domain: phys sde

text:
Mickaeel Lheritier
email: mickael.lheritier@univ-lyon1.fr

Maeva Perroux

Jean Vannier

Gilles Escarguel

Thomas Wesener

Leif Moritz

Dominique Chabard

Jérôme Adrien

Vincent Perrier

Mickaël Lheritier

Maëva Perroux

Jérome Adrien

Fossils from the Montceau-les-Mines Lagerstatte (305 Ma) shed light on the anatomy, ecology and phylogeny of Carboniferous millipedes

Keywords: Myriapoda, Diplopoda, Montceau-les-Mines Lagerstätte, Carboniferous, Pentazonia, Juliformia

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Introduction

Arthropods are key elements of modern aquatic and terrestrial ecosystems with more than one million species described so far. As inhabitants of a huge variety of aquatic, terrestrial and aerial environments they play a pivotal role in food chains and trophic webs. Their rich Cambrian fossil record exemplified by Burgess-Shale-type (BST) Lagerstätten reveals the very ancient origin and diversification of the group from possible cycloneuralian worm-like ancestors and its early split into chelicerates and mandibulates (crustaceans, insects and myriapods) during the Cambrian [START_REF] Vannier | Waptia fieldensis Walcott, a mandibulate arthropod from the middle Cambrian Burgess Shale[END_REF][START_REF] Aria | The origin and early evolution of arthropods[END_REF]). Together with insects, arachnids and some crustaceans (e.g. isopods), myriapods are among the most successful colonizers of terrestrial environments, with more than 16, 000 described extant species distributed in 160 families [START_REF] Wilson | Taxonomy and trunk-ring architecture of pleurojulid millipedes (Diplopoda: Chilognatha: Pleurojulida) from the Pennsylvanian of Europe and North America[END_REF][START_REF] Stoev | Myriapods (Myriapoda). Chapter 7.2[END_REF][START_REF] Brusca | Invertebrates[END_REF]. Myriapods are characterized by an elongated body with multiple leg-bearing segments [START_REF] Stoev | Myriapods (Myriapoda). Chapter 7.2[END_REF], and are divided into four classes: Chilopoda (centipedes), Symphyla (garden centipedes), Pauropoda and Diplopoda (millipedes). While most centipedes are fast running predators (e.g. Scolopendra), with only one pair of legs per segment [START_REF] Brusca | Invertebrates[END_REF], most of the 12, 000 described diplopods (millipedes) are detritivores, being characterized by diplosegments bearing two pairs of legs each [START_REF] Stoev | Myriapods (Myriapoda). Chapter 7.2[END_REF].

Diplopoda typically burrow into soil and litter, thus being important recyclers of vegetable matter [START_REF] Lavelle | Soil Ecology[END_REF].

Myriapods can be traced back to at least the Silurian, (Ludlow Series, ca 425 Ma) with archipolypods millipedes and kamperids being the earliest known myriapods and arthropod colonizers of terrestrial environment [START_REF] Almond | The Silurian-Devonian fossil record of the Myriapoda[END_REF]. Millipedes strongly diversified into various groups during the Devonian such as the Eoarthropleurida [START_REF] Størmer | Part 5. Myriapods and additional forms, with general remarks on the fauna and problems regarding invasion of land by arthropods. In: Arthropods from the Lower Devonian (Lower Emsian) of Alken an Der Mosel[END_REF]) and the Microdecemplicida [START_REF] Wilson | Microdecemplicida, a new order of minute arthropleurideans (Arthropoda: Myriapoda) from the Devonian of New York State, USA[END_REF][START_REF] Kraus | Fossil giants and surviving dwarfs. Arthropleurida and Pselaphognatha (Atelocerata, Diplopoda): characters, phylogenetic relationships and construction[END_REF]. It was also during the Devonian that derived clades like the Helminthomorpha with derived gonopods [START_REF] Wilson | Morphology and taxonomy of Paleozoic millipedes (Diplopoda: Chilognatha: Archipolypoda) from Scotland[END_REF] appeared.

Millipedes step into the Lower Carboniferous with other archipolypods [START_REF] Wilson | Morphology and taxonomy of Paleozoic millipedes (Diplopoda: Chilognatha: Archipolypoda) from Scotland[END_REF]) and diversify through the Upper Carboniferous being typically associated with coal swamp environments [START_REF] Shear | The geological record and phylogeny of the Myriapoda[END_REF]. These upper Carboniferous myriapods include archipolypods [START_REF] Burke | Notes on the morphology of Acantherpestes (Myriapoda, Archipolypoda) with the description of a new species from the Pennsylvanian of West Virginia[END_REF][START_REF] Burke | A New Millipede Genus, Myriacantherpestes (Diplopoda, Archipolypoda) and a New Species, Myriacantherpestes Bradebirski, from the English Coal Measures[END_REF] and other extinct forms that have been placed into groups with various taxonomic ranking such as Pleurojulida [START_REF] Wilson | Taxonomy and trunk-ring architecture of pleurojulid millipedes (Diplopoda: Chilognatha: Pleurojulida) from the Pennsylvanian of Europe and North America[END_REF], Pentazonia [START_REF] Hannibal | Systematics and functional morphology of oniscomorph millipedes (Arthropoda: Diplopoda) from the Carboniferous of North America[END_REF][START_REF] Hannibal | Pill millipedes from the Coal Age[END_REF][START_REF] Racheboeuf | A new species of the diplopod Amynilyspes (Oniscomorpha) from the Stephanian Lagerstätte of Montceau-les-Mines, France[END_REF], Helminthomorpha [START_REF] Hoffman | New genera and species of Upper Paleozoic Diplopoda[END_REF][START_REF] Hannibal | A juliform milliped from the Upper Pennsylvanian (Virgilian) Bursum Formation, Carrizo Arroyo, of central New Mexico[END_REF]) and Arthropleurida. The latter are distinguished from the aforementioned taxa by their very large size approaching over 2 m in length and 40 cm in width [START_REF] Briggs | A giant myriapod trail from the Namurian of Arran, Scotland[END_REF][START_REF] Briggs | Arthropleura trails from the Westphalian of eastern Canada[END_REF][START_REF] Kraus | Fossil giants and surviving dwarfs. Arthropleurida and Pselaphognatha (Atelocerata, Diplopoda): characters, phylogenetic relationships and construction[END_REF][START_REF] Martino | Walking trails of the giant terrestrial arthropod Arthropleura from the Upper Carboniferous of Kentucky[END_REF][START_REF] Davies | The largest arthropod in Earth history: insights from newly discovered Arthropleura remains (Serpukhovian Stainmore Formation, Northumberland, England)[END_REF].

The Upper Carboniferous, Kasimovian (ca 305 Ma) Montceau-les-Mines Lagerstätte (Saône-et-Loire, France) is a rich source of information on the colonization of terrestrial environments by plants and animals and is a unique window on the evolution of groups such as myriapods and chelicerates. The myriapods from Montceau are typically found embedded in sideritic nodules and preserved in three dimensions [START_REF] Perrier | The Montceau-les-Mines Lagerstätte (Late Carboniferous, France)[END_REF][START_REF] Mccoy | Factors controlling exceptional preservation in concretions[END_REF]. They are represented by two diplopod species: Amynilyspes fatimae [START_REF] Racheboeuf | A new species of the diplopod Amynilyspes (Oniscomorpha) from the Stephanian Lagerstätte of Montceau-les-Mines, France[END_REF] and Blanziulus parriati [START_REF] Langiaux | Première découverte d'un myriapode dans le Paléozoïque Supérieur du Massif Central Français[END_REF]. Techniques used by previous authors [START_REF] Racheboeuf | A new species of the diplopod Amynilyspes (Oniscomorpha) from the Stephanian Lagerstätte of Montceau-les-Mines, France[END_REF]) such as invasive mechanical preparation and latex casts damaged fine anatomical structures (e.g. appendages, head parts). In order to re-study this exceptional material in optimal conditions we gave preference to nondestructive techniques such as X-Ray microtomography (µCT) that allows highresolution anatomical exploration to be performed [START_REF] Garwood | Anatomically modern Carboniferous harvestmen demonstrate early cladogenesis and stasis in Opiliones[END_REF][START_REF] Garwood | Almost a spider: a 305-million-year-old fossil arachnid and spider origins[END_REF] for similar methods applied to other arthropods from Montceau). New morpho functional interpretations of these Carboniferous millipedes are also proposed based on detailed comparisons with extant diplopods, that altogether shed light on still poorly known aspects of extinct millipedes' autecology, habitats and adaptations to living on land. Phylogenetic analyses were performed based on a new and enriched set of characters obtained from µCT reconstructions; they clarify the position of the Montceau millipeds in the evolutionary tree of myriapods.

Geological and environmental context

The Montceau-les-Mines Lagerstätte (Late Pennsylvanian, Kasimovian, 307. 0 ± 0. 1 Ma -303. 7 ± 0. 1 Ma; [START_REF] Cohen | The ICS International Chronostratigraphic Chart: Episodes[END_REF]) lies within the Blanzy-Montceau-les-Mines coal basin at the southern boundary of the Stephano-Permian graben of Blanzy-Le Creusot-Bert [START_REF] Perrier | The Montceau-les-Mines Lagerstätte (Late Carboniferous, France)[END_REF]Fig. 1). The Late Pennsylvanian Series exposed at Montceau-les-Mines consists of silty claystones with intercalations of sandstones and iron carbonates [START_REF] Perrier | The Montceau-les-Mines Lagerstätte (Late Carboniferous, France)[END_REF] and includes, from the base to the top: the Great Seams Formation (Assise de Montceau), the Upper Seams Formation (Assise des Carrières) and the later Pennsylvanian-Permian transition (Assise du Ponsard) [START_REF] Perrier | The Montceau-les-Mines Lagerstätte (Late Carboniferous, France)[END_REF].

