New opabiniid diversifies the weirdest wonders of the euarthropod lower stem group

Once considered ‘weird wonders’ of the Cambrian, the emblematic Burgess Shale animals Anomalocaris and Opabinia are now recognized as lower stem-group euarthropods. Anomalocaris and its relatives (radiodonts) had a worldwide distribution and survived until at least the Devonian, whereas - despite intense study - Opabinia remains the only formally described opabiniid to date. Here we reinterpret a fossil from the Wheeler Formation of Utah as a new opabiniid, KUMIP 314087. By visualizing the sample of phylogenetic topologies in treespace, our results fortify support for the position of KUMIP 314087 beyond the nodal support traditionally applied. Our phylogenetic evidence expands opabiniids to multiple Cambrian Stages spanning approximately five million years. Our results underscore the power of treespace visualization for resolving imperfectly preserved fossils and expanding the known diversity and spatiotemporal ranges within the euarthropod lower stem group. Additional note This work contains a new biological name. New names in preprints are not considered available by the ICZN. To avoid ambiguity, the new biological name is not included in this preprint, and the specimen number (KUMIP 314087) is used as a placeholder. Cover image. Artistic reconstruction of the new opabiniid from the Wheeler Formation, Utah, USA (Cambrian: Drumian). Artwork by F. Anthony.


New opabiniid diversifies the weirdest wonders of the euarthropod lower stem group
Stephen Pates 1,2,4,* , Joanna M. Wolfe 1,4,* , Rudy Lerosey-Aubril 1 , Allison C. Daley 3 , and Javier Ortega-Hernández 1 Introduction Euarthropods (e.g. chelicerates, myriapods, and pancrustaceans including insects) have conquered Earth's biosphere, comprising over 80% of living animal species (Santos, de Almeida and Fernandes, 2021). Indeed, Euarthropoda has been the most diverse animal phylum for over half a billion years, documented by prolific trace and body fossil records that extend back to the early Cambrian (~537 and ~521 million years ago respectively) (Daley et al., 2018). As the majority of these earliest euarthropods did not contain mineralised hard parts, we rely on remarkable fossil deposits such as the Burgess Shale, which preserve soft-bodied components of ancient biotas, to reveal critical data on the extraordinary diversity, disparity, and early evolution of Cambrian euarthropods (Gould, 1989).
Two of the most peculiar Burgess Shale animals, Anomalocaris and Opabinia, illustrate the complicated history of research of many Cambrian soft-bodied taxa -a result of their unfamiliar morphologies compared to the occupants of modern oceans Briggs, 2015b). Both Anomalocaris and Opabinia possess compound eyes, lateral swimming flaps, filamentous setal structures, and a tail fan Whittington and Briggs, 1985;Budd and Daley, 2012;Daley and Edgecombe, 2014). Recent work has revealed that Anomalocaris and its relatives, the radiodonts, are united by the presence of paired sclerotized protocerebral frontal appendages and mouthparts composed of plates of multiple sizes, forming a diverse group containing over 20 taxa Cong et al., 2014;Vinther et al., 2014;Ortega-Hernández, Janssen and Budd, 2017;Liu et al., 2018;. Radiodonts range in age from the early Cambrian to at least the Devonian, and have been recovered from numerous palaeocontinents (Kühl, Briggs and Rust, 2009;Daley and Budd, 2010;Cong et al., 2014;Daley and Legg, 2015;Fu et al., 2019). Meanwhile, the most celebrated animal from the Burgess Shale (Budd, 1996;Briggs, 2015a), Opabinia regalis, with its head bearing five stalked eyes and a proboscis, remains the only opabiniid species confidently identified and is only known from a single quarry in the Burgess Shale. Myoscolex ateles from the Emu Bay Shale was proposed as a possible close relative (Briggs and Nedin, 1997), though this interpretation was hotly contested, and other authors have proposed a polychaete affinity (Glaessner, 1979;Dzik, 2004).
