "?tabular" in the reconstruction are guesses-the presence and independence of the bone are evident, but not its shape or size. In the crushed holotype (Jenkins et al. 2007: fig. 2;Maddin et al. 2012a: fig. 1A), the left "?tabular" is caudally broken, but the right one may well have reached the caudal edge of the skull table (pers. obs. H. M. and D. M.), reopening the possibility that it is in fact a tabular and not homologous to the supratemporal of Chinlestegophis. Pardo et al. (2017a) actually scored the tabular as present in Eocaecilia (state 0 of character 239). However, given the uncertainty surrounding the element, we changed this score to unknown (?), and retained the scores of "unknown" in the tabular-related characters 62, 63 and 65-67. We also followed Gee (2022) and [START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF] in changing the scores of all salamanders to not applicable (-) for the tabularrelated character 63, because they clearly lack tabulars, and changed the scores of all lissamphibians (including Eocaecilia) to inapplicable for character 71, which references tabular horns.

The implication later in the same paragraph (Pardo et al. 2017a: E5390) 10), which indeed shows the tentacular foramen inside the orbit of the extant Epicrionops and a "tentacular sulcus" on the orbital margin of the maxilla of Eocaecilia. Evidence of the caecilian tentacle, a body part composed mostly of the nasolacrimal duct and eye musculature and associated with chemosensation in extant caecilians, has not been reported from any vertebrates other than Gymnophiona and Eocaecilia. In Chinlestegophis, the maxilla does not reach the orbit, being excluded by a contact of the prefrontal and the lateral exposure of the palatine (Pardo et al. 2017a: fig. 1, S4). The nasolacrimal duct is housed in the maxilla and meets the orbit in two pores well medial of the skull surface (Pardo et al. 2017a: fig. S4C). Although the sulcus is stated to be in the orbital margin in part F of the supplementary material, it was not reconstructed in fig. 1J, which instead shows an elliptical orbit devoid of any corners; the reconstruction in fig. 1I shows a more angular orbit, fitting the μCT images in fig. 1E-G, but these corners are very wide, obtuse and rounded, offering no evidence of a tentacular sulcus.

A nasolacrimal duct that is separated from the surface of the head would not function in sensory reception, and seems unlikely to explain the evolution of the caecilian tentacle.

Funcusvermis also lacked a tentacular sulcus unless the sulcus had an unusually far dorsal position, i.e., at the dorsoventral midpoint of the rostral orbit margin at minimum (Kligman et al. 2023: fig. 1a, g-i). In any case, no feature relating to the nasolacrimal duct or the shape of the orbit is coded in the published matrix.

Results

See Table 1 for a brief overview of our analyses and their results. Pardo et al. (2017a) Our unconstrained analysis (a1; Fig. 2 Of the 319 characters, 292 are parsimony-informative.

Analyses of the unpublished matrix of

The MPTs form two islands that differ in their resolution of Lissamphibia: (1) Gerobatrachus as the sister-group of Lissamphibia, within which "frogs" + Triadobatrachus is the sistergroup of a clade formed by "salamanders" + Karaurus on one side and Albanerpetidae + Eocaecilia and crown caecilians on the other; ( 2) crown caecilians + Eocaecilia as the sistergroup of the other lissamphibians, within which Gerobatrachus is the sister-group of a clade formed by "frogs" + Triadobatrachus on one side and Albanerpetidae + ("salamanders" + Karaurus) on the other. Note that only ( 2) is compatible with phylogenies of extant amphibians based on molecular data (Hime et al. 2020, and references therein). S6B). The two islands are represented by the duplication of Lissamphibia and its sister-group (on one island) or member (on the other island) Gerobatrachus. The branch marked "(wrong)" contradicts the molecular consensus [START_REF] Hime | Phylogenomics reveals ancient gene tree discordance in the amphibian tree of life[END_REF]. The application of the name Rhachitomi as defined by Schoch ( 2013) is unclear due to the absence of Mastodonsaurus from the matrix, the application of the name Amphibamiformes as defined by [START_REF] Schoch | The putative lissamphibian stem-group: phylogeny and evolution of the dissorophoid temnospondyls[END_REF] is unclear due to the absence of Dissorophus. Colored rectangles and boldface, as well as "Asaphestera" and Dendrerpetidae, as in Fig. 1; red rectangle for Chinlestegophis, brown rectangle for crown-group caecilians (Gymnophiona). 2017a) in an analysis (a2; see Table 1) constrained against the "temnospondyl hypothesis" of lissamphibian origins; a version of the "lepospondyl hypothesis" results. Colors, boldface, "Asaphestera" and Dendrerpetidae as in Fig. 2.

↓ Figure 2. Strict consensus of the 12 MPTs obtained from our analysis a1 (see

Constraining Eocaecilia to be closer to the lepospondyl Carrolla (analysis a2; Fig. 3) than to the temnospondyl Doleserpeton produced 48 MPTs of a very similar length (1454 steps) and very similar indices (CI excluding uninformative characters = 0.2661, RI = 0.6519, RC = 0.1807). The positions of Chinlestegophis and Rileymillerus remain unchanged compared to Pardo et al. (2017a: fig. S6). Although the "lepospondyl hypothesis" is supported in this experiment, Lissamphibia contains Gerobatrachus, and it nests far from Carrolla, indeed on the other side of the lepospondyl tree-next to the limbless aïstopods, followed by the limbreduced Brachydectes, much as in [START_REF] Marjanović | The origin(s) of modern amphibians: a commentary[END_REF]Fig. 1) whose matrix has a common ancestor with this one (Anderson et al. 2008a). The strict consensus shows a less well resolved version of the abovementioned topology ( 2).

The differences in fit to the matrix between the unconstrained and the constrained trees are not significant (Kishino/Hasegawa test: p = 0.6284; Templeton test: p = 0.6276; winningsites test: p = 0.7160).

Analyses of the unmodified previously published matrix

Reanalysis of the published matrix (analysis b) yielded identical results to those of Pardo et al. (2017a), [START_REF] Marjanović | Phylogeny of Paleozoic limbed vertebrates reassessed through revision and expansion of the largest published relevant data matrix[END_REF] fig. 30I-K), Serra [START_REF] Silva | On defining and finding islands of trees and mitigating large island bias[END_REF] and [START_REF] Gee | The disadvantage of derivation: conserved systematic flaws in primary data have repeatedly biased the phylogenetic inference of Temnospondyli (Tetrapoda, Amphibia)[END_REF], returning 882 MPTs each with a length of 1,514 steps, CI excluding uninformative characters = 0.2548, RI = 0.6858, RC = 0.1812. Of the 345 characters, 322 are parsimony-informative. The MPTs are spread across the five islands found and described by Serra [START_REF] Silva | On defining and finding islands of trees and mitigating large island bias[END_REF]. The strict consensus trees of two islands (illustrated by Marjanović and Laurin 2019: fig. 30I; Serra Silva and Wilkinson 2021: fig. 3a,c) both retrieve a monophyletic Lissamphibia nested within the amphibamiform dissorophoids. In one of them (Serra Silva and Wilkinson 2021: fig. 3a), Chinlestegophis is the sister taxon to Eocaecilia, while in the other it is a stereospondyl that lies next to Rileymillerus. The strict consensus trees of two other islands (Marjanović and Laurin 2019: fig. 30J;Serra Silva and Wilkinson 2021: fig. 2b, 3d) retrieve Batrachia within amphibamiforms, whereas caecilians (including Eocaecilia) are the sister taxon to Chinlestegophis within Stereospondyli, as presented by Pardo et al. (2017a). The strict consensus of the remaining island (Marjanović and Laurin 2019: fig. 30K;Serra Silva and Wilkinson 2021: fig. 3b) retrieves Lissamphibia as the sister taxon to Chinlestegophis + Rileymillerus within Stereospondyli. Thus, in only three of the five islands of optimal trees is the configuration of Chinlestegophis as a stemcaecilian obtained, and in one of them it is a lissamphibian nested within Amphibamiformes rather than Stereospondyli.