Horizons with concentrations of fossiliferous sideritic nodules are bounded with thin iron carbonate layers [START_REF] Perrier | The Montceau-les-Mines Lagerstätte (Late Carboniferous, France)[END_REF] and swamps whereas mesoxerophytes presumably lived in drier areas [START_REF] Doubinger | Etudes palynologiques dans le bassin stéphanien de Montceau-les-Mines (1ère couche): aspects stratigraphiques et paléoécologiques[END_REF][START_REF] Doubinger | Spores et pollen du bassin carbonifère et permien de Blanzy-Montceau (Massif Central -France)[END_REF][START_REF] Langiaux | Macroflore stéphanienne (Carbonifère supérieur) du bassin houiller intramontagneux de Blanzy-Montceau (Massif Central -France)[END_REF][START_REF] Charbonnier | Diversity and Paleoenvironment of the Flora From the Nodules of the Montceau-Les-Mines Biota (Late Carboniferous, France)[END_REF]. Arthropods seem to have dominated the fauna in diversity and abundance with crustaceans such as syncarids [START_REF] Perrier | Syncarid Crustaceans from the Montceau Lagerstätte (Upper Carboniferous; France)[END_REF], ostracods and branchiopods (conchostracans see [START_REF] Vannier | Spinicaudatans and ostracods (Crustacea) from the Montceau Lagerstätte (Late Carboniferous, France): morphology and palaeoenvironmental significance[END_REF] and terrestrial elements such as arachnids [START_REF] Garwood | Almost a spider: a 305-million-year-old fossil arachnid and spider origins[END_REF], insects [START_REF] Langiaux | Blattes fossiles du bassin de Blanzy-Montceau[END_REF][START_REF] Béthoux | Description of a new grylloblattidan insect from Montceau-les-Mines (Late Carboniferous; France) and definition of Phenopterum (Carpenter, 1950)[END_REF][START_REF] Garwood | Tomographic Reconstruction of Carboniferous Arthropods[END_REF][START_REF] Garwood | Tomographic Reconstruction of Neopterous Carboniferous Insect Nymphs Butler[END_REF], myriapods [START_REF] Langiaux | Première découverte d'un myriapode dans le Paléozoïque Supérieur du Massif Central Français[END_REF][START_REF] Racheboeuf | A new species of the diplopod Amynilyspes (Oniscomorpha) from the Stephanian Lagerstätte of Montceau-les-Mines, France[END_REF]) and merostomes [START_REF] Racheboeuf | A New Three-Dimensionally Preserved Xiphosuran Chelicerate from the Montceau-Les-Mines Lagerstätte (Carboniferous, France)[END_REF]. Other members of the fauna include abundant bivalves [START_REF] Babin | Le genre Anthraconaia (Bivalvia, Myalinidae) dans le Stéphanien de Montceau-les-Mines (Saône et Loire, France)[END_REF][START_REF] Babin | Le bivalve dulcicole Anthraconaia du Stéphanien (Carbonifère supérieur) du Bassin de Montceau-les-Mines[END_REF], annelids [START_REF] Pacaud | Quelques Invertébrés Nouveaux Du Stéphanien de Montceau-Les-Mines[END_REF][START_REF] Pleijel | Carboniferous fireworms (Amphinomida: Annelida), with a discussion of species taxa in palaeontology[END_REF], hagfishes [START_REF] Poplin | Un Myxinoı̈de (Craniata, Hyperotreti) dans le Konservat-Lagerstätte Carbonifère supérieur de Montceau-les-Mines (Allier, France)[END_REF], chondrichthyans [START_REF] Langiaux | Éléments pour une étude écologique d'un paysage de l'époque houillère. Faune du Stéphanien terminal de Blanzy[END_REF][START_REF] Heyler | Les poissons stéphaniens (Carbonifère supérieur) du Bassin de Montceau-les-Mines[END_REF], sarcopterygians [START_REF] Olive | First occurrence of the lungfish Sagenodus (Dipnoi, Sarcopterygii) from the Carboniferous Lagerstätte of Montceau-les-Mines, France[END_REF], acanthodians, actinopterygians [START_REF] Langiaux | Éléments pour une étude écologique d'un paysage de l'époque houillère. Faune du Stéphanien terminal de Blanzy[END_REF][START_REF] Heyler | Les poissons stéphaniens (Carbonifère supérieur) du Bassin de Montceau-les-Mines[END_REF]) and tetrapods [START_REF] Dutuit | Rachitomes, lépospondyles et reptiles du Stéphanien (Carbonifère supérieur) du Bassin de Montceau-les-Mines[END_REF][START_REF] Germain | A new phlegethontiid specimen (Lepospondyli, Aistopoda) from the Late Carboniferous of Montceau-les-Mines (Saône-et-Loire, France)[END_REF]).

[Insert Fig 1 here]

Material and Methods

Fossil material

Pioneer workers used to split nodules collected in the field and prepare fossils mechanically in the lab. External moulds were typically prepared by removing mineral in-fillings from cavities before making silicon or latex casts (e.g. [START_REF] Racheboeuf | A New Three-Dimensionally Preserved Xiphosuran Chelicerate from the Montceau-Les-Mines Lagerstätte (Carboniferous, France)[END_REF][START_REF] Racheboeuf | A new species of the diplopod Amynilyspes (Oniscomorpha) from the Stephanian Lagerstätte of Montceau-les-Mines, France[END_REF]. This method generally failed to provide a faithful replica of the whole animal, (e.g. embedded appendages and internal organs missing). X-ray microtomography is used here to overcome these drawbacks to obtain high-definition anatomical details in a non-destructive way and eventually 3D-models allowing virtual dissection to be made.

We studied five specimens. µCT data were obtained for three specimens of Amynilyspes fatimae [START_REF] Racheboeuf | A new species of the diplopod Amynilyspes (Oniscomorpha) from the Stephanian Lagerstätte of Montceau-les-Mines, France[END_REF]) from the Saint-Louis site: MNHN.F.SOT 2134 (holotype), MNHN.F.SOT 14983 (paratype) and MNHN.F.SOT 2129 (paratype) (Fig. 2A,B,C). The remaining specimens MNHN.F.SOT. 73422c and MNHN.F.SOT. 2124 (described as Arthropleura sp. but re-identified as A.

fatimae with the scan results) were not included in the present study due to their poor preservation and the lack of information they give in comparison to the previously cited specimens. We also studied 65 specimens (mainly from the Saint-Louis site) of Blanziulus parriati [START_REF] Langiaux | Éléments pour une étude écologique d'un paysage de l'époque houillère. Faune du Stéphanien terminal de Blanzy[END_REF]. Four of them were CT-scanned: were also scanned with a µCT SKyscan 1272 of the Morphology Laboratory at the Research Museum Alexander Koenig, Bonn, Germany, operated at 100 kV with a source current of 61 µA and a voxel size of 6 µm. Scans were segmented with the Avizo® software. 3D models of each specimen described in this paper are present in the MorphoMuseumM journal under this 3D dataset: Lheritier M., Vannier J., Escarguel G., Perrier V., 2022. 3D models related to the publication: Fossils from the Montceau-les-Mines Lagerstätte (305 Ma) shed light on the anatomy, ecology and phylogeny of Carboniferous millipedes. Photos and images were edited using Inskcape (v. 0.92.4) and Gimp (v. 2.10.18).

Extant myriapods

Glomeris marginata (Villers, 1789) and Glomeris guttata (Risso, 1826) were used for anatomical comparisons with the fossils from Montceau. They were collected by Jean Vannier in Provence near Saint-Pantaléon (Luberon Massif, Vaucluse, France; 43°53, 17' 94'' N; 5°13, 3' 08'' E) from litter and soils planted with oak trees and kept with their original substrate in a humid terrarium. Selected specimens were fixed with 5% glutaraldehyde, transferred to alcoholic series before being dried through the critical point method, then mounted on stubs for being imaged with a Quanta 250 Scanning Electron Microscope (SEM) at the Centre Technologique des Microstructures (CTµ) of the Université Claude Bernard Lyon 1.

Phylogenetic analyses

We investigated the phylogeny of fossil and extant diplopod myriapods through a two-level approach first focusing on Montceau's fossil taxa Amynilyspes fatimae and Blanziulus parriati, then extending the analyses to other fossil taxa. In both cases, analyses where done first at a larger-scale, Diplopoda class level, then focussing on relationships within the Pentazonia subclass. All four resulting morphological datasets were analysed through Maximum Parsimony (MP) and Bayesian Inference (BI) methods.

Analyses focusing on Amynilyspes fatimae and Blanziulus parriati. The phylogenetic relationships of Amynilyspes fatimae and Blanziulus parriati where first investigated through a two-step approach including a larger-scale analysis at the Diplopoda class level and a smaller-scale analysis at the Pentazonia subclass level.

At the larger-scale level, 15 extant orders of Diplopoda were included along with Amynilyspes fatimae and Blanziulus parriati. The class Pauropoda was coded as the outgroup. The data matrix, comprising 45 morphological characters, was based on the matrix from [START_REF] Blanke | Revival of forgotten characters and modern imaging techniques help to produce a robust phylogeny of the Diplopoda (Arthropoda, Myriapoda)[END_REF], including 18 head characters, 22 body characters and 5 sexual characters. The MP analysis (unordered multistate Wagner Parsimony using the branch-and-bound algorithm and ACCTRAN character-state optimization) was made using PAUP_ v. 4.0a169 software [START_REF] Swofford | PAUP : Phylogenetic Analysis Using Parsimony[END_REF].

Alongside consistency index (CI), retention index (RI) and rescaled consistency index (RC); nonparametric bootstrap supports (1000 replicates) of the internal nodes were calculated. The BI analyses were made with MrBayes v. 3.2.7 software [START_REF] Ronquist | MrBayes 3.2: Efficient Bayesian Phylogenetic Inference and Model Choice Across a Large Model Space[END_REF]. The analyses were made using four chains (one cold and three heated) and two independent runs, a temperature parameter for heated chains of 0.02, two million cycles of the MCMC algorithm including a 25% burn-in phase and a Markov chain sampling rate of 1,000 cycles, following three different models of evolutionary rates distributions: a constant mutation rate, a non-constant rate following a Gamma law distribution and a non-constant rate following a Log-Normal law distribution.

Other data (e.g. minESS and PSRF diagnostic metrics) are included in Appendix 2.

In addition to this Diplopoda class-level analysis, we more specifically focused on the Pentazonia subclass by considering a dataset made of A. fatimae plus eight extant species : Eupeyerimhoffia archimedis (Strasser, 1965) and Glomeris marginata for the order Glomerida; Procyliosoma leae (Silvestri, 1917) and Sphaerotherium giganteum (Porat, 1872) for the order Sphaerotheriida; Glomeridesmus sp. and Termitodesmus ceylonicus (Silvestri, 1911) for the order Glomeridesmida and Madabolus maximus (Wesener & Enghoff, 2008) and Pseudocentrobolus aureus (Wesener, 2009) for the order Spirobolida. Madabolus maximus was coded as the outgroup. The data matrix includes 47 morphological characters selected from [START_REF] Blanke | Revival of forgotten characters and modern imaging techniques help to produce a robust phylogeny of the Diplopoda (Arthropoda, Myriapoda)[END_REF], Wesener (2016a) and [START_REF] Oeyen | A first phylogenetic analysis of the pill millipedes of the order Glomerida, with a special assessment of mandible characters (Myriapoda, Diplopoda, Pentazonia)[END_REF] for their ability to discriminate these four Pentazonia orders. Among them, 21 are head characters, 18 are body characters, and 8 are sexual characters. The settings for the MP and BI analyses are the same as cited previously.

Analyses including different diplopod fossils.

A second set of analyses, including other Mesozoic and Cenozoic extinct diplopods, was made at both Diplopoda class and Pentazonia subclass levels in order to investigate their potential effect on the phylogenetic position of A. fatimae and B. parriati. Five extinct species, all from the Burmese ambers (98.79 M.a, [START_REF] Shi | Age constraint on Burmese amber based on U-Pb dating of zircons[END_REF], were added to the Diplopoda phylogeny: the Platydesmida Andrognathus burmiticus (Moritz & Wesener 2019), the Siphonophorida Siphonophora hui [START_REF] Jiang | One hundred million years of stasis: Siphonophora hui sp. nov., the first Mesozoic sucking millipede (Diplopoda: Siphonophorida) from mid-Cretaceous Burmese amber[END_REF], the Spirostreptida Electrocambala ornata [START_REF] Moritz | Electrocambalidae fam. nov., a new family of Cambalidea from Cretaceous Burmese amber (Diplopoda, Spirostreptida)[END_REF], the Callipodida Burmanopetalum inexpectatum [START_REF] Stoev | Dwarfs under dinosaur legs: a new millipede of the order Callipodida (Diplopoda) from Cretaceous amber of Burma[END_REF]) and the Polyxenida Phryssonotus burmiticus [START_REF] Cockerell | Arthropods in Burmese amber[END_REF][START_REF] Su | Revision of Phryssonotus burmiticus (Diplopoda, Polyxenida, Synxenidae) in mid-Cretaceous amber from Myanmar[END_REF].