Radiodonts and Opabinia are now confidently placed within the lower stem of Euarthropoda (Budd, 1996;Ortega-Hernández, 2016), following the assignment of nearly all Cambrian soft-bodied animals to stem and crown groups of modern phyla (e.g. Budd and Jensen, 2000). Fossils illustrating the sequence of character evolution along the euarthropod stem lineage provide the framework for understanding the evolutionary origins of the segmented, modular exoskeleton and the specialized appendages that underpin the ecological success of this phylum (Ortega-Hernández, 2016). Difficulties remain in interpreting the anatomical details, morphology, and phylogenetic placement of exceptional Cambrian fossils. In Opabinia, the presence of lobopodous limbs in addition to the swimming flaps cannot be confirmed, and the architecture of the flaps and associated setal blades remains elusive (Budd, 1996;Zhang and Briggs, 2007;Budd and Daley, 2012). Consequently, the phylogenetic position of Opabinia relative to radiodonts and deuteropods remains hotly debated. The identification of plesiomorphic and apomorphic characters has required new imaging and reinterpretations of existing specimens, the discovery of new fossil material and localities, and, crucially, the improvement of phylogenetic analysis methods to evaluate alternative relationships of enigmatic taxa.
Here we redescribe a fossil specimen from the Drumian Wheeler Formation of Utah, previously described as an anomalocaridid radiodont (Briggs et al., 2008). KUMIP 314087 is a new genus and species that shares characters with both radiodonts and Opabinia regalis. We evaluate its phylogenetic position using both maximum parsimony (MP) and Bayesian inference (BI) and further interrogate the support for alternative relationships for KUMIP 314087 by visualizing the frequency and variation of these alternatives in treespace (Hillis, Heath and St. John, 2005;Wright and Lloyd, 2020). All analyses support an opabiniid affinity for KUMIP 314087. Our results evaluate the relative support for different hypotheses relating to the evolutionary acquisition of characters that define crown group euarthropods.

Systematic Palaeontology.
Superphylum PANARTHROPODA Nielsen, 1995Family OPABINIIDAE Walcott, 1912 Diagnosis. Panarthropod with a short head region bearing a single unjointed appendage ('proboscis'); slender trunk with dorsally transverse furrows delimiting segments; one pair of lateral flaps per body segment; setal blades cover at least part of anterior margin of lateral flaps; caudal fan composed of paired caudal blades; pair of short caudal rami with serrated adaxial margins.
Description. KUMIP 314087 represents a complete specimen preserved as a compression in dorsolateral view, with a length (sagittal) of 29 mm (Fig. 1). The overall organization consists of a short head, an elongate trunk with lateral body flaps, and a posterior tail fan.
The head region measures ~10% of the total body length, and preserves traces of eyes, the mouth and the proboscis. In the ventral posterior region of the head, two curved red structures surround a circular opening, interpreted as a mouth opening ("mo" in Fig. 2b). The mouth opening is immediately proximal to a dark red region of two overlapping oval shapes, tentatively interpreted as a pair of lateral eyes ("ey?" in Fig. 2b). Ventral to this, a creamcoloured elongated conical structure extends from the head ventrally ("pb" in Fig. 2b), with a sub-millimetric orange linear structure of variable width located along its midline ("ic" in Fig.  2b). This is tentatively identified as a proboscis with an internal cavity (Fig. 2b).
