# Taxonomy and evolutionary history of peradectids (Metatheria): new data from the early Eocene of France

Killian Gernelle<fnref n="1" />,*, Guillaume Billet<fnref n="2" />, Emmanuel Gheerbrant<fnref n="2" />, Marc Godinot<fnref n="3" />, Bernard Marandat<fnref n="1" />, Sandrine Ladevèze<fnref n="2" />,† and Rodolphe Tabuce<fnref n="1" />,†

Killian Gernelle

Email address: [killian.gernelle@umontpellier.fr](mailto:killian.gernelle@umontpellier.fr)

ORCID identifiers: Killian Gernelle: https://orcid.org/0000-0001-9698-0223

Guillaume Billet: https://orcid.org/0000-0002-3200-1548

Emmanuel Gheerbrant: https://orcid.org/0000-0003-3355-458X

Sandrine Ladevèze: https://orcid.org/0000-0001-6009-4107

Rodolphe Tabuce: https://orcid.org/0000-0002-4713-3981

<footnote n="1">¹ Institut des Sciences de l'Évolution de Montpellier (ISEM, UMR 5554), Univ Montpellier, CNRS, IRD, cc64, Place Eugène Bataillon, F-34095 Montpellier Cedex 05, France</footnote>

<footnote n="2">² Centre de Recherche en Paléontologie - Paris (CR2P, UMR 7207), Sorbonne Université, Muséum National d'Histoire Naturelle, CNRS, 8 rue Buffon, F-75005, Paris, France</footnote>

<footnote n="3">³ Ecole Pratique des Hautes Etudes, PSL, UMR 7207, CR2P, 8 rue Buffon, F75005, Paris, France</footnote>

<footnote>† Co-senior authors</footnote>

<footnote>* Corresponding author:</footnote>
**Abstract** Peradectidae are Paleogene ‘opossum-like’ stem-metatherians, largely Laurasian, whose evolutionary history remains unclear. Based on new remains (mainly dental) discovered in several French localities, we carry out a comprehensive systematic revision of all early Eocene peradectids from Europe (~MP7 reference level to MP10-11 interval). We describe well-preserved specimens from Palette (Southern France, MP7-MP8+9 interval) documenting the earliest European peradectid, *Peradectes crocheti* sp. nov. This new species exhibits an interesting mosaic of characters, including plesiomorphic traits found in the North American type species, *Peradectes elegans* Matthew and Granger, 1921. Molars allocated to the strikingly ubiquitous *Peradectes crocheti* sp. nov. are found in eight additional localities from northwestern and southwestern Europe, all limited to the time interval MP7-MP8+9. Moreover, the study of unpublished material of the MP8+9 and ~MP8+9 peradectids allows us to recognize two younger coeval species (*Peradectes louisi* Crochet, 1979, and *Peradectes russelli* Crochet, 1979). Our taxonomic conclusions are supported by the first quantitative assessment of the variation in height of metatherian stylar cusps. The holotype of *Peradectes louisi* is reinterpreted, and *Peradectes mutigniensis* Crochet, 1979 appears to be a junior synonym of *Peradectes russelli*. In addition to size, the otherwise similar *Peradectes louisi* and *Peradectes russelli* can be distinguished based on subtle yet consistent differences, such as lower molar proportions. Phylogenetic analyses using a novel matrix of dental characters shed new light on the relationships among Eocene peradectids, confirming the paraphyly of *Peradectes* with respect to *Armintodelphys* and *Mimoperadectes*. Our results suggest a single dispersal from North America to Europe in the evolutionary history of peradectids, which likely occurred immediately after the Paleocene-Eocene Thermal Maximum, *Peradectes crocheti* sp. nov. being recovered as the earliest offshoot of the European clade. Scarce lower molars from the MP10 reference locality and ~MP10 localities analyzed within this constrained phylogenetic
framework reveal a trend towards shrinking of the entoconid in the European lineage
throughout the early Eocene.

**Keywords** dentition, Europe, paleobiogeography, Paleogene, Peradectidae, systematics

This article is registered in ZooBank under urn:lsid:zoobank.org:pub:CCD67F33-98A5-40DC-B1C1-C1D1F549FA96

**Introduction**

Peradectidae are an assemblage of extinct and small Cenozoic stem-metatherians with a superficially ‘opossum-like’ unspecialized tribosphenic dentition (e.g., Ladevèze et al. 2020). They have long been distinguished based on plesiomorphic dental features within Metatheria (but see Williamson et al. 2012, 2014), and were likely arboreally adapted (e.g., Szalay 1994; Kurz 2005; Rose 2012; Rose et al. 2012). Most of their occurrences are from North America (earliest Paleocene to early Oligocene; e.g., Korth 2008, 2018) and Europe (early to possibly earliest middle Eocene; Crochet 1979, 1980b; Kurz 2007). Putative peradectid isolated molars have also been identified in South America (early Paleocene to early Eocene; Sigé 1971, 1972; Marshall and Muizon 1988; Muizon 1991; Tejedor et al. 2009), Asia (early Oligocene to Early Miocene; Ducrocq et al. 1992; Mein and Ginsburg 1997; Storch and Qiu 2002; Ni et al. 2007) and Africa (early Eocene; Crochet 1986; Crespo and Goin 2021; but see Hooker 1998: p. 443; Gunnell 2010). Although Peradectidae is a key metatherian taxon for paleobiogeographic reconstructions, controversies remain about its monophyly and phylogenetic affinities (e.g., Horovitz et al. 2009; Williamson et al. 2012; Maga and Beck 2017; Ladevèze et al. 2020; Beck 2023). This is particularly true due to the apparent uniformity of their dental morphology, and because early Eocene European peradectids, last studied in detail by Crochet (1977a, 1977b,
1979, 1980a, 1980b), have not been revised in light of new material nor included in
phylogenetic analyses.

Two genera first defined in North America are hitherto recognized in Europe, namely *Peradectes*, with at least three species, mostly known from French localities (Crochet 1980b), and possibly *Armintodelphys*, with one species from Belgium (Smith and Smith 2013). *Peradectes* is a genus of uncertain monophyly spanning the whole of the Paleocene and Eocene epochs (e.g., Krishtalka and Stucky 1983b; Williamson et al. 2012). The earliest reports of European *Peradectes* were made by Crochet (1977a, 1979, 1980b), who recognized up to four species from early to late early Eocene localities of France, mainly represented by isolated molars. Crochet (1979) also coined the tribe *Peradectini*, later elevated to a familial rank (Reig et al. 1985, 1987). Contrary to the fossil record of North America, peradectids and metatherians as a whole are absent from the Paleocene of Europe (Gheerbrant 1991). Peradectids first appeared in Europe in various localities following the Paleocene-Eocene Thermal Maximum (PETM), which are somewhat younger than the reference level MP7 (earliest Eocene; BiochroM'97 1997) but older than MP8+9 and ~MP8+9 (i.e., MP7-MP8+9 interval) (Crochet 1980b; Godinot 1981; Russell et al. 1988; Marandat 1991; Louis 1996; Hooker 2010, 2020; Smith et al. 2011). Consequently, the dispersal of peradectids from North America to Europe after the PETM was formally proposed by Hooker (1998: p. 434, 2015: fig. 8), but is still blurred by the lack of identified morphological intermediate(s) between representatives of the two continents.

In this study, we report fossils of a new early European peradectid species, *Peradectes crocheti*, collected after recent excavations (2017-2019) in Palette (Provence, southern France), a locality within the MP7-MP8+9 interval (Cojan et al. 2000; Marandat et al. 2012; Yans et al. 2014), although initially considered close to MP7 (Godinot et al. 1987). These new specimens represent the most comprehensive assemblage attributed to *Peradectes* since the definition of
its type species (Matthew and Granger 1921; Simpson 1928, 1935). We identified *Peradectes crocheti* sp. nov. in all MP7-MP8+9 interval localities that have yielded rare peradectid specimens (e.g., Fordones and Meudon). Moreover, the characterization of the morphology of the earliest European peradectids allowed us to carry out a revision of the species from the middle early Eocene (MP8+9 and ~MP8+9) of the Paris Basin, first described by Crochet (1979). This includes the referral of numerous unpublished dental specimens from the MP8+9 reference locality (Avenay) and various ~MP8+9 localities (Mutigny, Condé-en-Brie, Sables de Brasles, Sézanne-Broyes and Saint-Agnan). The greater abundance of remains of these later occurring species enabled us to account for intraspecific variation, and to refine their diagnostic characters and taxonomic status. In order to provide a more complete revised picture for the early Eocene, we also discuss the taxonomic status of the rare MP10 and ~MP10 peradectids. The phylogenetic position of the European taxa within Peradectidae was finally assessed via a phylogenetic analysis including most late Paleocene – middle Eocene Peradectidae sensu stricto, to provide formal insights on the origin of its European representatives, and on the Laurasian evolution of peradectids.

# Material and methods

## Provenance of the specimens

Most of the material from the fossiliferous locality of Palette (MHN.AIX.PV.), including the dental rows assigned to *Peradectes crocheti* sp. nov., was found after the field expeditions conducted between 2017 and 2019 by some of us (GB, EG and RT). The material was isolated after processing the sampled sediment by careful acid etching, use of screen-washing, and sorting methods. This is the first occurrence of a peradectid metatherian in the Palette fauna, which adds to the 16 previously listed mammalian species in this locality (Table 1), most of
**Table 1** Updated list of mammals from Palette (Provence; MP7-MP8+9 interval, ~55 Ma). Attributions up to family rank are from Godinot et al. (1987), Russell and Godinot (1988), Marandat (1991), Rose et al. (1994), López-Martínez et al. (2006), Hooker and Russell (2012), Marandat et al. (2012), Hand and Sigé (2017), Boivin et al. (2018), Solé et al. (2018, 2023), Vautrin et al. (2020), Vianey-Liaud and Marivaux (2021), and this study.

**Metatheria**

Peradectidae
*Peradectes crocheti* sp. nov.

Herpetotheriidae
*Peratherium constans*

**Eulipotyphla**

Nyctitheriidae
*Saturninia* sp. or *Leptacodon* sp.

**Order incertae sedis**

Adapisoricidae
*gen. and sp. indet.*

**Chiroptera**

?Archaeonycteridae
*gen. and sp. indet.*

**Pantolesta**

Paroxyclaenidae
*Merialus martinae*

**Plesiadapiformes**

Paromomyidae
*Arcius rougieri*

**Primates**

Notharctidae
*Donrussellia magna*

**Rodentia**

Ischyromyiformes, family *incertae sedis*
*Corbarimys cezannei*
*gen. and sp. indet.*

**'Condylarthra'**

Hyopsodontidae
*Lessnessina praecipuus*

Louisinidae
*Paschatherium plaziati*

**Mesonychia**

Mesonychidae
*Hyaenodictis rougierae*

**Hyaenodonta**

Hyaenodontidae
*Parvagula palulae*

**Artiodactyla**

Diacodexeidae
*Diacodexis* cf. *gigasei*

**Perissodactyla**

Lophiodontidae
*Lophiaspis maurettei*

Equoidea, family *incertae sedis*
*Cymbalophus hookeri*

which correspond to eutherian taxa that have been extensively studied (Godinot 1984, 1992; Godinot et al. 1987; Russell and Godinot 1988; Marandat 1991: 110; Ramdarshan et al. 2015;
Solé et al. 2015, 2018, 2023; Boivin et al. 2018; Orliac et al. 2018; Vautrin et al. 2020; Vianey-Liaud and Marivaux 2021). *Peradectes crocheti* sp. nov. represents the first addition to the alpha diversity of the mammalian fauna of Palette (excepting an unidentified rodent species; Marandat et al. 2012: p. 427) since the establishment of the first and single faunal list of Godinot et al. (1987) for mammals, although the taxonomic status or classification of some taxa have changed (Table 1).

The new peradectid specimens from Palette are permanently stored at the Muséum d'Histoire Naturelle of Aix-en-Provence (France). Other studied specimens are also the result of past or recent long and fruitful field research. The specimens from Meudon, Rians, Soissons, Avenay, Condé-en-Brie, Mutigny, Sables de Brasles, Sézanne-Broyes, Saint-Agnan, Cuis and Grauves (MNHN.F.) are housed in the paleontological collections of the Muséum National d'Histoire Naturelle (Paris, France). Specimens from Fordones, Fournes, one specimen from Palette, one specimen from Coulondres, two specimens from Mas de Gimel, and one specimen from Vielase, are housed at the University of Montpellier (France). The two specimens from Sotteville-sur-Mer are housed at the Royal Belgian Institute of Natural Sciences (Brussels, Belgium). The single specimens from Croydon and Abbey Wood are housed at the Natural History Museum, London (England), and were studied via photographs available in the literature. Casts of North American peradectids (AMNH, UCMP, UM, USNM) were used for comparisons with European peradectids. We accounted for intraspecific variation in the descriptions of dental material based on comparisons with the variation ranges of morphological characters known in other marsupialiforms, such as *Pucadelphys* (Ladevèze et al. 2011) and *Peratherium* (Ladevèze et al. 2012).

## Ages of the localities
The nine studied fossil-bearing localities of the MP7-MP8+9 interval are younger than the PETM (MP7). Four of them are located in southern France ( Palette and Rians, in Provence; Fordones, in Corbières; Fournes, in Minervois), the five others being in northern France ( Meudon, Île-de-France; Soissons, Aisne; Sotteville-sur-Mer, Normandie) and England ( Abbey Wood and Croydon, London) (Fig. 1a). Palette and Fordones, correlated in age with Le Clot locality (Corbières) based on evolutionary stages of mammalian lineages (Marandat et al. 2012), are considered by chemostratigraphic analysis approximately 1 myr younger than the MP7 reference locality of Dormaal (Belgium; ~56 Ma), and hence close to 55 Ma (Yans et al. 2014). Fournes (Minervois) is positioned by marine correlation and chemostratigraphic analysis just after the ETM2 (~54 Ma), closer to the MP8+9 than to the MP7 reference level (Noiret et al. 2016: fig. 2), and is probably coeval with the Wasatchian Wa-5 mammal fauna (Noiret et al. 2016: p. 477). Rians (Provence) is a locality possibly similar in age to Fournes, based on mammalian biostratigraphy (Marandat et. 2012; Noiret et al. 2016; Philip et al. 2017: p. 328). Fournes and Rians are the youngest faunas of the MP7-MP8+9 interval here studied. The age retained for Abbey Wood (London; biozone PE III of Hooker 1996) is 55.12 Ma (Hooker 2010), and therefore older than Fournes and Rians. Sotteville-sur-Mer is probably the oldest of all the MP7-MP8+9 localities studied. It is probably older than Soissons and Meudon (both in biozone PE II; Hooker 1996) according to Smith et al. (2011), and was thus assigned to biozone PE II (Hooker 2015). These two northern localities are considered pene-contemporaneous with the southern localities of Palette and Fordones (Marandat et al. 2012). Altogether, except Fournes and Rians, the MP7-MP8+9 interval localities are bracketed between the PETM and the Eocene Thermal Maximum 2 (ETM2), and are closer to MP7 than to MP8+9 given the approximate age of Mutigny, the oldest ~MP8+9 locality (see below).
<figure><img src="image_1.png" /></figure>

**Fig. 1** Geographical and temporal positions of the studied MP7-MP8+9 interval and ~MP8+9 faunas (including that of Avenay, the MP8+9 reference locality) that yielded peradectid remains. **a.** paleogeographic map of France and England during the early Eocene (modified from Marandat et al. 2012) with the position of studied localities. *, the Saint-Agnan locality is more likely in the MP8+9-MP10 interval rather than MP8+9 or MP10. **b.** schematic relative temporal positioning of MP7-MP10 reference levels, PETM and ETM2, and selected MP7-MP10 localities mentioned in the main text. The dashed parts of the temporal extension indicate uncertain temporal gaps. The age of localites in bold have been discussed via chemostratigraphic data (Cojan et al. 2000; Steurbaut et al. 2003; Noiret et al. 2016).

Five localities MP8+9 or ~MP8+9 in age from the Paris Basin (northwestern Europe) are here studied, namely Mutigny (Marne), Avenay (MP8+9 reference level, Marne), Condé-en-Brie (Aisne), Sables de Brasles (='Gland', Aisne) and Sézanne-Broyes (Marne) (Fig. 1a). Mutigny
(biozone PE IV) is the oldest ~MP8+9 locality considered (slightly older than MP8+9), with an approximate age of 54 to 52 Ma (Neal 1996; Duprat 1997). Avenay, Condé-en-Brie and Sables de Brasles (biozone PE V) must be slightly younger than Mutigny according to the study of metatherian and rodent lineages (Schmidt-Kittler et al. 1987; Escarguel 1999), and slightly older than Sézanne-Broyes (also in PE V; Hooker 1996) (Louis 1970; Louis and Laurain 1983). Saint-Agnan (Aisne), of which the attribution of the single peradectid specimen is here revised, has been alternatively placed in the MP8+9 and MP10 reference level, depending on authors (e.g., Bronnert and Métais 2023 vs BiochroM'97 1997: table 1). The Saint-Agnan fauna is probably younger than MP8+9, and might be positioned in the MP8+9-MP10 interval according to most authors (Louis and Laurain 1983; Lecomte 1994; Escarguel 1999; Solé et al. 2018). Finally, rare localities from the late early Eocene have yielded peradectids (see Discussion), notably Grauves and Cuis (MP10, Paris Basin, BiochroM'97 1997), Mas de Gimel (~MP10; Vianey-Liaud et al. 2024) and Vielase (?MP10-11, Quercy, Legendre et al. 1992). The localities of Grauves and Cuis have long been considered distinct (Stehlin 1940: p. 293; Rat 1965: p. 251), but the two names may designate the same locality (e.g., Escarguel 1999).