For the Pentazonia-level phylogeny, two extinct species were added: the Glomerida Hyleoglomeris groehni [START_REF] Wesener | The oldest pill millipede fossil: A species of the Asiatic pill millipede genus Hyleoglomeris in Baltic amber (Diplopoda: Glomerida: Glomeridae)[END_REF]) from the Baltic Amber (28-40 M.a, Weitschat & Wichard 2010) and an unnamed specimen assigned to Spirobolida: BuB1145 from the Cretaceous Burmese amber [START_REF] Wesener | Checklist of the Myriapoda in Cretaceous Burmese amber and a correction of the Myriapoda identified by Zhang[END_REF]. BuB1145 was coded as the outgroup here.

In all cases, the parameters for the MP and the BI analyses were the same as their equivalent in the first set of analyses.

Systematic palaeontology

Subphylum Myriapoda Latreille, 1802

Class Diplopoda Blainville in [START_REF] Gervais | Études pour servir à l'histoire des myriapodes (thèse de zoologie)[END_REF] Order Amynilyspedida [START_REF] Hoffman | Myriapoda, exclusive of Insecta[END_REF] Diagnosis (emended from [START_REF] Racheboeuf | A new species of the diplopod Amynilyspes (Oniscomorpha) from the Stephanian Lagerstätte of Montceau-les-Mines, France[END_REF]).-Moderate to large-sized diplopods with 13 terga and an anal shield. Dorsal surface of terga may be flattened.

Remarks.-The studied Amynilyspedida have 13 terga against 12 in sphaerotheriids (e.g. Wesener 2014) and 10/11 in glomerids (e.g. [START_REF] Enghoff | Diplopoda -taxonomic overview[END_REF].

Family Amynilyspedidae [START_REF] Hoffman | Myriapoda, exclusive of Insecta[END_REF] Diagnosis (emended from [START_REF] Racheboeuf | A new species of the diplopod Amynilyspes (Oniscomorpha) from the Stephanian Lagerstätte of Montceau-les-Mines, France[END_REF]).-Up to 30 mm long amynilyspedids with 14 terga and prominent, simple spines. Large ovoid ocular fields with ommatidia. No ozopores Remarks.-Amynilyspedidae is monogeneric (Amynilyspes).

Genus Amynilyspes Scudder, 1882

Diagnosis.-As for the family.

Remarks-Four species have been assigned to the genus: Amynilyspes wortheni [START_REF] Scudder | Archipolypoda, a subordinal type of spined myriapods from the Carboniferous Formation[END_REF]) from the Mazon Creek Lagerstätte (Upper Carboniferous, Illinois, USA); A. typicus [START_REF] Fritsch | Fauna der Gaskohle und der Kalksteine der Performation Böhmens[END_REF] from the Gaskohle in Nýrany (Upper Carboniferous, Bohemia, Czech Republic); A. crescens [START_REF] Fritsch | Fauna der Gaskohle und der Kalksteine der Performation Böhmens[END_REF]) from the same locality as A. typicus, and A. fatimae from Montceau-les-Mines. A. wortheni has been revised by [START_REF] Racheboeuf | A new species of the diplopod Amynilyspes (Oniscomorpha) from the Stephanian Lagerstätte of Montceau-les-Mines, France[END_REF] and might be conspecific to A. typicus. A. crescens was only known from one specimen which is currently missing [START_REF] Förster | Ein Diplopoden-fund aus dem Oberkarbon des Saarlandes[END_REF]). Copeland (1957) described the species: A. springhillensis that was later revised [START_REF] Rolfe | Arthropleurida. Part R. Arthropoda[END_REF] and assigned to Arthropleura. Amynilyspes fatimae [START_REF] Racheboeuf | A new species of the diplopod Amynilyspes (Oniscomorpha) from the Stephanian Lagerstätte of Montceau-les-Mines, France[END_REF] Amynilyspes typicus. Fritsch 1899 Amynilyspes typicus [START_REF] Langiaux | Éléments pour une étude écologique d'un paysage de l'époque houillère. Faune du Stéphanien terminal de Blanzy[END_REF], p. 55, fig. 9.4a. Amynilyspes cf. typicus. Poplin 1994, p. 294.

Amynilyspes fatimae new species., Racheboeuf et al. 2004, figs. 2-6. Amynilyspes fatimae. Charbonnier 2010, fig. IV.2 Holotype: MNHN.F.SOT 2134 from Montceau-les-Mines, Saint-Louis site [START_REF] Racheboeuf | A new species of the diplopod Amynilyspes (Oniscomorpha) from the Stephanian Lagerstätte of Montceau-les-Mines, France[END_REF]. [START_REF] Racheboeuf | A new species of the diplopod Amynilyspes (Oniscomorpha) from the Stephanian Lagerstätte of Montceau-les-Mines, France[END_REF]).-Amynilyspes with terga 3-13 dorsally flattened in their anterior half and weakly to markedly rounded in their posterior half, without transverse sulcus between the two areas; two rows of dorsolateral spines; shield without spines. Twenty pairs of legs each connected to a stigmatic plate. Head with a pair of seven-segmented antennae and a pair of welldeveloped ocular fields. Male with at least one pair of telopods at the posterior body end. in the shape of enlarged claspers (length of 0.9 mm) with a reduced claw (Fig. 5D).

Diagnosis (emended from

Description

Discussion.-The presence of a pair of claspers of this shape in male individuals was only observed on extant millipedes from the Julida order until now. However, molecular phylogeny [START_REF] Miyazawa | Molecular phylogeny of Myriapoda provides insights into evolutionary patterns of the mode in post-embryonic development[END_REF] asserts a Triassic origin to the Julida order. As no other Palaeozoic fossil millipedes with this same kind of sexual dimorphism was ever found, we cannot infer that the presence of these claspers are a diagnostic character of the Blanziulius genus, the Xyloiulidae family or even the Xyloiulidea superfamily.

Phylogenetic results

Amynilyspes fatimae

As for the first Pentazonia-level phylogenetic analysis (including eight extant species plus A. fatimae), the maximum parsimony (MP) branch-and-bound research returns one MP tree with a total length of 62 steps involving 46 parsimony-informative characters, a consistency index of 0.903, a retention index of 0.912 and a rescaled consistency index of 0.824. A. fatimae branches as a sister taxon of the Sphaerotheriida (Fig. 6B). The resulting clade is defined by characters 31B, 41 and 42 (see Appendix 1 for the characters used and their different states). They share twenty or so leg pairs (character 31B) and a male penultimate leg pair modified into an anterior telopod (character 41) with a long femur (character 42). Bootstrap supports indicate that the tree is globally robust, the two weakest nodes being related to the relationship between A. fatimae and the Sphaerotheriida and the relation between them and the Glomerida. The Bayesian Inferences (BI) shows the same result regardless of the selected evolutionary rate distribution, pointing toward a phylogenetic signal robust to the evolutionary rate variation model imposed to the inference algorithm (Annex 3). In the BI, we observe the same synapomorphies as in the MP tree (characters 31B, 41 and 42).

[Insert Fig 6 here]

As for the second Pentazonia-level analysis (including two additional extinct taxa:

Hyleoglomeris groehni and BuB1145), the MP branch-and-bound research returns one MP tree with a total length of 72 steps with all characters being parsimonyinformative, a CI of 0.778, a RI of 0.816 and a RC of 0.635. Bootstrap supports remain high but a partial non-resolution of H. groehni and A. fatimae positions is obtained (Fig. 7B), as the likely consequence of the high amount of unobserved character states in the two added fossil taxa. We observe the same synapomorphies for the clade Sphaerotheriida + A. fatimae as in the first Pentazonia-level phylogenetic MP analysis. As for the Bayesian inferences, the three evolutionary rate models group A. fatimae with Sphaerotheriida with the same synapomorphies than in the first Pentazonia-level BI analyses. However, in these trees, the clade Glomerida is more closely related to the clade Glomeridesmida than to the clade Sphaerotheriida, a grouping that is also observed in molecular phylogenies [START_REF] Benavides | Re-evaluating and dating myriapod diversification with phylotranscriptomics under a regime of dense taxon sampling[END_REF]. This Glomerida-Glomeridesmida clade is defined by an antennae placed centrally (character 5A), a large, horse-shoe-shaped Tömösváry organ (character 8), and a gnathochilarium with a very large gula (character 9).

In the two Pentazonia-level phylogenetic analyses, we observe an autapomorphy for Amynilyspes fatimae which possesses 13 terga unlike in Glomerida and

Sphaerotheriida (character 19).

In the two Diplopoda-level analyses, A. fatimae appears, as for the Pentazonia-level analyses, included in the Subclass Pentazonia as a sister-taxon of the Order Sphaerotheriida with relatively high bootstrap supports (Fig 6A and Fig 7A). However, there are no clear synapomorphic characters for this grouping, the only shared character being a reversion to eyes with numerous ocelli (character 5, see Appendix 1). Finally, we observe the same phylogenetic scenario for A.fatimae in the four different phylogenies, providing strong evidence for the position of A. fatimae as sister-taxon of the order Sphaerotheriida.

Blanziulus parriati

As for the first Diplopoda-level analysis (15 extant orders plus A. fatimae and B. parriati), the MP analysis returns a MP tree with a total length of 77 steps and 43 parsimony-informative characters, a CI of 0.727, a RI of 0.870 and a RC of 0.632.

Bootstrap supports are high. Based on available data, B. parriati is placed in an unresolved position inside the Superorder Juliformia (Fig 6A). The same result as for MP is obtained through BI for all three evolutionary rate distributions, with high Bayesian scores except for the branching of B. parriati (Appendix 2).

[Insert Fig 7 here]

For the second Diplopoda-level analysis (including six additional Cretaceous species:

Andrognathus burmiticus, Siphonophora hui, Electrocambala ornata, Burmanopetalum inexpectatum, and Phryssonotus burmiticus), we obtain one MP tree with a total tree length of 84 steps, 43 parsimony-informative characters, a CI of 0.670, a RI of 0.873 and a RC of 0.592. The scores remain high in the MP analysis (Fig. 7A). A partial non-resolution of the position of Siphonophora hui, inside the Colobognatha and Electrocambala ornata inside the Juliformia are obtained. The BI analyses show the same results as the MP analysis whatever the evolutionary rate distribution (Appendix 2). The lower scores and the partial non-resolution are due to the high amount of unobserved character states in the additional fossil taxa.

Discussion

Feeding

The feeding apparatus of extant pill millipedes is composed of a pair of mandibles and a pair of first maxilla called the gnathochilarium. The mandibles themselves have two distinct elements: a mandibular base and a gnathal lobe (Fig 8A). In modern pill millipedes, the function of this gnathal lobe is to grasp food with a movement opposed to that of the gnathochilarium. In other words, if the gnathochilarium lowers, the gnathal lobes would automatically open to help bring food into the mouth (Koch 2015a). The mandibular apparatus in A. fatimae is morphologically similar to that of extant pill millipedes with a mandible base, a gnathal lobe and a gnathochilarium (only the gnathochilarial stipes are observed on A. fatimae) (Fig 8D). Like in extant pill millipedes, the mandible base of A. fatimae is relatively voluminous (width larger than head width) (Fig 8A ,D). These mandibular features are typically seen in extant chewing-biting millipedes that feed on hard remains like dead trunks or twigs (Koch 2015a).

