Comparative crystallography suggests maniraptoran theropod affinities for latest Cretaceous European ‘geckoid’ eggshell

Thin fossil eggshell from Upper Cretaceous deposits of Europe, characterized by nodular ornamentation similar to modern gekkotan eggshell, has mostly been interpreted as gekkotan (=‘geckoid’) in origin. However, in some cases, as for the oogenus Pseudogeckoolithus, a theropod affinity has also been suggested. The true affinity of these fossil ‘geckoid’ eggshells has remained controversial due to the absence of analytical methods for identifying genuine gecko eggshell in the fossil record. In this study, we apply electron backscatter diffraction (EBSD) analysis to latest Cretaceous European ‘geckoid’ (including Pseudogeckoolithus) eggshell, in comparison with modern gekkotan and theropod (avian) eggshell. We found that Pseudogeckoolithus has a definite theropod eggshell‐like crystallographic configuration, in clear contrast to that seen in modern ‘gecko eggshells’. Furthermore, the crystallography of the nodular ornamentation in Pseudogeckoolithus is similar to that seen in megapode eggshell, but different from that of gecko eggshell, despite superficial morphological similarity. The remarkable morphological similarities between Pseudogeckoolithus and modern gecko eggshells are thus convergent, and the ‘gekkotan affinity’ hypothesis can be dismissed for Pseudogeckoolithus. This study provides a template for differentiating true gekkotan from dinosaurian eggshells in the fossil record. The potential functional significance of eggshell ornamentation, lost in most modern birds, requires further study, and experimental zoological approach may shed light on this issue. Finally, the present results suggest caution about the dangers of using potentially homoplastic eggshell characters in eggshell parataxonomy.

F O S S I L eggs and eggshells provide a unique opportunity to study aspects of the reproductive biology of extinct amniotes (e.g. Tanaka et al. 2015Tanaka et al. , 2019Varricchio & Jackson 2016;Amiot et al. 2017;Wiemann et al. 2018;Choi et al. 2019a). Among extant oviparous (egg-laying) amniotes, all archosaurs and some turtles lay rigid-shelled eggs, while the eggs of most lepidosaurs (squamates and rhynchocephalians) have a soft, leathery shell with a low degree of mineralization (Sander 2012; Skawi nski & Tałanda 2014). Because soft eggshell has a low preservation potential (Hirsch 1996), almost all previously studied fossil eggshells have been found to belong to archosaurs or chelonians. Nevertheless, there are also a small number of fossil squamate eggshell reports in the literature (Choi et al. 2019b, table S1). These shells are very thin and share similarities in their ornamentationand in some cases also in their microstructurewith eggshells of Gekkota (Squamata), the only extant lepidosaurian clade besides the Dibamidae, with some of its members laying rigid-shelled eggs (Sander 2012;Skawi nski & Tałanda 2014), and with a fossil record dating back to the Early Cretaceous (Daza et al. 2014). Given that many maniraptoran (Dinosauria, Theropoda; a clade of bird-like theropods, including modern birds) eggshells are characterized by prismatic shell units (e.g. Mikhailov 1997a;Zelenitsky et al. 2002;Varricchio & Jackson 2004) and modern gekkotan eggshells have a similar-looking jagged columnar structure (Schleich & K€ astle 1988;Packard & Hirsch 1989;Hirsch 1996;Mikhailov 1997a;Choi et al. 2018), the gekkotan or maniraptoran affinities of some fossil eggshells remained undecided. Thus, in the absence of in ovo embryos or at least body fossils in close association with the eggs or eggshells, there has been no rigorous way to test whether superficially gecko-like fossil eggshells are genuinely gekkotan or, in fact, archosaurian in origin.
Representative cases of fossil eggshell with such ambiguous identity were Pseudogeckoolithus and 'morphotype geckono€ ıde' ( Vianey-Liaud & Lopez-Martinez 1997;Garcia 2000) described from the upper Upper Cretaceous (Campanian-Maastrichtian) continental deposits of western Europe. These eggshells are characterized by dispersituberculate ornamentation, which is very similar to that of Gekko gecko (Gekkota) eggshell (Schleich & K€ astle 1988;Packard & Hirsch 1989;Choi et al. 2018). According to Vianey-Liaud & Lopez-Martinez (1997), Pseudogeckoolithus, as its name implies, is macroscopically similar to gecko eggshell, but its micro-and ultrastructural features were identified as a 'dinosauroid prismatic type', thus arguing for a dinosaurian origin. However, Garcia (2000) also reported gecko-like eggshells that are morphologically reminiscent of Pseudogeckoolithus but which she nevertheless referred to as morphotype geck-ono€ ıde, pointing out their microstructural similarity with extant gekkotan eggshell. Moreover, Sell es (2012) argued that even Pseudogeckoolithus lacks a mammillary layer and is merely composed of irregular prisms, hence, it is not of dinosaurian origin, but represents instead a Mesozoic lizard eggshell. Accordingly, European Late Cretaceous eggshells, which are very similar to either Pseudogeckoolithus or 'geckono€ ıde' eggshells, have been usually associated with Gekkota (e.g. Garcia & Vianey-Liaud 2001; Csiki-Sava et al. 2015Botfalvai et al. 2017). In contrast, Prondvai et al. (2017) concluded recently that the most abundant fossil eggshells ('morphotype I' or 'MT I') from the Santonian of Ihark ut, Hungary, which resemble both Pseudogeckoolithus and the French 'geckono€ ıde' morphotype, have a theropod affinity based on the presence of a mammillary layer, in agreement with Vianey-Liaud & Lopez-Martinez (1997). Furthermore, Prondvai et al. (2017) suggested that, along with the Hungarian MT I eggshells, putative 'gecko-like' eggshells from the Upper Cretaceous deposits in Romania, Spain and France might have theropod affinities as well, consistent with the interpretation of North American dispersituberculate eggshells (e.g. Zelenitsky et al. 1996;Jackson & Varricchio 2010; Table 1). These conflicting views on the nature of these Late Cretaceous 'geckoid' eggshells can only be resolved with a diagnostic methodology that allows identification of genuine gekkotan eggshells in the fossil record.
Using electron backscatter diffraction (EBSD) analysis, Choi et al. (2018) showed that crystallographic configuration of extant gekkotan eggshell is fundamentally different from that of dinosaurian (including avian) eggshell (see Choi et al. 2019a, table 1). Hence, EBSD is adequate for differentiating gekkotan from theropod eggshell in the fossil record. Here, we apply EBSD analysis to different 'geckoid' eggshell samples recovered from European Upper Cretaceous deposits in order to test their putative gekkotan affinity by comparing them with diverse sauropsid eggshells including those of extant Gekkota and Aves. During our study, we identified several distinct construction pathways of nodular eggshell ornamentation, and the parataxonomic importance of these is also discussed. Vertebrate-bearing Upper Cretaceous (Santonian-Maastrichtian) continental beds are distributed discontinuously across a wide area in Europe ( Csiki-Sava et al. 2015;Fig. 1A). These deposits were laid down in marginal marine, coastal plain or inland fluvial settings in an archipelago on the northern margin of the Neotethyan area. Although most of these former 'islands' yielded only few fragmentary fossils, some of them hosted a wide variety of vertebrate taxa. The most important of these are ' Bakony Island' in present-day Csiki-Sava et al. 2016); and the much larger 'Ibero-Armorican Landmass' covering the Iberian Peninsula and the southern part of present-day France (with numerous localities spanning the early Campanianlatest Maastrichtian time interval; e.g. Vila et al. 2016;Fondevilla et al. 2019). All three areas have yielded, besides diverse vertebrate remains, 'geckoid' eggshells (Figs 1A,2). We will review here briefly the general geological setting for these areas, as well as the geology and fossil content of the localities that yielded specimens used in the present study (for more details, see Choi et al. 2019b, texts S1, S2).
A rich assemblage of continental organisms is known from these deposits, including invertebrates, plants and vertebrates, the latter (best represented in the Hațeg Basin; In the Hațeg Basin, the chronostratigraphically older locality is the early Maastrichtian V alioara-Fântânele locality (Figs 1, 2B; Grigorescu et al. 1999;Csiki-Sava et al. 2016). It was formed in a small depression with ponded, oxygen-poor waters, developed within the confines of a braided river floodplain (Vasile & Csiki 2010). The fossil accumulation is a classical MvBB with a rich and diverse vertebrate assemblage ( Csiki-Sava et al. 2016;Choi et al. 2019b, text S2). These are associated with invertebrates and eggshells, including common 'geckoid' (= Pseudogeckoolithus; see Systematic Palaeontology, below) ones.
The third, and geologically youngest, Romanian locality surveyed in the present study (Pui-Classic; Figs 1, 2B) is located near Pui; it is most probably late (although probably not latest) Maastrichtian in age ( Csiki-Sava et al. 2016;Choi et al. 2019b, text S2). The fossiliferous bed formed in a well-drained floodplain setting, and represents a typical MvBB dominated by shed archosaur teeth, associated with other organic remains including common 'geckoid' eggshells.