The slender trunk (~72% total body length) is widest towards the anterior and tapers towards the posterior. The dorsal margin bears a 'corrugated' appearance, with indents marking the point where dorsal intersegmental furrows intersect with the margin of the body ("df" in Figs. 1, 3). Blocks consisting of dozens of parallel darkly pigmented fine linear structures are arranged along the dorsal furrows and are interpreted as setal blades ("sb" in Figs. 1, 3). These blocks extend across the entire dorsal surface of the animal and continue laterally over the change in slope on the right side of the body. These setal structures display a triangular termination, which overlaps the anterior part of the base of the flaps (Figs. 1, 3).  (Figs. 1, 3). Towards the posterior of the animal, a thin structure protruding from underneath a lateral flap could represent part of a ventral lobopodous limb, though the presence of additional material in the matrix of a similar width and orientation makes such an identification only very tentative ("ll?" in Fig. 3). Structures of a similar width can be seen related to flaps seven and eight ("ll?" in Fig. 1), though these may represent a poorly preserved anterior margin of these flaps. The posterior of the body (~18% total body length) consists of a tail fan composed of paired elongate blades, and a pair of caudal rami. The tail has been twisted slightly and the right set of tail blades has been preserved flattened ventrally due to the dorsolateral aspect of preservation. The tail fan has seven, likely eight blades on the left side ("cb" in Fig. 2), while those on the right cannot be counted with certainty. Unlike the body flaps, these caudal blades are not associated with setal structures. They overlap one another proximally, a given blade largely concealing the blade immediately anterior to it. Each blade has the outline of an elongate parallelogram, longer on the anterior than posterior margin, and their acuminate distal regions splay out. The caudal rami are short (~3 mm length), converge towards a common point at the posterior of the animal, extend from the body at a different angle to the caudal blades, and exhibit serrated axial margins ("cr" in Figs. 1, 2).

Remarks.
KUMIP 314087 was originally described as an anomalocaridid radiodont based on the similarity in the shape of caudal blades to Anomalocaris taxa and the reverse imbrication of the flaps (Briggs et al., 2008). KUMIP 314087 also shares with radiodonts the presence of setal blades that extend over the dorsal midline of the body. The recognition herein of a putative proboscis with internal cavity, dorsally transverse furrows that delimit segments in the trunk, and a short pair of caudal rami with serrated axial margins, support closer affinities of this animal with Opabinia regalis, rather than with Anomalocaris. The unique combination of characters, and novel features such as the elaborate tail fan, warrant the erection of a new genus and species.
Among members of the euarthropod lower stem-group, a proboscis has only been reported previously in Opabinia . The proboscis of KUMIP 314087 protrudes from the head in a similar position relative to the tentatively interpreted eyes as in Opabinia. In addition, a feature comparable to the internal cavity within the proboscis of Opabinia can be observed in KUMIP 314087 (Fig. 2). However, unlike Opabinia, no annulations can be seen in this structure, as it is too poorly preserved. KUMIP 314087 also has dorsal furrows delineating the body segments. Such dorsal epidermal segmentation is seen in Opabinia but is unknown in all other lower stem group euarthropods (including Kerygmachela, Pambdelurion and all radiodonts) (Ortega-Hernández, 2016).
KUMIP 314087 also displays characters known in both radiodonts and Opabinia. The slender, broadly rectangular dorsal outline of the body in KUMIP 314087 is comparable to what is observed in both Opabinia and the radiodonts Aegirocassis and Hurdia. This outline contrasts with the diamond-like outline of many radiodonts, including Amplectobelua symbrachiata, Anomalocaris canadensis, and Peytoia nathorsti (Whittington and Briggs, 1985;Chen, Ramsköld and Zhou, 1994;Daley and Edgecombe, 2014). In addition, both Opabinia and radiodonts possess setal blades, in varying arrangements (Supplementary Fig. 1). In Aegirocassis and Peytoia nathorsti, these structures form a single block