The mandibular apparatus of extant Juliformia is different from that of pill millipedes. It has a mandibular base (composed of a cardo and a stipes), a gnathal lobe and a gnathochilarium (Fig 8H). It is also less voluminous than that of pill millipedes like in other extant Helminthomorpha (Koch 2015a). In B. parriati, the mandibular apparatus is morphologically similar to that of extant Juliformia with a mandible base made a cardo + a stipes (Fig 8K). Its less voluminous shape suggests a preference for softer remains such as dead leaves. Neither the gnathal lobe nor the gnathochilarium were found in B. parriati. However, since the feeding apparatus of B. parriati and extant Juliformia both share important similarities, the lack of these two elements is attributed to preservation.

The digestive system of extant millipedes is divided into a foregut, midgut, and hindgut (Fig 9A). The foregut runs from the mouth to the esophageal valve and accommodates the salivary glands. The midgut where the major part of the digestion occurs runs from the esophageal valve to the pylorus. Final stages of digestion occur through the hindgut and feces are excreted via the rectum. None of the specimens from Montceau display a complete digestive tract. In A. fatimae it appears as an evenly tubular midgut that extends into a hindgut with a differentiated rectum (Fig 9B ,C). The digestive tract of B. parriati is similarly incomplete and mainly represented by a tubular midgut and possible remains of a pylorus (anterior most part of the hindgut) and a rectum (MNHN.F. SOT. 81522;Fig 9D). No identifiable gut content is preserved that could be used to infer the diet of A. fatimae and B. parriati. However, the mandibular morphology of both species strongly indicates capacities to process relatively hard detritus such as fragments of wood bark for A. fatimae and possibly softer food such as fern remains for B. parriati. These feeding modes and diets are common among extant millipedes.

[Insert Fig 8 here]

Sensory organs

The most visible sensory organs of extant millipedes are the antennae that bear apical cones (autapomorphy of diplopods) and more or less developed eyes.

Antennae are inserted either frontally or more laterally following the groups.

Antennae play a leading role as a major tactile and chemical sensory organ.

Millipedes tap the substrate with their antennae for environmental identification [START_REF] Müller | Diplopoda -sense organs[END_REF] and the antennae are considered to have a major role in sensing the environment in blind millipedes [START_REF] Hopkin | Biology of Millipedes[END_REF]. Various hypotheses have been proposed concerning the function of these organs such sensing vibrations or sound [START_REF] Verhoeff | Bronn's KIassen und Ordnungen des Tier-Reichs[END_REF][START_REF] Pflugfelder | Über den feineren Bau der Schläfenorgane der Myriapoden[END_REF][START_REF] Schömann | Zur Biologie von Polyxenus lagurus (L. 1758)[END_REF][START_REF] Meske | Untersuchungen zur Sinnesphysiologie von Diplopoden und Chilopoden[END_REF], or detecting CO2 [START_REF] Yamana | Electrophysiological studies on the temporal organ of the Japanese house centipede, Thereuonema hilgendorfi[END_REF][START_REF] Yamana | Ionic mechanism of the carbon dioxide reception in the Japanese house centipede, Thereuonema hilgendorfi[END_REF][START_REF] Yamana | Intracellular recording from receptor cells of the temporal organ of the japanese house centipede, Thereuonema hilgendorfi: Receptor potential and conductance changes[END_REF]. No trace of this organ has been found in the fossil specimens from Montceau.

Locomotion

The leg of extant diplopods consists of seven podomeres, from proximal to distal: coxa, prefemur, femur, postfemur, tibia, tarsus and claw (Fig 8C). There are two pairs of legs per segment. The only exceptions are Helminthomorpha in which the collum and several adjacent segments (depending on the group) bear a single pair of legs.

These segments bearing a single pair of legs are usually referred as the thorax of millipedes (Koch 2015a). Two types of locomotion are observed in extant millipedes: 1) one in which body stretching plays a major role (e.g. pill millipedes, Koch 2015b),

2) a second one with less body deformation, seen in ring-forming and more elongated millipedes such as Juliformia and Nematophora [START_REF] Fattahi | A Timoshenko beam reduced order model for shape tracking with a slender mechanism[END_REF]. parriati consists of the collum and the second pleurotergum (Fig 5A). As the pair(s) of legs are not preserved on the third pleurotergum, it is uncertain whether this pleurotergum is a thoracic or non-thoracic segment. Comparisons with the legs of extant myriapods suggest that the locomotion mode of A. fatimae was comparable with that of extant pill millipedes and that of B. parriati was close to that of ringforming millipedes (millipede with fused pleura and terga, e.g. Julida). We suggest that A. fatimae and B. parriati could move through their environment (litter or hard/semihard substratum) in a manner comparable with that of modern diplopods.

Gas exchange

Diplopods are terrestrial arthropods that breath through a tracheal system open to the exterior via spiracles (cuticular openings through which dioxygen and carbon dioxide exchange occur; Fig. 10A,B). This tracheal system is composed of either branched (Pentazonia and Penicillata) or unbranched (Helminthomorpha) pouches used as aircollecting sacks, dust containers [START_REF] Verhoeff | Bronn's KIassen und Ordnungen des Tier-Reichs[END_REF]) and possibly tracheoles. A. fatimae from Montceau preserves no trace of such respiratory system. In contrast, small cuticular openings occur along the sternites of B. parriati (Fig 10C,D) that may be interpreted as spiracles. However, the spiracles of extant diplopods are much smaller than the openings observed in B. parriati (80 µm long and 10 µm wide for extant spiracles versus 700 µm and 300 µm in B. parriati). This discrepancy may be explained by taphonomic alterations such as the loss of thin cuticular material around spiracles after death that possibly enlarged openings. If this interpretation is correct, then B. parriati may have possessed spiracles and a tracheal system typical of terrestrial arthropods and corresponding to that of other Helminthomorpha (spiracles, tracheal pouches, unbranched tracheal stems and tracheoles).

[Insert Fig 10 here]

Reproduction

Extant millipedes have a well-marked sexual dimorphism. Males have reduced or modified pairs of appendages (i.e., telopods in Pentazonia or gonopods in Helminthomorpha) and are generally smaller. In some species with fixed number of rings, males may have more leg pairs than their female counterparts [START_REF] Minelli | Diplopoda -reproduction[END_REF]. These specialised appendages are usually involved in sperm transfer and/or for grasping the partner during copulation. In some other groups (e.g. Chordeumatida), females can also bear reduced of modified pairs of sexual appendages. In extant Pentazonia (Glomerida and Sphaerotheriida) the differentiated penultimate and most distal appendages (called telopods) are used by males to seize the female antennae and transfer sperm to the vulva [START_REF] Haacker | Spermaübertragung von Glomeris (Diplopoda)[END_REF].

One specimen of A. fatimae has telopods and can be reasonably interpreted as a male (Fig 11A ,C). Larger conspecific specimens lack this dimorphic feature and may represent females or alternatively sexually immature individuals. In extant Glomerida and Sphaerotheriida, males have generally more legs than females [START_REF] Minelli | Diplopoda -reproduction[END_REF]. Possible missing legs make the presence of this dimorphic feature uncertain in the fossil specimens. The specialised appendages seen in males of A. fatimae are likely to have been involved in copulatory behaviour as observed in extant taxa such as Sphaerotherium [START_REF] Haacker | Sexualverhalten von Sphaerotherium dorsale (Myriapoda, Diplopoda)[END_REF]) in which sexual partners make contact head to tail with their ventral side.

[Insert Fig 11 here]

Another dimorphic feature is seen in one specimen of B. parriati that has specialised first legs armed with enlarged claspers (see Fig 11B,D). This feature has counterparts in male individuals of extant mongoliulid and parajulid millipedes (Julida). The other specimen with the front part preserved has no such feature and is approximately twice as small as the presumed male. However, as females are generally larger than males in extant species, uncertainty remains concerning its sexual identity. It may rather represent a sexually immature juvenile. We assume that B. parriati had a mating behaviour comparable with that of extant Mongoliulidae and Parajulidae -i.e. that males positioned themselves on female by grasping the mouth parts of females with their claspers [START_REF] Minelli | Diplopoda -reproduction[END_REF].

Defence

Extant diplopods have evolved morphological defence systems such as volvation (fig. 12C) and spines. Diplopods have also evolved chemical deterrence through repugnatorial glands whose openings are scattered over the exoskeleton (i.e. ozopores). The morphology of A. fatimae is consistent with the capacity to enrol as indicated by well-developed potentially overlapping margins (Fig 12A ,D) and the presence of an antennal groove along the head sides (Fig 12B ,F). These grooves may correspond to the openings seen in extant millipedes (e.g. Glomerida and Sphaerotheriida), through which antennae exit when the animal in enrolled [START_REF] Wesener | Revision of the American Pill Millipedes I: Onomeris and Trichomeris (Diplopoda, Glomerida, Glomeridae)[END_REF][START_REF] Hadrián | Conglobation as a defensive behaviour of pill millipedes (Diplopoda: Glomerida)[END_REF]. A. fatimae had spines (Fig 12F) that may have provided the animal with additional physical protection against predators if we assume that it could roll up on itself. In extant pill millipedes and isopods [START_REF] Smigel | Conglobation in the Pill Bug, Armadillidium vulgare , as a water conservation mechanism[END_REF], volvation is often interpreted as limiting water loss [START_REF] Hadrián | Conglobation as a defensive behaviour of pill millipedes (Diplopoda: Glomerida)[END_REF]. Similarly, one may speculate that A. fatimae also used volvation to resist desiccation which remains a major challenge for arthropods living on land. Like [START_REF] Racheboeuf | A new species of the diplopod Amynilyspes (Oniscomorpha) from the Stephanian Lagerstätte of Montceau-les-Mines, France[END_REF], we did not find any traces of ozopores (repugnatorial glands openings) on A. fatimae. It is noteworthy that ozopores are present in some Pentazonia (notably in Glomerida) (Koch 2015a). It is uncertain whether A. fatimae had comparable defence organs. The absence of ozopores may be original or the result of taphonomic alteration. Even though extant millipedes are able to defend themselves by various chemical of physical ways, they are preyed upon by animals as vertebrates [START_REF] Hopkin | Biology of Millipedes[END_REF], beetles [START_REF] Eisner | Rendering the inedible edible: Circumvention of a millipede's chemical defense by a predaceous beetle larva (Phengodidae)[END_REF][START_REF] Brunke | Generalist predators (Coleoptera: Carabidae, Staphylinidae) associated with millipede populations in sweet potato and carrot fields and implications for millipede management[END_REF], ants [START_REF] Suzzoni | Essential and alternative prey in a ponerine ant: variations according to the colony life cycle[END_REF], arachnids [START_REF] Carrel | The Whip Scorpion, Mastigoproctus Giganteos (Uropygi: Thelyphonidae), Preys on the Chemically Defended Florida Scrub Millipede, Floridobolus Penneri (Spirobolida: Floridobolidae)[END_REF] and slugs [START_REF] Herbert | Dining on diplopods: remarkable feeding behaviour in chlamydephorid slugs (Mollusca: Gastropoda)[END_REF]. Potential predators in the Montceau biota are numerous and may have included early terrestrial vertebrates such as Phlegethontia, aistopods (early "snake-like" vertebrates) [START_REF] Germain | A new phlegethontiid specimen (Lepospondyli, Aistopoda) from the Late Carboniferous of Montceau-les-Mines (Saône-et-Loire, France)[END_REF] as well as spiders [START_REF] Garwood | Almost a spider: a 305-million-year-old fossil arachnid and spider origins[END_REF] or scorpions [START_REF] Vachon | Description d'une nouvelle espèce de Scorpion: Buthiscorpius pescei (Stéphanien de Montceau-les-Mines, France). Remarques sur la classification des Scorpions (Arachnida) du Carbonifère[END_REF].