The bootstrap tree of analysis b (Fig. 4) shows moderate support for the diphyly of modern amphibians as presented by Pardo et al. (2017a): the three caecilians form the sister-group of the stereospondyl Chinlestegophis in 52% of the bootstrap replicates, while the batrachians are found as amphibamiform dissorophoids closest to Gerobatrachus in only 43%, and adding any further dissorophoids depresses this value to a maximum of 35%. This latter value is the highest that separates caecilians and batrachians + karaurids; even Rileymillerus occurs as the sister-group of Chinlestegophis and the caecilians together in only 32%. Most bootstrap values in the rest of the tree, except for the majority of the most highly nested nodes, are even lower.

Inspection of the list of bipartitions in the output of PAUP* (Supplementary Table 1), including those that are incompatible with the bootstrap tree, shows that Lissamphibia was found in 37% of the bootstrap replicates-support comparable to that for Dissorophoidea including Batrachia (35%), which is shown in the bootstrap tree (Fig. 4). An exclusive clade of all lissamphibians and Chinlestegophis occurs in 21% of the replicates and combines with Rileymillerus in 20%; all lissamphibians and any or all dissorophoids form an exclusive clade in no more than 16% of the replicates. Stereospondyli excluding Chinlestegophis and optionally Rileymillerus appears in only 9%, as often as, e.g., an improbable clade of all lissamphibians except Eocaecilia. Only 8% group all lissamphibians, Chinlestegophis and Gerobatrachus exclusively. (2017a) when all characters are unordered (analysis b). The bootstrap tree shows moderate support (52%) for the diphyly of extant amphibians. Colors and boldface as in Fig. 3, bootstrap values ≥ 50% also in boldface; darker brown rectangle for Lapillopsis, a small temnospondyl thought to be a stereospondyl convergent to dissorophoids. The blue rectangle for Temnospondyli is omitted because all OTUs except Greererpeton and Proterogyrinus are (inferred to be) temnospondyls; the cyan rectangle for Lissamphibia is omitted because the name Lissamphibia does not apply on this tree. Tr.-oidea = Trematosauroidea. The Dendrerpetidae OTU was called "Dendrerpeton acadianum" by Pardo et al. (2017a) but is mostly based on its apparently close relative Dendrysekos. In this and the following figures we have also corrected spelling mistakes in taxon names compared to the matrix and the figures of Pardo et al. (2017a).

Addition of Albanerpetidae to the previously published matrix

The matrix of Daza et al. (2020: fig. 4E, S14), i.e., the published matrix of Pardo et al. (2017a) with Albanerpetidae added, yielded a single island of 45 MPTs (analysis c; length = 1565 steps, CI excluding uninformative characters = 0.2510, RI = 0.6795, RC = 0.1741).

Their strict consensus (Fig. 5) is topologically identical to that of [START_REF] Daza | Enigmatic amphibians in mid-Cretaceous amber were chameleonlike ballistic feeders[END_REF] fig. S14), except for slightly lower resolution: Dissorophidae, Trematopidae, and a node supporting Edingerella, Benthosuchus, Capitosauroidea and Trematosauroidea + Brachyopoidea are unresolved. Interestingly, all nodes marked "95" in the MRC of Daza et al. (2020: fig. S14) are present in the strict consensus of our analysis, whereas a few of those marked "100" are not. Amphibamiformes, including Lissamphibia, is resolved exactly as in [START_REF] Daza | Enigmatic amphibians in mid-Cretaceous amber were chameleonlike ballistic feeders[END_REF] fig. 4E,S14): there is a clade (Apateon (Albanerpetidae (Karauridae, Lissamphibia))) which is the sister-group of (Micropholis (Platyrhinops (Amphibamus (Doleserpeton, Bootstrapping analysis e4 reveals (Fig. 18) considerable support for Lissamphibia (71%), within which Albanerpetidae (42%) and Karauridae (65%) lie on the batrachian stem but not in Batrachia (75%). Lissamphibia is, with limited support, placed next to Apateon (27%) in Dissorophoidea (36%); similar support is recovered for placing Chinlestegophis (and Rileymillerus) close to brachyopoids and plagiosaurids (33%) in Stereospondyli (35%).

Groupings not compatible with the bootstrap tree (Supplementary Table 4) include Chinlestegophis + Rileymillerus as gymnophionomorphs (18%) or in an exclusive clade with Lissamphibia (23%); comparable support exists for Lissamphibia without Albanerpetidae (26%) or Lissamphibia without Karauridae or Albanerpetidae (20%), both of which are also incompatible with the bootstrap tree. An exclusive clade of lissamphibians and stereospondyls occurs in only 9% of the bootstrap replicates.

Discussion

Support for alternative topologies

Our work corroborates some of the results of the analyses performed by Pardo et al. (2017a), but also highlights weaknesses in the phylogenetic signal that was claimed to support caecilian affinities of Chinlestegophis. Indeed, Pardo et al. (2017a: abstract) claimed: "Our results place the taxon confidently within lissamphibians." On the contrary, our results demonstrate that the affinities of Chinlestegophis cannot be ascertained with confidence based on either of the two matrices of Pardo et al. (2017a).

First, we stress that the unpublished matrix (our analysis a1, see Table 1; Fig. 2; Pardo et al. 2017a: fig. S6) yielded a commonly recovered Lissamphibia, nested within dissorophoids and optionally containing Gerobatrachus but never Chinlestegophis. Forcing a version of the "lepospondyl hypothesis" of amphibian ancestry by constraining Eocaecilia to nest among lepospondyls (analysis a2; Fig. 3) results in only slightly longer trees (4 steps added to the 1450 of the unconstrained trees) that are not significantly different from the unconstrained trees (p between 0.62 and 0.72 according to the three usual tests). This is important because it suggests that when a broader sample of extinct tetrapods is included, a more mainstream hypothesis of both lissamphibian ancestry and Paleozoic tetrapod relationships is produced, and the stereospondyls represented in this matrix, Rileymillerus and Chinlestegophis, are distanced from lissamphibian origins.

All of our remaining analyses focused on the published matrix of Pardo et al. (2017a).

Unsurprisingly, we confirmed (analysis b) the results of Marjanović and Laurin (2019: fig. 30I-K), Serra [START_REF] Silva | On defining and finding islands of trees and mitigating large island bias[END_REF] and Gee (2022) that Pardo et al. (2017a) found all MPTs that fit this matrix, that the MRC tree they reported is accurate as such, and that the MRC tree is a highly incomplete representation of the MPTs: it is equally parsimonious for Batrachia and Gymnophiona to lie in Stereospondyli or Amphibamiformes, and for them to form Lissamphibia or not, which may or may not contain Chinlestegophis. We further contribute the first fully published bootstrap analysis of this matrix (Fig. 4, Supplementary Table 1); contrary to Pardo et al. (2017a: fig. S7B), it supports diphyly of extant amphibians, although the support is not strong (52% for grouping Chinlestegophis with the caecilians; 43% for grouping Gerobatrachus with the batrachians; only 35% for grouping all dissorophoids with the batrachians to the exclusion of any caecilians). Pardo et al. (2017a: fig. S7B) found no bootstrap values of 50% or higher on any node that separates caecilians and batrachians (they did not publish values below 50%). Although we used 200 bootstrap replicates of 500 addition-sequence replicates each, Pardo et al. (2017a) used 1000 bootstrap replicates of 100 addition-sequence replicates each (J. Pardo pers. comm. 2023; the settings were not published); this may explain the different result. It is possible and indeed likely that the differences are slight, e.g., where we found 52% support for caecilians + Chinlestegophis, they probably found support between 40% and 49%.