per body segment, which covers the entire dorsal surface (Van Roy, , while in Opabinia the setal structures cover the anterior margin of the flaps (Budd and Daley, 2012). KUMIP 314087 appears to display a combination of these two states, with setal blades covering the dorsal surface in a single block, which extends laterally to the basal region of the anterior margins of corresponding flaps (Fig. 3). Strengthened anterior margins of lateral flaps have also been reported in a juvenile specimen of the amplectobeluid radiodont Lyrarapax (Liu et al., 2018). A tail fan associated with caudal rami is also known in both Opabinia and some radiodonts, though the number of blades known in KUMIP 314087 (at least seven, likely eight, on each side) by far exceeds what is known in either Opabinia (three) or any radiodont (ranging from zero to three). The acuminate tips of elongate caudal blades of KUMIP 314087 are most similar in morphology to those of Anomalocaris, and contrast to the more lobate caudal structures known in Opabinia and other radiodonts such as Hurdia (Fig. 2) Chen, Ramsköld and Zhou, 1994;Daley, Budd and Caron, 2013;Daley and Edgecombe, 2014). Paired caudal rami are also known in Anomalocaris saron, though these are much more elongate than in both KUMIP 314087 and Opabinia and lack the serrated adaxial margin common to the opabiniid taxa ( Fig. 2) Chen, Ramsköld and Zhou, 1994). Phylogenetic results. To test the affinities of KUMIP 314087 relative to Opabinia and radiodonts, we scored this specimen into a morphological matrix. Regardless of whether the matrix was analyzed with Bayesian inference (BI; Fig. 4a, Supplementary Fig. 2a, 2b) or maximum parsimony (MP; Supplementary Fig. 2c), a clade comprising KUMIP 314087 and Opabinia was resolved, warranting the assignment of the new taxon to family Opabiniidae. As the evidence for a proboscis in KUMIP 314087 is tentative (Fig. 2b), we conducted sensitivity analyses by building phylogenies where the proboscis (character 14) was coded as uncertain. With BI, opabiniids remained monophyletic (with lower nodal support; Supplementary Figs.  3a, 3b). With MP and an uncertain proboscis, the monophyly of opabiniids collapsed to a polytomy with deuteropods (Supplementary Fig. 3c). As the support values were poor for a morphological analysis (Fig. 4a, Supplementary  Fig. 2: posterior probabilities of 0.68 and 0.69 with BI; jackknife value of 57 and GC value of 65 with MP), we visualized treespace (Hillis, Heath and St. John, 2005). Such plots identify whether uncertainty in support for opabiniid relationships in the posterior sample (n = 4512 trees for analyses where proboscis is coded as present; Table 1) and MPTs (n = 12 trees) is restricted to tree islands with otherwise similar topologies, or spread throughout a large region of occupied treespace. While treespace has been previously explored in meta-analyses of fossil datasets (Brazeau, Guillerme and Smith, 2019;Koch and Parry, 2020;Wright and Lloyd, 2020), this is, to our knowledge, the first attempt to use such a visualization to interrogate the distribution of bipartitions for the position of a focal fossil taxon. Several possible hypotheses are subsets: KUMIP 314087 could be part of a clade with either Opabinia or Deuteropoda (pink and dark purple colors, respectively, in Fig. 4b), and could be part of both those clades (light purple in Fig. 4b). Our overall treespace for KUMIP 314087 can nevertheless be grouped by islands of trees where the supermajority of trees are related to opabiniids (n = 3102 trees total for analyses where proboscis is coded as present) or a minority to deuteropods (n = 251 trees total). A sparse, slender zone (n = 28 trees total) of the alternative exclusive hypothesis that KUMIP 314087 is a radiodont (Briggs et al., 2008) transitions between the opabiniid and deuteropod islands.
Interspersed sparsely within the opabiniid island are topologies supporting KUMIP 314087 with both radiodonts and deuteropods, but excluding Opabinia (blue in Fig. 4b); most of these trees depict Opabinia as the direct outgroup rather than a wildcard taxon (occupying different positions that are topologically distant). Choice of BI model parameters did not substantially impact the treespace (Fig. 4c: grey and open circles overlap completely on axis 1 and much of axis 2), while the MPTs (Fig. 4c: black circles) formed a small but distinct cluster.