Campanian-Maastrichtian of northern Spain and southern France
Upper Cretaceous continental and transitional deposits are widespread in central and northern Spain (most importantly in the Southern Pyrenean Foredeep, where they are represented by the Ar en and Tremp formations: red and grey marls and clays, sandstones with local limestone levels; Mey et al. 1968), as well as in southern France (e.g. Csiki-Sava et al. 2015) (Figs 1, 2C). These deposits represent the lowermost Campanianuppermost Maastrichtian interval in southern France, and the Campanianuppermost Maastrichtian in Spain, and are usually divided into local chronostratigraphic units that are often difficult to correlate with the standard chronostratigraphic divisions (e.g. Cojan & Moreau 2006; Csiki-Sava et al. 2015). Given that the Pyrenean area includes K-Pg boundary continental outcrops, a large number of magnetostratigraphic and biostratigraphic studies have been carried out in recent years, resulting in a detailed, although somewhat controversial, chronostratigraphic framework for the uppermost Creta  Moreno-Azanza et al. 2014a). Furthermore, Pseudogeckoolithus or 'geckoid' eggshells (often identified as morphotype geckono€ ıde by Garcia 2000) were also reported from the Maastrichtian Spanish Quintanilla del Coco locality (Fig. 2C;Pol et al. 1992), as well as from several localities spread across southern France (e.g. Kerourio 1982;Cousin 1997;Garcia 2000;Valentin et al. 2012;Fig. 2C).
Materials included in this study come from the Blasi 2 locality, an MvBB located on the northern flank of the Tremp Syncline (

Late Cretaceous Pseudogeckoolithus
The most characteristic feature of the oogenus Pseudogeckoolithus, erected by Vianey-Liaud & Lopez-Martinez (1997) based on six eggshell fragments collected from the early Maastrichtian (magnetochron C31N) Fontllonga-6 locality (Lleida Province, Spain), is its dispersituberculate ornamentation. Although the holotype fragments are seemingly lost, this oogenus has been identified in several other localities across Ibero-Armorica (see review in Choi et al. 2019b, text S2; Fig. 2), as well as in northern Africa (Morocco; Vianey-Liaud & Garcia 2003; Fig. 1). The 'geckonoid' eggshell type described by Garcia (2000)  diverse appearance (Table 1), all dispersituberculate eggshells included in this study are relatively thin (<350 lm, including ornamentation) and show pore openings at the top of some of the ornamental nodes ( Fig. 3), which are further diagnostic features of the oogenus Pseudogeckoolithus.
From the specimens included in this study, the 'geckoid' eggshells from the Romanian locality of V alioara-Fântânele and the Spanish locality of Blasi 2 (Fig. 3C, E) are thicker and have less dense ornamentation than specimens from the Hungarian locality of Ihark ut and the Romanian localities of Petrești-Black Lens and Pui-Classic (Fig. 3A, B, D). Therefore, the former specimens are referred to as Pseudogeckoolithus cf. nodosus ( Vianey-Liaud & Lopez-Martinez 1997), whereas the latter as

