Gigantoproductid shell spiral and microstructure of tertiary layer: evaluation as taxonomical characters

ABSTRACT Brachiopod taxonomy is based on descriptions of shell morphology and key characters, but diagenesis generally modifies or erases some of them, hindering brachiopod identification. Brachiopods that are taxonomically related usually present shells with similar appearance but can differ in size (i.e., Rhynchonellata). Some aspects of morphology – for example the angular measurement of the curvature of the shell or details of shell microstructure – could aid taxonomic identification. Gigantoproductids, which lack a robust taxonomy, have the largest shells among brachiopods and are ideal for this kind of study because of their gigantic size and morphological variability. Furthermore, they have a great abundance and worldwide distribution during the mid-Carboniferous. More than 700 samples have been collected from Sierra Morena (Spain), Montagne Noire (France) and Adarouch (Morocco) identifying up to six gigantoproductid genera: Globosoproductus, Semiplanus, Kansuella?, Latiproductus, Gigantoproductus and Datangia. Microstructural features from 170 thin sections belonging to gigantoproductid ventral valves have been studied, and six crystal morphologies have been distinguished within the tertiary layer: subhorizontal, imbricated, crenulated, acicular, short and long columnar morphologies. Moreover, 23 complete shells from all genera have been selected to investigate shell size and curvature. Results from this study emphasise that shell size, curvature and crystal shape are taxa-related. Finally, a remarkable morphological change in the gigantoproductid populations from the western Palaeo-Tethys occurred during the Viséan–Serpukhovian, from thin-shelled genera with subhorizontal morphology (Viséan) to thick-shelled genera with a tertiary layer consisting of long columnar crystals (Serpukhovian). This study proves that microstructure, maximum thickness and shell spiral characterisation are robust characters when applied to gigantoproductid taxonomy, but also have great potential in other brachiopod groups.


Introduction
Brachiopod taxonomy has been developed based on descriptions of shell morphology, but fossil shells, about 95% of the phylum (Williams et al. 1996), usually have relatively few taxonomic characters due to taphonomic loss or the characters being obscured by matrix.This lack of preserved characters highlights the need to develop new tools to identify taxonomically significant shell characters.The shell shape, size and thickness are under significant phylogenetic influence in brachiopods (Rudwick 1959;Balthasar et al. 2020), as is the microstructure, which has been proposed as a potential character for taxonomic purposes (Motchurova-Dekova 2001;Motchurova-Dekova et al. 2002;Radulovic ́et al. 2007;Smirnova & Zhegallo 2022) as well as an environmental proxy (Ye et al. 2018).
Biologically controlled mineralisation in brachiopods determines the shell morphology and tailored microstructures (Pérez-Huerta et al. 2018), developing a spiral structure from the umbo to the commissure parallel to the sagittal plane, that grows during the lifespan by accretion, adding new material during secretion of the anterior stage (Ackerly 1992;Aldridge 1999;McGhee 2001).The shell spiral does not usually follow a perfect spiral path, varying during the ontogeny (Clark et al. 2016).In order to evaluate this variation, a promising tool was developed by Aldridge & Gaspard (2011), which compares the shell outline with a perfect logarithmic spiral.This method was successfully used for calculating the brachiopod ontogenetic age and for determining palaeoseasonal variations in trace elements (Pérez-Huerta et al. 2014;Clark et al. 2015Clark et al. , 2016;;Gaspard et al. 2018).
Nevertheless, brachiopod microstructure has been widely studied with different techniques such as petrological microscopy, scanning electron microscopy, electron backscatter diffraction and atomic force microscopy (Williams 1956(Williams , 1968;;Rush & Chafetz 1990;Motchurova-Dekova 2001;Garbelli 2017;Ye et al. 2018;Simonet-Roda et al. 2019, 2021).Three different layers have been identified in the brachiopod shell: a primary layer with microgranular appearance, usually absent in fossils; a secondary layer with laminar or fibrous microstructure; and a tertiary layer with a columnar microstructure (Williams 1968).The tertiary layer, despite showing the largest crystals, is poorly investigated compared with the secondary layer, which has been widely studied in extant and fossil brachiopods (Griesshaber et al. 2007;Radulovic ́et al. 2007;Garbelli 2017;Ye et al. 2018;Simonet-Roda et al. 2019).Ye et al. (2018) noted differences in crystal size and shape in the secondary layer between two species of the same genera, associated with environmental factors and ontogeny.Radulovic ́et al. (2007) noted size differences of fibres into the secondary layer and proposed a new genus of fossil brachiopod based on its microstructure.Recently, Simonet-Roda et al. (2021) studied the microstructure (crystal morphology and crystallographic orientation) of thecideide brachiopods within the context of the group's phylogeny.
Among brachiopods, gigantoproductids have one of the largest and thickest shells of all the fossil record (Angiolini et al. 2019), which make them exceptionally useful for microstructural studies; unfortunately, however, the microstructure of the group has only been vaguely described in the literature (Mii et al. 2001;Armendáriz et al. 2008;Angiolini et al. 2012Angiolini et al. , 2019;;Nolan 2017).
Here, combined microstructural and shell spiral studies of six gigantoproductid genera are analysed from different geological basins and ages (Viséan to Serpukhovian).The use of these potential tools as taxonomic characters sheds new light on the taxonomy of the group.