Discussion
The power of treespace for phylogenetic uncertainty of fossils. At first glance, our phylogenetic analyses provide only weak nodal support for the placement of KUMIP 314087 within Opabiniidae. Although similar nodal support with a similar data matrix has been used to reclassify enigmatic fossils (Howard et al., 2020), we further interrogated our results -especially important as our terminal of interest is represented by a single specimen. Therefore, we investigated the degree of uncertainty in bipartitions, finding an increased number of topologies ( Table 1) that support KUMIP 314087 related to at least one opabiniid, and not to an alternative taxon. Such calculations have been effective in summarizing the taxonomic uncertainty in fossil placement (Klopfstein and Spasojevic, 2019). Furthermore, our visualization of the sample of optimal trees (Hillis, Heath and St. John, 2005;St. John, 2017;Wright and Lloyd, 2020) illustrates the distribution of topological distances between conflicting and overlapping hypotheses. This technique allows the strength of support for competing hypotheses of relationships to be more comprehensively evaluated beyond an arbitrary cutoff value.
Phylogenetic analyses aiming to resolve the relationships of fossil taxa present challenges such as researcher-specific morphological interpretation and coding decisions, preponderance of missing data (common for exceptionally preserved Cambrian taxa, due to preservation of few specimens or taphonomic loss of labile morphology), and relatively simple models of character change that may not reflect true evolutionary history (Sansom, Gabbott and Purnell, 2010;Watanabe, 2016;Tarasov, 2019;Wright, 2019). Visualization of treespace investigates how these scenarios may affect a consensus topology. In the case of KUMIP 314087, the morphological description is based on a single specimen where we could only tentatively identify the proboscis. Therefore, we compared alternative codings to represent our uncertainty in interpretation, and the potential influence on the definition of opabiniids ( Supplementary  Figs. 3, 4). The sister group relationship of KUMIP 314087 with Opabinia (rather than radiodonts or deuteropods) is not driven by the proboscis character, and is maintained due to the other shared morphological characters (e.g. dorsal furrows, caudal rami).

Implications for opabiniid evolution and ecology.
Our phylogenetic results provide substantial support for an assignment of KUMIP 314087 to Opabiniidae, helping to clarify some debates about the morphology of Opabinia. Enigmatic triangular structures found along the body in Opabinia, have been variously interpreted as extensions of the gut Zhang and Briggs, 2007), or as lobopodous walking limbs (Budd, 1996;Budd and Daley, 2012). The potential lobopods extending from the ventral surface in KUMIP 314087 suggest that these walking limbs may be present in opabiniids generally. Additionally, two contrasting interpretations have been presented for the relationship between the lateral flaps and the blocks of setal blades in Opabinia: one where the setal blades are attached to the dorsal surface of the lateral flaps (Budd, 1996;Budd and Daley, 2012), and the other view suggesting the setal blades were attached as a fringe along the posterior margin of the lateral flap (Zhang and Briggs, 2007). The setal blades in KUMIP 314087 support the former interpretation, with the setal blades extending mainly along the dorsal surface of the body but also along the basal anterior margin of the flaps. Evidently the addition of even a single new specimen to the opabiniids provides crucial data informing on the group's morphological aspects.
The family Opabiniidae is now considered to comprise two taxa, expanding its range geographically from two quarries separated by only a few meters to two deposits ~1000 km apart during two Cambrian Stages (Nanglu, Caron and Gaines, 2020). Although both Opabinia and Anomalocaris underwent major redescriptions around the same time Briggs, 1979;Whittington and Briggs, 1985), our revised opabiniids have not nearly caught up to the known diversity or distribution of radiodonts (or even the monophyletic groupings recovered in this study, Hurdiidae and Amplectobeluidae + Anomalocarididae). Radiodont frontal appendages, mouthparts, and carapaces are sclerotized and are often among the first fossils recovered from Cambrian deposits preserving non-biomineralizing organisms, and indeed many radiodont taxa are only known from their frontal appendages (e.g. Daley and Budd, 2010;Pates and Daley, 2019). However, preservation potential alone is insufficient to account for the greater diversity and distribution of radiodonts relative to opabiniids, as even radiodonts known only from complete specimens greatly outnumber opabiniids, both globally and within the Burgess Shale. Thus, the absence of opabiniids in other deposits from which complete radiodonts are known likely reflects a true absence or much lower diversity, which could have an ecological explanation.