Fossil comparative materials
In order to narrow down the possible dinosaurian taxonomic affinities of Pseudogeckoolithus, EBSD images of several types of dinosaur fossil eggshells were analysed and compared with Late Cretaceous Pseudogeckoolithus. These include hadrosaur (cf. Maiasaura), sauropod (Megaloolithus cf. siruguei), troodontid (Prismatoolithus levis) and enantiornithine (Gobioolithus minor) eggshells. The EBSD images of the hadrosaur and sauropod eggshells were already presented in Moreno-Azanza et al. (2013) and Moreno-Azanza et al. (2016), respectively. Although the sauropod eggshell example discussed in Moreno-Azanza et al. (2016) shows sufficiently well the overall crystallography of a typical sauropod eggshell, it was nonetheless significantly altered by taphonomic effects, thus we recommend to inspect the EBSD image of a well-preserved sauropod eggshell figured in Grellet-Tinner et al. (2011) andEagle et al. (2015) as well. The EBSD images of the troodontid and enantiornithine eggshells are provided as representatives of confirmed maniraptoran eggshells; only brief accounts of these two maniraptoran eggshell types are given here as detailed descriptions were presented in Choi et al. (2019a).

Extant comparative materials
Modern gekkotan and avian eggshells were analysed in more detail, as control groups, to provide comparative neontological crystallographic data for the two clades (Gekkota and Theropoda) with the potential egg layers of Pseudogeckoolithus (see above). Among Gekkota, Gekko gecko and Phelsuma grandis are members of the Gekkonidae (Gamble et al. 2011;Pyron et al. 2013) that lay rigidshelled eggs, and their eggshells show the typical gekkotan crystallographic arrangement (Choi et al. 2018). Of these, the Gekko gecko eggshell has a nodular ornamentation similar to the dispersituberculate one of Pseudogeckoolithus (Fig. 3F), which led to the gekkotan-affinity interpretation of Pseudogeckoolithus in the past (e.g. Garcia 2000). The gekkotan eggshell materials included in the present study are those analysed in Choi et al. (2018).
We also included in our comparison the eggshells from an emu (Dromaius novaehollandiae) and from a domestic duck (Anas platyrhynchos domesticus), representing a palaeognath and a neognath bird, respectively. The emu eggshell is particularly appropriate for the purpose of this study because it presents ornamentation on its outer surface (Mikhailov 1997b; Grellet-Tinner 2006), which is a very uncommon trait in modern avian eggshells (Hauber 2014). It was found that palaeognath and neognath eggshells have different crystallographic features especially in their misorientation distribution (angular difference between the grains) and c-axis alignment (Choi et al. 2019a), and thus the emu and duck eggshells together cover a representative range of modern avian eggshell diversity. For further information, see Choi et al. (2019a). The avian eggshells used in this study were both available commercially.
Last, a crocodylian (Caiman latirostris) eggshell was also analysed to record the crystallography of the ornamentation in non-dinosaurian archosaur eggshell as well, and to compare it with that of Pseudogeckoolithus. The material was provided by Dr Kohei Tanaka (University of Tsukuba) to SC.

Electron backscatter diffraction
We followed the established methods of EBSD analysis of fossil and modern eggshells, and data curation ( Moreno-Azanza et al. 2013Choi et al. 2018Choi et al. , 2019a. The results are presented in inverse pole figure (IPF) maps, lower hemisphere pole figures, grain boundary maps, misorientation histograms, and d-value bar charts. Detailed description of the methodology and data curation can be found in Choi et al. (2019b, text S3).