However, adding Albanerpetidae to the matrix (analysis c; Fig. 5) confirms the result of [START_REF] Daza | Enigmatic amphibians in mid-Cretaceous amber were chameleonlike ballistic feeders[END_REF]: Lissamphibia is found in Amphibamiformes in all MPTs, while Chinlestegophis is always a stereospondyl. The omission of albanerpetids from the original matrix was clearly a suboptimal choice, given that all studies published since their discovery over half a century ago support close affinities between albanerpetids and lissamphibians, if not a position among lissamphibians (e.g., [START_REF] Estes | Prosirenidae, a new family of fossil salamanders[END_REF][START_REF] Estes | Les urodèles du Miocène de la Grive-Saint-Alban (Isère, France)[END_REF][START_REF] Fox | A reconsideration of the relationships of the fossil amphibian Albanerpeton[END_REF][START_REF] Mcgowan | Albanerpetontid amphibians from the Cretaceous of Spain[END_REF][START_REF] Maddin | Micro-computed tomography study of a three-dimensionally preserved neurocranium of Albanerpeton (Lissamphibia, Albanerpetontidae) from the Pliocene of Hungary[END_REF][START_REF] Daza | Enigmatic amphibians in mid-Cretaceous amber were chameleonlike ballistic feeders[END_REF][START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF]. Even the most unorthodox analysis of albanerpetid affinities that we know of suggests close affinities to batrachians [START_REF] Mcgowan | Albanerpetontid amphibians from the Lower Cretaceous of Spain and Italy: a description and reconsideration of their systematics[END_REF].

The effect of ordering characters within the original published matrix (i.e., without Albanerpetidae and without corrections other than renumbering the states of some ordered characters) (analysis d1; Fig. 6) narrowed down the five islands to one: Lissamphibia (which has 55% bootstrap support) forms the sister group of the stereospondyls Chinlestegophis and Rileymillerus. This arrangement only occurs in 35% of the bootstrap replicates, however (Fig. 7; Supplementary Table 2). Adding Albanerpetidae (analysis d2) moved Lissamphibia into the amphibamiform dissorophoids; it is equally parsimonious for Chinlestegophis and Rileymillerus to be stem-caecilians (Fig. 8) or brachyopoid stereospondyls (Fig. 9).

Bootstrapping this analysis (Fig. 10; Supplementary Table 3) revealed modest support for Lissamphibia (45%) and weak support for any position of that clade, but comparatively strong support against a position close to Gerobatrachus or Doleserpeton (62%).

A modest revision of the published matrix, without Albanerpetidae, replicated the basic results of analyses c and d1 as equally parsimonious when all characters were unordered (analysis e1;. Ordering (analysis e2; Fig. 14) restricted Lissamphibia to Stereospondyli as in analysis d1 (unmodified matrix, likewise ordered, likewise without Albanerpetidae). Adding Albanerpetidae without ordering (analysis e3; Fig. 15) essentially replicated analysis c, ordering (analysis e4; Fig. 16, 17) introduced variation within Lissamphibia but kept it in the same place as in analysis c-with strong bootstrap support: a lissamphibian-stereospondyl clade is not compatible with the bootstrap tree (Fig. 18) and only occurs in 9% of the replicates (Supplementary Table 4). The 71% support for Lissamphibia (with Albanerpetidae) excluding Chinlestegophis (or Rileymillerus, Gerobatrachus or any other traditional non-member) is worth highlighting.

In all four cases, ordering increased the resolution of the results. We interpret this as an example of ordering bringing out phylogenetic signal in data, congruent with results from simulations and some empirical examples (Marjanović andLaurin 2008, 2019;[START_REF] Grand | Phylogenetic inference using discrete characters: performance of ordered and unordered parsimony and of threeitem statements[END_REF][START_REF] Rineau | Experimental systematics: sensitivity of cladistic methods to polarization and character ordering schemes[END_REF][START_REF] Rineau | Impact of errors on cladistic inference: simulation-based comparison between parsimony and three-taxon analysis[END_REF]and references therein). As the same references show, ordering does not automatically increase the net resolution; in matrices that already contain one or more sufficiently strong false signals, revealing the phylogenetic signal introduces conflict and decreases the total resolution. Strikingly, none of our trees from analyses c, d1 or e (most parsimonious or bootstrap) support affinities between Chinlestegophis and caecilians to the exclusion of other lissamphibians, and in analysis d2 it is only one of two equally parsimonious options and only occurs in 44% of the bootstrap replicates (Supplementary Table 3). Although the bootstrap analysis of the original matrix under original conditions (analysis b; Fig. 4, Supplementary Table 1) does support diphyly of extant amphibians and an exclusive clade of Chinlestegophis and the three caecilians, this clade only occurs in 52% of the replicates, and an exclusive clade of frogs, salamanders, karaurids and Gerobatrachus to the exclusion of Chinlestegophis is found in only 43%. Our highly restricted revisions to the published matrix (analyses e1, e2; see Gee 2022 for a much more thorough, if cautious, revision), as well as the addition of Albanerpetidae to the taxon sample (analysis c) or the combination of both (analyses e3, e4), resulted in an exclusive clade comprising lissamphibians nested among dissorophoids (analyses c, e1, e3, e4 and its bootstrap analysis), or Lissamphibia as sister to Chinlestegophis + Rileymillerus within Stereospondyli (analyses e1, e2). The former is the currently most widespread hypothesis on the origin of the extant amphibian clades; the latter is new, but considerably less novel than extant amphibian diphyly as proposed by Pardo et al. (2017a).

It is worth noting again that the matrix contains evidence for a sister relationship between Lissamphibia and the Chinlestegophis + Rileymillerus clade, always within Stereospondyli, as recovered in analyses b (as one of several equal options), d1 (if only with 35% bootstrap support), d2 (as one of several equal options, with 27% bootstrap support), e1 (as one of two options) and e2. Although weakly supported, the fact that this result occurred in the original (analyses b-d) and the revised matrix (analyses e1, 2) suggests that Chinlestegophis may contribute important information about amphibian evolution in the context of the "temnospondyl hypothesis", even if it cannot be supported specifically as a stem-caecilian.