## Dental nomenclature

For upper molars, the nomenclatures and homologies of Williamson et al. (2014: fig. 3), Goin et al. (2016: fig. 1.2) and Muizon and Ladevèze (2022: fig. 1) are mostly followed. Following these studies, the internal edge of all teeth (upper and lower), including premolars and canines, is designated as lingual, and the external edge as labial. The anterior and the posterior edges are designated as mesial and distal, respectively (Fig. 2b, 2c). An updated nomenclature for upper molars (Fig. 2b) includes the following structures. The paraconular cristae are termed pre- and postparaconular crista and the metaconular cristae are termed pre- and postmetaconular crista, as in Muizon and Ladevèze (2022). The postparaconular and the premetaconular cristae are the
internal conular cristae. The term 'talon' designates the part of the crown which is lingual to the bases of the paracone and metacone (e.g., Marshall and Muizon 1995: fig. 5; Oliveira and Goin 2011: fig. 2); it includes the protocone, paraconule, metaconule, the conular cristae, the trigon basin (= protofossa of Crochet 1980b: fig. 2, or Gheerbrant 1992: fig. 1B), and the lingual part of the paracingulum. In occlusal view, a concave distal margin between the talon and stylar shelf is called a 'distal emargination' of the molariform tooth outline. The 'stylar cusp E' (not figured) corresponds to the labial termination of the postmetacrista, which is similar to a stylar cusp in labial view. The metastylar wing (e.g., Rothecker and Storer 1996; = 'metastylar lobe', e.g., Williamson and Taylor 2011; and 'metastylar area', e.g., Muizon and Ladevèze 2022) is the distolabial corner of the stylar shelf of molariform teeth, distal to the ectoflexus. It encompasses the stylar cusp D and the postmetacrista. The parastylar wing is the mesiolabial corner of the stylar shelf, mesial to the ectoflexus. It encompasses the stylar cusp A and the labial part of the paracingulum.

We propose a terminology of lower molars accounting for the dental peculiarities of European peradectids (Fig. 2c). We use the term ‘protocristid’ (= protolophid) as in Muizon and Ladevèze (2022), which encompasses the distolingual cristid of the protoconid (= postprotocristid) and the labial cristid of the metaconid; the latter was often considered as a ‘postmetacristid’ in metatherians (e.g., Goin et al. 2016). The metaconid of peradectids and other marsupialiforms, such as Glasbius (Williamson et al. 2014: fig. 3) and herpetotheriids (Wessels et al. 2024: fig. 1), also bears a sharp distal cristid in addition to this ‘postmetacristid’ (Fig. 2c). In the dental terminology of Williamson et al. (2014: fig. 3), the ‘postmetacristid’ of Goin et al. (2016) has thus been interpreted as the premetacristid and the distal cristid of the metaconid as the postmetacristid. However, some deltatheroidans (such as Oklatheridium) and early marsupialiforms (such as Arcantiodelphys) can have a mesial cristid of the metaconid (Averianov 2015: fig. 5), termed the ‘premetacristid’ (Vullo et al. 2009: p. 19912, fig. 2A).
Thus, the cristids described as the premetacristid and postmetacristid in Vullo et al. (2009) and Williamson et al. (2014) are not homologous. In order to avoid confusion and to maintain structural homology among therians, the labial cristid of the metaconid is here named the ‘protocristid lingual segment’, a term derived from the terminology of primitive tribosphenic molars (e.g., Van Valen 1966: fig. 1; Crochet 1980b; Gheerbrant 1992). The distal cristid of the metaconid is named the ‘postmetacristid’ due to its position (a cristid which is itself possibly not homologous with the ‘distal metacristid’ of some stem therians, see Martin et al. 2023). In the same way, the paracristid is subdivided into the preprotocristid, on the mesiolingual edge of the protoconid, and the ‘paracristid lingual segment’ on the labial edge of the paraconid. The ‘paracristid lingual segment’ is not a widely-used name in studies of metatherian molars. The labial cristid of the paraconid has been alternatively named the ‘postparacristid’ (e.g., Abello 2013: fig. 2D; Goin et al. 2016), or the ‘preparacristid’ (e.g., Ladevèze et al. 2012: p. 259; Muizon et al. 2018), by various authors. As before, in some deltatheroidans and stem marsupialiforms, a distal cristid of the paraconid (= postparacristid) lingually closes the trigonid basin, together with the premetacristid (Vullo et al. 2009: p. 19912, fig. 2A; Averianov 2015: fig. 5). Moreover, some peradectid molars studied here have a small cristid on the paraconid keel, mesial to the paraconid, which is the preparacristid. In lingual view, the lingual opening of the trigonid basin (= prefossid in Crochet 1980b and Gheerbrant 1992) refers to the opening between the paraconid and metaconid, and the lingual opening of the talonid basin (= postfossid) refers to the opening between the metaconid and the entoconid. The lingual opening between the entoconid and the hypoconulid is referred to as the entoconid – hypoconulid notch.

The entocristid of Crochet (1980b), Gheerbrant (1992), and Muizon and Ladevèze (2022) is named the pre-entocristid, as in Goin et al. (2016), because a small postentocristid often occurs in the entoconid – hypoconulid notch of peradectids (Fig. 2c). When present, the postentocristid is a true cristid; it differs from the ‘hypoconulid-entoconid talonid fold’ present in some
herpetotheriid and didelphid species (Hooker et al. 2008: p. 644, pl. 1, figs. 1-2) in being observable even on unworn lower molars. The distolingual cristid of the hypoconid is designated as the postcristid following Crochet (1980b) and Gheerbrant (1992), instead of the posthypocristid, because it generally implicitly includes the posthypocristid and also the unnamed labial cristid of the hypoconulid, which occurs in some peradectid specimens (Fig. 2c). In occlusal view, a concave labial margin between trigonid and talonid is called a labial emargination of the molar outline (not illustrated in Fig. 2c).

**Orientation of molariform teeth for descriptions and measurements**

Clemens (1966: p. 4) was the first author to stress the need for an orientation method of metatherian molariform teeth ensuring consistent descriptions and measurements. The repeatability of measurements and descriptions of the upper molars and deciduous premolar has been achieved using the paracone – metacone axis for orientation. This method was efficiently used by several authors working on upper molars of metatherians since the work of Clemens (1966) (see Rose 2010: p. 561).

Regarding metatherian lower molars, the orientation used for descriptions and/or measurements differ between authors and was often unspecified. The methodology of Crochet (1980b) and Korth (1994) to measure lower molars is not detailed, although their drawings (e.g., Crochet 1980b: figs. 3, 10; Korth 1994: fig. 1) suggest the chosen orientation of lower molars allowed their maximum length to be measured. This protocol has been used by other workers for measurements of small mammal teeth in general, and is still employed for metatherian lower molars in recent studies (e.g., Muizon and Ladevèze 2022). However, it does not allow to locate structures properly on the occlusal surface of lower molars and to define characters consisting in precise relative position of structures, because the chosen orientation may vary between
<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /><figcaption>**Fig. 2** Molar nomenclature and measurement methods used in this study, based on schematic drawings of peradectid molars. **a.** upper molar in labial view, with the two methods employed for estimations of the heights of stylar cusps C and D: (1) position of the most ventral point of the [stylar cusp C – stylar cusp D] mesiodistal extension parallel to the crown base, and (2) absolute basal height of stylar cusps C and D, with a ratio calculated from the two values. **b.** upper molar in occlusal view. **c.** lower molar in occlusal view. The measurement methods for length and width of lower molars are illustrated in grey. The dashed lines concern depressions on the occlusal surface (**b** and **c**). Cusps (except stylar cusps) / cuspids and conules are indicated</figcaption></figure>
in bold text, crests / cristids are in full text, and cingula / cingulids, emarginations of the crown and basins are in italics. The molar nomenclature is mainly derived from Crochet (1980b), Gheerbrant (1992), Williamson et al. (2014), Goin et al. (2016), and Muizon and Ladevèze (2022). Abbreviations: **st A**, stylar cusp A; **st B**, stylar cusp B; **st C**, stylar cusp C; **st D**, stylar cusp D. Schematic drawings are not to scale

specimens and dental loci. Lower molars have tentatively been precisely oriented using the paraconid - entoconid apices axis (Clemens 1966: p. 4) or the metaconid – entoconid apices axis (Lillegraven 1969: p. 16, fig. 5; Gheerbrant 1992: p. 80). On the lower molars of most metatherians, including herpetotheriids and the earliest *Peradectes* species *Peradectes minor* Clemens, 2006 (see also Williamson et al. 2012), and *Peradectes coprexeches* Williamson & Taylor, 2011, the paraconid, the metaconid, and the entoconid are aligned. As a consequence, the orientation of the lower molars for most Cenozoic metatherians varies little, no matter which lingual cuspid axis is chosen as reference. We noted that the relative configuration between the trigonid and talonid cuspids is different in most peradectids, such as the type species *Peradectes elegans* Matthew & Granger, 1921 (Gazin 1956: pl. 2, fig. 6; Krishtalka and Stucky 1983b: fig. 3), *Peradectes protinnominatus* McKenna, 1960 (see also Bown 1979: fig. 40b, Rose 1981: fig. 8A, Gingerich and Smith 2006: fig. 26b), all European peradectid species (this study), and the genus *Armintodelphys* (Krishtalka and Stucky 1983a: fig. 5; Krishtalka and Stucky 1984: fig. 4A), where the entoconid, pre-entocristid and postentocristid are oblique with respect to the mesiodistal axis. Such a 'curved talonid lingual edge' was first noted in a description of some peradectid lower molars by Smith and Smith (2013: p. 305), but it is not exclusive to the species included in *Armintodelphys* by these authors. A curved talonid implies that the paraconid, metaconid and entoconid are often not aligned on the lower molars of the concerned taxa. The entoconid apex is either more labial than the paraconid and metaconid apices if these two trigonid cuspids are chosen to form the reference axis for orientation, or the metaconid apex is
lingually deflected if the paraconid and entoconid apices are chosen as reference. The entoconid
has been highlighted as one of the most variable structures of lower molars of extant and extinct
metatherians, especially for the last lower molar (e.g., Martin 2005: fig. 4; Ladevèze et al. 2012:
p. 256). We consequently regard the use of the paraconid-metaconid apices axis as a reference
as the best way to produce reliable measurements (Fig. 2c) and dental descriptions (including
the coding of dental characters) of tribosphenic metatherian material, and we thus use it in this
study for both purposes.

Maximum values were retained for the mesiodistal length, parallel to the paraconid – metaconid apices axis, and the labiolingual width, perpendicular to the paraconid - metaconid apices axis.
All measurements are given with an accuracy of 0.01 millimetres. Measurement values for molars are presented in Online Resource 1: Tables S1-S3. Unbiased coefficients of variation (CV) were calculated to compare variability between dental measurements. Statistical treatment of the data was carried out using the R software environment (R Core Team 2020; v.4.0.2). In order to statistically compare mean molar proportions between *Peradectes louisi* Crochet, 1979, and *Peradectes russelli* Crochet, 1979 (at a 5% alpha risk), Welch's unequal variances *t*-test were performed (as recommended in Ruxton 2006). The measurement method for premolars is the one of Clemens (1966: p. 4). Mandibular heights were taken on the lingual aspect of the mandible, from its ventral edge to the adjacent dorsal molar alveolus. All measurements were made on screenshots of volume rendering or surface models of the scanned specimens (see below), using Avizo® 9.3 (Thermo Fisher Scientific-FEI) measurement tools, and/or via photographs of specimens taken with an optical stereomicroscope (Leica M 205C) connected to a camera (Leica DFC 420C), using tools of the Leica Application Suite v. 4.13. Body mass estimates were calculated using the predictive equation for M3 length (the most accurate predictor, as indicated by R² values) from the ‘pooled Didelphidae and Dasyuridae’ (i.e., dentally conservative marsupials) dataset of Gordon (2003: fig. 7).
Evaluation of the heights of stylar cusps

In studies directly addressing stylar shelf intraspecific variation among extant and extinct
metatherian taxa, no clear pattern of variation of the relative sizes of the stylar cusps C and D
for a given molar locus of a given species was noted, although the stylar cusps C and D are
known to vary in absolute size (confounded with height by most authors), morphology, and
position within a comprehensive series of metatherian teeth (e.g., Storer 1991: table 6; Johanson
1994: fig. 2; Eberle and Storer 1995: p. 791; Hershkovitz 1997: fig. 19; Flores and Abdala 2001:
p. 105; Hayes 2005: fig. 4; Korth 2018; but see Kihm and Schumaker 2015: p. 105). Few authors
formally used the sizes of stylar cusps to distinguish metatherian species or genera (e.g.,
Crochet 1979, 1980b; Marshall et al. 1990: tables 1-2; Korth 1994: table 2; Muizon and Lange-
Badré 1997: table 1), and in particular peradectid species (Williamson and Taylor 2011).
Although the vast majority of the fossil record of metatherians is composed of molars, there has
not been a procedure to objectively decide which one of two given stylar cusps on one specimen
is higher, nor an attempt to quantify the size of these stylar cusps.

For this purpose, we here propose two methods to evaluate the relative height of the stylar
cusps, examplified by the stylar cusps C and D, based on labial views of the upper molars (Fig.
2a). One can first find the most ventral point of the [st. C – st. D] mesiodistal extension parallel
to the base of the crown (Fig. 2a [1]). In previous works, the relative height of the stylar cusps
was probably implicitly estimated in this way. This method is used in the Systematic
Paleontology section of this study (in differencial diagnoses of species and comparative
descriptions).

Second, the absolute basal height of a stylar cusp corresponds to a measurement performed (in
mm, also in labial view) perpendicular to a baseline drawn between the most mesial and distal
points of this stylar cusp, that are the most dorsal (i.e the closest to the crown base). The
measurement is taken between the baseline of the stylar cusp and its most ventral point (i.e., the
stylar cusp tip) (Fig. 2a [2]). The measurements of the absolute basal heights of the stylar cusps
C and D were here conducted on stylar shelves with limited and homogeneous wear, of upper
molars of the three European peradectids *Peradectes crocheti* sp. nov., *Peradectes louisi* and
*Peradectes russelli*. For each available specimen, a ratio of the absolute basal height of the
stylar cusp C to the absolute basal height of the stylar cusp D was calculated for comparative
purposes, because one out of the three species studied (*Peradectes russelli*) is larger than the
others. This second method allows to precisely quantify the variation in height of the stylar
cusps. It is used in the Results section of this study, a posteriori of taxonomic attributions.
Measurements of stylar cusp heights and ratio values are available in Online Resource 1: Table
S4. Non-parametric Wilcoxon-Mann-Whitney tests were performed with the R software
environment on species pairs (the normality assumption was not met for the st. C / st. D heights
ratio values of *Peradectes crocheti* sp. nov. [Shapiro-Wilk normality test; W = 0.892, P =
0.042]), in order to define between which species the sum rank of the ratio values of the absolute
basal height of st. C / st. D differ significantly (at a 5% alpha risk). Parametric Welch's *t*-test
were alternatively performed on the same species pairs. The R package *ggplot2* (Wickham
2016) was employed to produce boxplots of absolute basal stylar cusp heights ratio values, as
well as bivariate diagrams of length x width of molars.

**High-resolution x-ray microtomography**

Illustrated specimens were scanned using a µ-CT-scanning station EasyTom 150 / Rx Solutions (Montpellier RIO Imaging, ISE-M, Montpellier, France). Images of these specimens were achieved using the ‘snapshot’ tool of Avizo® 9.3. The segmentation of the cheek teeth and
dentary of MHN.AIX.PV.2017.6.8 (scanned with a resolution of 6.5 µm) was performed with
the Avizo® 9.3 'blow' tool, in order to clarify the morphology and positioning of peradectid
premolars on the dentary. The segmentation of the holotype of *Peradectes crocheti* sp. nov.,
MHN.AIX.PV.2018.26.14 (scanned with a resolution of 5.3 µm), required the 'threshold' tool.
An attempt was made to position the segmented fragments of the maxilla
MHN.AIX.PV.2018.26.14 in anatomical position, using the MorphoDig® software (Lebrun
2018), with comparison to the complete maxilla of 'Peradectes' from Messel (Kurz and
Habersetzer 2004: figs. 2-3) and accounting for the typical crushing of fossil bones from Palette,
which may have suffered from synsedimentary compression (e.g., Vautrin et al. 2020: figs. 3-
4). The 'threshold' tool was also used for segmenting the isolated M3 MHN.AIX.PV.2017.6.7
and MNHN.F.SN18, as a way to numerically assemble the lingual and labial halves of the
former, and extract sediment from the trigon basin of the latter.