Crystallography of Pseudogeckoolithus
All European Pseudogeckoolithus eggshells analysed in the present study share several crystallographic features. First, the c-axis alignment generally increases from the inner towards the outer part of the shell (Fig. 4) Moreno-Azanza et al. 2013Eagle et al. 2015). In all of these features, both sauropod and hadrosaur eggshells are markedly different from those of Pseudogeckoolithus.
In contrast, marked microstructural similarities with Pseudogeckoolithus are definitively present in both the troodontid and the enantiornithine eggshells (see Choi et al. 2019b, fig. S2G-J). All of these ootaxa share: (1) the existence of an inner mammillary layer and an outer continuous layer, a typical feature of theropod eggshells (Mikhailov 1997a); and (2) rugged grain boundaries in the squamatic zone, which was suggested to be a diagnostic feature (squamatic ultrastructure) in maniraptoran eggshells (Choi et al. 2019a; see below). Also, the troodontid eggshell and at least some Pseudogeckoolithus specimens share the possible existence of an external zone, which may be diagnosed by the presence of linear The numbers on the vertical and horizontal axes in the histogram mean degree and frequency of misorientation, respectively. Abbreviation: ML, mammillary layer. Scale bars represent 100 lm. F I G . 6 . Eggshell electron backscatter diffraction (EBSD) images from modern representatives of the clades hypothesized to include Pseudogeckoolithus egg layers. A-B, Gekko gecko (Gekkota). C-D, Phelsuma grandis (Gekkota); gekkotan eggshell terminology follows Choi et al. (2018). E-F, Dromaius novaehollandiae (Aves, Palaeognathae). G-H, Anas platyrhynchos domesticus (Aves, Neognathae). In A, the lower hemisphere pole figures were constructed using the grains lying on the left of the white dashed line so that grains potentially influenced by the ornamentation are not included. In gekkotan eggshells (A, C), c-axis alignment becomes higher with vertical orientation towards the inner eggshell surface, the opposite pattern to that seen in Pseudogeckoolithus (Fig. 4) and extant avian eggshells (E, G;Choi et al. 2019a). The ornamentation in Gekko gecko eggshell is composed of randomly oriented calcite grains; that of emu eggshell is composed of wedge-shaped granular layer (GL) initiated in the middle of the squamatic zone (SqZ). Both of them are crystallographically discontinuous with the underlying eggshell. Note the trilaminate structure identified by differences in grain ruggedness in avian eggshell (F, H), similar to that seen in the Pui-Classic and Blasi 2 Pseudogeckoolithus (Fig. 4E, F). Gekko gecko eggshell has a low-angle-dominant misorientation distribution (B) compared with that of Phelsuma grandis eggshell (D). Key to EBSD interpretation same as in Figures  grain boundaries, in contrast with the rugged grain boundaries present in the squamatic zone lying below (Choi et al. 2019a; see below). As far as we are aware, there is no known non-theropod dinosaur eggshell that has the aforementioned morphological traits.
Comparison with modern eggshell Gekkotan eggs. The crystallographic architecture of modern gekkotan eggshell is unique among amniotes (Choi et al. 2018). The outer quarter of the eggshell is characterized by randomly oriented small calcite grains. The upright c-axis alignment (expressed by the intensity of red colour in the IPF map) becomes stronger towards the inner eggshell surface. In addition, the concentration of phosphorus, which is known to function as an inhibitor To the best of our knowledge, these crystallographic and compositional arrangements are observed only in the rigid gekkotan eggshells among amniotes.
The clear-cut crystallographic differences between gekkotan eggshell and Pseudogeckoolithus are also strongly expressed in their dispersituberculate ornamentation. Eggshell ornamentation in Gekko gecko is made up of randomly aligned calcite grains (Fig. 6A), usually with an enigmatic bulbous structure present inside ( fig. S9 in Choi et al. 2018). This bulbous structure, however, may not have a crystalline structure given that no Kikuchi pattern (a diffraction pattern used for interpreting the orientation of crystalline material in EBSD analysis) was detected ( Fig. 6A; Choi et al. 2018). In contrast, the ornamentation in Pseudogeckoolithus is made up of compact calcite that is crystallographically continuous with the underlying eggshell units (Fig. 4), and does not contain randomly arranged calcite grains. It also lacks the internal bulbous structure seen in the eggshell of Gekko gecko.
Avian eggs. In all crystallographic aspects, Pseudogeckoolithus is very similar to theropod (including avian) eggshell ( In the Dromaius (emu) eggshell there is a granular layer (GL; sensu Mikhailov 1997b) initiated in the middle of the squamatic zone (Fig. 6E) that forms a peculiar, hillock-like ornamentation (sensu Grellet-Tinner 2006). This ornamentation is, however, crystallographically discontinuous with the main eggshell microstructure, thus different from the ornamentation of Pseudogeckoolithus (Fig. 4). The Anas (domestic duck) eggshell is smooth and unornamented, as is the case for almost all modern avian eggshells.
Except for the presence of a nodular dispersituberculate ornamentation, the crystallographic arrangement of the European Pseudogeckoolithus is especially similar to that of the typical palaeognath eggshell as well as to that of Gobioolithus minor, an enantiornithine ootaxon ( Mikhailov 1996;Kurochkin et al. 2013), in that the upright caxis alignment is stronger than that present in neognath eggshells (  lov 1997b). Although the existence of an external zone must be confirmed by detailed ultrastructural study using scanning electron micrcoscopy, the occurrence of a linear grain boundary near the outer shell surface suggests that an external zone may be also present at least in some Pseudogeckoolithus.
Finally, in several types of avian eggshell examined (namely in Gallus  fig. S3C) eggshells) the concentration of phosphorus increases towards the outer surface, in contrast to the pattern present in gekkotan eggshell. To conclude, the crystallography and chemical composition of the gekkotan eggshells suggest an opposing growth direction compared with that seen in archosaurian eggshells, and is similarly opposite to that present in Pseudogeckoolithus (Fig. 6A fig. S4), which consisted only of maniraptoran eggshells.
Except for one V alioara-Fântânele specimen, all Pseudogeckoolithus have a d-value higher than 1.949, meaning that the neighbour-and the random-paired misorientations have a statistically significantly different distribution with probability higher than 0.999 (Fig. 7). The V alioara-Fântânele material has a d-value of 1.36, but its neighbour-and random-paired misorientations are still different with a probability higher than 0.95. The resulting d-values were consistent in all European Pseudogeckoolithus specimens investigated with the Type 2 We also calculated d-values for additional non-Pseudogeckoolithus eggshells analysed in this study as well as those presented elsewhere alongside EBSD data ( Moreno-Azanza et al. 2013Choi & Lee 2019). These sampled eggshells can be grouped into three categories: (1) maniraptoran eggshells (Dromaius, Reticuloolithus acicularis and Trigonoolithus amoae); (2) non-maniraptoran archosaur eggshells (Caiman latirostris, cf. Maiasaura, Guegoolithus turolensis and Megaloolithus cf. siruguei); and (3) gekkotan eggshells (Gekko gecko and Phelsuma grandis). Trigonoolithus showed typical Type 2 distribution as anticipated in Choi et al. (2019a). In the case of the Dromaius eggshells, the d-value was more similar to the Type 2 distribution, although it has the highest d-values compared with other Type 2 eggshells and still has a significant amount of low-angle grain boundaries under the neighbour-pair method (Fig. 6F) also has a higher d-value, but we would like to consider this as a provisional result because it is based on a taphonomically altered sauropod eggshell ( Moreno-Azanza et al. 2016) and should be updated with the results derived from better preserved material (e.g. Grellet-Tinner et al. 2011). The Caiman latirostris eggshell has a lower d-value, similar to the Type 2 distribution of maniraptoran eggshells. Finally, the two gekkotan eggshells show a remarkable contrast in their d-values. The d-value of the Gekko gecko eggshell was similar to the Type 1 distribution of maniraptoran eggshell, while Phelsuma grandis presents the Type 2 distribution of maniraptoran eggshell.