Following a renaissance in radiodont research, it has been recognised that radiodonts display impressive variation in body size (milimetre to metre scale), body shape (rectangular to diamond shape in outline), inferred feeding ecology (raptorial predators, sediment sifters, filter feeders), and niche differentiation where species co-occur (e.g. Daley and Budd, 2010;Daley, Budd and Caron, 2013;Daley and Edgecombe, 2014;Vinther et al., 2014;Liu et al., 2018;Lerosey-Aubril et al., 2020;Pates et al., 2021). In contrast, opabiniids show limited evidence for adaptations to different niches. Both taxa have rectangular body shapes and are centimetre scale (the single specimen KUMIP 314087 is ~50% the length of the largest Opabinia). The more elaborate tailfan of KUMIP 314087 may indicate a greater maneuverability of this taxon compared to Opabinia regalis, as the tailfan of Anomalocaris canadensis aided swift changes in direction (Sheppard, Rival and Caron, 2018).

Implications for the euarthropod stem group.
Our results have implications for larger scale questions, such as the relative phylogenetic positions of opabiniids and radiodonts along the euarthropod stem group, and detailed consideration of conflicting topologies. We replicate the dichotomy of recent publications, where matrices analyzed using MP find opabiniids as the sister group to deuteropods (Yang et al., 2016(Yang et al., , 2018Howard et al., 2020) and those analyzed using BI or maximum likelihood instead resolve radiodonts in that position (Fleming et al., 2018;Howard et al., 2020;. The branching order of these three clades has ramifications for the sequence of acquisition, and evolutionary reversals or convergences, of key crown group euarthropod characters (Ortega-Hernández, 2016), such as the posterior mouth and arthropodized appendages, as well as the dorsal expression of trunk segmentation (Supplementary Fig. 5). The scenario (favored by MP and an island of BI topologies) where opabiniids are sister group to deuteropods requires either the secondary loss of arthropodized appendages in opabiniids, or the convergent evolution of arthropodized appendages in radiodonts and deuteropods.
The consensus topology (Fig. 4a, Supplementary Fig. 5a), and the majority of topologies (yellow, pink, and maroon points in Supplementary Fig. 5c), support a single origin of arthropodization in euarthropods. A possible developmental framework would entail the single anterior protocerebral pair of arthropodized limbs in radiodonts becoming co-opted posteriorly to enable the arthropodization of all limbs (Jockusch, 2017;Chipman and Edgecombe, 2019). This scenario would require the convergent fusion of presumed protocerebral appendages in opabiniids to form a single proboscis, and of protocerebral limb buds in deuteropods to form the labrum (Chipman, 2015;Jockusch, 2017;Ortega-Hernández, Janssen and Budd, 2017;Park et al., 2018). Evolutionary reversals or convergences are also required by these topologies (Supplementary Figs. 5, 6). The posterior-facing mouth shared by Opabinia and deuteropods is either convergent or lost in radiodonts (Ortega-Hernández, Janssen and Budd, 2017). Additionally, the distinct dorsally transverse furrows delineating segment boundaries (reported in both opabiniids), which may represent a precursor to arthrodized tergites in deuteropods (Yang et al., 2015), could either be lost in radiodonts and regained in deuteropods, or represent a convergent expression of dorsal trunk segmentation.