Intrafamilial phylogenetic analysis

The aim of the phylogenetic analysis was to unravel relationships within part of Peradectidae
sensu stricto, with a focus on European representatives. Fourteen metatherian taxa were coded
for this purpose. The outgroup is composed of two stem-metatherian species, the deltatheroidan
(= non-marsupialiform metatherian) *Deltatheridium pretrituberculare* Gregory & Simpson,
1928, and the stem-marsupialiform *Asiatherium reshetovi* Trofimov & Szalay, 1994 (taxon data
used for coding are in Online Resource 2). Among marsupialiforms, *As. reshetovi* is usually
found to be more basal than Peradectidae (e.g., Williamson et al. 2014; Ladevèze et al. 2020;
Muizon and Ladevèze 2022; but see Maga and Beck 2017: fig. 38 vs fig. 39). All late Paleocene
– middle Eocene species of Laurasian Peradectidae sensu stricto were included in the ingroup
(12 taxa), with the exception of *Mimoperadectes houdei* Horovitz, Martin, Bloch, Ladevèze,
Kurz & Sánchez-Villagra, 2009, and *M. sowasheensis* Beard & Dawson, 2009, because we mainly aimed to resolve phylogenetic relationships of *Peradectes* and *Armintodelphys* species (both genera having been recognized in Europe and North America before this study), and because *M. sowasheensis* is known by a single isolated upper molar (Beard and Dawson 2009).

*Mimoperadectes* is thus only represented in this analysis by its type species, *Mimoperadectes labrus* Bown & Rose, 1979. The 11 remaining taxa of the ingroup belong to *Peradectes* and *Armintodelphys*. *Peradectes pauli* Gazin, 1956, was here not considered as a valid species, following Kurz (2007: p. 44) and Williamson et al. (2012); it is probably a junior synonym of the type species *Peradectes elegans* (Williamson et al. 2012: p. 631). Consequently, dental material previously ascribed to *Peradectes pauli* (Gazin 1956; Krishtalka and Stucky 1983b) was used here for the coding of *Peradectes elegans*, following Williamson et al. (2012: supplemental material, appendix 1). The ingroup taxa, along with their precise temporal extension (all occurring in the Eocene) and the nature of data used for their coding, are listed in Online Resource 2.

The fossil record of peradectids comprising predominantly isolated cheek teeth and incomplete dental rows, our dataset is composed of 37 characters which concern only the postcanine dentition. Among them, three are related to the morphology of lower premolars (characters 1 to 3), 18 to lower molars (characters 4 to 21) and 16 to upper molars (characters 22 to 37). The characters of these three subpartitions relate to the occlusal, lingual and labial morphology of cheek teeth. Approximately half of the characters (18) were either directly taken (8), or modified in their spelling or character states (10), from characters of the data matrices of Williamson et al. (2014) and Muizon and Ladevèze (2022). The others (19 characters) are here newly defined to reflect substantial differences observed among the dentition of peradectid taxa.

The only two multistate characters (3 and 34) were unordered because we did not hypothesize a hierarchical transformation for them (i.e., getting from state 0 to state 2, or vice versa, does
not necessarily involve an intermediate state 1). All characters were unweighted. Ranges of
measurements were coded onto four new discrete characters (4, 5, 14 and 22) by gap coding.
The characters implying comparisons of length and/or width between molar loci (4, 6, 22) were
coded using available means of dental measurements if these loci are known only by isolated
molars for the concerned taxon. Frequencies of observation of character states in our sample
were employed in four new characters (11, 31, 36 and 37). We paid attention to avoid cases of
similar characters being repeatedly scored at successive molar loci since these may highly
covary (serial homologs, see Billet and Bardin 2019). Thus, although 32 out of 37 characters
are restricted in their application to given molar loci because of their spelling, only two
characters (10 and 11) may represent serial homologs at successive molar loci (however, their
coding differs greatly). The illustration of most of the new characters is available in Online
Resource 3: Figs. S1-S12. The numbers in superscript used after a character number in the main
text and figures denote the character state.

The new character-taxon matrix (Online Resource 4) was edited with Mesquite v. 3.61
(Maddison and Maddison 2019). The parsimony analysis was performed with PAUP* v.
4.0a169 (Swofford 2002), through the Heuristic search method, with a random step-wise
addition (1000 replications with randomized input order of taxa) and tree-bisection-
reconnection (TBR) branch swapping options. Intraspecific variation was accounted as
polymorphic states in PAUP* (noted ‘x&y’ in Mesquite and ‘(xy)’ in PAUP*). Non-applicable
states have been coded ‘-‘ in Mesquite. The robustness of each clade was evaluated with Bremer
indices (BI, Bremer 1994), going up to five additional steps. A second analysis, with the same
parameters, was run with a new scoring of characters requiring frequencies of observation to
be scored (characters 11, 31 and 36). The frequencies were replaced by polymorphism when
needed. Character 37 was additionally scored as such in a third analysis. The changes in the
spelling of characters and scoring, and the result of the second and third analysis are presented
in *Online Resource 5*. A fourth analysis with the same scoring as the previous one (i.e., polymorphism included in the scoring of the characters 11, 31, 36 and 37) was performed, but with implied weighting instead of unweighted characters, with the Goloboff constant (k) value = 3 (as recommended by Goloboff 1993) in order to downweight homoplastic characters. Finally, the multistate characters (3 and 34) were ordered in a fifth analysis, which is otherwise identical to the first one.

**Abbreviations**

**Institutions and localities:** AMNH, American Museum of Natural History, New York; MHN.AIX.PV., Muséum d'Histoire Naturelle d'Aix en Provence, collection from Palette; MNHN.F., Muséum National d'Histoire Naturelle, Paris, fossil collections; MNHN.F.Av, Avenay; MNHN.F.CB, Condé-en-Brie; MNHN.F.GL; Sables de Brasles (= ‘Gland’); MNHN.F.Gr, Grauves; MNHN.F.Me, Meudon; MNHN.F.Mu, Mutigny; MNHN.F.Ri, Rians; MNHN.F.SN, Soissons; MNHN.F.STA, Saint-Agnan; MNHN.F.SZ, Sézanne-Broyes; NHMUK.PV.M, Natural History Museum, London, UK, palaeontological vertebrate collections; UCMP, University of California Museum of Paleontology, Berkeley; UM, University of Michigan Museum of Paleontology; UM-AV-SK, Avenay, Université de Montpellier (France), Schmidt-Kittler collection; UM-BRT, Le Bretou, Université de Montpellier; UM-CLR, Coulondres, Université de Montpellier; UM-FDN, Fordones, Université de Montpellier; UM-FNR2, Fournes 2, Université de Montpellier; UM-MGL, Mas de Gimel, Université de Montpellier; UM-PAT, Palette, Université de Montpellier; UM-VIE, Vielase, Université de Montpellier; USNM, United States National Museum.

**Other abbreviations:** L, maximal mesiodistal length; st., stylar cusp; W, maximal labiolingual width.
**Reference levels and biozones:** MP, Mammal Paleogene reference level (BiochroM'97 1997);
~MP is used when the designated locality/localities is/are similar in age to the reference locality
(i.e., possibly slightly older or younger); PE, Paleocene-Eocene biozone (Hooker 1996).

**Dental loci:** C, upper canine; c, lower canine; dPX, upper deciduous premolar; dpX, lower deciduous premolar; MX, Xth upper molar; mX, Xth lower molar; PX, Xth upper premolar; pX, Xth lower premolar.

**Systematic Paleontology**

Mammalia Linnaeus, 1758

Metatheria Huxley, 1880

Marsupialiformes Vullo, Gheerbrant, Muizon & Néraudeau, 2009

Peradectidae Crochet, 1979

*Peradectes* Matthew & Granger, 1921

**Type species:** *Peradectes elegans* (see Krishtalka and Stucky 1983b; Fox 1983), early Tiffanian (middle Paleocene) to early Wasatchian (early Eocene).

*Peradectes crocheti* sp. nov.

LSID urn:lsid:zoobank.org:act:DDB4D655-E26D-46AA-96BA-192DB23B61D4

Figures 3, 4, 5, 6, 7, 8

1980b *Peradectes louisi* Crochet; Crochet: p. 39-42 (in part).

1981 *Peradectes louisi* Crochet; Godinot: p. 51-52, pl. 1, fig. 1 (no fig. 4a; pl. 1, fig. 2) (in part).

1987 *Peratherium constans* Teilhard de Chardin; Godinot et al.: p. 283 (in part).

1988 *Peradectes* sp.; Russell et al.: p. 431.
1991 *Peradectes* sp. indet. (cf. *Peradectes* sp. indet. in Crochet 1980); Marandat: p. 66-68, pl. 1, figs. 1-2, 18 (in part).

1991 *Peratherium constans* Teilhard de Chardin; Marandat: p. 68-69 (in part).

1991 *Amphiperatherium* cf. *brabantense* Crochet; Marandat: p. 71-72 (no pl. 1, fig. 4) (in part).

1996 *Peradectes louisi* Crochet; Louis: p. 94, pl. 2, fig. 7.

2010 *Peradectes* sp.; Hooker: p. 17, fig. 8a-b.

2011 *Peradectes* sp. 2; Smith et al.: p. 18, fig. 5.18.

2020 *Peradectes louisi* Crochet; Hooker: p. 461, fig. 3F-G.

**Holotype:** MHN.AIX.PV.2018.26.14 (Fig. 3a-c), fragmentary left maxilla with C-P1, anterior root of P2, and M1-M3, housed at the Natural History Museum of Aix-en-Provence. A 3D surface model of this specimen is available on MorphoMuseum (Lebrun and Orliac 2016).

**Etymology:** Dedicated to Jean-Yves Crochet, who was the first to describe peradectids from Europe (Crochet 1977a), and who erected the tribe Peradectini (Crochet 1979), later elevated to familial rank (Reig et al. 1985, 1987).

**Nomenclatural remark:** This new species must be referred to as *Peradectes crocheti* Gernelle, 2024, following the article 50.1 and the recommendation 50A concerning multiple authors of the International Code of Zoological Nomenclature (ICZN 1999: p. 52).

**Remark on abbreviations:** We use the abbreviation ‘*Pd.*’ for the genus *Peradectes* in order to avoid confusion with species of the genus *Peratherium*, which is abbreviated ‘*Pt.*’. In fact, the type species of these genera, mentioned for comparative purposes in this study, have the same species name: *Peradectes elegans* and *Peratherium elegans* (Aymard, 1846).

**Type locality:** Palette, in Provence, France; early Eocene, MP7-MP8+9 interval, ~55 Ma.
<figure><img src="image_5.png" /><figcaption>**Fig. 3** Composite upper dental row of *Peradectes crocheti* sp. nov. from Palette (Provence; MP7-MP8+9 interval). **a-c.** MHN.AIX.PV.2018.26.14, holotype, fragmentary left maxilla with C-P1, anterior root of P2, and M1-M3 (surface model); **a.** labial (lateral) view; **b.** occlusal (ventral) view; **c.** lingual (medial) view. **d-f.** MHN.AIX.PV.2017.6.6, left P2; **d.** labial view; **e.** occlusal view; **f.** lingual view. The arrows indicating mesial and lingual directions apply to the occlusal view of M1 and M2 (**b**). Scale bar equals 1 mm.</figcaption></figure>
**Other localities:** Fordones, Fournes and Rians in southern France; Meudon, Soissons and Sotteville-sur-Mer in northern France; Abbey Wood and Croydon in England.

**Age:** Early Ypresian, known from localities younger than the reference level MP7 and older than MP8+9 (~ mammalian biozones PE II and PE III).

**Material:** Additional material from Palette: left P2 (MHN.AIX.PV.2017.6.6), mesiolabial fragment of left M1 (MHN.AIX.PV.2017.6.11), right M1 (MHN.AIX.PV.2018.26.20), left M3 (MHN.AIX.PV.2017.6.7), talon of left M3 (MHN.AIX.PV.2017.6.13), lingual fragment of left M4 (MHN.AIX.PV.2017.6.12), fragment of right dentary with alveoli of p1, and p2–m3 (MHN.AIX.PV.2017.6.8), left m1–m4 with fragments of dentary (MHN.AIX.PV.2017.6.9), left worn m3 lacking enamel (MHN.AIX.PV.2017.6.10), right worn m3 (UM-PAT-103), right astragalus (MHN.AIX.PV.2017.6.14). 3D surface models of the specimens MHN.AIX.PV.2017.6.6, MHN.AIX.PV.2017.6.7, MHN.AIX.PV.2017.6.8, MHN.AIX.PV.2017.6.9 and MHN.AIX.PV.2017.6.14 are available on MorphoMuseuM.

Material from Fordones: right M1 (UM-FDN-1, Marandat 1991: pl. 1, fig. 1), fragmentary right M1 (UM-FDN-2), right partial maxillary with fragmentary M2-M3 (UM-FDN-21), labial fragment of right M2 (UM-FDN-285), distal fragment of right M2 (UM-FDN-287), worn fragment of left M2 (UM-FDN-288), labial fragment of right M3 (UM-FDN-23, Marandat 1991: pl. 1, fig. 2), labial fragment of right M4 (UM-FDN-286), worn fragment of left M4 (UM-FDN-289).

Material from Soissons: left M1 (MNHN.F.SN76), left M3 (MNHN.F.SN18), fragment of left M3 (MNHN.F.SN78), right m1 (MNHN.F.SN121), right m3 (MNHN.F.SN2508; Louis 1996: pl. 2, fig. 7).
Material from Meudon: right worn M1 (MNHN.F.Me16079), labial fragment of right M2 (MNHN.F.Me15975), left M4 (MNHN.F.Me16084), left m2 (MNHN.F.Me16101), left trigonid (MNHN.F.Me16167).

Material from Sotteville-sur-Mer: right M3 (Smith et al. 2011: fig. 5.18).

Material from Croydon: right M2 (NHMUK.PV.M66046; Hooker 2020: fig. 3F-G).

Material from Abbey Wood: labial fragment of left M2 (NHMUK.PV.M44991; Hooker 2010: fig. 8a-b).

Material from Fournes: left M1 (UM-FNR2-1), fragment of left M2 (UM-FNR2-2). The acronym FNR2 is relative to a recent sampling of the fossiliferous level, lateral to the classic FNR locality (Marandat 1991).

Material from Rians: right m1 (MNHN.F.Ri516), left m2 (MNHN.F.Ri221; Godinot 1981: pl. 1, fig. 1).

**Differential diagnosis:** Differs from all other European peradectids (*Pd. russelli*, *Pd. louisi* and *'Armintodelphys' dufraingi* Smith & Smith, 2013) in having lower molars with: (i) a weaker, sometimes absent, labial emargination of the crown; (ii) trigonid as labiolingually wide as talonid on m3; (iii) relatively higher entoconid and hypoconulid separated by a deeper notch; and (iv) distinct postcingulid on m4. Further differs from *Pd. louisi* and *Pd. russelli* in having stylar cusp C apex as or more ventral than stylar cusp D apex on M3 (upper molars of *'Arm.' dufraingi* are unknown). Further differs from *Pd. louisi* and *'Arm.' dufraingi* in: (i) its relatively wider lower molars; and (ii) always curved instead of at least most often rectilinear postcristid. Further differs from *Pd. louisi* in having: (i) stylar cusp D labial instead of distolabial to metacone apex on M3; and (ii) stylar cusp C apex as or more ventral than stylar cusp D apex also on M1 and M2. Further differs from *Pd. russelli* in its smaller size. Further differs from
‘Arm.’ *dufraingi* notably by: (i) entoconid higher than hypoconulid on m2 and as high as hypoconulid on m3; and (ii) larger postcingulid on m2 and m3.

*Peradectes crocheti* sp. nov. differs from the North American species *Pd. elegans* (type species) and *Pd. protinnominatus* (Fig. 4) in having: (i) p3 higher than m1; (ii) stylar cusp D distolabial instead of labial to metacone apex on M1; (iii) stylar cusp B labial instead of mesiolabial to paracone apex on M3; (iv) asymmetric ectoflexus on M3; and (v) less disparity between length to width ratio of M2 and M3. Further differs from *Pd. elegans* in having: (i) m1 slightly shorter than m2; (ii) m4 shorter than m3; (iii) postcingulid that attenuates labially to the hypoconulid; (iv) stylar cusp B much larger than stylar cusp A on M3; (v) postmetaconular crista that ends lingually to the base of the metacone; (vi) less mesiodistally long talon on upper molars; and (vii) protocone strictly lingual to the paracone apex on M1 and M2.

**Comparative description**

**Remarks:** Due to its status as the oldest known European peradectid, and the relative completeness of allocated fossils, *Peradectes crocheti* sp. nov. is compared to Paleocene – Eocene North American peradectids (e.g., Fig. 4), in addition to other European species.

