In terms of an improved understanding of the ventral morphology, we focused on the overall shape of the specimens, the number of tergites, the composition of the antennulae, and the number of pygidial appendages in general and with special regard to possible limb buds. We compare our results with the recent morphological understandings of Sinoburius lunaris made by Chen et al. . Additionally, we want to draw attention to previous morphological understandings and misconceptions.
The understanding of the morphology of Sinoburius lunaris and its change through time
Up to now, seven specimens of Sinoburius lunaris have been mentioned in literature. In addition to the holotype (NIGPAS Cat. No. 115287) and the paratype (NIGPAS Cat. No. 115288) (, Fig. 4; ), further figured specimens are ELRC 19550 (, Fig. 215; ), as well as ELRC 19551 (; , Figs. 88, 89). The herein considered analyses of  contributed three additional specimens (YKLP 11407, YRCP 0011, and Hz-f-10-45), whilst the latter one had already been presented in Ref. (, Pl. II, Fig. 4).
Thus, this species is still rare, and detailed morphological analyses before Chen et al.  used 'traditional methods' such as light microscopy and needle preparation, resulting in different morphological observations.
The original description of Sinoburius lunaris  considered the holo- and the paratype. Not much known was about the appendage morphology. The head was assumed to have a pair of antennulae (originally termed 'antennae') followed by three or four pairs of additional post-antennular head appendages . The antennulae were drawn as being composed of numerous articles (, Figs. 78c, 79). This was assumed due to the presence of shallow furrows on the head shield in the posterior part of the paratype. Later, the same specimen (Hz-f-10-45) was re-figured  which was investigated in both, Chen et al.  and our study. 'Two pairs of antennae' instead of a single pair were also reported . They mentioned a supposedly ´interior` pair (i.e., the inner ones) being smaller (, p. 130). If we compare this statement to our understanding of the morphology of specimen Hz-f-10-45 (see Figs. 1c, 2h, 3c herein; consider also Fig. 6 in ), we can assume that  misinterpreted the first pair of post-antennular exopods as a kind of 'exterior antennae', while their reference to the inner' ones represented the antennulae. The interpretation of  is especially interesting, as  already identified the antennulae and recognized the supposed 'exterior' ones as parts of a biramous appendage (in this case, however, they thought of endopods; see Len1 in (, Fig. 78b).
The antennulae in Sinoburius lunaris according to Chen et al.  consist of five observable articles. Nevertheless, Figs. 6a, b in  indicate that the antennulae indeed might have been even longer, considering the furrows on the slab. In the earlier studies, the illustration of the head region of this specimen does not seem to represent the original length of the antennulae (, Fig. 79). The so-called 'antennal scale' (see , p. 2), however, might have been a filament-like structure and much longer than preserved, possibly also protruding under the head shield like the antenniform first exopods. But there is no confirmation of their original length. Regarding the trunk, each of the seven tergites formed by the respective body segments was thought to possess one pair of biramous appendages due to visible furrows . The former investigation on S. lunaris  demonstrated that two tergites correspond to more than one pair of appendages in specimen YKLP 11407 (tergite 4, tergite 7) and one in Hz-f-10-45 (tergite 7), making up eight respectively nine pairs of trunk appendages. We refute the presence of diplotergites at least for specimen YKLP 11407, resulting in nine tergites, each corresponding to one pair of biramous post-antennular appendages. Another morphological structure that has caused controversy is the pygidium. This was once assumed to be composed of at least ten segments with the anterior six bearing biramous appendages (, p. 2). This conclusion was drawn based on the posterior part of the holotype NIGPAS Cat. No. 115287 (see Figs. 77a, 78a in ref. ). The previous investigation on Sinoburius lunaris  contrasted with the assumption of three or four pairs of pygidial appendages. Yet, due to the limitations of preservation neither volume nor surface renderings could provide clear results. Only via comparisons of 2D slices, we are able to show that there are indeed four pairs of pygidial appendages in all three analyzed specimens.