Geological setting
Brachiopods were sampled in Sierra Morena (SE of Iberian Massif, Spain), Montagne Noire (Hérault, SW of Central Massif, France) and Adarouch areas (NE of the Variscan Massif of Morocco) (Fig. 1).In total, 27 stratigraphic sections have been sampled, mainly limestones and marlstones.More than 700 gigantoproductid specimens, both complete and fragmentary, were collected.Sierra Morena samples were collected from 12 sections in the Guadiato and Guadalmellato valley (close to Adamuz): Sierra Boyera, Cerro de Los Pradillos, Alcolea, Sierra de la Estrella, Cantera del Castillo, El Collado, Valdemilano, Fuenteagria, La Lozana, La Caridad, San Antonio and La Urraquilla.In addition, two sections yielding gigantoproductids have been investigated and sampled from Los Santos de Maimona Basin: Los Santos de Maimona and Cerro Almeña.The Guadiato Valley has been interpreted as an inner platform of Viséan-Westphalian age (Cózar & Rodríguez 1999), Guadalmellato Valley as platform to slope facies with Brigantian to Pendleian age strata (Cózar & Rodríguez 2004;Cózar et al. 2006) and Los Santos de Maimona as an inner platform to slope facies (Rodríguez et al. 1992).The Southern Montagne Noire is the most northerly sampled area based on seven sections: Tour de Castellas, Roc du Cayla, Roque Redonde, Les Pascales-2, Escandolge-1, Castelsec, La Serre and Escandolge-2, interpreted as shallow platform to slope facies with several olistoliths (Vachard et al. 2016(Vachard et al. , 2017;;and references herein).The samples from the southeastern Montagne Noire have a Viséan to Serpukhovian age.In Adarouch, five sections have been sampled: Tizi ben Zizouit, Akerchi-2, Idmarrach-2, Tirhela and Akerchi-1.Adarouch facies have been interpreted as part of a foreland basin of late Viséan to Serpukhovian age (Cózar et al. 2011).The biostratigraphy of the sections is summarised in Table 1.

Material and methods
Specimens were carefully cleaned and sectioned in halves from the umbo to the commissure, whenever possible, as some shells were incomplete or had suffered decortication.Each slab was polished with carborundum down to 1200 grain size, and with 1 μm and 0.3 μm alumina powder.Polished sample slabs were scanned to enable digital cross-reference with micrographs obtained by optical techniques, and 270 thin sections were prepared.The material is housed in the palaeontological collections of the Paleontology Area, Complutense University of Madrid (UCM).
A petrographic microscope (LM Leica DMLP) with coupled camera (Leica DC 300) was used to photograph the thin sections with the purpose of characterising the brachiopod microstructure using cross-polarised filters in petrological microscopy.
In addition, natural breakage fragments and polished slabs were studied with scanning electron microscopy (SEM).Polished slabs of the whole gigantoproductid section were etched in 5 % HCl solution for 10-15 s.These samples were gold-coated and analysed using a model JEOL 6400 JSM located in the Spanish National Centre for Electron Microscopy of the UCM.A combination of petrological microscopy and SEM was used to evaluate shell preservation and to measure the well-preserved crystals.
Crystal length, width and orientation were measured in each crystal in different regions of the shells.Measurements, in millimetres (mm) and degrees, were made via micrographs of the thin sections using the plug-in ObjectJ 1.03w (Vischer et al. 1994) of the open-source ImageJ 1.47v image processing software (Abràmoff et al. 2004) and the statistics were processed using Originpro2019 software 9.6.More than 10,000 columnar crystals from the tertiary layer of 170 gigantoproductid ventral valve shells were measured in complete and fragmented specimens.Columnar crystal disorientations have been calculated in well-preserved areas of each sample, by comparing all orientations measured with a selected arbitrary reference crystal and measuring the disorientation angle of each crystal relative to the reference crystal.
In addition, each shell spiral was measured in 23 ventral valves, corresponding to complete shells continuous from the umbo to the commissure.Shell spiral coordinates of each valve were obtained outlining the ventral valve using ObjectJ 1.03w plugin in ImageJ, with the concavity of the ventral valve faced down, the umbo at the left and the commissure at the right (brachiopod in life position).Spirals were grouped using a 2D convex hull algorithm with Originpro2019 software 9.6.The shell spiral deviations of 23 samples from this study and 14 samples from the literature were measured using R software V. i386 4.0.3 using the algorithm developed by Aldridge (1999) and updated in Clark et al. (2015).
Gigantoproductus shells have a large shell size, 150-250 mm wide from ear to ear, with thickness of 15-22 mm, rounded shape and fine ribbing that becomes more sinusoidal towards the commissure.Two morphotypes have been distinguished in this study: Gigantoproductus sp. 1 with a larger and thicker shell and more reticulate ribs than Gigantoproductus sp. 2. Gigantoproductus sp. 1 occurs in seven sections (Fuenteagria, La Caridad, San Antonio, Akerchi-1 and 2, Idmarrach-2 and Tirhela) from Sierra Morena and Adarouch; Serpukhovian in age (Brigantian-Arnsbergian).Gigantoproductus sp. 2 occurs in two sections (Cantera del Castillo and La Urraquilla) from Sierra Morena; late Viséan-Serpukhovian in age (late Asbian-Pendleian).
Datangia shells resemble Gigantoproductus but are slightly smaller in size, 116 mm, and have a more incurved shell, similar shell thickness, 21 mm, although the ribbing is stronger, and with longer and more triangular ears.Datangia occurs in three sections (Escandolge-1 and 2 and La Serre) in the Montagne Noire; Serpukhovian in age (Brigantian-Pendleian).