Lifestyle

Although extant millipedes generally live in forest litter [START_REF] Golovatch | Millipede (Diplopoda) distributions: A review[END_REF]), many of them display adaptations to specific habitats and lifestyles. [START_REF] Kime | Trends in the ecological strategies and evolution of millipedes (Diplopoda)[END_REF] and [START_REF] Golovatch | Millipede (Diplopoda) distributions: A review[END_REF] recognized various ecological morphotypes such as: 1) "bulldozers" (e.g. Juliformia) with a cylindrical body and short walking legs adapted to move relatively deep into the soil; 2) "litter-splitters" (e.g. Polydesmoida) with a flat back adapted to enter crevices and 3) "borers" (e.g. Platydesmoida) similar to morphotype 1 and 2 but with a more flexible body shape and a tapering anterior end, making them well adapted to live within the litter.

Additional morphotypes have been proposed such as: 1) "rollers" i.e. short-bodied millipedes that are able to roll up (Pentazonia, pill millipedes) as a defence behaviour and 2) "bark dwellers" represented by bristly Penicillata millipedes that shelter in the small crevices of tree barks.

Many ecological morphotypes have been proposed by authors as an attempt to categorize behaviours in relation with habitats and substrates. Most extant diplopods would belong to the "stratobiont" ecotype that encompasses species living within the litter or upper soil layers, whereas juliforms, some glomerids and platydesmoids that preferentially colonize deeper soil layers would fall into the category of "pedobionts/geobionts". According to this classification, other small (polyxenoids, glomerids) or flat-backed (polydesmoids, platydesmoids) millipedes that conceal themselves under bark fragments should be called "xylobionts". Other specialized ecotypes refer to millipedes adapted to arborescent life in tropical and subtropical area ("epiphytobiont";[START_REF] Manton | The Arthropoda: Habits, Functional Morphology and Evolution[END_REF][START_REF] Enghoff | Adaptive radiation of the millipede genus Cylindmiulus on Madeira: habitat, body size and morphology (Diplopoda,Julida, Julidae)[END_REF]. Applying these precise ecological categories to Palaeozoic myriapods remains a challenge because of the lack of direct information on their habitat. However, the diplopods from Montceau lived in a highly vegetated environment where arborescent sphenopsids, filicophytes (tree ferns) and pteridosperms [START_REF] Charbonnier | Synthèse sur la flore des nodules du Lagerstätte de Montceau-les-Mines (Carbonifère supérieur, France)[END_REF]) offered animals potential fresh (in-situ leaves) and decayed (litter) food and also a rich variety of sheltering micro-habitats. It is not inconceivable that some millipedes such as A. fatimae had colonized such arboreal niches.

Blanziulus parriati.

Close morphological similarities with extant Juliformia would suggest that Blanziulus parriati belonged to the "bulldozer" type. Indeed, its robust head and body shape seem to have been adapted for digging into soil and litter and possibly move through it. Blanziulus parriati had a large collum. This feature protects the head of extant Juliformia when digging into soil [START_REF] Enghoff | Phylogeny of millipedes -a cladistic analysis[END_REF]. Going back to the ecotype, B. parriati may belong to the "stratobiont" or "pedobiont" ecotype (Fig 13C).

The mouth apparatus of B. parriati is almost identical to that of extant Juliformia. This suggests that B. parriati exploited food sources such as decaying leaves or other plant detritus [START_REF] David | Diplopoda -ecology[END_REF] as do extant Juliformia. Most extant burrowing millipedes actually feed on a great variety of detritus. Whether B. parriati had such an opportunist feeding mode is hypothetical and would require to be tested by the

Conclusion

The non-destructive µCT analysis of Amynilyspes fatimae and Blanziulus parriati revealed an array of new morphological features that had been overlooked by previous authors (e.g. [START_REF] Langiaux | Première découverte d'un myriapode dans le Paléozoïque Supérieur du Massif Central Français[END_REF][START_REF] Racheboeuf | A new species of the diplopod Amynilyspes (Oniscomorpha) from the Stephanian Lagerstätte of Montceau-les-Mines, France[END_REF]) and led to unprecedented detailed 3D-reconstructions of these ancient myriapods. Key features (e.g. margins and antennal ridges) involved in the volvation process confirm the placement of A. fatimae within the Order Amynilyspedida. A. fatimae is seen as a detritus feeder based on its mandibular apparatus similar to that of extant pill millipedes. Its sensory organs (eyes, antennae) were similar to those of extant Sphaerotheriidae. A. fatimae had legs adapted to moving on/within litter as in extant millipedes. Its diplopody confirms that A. fatimae is a millipede. A. fatimae and extant pill millipedes share the same type of sexual dimorphism with presumed males bearing telopods posteriorly. Our study suggests that A. fatimae 1) possibly belonged to the "roller" ecological type defined by biologists, based on similarities with modern pill millipedes and 2) was a "stratobiont" or an "epiphytobiont" with a behaviour possibly resembling that of extant tropical Sphaerotheriidae.

B. parriati is placed within the Superorder Juliformia. Its mandibular apparatus points to a detritus feeding mode. Sensory organs and leg morphology are close to those of extant Juliformia. The presence of tracheal openings as in extant Juliformia, confirm that it was adapted to terrestrial environments. Sexually dimorphic appendages close to those of modern Mongoliulidae and Parajulidae shed light on its possible copulatory behaviour. B. parriati may belong to the "bulldozer" ecological type and a "stratobiont" or a "pedobiont" ecotype. Its behaviour seems to have been close to that of extant juliforms.

Our results added to previous successful microtomographic studies on other arthropod species from Montceau, (e.g. [START_REF] Garwood | Tomographic Reconstruction of Carboniferous Arthropods[END_REF][START_REF] Garwood | Tomographic Reconstruction of Neopterous Carboniferous Insect Nymphs Butler[END_REF][START_REF] Garwood | Almost a spider: a 305-million-year-old fossil arachnid and spider origins[END_REF] demonstrate that non-invasive techniques such as µCT are most suitable for the study of fossils preserved in nodules. µCT revealed fine morphological details of great importance for taxonomy and ecology such as head appendages, sexual dimorphism and chemical deterrence. This promising technique will soon be applied to other myriapods from Montceau such as Arthropleura [START_REF] Kraus | Fossil giants and surviving dwarfs. Arthropleurida and Pselaphognatha (Atelocerata, Diplopoda): characters, phylogenetic relationships and construction[END_REF] and euthycarcinoids [START_REF] Racheboeuf | A new species of the diplopod Amynilyspes (Oniscomorpha) from the Stephanian Lagerstätte of Montceau-les-Mines, France[END_REF] that are now resolved as stem myriapods in recent phylogenetic trees [START_REF] Edgecombe | Aquatic stem group myriapods close a gap between molecular divergence dates and the terrestrial fossil record[END_REF]. µCT may also be used for scanning the numerous unopened nodules (ca 30,000; see Sotty 2014) that are still awaiting to be studied. This will hopefully lead to the discovery of other myriapods such as chilopods (centipedes) that are found associated with diplopods in coeval deposits such as the Mazon Creek Lagerstätte [START_REF] Mundel | The centipedes (Chilopoda) of the Mazon Creek[END_REF].

  . Research on the Montceau Lagerstätte led by professional scientists and amateurs started during the 1970's and concentrated on three main sites (Saint-Louis, Saint-François and Sainte-Hélène; Charbonnier 2014) until the exploitation of coal measures came to an end in the 1990's and all open mines were flooded making new exploration impossible. Over the years, fossiliferous layers yielded abundant nodules (about 120 000, Sotty 1980) containing remains of plants and animals, often exquisitely preserved in three dimensions and now deposited in the collections of the Natural History Museum in Autun (Saône-et-Loire, France). Plant remains clearly indicate that the paleoenvironment associated with the Montceau Lagerstätte was humid and densely occupied by arborescent and herbaceous plants in the vicinity of riverbanks, lakes

  MNHN.F.SOT 2114A; MNHN.F.SOT 5148; MNHN.F.SOT 2113 and MNHN.F.SOT 81522 (Fig 2E, F, G, H). All studied specimens are deposited in the collections of the Muséum d'Histoire Naturelle d'Autun (repository numbers MNHN.F.SOT). [Insert Fig 2 here] Imaging methods All specimens were photographed with a Canon EOS 5D SR camera mounted with a Canon 100 mm macro lens. µCT data were obtained with a GE Sensing & Inspection Technologies Phoenix X-ray Phoenix v|tome|x CT-scan at the MATEIS laboratory of INSA, Lyon, operating at 140 kV for all specimens. The intensity of the source current was 80 µA for all specimens of A. fatimae and B. parriati (MNHN.F.SOT. 2113; MNHN.F.SOT 2114a and MNHN.F.SOT. 5148) and 100 µA for B. parriati (MNHN.F.SOT. 81522). Voxel size was 25 µm for all specimens of A. fatimae and B. parriati (MHNHN.F.SOT.5148), 30 µm for B. parriati (MHNH.F.SOT 2113) and 10 µm for B. parriati (MHNH.F.SOT 2114a and MHNHN.F.SOT 81522). The type specimens of A. fatimae (MNHN.F.SOT 2134, MNHN.F.SOT 14983 and MNHN.F.SOT 2129)