More likely, however, it may highlight convergence between the Chinlestegophis + Rileymillerus clade and lissamphibians in general or caecilians in particular; this is, moderately, supported by our bootstrap of analysis e4 (Fig. 18; Supplementary Table 4), where Chinlestegophis + Rileymillerus were recovered next to Lissamphibia in only 23% and as gymnophionomorphs in only 18% of the bootstrap replicates while a lissamphibianstereospondyl clade only has 9% bootstrap support (all three groupings are incompatible with the bootstrap tree: Fig. 18), as well as by the bootstrap analysis conducted by [START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF] extended data figure 6), where Lissamphibia excluding Chinlestegophis and Rileymillerus occurred in 55% of the replicates and Stereospondyli including a Chinlestegophis + Rileymillerus clade in 57%. Minimally, our results highlight the importance of albanerpetids for understanding lissamphibian relationships. Note that the first known complete and undistorted albanerpetid skull [START_REF] Daza | Enigmatic amphibians in mid-Cretaceous amber were chameleonlike ballistic feeders[END_REF] was not used by [START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF], who preferred using Celtedens ibericus-known from complete skeletons which are, however, thoroughly flattened and split through the bone, making certain parts very hard to interpret (McGowan 2002)-over a composite Albanerpetidae OTU. Using more than one albanerpetid OTU would probably require adding albanerpetidrelated characters to the matrix. Pardo et al. (2017a) emphasized that the topology they presented was supported by Bayesian inference. As discussed above (Matrices, Methodologies, and Missteps: Bayesian inference of phylogeny), missing data have unpredictable, sometimes very strong, effects on parametric methods of phylogenetics such as Bayesian inference, while the non-parametric method called parsimony is unaffected by this particular issue and therefore safer for paleontological data. Matrix quality remains more important than the method of analysis [START_REF] Simões | Giant taxon-character matrices: quality of character constructions remains critical regardless of size[END_REF][START_REF] Marjanović | Phylogeny of Paleozoic limbed vertebrates reassessed through revision and expansion of the largest published relevant data matrix[END_REF][START_REF] Gee | Returning to the roots: resolution, reproducibility, and robusticity in the phylogenetic inference of Dissorophidae (Amphibia: Temnospondyli)[END_REF][START_REF] Gee | The disadvantage of derivation: conserved systematic flaws in primary data have repeatedly biased the phylogenetic inference of Temnospondyli (Tetrapoda, Amphibia)[END_REF]and references therein).

Assessment of qualitative arguments

As further support for a close relationship between Chinlestegophis and caecilians, Pardo et al. (2017a) proposed a number of features supposedly shared between both taxa, and in some cases with other stereospondyls. Most of them are coded in the matrix in some form. We have reviewed them all above (Materials and Methods: Evaluation of potential synapomorphies and revisions to the published matrix) and find serious problems in all of them; none supports placing caecilians as the sister taxon of Chinlestegophis (or Chinlestegophis + Rileymillerus), or in stereospondyls in general. In many ways, the original discussion of features proposed to link Chinlestegophis and caecilians (Pardo et al. 2017a) described transformations that would be required for brachyopoids to give rise to caecilians, not what is actually visible in the preserved material.

Outside of characters addressed directly in Pardo et al. (2017a) we noted several other features by which Chinlestegophis resembles other stereospondyls but differs starkly from caecilians. The elongate nature of the basicranial articulation in Chinlestegophis superficially resembles that of Eocaecilia and Gymnophiona. However, in Chinlestegophis, the basicranial joint forms a strong girder, tightly sutured (Pardo et al. 2017a), similar to the condition seen in other stereospondyls. In caecilians, the basicranial joint is instead elongate, with a loosely constructed connection and thick cartilage covering the bony joint surfaces of both the os basale and the (epi)pterygoid or pterygoquadrate (Maddin et al. 2012b). Furthermore, the occipital morphology of Chinlestegophis is unlike that of any caecilian-or any other lissamphibian-in its possession of well-developed posttemporal fenestrae. In that respect, Chinlestegophis is very similar to brachyopoid stereospondyls, and loss of those fenestrae in caecilians and other lissamphibians is convergent under the topology advocated by Pardo et al. (2017a: fig. 2C).

What little is known and described of the postcranial skeleton (Pardo et al. 2017a: fig. S5) also resembles other stereospondyls but starkly differs from caecilians. The interclavicle of Chinlestegophis is a large plate, as usual for stereospondyls; in lissamphibians and albanerpetids, no trace of an interclavicle is known. Similarly, the clavicles consist mostly of a large plate and look unremarkable for a stereospondyl in all details of their shape; clavicles are absent in albanerpetids, caecilians (including Eocaecilia) and salamanders, and those of frogs are robust curved struts without any plate-like component, more similar to those of extant amniotes. A few neural arches are preserved in Chinlestegophis, but centra are not; this is standard for morphologically immature temnospondyls, but only observable (as presence or absence of ossification) in a very short phase in the ontogeny of frogs and hynobiid salamanders, and not known in caecilians-in Gegeneophis and in Caecilia orientalis Taylor, 1968, the centra ossify before the neural arches [START_REF] Müller | Ontogeny of the skull, lower jaw, and hyobranchial skeleton of Hypogeophis rostratus (Amphibia: Gymnophiona: Caeciliidae) revisited[END_REF][START_REF] Pérez | The morphology of prehatching embryos of Caecilia orientalis (Amphibia: Gymnophiona: Caeciliidae)[END_REF])-or albanerpetids (though albanerpetid ontogeny is virtually unknown). Indeed, early ossification of the centra (earlier than the neural arches or not long after them), quickly followed by suturing or even fusion to the neural arches, is a synapomorphy of lissamphibians and probably a few amphibamiforms (notably Doleserpeton and Gerobatrachus) under the "temnospondyl hypothesis", or of Seymouriamorpha, Chroniosuchia and Tetrapoda under the "lepospondyl hypothesis" [START_REF] Laurin | A new perspective on tetrapod phylogeny[END_REF][START_REF] Danto | How informative is vertebral development for the origin of lissamphibians?[END_REF]). It should be stressed that full neurocentral fusion is not found outside these clades (and Albanerpetidae), but is found in all known vertebrae of Eocaecilia [START_REF] Jenkins Fa | Anatomy of Eocaecilia micropodia, a limbed caecilian of the Early Jurassic[END_REF]) and the lone vertebra referred to Funcusvermis [START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF]. The ribs of Chinlestegophis are, plesiomorphically, longer than three successive vertebrae; they are shorter in amphibamiforms and a few select lepospondyls (Marjanović andLaurin 2008, 2019), and much shorter, about as long as one vertebra, in albanerpetids and all lissamphibians except a few peramorphic salamandrids (Marjanović and Witzmann 2015, and references therein). The only known similarity of the postcranium of Chinlestegophis to that of caecilians is body elongation; the massive dermal shoulder girdle does not suggest limb reduction, and indeed the presumed ulna has an unremarkable size.

Homoplastic rather than stepwise evolution

Interpretations of functional biology and evolutionary trends rely on our perspective of phylogenetic relationships. In the original description of Chinlestegophis, once a consensus tree was selected and reported, a number of the characteristics used in the matrices and discussed above were used to infer a stepwise evolution of traits toward the specialized fossorial and head-first burrowing lifestyle of caecilians. Those features include fusion of the lacrimal + maxilla and exoccipital + opisthotic (interpreted to represent stages in the consolidation of the skull), repositioning of the jaw suspension, small and laterally oriented eyes, etc. However, as we demonstrate above, most of those features have a wider distribution across Paleozoic tetrapods or present confounding problems of homoplasy across many disparate clades, extinct and extant.

When taxa exhibit traces of "specialized" morphology, care should be taken to avoid circular arguments based on functional considerations. In the case of potentially fossorial or burrowing vertebrates, in which selective pressures lead to a narrow range of morphologies regardless of ancestry (e.g., [START_REF] Barros | Head shape evolution in Gymnophthalmidae: does habitat use constrain the evolution of cranial design in fossorial lizards?[END_REF][START_REF] Sherratt | Evolution of cranial shape in caecilians (Amphibia: Gymnophiona)[END_REF][START_REF] Silva | The ecological origins of snakes as revealed by skull evolution[END_REF], Evans et al. 2022), it is particularly important that matrices be constructed to minimize redundant characters, and that characters sample anatomy broadly to avoid inadvertently "stacking the deck" and focusing on a heavily modified region. Through the use of tree statistics, character partitions and other methods to ascertain robustness, resulting topologies should be explored for potentially misleading signals. As mentioned above, tree statistics were mostly lacking from the original report of Chinlestegophis as a stem-caecilian, and Pardo et al. (2017a) did not discuss whether the specific characters uniting that taxon and caecilians might be correlated homoplasies associated with burrowing.