Results
The results section combines descriptions and measurements made on our material (i.e., from Sierra Morena, Montagne Noire and Adarouch areas), and some specimens from the literature, which have been measured and analysed using the same aforementioned methods.

Characterisation of the gigantoproductids' ventral valve
Fossil gigantoproductids have concave-convex shells consisting of three layers (Fig. 2): the primary layer in the outer shell is always erased by diagenesis; this is followed by the laminar secondary and the columnar tertiary layers; the tertiary layer is the widest and occupies the innermost portion of the shell.Spiral growth of brachiopods creates a new commissure that thickens and lengthen the shell (Fig. 2).Each stage is separated by a growth line.The growth lines are interruptions or decelerations during the shell growth (sensu Hiller 1988), associated with a microstructural change.The growth lines are not perfectly parallel and equidistant from each other, which creates differences in growth of the shell spiral (Gaspard et al. 2018).These differences in growth, which correspond to ontogenetic stages, may modify the external shape of the shells in the form of shell spiral deviations.
3.1.1.Morphology of the ventral valve.Gigantoproductids' ventral valves have an ellipsoidal shape, more rounded in Gigantoproductus and Globosoproductus.In contrast, Datangia has triangular ears, which elongate the hinge line and show a more triangular aspect than Gigantoproductus.Latiproductus and Semiplanus have a narrower ellipse contour, elongated from ear to ear.Kansuella?shows an ellipsoidal shape but with a straight edge at the umbo.Some descriptions from the literature have been used for comparisons with other gigantoproductid genera such as Titanaria, which resembles Gigantoproductus in size and shape but may be differentiated by the morphology of the cardinal process and muscle scars (Muir-Wood & Cooper 1960).On the other hand, Beleutella has a smaller size than Gigantoproductus and Titanaria, is much less incurved, and the ribs are narrow with a low number of spines and more widely spaced (Legrand-Blain 1987).
Besides the distinctive morphological features, size differences (i.e., valve thickness and arc length, also called spiral length) between genera are noticeable, too, and they can be grouped into two clusters (Fig. 3): Gigantoproductus and Datangia have the largest shells with greater variation in size than Globosoproductus, Latiproductus and Semiplanus.Dimensions among this last cluster are closer with smaller and thinner ventral valves (Fig. 3a).On the other hand, additional genera from literature included in this study (e.g., Titanaria and Belleutela) exhibit similar dimensions to those genera from the second cluster (i.e., Globosoproductus, Latiproductus and Semiplanus).Titanaria occupies an intermediate position with species in both clusters, whereas Belleutela and Kansuella have similar valve thicknesses, although Belleutela is longer.
Shell spiral measurements are summarised in Table 2. Ventral valve length (linear measurement) and the arc length (i.e., length of the shell spiral from the umbo to the commissure) are measured to identify the larger and smaller genera.Gigantoproductus sp. 1 has the largest ventral valve, followed closely by Datangia, with avery similar valve thickness (∼20 mm).Gigantoproductus sp. 2 is smaller and thinner (∼12 mm) than Gigantoproductus sp. 1 and Datangia.Latiproductus, Globosoproductus and Semiplanus show similar size between them and have thinner ventral valves than the previous thick genera; Semiplanus is the thickest genera of this cluster.Differences in shell spiral are due to the incurvation degree (i.e., convexity) of the shell, represented by the (k) parameter.This parameter indicates the valve shape: higher (k) values describe more flattened valves and lower (k) values describe more incurved valves (Table 2).The thicker valves of Gigantoproductus sp. 1, G. sp. 2 and Datangia show similar curvature values (Fig. 3), whereas the thinner valves show more variability.Globosoproductus exhibits the most incurved shell of the analysed taxa, followed by Semiplanus and Latiproductus, which have similar flatness.The theoretical beginning of the spiral is represented by the (a) parameter.Low (a) values indicate a better fitting of the specimen spiral and the theoretical spiral at the beginning of the spiral (Table 2).Latiproductus and Gigantoproductus sp. 1 have the best fit to a theoretical spiral, followed by Semiplanus.Globosoproductus, Datangia and Gigantoproductus sp. 2 show higher (a) values, which corresponds to a considerable distance between the beginning of the theoretical spiral and the real spiral of the ventral valve.
The growth spiral of the brachiopod shells does not perfectly match the idealised theoretical spiral: deviations from the theoretical spiral occur with positive (towards the centre) and negative (outwards from the centre) deflections from the theoretical trajectory (Fig. 4).When these deviations occur outwards, the spiral (i.e., the external part of valve) is defined as the maxima, whereas if spiral deviations occur inwards the spiral (i.e., the central part of the valve) is defined as the minima.Analysed shell spirals show differences in the magnitude of deviations, with wider and larger ones with 2-4 maxima and minima across the shell, and multiple narrow and smaller ones, which seem more randomly located.Figure 4 shows different spiral deviation plots calculated over the outer line of Gigantoproductus sp. 1, Latiproductus and Semiplanus shells of this study and compared with specimens of the same genera from literature.The upper row represents the spiral deviations calculated for collected samples of this study; the lower row represents the spiral deviations calculated from specimens of the literature.Larger deviations of the shell spiral are usually located at the umbo, the middle part of the shell and the final portion of the shell, as shown in Semiplanus or Gigantoproductus meridionalis specimens.