**Maxillary region:** The holotype MHN.AIX.PV.2018.26.14 is composed of three fragments of maxillary. The fragment bearing the canine, P1, the anterior root of P2 and part of the palate is crushed transversally (Fig. 3a-c). On the fragment bearing M1, the wide distal opening of the infraorbital foramen, with a vertical and straight distal edge, was positioned dorsally to P3 (Fig. 3a). This is congruent with the position of the infraorbital foramen in the other few peradectids in which the maxillary is known, namely *Pd. gulottai* Rose, 2010, *M. houdei* (Horovitz et al. 2009: fig. 2B), and a possible unnamed peradectid from Messel (Kurz and Habersetzer 2004: fig. 2). A small foramen is present dorsally to the anterior root of P2. Compared to the position
<figure><img src="image_6.png" /><figcaption>**Fig. 4** Interpretative drawings of the occlusal morphology of upper molar rows (M1-M3) of *Peradectes elegans*, *Pd. protinnominatus* and *Pd. crocheti* sp. nov. *a*. *Peradectes elegans*, based on a cast of AMNH 17383 (attribution from Simpson 1935). Grey coloured areas are either broken or lacking on the available cast. *b*. *Peradectes protinnominatus*, based on casts of the holotype, UCMP 44077. The metacone is broken (here in grey coloured area) on the M3 of the original specimen (McKenna 1960). *c*. *Peradectes crocheti* sp. nov., based on the original specimen MHN.AIX.PV.2018.26.14 (reversed view). Note the progressive loss of metastylar wing preservation from M1 to M3 on this specimen. The grey coloured areas are either broken (metacone) or worn (stylar cusps A and B, and mesial edge of the talon). The dashed lines concern depressions on the occlusal surface on all drawings. Main morphological differences</figcaption></figure>
between the three dental rows are figured on drawings. Abbreviations: **emarg**, distal emargination; **pmc**, postmetaconular crista; **protoc**, protocone; **st A**, stylar cusp A; **st B**, stylar cusp B; **st D**, stylar cusp D. Black arrows indicate the offset position of a cusp or stylar cusp compared to the axis perpendicular to the paracone – metacone axis. Scale bar equals 1 mm.

that would be expected for an incisivomaxillary foramen (just mesial to the infraorbital foramen; e.g., Rose 2010), it is more ventral and probably more mesially positioned. The fragment bearing the M1 extends more dorsally than the two others. It potentially preserved the most external part of the lacrimal on its dorsoposterior crushed region. The maxillary-jugal suture is not visible, as in *Pt. cuvieri* (Fisher, 1829) (Selva and Ladevèze 2017: p. 5). However, the rostrum fragment with the M2 and the M3 probably includes part of the jugal in addition to the maxillary, because the orbital rim is preserved on the most dorsal points between M1 and M3 (Fig. 3a). The most ventral point of the orbital rim is distal to the infraorbital foramen. The orbital rim ascends dorsally on the maxillary distally to the infraorbital foramen, and dorsally to the posterior root of the M1. These observations are also congruent with the position and morphology of the orbital rim in other peradectids. The palate region of the maxillary is preserved without apparent deformation distolingually to M1, and lingually and around M2 and M3 (Fig. 3b-c). M1-M4 alveoli are separated by deep embrasure pits (Fig. 3c).

**Upper canine:** MHN.AIX.PV.2018.26.14 documents the most complete upper canine of *Peradectes*. Only the apex of the crown is not preserved. The whole tooth is sharp and distally curved. The base of the crown is transversally compressed, less than twice as long as wide (Table 2). The crown is relatively low compared to the root, the latter being dorsoventrally longer (Fig. 3a). The crown is also less than twice as high as the one of P2. In *Mimoperadectes*, the crown of the upper canine is on the contrary much higher than its root and more than twice as high as P2 (Horovitz et al. 2009: fig. 2B). Compared to the upper premolars, the upper canine has an oval-shaped cross-section with equally convex lingual and labial edges. This tooth is
particularly short in cross-section, being mesiodistally longer than P1 (MHN.AIX.PV.2018.26.14), but shorter than P2 (MHN.AIX.PV.2017.6.6). Such a mesiodistally relatively short upper canine is known in *Pd. elegans*, for which the section of a partial right canine is documented (Simpson 1935: fig. 3), but not in *Mimoperadectes*, in which the single specimen preserving this tooth has a upper canine longer than the P2 (Horovitz et al. 2009: fig. 2B). The relative height and length of the upper canine of MHN.AIX.PV.2018.26.14 are similar to those of specimens interpreted as females of *Pucadelphys* by Ladevèze et al. (2011) (Muizon and Ladevèze 2022: p. 616-617), and to some herpetotheriids (Crochet 1980b: figs. 165-167; Sánchez-Villagra et al. 2007: fig. 1c). The crescentiform distal edge of the crown is labiolingually pinched, unlike the convex mesial edge. Mesial and distal edges are both flanked by a small bulge positioned at the base of the crown. The upper canine is separated from the premolars by a small space, which could be the result of fragmentation (see the lingual view, Fig. 3c). Furthermore, no diastema is present between the upper canine and the P1 of *Pd. elegans* (Simpson 1935: fig. 3), *Mimoperadectes houdei* (Horovitz et al. 2009: figs. 1A, 2B), or the most complete possible peradectid specimen from Messel (Kurz and Habersetzer 2004: fig. 3B).

<table><caption>**Table 2** Measurements (in mm) of selected teeth of *Peradectes crocheti* sp. nov. from Palette (MHN.AIX.PV.).</caption><thead><tr><th rowspan="2">Locus</th><th colspan="4">Length (mm) x Width (mm) [Length / Width]</th></tr><tr><th>MHN.AIX.PV.2018.26.14<br>(upper)</th><th>2017.6.6 (upper)</th><th>2017.6.8 (lower)</th><th>2017.6.9 (lower)</th></tr></thead><tbody><tr><td>C</td><td>1.23 x 0.69 [1.78]</td><td>-</td><td>-</td><td>-</td></tr><tr><td>P1</td><td>0.93 x 0.44 [2.11]</td><td>-</td><td>-</td><td>-</td></tr><tr><td>P2 or p2</td><td>-</td><td>1.35 x 0.64 [2.11]</td><td>? x 0.71</td><td>-</td></tr><tr><td>p3</td><td>-</td><td>-</td><td>1.20 x 0.68 [1.76]</td><td>-</td></tr><tr><td>M1 or m1</td><td>1.55 x 1.59 [0.97]</td><td>-</td><td>-</td><td>1.57 x 0.93 [1.69]</td></tr><tr><td>M2 or m2</td><td>1.50 x 1.70 [0.88]</td><td>-</td><td>1.65 x 1.04 [1.59]</td><td>1.64 x 1.03 [1.59]</td></tr><tr><td>M3 or m3</td><td>1.40 x 1.77 [0.79]<sup>a</sup></td><td>-</td><td>1.66 x 1.04 [1.60]</td><td>1.68 x 1.06 [1.58]</td></tr><tr><td>m4</td><td>-</td><td>-</td><td>-</td><td>1.55 x 0.92 [1.68]</td></tr></tbody></table>

<footnote>a Metastylar wing worn; length value possibly slightly underestimated</footnote>
**Upper premolars:** The upper premolars are two-rooted. The mesial root of P2 has a much larger diameter and is higher than the roots of P1 (MHN AIX.PV.2018.26.14, Fig. 3a-b); thus, P2 was considerably larger than P1. The mesial root of P2 is aligned with the roots of P1. The crown of P1 is asymmetric, with the apex of the main cusp mesially placed, ventral to the posterior margin of its anterior root. The convex anterior edge of the crown is slightly triangular in shape in lateral view. The most mesial point of the crown is closer to the base than to the apex of the crown. The lingual and labial edges of P1 are equally convex. The main cusp of P1 bears a relatively long and worn distal crista. In lateral view, this distal crista is not strictly rectilinear, but more vertically inclined near the apex. There are no basal accessory cusps nor cingula on P1. P1 and P2 are separated by a small diastema, slightly longer than the space between C and P1. P1 and P2 are also separated by a diastema in *Mimoperadectes houdei* and in the most complete peradectid-like specimen from Messel, but not in *Pd. elegans*. No crown of P2 or P3 is preserved on the holotype, but an isolated premolar crown from Palette is interpreted as a left P2 (MHN.AIX.PV.2017.6.6, Fig. 3d-f), based on its similarity with that premolar locus in other peradectids, as detailed below. It is longer and wider than the crown of P1, and approximately twice as high as P1, as for *Pd. elegans* (Simpson 1935: fig. 3), whereas it is much higher in *Mimoperadectes* (Horovitz et al. 2009). P1 and P2 of *Pd. crocheti* sp. nov. have the same value for their length to width ratio (Table 2). Similarly to *Pd. elegans* and *Mimoperadectes*, the P2 MHN.AIX.PV.2017.6.6 is relatively less mesiodistally elongated than that of *Pd. gulottai*. P2 is less asymmetric than P1, the apex of the former being positioned more distally relatively to the ventral inter-alveolar septum. In occlusal view, the labial edge of the crown is almost rectilinear, whereas the lingual edge is convex. The main cusp is surrounded by one mesial and one distal basal accessory cusp. The mesial accessory cusp is placed slightly labially to the mesiodistal axis of P2. Each accessory cusp is connected to a lingual and a labial cingulum. Both accessory cusps of P2 are the same height, but the distal one is longer, wider,
and has stronger cingula. In *Pd. elegans* and *Pd. gulottai*, for which both P2 and P3 are documented, the mesial accessory cusp of P3 has more distally extended cingula than the one of P2 in occlusal and lingual views. The whole labial edge of P3 in *Pd. elegans* is evenly surrounded by a cingulum. The mesial accessory cusp of MHN.AIX.PV.2017.6.6 has cingula relatively weakly developed, like the P2 of other peradectid species (Fig. 3d-e). In lateral view, the mesial edge of the main cusp is convex and the crested distal edge is slightly concave near the apex (Fig. 3d, f). In the same view, there is a notch between the distal crista of the main cusp and the distal accessory cusp, as on all P2 and P3 known for *Peradectes*, namely *Pd. elegans* (AMNH 17383, pers. obs.), *Pd. gulottai* (Rose 2010: fig. 1) and *Peradectes californicus* (Stock, 1936) (Lillegraven 1976: fig. 6). By contrast, the distal crest and accessory cusp are highly connected in *Mimoperadectes* and in most herpetotheriids, so that this notch is absent in, for example, *Herpetotherium* (e.g., Lillegraven 1976: pl. 5, figs. 1-2; Sánchez-Villagra et al. 2007: fig. 1c; Korth 2018: figs. 1c, 9a), *Peratherium* (e.g., Crochet 1980b: fig. 205) and the type species of *Amphiperatherium* (Koenigswald 1970: fig. 16). In occlusal and distal views, the distal crista of the main cusp is slightly curved lingually, so that it distally terminates mesiolingually to the distal accessory cusp.

**Upper molars:** Upper molars are three-rooted. M1 are triangular in shape, almost as long as wide. M2 are shorter and wider than M1 (Table 2). In turn M3 are shorter and wider than M2, so that the length to width (L/W) ratio decreases from M1 to M3 on the holotype (Table 2). The low disparity of length to width ratio between M2 and M3 (L/W M2 - L/W M3 < 0.10, Table 2) evidences a low discrepancy of proportions between upper molars of MHN.AIX.PV.2018.26.14. The protocone is strictly lingual to the paracone on M1 and M2, like *Pd. protinnominatus*, but unlike *Pd. elegans*, in which the protocone is distolingual to the paracone on these upper molar loci (Fig. 4), and is slightly distolingual to the paracone on M3
and M4 (Figs. 4c, 5t). The protocone may be more mesial on other M3 (e.g., UM-FDN-21, Fig. 5d; MNHN.F.SN18, Fig. 5q) or almost lingual to the centrocrista midpoint on the M3 of the holotype (Fig. 4c). The talon is more mesiodistally expanded on M1 and M2 than on M3. Among M3, the talon is distinctly mesiodistally narrow only on MNHN.F.SN78. A sharp ridge is present on the lingual edge of the acute protocone of the M3 of UM-FDN-21 (Fig. 5d). Such a sharp protocone ridge occurs at least in some other peradectid species (e.g., McGrew 1937: fig. 3). The protocone is always procumbent and lower than the paracone, on all upper molar loci (e.g., Fig. 5n, s). Both conules are relatively small. The metaconule is larger than the paraconule (e.g., Fig. 5n), although still low in distolingual view (Fig. 3c). The paraconule is positioned slightly more labially than the metaconule. The preparaconular crista extends labially to form the mesial edge of the paracingulum, and the postmetaconular crista ends lingually to the base of the metacone. Faint internal conular cristae often connect the conules to the base of the paracone or metacone, mostly on M1 (e.g., Figs. 4c, 5e, k). Such serial variation for the presence of the internal conular cristae is noted in the dental rows of *Pd. elegans* and *Pd. protinnominatus*, with their M3 lacking the internal conular cristae (Fig. 4b-c). Only one M3 of *Pd. crocheti* sp. nov. has an internal conular crista, on the metaconule (Smith et al. 2011: fig. 5.18B). A deep basin is present on the talon distolabially to the paraconule and mesiolabially to the metaconule of all upper molars.

The distal edge of M1-M3 is often emarginated between the talon and stylar shelf. This emargination is deep (e.g., UM-FNR2-1, Fig. 5k) to occasionally absent on Palette specimens (MHN.AIX.PV.2017.6.7 and MHN.AIX.PV.2018.26.20, Fig. 5g, m). The distal emargination is present on M3 of *Pd. protinnominatus*, but not on M3 of *Pd. elegans*, for which the postmetaconular crista extends distolabially to the lingual extremity of the metacone base (Fig. 4a; Krishtalka and Stucky 1983b: fig. 3) unlike the M3 of both *Pd. crocheti* sp. nov. and *Pd. protinnominatus*. The paracingulum is straight and mesiodistally long on most specimens,
<figure><img src="image_7.png" /><figcaption>**Fig. 5** Upper molars of *Peradectes crocheti* sp. nov. from Fordones, Fournes, Meudon, Palette and Soissons (France; MP7-MP8+9 interval). **a-b.** UM-FDN-286, labial fragment of right M4; **a.** labial view; **b.** occlusal view. **c-d.** UM-FDN-21, right partial maxillary with fragmentary M2-M3; **c.** labial view; **d.** occlusal view. **e.** UM-FDN-2, fragmentary right M1 in occlusal view. **f-g.** MHN.AIX.PV.2017.6.7, left M3 (surface model); **f.** labial view; **g.** occlusal view. **h-i.** UM-FDN-285, labial fragment of right M2; **h.** labial view; **i.** occlusal view. **j-k.** UM-FNR2-1, left M1; **j.** labial view; **k.** occlusal view. **l-n.** MHN.AIX.PV.2018.26.20, right M1; **l.** labial view;</figcaption></figure>
**m.** occlusal view; **n.** mesial view. **o-p.** MNHN.F.Me15975, labial fragment of right M2; **o.** labial view; **p.** occlusal view. **q-r.** MNHN.F.SN18, left M3 (surface model); **q.** occlusal view; **r.** labial view. **s-t.** MNHN.F.Me16084, left M4; **s.** distal view; **t.** occlusal view. The arrows denoting the stylar cusp C on labial views are followed by '+' if the most ventral point on the st. C - st. D mesiodistal extension is reached on the st. C, and by '-' if this most ventral point is reached on the st. D. The segments on the occlusal views of MHN.AIX.PV.2017.6.7 and MNHN.F.SN18 (**g** and **q**) are positioned on the paracone - metacone axis and its perpendicular line. Abbreviation: **st D**, stylar cusp D. Scale bar equals 1 mm.

whereas the mesial edge is slightly emarginated mesially to the paracone on the M1 of the holotype (Fig. 3b), the M2 from Croydon (Hooker 2020: fig. 3G), and more strongly emarginated on the M1, M3 and one M4 from Fordones (UM-FDN-286, Fig. 5b; UM-FDN-21; Fig. 5d; UM-FDN-23; Marandat 1991: pl. 1, fig. 2). The height of the paracone and metacone varies for a given molar locus, but the paracone is always lower on M1-M3. For example, on the unworn M1 the paracone and metacone can be subequal in height, the paracone being slightly lower (e.g., MHN.AIX.PV.2017.6.11, MHN.AIX.PV.2018.26.20; Fig. 5l), or the paracone can be much lower than the metacone (e.g., MNHN.F.SN76). It is worth mentioning that a paracone and metacone that are subequal in height have also been documented in *Pt. constans* (e.g., Ladevèze et al. 2012: fig. 5Ga). The paracone is also less mesiodistally long than the metacone. The paracone and metacone are conical, with a convex labial edge contrary to herpetotheriids, where these main cusps are triangular. The labial edge of these cusps is narrower labiolingually than their lingual edge. The centrocrista is straight, unlike the V-shaped centrocrista of most herpetotheriids. Some upper molars have a less straight centrocrista than M1-M3 of the holotype, such as UM-FDN-1 for M1 (Fig. 5e), UM-FDN-21 for M2 (Fig. 5d), MNHN.F.SN18 for M3 (Fig. 5q) and MNHN.F.Me16084 for M4 (Fig. 5t). The same variation is established for *Pd. elegans* specimens, with the centrocrista of AMNH 17383 upper molars being more V-shaped (especially on the M3 and M4, Fig. 4a) with respect to the strictly straight
centrocrista of the upper molars of the paratype AMNH 17369 (Krishtalka and Stucky 1983b: fig. 3). The postmetacrista is generally low, and it does not define a distal wall on the less worn stylar shelf (e.g., MHN.AIX.PV.2017.6.7, Fig. 5g; MNHN.F.Me15975, Fig. 5p), except on two upper molars, namely the M1 MHN.AIX.PV.2018.26.20 (Fig. 5n) and the fragmentary M3 MNHN.F.SN78. Distal to the metacone, the distal margin of the tooth is mesiodistally long instead of being strictly vertical on one M3 and two M1 from Palette (MHN.AIX.PV.2017.6.7, Fig. 5g; MHN.AIX.PV.2017.6.11 and MHN.AIX.PV.2018.26.20, Fig. 5m). The same variation is seemingly also present in the herpetotheriid *Peratherium constans* Teilhard de Chardin, 1927 (Ladevèze et al. 2012: fig. 5Gb vs fig. 5Hb). The stylar shelf labiolingually widens relative to the talon from M1 to M4. It is approximately slightly narrower than the talon on M3, and subequal in width with the talon on the M4 MNHN.F.Me16084 (Fig. 5t).