A related problem in this regard was the aforementioned removal of all lepospondyls from the unpublished matrix to create the published matrix after the initial recovery of Chinlestegophis as a temnospondyl by Pardo et al. (2017a). Lepospondyls have presented various challenges to reaching a consensus on lissamphibian origins [START_REF] Anderson | The phylogenetic trunk: maximal inclusion of taxa with missing data in an analysis of the Lepospondyli (Vertebrata, Tetrapoda)[END_REF][START_REF] Marjanović | A reevaluation of the evidence supporting an unorthodox hypothesis on the origin of extant amphibians[END_REF], 2009, 2013[START_REF] King | Which morphological characters are influential in a Bayesian phylogenetic analysis? Examples from the earliest osteichthyans[END_REF][START_REF] Laurin | What do ossification sequences tell us about the origin of extant amphibians?[END_REF][START_REF] Jansen | The scratch-digging lifestyle of the Permian "microsaur" Batropetes Carroll & Gaskill, 1971 as a model for the exaptative origin of jumping locomotion in frogs[END_REF][START_REF] Mann | Osteology and phylogenetic position of the diminutive 'microsaur' Odonterpeton triangulare from the Pennsylvanian of Linton, Ohio, and major features of recumbirostran phylogeny[END_REF]and references therein). Thus, including lepospondyls in tests of the origins of extant amphibians is critical to represent the full range of morphology during the Paleozoic and reveal potential homoplasy. Removing those taxa from analyses, and thus removing many different pathways and anatomical combinations, could make it more likely that any elongate, fossorial, or burrowing taxa be placed together incorrectly in the phylogeny, such as Chinlestegophis clustering with caecilians in some tree islands produced from the published matrix. [START_REF] Schoch | A Triassic stem-salamander from Kyrgyzstan and the origin of salamanders[END_REF] added three lepospondyls to the published matrix of Pardo et al. (2017a), but they did not add any characters that would help resolve their phylogeny or their relationship to lissamphibians. This was not changed by [START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF], in which those three lepospondyls form the sister-group of Greererpeton [START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF]: extended data fig. 567), an Early Carboniferous colosteid that is a more appropriate outgroup than the anthracosaur Proterogyrinus that was used as such.

Considering that alternative hypotheses of relationships are equally supported by the published matrix, even without broader taxonomic sampling to include lepospondyls, the proposed stepwise evolution of caecilian features falls apart. Rather than traits linking Chinlestegophis and caecilians, those same characteristics appear to represent homoplasy, as shown in trees that place Chinlestegophis close to but outside Lissamphibia (our analyses a, d, e2 and some MPTs plus the bootstrap tree of b), or far away (our analyses c, e1 and some

MPTs of b).

The adsymphysial bone and the lingual toothrow [START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF] made the novel argument that the lingual toothrow in the lower jaw of caecilians is borne not on a coronoid, but on the adsymphysial, a bone that is plesiomorphically present between coronoid 1 and the symphysis in tetrapodomorphs but generally thought to be absent in all lissamphibians, all lepo-and all temnospondyls among others. Where present, it usually bears teeth, often including a toothrow. [START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF] proposed to equate this toothrow with the short lingual toothrow seen at the symphysis of at least some Doleserpeton specimens and with the lingual toothrow of caecilians, including Funcusvermis, noting the absence of teeth in this region in Chinlestegophis. To populate the long branch between the non-temnospondyl Greererpeton and Doleserpeton in their fig. 3, they relied on isolated reports of an adsymphysial bone (also called "parasymphysial bone" or "parasymphysial plate") in other temnospondyls, listed in part 3 of their supplementary information. We find all of them questionable.

The most recent report of an adsymphysial in a temnospondyl concerns Cacops aspidephorus Williston, 1910[START_REF] Anderson | The anatomy of the dermatocranium and mandible of Cacops aspidephorus Williston, 1910 (Temnospondyli: Dissorophidae), from the Lower Permian of Texas[END_REF]), a reasonably close relative of Doleserpeton as shown in Kligman et al. (2023: fig. 3). Despite its novelty, Anderson et al. (2020: 9-10) did not argue for the interpretation they proposed, but merely briefly presented it as an uncontroversial fact; it is not mentioned in their Discussion section. The photos in their fig. 8 are not clear enough to demonstrate the suture between the adsymphysial and the dentary. In the photo in lingual view, we can see the line that is drawn solid as part of the suture in the interpretative drawing; but we cannot see the part that is drawn stippled, and we can see several other lines in the supposed adsymphysial and even in the supposed dentary that could be sutures or fractures. The photo in ventral view is even less clear. The proposed adsymphysial would bear the "tusks"/"fangs" that lie lingual of the (dentary) toothrow (Anderson et al. 2020: fig. 8;Kligman et al. 2023: fig. 3); it should be noted that this combination of a toothrow on the dentary with "tusks" on the adsymphysial but no other teeth in this region has not been documented elsewhere. In numerous non-temnospondyls with an uncontroversial adsymphysial bone, there are "tusks" on the dentary, followed labially by the dentary toothrow and lingually sometimes by an adsymphysial toothrow and/or, yet further lingually, adsymphysial "tusks" (e.g., [START_REF] Ahlberg | Lower jaws, lower tetrapods-a review based on the Devonian genus Acanthostega[END_REF][START_REF] Lombard | The mandible of Whatcheeria deltae, an early tetrapod from the Late Mississippian of Iowa[END_REF]. Not having studied the C. aspidephorus specimen, we will not argue for or against either interpretation any further, but we reiterate that the published case is insufficient to decide the question.

An adsymphysial was previously reported in Cacops morrisi [START_REF] Reisz | The armoured dissorophid Cacops from the Early Permian of Oklahoma and the exploitation of the terrestrial realm by amphibians[END_REF], in a single sentence and not illustrated (Reisz et al. 2009: 794). Sutures around the putative adsymphysial are not present in the remarkably few published specimens of Doleserpeton (e.g., Sigurdsen and Bolt 2010: fig. 6A;Kligman et al. 2023: fig. 3). In Georgenthalia, a close relative of Doleserpeton, the usual expansion of the dentary at the symphysis (compare Salamandra: Kligman et al. 2023: fig. 3) was suggested to be an adsymphysial in what seems to be an overedited paragraph that is not quite clear (Anderson et al. 2008b: 67). No sutures were reported or illustrated, and the preservation in ventral view obscures any teeth.

The evidence for an adsymphysial in the stereospondyl Parotosuchus (Shishkin and Sulej 2009: 52-53, 69) consists of nothing but a notch in the occlusal face of the mesial end of the dentary of early juveniles, between the toothrow and the tusks, that was identified in that paper as marking the mesial end of Meckel's cartilage, with the dentary growing around it in later documented ontogenetic stages. The unspoken assumption that every notch must be a marker of fusion of two separate bones was routinely used in the 1930s to infer about three times as many bones in the skulls of immature caecilians as have actually been observed (Müller 2006: 983); it should not be perpetuated.