3.1.2.Ventral valve crystal morphologies.The microstructure of the ventral valve of gigantoproductids is shaped by two crystal morphologies: laminar in the secondary layer and columnar in the tertiary layer.The secondary layer, located at the most external part of the gigantoproductid brachiopod's shell, is characterised by lath crystals, which constitute the laminar microstructure and are characteristic of the growth lines sandwiched between columnar microstructure into the tertiary layer.Moreover, six crystal morphologies have been identified in the tertiary layer of the ventral valve, characterised by a column-like crystal morphology.Six columnar morphologies have been identified in the tertiary layer associated with crystal shape differences: long columnar, short columnar, acicular columnar, imbricated columnar, subhorizontal columnar and crenulated (Fig. 5).
Each crystal morphology identified varies in shape and size between different genera or morphotypes in the case of Gigantoproductus (Figs 5 and 6; Table 3).The tertiary layer in Gigantoproductus sp. 1 and Datangia is characterised by long columnar crystals, whereas Gigantoproductus.sp. 2 has acicular columnar crystals.Globosoproductus exhibits subhorizontal columnar crystals, whereas imbricated crystals are characteristic in Semiplanus.The short columnar morphology is found in Latiproductus specimens and Kansuella? is characterised by columns with crenulated appearance.Moreover, other microstructures appear in Kansuella?, such as columns similar to the subhorizontal columns of Globosoproductus and columnar crystals similar to Latiproductus but sandwiched into the subhorizontal-like columnar crystals.This feature makes Kansuella?unsuitable for microstructural comparisons with other genera from this study and their specimens have not been measured.
Columnar crystals in Gigantoproductus sp. 1, Datangia and Latiproductus have a higher width/length ratio and straighter crystal contacts than Semiplanus, Globosoproductus and Gigantoproductus.sp. 2, which have more elongated columns and undulating contacts between crystals.Microstructural features and crystal measurements are summarised in Table 3. Gigantoproductus sp. 1 and Datangia have the highest average crystal width, with the longest crystal measurement (9.55 mm).Gigantoproductus sp. 2 exhibits a higher average crystal length than Gigantoproductus sp. 1, but they are narrower in width.Latiproductus and Globosoproductus show similar average crystal length whereas Globosoproductus has narrower crystals.Semiplanus has the highest average crystal length but narrower crystals than the rest of the genera except Globosoproductus.Kansuella?has a crenulated microstructure in the tertiary layer (Fig. 5).
3.1.3.Intra-shell crystal size variations.Crystal length and width of each morphology have been measured across the whole shell profile from the umbo to the commissure.Crystals have been grouped into five regions as a function of their relative position in the gigantoproductid ventral valve.The five shell regions were defined based on differences in growth line spacing into the ventral valve, and are named as umbonal (U), thick (Tk), thin (T), inner-thick (ITk) and inner-thin (IT) regions.U-region corresponds to the umbonal part of the shell; Tk-region corresponds to the middle part of the shell, where the shell and the growth line spacing are wider; T-region corresponds to the thinner part of the shell until the commissure, where the growth line spacing decreases; the ITk-and IT-regions correspond to the innermost parts of Tk-and T-regions respectively, where the growth line spacing decreases progressively.This methodology has been extended in this study by measuring the crystal column length and width of each region in five studied gigantoproductids genera (Globosoproductus, Semiplanus, Latiproductus, Datangia and Gigantoproductus) to compare microstructural differences (Fig. 7).
Each crystal morphology shows differences in length and width at different shell regions (Fig. 7; Table 4).In all morphologies the Tk-region usually has the longest crystals followed by the T-region and U-region.The ITk-and IT-regions have the shortest crystal column.The crystal width describes a similar trend to crystal length but shows much less size variability.The big and acicular columnar morphologies, which belong to the thickest and biggest shells, show more crystal size variation than the smaller shell morphologies, while the imbricated morphology shows more uniform crystal size across the shell and the subhorizontal morphology shows similar width within the shell regions.
3.1.4.Crystal disorientation in the ventral valve.Crystal disorientations were measured in each crystal morphology of the tertiary layer of the gigantoproductid genera.Generally, crystals show low levels of disorientation regardless of crystal morphologies.Five histograms are plotted to compare crystal disorientation between genera (Fig. 7).A random distribution function was plotted in each histogram to help to compare the disorientation degree in each genus.
All the histograms (Fig. 7) show a Gaussian constrained distribution (i.e., lower standard deviation) in contrast to the random distribution function.The larger and thicker shells, those in Gigantoproductus and Datangia, show higher crystal disorientation than the thinner shelled Latiproductus, Globosoproductus and Semiplanus.Gigantoproductus sp. 1 and Datangia present highest disorientation (e.g., mean ∼18°) than other genera (e.g., mean ∼9°in Semiplanus).Additionally, disorientation of well-preserved compared with poorly preserved areas of Semiplanus samples were plotted.Widespread disorientation values of the poorly preserved areas were very similar to the random distribution function and broader than well-preserved areas, which show constrained values (from 0°to 48°).