The consensus topology is further complicated by the apparent paraphyly of radiodonts (Fig. 4A, Supplementary Figs. 2a, 2b, 3b). Traditional nodal support resolves a clade of amplectobeluids, anomalocaridids, and deuteropods with posterior probabilities of 0.52-0.61 (Supplementary Figs. 2a, 2b, 3a, 3b). The specific relationship of amplectobeluids and anomalocaridids with deuteropods might improve some aspects of limb evolution, as the loss of dorsal flaps (shared by opabiniids and hurdiids; Supplementary Fig. 1) prior to the proposed fusion of setal blades and ventral flaps into the deuteropod biramous limb removes the requirement to identify a dorsal flap homolog in deuteropods (Van Roy, . However, treespace visualization does not provide strong support for radiodont paraphyly, as overlapping islands resolve conflicting relationships among radiodonts and deuteropods (Supplementary Figs. 5c, 7, supplementary discussion). As many of the characters distinguishing internal relationships among radiodont families describe the protocerebral frontal appendages, and are coded as inapplicable to all other taxa, we propose revised models of character evolution (Tarasov, 2019;Wright, 2019) may be necessary to resolve these relationships; accordingly we place little weight on this particular result. It should be emphasized, however, that the position of KUMIP 314087 is not affected by this uncertainty, as its position as sister taxon to each radiodont clade was tested (with only non-zero results reported in Table 1).

Conclusions.
The "weird wonders", as popularized by (Gould, 1989), inspired a generation of Cambrian paleontologists, with Opabinia at the heart of his narrative. The reorganization of previously enigmatic Cambrian taxa into stem groups instead revealed their importance for reconstructing the origins of modern phyla. Resolving the phylogenetic placement of these species is crucial for understanding the sequence of evolution of diagnostic crown group characters, as well as reconstructing the diversity and paleogeography of early ecosystems and groups. Here we apply treespace visualization to the reinterpretation of the relatively poorly preserved fossil KUMIP 314087. Dissection of the phylogenetic support demonstrates that while evidence for radiodont paraphyly is weak, KUMIP 314087 can be confidently reassigned to Opabiniidae. The weirdest wonder of the Cambrian no longer stands alone.

Methods
Fossil imaging and measurements. KUMIP 314087, accessioned at the Biodiversity Institute, University of Kansas, Lawrence, Kansas, USA (KUMIP), was photographed using a Canon EOS 500D digital SLR camera and Canon EF-S 60 mm Macro Lens, controlled for remote shooting using EOS Utility 2. Comparative figured material of Opabinia regalis is accessioned at the Smithsonian Institution U. S. National Museum of Natural History (USNM). Both polarized and unpolarized lighting were employed, with the fossil surface both wet and dry. Measurements were taken digitally using ImageJ2 (Rueden et al., 2017).

Morphological matrix.
We added five fossil taxa (KUMIP 314087, Amplectobelua symbrachiata Hou, Bergström and Ahlberg 1995, Anomalocaris saron Hou, Bergström and Ahlberg 1995, Cambroraster falcatus Moysiuk and Caron 2019, and Hurdia triangulata Walcott 1912 and removed one fossil ('Siberian Orsten tardigrade') from a previously published morphological data matrix of panarthropods (Yang et al., 2016), for a total of 43 fossil and 11 extant taxa. 86 characters were retained from the original matrix, 14 characters were added from two radiodont-focused datasets (Lerosey-Aubril and , and 25 characters were newly developed or substantially modified herein, for a total of 125 discrete morphological characters. Details of all characters including original and new character descriptions and scorings may be downloaded from MorphoBank (O'Leary and Kaufman, 2012) (www.morphobank.org, reviewer login 'email address': 3874, reviewer password: opabiniids).

Phylogenetic analysis.