Maniraptoran affinity of Pseudogeckoolithus
The crystallographic features identified on EBSD analysis clearly show that Pseudogeckoolithus is definitively not a squamate eggshell. Crystallographic contrasts documented both in overall eggshell microstructure per se and in ornamentation between the Gekko gecko eggshell and Pseudogeckoolithus document the action of markedly different building pathways that underlay their distinctive architectures. Their apparently highly similar nodular ornamentations are thus truly homoplastic, and, more specifically, convergent sensu Hall (2003; i.e. they represent similarities arising through independent evolution via different developmental pathways). Accordingly, in line with the original interpretation of Vianey-Liaud & Lopez-Martinez (1997) and, more recently, of Prondvai et al. (2017), but contra Garcia (2000) and Sell es (2012), we firmly establish here the non-gekkotan affinity of the Pseudogeckoolithus material surveyed in this study. Furthermore, we suggest that the previously proposed gekkotan origin of other Late Cretaceous European 'geckoid' eggshell materials, such as that of morphotype geckono€ ıde of Garcia (2000), should undergo similar scrutiny, given that it shows remarkable external and microstructural similarity to the Pseudogeckoolithus materials studied herein.
Based on the aforementioned features and comparisons, Pseudogeckoolithus can be safely identified as a theropod eggshell. Indeed, Pseudogeckoolithus has at least a two-layered structure made up of a mammillary layer and a squamatic zone (Fig. 4A). This bilaminate structure is absent in sauropod ( Grellet-Tinner et al. 2006 (Mikhailov 1997a, b;Choi et al. 2019a). Also, hadrosaur and sauropod eggshells have abundant low-angle grain boundaries, whereas such are rarely observed in Pseudogeckoolithus. All these observations eliminate any potential hadrosaur or sauropod affinity for Pseudogeckoolithus, not to mention the extreme thinness of Pseudogeckoolithus, compared with the eggshells typical for the other two clades.
In contrast, admittedly, non-maniraptoran theropod eggs are as yet poorly known: the only definite cases are represented by eggs ascribed to the megalosaurid Torvosaurus (Carrano et al. 2012)  To conclude, within Theropoda, Pseudogeckoolithus can be assigned to a maniraptoran egg-layer on the basis of: (1) a two-layered structure, with the presence of a mammillary layer and a continuous layer, character shared with all maniraptoran taxa (Mikhailov 1997a)  (2) an angusticanaliculate pore system (Prondvai et al. 2017), shared with most maniraptorans including Aves (Mikhailov 1997a); and (3) the possible existence of an external zone, a character widespread within avian eggshells (Mikhailov 1997b) and which is also present in some derived maniraptorans eggshells (e.g. Trigonoolithus amoae, Triprismatoolithus stephensi and Prismatoolithus levis; Varricchio & Jackson 2004; Jackson & Varricchio 2010; Moreno-Azanza et al. 2014b). Moreover, its greatly reduced thickness, suggestive of a small-sized theropod egg-layer (Prondvai et al. 2017), may further support its maniraptoran affinity, given that most Late Cretaceous European maniraptorans (including non-avian paravians; the theropods of unknown affinity Richardoestesia and Euronychodon; as well as enantiornithine and ornithurine birds; Csiki-Sava et al. 2015) are characterized by small body size. Meanwhile, it is worth noting that all known non-maniraptoran Late Cretaceous theropods from Europe (abelisauroids, basal tetanurans) were medium to large-sized animals ( Csiki-Sava et al. 2015). Such a mutually exclusive body size distribution among the Late Cretaceous theropods of Europe minimizes the possibility that Pseudogeckoolithus is an ootaxon of a medium to large-sized non-maniraptoran theropod, considering the known positive correlations between adult body mass and egg size in extant Aves (Juang et al. 2017), and that between egg mass (hence, size) and eggshell thickness (Ar et al. 1979).
Nevertheless, further specimens, including more complete eggs (or fortuitous discoveries such as in ovo embryos or gravid females), are needed to firmly establish the affinity of Pseudogeckoolithus, given that assigning a particular ootaxon to a certain clade can be erroneous in the absence of an embryo preserved in ovo (see discussion in Choi & Lee 2019). Embryo in ovo specimens would also narrow the assignment of the Pseudogeckoolithus eggs to one of the maniraptoran groups that were present in Europe at the end of the Cretaceous. It is worth noting, nonetheless, that eggs and eggshells from the Maastrichtian of Romania reported to co-occur with skeletal remains of (and thus referred to) taxonomically indeter-