Discussion
Gigantoproductid taxonomy is based on descriptions of shell morphological features and key characters of the internal shell surface, such as the morphology of the cardinal process, the muscle scars, or the presence/absence of the brachial cones (Sarycheva 1928;Prentice 1950Prentice , 1956;;Sarycheva & Sokolskaya 1952;Muir-Wood & Cooper 1960;Ferguson 1978;Legrand-Blain 1980, 1985, 1987;Legrand-Blain et al. 1983;Zakowa 1985;Aretz et al. 2019).Homoeomorphy is challenging in all brachiopod studies (Muir-Wood & Cooper 1960), but in gigantoproductids it is complex due to the marked similarities between genera, as Williams et al. (2007) noted.Accordingly, other characters have become more significant: shell size and thickness; shell morphology; ribbing density; and shell curvature (Prentice 1956;Legrand-Blain 1973, 1980, 1987;Legrand-Blain et al. 1983).In the current study, less than 5 % of specimens preserve one or two of these internal shell characters not hidden by the matrix, but all of them show microstructural features, shell thickness, and complete specimens provide information about spiral and shell length, despite being embedded in matrix or fragmented.

Gigantoproductid shell size and microstructure through time
Gigantoproductid shells (Fig. 2) have long and thick shells (Muir-Wood & Cooper 1960), longer than any other brachiopods.This is an advantageous feature for palaeoenvironmental and palaeoclimatic studies (e.g., microstructural and geochemical studies), because shell size, thickness or microstructural features are larger than other brachiopod shells (helping microsampling and measuring).Muir-Wood & Cooper (1960) classified productids by their size: under 20 mm are considered small, 20-50 mm are medium size, over 50 mm are called large, and larger than 150 mm are gigantic.In this study, Latiproductus, Semiplanus, Kansuella?and Globosoproductus would be considered large in this classification, whereas Gigantoproductus and Datangia would be considered gigantic.
Figure 3 shows a correlation between the maximum thickness and the arc length of the shell.Longer genera such as Gigantoproductus sp. 1 have thicker shells.This is reasonable because during shell growth (in length) the commissure is thickened with a new calcite layer, and so on.It is noticeable that larger genera have more size variation and are clustered for a gap in size from the thin-shelled genera, which are closely grouped.Latiproductus varies more in length than in thickness, in contrast to Semiplanus.Furthermore, Globosoproductus is in an intermediate position.Gigantoproductus sp. 1 and G. sp. 2 have similar size variability, with G. sp. 1 being larger and thicker.It should be highlighted that thick-shelled genera, such as Gigantoproductus and Datangia, are more common during the Serpukhovian than thin-shelled taxa (Globosoproductus and Latiproductus), which are more common during the Viséan (Fig. 8; Table 1).Moreover, a microstructural shift of the tertiary layer has been illustrated through time, which is related to the shell thickness.
Gigantoproductid crystal columnar crystal morphology of the tertiary layer (Fig. 5) varies during the Viséan-Serpukhovian (Fig. 8) from a predominantly subhorizontal columnar crystal morphology to sub-perpendicular long column crystals.This means a progressive change in gigantoproductid populations from thin-shelled to thicker-shelled genera.Globosoproductus, with subhorizontal morphology, dominated during the late Asbian, followed by the imbricated morphology (Semiplanus and Kansuella?), which are a little bit thicker than Globosoproductus and exhibit less incurved shells.Gigantoproductus sp. 2 appears at the end of the late Asbian with thicker shells of the aforementioned genera and a curvature similar to Globosoproductus (Fig. 3).
A new microstructure appears during the Brigantian with the development of short columns in the tertiary layer, such as the short columnar morphology present in Latiproductus (Fig. 8; Table 1).Crystal columns of this genus show differences with respect to the crystal shape of Semiplanus and Globosoproductus, the last of these being more elongated than Latiproductus.Short column type has a lower length/width ratio, straight crystal contacts and sub-perpendicular crystal orientation to the shell surface.This microstructure occurs also in Pendleian specimens but is less common than taxa with long columnar microstructure (Gigantoproductus sp. 1 and Datangia).
During the late Brigantian and Pendleian the long columnar morphology in Gigantoproductus sp. 1 and Datangia are predominant over other microstructures, such as the subhorizontal and short columnar.Acicular microstructure is associated with Gigantoproductus sp. 2 and occurs only in two outcrops assigned to the Asbian-lower Brigantian and the Pendleian.Gigantoproductus sp. 1 is more common than Latiproductus during the Pendleian to Arnsbergian, confirming the dominance of the thicker-shelled genera during the Serpukhovian.Latiproductus seems a special case due to its occurrence during the Viséan-Serpukhovian interval in several basins and with similar shell thickness (Fig. 8).
The increasing shell size in gigantoproductids during the Viséan-Serpukhovian has been previously noted by other authors and can be tested by comparing with data in the literature.
In Stainmore and Northumberland (northern England), Pattinson (1981) reported thin-shelled and thin-ribbed gigantoproductid shells of Linoprotonia during the Holkerian and early Asbian, which changed to thicker-shelled gigantoproductids such as Gigantoproductus maximus, Gigantoproductus semiglobosus and Gigantoproductus submaximus during the late Asbian to Brigantian.
In the Zhanpo Formation, southern Shaanxi (China), Qiao & Shen (2012) observed that Gigantoproductus giganteus has a smaller shell during the Viséan than in the Serpukhovian.On the other hand, these authors described specimens of Gigantoproductus sp. with a shell shape and spiral very similar to the samples of the Guadiato area of this study (Fig. 3).
In Montagne Noire, Aretz et al. (2019) described the presence of thinner Datangia shells (Viséan, 4-8 mm) than the Serpukhovian Datangia samples from this study (shell thickness ∼19 mm).Moreover, Aretz et al. (2019) provided data about the abundance of Latiproductus and Datangia (shell thickness 4-8 mm) during the early Brigantian, which changed during the Pendleian to Kansuella sp. 1 and K. sp. 2 (shell thickness 11-15 mm).The shell thickness increase through time, which is latitude independent in extant brachiopods (Watson et al. 2012), is a common mechanism in gigantoproductids in the same genera and in the same evolutionary lineage.This trend is also latitude independent in gigantoproductids (China, England, Morocco, Algeria, Montagne Noire and Sierra Morena), although this group inhabited topical-subtropical seas.Balthasar et al. (2020) indicated a shell thickening trend in Orthida and shell thinning in Strophomenata and Clitambonitida during the Ordovician-Silurian.These authors suggested different phylogenetic mechanisms of shell thickness variation, which might be related to different strategies in response to environmental changes.
Gigantoproductids are large brachiopods (some of them giants) and possess one of the largest and thickest shells in the fossil record (Angiolini et al. 2019).Extant brachiopod species reach a maximum of 70 mm in length (Baumgarten et al. 2013) and 0.1-1.2mm in shell thickness (Foster 1974)  predation pressure (Vermeij 2016) and photosymbiotic lifestyle of Gigantoproductus (Angiolini et al. 2019).Variation of gigantoproductid shell morphology and size, and its relationship with environmental factors through this time interval, require further investigation.