The primary phylogenetic analyses were conducted using BI in MrBayes v.3.2.7 (Ronquist et al., 2012), implementing the Markov (Mk) model (Lewis, 2001) of character change under two different parameter regimes. We followed the 'maximize information' and 'minimize assumptions' strategies of Bapst, Schreiber and Carlson (2018). The 'maximize information' strategy assumes equal rate distribution across characters and that state frequencies are in equilibrium, as in most previously published BI morphological studies. The 'minimize assumptions' strategy (a) applies gamma distributed among-character rate variation, and (b) varies the symmetric Dirichlet hyperprior with a uniform distribution of (0,10) to relax assumptions about character state frequency transitions (Wright, Lloyd and Hillis, 2016). As with complex molecular substitution models, the 'minimize assumptions' strategy may allow a better fit of the model to the data. Each analysis implemented four runs of four chains each (for 5.5 million and 9.5 million generations, respectively), with 25% burnin. Convergence was assessed based on standard deviations of split frequencies < 0.01, reaching effective sample size >200 for every parameter, and by comparing posterior distributions in Tracer v.1.7.1 (Rambaut et al., 2018).
As the original matrix (Yang et al., 2016) was devised for MP analysis, we explored MP topologies in TNT v.1.5 (Goloboff and Catalano, 2016) using implied weights (k = 3) and New Technology. We required the shortest tree to be retrieved 100 times, using tree bisectionreconnection to swap one branch at a time on the trees in memory (Wolfe and Hegna, 2014).

Treespace analysis.
Supplemental to traditional clade support metrics, we used classical multidimensional scaling (MDS) to plot treespace (Gower, 1966;Hillis, Heath and St. John, 2005;St. John, 2017;Wright and Lloyd, 2020), with the goal of identifying the distribution of trees resolving key clades formed with KUMIP 314087 (Table 1). Our R script inputs the unrooted post-burnin posterior samples (resultant from BI) and MPTs (resultant from MP) using ape v.5.3 (Paradis and Schliep, 2019), and employs phangorn v.2.5.5 (Schliep, 2011) to calculate pairwise unweighted Robinson-Foulds distances (RF, the proportion of bipartitions defined by a branch in one tree that is lacking in another tree) (Robinson and Foulds, 1981) for the total set of trees resulting from all analyses. The classical MDS function is performed on the RF distances, with a constant added to all elements in the distance matrix to correct for negative eigenvalues (Cailliez, 1983). The treespace therefore approximates the RF distances between trees (Hillis, Heath and St. John, 2005).

Additional implications of our phylogenetic results
Radiodonta paraphyly?. Using MP, Radiodonta is resolved as a monophyletic group, alongside a very small percentage of BI posterior trees (teal points in Supplementary Fig. 7). The majority of BI posterior trees, and therefore the majority of the treespace, support radiodont paraphyly (Supplementary Fig. 7).
When the trees are separated by what is sister to deuteropods, around half the space is occupied by trees supporting a monophyletic Deuteropoda + Amplectobeluidae + Anomalocarididae, however the clade Amplectobeluidae + Anomalocarididae can be either monophyletic or paraphyletic in this plot (Supplementary Fig. 5). When this area of the treespace is compared to what is occupied by monophyletic Amplectobeluidae + Anomalocarididae (Supplementary Fig. 7), there is only limited overlap in these two areas, lowering the support for the tree topology depicted in the consensus.
There is evidence that internal radiodont relationships are not confidently resolved based on the data (character matrix) and/or model of morphological character change. For example, trees where the family Hurdiidae is recovered as monophyletic are spread across the whole treespace, but at a low density. Often a tree with monophyletic Hurdiidae is very close in the treespace (i.e. with a low RF value or similar overall topology) to multiple trees where Hurdiidae is not resolved as a monophyletic group (Supplementary Fig. 7). Future work (ongoing) aimed at better resolving radiodont internal relationships, as well as improving model and matrix design to deal with this kind of problem common to palaeontological datasets will allow more certainty to be placed on the monophyly or paraphyly of radiodonts. Little weight should be placed on this particular result from this study, as the support for radiodont monophyly is poor and not enhanced by additional bipartitions (as in opabiniids), and as other matrices consistently resolve radiodonts as a monophyletic group when analysed with both MP and BI (e.g. Lerosey-Aubril and Pates, 2018;.