EBSD, an adequate tool to identify true fossil squamate eggshell
Our EBSD analyses clearly show that Pseudogeckoolithus is not a gekkotan-related ootaxon; instead, it can be safely identified as belonging to a maniraptoran theropod group. In future studies, our approach can be extended and it should be applied to other putative fossil squamate eggshells (Choi et al. 2019b, table S1; text S5) in order to rigorously determine their accurate crystallographic arrangement and thereby assess the most likely phylogenetic affinity. whether it is more widespread among the rigid eggshellproducing squamates. Therefore, fossil rigid eggshells that are found without an associated embryo in ovo, and are probably not of archosauromorph origin, currently can be identified neither as gekkotan, nor as non-gekkotan squamate eggshells with certainty. Hence, for a comprehensive understanding of rigid eggshell evolution in Squamata, and in amniotes in general, as well as for correct taxonomic identification of fossil squamate eggshells, additional modern and fossil samples should also be analysed using EBSD. Choi & Lee 2019), members of the dinosaur clade giving rise to birds. Thus, ornamentation is highly likely to be a plesiomorphic character of the maniraptoran eggshell that disappeared in some extinct and most modern avian taxa (Lawver & Boyd 2018).
The maniraptoran affinity of Pseudogeckoolithus verified in the present study raises the question of why extremely similar dispersituberculate ornamentation exists in eggshells of such distantly related clades as Maniraptora and Squamata. Eggshells of extant megapode birds and Gekko gecko possess ornamentation with discrete and sparse nodes ( Grellet-Tinner et al. 2017;Choi et al. 2018), and a gecko-like dispersituberculate ornamentation is now also documented in the extinct maniraptoran Pseudogeckoolithus. Even though the nodular eggshell ornamentation seen in the modern maniraptoran megapodes is somewhat different in its gross morphology from that of the extinct maniraptoran Pseudogeckoolithus, megapode and Pseudogeckoolithus eggshells share similar basic crystallographic features. In the megapodes Alectura lathami and Leipoa ocellata the eggshell ornamentation is formed through extended shell deposition ( Grellet-Tinner et al. 2017), just as we document here in Pseudogeckoolithus (Fig. 4). This type of crystallographic make-up was also reported in oviraptorosaur eggshells (Elongatoolithus, Macroelongatoolithus; Choi et al. 2019a), although the ornamentation pattern itself is usually different in its morphology, being linear (Mikhailov 1997a) rather than nodular as in Pseudogeckoolithus (but also note that Macroelongatoolithus possesses dispersituberculate ornamentation as well; Simon et al. 2018). In addition, ornamentation of the anguimorph eggshell from the Lower Cretaceous of Thailand (Fernandez et al. 2015) also shows morphological similarity with that of the megapode eggshell. It is the only definitive case of squamate eggshell known in the fossil record (identification supported by associated in ovo embryos), meaning that rigid eggshell and its nodular ornamentation are not unique traits of gecko eggshells within squamates, but may have been more widespread among their fossil representatives.
The reason for the presence of ornamentation in sauropsid eggshell is a neglected topic in vertebrate palaeontology, except for one speculation ( Grellet-Tinner et al. 2017). Although the nesting microenvironment of Gekko gecko has never been studied, there are several studies on the nesting microenvironment of megapodes. Megapode eggs, which are buried in various substrates and are incubated by environmental heat instead of body heat (Booth & Thompson 1991), have a comparatively thinner shell than eggs laid by similar-sized avian taxa that use body heat in contact incubation. This relative thinness of the megapode eggshell was suggested to represent an adaptation that enhances gas exchange in the peculiar covered nesting environment of megapodes (Booth & Thompson 1991;Harris et al. 2014;Grellet-Tinner et al. 2017;but see Birchard & Deeming 2009 for an opposing view). Among maniraptoran-related ootaxa, the European Pseudogeckoolithus eggshells are also characterized by their remarkable thinness (Table 1; Choi et al. 2019b, text S4;Prondvai et al. 2017).
Given that the megapode and the G. gecko eggshell ornamentation represent outlier characters within their own clades (Aves and Gekkota, respectively), their similar gross morphology despite marked differences in underlying crystallographic make-up (resulting from different formational pathways, as shown by EBSD; see Choi et al. 2019b, text S6 for our view on the eggshell as an end-product of a complex eggshell calcite growth mechanism) may suggest an adaptive significance of this discrete nodular pattern of ornamentation, possibly driven by some kind of similar selection pressure in maniraptorans and gekkotans. Likewise, given that megapodes are derived neornithine maniraptorans (Prum et al. 2015), their eggshell ornamentation, which is similar only to that of the distantly related Cretaceous maniraptoran Pseudogeckoolithusis, is most likely to be a homoplastic feature that may have been caused by similar nesting microenvironmental settings in megapodes and Pseudogeckoolithus (see below). For these reasons, the eggshells of G. gecko and/or megapodes might be functionally comparable with, and informative for the interpretation of, the Santonian-Maastrichtian dispersituberculate theropod eggshells, including Pseudogeckoolithus (Table 1). Nevertheless, an alternative explanation, namely that this similarity in ornamentation may be only a random outcome of genetic drift and thus represents a non-adaptive retention or novel development of a functionless (and harmless) character in either clade (Gould & Lewontin 1979; Losos 2011), should not be overlooked.
We suggest that neontological experimental data should be gathered by ornithologists and/or herpetologists from the aforementioned extant taxa to shed light on the reason(s), if any, behind the presence of eggshell ornamentation, a feature that represented a dominant phenotypical trend for Mesozoic maniraptoran eggshells (Table 1). Experimental approaches to test its possible role(s), such as those implemented by Cedillo-Leal et al. (2017) for crocodylian eggshells, as well as detailed observations on the nesting microenvironments of megapodes and Gekko gecko, compared with those of other avian and gekkotan taxa, could help to clarify the evolutionary significance of eggshell ornamentation. This in turn might offer further insights into the reproductive palaeobiology of other dinosaurian and squamate clades with ornamented eggshells (Mikhailov 1997a;Fernandez et al. 2015), and may also give hints as to why eggshell ornamentation has disappeared in the majority of modern birds (Hauber 2014;Lawver & Boyd 2018).

Misorientation pattern in sauropsid eggshells
The presence of a crystallographic dichotomy (i.e. Type 1 and Type 2 misorientation distributions) within extinct and modern maniraptoran eggshells was first reported in Choi et al. (2019a). The enlarged dataset used in the present study provides further insights into the crystallographic features of diverse sauropsid eggshells. First, in Choi et al. (2019a), palaeognaths were represented only by ostrich and rhea, which both have definitive Type 1 distribution. However, the current study documents that the eggshell of the palaeognath Dromaius has a more Type 2-like distribution (at least in its d-value), similar to that of the neognath eggshells (Fig. 7), a finding that is further supported by the rarity of low-angled grain boundary in the emu eggshell (Fig. 6F). This implies that the distribution of Type 1 and Type 2 crystallographic patterns in avian eggshells is more complicated than that presented in Choi et al. (2019a, fig. 10), and thus a phylogenetically controlled sample derived from a wide range of avian clades, including palaeognaths and neognaths, should be analysed to better understand the evolutionary pattern.
Second, ornithopod and sauropod eggshells analysed in this study yielded high d-values (we would refrain from using the term 'Type 1' distribution for non-maniraptoran eggshells because it was initially coined only for maniraptoran eggshells, and furthermore, the question of whether the high d-value seen in ornithopod and sauropod eggshells and the Type 1 distribution of maniraptoran eggshells were both inherited from their common ancestor is far from being answered). Although the d-value obtained for the sauropod eggshell in the present study should be double-checked using better preserved eggshells, the results, if upheld, imply that, in general, higher d-values (such as those found in the maniraptoran Type 1 distribution) may be more widespread within Dinosauria than the lower d-values, and that the lower dvalues may be correlated with the unique reproductive strategy of maniraptoran dinosaurs (i.e. contact incubation;Varricchio & Jackson 2016;Choi et al. 2019a and references therein). Admittedly, this inference should be further checked using a more comprehensive sample of sauropod and ornithischian dinosaur eggshell material because (as documented in the case of the Dromaius eggshell, above) the phylogenetic distribution of high and low d-values may be rather complicated and can only be clarified through an extensive investigation. Nevertheless, the present results provide a first glimpse into the d-value distribution of non-maniraptoran dinosaur eggshells.
Finally, even though only two gekkotan species were analysed in this respect, surprisingly they show contrasting d-values. Similar to the case of maniraptoran eggshells reported by Choi et al. (2019a), a crystallographic dichotomy may also be present in gekkotan (or squamate, in general) eggshells, reinforcing the need for future comparative investigations into the microstructure and crystallography of a diverse array of squamate eggshells (see above).