The stylar line bears four stylar cusps, from stylar cusp A to stylar cusp D, in most specimens. However, there is a distinct stylar cusp E on a single specimen of the sample, MNHN.F.SN78, where it is as high as stylar cusps C and D, but less mesiodistally long. Stylar cusp B is dominant in size over the other stylar cusps in *Pd. crocheti* sp. nov. and *Pd. protinnominatus*, whereas it is subequal in length and width to stylar cusp A in *Pd. elegans* (Fig. 4b-c vs Fig. 4a). It is worth noting that stylar cusps A and B are of the same labiolingual width on the M3 of UM-FDN-21 (Fig. 5d). On M1-M3 of *Pd. crocheti* sp. nov., stylar cusp A is higher than stylar cusps C and D. The spur-like stylar cusp A can be mesiolabial or labial to the paracingulum on M1 (Figs. 3b, 5k vs Fig. 5m), M2 (Fig. 5d and UM-FNR2-2 vs Figs. 3b, 5i, p) and M3 (Fig. 5g, q vs Figs. 3b, 5d). Stylar cusp A bears a sharp mesial crest. Stylar cusp A is most frequently placed mesiolingually to stylar cusp B on M2 and M3, as in the European *Pd. louisi* and *Pd. russelli*, or *Peradectes chesteri* Gazin, 1952 (e.g., Murphey et al. 2018: fig. 13.3), and *Pd. californicus* (e.g., Lillegraven 1976: pl. 7, fig. 1c), wheareas the two stylar cusps are most often aligned in *Pd. elegans* and *Pd. protinnominatus* (e.g., Fig. 4; see also comparison in Online Resource 3).
Fig. S10). An exception for *Pd. crocheti* sp. nov. is the M3 of UM-FDN-21 on which stylar cusp A is strictly mesial to stylar cusp B. From M1 to M4, the preparacrista elongates, stylar cusps A and B are increasingly close, and the relative height of stylar cusp A gradually increases, so that stylar cusp A is higher than stylar cusp B on the unworn M4 (Fig. 5s). All these tendencies are evidenced on the composite upper molar series from Fordones (Fig. 5a-e). On the holotype MHN.AIX.PV.2018.26.14, the preparacrista labially connects stylar cusp B on the M1 and M2, and stylar cusp A on the M3 (Fig. 4c). In the whole sample, the connection of the labial end of the preparacrista is as such in 6 out of 8 of the M1 (e.g., Fig. 5m), 4 out of 6 of the M2 with available preparacrista and stylar cusps A and B (e.g., Fig. 5i), and 4 out of 6 of the M3 (e.g., Fig. 5d, g). M1 to M3 specimens with a different labial connection of this crest have a preparacrista that labially ends in an intermediate position between stylar cusps A and B, namely UM-FDN-2 and UM-FNR2-1 for M1 (Fig. 5e, k), MNHN.F.Me15975 for M2 (Fig. 5p) and MNHN.F.SN18 and the upper molar from Sotteville-sur-Mer for M3 (Fig. 5q; Smith et al. 2011: fig. 5.18B). The M2 of the holotype of *Pd. protinnominatus* also has a preparacrista that labially ends in an intermediate position between the anterior stylar cusps (Fig. 4b). One M2 of *Pd. crocheti* sp. nov. (UM-FDN-21) has a preparacrista that connects to stylar cusp A (Fig. 5d). The preparacrista of most M1 and M2 connects to stylar cusp B through a thin crest situated on the lingual edge of stylar cusp B. Even without connection between these structures on M3, such a crest may be present (e.g., UM-FDN-21, Fig. 5d). On M1-M3, stylar cusp B is conical, lower than the paracone (labial views of Fig. 5) and generally positioned strictly labially to the paracone apex. Stylar cusp B is relatively slightly more mesial on the M3 of the holotype (Fig. 4c), on UM-FDN-23 and maybe on the M3 of UM-FDN-21 (Fig. 5d), but the broken metacone of the latter prevents unequivocal observation. Stylar cusp B is mesiolabial to the paracone apex on M1-M3 of Paleocene - Eocene North American peradectids, such as *Pd. elegans* (Fig. 4a; Krishtalka and Stucky 1983b: fig; 3), *Pd. protinnominatus* (Fig. 4b; McKenna
1960: fig. 18b; Bown 1979: fig. 40a right), and *Pd. chesteri* (e.g., West 1973: pl. 1, figs. c-d).
We should mention that stylar cusp B is also strictly labial to the paracone apex on upper molars
of *Pd. protinnominatus* from the Clarkforkian-3 (late Paleocene) and Wasatchian-M (early
Eocene) localities of the northern Bighorn Basin (pers. obs.; Gingerich and Smith 2006: fig.
26E), and of cf. *Pd. protinnominatus* from the Wasatchian-0 of the southern Bighorn Basin
(Rose et al. 2012: fig. 14A-C).

Stylar cusps C and D are more labiolingually pinched than stylar cusp B. Stylar cusp C is labial to the midpoint of the centrocrista. The single upper molar with a double stylar cusp C is the M2 from Abbey Wood (Hooker 2010: fig. 8a-b), on which the distal stylar cusp C is larger than the mesial one. The doubling of stylar cusp C is as rare as in *Pd. louisi* (see below); it is more frequent in herpetotheriids such as *Pt. constans* (Ladevèze et al. 2012) and *Amphiperatherium maximum* Crochet, 1979 (Crochet 1980b: p. 98-100), and seemingly in *Mimoperadectes* (M2 in Bown and Rose 1979: fig. 2; Gingerich and Smith 2006: fig. 15C; Beard and Dawson 2009: fig. 4A; M1 in Horovitz et al. 2009: fig. S1C). Stylar cusp C has an intermediate position between stylar cusps B and D, with the exception of two M1 where stylar cusps B and C are more closely appressed together (MNHN.F.SN76 and UM-FNR2-1; Fig. 5j-k). On a given molar locus, stylar cusps C and D can be highly connected or separated by a fossa (e.g., for M3, Fig. 5f vs Fig. 5r). In occlusal view, the area occupied by stylar cusp C is less important than the area of stylar cusp D on M1 and M2 (especially on M1, Figs. 4c, 5i, k, m, p). Stylar cusps C and D are subequal in width on M3. In labial view, the apex of stylar cusp C is as ventral or more ventral than the apex of stylar cusp D on all M1-M3, with the exception of the M1 MHN.AIX.PV.2018.26.20 (Fig. 5l; 1 out of 18 available specimens). Altogether, the relative heights of the stylar cusps of M1 to M3 of *Pd. crocheti* sp. nov. are mostly as follows: st. B > A ≥ C ≥ D (Table 3). Among ascertained peradectids, the apex of stylar cusp C is also at least as ventral as the apex of stylar cusp D only in the oldest *Peradectes* species, namely *Pd. minor*,
<table><caption>**Table 3** Height relationships of stylar cusps (A to D) of all ascertained peradectid species for which M2 and/or M3 are known. See method [1] for estimating stylar cusp heights in Fig. 2a. Species positioned above the median horizontal line of the table have stylar cusp C apex at least as ventral as stylar cusp D apex; species positioned below the median horizontal line have stylar cusp C apex less ventral than stylar cusp D apex, at least on one locus, or have vestigial stylar cusp C. Height relationships of stylar cusps are partially in bold when stylar cusp B is not dominant over other stylar cusps. *, more than one specimen of the species (including illustrated specimens) has been observed in labial view in this study.</caption><thead><tr><th>Species</th><th>Stylar height relationships</th><th>References</th></tr></thead><tbody><tr><td>Armintodelphys dawsoni</td><td>M2: B = C</td><td>Krishtalka and Stucky (1984: p. 40)</td></tr><tr><td>Mimoperadectes labrus*</td><td>M2: B &gt; C ≥ D ≥ A M3: B &gt; A &gt; C &gt; D<sup>a</sup></td><td>Gingerich and Smith (2006: fig. 15C);<br>Rose et al. (2012: fig. 12E)</td></tr><tr><td>Mimoperadectes sowasheensis</td><td>M2: B &gt; A &gt; C &gt; D</td><td>Beard and Dawson (2009: fig. 4A)</td></tr><tr><td>Peradectes coprexeches</td><td>M3: C ≥ B &gt; D</td><td>Williamson and Taylor (2011: fig. 6.7)</td></tr><tr><td>Peradectes crocheti sp. nov.*</td><td>M2-M3: B &gt; A ≥ C ≥ D</td><td>this study; e.g., Smith et al. (2011: fig.<br>5.18A); Hooker (2020: fig. 3F)</td></tr><tr><td>Peradectes elegans</td><td>M2: B = C &gt; A = D M3: B &gt; A &gt; C ≥ D</td><td>cast of AMNH 17383 (in Simpson<br>1935: fig. 3)</td></tr><tr><td>Peradectes minor</td><td>M2-M3: B = A &gt; C &gt; D</td><td>Clemens (2006: fig. 2C, E)</td></tr><tr><td>Peradectes protinnominatus*</td><td>M2-M3: B &gt; A = C = D</td><td>cast of UCMP 44077 (holotype);<br>Gingerich and Smith (2006: fig. 26D)</td></tr><tr><td>Didelphidectes cf. pumilis</td><td>M3: B &gt; D &gt;&gt; C (vestigial or absent)</td><td>Kihm and Schumaker (2015: fig. 13N-O)</td></tr><tr><td>Mimoperadectes houdei</td><td>M2: B &gt; D &gt;&gt; A = C M3: B = A &gt; D &gt;&gt; C</td><td>Horovitz et al. (2009: fig. S1C)</td></tr><tr><td>Nanodelphys hunti</td><td>M2-M3: B &gt; D &gt;&gt; C (vestigial or absent)</td><td>McGrew (1939: 394, fig. 114); Korth<br>(1994: 390, fig. 7.1-2)</td></tr><tr><td>Peradectes californicus</td><td>M3: B = A &gt; D &gt;&gt; C</td><td>Lillegraven (1976: pl. 7, fig. 1a)</td></tr><tr><td>Peradectes chesteri</td><td>M2-M3: B &gt;&gt; C, D (vestigial or absent)</td><td>Krishtalka and Stucky (1983b, 1984);<br>Murphey et al. (2018)</td></tr><tr><td>Peradectes gulottai</td><td>M2: B &gt; A &gt; D &gt;&gt; C M3: B = A &gt; D &gt;&gt; C</td><td>Rose (2010: fig. 1.1)</td></tr><tr><td>Peradectes louisi*</td><td>M2: B &gt; A &gt; D &gt; C<sup>b</sup> M3: B &gt; A &gt;&gt; D &gt; C</td><td>this study</td></tr><tr><td>Peradectes russelli*</td><td>M2: B &gt; A = C = D M3: B &gt; A &gt; D &gt; C</td><td>this study</td></tr></tbody></table>

Pd. coprexeches, Pd. elegans, Pd. protinnominatus, and in Mimoperadectes labrus and M. sowasheensis (Table 3). Stylar cusp C is also relatively prominent (equal in size to stylar cusp B) on the only upper molar attributed to Armintodelphys (Table 3). In labial view, the distal crest of stylar cusp C is always mesiodistally longer than its mesial crest on M1-M3. Stylar cusp D is distolabial to the metacone on M1 (labial to the metacone on M1 of Pd. elegans and Pd.

<footnote><sup>a</sup> the relative height of stylar cusp A of M3 differs from the one reported by Bown and Rose (1979: p. 90) for the holotype.</footnote>

<footnote><sup>b</sup> in one M2 specimen (MNHN.F.CB3228; Fig. 10i), stylar cusp C is lower than stylar cusp D.</footnote>
*protinnominatus*; Fig. 4) and strictly labial to the metacone on M3. Stylar cusp D of M2 can be strictly labial or distolabial to the metacone (e.g., Fig. 5i vs Figs. 4c, 5p). This variation may occur also in *Pd. protinnominatus* because unillustrated M2 attributed to this species by Gingerich and Smith (2006: p. 254) (UM 113378 and UM 113391, pers. obs. of corresponding casts) have a stylar cusp D distolabial to the metacone contrary to the holotype of *Pd. protinnominatus* (Fig. 4b). The relatively lowest stylar cusp D of the sample is on the M3 UM-FDN-23 (Marandat 1991: pl. 1, fig. 2). The ectoflexus is absent on all M1, which have a straight labial margin unlike M1 in *Pd. protinnominatus* (e.g., Fig. 4b vs Fig. 4c). M2 have shallower asymmetric ectoflexus than M3. The ectoflexus is always long and asymmetric on M3, with a metastylar wing more labially extended than the parastylar wing. Variations in the depth and degree of asymmetry of the ectoflexus of M3 exist, both in Palette (MHN.AIX.PV.2018.26.14, Fig. 4c vs MHN.AIX.PV.2017.6.7, Fig. 5g) and Fordones (UM-FDN-21, Fig. 5d vs UM-FDN-23, Marandat 1991: pl. 1, fig. 2). The metastylar wing is worn on the M2 and M3 of MHN.AIX.PV.2018.26.14, especially on the M3 (Fig. 4c), resulting in the weak asymmetry of the ectoflexus mentioned. The metastylar wing is acute on unworn M1-M3.