Shell spiral deviations as response to ontogeny
The shell spiral had been used to detect changes during shell ontogeny in extant (Aldridge & Gaspard 2011;Pérez-Huerta et al. 2014) and fossil brachiopod shells (Clark et al. 2015(Clark et al. , 2016)).Deviations of the shell spiral are small curvature differences between the shell spiral and the theoretical spiral, which indicate changes in the growth rate (Aldridge & Gaspard 2011) in the form of deviations above (maxima) or below (minima) the line of the theoretical spiral.These changes prove that shell growth is not constant through time and the curvature of the shell varies.There are several factors that could affect brachiopod growth at the biological level (genetic, illness) and/or environmental factors (food availability, shell breakage due to predators or abiotic impacts, temperature, salinity, acidification events, and so on) that cannot be easily linked to deviations of the shell spiral (Aldridge & Gaspard 2011), but in combination with geochemical proxies demonstrate its potential to calculate ontogenetic states and palaeotemperature seasonal variations (Clark et al. 2016).
The shell spiral in gigantoproductids shows variations in (k) and (a) parameters, which seem genus-related, even speciesrelated (Fig. 3).This relation between species and curvature in gigantoproductids was originally shown by Prentice (1956) and Legrand-Blain (1973, 1987) by comparing the curvature of the shell spiral between different species (i.e., graphically outlining the valves).
Figure 3 shows a similar beginning of the spiral fitting and curvature (similar (a) and (k) values respectively), and low error between Latiproductus and Gigantoproductus sp. 1, but they have a very different ventral valve thickness.Both genera have a similar microstructure of the tertiary layer, and long columnar type, with Gigantoproductus sp. 1 larger than Latiproductus, which may explain the valve thickness differences.
Moreover, Gigantoproductus sp. 2 and Globosoproductus seem to be a similar case, with proximal (k) and (a) values and different ventral valve thickness, and Gigantoproductus sp. 2 thicker than Globosoproductus.Microstructure of the tertiary layer of these two species (Fig. 5) are more elongated (acicular and subhorizontal types) than Latiproductus and Gigantoproductus sp. 1 (long columnar type).Shell thickness differences in this case may be related to the orientation of the elongation axis of crystals, which is perpendicular to the shell surface in Gigantoproductus sp. 2 (acicular type) and parallel to the shell surface in Globosoproductus (subhorizontal type).Semiplanus exhibits intermediate values between both groups, which may be related to its characteristic microstructure (Fig. 5), whose crystals are tilted relative to the shell surface, an intermediate crystal orientation compared with the other genera (Fig. 7).
Deviations of the shell spiral (Fig. 4) were interpreted as variations in growth (Pérez-Huerta et al. 2014;Clark et al. 2015Clark et al. , 2016) ) and, thus, they can be used to infer changes in the growth rate through the ontogeny.Larger and wider deviations in magnitude are possibly related to shell morphology and the smaller deviations seem to be related to the periodical growth increments.The larger spiral deviations in gigantoproductids are usually in the middle part of the shell (Tk-part), which has the largest crystals and thus the highest valve thickness (Table 3; Fig. 7).Thicker shells such as Gigantoproductus sp. 1 show larger deviations in magnitude than thinner shells, such as Latiproductus or Semiplanus (Fig. 4).Gigantoproductus sp. 1 and Latiproductus show similar (a) and (k) values (Fig. 3) but higher differences in shell thickness.Gigantoproductus sp. 1 valves show the highest maxima and minima in the central part (Tk-region), where the thickness is maximum, about 22 mm.However, Latiproductus valves show similar spiral deviations to Gigantoproductus sp. 1, where the magnitude is lower due to valve thickness differences.It should be highlighted that larger magnitude deviations of the shell spiral in gigantoproductids are related to valve thickness.Deviations of the shell spiral magnitude generally decrease from the umbo towards the commissure (Fig. 7).It should be noted that thick-shelled taxa (Gigantoproductus sp. 1 and Datangia) which exhibit very incurved shells have larger crystal disorientations in the tertiary layer, relative to thin-shelled taxa, even if they are strongly incurved as in Globosoproductus.
Qualitative curvature information and shell size have been commonly used to distinguish gigantoproductid species (Prentice 1956;Legrand-Blain 1973, 1987;Pattison 1981), and shell size has been applied as a taxonomic character in other brachiopods such as Lingulidae (Kowalewski et al. 1997), although a priori this group does not show a large variation in shape.This study emphasises that quantitative curvature changes are taxa-related in gigantoproductids and can be a robust taxonomic criterion to cluster mainly thin-shelled brachiopods.
It should be highlighted that the identification by shell measurements of brachiopod shells with large intraspecific variation in size and shape, such as Terebratalia transversa, is difficult (Paine 1969), but they can be differentiated from other species by their microstructure, as demonstrated by Griesshaber et al. (2007).