Detecting homoplasy in eggshell evolution
Ornamentation morphology has been widely used as a criterion to classify ootaxa at the oofamily level (e.g. Mikhailov et al. 1996). However, the present results imply that ornamentation (similarly to other characters such as egg shape, shell unit shape and pore system ;Mikhailov 1997a) is also prone to homoplasy (Fig. 8).
Pseudogeckoolithus, 'Stillatuberoolithus', Macroelongatoolithus, a fossil anguimorph eggshell, as well as eggshell of Gekko gecko, megapodes, cassowary and emu, are all characterized by surface ornamentation although the morphology varies (Figs 4-6, 8;Mikhailov 1997b; F I G . 8 . Three types of ornamentation construction pathway in sauropsid eggshells and possible homoplasies. A, schematic crystallography of non-maniraptoran sauropsid eggshells used in this study. B, schematic crystallography of maniraptoran eggshells. In almost all sauropsid eggshells including Pseudogeckoolithus, ornamentation is crystallographically continuous with underlying eggshell, suggesting extended deposition ( Fig. 4; Moreno-Azanza et al. 2013; Grellet-Tinner et al. 2017;Choi et al. 2019a). In contrast, ornamentation of 'Stillatuberoolithus' and modern emu eggshells is initiated in the middle of the eggshell with wedge-shaped structures (Fig. 6E, F; Oser 2018), implying another pathway of ornamentation construction. In Gekko gecko eggshell, ornamentation is composed of randomly oriented calcite grains and contains non-crystalline material inside (Choi et al. 2018). The three different crystallographical patterns of ornamentation indicate homoplastic ornamentation evolution. Phylogenetic occurrences of smooth maniraptoran eggshells are indicated with grey branches. Instances of morphological similarity that can be interpreted as clear convergent evolution and possibly other types of homoplasy are marked with solid and dashed arrows, respectively. Note that only convergent evolution is clearly detectable by crystallographic electron backscatter diffraction analysis. Silhouettes are attributable to (http://www.phylopic.org): Emily Willoughby (Citipati); Scott Hartman (Archaeopteryx), Darren Naish and Michael Keesey (Dromaius). Silhouettes of Gekko, Caiman, hadrosaur, sauropod and Megapodius, SD. Grellet-Tinner 2006;Fernandez et al. 2015; Grellet-Tinner et al. 2017;Oser 2018;Choi et al. 2018Choi et al. , 2019a. We have shown that the similarlooking dispersituberculate eggshell ornamentation of Pseudogeckoolithus and Gekko gecko represents a clear case of convergent evolution. Meanwhile, the presence of uniform crystallography of the eggshell ornamentation (formed via extended deposition of the calcite grains) in the more closely related maniraptorans Pseudogeckoolithus, oviraptorosaurs (e.g. Macroelongatoolithus) and megapodes ( Fig. 8; Grellet-Tinner et al. 2017;Choi et al. 2019a) documents the emergence of a common pathway of ornamentation building in maniraptoran eggshells, despite their different overall morphology. Such a pathway appears to be a widely used template in ornamentation building in sauropsid eggshells (Fig. 8). In the case of 'Stillatuberoolithus' and of the extant Dromaius eggshells, however, the surface ornamentation is not crystallographically continuous with the underlying eggshell (Fig. 6E, F; Oser 2018). Instead, the appearance of ornamentation is 'programmed' crystallographically in the middle of the squamatic zone (Fig. 8), a feature so distinctive that the ornamentation was actually interpreted as a fourth layer in the case of the Dromaius eggshell by Grellet-Tinner (2006).