Additional description of the M4 can be made. This locus is documented by four specimens, of which only the left M4 from Meudon (MNHN.F.Me16084, Fig. 5s-t) is complete. The straight centrocrista of M4 is shorter than on more anterior molars, and this upper molar is mesiodistally shorter than others. On MNHN.F.Me16084, the protocone is lower than the paracone but higher than the metacone (Fig. 5s). On MHN.AIX.PV.2017.6.12, the protocone is higher than the metacone, and relatively more mesial than on MNHN.F.Me16084, so that it is strictly lingual to the paracone. A protocone higher than the metacone on M4 is known in other peradectids such as *Mimoperadectes labrus* (pers. obs., UM 66144) and *Pd. russelli*. The crescentiform paraconule is indistinct in lateral view on MHN.AIX.PV.2017.6.12, but present on MNHN.F.Me16084 (Fig. 5s). Both specimens have a tiny metaconule close to the lingual edge
of the metacone. The conules lack internal cristae. The distal edge of the talon of both
MNHN.F.Me16084 and UM-FDN-289 is deeply emarginated (Fig. 5t), whereas it is straight on
MHN.AIX.PV.2017.6.12. On all specimens, the paracone is much higher, longer and wider
than the metacone. The labial edge of the paracone of UM-FDN-286 is almost as convex as the
lingual edge, whereas MNHN.F.Me16084 has a more triangular paracone (Fig. 5s). The
preparacrista is directed towards stylar cusp A but it ends distolingually to it. Stylar cusps A
and B are placed mesiolabially to the paracone on both UM-FDN-286 and MNHN.F.Me16084.
Stylar cusps A and B are separated by a shallow notch on MNHN.F.Me16084 (this area is worn
on UM-FDN-286). On the specimen from Meudon, stylar cusp A is reduced in surface
compared to stylar cusp B, which is mesiodistally long and doubled (Fig. 5t). The specimen
from Fordones being worn in its most mesiolabial part, it is not possible to conclude whether
the stylar cusps in the A and B positions are a relatively large stylar cusp B and small stylar
cusp A, or a doubled stylar cusp B (Fig. 5b). Stylar cusp C is here the lowest stylar cusp, and
there is no stylar cusp D. Stylar cusp C is positioned mesiolabially to the midpoint of the
centrocrista in both specimens (Fig. 5b, t), as in *Pd. elegans* (Krishtalka and Stucky 1983b: fig.
3), but unlike, for example, certain European herpetotheriids in which it is strictly labial to the
centrocrista (e.g., *Peratherium constans*, Ladevèze et al. 2012: figs. 4D, 5D; *Pt. elegans*,
Ladevèze et al. 2012: fig. 7a; *Pt. cuvieri*, Selva and Ladevèze 2017: fig. 5Ab). Interestingly,
stylar cusp C is also mesiolabial to the midpoint of the centrocrista in some herpetotheriid
species (e.g., Crochet 1980b: figs. 109, 223). Stylar cusp C is more crescentiform on UM-FDN-
286 than on MNHN.F.Me16084. The ectoflexus is well-developed, again as in *Pd. elegans*,
which distinguishes the isolated M4 of *Pd. crocheti* sp. nov. from those of the coeval
herpetotheriid *Pt. constans* or the type species of herpetotheriids, *Herpetotherium fugax* Cope,
1873 (e.g., Fox 1983: fig. 2a), which lack the ectoflexus.
**Mandible and lower premolars:** The right dentary MHN.AIX.PV.2017.6.8 is preserved from the canine alveolus to the m3 (Fig. 6). The canine alveolus is labially broken. The dentary bears an anterior mental foramen situated below the posterior root of the p1 (Fig. 6b-c), and a posterior mental foramen situated below the posterior root of the m1 (Fig. 6c). The presence of mental foramina below p1 and m1 (with slight variations) is almost always observed in peradectids and herpetotheriids (e.g., Korth 1994: fig. 8; Ladevèze et al. 2012: fig. 3A-B; Smith and Smith 2013: fig. 4A; Korth 2018: fig. 14f; but see Korth 1994: p. 393, for *Armintodelphys*). The depth of the dentary gradually increases posteriorly to the canine alveolus. The unfused mandibular symphysis extends posteriorly to a point ventral to the posterior alveolus of the p2 (Online Resource 6), as in *Pd. elegans* (Simpson 1935: fig. 2; pers. obs. of a cast of AMNH 17376) and alphadontids (e.g., Clemens 1966: figs. 58a, 61a; Cifelli and Muizon 1998: fig. 2B). The maximum posterior dorsoventral width value of the mandibular symphysis of *Peradectes* is lower than the value of the width between the most posterodorsal point of the symphysis and the posterior alveolus of p2 (Online Resource 6), contrary to figured alphadontid hemimandibles with a preserved symphysis (Clemens 1966: figs. 58a, 61a), in which these two width values appear at least subequal (but see the juvenile alphadontid specimen in Cifelli and Muizon [1998: fig. 2B]). The symphyseal angle between the long axis of the symphysis and the horizontal axis of the tooth row measures approximately 20°; this is close to the lowest values obtained from similar measurements performed in several fossil and extant marsupialiforms (Muizon and Ladevèze 2020: table 7). The posterior root of the p1 is preserved within its posterior alveolus. It is much smaller than the posterior root of p2 and p3, and it descends less deeply ventrally, within the dentary (Fig. 6d). The whole p1 was thus much smaller than the p2 and p3. There are no diastemata between the lower premolars. In occlusal view, the position of the anterior alveolus of the p1, mesially or distally to the inter-alveolar septum, is unclear (Fig. 6a). A similar uncertainty applies to the holotype of both *Pd. elegans* (AMNH 17376) and *Pd*.
*californicus* (Stock 1936: pl. 1, fig. 2a), so that the p1 of *Pd. elegans* was first considered to be single rooted (Simpson 1935: p. 10). In occlusal view of MHN.AIX.PV.2017.6.8 (Fig. 6a), alike in *Pd. elegans* (pers. obs. of a cast of AMNH 17376), the alveolus apparently anterior to the posterior root of the p1 is larger than expected for this premolar locus. The p1 is actually two rooted in both *Pd. elegans* (Fox 1983: fig. 3) and *Pd. crocheti* sp. nov. (Fig. 6d), with a smaller anterior than posterior root in cross section, as revealed by computed tomography study of MHN.AIX.PV.2017.6.8 for the European species. In *Pd. crocheti* sp. nov., the anterior root of the p1 is laterally adjacent to the inter-alveolar septum separating the canine alveolus from the p1 roots (Fig. 6b, d). Consequently, there is no diastema between the p1 and lower canine, these two teeth being close together (Fig. 6b), as in *Pd. elegans* (Fox 1983).

Contrary to the lower molars, all lower premolars have mesiodistally curved roots (Fig. 6d).
This character has not been studied so far for both peradectids and herpetotheriids. Interestingly,
lower premolars of some Eocene herpetotheriids exhibit straight roots, similar to the lower
molars (e.g., holotype of *Amphiperatherium fontense* Crochet, 1979 [Crochet 1980b: fig. 123]);
pers. obs. of UM-BRT-574, *Amphiperatherium bourdellense* Crochet, 1979, Le Bretou, in
Quercy). The posterior root of all preserved cheek teeth of MHN.AIX.PV.2017.6.8 is larger
than the anterior root in cross section. The roots of all lower cheek teeth decrease in
circumference ventrally to the crown. The unworn p2 and p3 of MHN.AIX.PV.2017.6.8 are the
first lower premolar crowns allocated to European peradectids. The posterior heel of the p2 is
broken. The p2 and p3 are similar in width, the p2 being only slightly wider (Table 2). The p3
is relatively labiolingually wider than in *Pd. elegans* (Krishtalka and Stucky 1983b: table 2).
The apex of the p3, situated on the main cuspid, is slightly but distinctly higher than the apex
of the p2 and of the m1, which is situated on the protoconid for the latter (Fig. 6c-d; Online
Resource 6). On the p2 and p3, the apex overhangs its respective anterior root. The p2 is slightly
procumbent, because its apex is positioned dorsomedially to the most ventral point of the
<figure><img src="image_8.png" /><figcaption>**Fig. 6** Surface model of MHN.AIX.PV.2017.6.8, right hemi-mandible fragment with canine alveolus, posterior root of p1, partial p2, p3, partial m1, and m2-m3, of *Peradectes crocheti* sp. nov. from Palette (Provence; MP7-MP8+9 interval) in: **a.** occlusal (dorsal) view; **b.** mesiolabial (anterolateral) view with focus on c-p1 alveoli; **c.** labial (lateral) view; **d.** labial (lateral) view with transparent dentary. Abbreviation: **c alv**, canine alveolus. Scale bar equals 1 mm.</figcaption></figure>
anterior root, whereas the apex of the p3 is strictly dorsal to the most ventral point of its anterior
root. In lateral view, the main cuspid of the p2 and p3 forms the mesial edge of these teeth,
which is projected mesially to the anterior root. It is curved as in other *Peradectes* species (e.g.,
AMNH 17376, holotype of *Pd. elegans*; UCMP 45950, paratype of *Pd. protinnominatus*),
contrary to herpetotheriids in which it is V-shaped (e.g., Korth 1994: fig. 8.1 for
*Herpetotherium fugax*). In mesial view, the main cuspid is bent lingually. The distal cristid of
the main cuspid is straight in lateral view. The p3 is almost as long as high. The distal heel of
the p3 is short and bears two accessory cuspids (Fig. 6a), whereas the described p3 of North
American peradectids have only one accessory cuspid on their distal heel. The distal heel is
lower in *Mimoperadectes* and *Armintodelphys* (see illustration in Online Resource 3: Fig. S1).
Some rare herpetotheriid specimens also have double accessory cuspids on the heels of their
lower premolars (e.g., Hooker 2010: fig. 8n-p). These accessory cuspids are positioned on the
cingulid that surrounds the distal heel. The larger and higher distal cuspid, on the distal margin
of the p3, is connected to the distal cristid of the main cuspid (Fig. 6a). This first accessory
cuspid is pointed, dorsal to the ventralmost point reached by the distal cristid of the main cuspid.
The second distal cuspid is smaller, and is positioned on the distolingual margin of the p3. The
connection between the distal cristid of the main cuspid and the main accessory cuspid divides
the heel into unequal lingual and labial parts, the labial surface being both lower and less
laterally spread than the lingual surface. Both accessory cuspids of the heel of the p3 are
connected by a high cristid formed by the heel cingulid. The lingual cingulid is mesiodistally
longer than the labial cingulid. However, as in *Mimoperadectes* (Bown and Rose 1979: fig. 1),
the lingual cingulid is much shorter than in *Pd. elegans* and *Pd. protinnominatus*, in which it
ascends the distolingual edge of the main cuspid (e.g., Simpson 1935: fig. 2).

**Lower molars:** The description of the lower molars is primarily based on the two lower tooth rows from Palette (MHN.AIX.PV.2017.6.8, right, and MHN.AIX.PV.2017.6.9, left), possibly
representing the same individual. The partial right hemi-mandible MHN.AIX.PV.2017.6.9 (Fig. 7a-c) preserves a complete molar series (m1-m4). The m1 is smaller (in length and width) than the m2, which is in turn as large or slightly smaller than the m3 (Table 2). The m4 is the smallest locus of the lower molar row. The trigonid is narrower labiolingually than the talonid on the m1, the reverse on the m4. m2 have a labiolingually wider talonid than trigonid (e.g., MHN.AIX.PV.2017.6.9, Fig. 7a; MHN.F.Ri221, Fig. 7g), with the exception of the m2 from Meudon (MHN.F.Me16101, Fig. 7i), on which the trigonid and talonid are as wide. All m3 have a trigonid equal in labiolingual width to the talonid (e.g., MHN.AIX.PV.2017.6.9, Fig. 7a; MHN.F.SN2508, Fig. 7k), as in *Pd. elegans* and contrary to the other European peradectid species. The trigonid is longer than the talonid on all molars. One of the three known m1, MHN.F.SN121, has a trigonid less labiolingually wide than the m1 from Palette and Rians, with a relatively longer paracristid lingual segment, which is also found in *Pd. louisi* and *Pd. russelli*. On both molar rows from Palette (Figs. 6a, 7a), the m2 and m3 have a trigonid as mesiodistally long as labiolingually wide. Only one isolated m3, also from the type locality (MHN.AIX.PV.2017.6.10), exhibits a trigonid longer than wide.

On MHN.AIX.PV.2017.6.9, a groove on the mesial surface of the paraconid of the m3, lingual to the precingulid, contacts the hypoconulid of the m2. In anatomical position on the dentary, the apex of the hypoconulid of m2 is ventral to the apex of the paraconid of m3. The precingulid labiolingually extends from a point mesial or slightly mesiolabial to the apex of the paraconid, to a point mesial to the apex of the protoconid. In lingual view, the paraconid is less and less mesially projected from m1 to m4 (Fig. 7c), but its mesiolingual edge is always keel-like, as in all metatherians. The preparacristid is longer on the m2 from Meudon (Fig. 7i) than on the m2 of MHN.AIX.PV.2017.6.9. In occlusal view, the paracristid lingual segment elongates from m1 to m4. The postmetacristid shortens from m1 to m4 on occlusal view (Fig. 7a), so that it is almost vertical in lingual view on the m4 (Fig. 7c). On m1 and m2, the metaconid is longer than
<figure><img src="image_9.png" /><figcaption>**Fig. 7** Lower molars of *Peradectes crocheti* sp. nov. (except **d**) from Palette, Meudon, Rians and Soissons (France; MP7-MP8+9 interval). **a-c.** MHN.AIX.PV.2017.6.9, left m1-m4 row with fragments of dentary; **a.** occlusal view; **b.** labial view; **c.** reversed lingual view. **d.** comparison with UM-FDN-18, fragmentary right m2 from Fordones (Corbières) attributed to *Peratherium constans* (Marandat 1991: p. 68), in reversed occlusal view. **e-f.** MNHN.F.Ri516, right m1; **e.** reversed occlusal view; **f.** lingual view. **g-h.** MNHN.F.Ri221, left m2; **g.** occlusal</figcaption></figure>
view; **h**. reversed lingual view. **i-j**. MNHN.F.Me16101, left m2; **i**. occlusal view; **j**. reversed lingual view. **k-l**. MNHN.F.SN2508, right m3; **k**. reversed occlusal view; **l**. lingual view. Scale bar equals 1 mm.

the paraconid, and longer than the metaconid of m3 and m4. The metaconid of m3 is only slightly longer than the paraconid. Those two cuspids are of equivalent length on m4. The protoconid is the highest cuspid of the trigonid on all lower molars. The metaconid is higher than the paraconid, their height difference being less marked on m4 than on anterior molar loci (Fig. 7c). The metaconid is either well distolingual to the protoconid (e.g., Fig. 7a) or relatively closer to it mesiolabially (e.g., Fig. 7g). The paracristid is always longer than the protocristid. On the mesial edge of the protoconid, the preprotocristid is convex in mesiolabial view (Fig. 6c-d), except on m4. The labial edge of the protoconid is weakly convex in mesial or distal view.

The protocristid notch opens more ventrally than both the paracristid notch and the lingual opening of the trigonid basin. The latter is always higher than the lingual opening of the talonid basin, unlike in herpetotheriids. The difference in height between those two lingual openings increases gradually from m1 to m4 (Fig. 7c). The talonid basin is a deep, rounded depression. None of the lower molars are labially emarginated. The lingual edge of the talonid is curved, with an entoconid that is obliquely positioned relative to the paraconid – metaconid axis, as in all late Paleocene – Eocene peradectids (e.g., Hough 1961: fig. 2A, for the late Eocene genus *Didelphidectes*). The lingual edge of the talonid is straight and the entoconid is not obliquely oriented in the early peradectids *Pd. minor* (e.g., Williamson et al. 2012: fig. 8A, 8D) and *Pd. coprexeches* (e.g., Williamson and Taylor 2011: fig. 7A, 7D, 7J), as in herpetotheriids.

The entoconid and hypoconulid are labiolingually pinched. The entoconid is often labial to the paraconid – metaconid axis (e.g., Fig. 7a, **k**) but the three cuspids are aligned on some m2
specimens (e.g., MNHN.F.Ri221, Fig. 7g; MNHN.F.Me16101, Fig. 7i). The pre-entocristid is always sharp and joins the postmetacristid on the postmetacristid – pre-entocristid notch. The postentocristid is absent on the m2, but present on the m3 of MHN.AIX.PV.2017.6.9. The entoconid is positioned more and more distally to the metaconid from m1 to m4, so that the metaconid – entoconid notch mesiodistally elongates from m1 to m4 (Fig. 7c). In occlusal view, the entoconid of m2 and m3 is in intermediate position between the distal edge of the trigonid and the distal margin of the tooth, whereas the entoconid is closer to the distolingual corner of the tooth on equivalent loci in *Pd. elegans* (e.g., Krishtalka and Stucky 1983b: fig. 4b for occlusal view, McKenna 1960: fig. 17c [lower] for lateral view). The entoconid of m4 is closer to the distal margin of the tooth than from the distal wall of the trigonid. The entoconid has a symmetrical shape in lingual view, with equally long pre-entocristid and postentocristid. In absolute height, the entoconid of m1 and m2 are subequal (Fig. 7c, f, h), it is lower on m3 (e.g., Fig. 7l) and much lower on m4 (Fig. 7c).

The entoconid - hypoconulid notch is deep, as deep as the entoconid – metaconid notch on m2 (Fig. 6c), as in *Pd. protinnominatus* (e.g., Gingerich and Smith 2006: fig. 26a, c). In comparison, the lowest point of the entoconid – hypoconulid notch of *Pd. elegans* can be higher than the lowest point of the entoconid – metaconid notch (e.g., McKenna 1960: fig. 17c), even on m2 (e.g., pers. obs., AMNH 17376), or as high as the lowest point of the entoconid – metaconid notch (e.g., Fox 1983: fig. 3). The hypoconulid occupies approximately one third of the labiolingual width of the distal margin of the talonid on m2 and m3 and one half of it on m1 and m4 (Fig. 7a). The hypoconulid is lower than the entoconid on m1 and m2 (e.g., Fig. 7f, h, j), as high and as long on m3 (e.g., Fig. 7l), and much higher on m4 (see the increasing height of hypoconulid along the molar series, Fig. 7c). A lingual cristid of the hypoconulid descends on the entoconid – hypoconulid notch only on the m2 from Rians (MNHN.F.Ri221, Fig. 7g).
The hypoconid is mesiodistally pinched, with an angle of approximately 70° between the cristid obliqua and postcristid. This cuspid is mesiolabial to labial to the entoconid apex (e.g., Fig. 6a); distolabial to the protoconid on m1, m2, and m3, and strictly distal to the protoconid on m4. In distal view, the entoconid and hypoconid are subequal in height, unlike in herpetotheriids, in which the entoconid is higher (pers. obs.). The hypoconid of m4 is much lower than the hypoconid of more anterior lower molar loci. The cristid obliqua is curved on all loci, and its mesial end is positioned labially to the protocristid notch on all lower molar loci. The curvature of this crest is more pronounced on m4 than on more anterior molars (Fig. 7a). The cristid obliqua ascends slightly on the distal wall of the trigonid; it reaches approximately half the dorsoventral height of the distal wall of the trigonid, between the talonid basin and the protocrisid notch. The postingulid is lingually and labially convex; it attenuates labially to the hypoconulid instead of extending lingually towards it (see illustrations in Online Resource 3: Fig. S6). On the specimens from Palette, the hypoflexid is labiolingually wide, so that it is directly connected to the postcingulid. In this case, the hypoconid is totally internalized within the talonid (Figs. 6a, 7a).