  .-Head present in all specimens (Fig 3B, C and F) although poorly preserved in MNHN.F.SOT 14983. Maximum length (Fig 4A) and width (Fig 4C)2.1 mm and 2.4 mm, respectively. One antenna well preserved inMNHN.F.SOT 2134 (Fig 3B), complete pair preserved in MNHN.F.SOT 2129 (Fig.3F), with seven segments varying in length from 0.9 to 2.6 mm. MNHN.F.SOT 2134 and MNHN.F.SOT 2129 display key elements of mouth apparatus such as the mandibular base (maximum length and width 1.7 mm and 0.5 mm, respectively), the gnathal lobe (maximum length and width 1.5 mm and 1.1 mm) and the gnathochilarium bearing well-defined gnathochilarial stipes (maximum length and width 0.3 mm and 1.3 mm; best preserved in MNHN.F.SOT 2129) (Fig. 3B, F). Bulges interpreted as lateral eyes best seen in MNHN.F.SOT 2134 (only left eye) and MNHN.F.SOT 2129 (Fig. 3B, F), maximum eye width (fig. 4E) of 0.5 mm. Ommatidia not observed. Ridge present between antenna and mandible base in MNHN.F.SOT.2134 (Fig. 3B). Body consisting of 13 terga and an anal shield (Fig 3A, C, E) with a maximum body length (from terga 3 to the anal shield) (Fig 4A) of 22.6 mm. Tergum length from 1.3 to 1.5 mm, width from 3.4 to 5.6 mm and maximum margin thickness (Fig 4A) of 0.3 mm. First tergum (collum) much smaller, length from 0.4 to 2 mm and width from 0.8 to 2.8 mm. Second tergum (thoracic shield) much larger, 3.2 and 6.8 mm in maximum length and width respectively, maximum margin thickness (Fig 4C) of 0.2 mm. Anal shield from 1.1 to 2.1 mm long, 2.1 to 3.2 mm wide and margin thickness of 0.32 mm. Sternite 5 to 12 visible in MNHN.F.SOT 2134 (Fig. 3A) altogether 10.8 mm long, each sternite being approximately 1.3 mm long and 1.4 mm wide. Dorsal spines present on terga 3-12 of all specimens (MNHN.F.SOT. 2134; MNHN.F.SOT 14983; MNHN.F.SOT 2129, Fig 3A, C, E) with a maximum axial length (Fig 4A) of 2.2 mm. Incomplete digestive tract visible in MNHN.F.SOT. 2134 and MNHN.F.SOT. 2129 (Fig 3A, E), running below the terga and above the stigmatic plates. Twenty pairs of walking legs with two pairs per segments. Maximum leg length is 3.8 mm. Each leg consists of seven segments. Terminal podomere bearing claw usually poorly preserved. The penultimate legs of a presumed male (MNHN.F.SOT 14983) (Fig 3C) are modified into a pair of anterior telopods (length of 0.8 mm) and appear as a pincer-shaped, three-jointed apparatus formed by telopodites (Fig 3D) that may represent the functional analogue of the clasping apparatus seen in extant pill millipedes. Discussion.-Our study confirms major morphological differences between A. fatimae and other Amynilyspes species as already noted in Racheboeuf et al. 2004. The cuticle of A. wortheni, A. typicus and A. crescens is ornamented whereas that of A. fatimae is smooth. Moreover, A. wortheni has one more tergite than A. fatimae. The cephalic shield of A. wortheni has spines whereas its penultimate segment lacks ornament. The opposite situation is observed in A. fatimae. The detailed morphology of the head and appendages of other Amynilyspes remains poorly known, making interspecific comparisons difficult. [Insert Fig 3 here] Superorder Juliformia Attems, 1926 Diagnosis (emended from Enghoff in Minelli 2015).-Essentially cylindrical millipedes with an elongate body, length 4-344 mm, diameter 0.4-20 mm. Head usually with eyes, each consisting of one to at least 68 ommatidia, normally arranged in a triangular to ovoid patch, sometimes in a single line. Tömösváry organ absent. Antennae with six antennomeres plus apical disc, disc with four, exceptionally up to at least 20 sensory cones. Mandibles: gnathal lobe massive, with a simple or lobed premandibular tooth, a lobed dentate lamella, four or more pectinate lamellae and a prominently developed molar plate. Gnathochilarium variably composed, order and family-specific. Trunk with 18-101 body rings, excluding telson. Collum large, covering posterior part of head. Terga, pleurites, stigmatic plates and sternites fused into complete body rings, except that sterna may be free on the first few rings. Defence glands present, consisting of a single compartment, opening through lateral ozopores and mostly secreting benzoquinones. Legs with six podomeres (coxa, prefemur, femur, postfemur, tibia, tarsus). Coxal pores absent, except on leg-pair 2 in some Julida. Male leg-pairs 8 and 9 modified into gonopods. Male gonopores opening through paired penes behind leg-pair 2, or (Spirobolida) distal part of gonoduct eversible. Female gonopores opening through sclerotized vulvae behind leg-pair 2, each vulva consisting of a simple operculum and a more complicated bursa. [Insert Fig 4 here] Order Incertae sedis Superfamily Xyloiulidea Cook & Collins, 1895 Diagnosis (emended from Wilson 2006).-Juliforms with tergites, pleurites, and sternites fused into complete rings. Trunk rings ornamented with longitudinal striations. 40-50 trunk rings in adults. Ozopores present. Length of legs equal to half the height of the trunk rings or less. Remarks-Langiaux & Sotty 1976 placed B. parriati into this superfamily based on the longitudinal striations (diagnostic of the Xyloiulidea superfamily) observed in the holotype. No such striations were observed on the scanned specimens but the presence of transversal ridges in all specimens including the holotype seems to be diagnostic of B. parriati and seems to indicate that we have specimens of the same species. Other characters described as diagnostic of this superfamily such as the number of trunk rings, the fusion of terga, pleura and sternites (only the terga and pleura are fused in the studied specimens) and the full lengths of legs were not observed. As the superfamily Xyloiulidea is an extinct clade composed of only Palaeozoic species, the characters used for describing this taxon are based on specimens with inferior preservation thus the pertinence of these characters to describe this clade are highly debatable. That is why we consider that we can still place B. parriati (holotype and scanned specimens) as a Xyloiulidea even with this lack of diagnostic characters. Family Xyloiulidae Cook & Collins 1895 Diagnosis.-Xyloiulidea with entire prozonites and metazonites striated. No differences between the striations on the prozonite and those of the metazonite. Diameter of the metazonite slightly greater than that of the prozonite. Remarks-No such striations were observed on the scanned specimens. However, they are present on the holotype. As noted above, we can confirm that the scanned specimens represent the same species as the holotype of B. parriati. Thus we see no problem with placing the scanned specimens as B. parriati into the Xyloiulidae family. Genus Blanziulus Langiaux & Sotty 1976 Type species.-Blanziulus parriati. Monotypic genus. Holotype: MNHN.F.SOT 76-H-1-A from Montceau-les-Mines, Sainte-Hélène site (Fig 2D). Diagnosis (modified after Langiaux & Sotty 1976).-Xyloiulidae with at least 53 segments. Pleuroterga with thin transversal ridges. Blanziulus parriati Langiaux & Sotty 1976 Blanziulus parriati n. sp.; Langiaux & Sotty 1976,p. 43, fig. 1, pl. 4. Blanziulus parriati; Chabard & Poplin 1999, p. 183-184 ; fig p. 183. Unnamed myriapod; Perrier & Charbonnier 2014, p. 11, pl. 4, Fig N Diagnosis.-As for the genus. Description.-Left part of the head present in MNHN.F.SOT. 2114a (Fig. 5B) and MNHN.F.SOT. 5148 (Fig. 5D). Maximum length (Fig. 4B) and width (Fig. 4D) (for left part) of 3.4 mm and 1.2 mm respectively. Left antenna preserved in MNHN.F.SOT. 2114a, 2.6 mm long and consists of six segments. Mandibular apparatus present in MNHN.F.SOT. 2114a (Fig. 5B) with cardo (0.4 mm long and 0.3 mm wide) and stipes (0.8 mm long and 0.4 mm wide). Ovoid ocular fields preserved in MNHN.F.SOT. 2114a (only left eye) and MNHN.F.SOT. 5148 (Fig. 5B, D). Maximum field width of 0.7 mm (Fig. 4F). Ommatidia not observed. None of the studied specimens is complete (total number of pleuroterga unknown). Maximum number of pleuroterga observed is 53 (without collum and telson) on MNHN.F.SOT. 81522 (Fig. 5G), length of 50 mm. Pleurotergum length (Fig 4B) from 1.2 to 1.4 mm and width (Fig 4D) from 1 to 3.4 mm. First pleurotergum (collum) large, covering posterior part of the head (0.9 to 2 mm and 0.8 to 4.6 mm in length and width, respectively). Eight sternites in MNHN.F.SOT. 2113 (Fig 5E) altogether 6 mm long. Each sternite = 1 mm long and 2.9 mm wide. Longitudinal ridges present in the posterior part of each pleuroterga. Ridge length (Fig 4E) going from 0.2 to 0.5 mm. Digestive tract present in MNHN.F.SOT. 81522 (Fig. 5H) with a total length of 23.8 mm. Exact number of leg pairs unknown due to the incompleteness of specimens. 73 pairs in MNH.F.SOT. 81522 (Fig. 5G). Collum and second pleurotergum with one pair of legs. Pleuroterga 4-53 with two pairs of legs. Possible pair of legs for segment three not present on MNHN.F.SOT. 2114a (Fig. 5A) and MNHN.F.SOT. 5148 (Fig 5C) so it is impossible to determine if there is only one pair on this segment similarly to the collum and second pleurotergum (like in extant juliforms) or two pairs like the following pleuroterga. Maximum leg length of 4.6 mm. Each leg consists of seven segments. First pair of legs in assumed male (MNHN.F.SOT. 5148) modified

[

  Insert Fig 5 here]

  Most extant millipedes have eyes bearing more or less numerous ommatidia distributed over the ocular field. There are two types of eyes in extant diplopods: 1) large ocular fields with numerous ommatidia (50-90) (Fig 8J, N); 2) 1-2 rows of eyes with less than 10 ommatidia each (e.g. Glomerida, Fig 8B). The exact visual capacities and sensory importance of these eyes is still in debate (Müller & Sombke 2015). Since millipedes react to light (Cloudsley-Thompson 1951) and some species show a different behaviour if they are illuminated at night (McKillup 1988), these eyes are clearly sensitive to light variations. [Insert Fig 9 here] The antennae of A. fatimae are seven segmented and inserted laterally like those of extant Sphaerotheriida (Fig 8B, D, E). Those of B. parriati have close counterparts in modern Juliformia (Fig 8J, L). It is uncertain whether the absence of an apical cone (most distal antennomere) in both Carboniferous species is due to preservation or is an original biological origin. However, the tip of the antennae often appears to be broken (Fig 8E, L) which would confirm an artefactual origin. The ocular field of A. fatimae is similar to that of extant Sphaerotheriida (Fig 8G, N). That of B. parriati is larger, more ovoid and recalls the ocular configuration seen in extant Juliformia (Fig 8J, M). Inferring the visual properties of A. fatimae and B. parriati requires the recognition of ommatidia that are unfortunately lacking in the studied fossil specimens. Many extant millipedes have additional paired sensory features known as the Tömösváry organs located posteriorly to the antennal basis (Fig 8A, B). Homology of these organs among arthropods as well as their exact function are still unresolved.

  Many recent diplopods have a very elongated and flexible body and a large number of legs that allow them to move into interstices and find their way through loosely compressed plant-based litter. The legs of A. fatimae and B. parriati are virtually identical to those of extant millipedes in their basic architecture and distribution. They have seven podomeres (Fig 8F, I) and each tergum (for A. fatimae) and non-thoracic pleurotergum (for B. parriati) is provided with two pairs of them (Fig 3A, C, D and Fig 5A). The thorax of B.

[

  Insert Fig 12 here] No spines or traces indicating other physical and chemical defence (ozopores) occur in B. parriati either. Ozopores are common in extant Helminthomorpha and also occur in Lower Carboniferous (Shear 1993) and possibly Lower Devonian (Wilson 2006) representatives of the group. Ozopores are always extremely small (size about 50 µm). If originally present in B. parriati they might have disappeared through taphonomic processes.