Microstructure as taxonomic criterion
Microstructure as taxonomic character has been evaluated in fossil brachiopod shells (Motchurova-Dekova 2001;Radulovic ét al. 2007;Manceñido & Motchurova-Dekova 2010) to distinguish taxa by comparing dimensions and textures of the secondary layer (e.g., fibres), while Garbelli (2017) reported differences in the columnar crystals of the tertiary layer between Strophomenata and Rhynchonellata.Gigantoproductids in this study show a crystal microstructure that is taxon-specific (e.g., genera or species).Taxa with elongated crystals (e.g., long columnar and acicular) have thicker valves, more growth lines, larger crystals and higher crystal size variation than Latiproductus (short column type), Globosoproductus (subhorizontal type) and Semiplanus (imbricated type).Some variability exists, for instance between Gigantoproductus sp. 1 and Datangia, which have long column type microstructure, but Gigantoproductus sp. 1 has larger crystals (mean: 0.97 mm in length and 0.08 mm in width) than Datangia (mean: 0.64 mm in length and 0.06 mm in width) when comparing samples of similar shell size.Latiproductus has a similar microstructure to Gigantoproductus sp. 1 and Datangia (i.e., short columnar and long columnar respectively) with smaller crystals and less crystal size variation (Fig. 6).Gigantoproductus sp. 1 and Datangia have thicker ventral valves with a higher amount of growth lines (∼15-20) in comparison with Latiproductus (∼5-8).Microstructural variations in crystal size between genera seem to be related to the variations of the ventral valve thickness, while the crystal shape seems to be genus-related.
Microstructures in gigantoproductid specimens illustrated in this study may be compared with those already reported in the literature, offering a novel taxonomic character for brachiopod systematics (Mii et al. 2001;Armendáriz et al. 2008; Angiolini et al. 2012, 2019;Nolan 2017).However, big columnar crystals can be identified all Gigantoproductus specimens except in Armendáriz et al. (2008), which shows subhorizontal and short columnar crystals.Microstructure and shell thickness strongly suggest that taxa illustrated by Armendáriz et al. (2008) are Globosoproductus and Latiproductus.
Crystal size may be related to shell size differences because larger genera exhibit larger crystals, except for Semiplanus, which has longer crystals but with inclined orientations.The crystal size and orientation in each shell region may influence the external shape of the shell, although this relationship needs to be further investigated.
Brachiopod shells are assembled from numerous crystals of different sizes (length and width), probably related to the external shell morphology (i.e., spiral development), and clearly related to the different ontogenetic areas and hence to growth rates.Gigantoproductid microstructure shows that the largest crystals occur in thicker shell parts (e.g., Tk-and U-parts), and shorter crystals are situated in the thinnest and the innermost parts of the shell (T-and ITk-parts).Thick-shelled taxa (Gigantoproductus sp. 1 and Datangia) show more differences in crystal size between parts than thinner-shelled taxa (Globosoproductus, Latiproductus and Semiplanus), because the thickness variation across the shell is higher.Gigantoproductus sp. 2 valves exhibit intermediate crystal size variations between two groups.
Brachiopod shells have been classified in the literature in terms of the function of microstructure and geochemical differences between each valve (Pérez-Huerta & Reed 2018) or at intra-shell level; for instance the umbo is systematically enriched in magnesium (Buening & Carlson 1992).Differences in fibre sizes within the secondary shell layers of extant Terebratulida and Rhynchonellida, at different positions within the shell growth spiral, were reported by Ye et al. (2018).Larger fibres were systematically located towards the innermost part of the shell and this was interpreted by Ye et al. (2018) as an ontogenetic trend.Furthermore, crystal size differences have been reported in genera possessing shells of two-and threelayered construction, with the size of crystal fibres of the secondary layer being larger in genera with two-layered shells (Ye et al. 2018).In gigantoproductids, the tertiary layer represents almost the entire shell and influences the shell morphology (i.e., spiral development).The column elongation is sub-perpendicular to the shell surface, except in Globosoproductus (subhorizontal microstructure) and Kansuella?(crenulated), thus the crystal length of the tertiary layer is an optimal parameter to compare size trends among gigantoproductids.Crystal length (Fig. 7) ontogenetically varies, in a longitudinal growth trend, from one or two stages of short crystals at umbonal part, which rapidly increases its size towards the Tk-part and decreases towards commissure (T-part).In transverse growth crystal sizes decrease from the external and middle parts towards the internal parts (i.e., ITk-and IT-parts, respectively).These ontogenetic trends are different from those illustrated by Ye et al. (2018), which might be related to orientation differences in the elongation axis of columns, different regimes in shell secretion of the secondary and tertiary layer or lineage-specific differences (different brachiopod orders).The understanding of the shell morphology and thickness through the evolution of microstructural changes during the Viséan-Serpukhovian could be the key to understanding the environmental changes during the mid-Carboniferous.(Thomson 1927;Williams 1956).Some authors noted that juvenile brachiopod shells have few or even non-diagnostic characters of adult specimens; this fact stressed the need for ontogenetic information in taxonomic diagnoses and descriptions (Lee & Wilson 1979).The combination of tertiary layer microstructure, maximum shell thickness and the shell growth spiral seems to offer a robust taxonomic framework for gigantoproductid taxonomy, especially when key characters are obliterated by taphonomic processes (i.e., ribbing spacing and thickness, muscle scars, morphology of the cardinal process and median septum).These features are highly taxon-specific and may be measured in fragmented and complete samples, and are promising for application to the systematics of other brachiopod groups.