**Postcranial:** The sole postcranial material attributed to *Peradectes crocheti* sp. nov. is a minute, complete right astragalus (MHN.AIX.PV.2017.6.14, Fig. 8) not found in association with dental remains of this species. This specimen has been confidently attributed to *Pd. crocheti* sp. nov. based on the following: i) compatibility of size (proximodistal length = 1.97 mm; mediolateral width = 1.59 mm); ii) morphological and size similarity with a left astragalus of cf. *Peradectes protinnominatus* from the Wasatchian-0 of the southern Bighorn Basin (Rose et al. 2012: fig. 11E-H) and with Wasatchian peradectid astragali described by Szalay (1994: fig. 6.10D-F); iii) *Pd. crocheti* sp. nov. is the only peradectid recorded in Palette, based on dental remains. In dorsal view (Fig. 8a), the trochlea is smooth and nearly ungrooved, and there is no
distal astragalar tubercle. The astragalar neck and head are relatively proximodistally long (Fig. 8a-b). In turn, the astragalar neck and head have the same mediolateral width, the two being well distinguished in ventrolateral view (Fig. 8c). In distal view, the astragalus is relatively flat (Fig. 8d). Its medial tibial facet is only gently sloping, so that there is a rounded angle between the medial and lateral tibial facets (Fig. 8d). The distal end of the lateral tibial facet is located on the astragalar neck.

<figure><img src="image_10.png" /><figcaption>**Fig. 8** Right astragalus of *Peradectes crocheti* sp. nov. from Palette (Provence, MP7-MP8+9 interval), MHN.AIX.PV.2017.6.14. **a.** dorsal view; **b.** ventral view; **c.** ventrolateral view; **d.** distal view. Abbreviations, terminology following Rose et al. (2012): **as**, astragalar sulcus; **ef**, ectal facet; **ff**, fibular facet; **ltf**, lateral tibial facet; **mpt**, medial plantar tubercle; **mtf**, medial tibial facet; **nf**, navicular facet; **of**, ovoid fossa; **sf**, sustentacular facet. Scale bar equals 1 mm.</figcaption></figure>

In contrast to MHN.AIX.PV.2017.6.14, known herpetotheriid astragali are less dorsoventrally flat, and have a more grooved trochlea in addition to an almost vertical medial tibial facet (Rose 2012; Rose et al. 2012), characters which would be expected on astragali of the coeval herpetotheriid *Pt. constans* in Palette (only calcanei of *Pt. constans* are known from its type locality; Coillot et al. 2013). Unlike in cf. *Pd. protinnominatus* and *M. labrus*, the medial border of the astragalar neck of MHN.AIX.PV.2017.6.14, formed by the proximal extension of the large navicular facet, does not reach the trochlea (Fig. 8b-c). The ovoid fossa is thus more open medially than in cf. *Pd. protinnominatus*. The ovoid fossa of the composite drawing of Szalay (1994: fig. 6.10E) for Wasatchian peradectid astragali is also open, but relatively more distally.
MHN.AIX.PV.2017.6.14 compares better with the astragalus of cf. *Pd. protinnominatus* than with the one of the larger *Mimoperadectes labrus* (Rose et al. 2012: fig. 11A-D), for example in having an astragalar sulcus (narrower than in *Herpetotherium innominatum* [Simpson, 1928]) and shorter ectal facet with a rounded instead of triangular distolateral extremity (Fig. 8b).

*Peradectes louisi* Crochet, 1979

Figures 9, 10, 11 (except 11g-h)

1977a *Peradectes* sp. nov. 1; Crochet: p. 359.

1979 *Peradectes louisi* Crochet; Crochet: p. 367, fig. 1.

1980b *Peradectes louisi* Crochet; Crochet: p. 39-42, figs. 6-13 (in part).

1980b *Peradectes* sp.; Crochet: p. 49-51, figs. 26-27, 29 (in part).

**Holotype:** left M3, MNHN.F.GL197, first figured by Crochet (1979: fig. 1, 1980b: fig. 9a, b) and housed in the collections of the Muséum National d'Histoire Naturelle, Paris.

**Localities:** Sables de Brasles (type locality), Avenay, Mutigny, Condé-en-Brie and Sézanne-Broyes; all in the eastern Paris Basin.

**Age:** middle Ypresian (middle early Eocene), MP8+9 and ~MP8+9 reference level (~ mammalian biozones PE IV and PE V).

**Remarks:** We here propose a revision of *Pd. louisi* based on a re-description of the holotype, and allocate to this species several new upper and lower molar remains from its type locality (Fig. 9), and other MP8+9 and ~MP8+9 Paris Basin localities in order to study polymorphism and enhance comparisons with other European peradectids.

**Translation to English of the original French diagnosis (Crochet 1979):** 'European species of small size. On M3, stylar cusp B subequal in height to C and D. Ectoflexus poorly formed
and symmetric; conules weak; M3 relatively long. Lingual opening of the prefossid higher than
the entocristid notch located between the metaconid and entoconid. Except on m4, base of the
hypoconid mesio-distally pinched and cristid obliqua with a concavity before joining the
posterior base of the trigonid. m4 smaller than m3.'

<figure><img src="image_11.png" /></figure>

**Fig. 9** Upper molars of *Peradectes louisi* from its type locality, Sables de Brasles (Aisne, France; ~MP8+9). **a-b.** MNHN.F.GL1, left M1; **a.** labial view; **b.** occlusal view. **c-d.** MNHN.F.GL272, labial half of left M2; **c.** labial view; **d.** occlusal view. **e-h.** MNHN.F.GL197, holotype, left M3; **e.** labial view; **f.** occlusal view, the segments are positioned on the paracone – metacone axis and its perpendicular line; **g.** lingual view; **h.** mesial view. The arrows denoting stylar cusp C on the labial views **a** and **c** are followed by ‘-’, meaning the most ventral point on the [stylar cusp C – stylar cusp D] mesiodistal extension is reached on stylar cusp D. Abbreviations: **st C**, stylar cusp C; **st D**, stylar cusp D. Scale bar equals 1 mm.

**New differential diagnosis:** Differs from *Pd. crocheti* sp. nov. and *Pd. russelli* in having: (i) relatively mesiodistally longer lower molars; (ii) stylar cusp D distolabial to metacone apex on M3 (upper molars of ‘Arm.’ *dufraingi* are unknown); and (iii) stylar cusp C less ventral than stylar cusp D apex on M1 and M2. Further differs from *Pd. crocheti* sp. nov. by: (i) stylar cusp C less ventral than stylar cusp D apex also on M3; (ii) presence of crown labial emargination on all lower molars; (iii) trigonid more labiolingually wide than talonid on m3; (iv) relatively lower entoconid and hypoconulid separated by a shallower notch; and (v) in lacking
postcingulid on m4. Further differs from *Pd. russelli* in being noticeably smaller. Differs from
‘*Armintodelphys*’ *dufraingi* in: (i) being larger; in having (ii) talonid mostly labiolingually as
wide or wider than trigonid on m2; (iii) entoconid higher than hypoconulid on m2 and as high
as hypoconulid on m3; and (iv) larger postcingulid on m2 and m3.

**Material:** Additional material from Sables de Brasles: left M1 (MNHN.F.GL1, MNHN.F.GL296), worn left M1 (MNHN.F.GL57), worn right M2 (MNHN.F.GL154), labial half of left M2 (MNHN.F.GL272), worn right M3 (MNHN.F.GL265), right m1 (MNHN.F.GL136), left m3 (MNHN.F.GL261, MNHN.F.GL263), right m3 (MNHN.F.GL383), right m4 (MNHN.F.GL301).

Material from Mutigny: right dP3 (MNHN.F.Mu18005; Crochet 1980b: fig. 6), left M1 (MNHN.F.Mu18006; Crochet 1980b: fig. 26), left M2 (MNHN.F.Mu6511; Crochet 1980b: fig. 8), left worn M3 (MNHN.F.Mu18001).

Material from Avenay: left M1 (MNHN.F.Av16023, MNHN.F.Av16036; Crochet 1980b: fig. 7, UM-AV-1-SK, UM-AV-3-SK), right M1 (MNHN.F.Av16057, UM-AV-2-SK), mesial fragment of left M2 (MNHN.F.Av4582), left M2 (MNHN.F.Av18003), right M2 (MNHN.F.Av18004), left m1 (UM-AV-7-SK, UM-AV-12-SK), right m1 (MNHN.F.Av16028; Crochet 1980b: fig. 10, MNHN.F.Av7229), left m2 (MNHN.F.Av16016, MNHN.F.Av16044, MNHN.F.Av18001, MNHN.F.Av6830, UM-AV-10-SK, UM-AV-11-SK), right m2 (MNHN.F.Av16027; Crochet 1980b: fig. 11), left m3 (MNHN.F.Av18000, UM-AV-4-SK, UM-AV-5-SK), right m3 (MNHN.F.Av18002; Crochet 1980b: fig. 12, MNHN.F.Av16149, MNHN.F.Av16158, UM-AV-6-SK, UM-AV-9-SK), fragmentary right m3 (UM-AV-8-SK), fragment of left dentary with worn m3 and trigonid of m4 (MNHN.F.Av4642), left m4 (MNHN.F.Av16032, MNHN.F.Av16037; Crochet 1980b: fig. 13).
Material from Condé-en-Brie: left M2 (MNHN.F.CB1486, MNHN.F.CB3707, MNHN.F.CB3637), left worn M2 (MNHN.F.CB835, MNHN.F.CB4183), right M2 (MNHN.F.CB1080; Crochet 1980b: fig. 27, MNHN.F.CB3213, MNHN.F.CB3228), right M3 (MNHN.F.CB4182), left m1 (MNHN.F.CB962, MNHN.F.CB4391), right dentary with fragmentary m2-m4 (MNHN.F.CB226; Crochet 1980b: fig. 29), left m2 (MNHN.F.CB5090, MNHN.F.CB5092, MNHN.F.CB5097, MNHN.F.CB828), right m2 (MNHN.F.CB872, MNHN.F.CB878), left m3 (MNHN.F.CB5104, MNHN.F.CB959), right m3 (MNHN.F.CB4213).

Material from Sézanne-Broyes: right M3 (MNHN.F.SZ18005), worn left M3 (MNHN.F.SZ18000), left M4 (MNHN.F.SZ18004), left m1 (MNHN.F.SZ18003), left m2 (MNHN.F.SZ18001), left m3 (MNHN.F.SZ18006).

## Comparative description

**Remark:** *Peradectes louisi* being similar to *Pd. crocheti* sp. nov., detailed comparisons of *Pd. louisi* with North American peradectids are not proposed, except where necessary (see 'Deciduous upper premolar' below).

**Deciduous upper premolar:** Only one isolated DP3, from Mutigny, is known for European peradectids (MNHN.F.Mu18005, Fig. 10a-b). This specimen was part of the hypodigm of *Pd. louisi* (Crochet 1979). Although *Pd. louisi* is coeval with *Pd. russelli* in Mutigny, MNHN.F.Mu18005 certainly belongs to *Pd. louisi* instead of *Pd. russelli* due to its small size (L = 1.54 mm; W = 1.26 mm). It is as long and less wide than the M1 of *Pd. louisi*. The dP3 is also identified as such by the long and wide stylar cusp A spur and the deep mesial emargination of the short paracingulum. Compared to dP3 of *Pd. chesteri* (Murphey et al. 2018: fig. 13.1) and *Pd. californicus* (Rothecker and Storer 1996: fig. 1O), the only other described and figured
peradectid dP3 with ascertained specific attribution, MNHN.F.Mu18005 is relatively longer.
The ratio of the labiolingual width of dP3 to the labiolingual width of M1 is similar in *Pd. louisi*
and *Pd. chesteri*. The protocone is strictly lingual to the midpoint of the centrocrista on
MNHN.F.Mu18005. The paracone and metacone are identical in mesiodistal length and height,
whereas the protocone is much smaller. Contrary to *Pd. chesteri*, the paraconule and the
ectoflexus are absent, and the distal emargination of the crown is present. MNHN.F.Mu18005
retains a postparaconular crista reaching the base of the paracone. Stylar cusps C and D are
present in this specimen. Stylar cusp C is vestigial compared to stylar cusp D, whereas stylar
cusp C is absent in *Pd. chesteri* and *Pd. californicus* (note that the long stylar cusp in the D
position in *Pd. chesteri* was interpreted as a stylar cusp C by Murphey et al. 2018). Stylar cusp
D is placed slightly distolabially to the metacone apex on MNHN.F.Mu18005. Stylar cusp D is
rather mesiolabial to the metacone apex in *Pd. californicus* according to the available
illustration.

**Upper molars:** The protocone is lower than paracone and metacone as in other European peradectids (Fig. 9h). The trigon basin is in intermediate position between the protocone, paracone and metacone on M1 (Fig. 9b). The protocone is positioned more lingually on M3, so that the trigon basin is closer to the paracone and metacone (Fig. 9f). A sharp ridge is present on the lingual edge of the acute protocone of the M3 on which this cusp is mesiodistally pinched (MNHN.F.SZ18005, Fig. 10n-o). The paraconule is faint. The holotype bears a premetaconular crista unlike the other unworn M3, which lack internal conular cristae (the worn MNHN.F.GL265 retains internal conular cristae). Various M1 and M2 have faint internal conular cristae (e.g., Fig. 10d, f, h). The postmetaconular crista elongates from M1 to M3. Similar to *Pd. crocheti* sp. nov., the paracingulum is either of constant mesiodistal length or it is occasionally emarginated mesially to the paracone apex (e.g., MNHN.F.Mu6511, Fig. 10l for M2, MNHN.F.SZ18005, Fig. 10o for M3). The distal emargination of the crown is rarely
<figure><img src="image_12.png" /><figcaption>**Fig. 10** Upper molars of *Peradectes louisi* from Avenay (MP8+9), Condé-en-Brie, Mutigny and Sézanne-Broyes (~MP8+9), all in the Paris Basin. **a-b.** MNHN.F.Mu18005, right dP3; **a.** lingual view; **b.** occlusal view. **c-d.** MNHN.F.Mu18006, left M1; **c.** labial view; **d.** occlusal view. **e-f.** UM-AV-1-SK, left M1; **e.** labial view; **f.** occlusal view. **g-h.** MNHN.F.CB3213, right M2; **g.** labial view; **h.** occlusal view. **i-j.** MNHN.F.CB3228, right M2; **i.** labial view; **j.** occlusal view. **k-l.** MNHN.F.Mu6511, left M2; **k.** labial view; **l.** occlusal view. **m-o.** MNHN.F.SZ18005, right M3; **m.** labial view; **n.** lingual view; **o.** occlusal view. **p.** MNHN.F.CB4182, right M3 in occlusal view. **q-r.** MNHN.F.SZ18004, left M4; **q.** labial view; **r.** occlusal view. The arrows denoting stylar cusp C on labial views are followed by '+' if the</figcaption></figure>
most ventral point on the [stylar cusp C – stylar cusp D] mesiodistal extension is reached on stylar cusp C, and by ‘-‘ if this most ventral point is reached on stylar cusp D. The segments on the occlusal views of MNHN.F.SZ18005 (o) and MNHN.F.CB4182 (p) are positioned on the paracone – metacone axis and its perpendicular line. Abbreviation: st D, stylar cusp D. Scale bar equals 1 mm.

lacking, the distal margin being straight on the M1 MNHN.F/GL1 (Fig. 9b) and the M3 MNHN.F.CB4182 (Fig. 10p). The preparacrista elongates from M1 to M3 as illustrated on the molar series from the type locality (Fig. 9). This crest is connected to stylar cusp A on M1 and M2 and to stylar cusp B on M3 and M4. The M2 MNHN.F/GL272 has an unworn and salient postmetacrista forming a high distal wall on the stylar shelf (Fig. 9c-d), which is not found in *Pd. crocheti* sp. nov. This distal wall is absent in most specimens (e.g., Fig. 10n).

Stylar cusp A is positioned mesiolingually to stylar cusp B on M2 and M3, except for the M2 MNHN.F.CB3228 having a stylar cusp A strictly mesial to stylar cusp B (Fig. 10j). Stylar cusp B is more conical on the M3 holotype than on the M3 MNHN.F.CB4182 (Fig. 10p) or MNHN.F.SZ18005 (Fig. 10o) for which it is labiolingually pinched. This stylar cusp is labial to the paracone apex on M1 and M2, and mesiolabial to the paracone apex on M3. Stylar cusp B of the holotype (Fig. 9f) and of MNHN.F.SZ18005 has a small crest on its lingual edge directed towards the preparacrista, similar to the one connected to the preparacrista on M1 and M2.