[

  Insert Fig 13 here] Amynilyspes fatimae. Comparisons with pill millipedes (e.g. overlap features such as margins on terga edges, lateral ridges on head) and phylogenetic affinities with Sphaerotheriida (Fig 6) both suggest that A. fatimae was a pill-millipede of the "roller" type. A. fatimae is likely to have been a stratobiont (Fig 13A) or a epiphytobiont (Fig 13B) and possibly lived in the litter and upper soils layers that were probably abundant in the forest-like environments of Montceau. Its spines may have been used to push out coarse detrital elements and should not be considered as a disadvantage for tunnelling into an heterogenous and loosely packed substrate. Some extant Sphaerotheriida species, such as Zoosphaerium arboreale (Madagascar), are arboreal (Haacker & Fuchs 1972; Wesener & Sierwald 2005) and live in rainforest environments. They closely resemble A. fatimae in their overall morphology. Whether A. fatimae was similarly an epiphytobiont remains hypothetical.

  analysis of gut contents. B. parriati and A. fatimae are particularly well represented at the Saint-Louis (Fig 1C) fossil site where arborescent flora is particularly abundant and diverse (Charbonnier 2014). This would indicate a possible correlation between myriapod occurrence and food availability. Relative abundance of millipedes at Montceau. B. parriati is far more abundant than A. fatimae with 65 against four specimens found in opened nodules. This might indicate that B. parriati was effectively more abundantly represented than A. fatimae in the Montceau biota. However, taphonomy should be taken into consideration as a potentially bias. Recent taphonomic scenarios suggest that most animals of the Montceau biota were transported from their original habitat into neighbouring swamps and rivers by landslides and storm-induced water flows, where they were eventually buried (Perrier & Charbonnier 2014). This scenario is consistent with the equatorial and humid climate that supposedly prevailed at Montceau and the presence of potential steep relief and slopes (Hercynian Mountain range e.g. Charbonnier 2014). In this context, small arthropods living in litter and soil such as B. parriati would have been more easily swept away by water and mud flows that those possibly inhabiting trees. If we follow our hypothesis of A. fatimae inhabiting trees (possible epiphytobiont) instead of litter, then its relative under-representation may be explained by the fact that it was more rarely transported by water and mud. Or B. parriati may have simply been more abundant that A. fatimae in the Montceau palaeoenvironment. Only a quarter of the 120, 000 nodules collected at Montceau (Sotty 2014) have been split open and observed. One may expect that the study of the whole fossil collection will provide more conclusive results on the relative diversity and numerical abundance of plant and animal species.

Fig 1 .

 1 Figure captions:

Fig 4 .

 4 Fig 4. Schematic diagrams of A. fatimae and B. parriati indicating main morphological parameters. (A) Right lateral view of A. fatimae. (B) Right lateral view of B. parriati. (C) Dorsal view of A. fatimae. (D) Dorsal view of B. parriati. (E) Three-quarter view of A. fatimae. (F) Three-quarter view of B. parriati. AL, antenna length; ASL, anal shield length; BL, body length; CL, collum length; CW, collum width; CaL, mandibular cardo length; CaW, mandibularcardo width; GL, gnathal lobe length; GW, gnathal lobe width; GnL, gnathochilarium length; GnW, gnathochilarium width, HL, head length; HW, head width; LL, leg length; ML, mandibular base length, MT, margin thickness; MW, mandibular base width; OW, ocular field width; PL, pleurotergum length; PW, pleurotergum width; RL, ridge length; SAL, spine axial length; SL, mandibular stipes length; SW, mandibular stipes width; TL, tergum length; TMT, thoracic shield margin thickness; TSL, thoracic shield length; TSW, thoracic shield width; TW, tergum width.

Fig 7 .

 7 Fig 7. Consensus of maximum parsimony morphological phylogeny for the two Montceau species, extant Diplopoda orders/ species and other extinct Diplopoda species. (A) Consensus for A. fatimae, B parriati, extant orders and six extinct species of the class Diplopoda. (B) Consensus for A. fatimae, extant species and two extinct species of the subclass Pentazonia. (A) and (B) Same colour code and node values as in Fig. 6.

Fig 8 .

 8 Fig 8. Comparisons between Amynilyspes fatimae and Glomeris marginata and between Blanziulus parriati and an extant Juliformia. (A) Head of G. marginata. (B) Sense organs of G. marginata. (C) Leg of G. marginata. (D) Head of A. fatimae. (E) Antenna of A. fatimae. (F) Legs of A. fatimae. (G) Ocular fields of A. fatimae. (H) Head of an unidentified Juliformia. (I) Legs of B. parriati. (J) Sense organs of an unidentified Juliformia. (K) Head of B. parriati. (L) Antenna of B. parriati. (M) Ocular field of B. parriati. (N) Ocular field of Zoosphaerium sp.(Wesener 2016b). AC, apical cones; aG, antennal groove; aO, aberrant ocellus; An, antenna; c, coxa; Ca, mandibular cardo; cl, claw; f, femur; GL, gnathal lobe; GS, gnathochilarial stipes; ISP, inner stipital palps, La, labrum; LL, lamellae lingualis; MB,

Fig 13 .

 13 Fig 13. Reconstruction of possible ecotypes of Amynilyspes fatimae and Blanziulus parriati in in their supposed environment. (A) Amynilyspes fatimae with a stratobiont strategy. (B) Amynilyspes fatimae with an epiphytobiont strategy. (C) Blanziulus parriati with stratobiont and pedobiont strategies.

Acknowledgements

We thank MATEIS at INSA Lyon and the Zoological Research Museum Alexander Koenig for µCT facilities, and the Centre Technologique des Microstructures (CTµ) for access to Scanning Electron Microscopy. We thank Henrik Enghoff at the Natural History Museum of Denmark for advice and expertise on myriapod anatomy. We also thank S. Greene (Associate Editor) and two anonymous reviewers for their constructive advices and editorial assistance that helped improve our manuscript.

Fig 2. Specimens of Amynilyspes fatimae and Blanziulus parriati. A-C: Amynilyspes fatimae. (A): Holotype MNHN.F.SOT.2134. (B): Paratype MNHN.F.SOT.14983. (C): Paratype MNHN.F.SOT.2129. D-H: Blanziulus parriati. (D): Holotype MNHN.F.SOT.76-H-1-A. (E): MNHN.F.SOT.2114a. (F): MNHN.F.SOT.5148. (G): MNHN.F.SOT.81522. (H): MNHN.F.SOT.2113. Scale bars represent: 1 cm (A-G); 3 mm (H).


Major genetic transitions in Europe

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Fine

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	It is made The copyright holder for this preprint (which . . CC-BY-NC-ND 4.0 International license this version posted May 5, 2022. ; https://doi.org/10.1101/2022.05.04.490594 CC-; https://doi.org/10.1101/2022.05.04.490594 available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made doi: bioRxiv preprint doi: bioRxiv preprint The copyright holder for this preprint (which this version posted May 5, 2022. ; https://doi.org/10.1101/2022.05.04.490594 doi: bioRxiv preprint

  International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is madeThe copyright holder for this preprint (which this version posted May 5, 2022. CC-BY-NC-ND 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is madeThe copyright holder for this preprint (which this version posted May 5, 2022. ; https://doi.org/10.1101/2022.05.04.490594 doi: bioRxiv preprint Archaeol.Anthropol. Sci. et al. Proc. Natl. Acad. Sci. U. S. A.

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HECTD4

All other analyses relied upon available software which has been fully referenced in the manuscript and detailed in the relevant supplementary notes.

Science et al. Science

The First Farmers of Europe: An Evolutionary Perspective


domain: phys spi

text:
Jean-Baptiste Casanova
email: jean-baptiste.casanova@st.com

Danika Perrin
email: danika.perrin@st.com

Sandrine Nicolas
email: sandrine.nicolas@st.com

Andreas Kaiser
email: andreas.kaiser@junia.com

A Very Low Power 12 bit 64-MS/s 2 step SAR Assisted Bidirectional Digital Slope ADC

Keywords:

This paper presents a novel architecture of a SAR assisted 2 step ADC where the SAR residue is quantized with a bidirectional digital slope time-based converter. The bidirectional slope halves the conversion time of the second stage. Furthermore, the redundancy requirements in the second stage are considerably reduced through a unified global calibration scheme. A practical example is given for a 12-bit 64 MS/s ADC with 67 dB SNDR and 208 µW estimated power consumption targeted at ultra-low power RF receivers. The complete architecture including calibration has been validated with VerilogA models including capacitor mismatch, comparator offsets and noise.

I. INTRODUCTION

The Successive Approximation Register (SAR) ADC has become the dominant architecture in the state of the art for low power applications with several MHz bandwidth and mid resolutions (8∼10 bits) [1] [START_REF] Li | A SAR ADC with Reduced kT/C Noise by Decoupling Noise PSD and BW[END_REF]. They are particularly well adapted to RF receiver circuits where the ADC performance is a major contributor to the overall performance. High resolution and wide bandwidth ADCs relax constraints on other blocs in the Rx chain [1].

Power consumption in SAR ADCSs at low supply voltages and high resolution is dominated by the comparator [START_REF] Inerfield | An 11.5-ENOB 100-MS/s 8mW dual-reference SAR ADC in 28nm CMOS[END_REF] because of low noise requirements. 2-stage pipelined SAR ADCs with an interstage residue amplifier [START_REF] Wang | A Calibration-Free 14-b 0.7-mW 100-MS/s Pipelined-SAR ADC Using a Weighted-Averaging Correlated Level Shifting Technique[END_REF]- [START_REF] Lee | A SAR-Assisted Two-Stage Pipeline ADC[END_REF] can relax these requirements. However, the interstage amplifier becomes critical because of gain and noise constraints.

Alternative architectures of SAR-assisted 2-stage ADCs without the need for a residue amplifier have been proposed. M. Zang et al. proposed in [START_REF] Zhang | 3.5 A 0.6V 13b 20MS/s Two-Step TDC-Assisted SAR ADC with PVT Tracking and Speed-Enhanced Techniques[END_REF] a Voltage-to-time converter (VTC) that transforms the SAR conversion residue in a time window which is then discretized by a delay line-based timeto-digital converter. The voltage-to-time conversion is achieved by discharging the node holding the residue with a constant current. The VTC is fundamentally linear, and the resolution is only limited by the various noise sources. However, precise matching between then VTC and Time to digital converter (TDC) time constants is needed in such an approach. Conceptually similar architectures [START_REF] Liu | A 12 bit 100 MS/s SAR-Assisted Digital-Slope ADC[END_REF]- [START_REF] Zhao | A 0.97mW 260MS/s 12b Pipelined-SAR ADC with Ring-TDC-Based Fine Quantizer for PVT Robust Automatic Cross-Domain Scale Alignment[END_REF] propose to use a delay-line driven digital slope (DS) with 1-LSB steps as second stage, combining the discharge of the residue and the time-to-digital conversion into a single operation. The state of the delay-line at zero crossing of the digital slope represents the output code in thermometric representation. The resolution of this approach is limited by the discretized voltage steps of the digital slope. Both implementations apply the digital slope on the positive branch only of the differential circuit in monotonic switching, requiring to first level shift the SAR residue to the positive domain. Limiting the bandwidth of the comparator has the effect of time interpolation between consecutive steps which can increase the achievable resolution by up to 3 bits [START_REF] Zhao | A 0.97mW 260MS/s 12b Pipelined-SAR ADC with Ring-TDC-Based Fine Quantizer for PVT Robust Automatic Cross-Domain Scale Alignment[END_REF]. This paper presents a 2 step SAR Assisted ADC with a pseudo-differential approach allowing a bidirectional digital slope. It also proposes a unified calibration scheme for comparator offsets and the digital-slope delay. Key advantages of the proposed architecture are a reduced number of capacitors, minimized cross-point voltage variations and reduced conversion time. Target specifications for the ADC architecture have been derived from the needs of a low power receiver aimed at connectivity applications such as Bluetooth., i.e. a 12 bit 64 MS/s ADC with 68 dB SNR. These specifications are used for dimensioning a reference implementation of the proposed architecture.