Acknowledgements
Financial support through the Spanish Ministerio de Economía y Competitividad (research projects CGL2012-30922BTE and CGL2016-78738-P) and the Complutense University Research Group ( 910231) is gratefully acknowledged.J.R.M.-C.acknowledges financial support through an FPI-MINECO grant.This article is a contribution to the Spanish Working Group IGCP 596 (UNESCO).We thank the anonymous reviewers and the editor for their corrections and suggestions, which improved an earlier version of this manuscript.

Figure 2
Figure 2 Gigantoproductus sp. 1. (A) Outer ventral valve and section view (C).(B) Graphic scheme of the gigantoproductid shell layers situation.(D) Growth vectors of the shell.

Figure 3
Figure 3 (A) Dispersion graph comparing the shell length/width of different gigantoproductid genera.(B) Dispersion graph showing the (a) and (k) parameters of different gigantoproductid genera from this study (grey squares) and from literature (red dots).(a) is the distance from the spiral to the first point measured in the umbo and (k) indicates the convexity of the shell; the higher values describe a flatter shell and the low values high incurved shells.Schematic shell sections from the studied genus and its associated microstructure (right bottom) have been projected in the upper graph.

Figure 5
Figure 5 Six columnar morphologies shown under petrological microscopy, synthetic diagram of the crystals and SEM images.Images correspond with transverse sections from the umbo to the commissure.(A) Long columnar morphology of the thick and thin regions in Gigantoproductus sp.1.(B) Short columnar morphology of the thick and thin regions in Latiproductus.(C) Acicular columnar morphology of the thick region in Gigantoproductus sp.2.(D) Imbricated morphology of the thin region in Semiplanus.(E) Subhorizontal morphology of the thick region in Globosoproductus.(F) Crenulated morphology of the thick region in Kansuella?.

Figure 6
Figure 6 Violin plots (bottom) with the column length and width from studied genera.
, whereas gigantoproductids may reach 300-400 mm in width (Muir-Wood & Cooper 1960) and up to 23 mm in maximum ventral valve thickness (Table 2).The size increases observed in this study during the interval between the late Viséan to mid Serpukhovian can fit with one or several of proposed hypotheses about their size, such as available oxygen increasing (shift in tropical forests, Mottin et al. 2022), primary productivity (Zhang et al. 2015), global cold intervals (C1-C2 glacial intervals, Fielding et al. 2008),

Figure 7
Figure7Histograms with intra-shell crystal variations in each shell region of studied gigantoproductid genera (left).Histograms with crystal disorientation in different gigantoproductid genera (right).Crystal disorientation of imbricated morphology (bottom left) compared with a random distribution function.

Figure 8
Figure 8 Stratigraphic ranges of sampled sections (coloured bars) and outcrop range (white bars) during the Viséan-Serpukhovian (left).Stratigraphic ranges (black lines) of the genera in this study during the Viséan-Serpukhovian (right).

Table 1
Summary of sampled stratigraphic sections and genera assignation.

Table 2
Shell measurements from analysed gigantoproductid taxa.Abbreviations: Max length = Maximum length; arc length = length of the shell spiral; n = number of digitised points; mm dig −1 = average point distance in mm; Max thickness = maximum thickness of the shell; a = distance in mm of the beginning of the real and theoretical spiral; k = shell curvature.
Figure 4 Deviations of the shell spiral in three gigantoproductid genera (top) compared with equivalent genera from the literature (bottom).

Table 3
Characterisation of microstructural elements and measurements in the analysed gigantoproductids.Abbreviation: S.D = standard deviation.

Table 4
Measurements of crystal length and width in each shell part.Abbreviation: S.D = standard deviation.
• Taxonomic identifications of gigantoproductids from sections in southern Spain, southern France and central Morocco have been assessed in Globosoproductus, Kansuella?, Semiplanus, Latiproductus, Gigantoproductus (G.sp. 1 and G. sp. 2) and Datangia using morphological criteria such as ribbing density, shell dimensions and shell morphology.• Detailed microstructural characterisation of ventral valves shows that all valves consist of two preserved layers, laminar secondary and columnar tertiary, in which six different crystal morphologies in the tertiary layer are recognised: subhorizontal columnar morphology in Globosoproductus, imbricated columnar in Semiplanus, crenulated in Kansuella?, short columnar in Latiproductus, acicular columnar in Gigantoproductus sp. 2 and long columnar in Gigantoproductus sp. 1 and Datangia.These crystal morphologies in the tertiary layer are taxon-specific.• Thicker-shelled genera (Gigantoproductus and Datangia) have higher variation in crystal size and higher crystal lengths than thinner-shelled genera (Latiproductus, Globosoproductus and Semiplanus), although shell spiral development is independent of shell thickness.• During the Viséan-Serpukhovian interval gigantoproductid populations changed gradually from thinner-shelled with subhorizontal columnar morphology to a thicker-shelled genus with long columnar crystal morphology.• Morphological comparison between shell characters plays an important role in brachiopod classification