Specimen-dependent morphological differences
The way representatives of Euarthropoda are segmented and the overall meaning of segmentation has long been discussed [34,35,36,37]. A direct match between body segments (or rather dorsal and ventral sclerites) and appendages is the most common mode with one pair of appendages belonging to one body segment. Contrarily, a segmental mismatch describes a discordance between those sclerites of tergites and sternites. In some extant representatives of Euarthropoda, there is a high variability with, for instance, symphylans and some centipedes having more dorsal sclerites than pairs of trunk appendages. Vice versa, pauropods, and millipedes have fewer tergites than pairs of trunk appendages [38, 39]. Also, segments possessing more than one pair of appendages occur in notostracans .
For Sinoburius lunaris, segmental mismatch was also demonstrated . According to its former analysis , two specimens (YRCP 0011 and Hz-f-10-45) had 16 pairs of biramous post-antennular appendages and seven tergites in the trunk (counting for seven distinguishable trunk segments) with only the seventh trunk segment bearing two appendage pairs. This we could also confirm. For the other specimen (YKLP 11407), a total of 17 post-antennular biramous appendages was found, also seven trunk segments but with trunk segment four and seven each carrying two pairs of biramous appendages .
We could enlighten this discordance, as we found specimen YKLP 11407 having rather nine than seven trunk segments–giving that one trunk segment is forming one tergite dorsally. However, there is still inconsistency between the three specimens of S. lunaris, that said given the variability of tergites, and possible diplotergites or syntergites.
This could be due to several reasons. It might be just a case of intraspecific variability, making this species highly variable concerning major morphological features. In extant notostracans , the number of biramous trunk appendages can vary greatly, and for epimorphic centipedes and adesmatan geophilomorphs, high variability in segment numbers within one species has also been described [41, 42]. However, the variability in segment numbers in some centipedes should not be confused with a dorso-ventral mismatch of segmental structures.
Sexual dimorphism could be another case to take into consideration and also explain not only the different number of trunk segments (dorsally forming tergites) but also the different number of total appendages within all three specimens. In some extant polydesmidan millipedes and adesmatan centipedes, females possess more segments than males , whereas in some notostracans this is the other way around . Additionally, for the latter group, even within-sex intraspecific variability is described, with males having 38–44 leg-bearing trunk segments , see also survey in ref. .
A third scenario may be shown by all Sinoburius lunaris specimens representing different ontogenetic stages. Thus, an anamorphic development could be addressed. This implies that segmental units are added during post-embryonic ontogeny, as it is found in many crustaceans, but also in proturan insects  and many myriapods (e.g., compare survey in ref. ). Furthermore, also for trilobites [45,46,47] and megacheiran Cambrian arthropods , this developmental pattern is described, following an anterior–posterior developmental gradient.
The total size of the investigated specimens, however, may refute this idea, as the smallest specimen is YKLP 11407, being also the one with the higher number of both tergites and total post-antennular appendages. However, the size of post-embryonic ontogenetic stages of arthropods depends also on food and temperature . Thus, YKLP 11407 can be the most advanced developmental stage despite being the smallest individual specimen, like given the ventral parts of segments develop at a faster pace compared with the dorsal parts . Overall, the range of total body size within the three specimens is not that high. The question for the reason of the morphological inconsistency may finally only be entangled with a higher number of investigated specimens of different total body sizes.
A last scenario might be given if the three investigated specimens would belong to more than just the one described Sinoburius lunaris species. At least the differences in the shapes of the head shields, the tergites, and the head appendages between YKLP 11407 and YRCP 0011 suggests this. Again, a wider taxon sampling of different body sizes in the future could shed light on this aspect.
Amira vs. Drishti in the light of virtual palaeontology
Both, Amira [49, 50] and Drishti  provide a useful software to process µCT data on extinct and extant arthropods and to visualize certain aspects of their morphology. Together with other programs like MeshLab or Blender, one can visualize its µCT-generated models in a variety of ways .