II. SAR-ASSISTED DIGITAL SLOPE ARCHITECTURE

Figure 1 shows a block diagram of the proposed architecture. The first stage is a 9-bit CDAC based SAR ADC with an additional bit because of built-in redundancy. The residue voltage of the SAR ADC is further quantized by a digital slope time-domain ADC. An inverter-based delay line connected to an array of unit capacitors generates the digital slope. The latched comparator (D-CMP) for the SAR and the continuous time comparator (CT-CMP) of the time-domain ADC share the same input signal. However, they are only active during respective conversion operations. The remaining part of the CDAC (CDAC ) is binary weighted and used for foreground calibration of the comparators. CDAC adds an appropriate voltage during SAR and continuous time conversion to the internal differential node to compensate respectively the offset of the discrete-time and continuous-time comparator. The value of the correction for each comparator is determined in a foreground calibration phase described in section III.

The total capacitance in each branch is theoretically equal to 2048*C. The digital slope adds 4 additional unit capacitors, while the calibration CDAC adds a total of 32 unit capacitors. This does not impair the performance other than reducing the LSB voltage step and full-scale input voltage by 1,5% with respect to the theoretical value.

III. PSEUDO-DIFFERENTIAL DIGITAL SLOPE STAGE

A. Unidirectional Digital Slope

SAR-Assisted digital slope ADCs in prior art use a monotonic switching scheme on a single branch, the other branch remaining at a fixed voltage [START_REF] Liu | A 12 bit 100 MS/s SAR-Assisted Digital-Slope ADC[END_REF]- [START_REF] Zhao | A 0.97mW 260MS/s 12b Pipelined-SAR ADC with Ring-TDC-Based Fine Quantizer for PVT Robust Automatic Cross-Domain Scale Alignment[END_REF]. Consequently, the discharging operation is always in the same direction. Assuming a negative direction, the initial residue voltage must be positive to reach the zero-crossing. A sufficiently large positive offset is therefore added to the residue voltage prior to the conversion to meet this requirement regardless of the actual sign of the residue voltage. Figure 3 represents the dynamic of residue at the end of the SAR conversion, which is equal to twice the LSB voltage of the SAR. In practice an additional margin is needed to consider errors induced by various sources during the SAR conversion. Under the assumption that an additional bit is needed for redundancy, the range to be quantified can be as large as 4 times the SAR LSB voltage. To produce 3 additional bits with the continuous time digital slope ADC, 5 bits are needed for the continuous time ADC. The advantage of the monotonic one-sided slope is the robustness and simplicity of implementation. However, the sign-bit of the SAR is not used and the conversion time is higher than theoretically necessary. Finally, the voltage corresponding to the zero-crossing depends on the residue voltage on the opposite node and is signal dependant. This could potentially cause non-linear distorsion.

B. Pseudo-differential bidirectional digital slope

The proposed pseudo differential bidirectional Digital Slope consists in switching alternatively capacitors on the positive and negative branches. Alternate switching of the unit capacitors on both positive and negative branches increases the step resolution by 1 bit (C instead of 2C changing state at a given time) and keeps the common-mode voltage at zero-crossing within a 1 CT-ADC LSB window. Furthermore, slopes in the positive or negative direction can easily be created thanks to the split switching scheme adopted in this CDAC architecture. This allows conversion of positive or negative residue voltages with the sign bit of the SAR ADC determining the direction which halves the range that needs to be covered by the digital slope. A small level shift voltage is however still required to correct any residual offset and noise errors of the SAR comparator. Figure 4 presents examples of the proposed approach for residues of positive and negative signs. As shown, a small level shift is first applied for redundancy purposes only. Fig. 5 shows the proposed implementation of the 3 bits pseudo differential DS. The capacitor array is composed of 6 capacitors pairs on each side. When sampling the input signal, half of the Figure 6 shows the detailed switching scheme for positive and negative slopes with examples of negative and positive residues. For negative residues, first capacitors C1, C2, C13 and C14 are switched simultaneously to create a 4 LSB offset. Then the conversion starts on the rising edge of Tst and C12 to C7 on positive side and C24 to C19 on negative side are alternatively switched to generate the digital slope creating 12 LSB steps. The final 4 LSB steps are created by switching C2, C14, C1 and C13 successively to their original state. The zero-crossing point depends on the value of the residue, but it always occurs within a ± 0.5 window around the common mode voltage. Operation for positive residues is similar, but slopes are inverted. The detailed logic function to control capacitors generation the level shifts can be seen on Figure 5. The remaining capacitors are directly switched by the appropriate outputs of the delay line.

This pseudo differential implementation speeds up the overall conversion while reducing the number of capacitances used for redundancy. Bidirectional slopes are generated without reducing the size of unit capacitors. Furthermore, the common mode variation [START_REF] Liu | A 10-bit 50-MS/s SAR ADC With a Monotonic Capacitor Switching Procedure[END_REF]- [START_REF] Liu | A 1V 11fJ/conversion-step 10bit 10MS/s asynchronous SAR ADC in 0.18µm CMOS[END_REF] for the comparator switching point is limited to one LSB voltage step.

C. Foreground calibration

Capacitor mismatch, incomplete settling and comparator offset and noise are the major impairments limiting the performance of the SAR ADC. Redundancy in the second stage can correct these impairments. The remaining critical parameters are the noise and offset of the continuous-time comparator. Foreground calibration allows to reduce the impact of the comparator offset. The foreground calibration has been extended to the discrete-time comparator of the SAR to relax the redundancy requirements of the second stage. A common way to correct the comparator offset is to add calibration circuitry into the pre-amplifier of the comparator [START_REF] Zhao | A 0.97mW 260MS/s 12b Pipelined-SAR ADC with Ring-TDC-Based Fine Quantizer for PVT Robust Automatic Cross-Domain Scale Alignment[END_REF]- [START_REF] Yoshioka | A 10b 50MS/s 820µW SAR ADC with on-chip digital calibration[END_REF]. We propose an alternative approach by extending the CDAC for calibration purposes. It allows to independently calibrate both comparators and to implement the calibration algorithm on-chip. The CDAC part of the CDAC is dimensioned in powers of 2 (Figure 2). In the foreground phase the offset of each comparator is determined by a successive approximation algorithm. Averaging is used to filter out the comparator noise contribution over multiple measurements. In the normal mode, the respective corrections are applied when using the SAR and DS mode.

In foreground phase, the comparator delay is also calibrated once offset compensation is applied. By applying a zero differential input voltage to the 2 nd stage the corresponding output represents the delay with a ±0.5 accuracy. By extending the delay line with a few extra unit delay cells (not represented in Figure 5) the comparator's delay can be perfectly compensated [START_REF] Liu | A 12 bit 100 MS/s SAR-Assisted Digital-Slope ADC[END_REF]. By this unified calibration scheme the nonidealities of the critical blocks could be self-corrected with sufficient precision without extra circuitry nor consumption.

D. Redundancy sizing

The conversion time and consequently the power consumption of the 2 nd stage is proportional to its input range. The input range of the second stage has been extended by 50% with respect to the maximum theoretical residue of the first stage. This introduces redundancy in the second stage allowing error correction in a range of ±4 [START_REF] Harpe | A 7-to-10b 0-to-4MS/s flexible SAR ADC with 6.5-to-16fJ/conversion-step[END_REF]. As shown in III.C the offset is calibrated within a ±0.5 range so D-CMP noise is the major error source. With ±4 of redundancy between stages and 430 µV CT-ADC LSB and 5σ margin, input-referred noise (IRN) of the D-CMP needs be less than 300µ .

IV. ADC DIMENSIONING AND SIMULATION RESULTS

The proposed ADC has been scaled to the needs of a low power RF receiver with 12 bits resolution, 64 /" sampling rate and 68$ SNR. The target process is 28nm CMOS with 0.9V power supply. The sampling noise budget has been set equal to the quantization noise to keep low power consumption and area. The resulting % &'( )* is equal to 0.615,with units capacitors of % . = 0.30F. The remaining major noise contributor is the CT-CMP. To reach the noise requirement of 68 dB SNR its noise specifications is an IRN < 157.7µ

. In the simulation an IRN of 157µ has been used. To reduce the impact of capacitor's mismatch the 3 MSB capacitors (480%, 256% & 128%) are thermometrically split in groups of 128%. Mismatch is simulated with an overestimated value of = 1.25% compared to technology performances. Simulations with VerilogA models validate the concept of the architecture, the performance of the self-calibrated scheme and the impact of the major noise contributors. Figure 7 presents the simulated FFT of the architecture including mismatch and noise contributions. DC offsets are put on both comparators and corrected by the foreground calibration phase. The unit delay of 2 nd stage is 50ps. The simulated SNDR reaches 67.15dB.

Table 1 compares the simulated performances of the proposed architecture with references of the state of the art. By extrapolation from measurements of a similar architecture implemented in 28nm CMOS [START_REF] Liu | A 12 bit 100 MS/s SAR-Assisted Digital-Slope ADC[END_REF] the power consumption of the different blocs has been estimated. The proposed 2 nd stage resolution is 3 bits versus 5 bits in [START_REF] Liu | A 12 bit 100 MS/s SAR-Assisted Digital-Slope ADC[END_REF] with identical unit delays. The conversion time is reduced by a factor 4, resulting in 4 times lower power consumption. Our estimate includes a 30% margin, so the 2 nd stage power consumption is estimated as one third of the power consumption reported in [START_REF] Liu | A 12 bit 100 MS/s SAR-Assisted Digital-Slope ADC[END_REF]. Conversely the proposed SAR has 2 additional steps compared to [START_REF] Liu | A 12 bit 100 MS/s SAR-Assisted Digital-Slope ADC[END_REF], increasing the SAR power consumption by 25%. For an identical sampling rate of 100MS/s, the estimated power consumption would be 318.75 µW. The power consumption also scales with the sampling rate leading to a final estimate of 204µW power consumption. This leads to a -9 :;<*=*< of 179.1 dB considering an SNDR of 67.12 dB. This places the proposed architecture in a favorable position compared to other digital slope implementations. There still is a margin with continuous slope implementations [START_REF] Zhang | 3.5 A 0.6V 13b 20MS/s Two-Step TDC-Assisted SAR ADC with PVT Tracking and Speed-Enhanced Techniques[END_REF]. However continuous slope implementations suffer from high PVT sensitivity and longer conversion time.

V. CONCLUSION

This paper proposes a novel approach to implement a bidirectional digital slope time-based converter resulting in faster conversion time and lower power consumption. The concept has been modeled in a 2 step SAR assisted ADC architecture, targeted on 12 bits resolution and sample rate of 64MS/s. The VerilogA model includes careful estimations of error sources and predicts an SNDR of 67.12 dB. Based on measured data from [START_REF] Liu | A 12 bit 100 MS/s SAR-Assisted Digital-Slope ADC[END_REF] power consumption is estimated at 204µW yielding to -9 of 179.1 dB which compares favorably to the state of the art. >?@ = 67.13 $ >@ = 67.91 $ -?@ = 77.15 $ BC? = -74.87 $

Figure 1 -

 1 Figure 1 -SAR-Assisted Two stages differential DS

Figure 3 -Figure 2 -

 32 Figure 3 -Operation of a monotonic 2nd stage digital slope

Figure 6 -Figure 4 -

 64 Figure 6 -3 bits Pseudo differential Digital Slope with redundancy a) for positive residue -(b) for negative residue

[ 1 ]

 1 Wei Deng, R. Mahmoudi, P. Harpe and A. van Roermund, "An alternative design flow for receiver performance optimization through a trade-off between RF and ADC," 2008 IEEE Radio and Wireless Symposium, 2008, pp. 699-702, doi: 10.1109/RWS.2008.4463588.

Figure 7 -

 7 Figure 7 -Simulated 8192 points FFT of the proposed ADC with noise, offset and mismatch models