Zelenitsky & Modesto 2003;
In summary, there are at least three different ways of producing dispersituberculate ornamentation in sauropsid eggshells: the gecko style; the Pseudogeckoolithus style; and the 'Stillatuberoolithus' style; each of which can be unambiguously detected with EBSD analysis. The occurrence and distribution of these three different crystallographic patterns of ornamentation building in sauropsid eggshells document clear cases of homoplasy (Fig. 8). Considering that the eggs of almost all modern avian taxa have lost ornamentation (see above), the similarity recorded between Pseudogeckoolithus and the megapode eggshell is probably homoplastic unless an alternative scenario is true: that a relict ornamentation of a non-avian maniraptoran eggshell is uniquely retained by an avian clade, the megapodes.
In the case of the ornamentation of 'Stillatuberoolithus', it is underlain by a profoundly different generative mechanism from that seen in the typical two or three-layered maniraptoran eggshells (Zelenitsky & Modesto 2003; Grellet-Tinner 2006;Lawver & Boyd 2018;Oser 2018), one also typified by Pseudogeckoolithus as we have shown. Accordingly, 'Stillatuberoolithus' documents the emergence of a second ornamentation-building pathway in maniraptoran eggshell evolution. The presence of these two widely divergent building patterns shows that even though the dispersituberculate ornamentation of 'Stillatuberoolithus' is extremely similar to that of Pseudogeckoolithus, this gross similarity clearly represents a case of convergent morphology. Similar instances of independent evolutionary acquisition and disappearance of closely comparable character states were also suggested in another eggshell component, the cuticle (D'Alba et al. 2016). Likewise, calcified eggshell thickening has most likely evolved in diverse amniote clades, even within Dinosauria, several times independently (Stein et al. 2019).
The susceptibility of ornamentation to homoplasy has important implications for eggshell parataxonomy. It was argued that many eggshell characters are highly modular (sensu Klingenberg 2008) and are driven by mosaic evolution resulting in independent character combinations (Varricchio & Jackson 2004;Jackson et al. 2013;Lawver & Boyd 2018). The morphology of ornamentation is diverse in dinosaurian eggshells (Mikhailov 1997a), but we document here that even markedly different microstructure and crystallography can result in (or generate) almost identical gross morphologies, as shown in the cases of 'Stillatuberoolithus' and Pseudogeckoolithus (Fig. 8).
For these reasons, we suggest that both morphology and its underlying crystallography (which can be used as a proxy of the eggshell calcite growth mechanism; see Choi et al. 2019b, text S6) have to be considered together before using superficial similarities as diagnostic eggshell characters implying homology in parataxonomical assessments. However, there is still difficulty even in such mechanismbased identifications. Although EBSD can be used to identify definitive cases of convergent evolution in eggshell formation, characterized by different underlying mechanisms on crystallography, the reverse does not necessarily hold true: detecting the presence of a uniform mechanism does not always guarantee homologous origin of a feature, especially if the taxa of interest are distantly related (see also Hall 2003;Shubin et al. 2009 for a more complicated case called 'deep homology'). Considering the limited number of possible ways to build ornamentation or even a hard eggshell per se (Stein et al. 2019), we may expect to find identical crystallography expressed in distantly related clades that nevertheless acquired (or re-invented) their common traits independently. So far, none of the known approaches in eggshell research has provided a way to safely separate true homology from homoplasy if a character shared by several taxa has both similar morphology and a similar underlying mechanism. Such difficulties notwithstanding, in the effort to establish monophyletic groups in eggshell parataxonomy, clearly convergent characters (such as the ornamentation in G. gecko eggshells and Pseudogeckoolithus, as demonstrated in this study) have to be identified, and handled accordingly (for further criticism on current practices in parataxonomy see also Zelenitsky et al. 2002;Varricchio & Jackson 2004;Grellet-Tinner 2006; but see Mikhailov 2014 for a contrary opinion). Only such rigorous approaches to phylogenetic analysis will make parataxonomic classification of the diverse fossil eggshell record a biologically and evolutionarily meaningful effort.
Emended diagnosis. After Vianey-Liaud & Garcia (2003). Thin prismatic eggshell (200-350 lm including ornamentation), outer surface with dispersituberculate ornamentation, formed by irregular nodes, which are tubercle-or crater-like in shape. Wide pore openings at the top of some nodes. Egg shape and size unknown. Remarks. Eggshells referred in this study to Pseudogeckoolithus aff. tirboulensis resemble those described by Vianey-Liaud & Garcia (2003) from the Upper Cretaceous of Morocco in thickness, ornamentation and general histological structure. Nevertheless, they differ from the type material of Pseudogeckoolithus tirboulensis in the mammillary : continuous layer ratio, which in the African material is much higher (1:2). Accordingly, the Pseudogeckoolithus material from Hungary (see also Prondvai et al. 2017), and most probably that described here from the Romanian localities of Petrești-Black Lens and Pui-Classic, may represent a new oospecies of Pseudogeckoolithus.

CONCLUSIONS
The contentious affinity of enigmatic 'geckoid' eggshells from Upper Cretaceous deposits of Europe was resolved: they were identified as theropod eggshells using a crystallographic approach (EBSD). This study provides a template case to enable potential squamate eggshells, a poorly investigated category in vertebrate palaeontology, to be rigorously tested and positively identified using EBSD. More importantly, we show that among nodular sauropsid eggshells, there are at least three different mechanisms that generate ornamentation (as shown by crystallography). Until recently, when a certain eggshell phenotype (= character) was found to share similar morphology across several taxa, these were usually treated as homologies, and were coded into the character-taxon matrix accordingly. However, similar morphology does not always represent homology, and may be homoplastic instead. Using a crystallographic approach, such hidden homoplasies (especially convergence) can be detected in the case of fossil and modern eggshells. Hence, before identifying a particular morphological similarity as a potential homology, its underlying mechanism should also be considered, in order to avoid treating homoplasy as homology. Finally, detailed crystallographic investigation of a more extensive sample of dinosaur (including Aves) and squamate eggshells is necessary, given that the present results point to a more complicated evolutionary history of the sauropsid eggshell crystallography (and also that of its production mechanisms) than was previously thought, with significant implications for the reconstruction of the reproductive (palaeo) biology of amniotes. for providing access to Spanish specimens; Delphine Angst (University of Bristol) for contributing French thin-shelled eggshell specimens useful in comparisons; Eric Buffetaut (CNRS) for sharing information and providing references on French 'geckoid' eggshell occurrences; and Hiroki Echizenya (Hokkaido University Museum) and Kohei Tanaka for providing modern crocodylian eggshells. We appreciate Daniel Lawver (Stony Brook University), an anonymous referee and editors Imran Rahman and Sally Thomas for their constructive comments that helped to improve the previous version of this MS. Silhouettes  Author contributions. SC and EP conceived the study. SC, EP and YNL designed the study. MMA, ZCS and EP provided fossil material and SC and YNL provided modern eggshells. SC performed analysis and collected data. All authors interpreted results. SC, MMA, ZCS and EP wrote the manuscript. All authors gave final approval for publication.

DATA ARCHIVING STATEMENT
Data for this study are available in the Dryad Digital Repository: https://doi.org/10.5061/dryad.v75qf08 Editor. Imran Rahman