In two specimens of the stereospondyl Plagiosuchus, "there is evidence for the presence of an additional small, toothless, dorsal symphyseal ossification" which "probably represents an adsymphyseal" according to Damiani et al. (2009: 363). The photo of one these specimens (fig. 4A), and probably the preservation as well, is insufficient to determine if the "ossification" is surrounded by sutures or, for example, continuous with the ossified Meckelian part of the symphysis.

Finally, in one of the four partial lower jaws referred to the stereospondyl Qantas, "the symphyseal plate contains not only the dentary, but also an additional bone, the dorsal surface of which has symphyseal canines. This additional ossification is probably homologous to the adsymphyseal" (Novikov 2012: 183) We conclude that the evidence to equate the lingual toothrow of caecilians to that of Doleserpeton, or the bone which bears it to the adsymphysial, is at present very weak even if caecilians are assumed to be temnospondyls. Admittedly, coronoids that reach the symphysis have not been documented either (the gap is smaller in the lepospondyls Pantylus and Euryodus than in Chinlestegophis, but still clear [START_REF] Romer | The cranial anatomy of the Permian amphibian Pantylus[END_REF][START_REF] Gee | Computed tomographic analysis of the cranium of the early Permian recumbirostran 'microsaur' Euryodus dalyae reveals new details of the braincase and mandible[END_REF]; the best candidates are Platyrhinops, a close relative of Doleserpeton and Georgenthalia, in which the denticle-bearing lingual surface of the lower jaw extends to the symphysis or nearly so, but the denticles obscure any sutures [START_REF] Clack | Morphology and systematics of the Pennsylvanian amphibian Platyrhinops lyelli (Amphibia: Temnospondyli)[END_REF], and Acheloma, where the dentary bears "tusks" lingual of the toothrow and is lingually followed by a separate bone which carries a denticle field and participates in the symphysis, but the jaw fragments illustrated by Polley and Reisz (2011: fig. 9, 10) are too short to clarify the identity of this bone.

Evolutionary ecology

The grooves for the lateral-line organ identified by Pardo et al. (2017a) on the skull of Chinlestegophis indicate an animal that was strictly aquatic for at least part of its adult life. In contrast, there is no evidence of lateral-line grooves or other aquatic features in Eocaecilia or the admittedly fragmentary Funcusvermis, and among extant caecilians aquatic lifestyles are restricted to larvae (of those few taxa that have them) and the highly nested clade Typhlonectidae. The inference of an aquatic lifestyle in Chinlestegophis is further supported by its poorly ossified vertebral column and probably also by its craniocaudally elongate platelike clavicles. Perhaps aquatic vs. terrestrial lifestyles explain why Chinlestegophis was able to coexist with caecilians like the slightly older Funcusvermis; the wide, flat vertebra referred to the latter lacks a neural spine, interpreted as a fossorial adaptation by [START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF].

Matrix quality, taxon sampling and character sampling

The discussion above takes at face value both the coding and scoring of the two matrices, and their character and taxon samples, apart from our limited modifications in analyses c, d2 and e; but these issues deserve comments. We have not scrutinized the matrices in full (see [START_REF] Gee | The disadvantage of derivation: conserved systematic flaws in primary data have repeatedly biased the phylogenetic inference of Temnospondyli (Tetrapoda, Amphibia)[END_REF] for a cautious but comprehensive treatment of the published matrix of Pardo et al. [2017a]), as we wished only to test whether alternative topologies can be equally (or better) supported by the original matrices, and to show the impact of a few scoring changes that were obviously needed. The absence of lepospondyls in the matrix published by Pardo et al. (2017a) prevents us from looking into how many extra steps an origin of lissamphibians among them would imply, compared to an origin among temnospondyls. Similarly, the removal of characters that are variable only among lepospondyls prevents using the published matrix as a starting point for such comparisons; unfortunately, this was not changed by [START_REF] Schoch | A Triassic stem-salamander from Kyrgyzstan and the origin of salamanders[END_REF] or [START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF] despite the former's addition of three lepospondyl taxa which the latter then retained. The heretofore unpublished precursor matrix remains available for this purpose, but it would need to be updated and greatly enlarged; in its present form, only four extra steps need to be added to the original 1450 to make an odd version of the lepospondyl hypothesis possible.

Conclusions

Published in one of the most prestigious journals, the description of Chinlestegophis (Pardo et al. 2017a) resulted in a new hypothesis about the origins of the extant amphibian clades and a new scenario for the origin of caecilians and their fossorial lifestyle that has attracted attention far beyond that of specialist researchers [START_REF] Pough | Vertebrate Life[END_REF]. We show that these exciting proposals are poorly supported by the original datasets and the original methods of analysis, as well as by limited revisions to one of the datasets aimed at eliminating the most conspicuous cases of character redundancy and a few questionable anatomical interpretations of Chinlestegophis and other taxa. The question of lissamphibian origins remains unsolved, although our revisions to the matrix reveal further support for Lissamphibia excluding Chinlestegophis and any Paleozoic taxa. In any case, we join [START_REF] Kligman | Triassic stem caecilian supports dissorophoid origin of living amphibians[END_REF] in cautioning against calibrating the divergence of caecilians and batrachians according to the phylogenetic hypothesis of Pardo et al. (2017a), i.e., by using the Late Carboniferous age of certain dissorophoid temnospondyls as the calibration date.

Concerning phylogenetics, we reiterate that the majority-rule consensus is not a useful representation of the result of a parsimony analysis, and that not all issues with Bayesian analysis of matrices with missing data have been solved; but most importantly, matrix quality remains paramount in phylogenetic analysis. This concerns typographic errors, misinterpretations of published literature, redundant characters (in the dataset we revised, the double toothrow in the lower jaw of caecilians was coded as seven characters that an analysis could only treat as independent), characters that represent two or more independently varying features, and inconsistencies in scoring.

↓ Figure 1 .

 1 Strict consensus of the four MPTs obtained by Marjanović & Laurin (2009: electronic supplementary material 2) from their modified version of the matrix of Anderson et al. (2008a) with ordering of clinal characters. Note that contrary to Anderson

  The published matrix(Pardo et al. 2017a: supporting information part D), which generated the trees shown in Pardo et al. (2017a: fig. 2, 3, S7), has 345 characters (23 parsimonyuninformative) and 76 OTUs. It is built on the unpublished matrix by the addition of characters and taxa taken primarily from Schoch (2013)-see Gee (2022) for a thorough discussion of that lineage of matrices.

  Daza et al. (2020: fig. 4E, S14) added Albanerpetidae-as a composite OTU based mainly on

  and discussed by Theska et al. (2018), is ontogenetic fusion of the lacrimal to the maxilla documented (Hypogeophis rostratus [Cuvier, 1829]: Müller 2006; Gegeneophis ramaswamii Taylor, 1964: Müller et al. 2005; probably Idiocranium russeli Parker, 1936: Theska et al. 2018; possibly the "prefrontal" of Dermophis mexicanus [Duméril and Bibron, 1841]: Wake and

"

  denticles": Gee et al. 2017) on the splenial of any species of Trimerorhachis has never been claimed or illustrated in the literature (most recently Milner and Schoch 2013), and D. M.

Finally,

  Chinlestegophis was scored as unknown; we have corrected this to 1 because Pardo et al. (2017a: fig. S3) depicted the absence of teeth on the splenial. It is worth mention that Pardo et al. (2017a) agreed on the absence of splenials in caecilians: all three were scored in the published matrix as lacking splenials (state 2 of character 264).

( 1 )

 1 , smaller than marginal(2)." State 1 was scored exclusively for the three caecilians, Chinlestegophis and the stereospondyl Benthosuchus. We rescored Chinlestegophis as possessing state 2 because Pardo et al. (2017a: fig.S3) showed that the coronoid teeth are smaller than the marginal teeth.