While Amira is a single program containing a delightful set of volume and surface rendering modes, Drishti comes with three distinct programs (Drishti Import, Drishti Paint and Drishti, the renderer itself). Both, Amira and Drishti possess a diverse range of user-friendly options to work in 3D on the volume models as well as in 2D on the single TIFF slices. The biggest advantage of Amira might be the opportunity to directly process a surface reconstruction based on the segmentation of individual structures. Those surface models later can be exported to use in other 3D modelling programs like Blender or Autodesk Maya in terms of a kinematic approach . Nevertheless, this surface reconstruction method is also feasible in Drishti Paint. Besides surface reconstruction, both programs also offer a great anmount of volume rendering tools.
We reinvestigated the three Sinoburius lunaris specimens with Amira in order to make advance of its different volume rendering settings VRT and MIP. VRT is a texture-based volume rendering with different shading options like Diffuse or Specular. Diffuse VRT sets a diffuse light source, whereas the Specular VRT option offers a simulation of a specular visualization of the specimen. The latter one may most likely resemble the pre-sets of Drishti volume rendering making the objects look more vivid. The MIP (maximum intensity projection) volume rendering mode otherwise displays the brightest data value along each ray of sight instead of showing the result of the emission absorption model. This makes it possible to look through the fossil and detect for example underlying structures. Hence, we used this volume rendering mode for the visualization of the entire specimens (Fig. 1), whereas we used the VRT mode the get a more vivid and plastic look of the appendages (Fig. 5f). We think, in the near future fossils could–in the light of virtual paleontology–benefit from a variety of 3D visualization and modelling programs to explore their morpho-functionality in many different ways.
Applicability of morphometrics to analyses of Chengjiang arthropods
This is the first study in which a PCA based on Burnaby-Back Projection size-corrected data was run when analyzing Chengjiang arthropods.
A PCA is the most abundant and reliable multivariate method to ordinate data but has essential preconditions, one being normally distributed data. Testing for normal distribution makes no sense regarding a sample size of only three specimens. However, according to the Central Limit Theorem —which states that the sampling distribution of the sample average approximates a normal distribution as the sample size gets larger—a calculation of a PCA is possible, though.
Speaking of large sample sizes, the question of the minimum number of variables in a PCA calculation is another topic [53, 54], and so is the bias of the resulting plots considering outliers. Our analysis could, of course, be enhanced by a larger set of specimens of Sinoburius lunaris, resulting in more clusters to compare. A statistically more comprehensive analysis could be done considering all post-antennular biramous appendages. This was not possible due to the fact that a BBP only works with the same number of articles, and we could only measure five articles in the pygidium. Thus, we could not include size-corrected BBP data for endopods with seven articles in this PCA, which all other anterior most appendages bear.
Size-correction is a pivotal precondition when working with metric data. Otherwise, analyses would just show size-dependent patterns, hence skewing the real information. The most common size-reduction method is creating ratios, i.e., dividing the measured body parts through the body length of the respective specimen or species. Despite its common use, several authors have criticized such data still being size-dependent [55,56,57].
Another widely used method, as said, is size-correction via the so-called Burnaby-Back Projection. The theory of this method was introduced in 1966  and further developed by . The BBP size-correction model, in the end, provides the information of the location of a data point in space and its relative position to all other points while neglecting the assumed growth vectors created for all of those data points (for a further description, see [60, 61]). For this reason, we favored this size-correction method.
Furthermore, it is crucial to work with missing values. If any article in the middle of an endopod is missing, i.e., it is not preserved in a good way to measure, then there are several ways to handle this problem, like iterative computation. This might work also for missing terminal articles—but only, if they were not preserved. In our data, we could count seven articles for the post-antennular biramous head and trunk appendages (despite endopod 2 of specimen YRCP 0011), while pygidial appendages only showed five. For this arrangement, a complete PCA of the entire data set is not possible, and neither a BBP is, as mentioned above.