  Chatterjee 2000: fig. 1.2, 2.2); Epicrionops and Ichthyophis have rostrally pointed cultriform processes that widen rather suddenly at the caudal ends of their contacts with the (maxillo)palatines (Jenkins et al. 2007: fig. 6B, D). But, in any case, Chinlestegophis and Eocaecilia were correctly scored 0, so (like Gee 2022 and Kligman et al. 2023) we have not modified this character or its scores. "[O]ccipital condyles extend far beyond posterior edge of skull roof" is the next character state proposed to be shared by Chinlestegophis and caecilians (Pardo et al. 2017a: E5390). It is coded in the published matrix as character 137: "Exoccipital condyles. Short and broad base, projecting only with their posterior half behind the rim of the skull table (0), or almost the complete element posterior to level of occipital flange (1)". State 1 was scored exclusively for most trematosauroids and brachyopoids, Rileymillerus, Chinlestegophis, Eocaecilia, Cryptobranchus and Ambystoma. However, that state (which appears to be more widespread among stereospondyl and dvinosaurian temnospondyls: Kligman et al. 2023: supp. inf. part 3) can be reached by elongating the condyles, reducing the caudal extent of the skull roof, extending the braincase caudally, or a combination of two or all three factors. The stalked occipital condyles of Chinlestegophis (and Rileymillerus: Bolt and Chatterjee 2000) are standard for stereospondyls, but are not found in any caecilians; this was beautifully illustrated by Pardo et al. (2017a: fig. 3). Rather, lissamphibians (and albanerpetids: Daza et al. 2020) generally expose large parts of the otic capsules in dorsal view, resulting in the occipital condyles lying entirely far beyond the posterior edge of the skull roof. The condyles themselves are weakly elongated in some caecilians and not at all in others, as again shown by Pardo et al. (2017a: fig. 3) and described and illustrated by Jenkins et al. (2007: fig. 1-4, 6

  . S1: 35), the statement of identity rests entirely on the reconstruction drawing published by Jenkins et al. (2007: fig. 1), which shows almost no uncertainty (by dashed lines, differential shading or any other means), but rather depicts a preferred hypothesis of what an undamaged skull looked like. The text, specimen drawings, and photos in Jenkins et al. (2007), further supported by the μCT rendering in Maddin et al. (2012a: fig.

  that the real tabular could be part of the os basale in Eocaecilia is unfounded: there is no reason to think, from their shapes or topological relationships, that the dorsal sides of the ossa basalia contain tabulars or any other dermal bones of the skull roof (Jenkins et al. 2007: fig. 2, showing the holotype; compare extant caecilians and their ontogeny: Wake and Hanken 1982; Müller et al. 2005; Müller 2006; Theska et al. 2018). In their Discussion section, Pardo et al. (2017a: E5393) made a far-reaching claim: "a sulcus associated with the opening of the nasolacrimal duct in the orbit is present in both Chinlestegophis and Eocaecilia in a similar position to the tentacular sulcus of the basal caecilian Epicrionops petersi", citing Jenkins et al. (2007: fig.

  ) found 12 MPTs of 1450 steps, as reported in Part G of the supplementary information of Pardo et al. (2017a); their previously unreported indices are: CI excluding uninformative characters = 0.2668, RI = 0.6532, RC = 0.1815. The resulting strict consensus is identical to that of Pardo et al. (2017a: fig. S6B), with Chinlestegophis and Rileymillerus positioned as the sister-group to all other amphibamiform temnospondyls including Lissamphibia, which in turn contains Eocaecilia and Gymnophiona.

Figure 3 .

 3 Figure 3. Strict consensus of the 48 MPTs obtained from the unpublished matrix used by Pardo et al. (2017a) in an analysis (a2; seeTable 1) constrained against the

↓ Figure 4 .

 4 Bootstrap tree obtained from the published matrix used by Pardo et al.

  Gerobatrachus)))) within Dissorophoidea. Likewise, Chinlestegophis and Rileymillerus are positioned as in Daza et al. (2020: fig. S14), as the sister-group to Brachyopoidea within Stereospondyli. The addition of Albanerpetidae renders seven characters parsimony-informative, so that 329 of the total of 345 now have this status. ↓ Figure 5. Strict consensus of the 45 MPTs obtained from the published matrix of Pardo et al. (2017a) with addition of Albanerpetidae from Daza et al. (2020); all characters are unordered (analysis c). The resolution differs slightly from Daza et al. (2020: fig. S14) because we used parsimony with equal rather than implied weights. Colors, boldface and Dendrerpetidae as in Fig. 3 and 4 here and in all following figures; Tr.-oidea = Trematosauroidea. ↑ Figure 18. Bootstrap tree of analysis e4 (published matrix of Pardo et al. [2017a] after revision, Albanerpetidae added from Daza et al. [2020], clinal characters ordered). Bootstrap values ≥ 50% in boldface. B. = Brachyopoidea; Tr.-oidea = Trematosauroidea.

  . There is no further description or illustration; the line drawings of the holotype, another lower-jaw ramus, lack any indication of such an extra bone (fig. 1(b), (c)).

  : fig. S7B) is almost entirely identical (Serra Silva and Wilkinson 2021: fig. 2) to the MRC of that one island and fails to represent the MPTs on the

	other islands.
	Of the other islands, one (figured by Marjanović and Laurin, 2019: fig. 30I; Serra Silva and
	Wilkinson 2021: fig. 3c) agrees with the most popular hypothesis of lissamphibian origins,
	which is also supported by the previously unpublished matrix of Pardo et al. (2017a: fig. S6):
	that Lissamphibia (including Eocaecilia but excluding Chinlestegophis and Rileymillerus)

Table 1 .

 1 Overview of analyses and results presented here. 381

	Analysis Our	Base matrix	Modifications	Ordering		Length	Topology
		figure	of Pardo et	from Pardo et	of clinal	inf. char.	of
			al. (2017a)	al. (2017a)	characters		MPTs
	-	1	-	n/a	yes	212	1264	Marjanović & Laurin (2009: supplementary figure), matrix modified
								from Anderson et al. (2008a), clinal characters ordered; LH:
								Lissamphibia next to Brachydectes (Lysorophia), Gerobatrachus in
								Amphibamiformes
	a1	2	unpublished:	none	no	292	1450	as in Pardo et al. (2017a: fig. S6B)
			SF 1
	a2	3	unpublished:	constraint for	no	292	1454	LH; Lissamphibia contains Gerobatrachus, positions of
			SF 1	LH				Chinlestegophis + Rileymillerus as in a1
	b	-	published: SF 3	none	no	322	1514	five (2017a: fig. S7B)
	bootstrap	4	published:	none	no	322	n/a	Diphyly of modern amphibians: Karauridae + Batrachia next to
	of b		SF 3					Gerobatrachus (43%), caecilians next to Chinlestegophis (52%) in
								Stereospondyli
	c	5	published:	addition of	no	329	1565	as in Daza et al. (2020: fig. S14) except for slightly lower resolution;
			SF 3	Albanerpetidae				(Albanerpetidae (Karauridae, Lissamphibia)) in Amphibamiformes,
				from Daza et				Chinlestegophis + Rileymillerus in Stereospondyli
				al. (2020)
	d1	6	published:	none	yes	324	1563	Lissamphibia next to Chinlestegophis + Rileymillerus in
			SF 4					Stereospondyli

islands: caecilians next to batrachians, Lissamphibia, when present, in Amphibamiformes or Stereospondyli; Chinlestegophis in Gymnophionomorpha and/or Stereospondyli; figures in Serra Silva & Wilkinson (2021: fig. 2-4), simplified figures in Marjanović & Laurin (2019: fig. 30I-K), only one island figured by Pardo et al. Lissamphibia (71%) in Amphibamiformes (Dissorophoidea: 36%), Chinlestegophis + Rileymillerus in Stereospondyli (35%); Chinlestegophis + Rileymillerus as gymnophionomorphs (18%) or next to Lissamphibia (23%), let alone Lissamphibia in Stereospondyli (9%

Table 1 ), using the unpublished matrix used by Pardo et al. (2017a: fig.

 1

Acknowledgments

Jason Pardo and Adam Huttenlocker kindly sent us both matrices, and J. Pardo and Ben Kligman discussed certain characters with us. D. M.'s understanding of current issues in phylogenetics benefited from a course taught by Tiago Simões and Oksana Vernygora and organized by Transmitting Science.

Ordering continuous characters

Ordering of clinal characters (analysis d1) in the otherwise unmodified published matrix of Pardo et al. (2017a) rendered two characters parsimony-informative (for a total of 324 of the 345 characters in the matrix) and resulted in a single island of 14 MPTs (length = 1563 steps, CI excluding uninformative characters = 0.2500, RI = 0.6882, RC = 0.1770). The strict consensus is almost completely resolved (Fig. 6) and shows Lissamphibia as the sister-group of the clade formed by Chinlestegophis and Rileymillerus, nested within the brachyopoid stereospondyls.

The bootstrap tree of analysis d1 (Fig. 7) recovers a moderately supported (55% frequency) Lissamphibia with the same sister-group, and the Chinlestegophis-Rileymillerus clade is again less supported (41%). Affinities between the Chinlestegophis-Rileymillerus clade and Lissamphibia are slightly better supported than with unordered states, but at 35%, this clade is still weak. The position of Chinlestegophis as a stem-caecilian, incompatible with the bootstrap tree, occurs with a frequency of 39% (Supplementary Table 2). Lissamphibia is separated from Doleserpeton or Gerobatrachus by bootstrap values no higher than 36%, but an exclusive clade of frogs, salamanders, karaurids and Gerobatrachus has only 31% support (even less if any other dissorophoids are added) and an exclusive Lissamphibia-Gerobatrachus clade only 18% (likewise less if others are added; Supplementary Table 2). Gerobatrachus or Doleserpeton is comparatively high (62%), but the support for exclusion from Trematosauria within Stereospondyli is low (26%). Noteworthy, on the other hand, is the support (72%) for excluding Karauridae (Karaurus and Kokartus), universally considered a clade of stem-salamanders (Jones et al. 2022, and references therein), from Batrachia (frogs + salamanders). An exclusive clade of Albanerpetidae, Karauridae and Batrachia has 63% support, contradicting [START_REF] Matsumoto | The first record of albanerpetontid amphibians (Amphibia: Albanerpetontidae) from East Asia[END_REF] and [START_REF] Daza | Enigmatic amphibians in mid-Cretaceous amber were chameleonlike ballistic feeders[END_REF]; this may be due to character sampling.

↓

The list of bipartitions not compatible with the bootstrap tree (Supplementary Table 3) reveals 44% bootstrap support for a clade of Chinlestegophis and the three caecilians (slightly more than the 38% without ordering and without Albanerpetidae) and 30% for a clade that includes these four and Rileymillerus. Chinlestegophis and Rileymillerus are excluded from Dissorophoidea + Lissamphibia in 21% of the bootstrap replicates. The support for exclusion of Albanerpetidae from Lissamphibia (17%) is lower than it could be given the 63% for a specific placement in Lissamphibia mentioned above; 13% of the replicates find all dissorophoids, all batrachians, the karaurids and Albanerpetidae in an exclusive clade, 7% group the caecilians with Albanerpetidae, 6% group all lissamphibians with Chinlestegophis to the exclusion of Albanerpetidae.

Revised published matrix

The matrix including the changes we proposed was run both with all characters unordered, as they were in Pardo et al. (2017a), and with the herein proposed characters that form morphological clines ordered; both of these options were used both without and with the addition of Albanerpetidae from [START_REF] Daza | Enigmatic amphibians in mid-Cretaceous amber were chameleonlike ballistic feeders[END_REF]. The analysis with all characters unordered and Albanerpetidae excluded (e1) resulted in 1341 MPTs, each with a length of 1514 steps (CI excluding uninformative characters = 0.2535, RI = 0.6849, RC = 0.1801), distributed over seven islands of optimal trees. Of the 344 characters, only 319 are parsimony-informative. In all seven islands, Lissamphibia is recovered and excludes Chinlestegophis (as well as Rileymillerus). One island (Fig. 11) places (Brachyopoidea (Lissamphibia (Chinlestegophis, Rileymillerus))) in Stereospondyli, and Karauridae on the batrachian stem; the others recover Lissamphibia next to Gerobatrachus in Amphibamiformes while the Chinlestegophis-Rileymillerus clade remains nested in Stereospondyli next to or inside Brachyopoidea, and Lissamphibia is either (frogs (karaurids (caecilians, salamanders))) (Fig. 12), contradicting the molecular consensus [START_REF] Hime | Phylogenomics reveals ancient gene tree discordance in the amphibian tree of life[END_REF], or (caecilians (frogs (karaurids, salamanders))) (Fig. 13).

↓ Figure 11. Strict consensus tree of some of the 1341 MPTs recovered in analysis e1

(published matrix of Pardo et al. [2017a] after revision, all characters unordered). For the other MPTs, see Figs. 12 and 13. Br.-oidea = Brachyopoidea.

↓↓ Figure 12. Strict consensus of each of two further islands of MPTs from analysis e1.

For space reasons, one of the two resolutions of Trematosauria is mirrored and presented without species names. Tr.-oidea = Trematosauroidea. The branch marked "(wrong)" contradicts the molecular consensus [START_REF] Hime | Phylogenomics reveals ancient gene tree discordance in the amphibian tree of life[END_REF].

↓↓↓ Figure 13. Strict consensus of each of the remaining four islands of MPTs from

analysis e1. Except for Lissamphibia, the part depicted here is identical in all four islands; Lissamphibia is resolved either as shown or as in Fig. 12, Stereospondyli is resolved as in In the ordered analysis e4, 36 MPTs are recovered (1619 steps, CI without uninformative characters = 0.2425, RI = 0.6812, RC = 0.1687). They all group the Rileymillerus + Chinlestegophis clade with Brachyopoidea as in analysis e3, while Lissamphibia is nested among the amphibamiform dissorophoids, closer to Apateon than to Gerobatrachus or Doleserpeton. PAUP* groups the MPTs into three islands depending on how they resolve amphibamiform phylogeny: one island (Fig. 16) has (Doleserpeton (Gerobatrachus (Apateon, Lissamphibia))) inside Amphibamidae, Albanerpetidae on the caecilian stem and Karauridae on the batrachian stem; the other two (Fig. 17

List of supplements:

Supplementary File 1: Mesquite NEXUS file of Pardo et al. (2017a: fig. S6), previously unpublished. We have added a PAUP block that repeats our unconstrained and constrained analyses (a1, a2) if the file is executed in PAUP*, and a TREES block that contains one tree resulting from each analysis; before conducting the analyses, the PAUP block performs the statistical tests comparing the trees in the TREES block. Otherwise the file remains as provided by J. Pardo and A. Huttenlocker. Supplementary File 2: Supplementary Tables 1234