Stylar cusp C is absent on the holotype (Fig. 9e-g) and on the M3 MNHN.F.CB4182. Variation in the positioning of this stylar cusp exists, as in *Pd. crocheti* sp. nov., so that it can be closer to stylar cusp B than to stylar cusp D (e.g., for M2, MNHN.F.CB1486 or MNHN.F/GL272, Fig. 9c vs MNHN.F.Mu6511, Fig. 10k). The doubling of stylar cusp C occurs only in one specimen (MNHN.F.CB1080, Crochet 1980b: fig. 27), as in *Pd. crocheti* sp. nov. Unlike other peradectid species, stylar cusp D is distolabial to the metacone apex on M3, in addition to M1 and M2
(e.g., molar series of Fig. 9). Conversely, M2 specimens from various localities have a stylar cusp D strictly labial instead of distolabial to the metacone apex (MNHN.F.Mu6511, Fig. 10l; MNHN.F.Av18004; MNHN.F.CB3213, Fig. 10h). On M2, stylar cusp D is either conical (e.g., Fig. 10l) or labiolingually pinched (Figs. 9d, 10j). The apex of stylar cusp C is less ventral than the apex of stylar cusp D on all M1 to M3, except on the M2 MNHN.F.CB3228 (Fig. 10i). Altogether, the relative heights of the stylar cusps A to D of M1 to M3 of *Pd. louisi* are mostly as follows: st. B > A > D > C (Table 3). Among ascertained peradectids, the apex of stylar cusp C is also less ventral than the apex of stylar cusp D on M2 and M3 only in *Pd. russelli* (only on M3), *M. houdei* (differs from *M. labrus* and *M. sowasheensis*, pers. obs.), *Pd. gulottai*, *Pd. californicus*, *Nanodelphys hunti* (Cope, 1873) (stylar cusp C is absent on the holotype, preserving M2 and M3 [McGrew 1937: figs. 3-4]) and *Didelphidectes cf. pumilis* (stylar cusp C is absent and stylar cusp D is present in the latter) (Table 3). Stylar cusp C is also vestigial in *Pd. chesteri* (Table 3). Stylar cusp E is notably present in UM-AV-1-SK, on which it is as high as stylar cusp D (Fig. 10e), and on UM-AV-2-SK. Stylar cusp E occurs more frequently than in *Pd. crocheti* sp. nov.

M1 lack the ectoflexus (e.g., Figs. 9b, 10f), except UM-AV-2-SK on which it is narrow and MNHN.F.Mu18006 with a longer ectoflexus (Fig. 10d). The ectoflexus is asymmetric on M3 as in other European peradectids (e.g., Fig. 9f), particularly on MNHN.F.SZ18000 with a metastylar wing much more labially extended than the parastylar wing. The asymmetry is less marked on MNHN.F.SZ18005 (Fig. 10o) from the same locality. The ectoflexus of M2 can be deeper than on M3 (e.g., Figs. 9d, 10h vs Fig. 9f).

We report the first M4 of *Pd. louisi*, from Sézanne-Broyes (MNHN.F.SZ18004, Fig. 10q-r). The ectoflexus is deep as in other peradectids. The talon is relatively labiolingually wider than on M4 of *Pd. crocheti* sp. nov. As in *Pd. russelli* (Crochet 1979: fig. 2) and contrary to *Pd. crocheti* sp. nov., stylar cusp C is greatly reduced (Fig. 10q). Stylar cusp A is the highest.
Contrary to the M4 of both *Pd. crocheti* sp. nov. and *Pd. russelli*, the metastylar wing is relatively larger, and the protocone is subequal in height to the metacone instead of being higher. The paracone and metacone are subequal in height, but both cusps are worn.

**Lower molars:** m2 have a talonid most often as labiolingually wide or wider than the trigonid (e.g., Fig. 11m, o), as in *Pd. crocheti* sp. nov. and almost all m2 of *Pd. russelli*. However, one m2 has a talonid slightly narrower than the trigonid (MNHN.F.SZ18001, Fig. 11k), resembling the condition seen in the m2 of ‘*Arm.*’ *dufraingi*. The m3 MNHN.F.Av16149 has a trigonid relatively longer (L/W trigonid = 1.20) than any other m3 of *Pd. louisi*, for which the trigonid is most often as long as wide (e.g., Fig. 11r, t, v, x). The development of the precingulid varies for a given molar locus (e.g., Fig. 11r vs 11t). The protoconid is always markedly higher than on m4 of ‘*Arm.*’ *dufraingi*. The metaconid is always distolingual to the protoconid. On m3, the paraconid and metaconid are either equal in mesiodistal length (e.g., Fig. 11s) or the metaconid is longer (e.g., Fig. 11y).

The cristid obliqua is almost straight on some m2 (e.g., MNHN.F.CB878, Fig. 11o; MNHN.F.Av16027, Crochet 1980b: fig. 11), m3 (e.g., MNHN.F.GL261; Fig. 11v) and m4 (MNHN.F.GL301; Fig. 11e), whereas it is curved on most lower molar specimens (Fig. 11). There is notable variation of the positionning of the mesial end of the cristid obliqua for a given molar locus. For example, the cristid obliqua ends mesially labial to the protocristid notch on the m3 MNHN.F.CB4213 (Fig. 11r), but is close to the protocristid notch on the m3 MNHN.F.Av18002 (Fig. 11t). The postcristid is straight instead of curved (i.e., the hypoconulid is weakly distally projected) on all m1 (e.g., Fig. 11a, c), 8 out of 13 m2 specimens (e.g., MNHN.F.CB828, Fig. 11m; MNHN.F.CB878, Fig. 11o), only 6 out of 17 m3 specimens (e.g., MNHN.F.Av4642, Fig. 11i; UM-AV-6-SK), and 2 out of 3 m4 specimens (MNHN.F.GL301, Fig. 11e; MNHN.F.Av16037, Crochet 1980b: fig. 13).
<figure><img src="image_13.png" /><figcaption>**Fig. 11** Lower molars of *Peradectes louisi* (except **g-h**) from Avenay (MP8+9), Condé-en-Brie, Sables de Brasles, Sézanne-Broyes (~MP8+9) and of *Peradectes* cf. *louisi* from Saint-Agnan (MP8+9-MP10 interval), all localities being in the Paris Basin. **a-b.** MNHN.F.GL136, right m1; **a.** occlusal view; **b.** labial view. **c-d.** MNHN.F.SZ18003, left m1; **c.** occlusal view; **d.** lingual</figcaption></figure>
view. **e-f.** MNHN.F.GL301, right m4; **e.** occlusal view; **f.** mesiolabial view. **g-h,** comparison with MNHN.F.STA296, left m4 of *Peradectes cf. louisi* from Saint-Agnan (Aisne, MP8+9-MP10 interval); **g.** occlusal view; **h.** lingual view. **i.** MNHN.F.Av4642, left hemi-mandible fragment with fragmentary trigonid of m2 and worn m3 in occlusal view. **j.** MNHN.F.CB226, m2-m4 from a right hemi-mandible fragment in occlusal view. **k-l.** MNHN.F.SZ18001, left m2; **k.** occlusal view; **l.** lingual view. **m-n.** MNHN.F.CB828, left m2; **m.** occlusal view; **n.** labial view. **o-p.** MNHN.F.CB878, right m2; **o.** occlusal view; **p.** lingual view. **q-s.** MNHN.F.CB4213, right m3; **q.** distal view; **r.** occlusal view; **s.** lingual view. **t-u.** MNHN.F.Av18002, right m3; **t.** occlusal view; **u.** labial view. **v-w.** MNHN.F.GL261, left m3; **v.** occlusal view; **w.** labial view. **x-y.** MNHN.F.GL263, left m3; **x.** occlusal view; **y.** lingual view. Abbreviation: **e – h notch,** entoconid – hypoconulid notch. Scale bar equals 1 mm.

On the partial hemi-mandible MNHN.F.CB226, the only partial molar row known for *Pd. louisi*, the m3 has a much smaller entoconid than the m2, so that the entoconid is minute on the m3 (Fig. 11j). The talonid is slightly labiolingually wider on the m2 than on the m3 on this specimen. The talonid is as labiolingually wide as the trigonid on most of the m2 specimens (see above), whereas the talonid is narrower than the trigonid on the m3 (e.g., Fig. 11k, m, o for m2 vs Fig. 11r, t, v, x for m3). Among the 46 lower molar specimens, 41 have a strong labial emargination of the crown. The emargination is weaker in five specimens with a relatively wider hypoflexid, namely the m1 MNHN.F.CB4391 and UM-AV-12-SK, the m2 MNHN.F.Av16016 and MNHN.F.CB5092, and the m3 MNHN.F.GL383. Among them, only MNHN.F.Av16016 and MNHN.F.GL383 have a labial emargination as weak as in equivalent molar loci in *Pd. crocheti* sp. nov.

The entoconid and hypoconulid are small on all molars, so that the entoconid – hypoconulid notch is shallow (Fig. 11j). These two cuspid are sometimes so minute on the m3 that the notch between them is shallower than on m1 and m2 (e.g., MNHN.F.GL261, Fig. 11w) to indistinct (e.g., MNHN.F.GL383, UM-AV-5-SK). The entoconid is asymmetrical in lateral view because the entoconid – metaconid notch is deeper than the entoconid – hypoconulid notch. The
postentocristid is sometimes absent on m2 (e.g., MNHN.F.CB878; Fig. 11o vs Fig. 11j, m) and m3 (e.g., MNHN.F.CB4213; Fig. 11r vs Fig. 11j, t, v), so that the entoconid and hypoconulid are not connected by a crest on the concerned specimens. Even on the m2 with a small entoconid (e.g., MNHN.F.SZ18001, Fig. 11l), the entoconid is always at least slightly higher than the hypoconulid. These two cuspids are mostly subequal in height on the m3 (Fig. 11s, u, w, y), but some specimens have a slightly higher entoconid as for the m2 (e.g., UM-AV-4-SK). The relative length of the entoconid of the m3 varies from shorter than the hypoconulid (e.g., MNHN.F.GL263, Fig. 11y) to as long as the hypoconulid (e.g., MNHN.F.CB4213, Fig. 11s). The entoconid is as high as the hypoconid in distal view (Fig. 11q). MNHN.F.Av18002 has a lingually unreduced postcingulid (Fig. 11t). The degree of lingual curvature of the talonid also varies, especially on m3 (e.g., Fig. 11v vs Fig. 11x).

The lower molar MNHN.F.Av16032 exhibits typical peradectid traits such as a lingually curved talonid and a hypoconid mesiolabial to entoconid, and is similar to other *Pd. louisi* m4 in occlusal view in having a small labiolingually pinched talonid with an almost centered hypoconulid on the distal margin of the talonid, and an absence of a prominent postcingulid reaching the base of the hypoconulid (e.g., MNHN.F.GL301, Fig. 11e). However, although other peradectid m4 have an entoconid much lower than the hypoconulid (Fig. 11f, h), and other *Pd. louisi* m4 (MNHN.F.GL301 and MNHN.F.Av16037) have a straight postcristid, on MNHN.F.Av16032 the entoconid is large, as high as the hypoconulid and higher than the hypoconid, and the postcristid is curved. Because the relative height of the entoconid varies as such in *Pt. constans* m4 (e.g., Ladevèze et al. 2012: fig. 6Hc vs fig. 6Ic) and because m4 of the closely related *Pd. crocheti* sp. nov. and *Pd. cf. louisi* have a curved postcristid (Figs. 7a, 11g), MNHN.F.Av16032 is identified as m4 of *Pd. louisi*. The hypoconid apex is placed slightly distolabially to the protoconid apex on MNHN.F.Av16032, this character being observed also in ascertained peradectid m4 (e.g., Fig. 11g). The preprotocristid is not convex in labial view
on two m4 specimens (MNHN.F.Av16037, Crochet 1980b: fig. 13a; MNHN.F.GL301, Fig. 11f) contrary to other molar loci (e.g., Fig. 11b vs Fig. 11f) and to the m4 MNHN.F.Av16032.

*Peradectes cf. louisi*

Figure 11g-h

? 1983 *Peradectes mutigniensis* Crochet; Louis and Laurain: p. 8.

**Material:** MNHN.F.STA296, left m4.

**Locality and age:** Saint-Agnan, Aisne, eastern Paris Basin; MP8+9 – MP10 interval (see Louis and Laurain 1983; Lecomte 1994; Escarguel 1999; Solé et al. 2018).

**Description and comment:** The only peradectid specimen from Saint-Agnan is the m4 MNHN.F.STA296. It is much smaller than the m4 of *Pd. russelli*, and larger and with a higher crown than the m4 of *'Arm.' dufraingi*. MNHN.F.STA296 does not differ in size and morphology from the m4 of *Pd. louisi* MNHN.F.GL301 and MNHN.F.Av16037 (e.g., Fig. 11e-f vs Fig. 11g-h; Online Resource 1: Table S2). However, peradectid m4 are rare and bear less diagnostic characters than m2 and m3. For example, the relative height of the entoconid and hypoconulid in addition to the morphology of the notch between them allow to distinguish the European species *Pd. crocheti* sp. nov., *Pd. louisi* / *Pd. russelli* and *'Arm.' dufraingi* based on m2 and m3. On m4, the configuration of these cuspids is the same for the four valid species and MNHN.F.STA296, with the entoconid much lower than the hypoconulid (Fig. 11h; except MNHN.F.Av16032). Because of this, and the lack of other molar loci from Saint-Agnan, MNHN.F.STA296 can only be tentatively ascribed to *Peradectes cf. louisi*. Furthermore, it is worth mentioning that undescribed peradectid species, also equivalent in size to *Pd. louisi*, probably occur in localities younger than MP8+9 (see Discussion, 'Revision of putative occurrences of typical MP8+9 and ~MP8+9 peradectids in MP10 and ~MP10 faunas').
*Peradectes russelli* Crochet, 1979

Figure 12

**Remark:** *Peradectes 'mutigniensis'* Crochet, 1979, is considered a junior synonym of *Pd. russelli* (see Discussion).

1977a *Peradectes* sp. nov. 2; Crochet: p. 359, pl. 1, fig. C.

1979 *Peradectes russelli* Crochet; Crochet: p. 367-368, fig. 2 (in part).

1979 *Peradectes mutigniensis* Crochet; Crochet: p. 368, fig. 3.

1980b *Peradectes louisi* Crochet; Crochet: fig. 4a (in part).

1980b *Peradectes russelli* Crochet; Crochet: p. 43-46, figs. 14-17 (no fig. 18) (in part).

1980b *Peradectes mutigniensis* Crochet; Crochet: p. 46-49, figs. 19-25.

1980b *Peradectes* sp.; Crochet: p. 51 (in part).

**Holotype:** MNHN.F.CB924, fragment of right maxilla with M3-M4, housed at the Muséum National d'Histoire Naturelle (Paris), and figured by Crochet (1977a: pl. 1, fig. C₃, 1979: fig. 2; 1980b: fig. 16).

**Localities:** Condé-en-Brie (type locality), Avenay, Mutigny, Sables de Brasles, Sézanne-Broyes; all in the eastern Paris Basin.

**Age:** middle Ypresian (middle early Eocene), MP8+9 and ~MP8+9 reference level (~ mammalian biozones PE IV and PE V)

**Material:** Additional material from Condé-en-Brie: left M1 (MNHN.F.CB2501; Crochet 1977a: pl. 1, fig. C₁, 1980b: fig. 14, MNHN.F.CB3275), right M1 (MNHN.F.CB3007), left M2 (MNHN.F.CB5103; Crochet 1977a: pl. 1, fig. C₂, 1980b: fig. 15, MNHN.F.CB840, MNHN.F.CB850), right M2 (MNHN.F.CB3644), labial half of right M2 (MNHN.F.CB2753), left M3 (MNHN.F.CB742), right M3 (MNHN.F.CB2502), right m1 (MNHN.F.CB3021), right
m2 (MNHN.F.CB5098, MNHN.F.CB5100, MNHN.F.CB928), fragment of right dentary with
worn m2 (MNHN.F.CB925).

Material from Avenay: left M1 (UM-AV-13-SK), right M1 (MNHN.F.Av16024; Crochet 1980b: fig. 19), right M3 (MNHN.F.Av4813; Crochet 1980b: fig. 4a, MNHN.F.Av6837), left m2 (MNHN.F.Av7235; Crochet 1980b: fig. 17, UM-AV-14-SK), right m2 (UM-AV-15-SK).

Material from Mutigny: left M1 (MNHN.F.Mu18004; Crochet 1980b: fig. 20), right M1 (MNHN.F.Mu5532), left M2 (MNHN.F.Mu18002; Crochet 1980b: fig. 21), right M3 (MNHN.F.Mu5521; Crochet 1980b: fig. 22), right m2 (MNHN.F.Mu18000; Crochet 1980b: fig. 23), left m3 (MNHN.F.Mu6451; Crochet 1980b: fig. 24), right m4 (MNHN.F.Mu18003).

Material from Sables de Brasles: right m2 (MNHN.F.GL92; Crochet 1980b: fig. 25), right m3 (MNHN.F.GL410).

Material from Sézanne-Broyes: left m1 (MNHN.F.SZ18002).

**Translation to English of the original French diagnosis (Crochet 1979):** 'European species of median size. On M3, stylar cusp B slightly higher than other stylar cusps. Ectoflexus symmetric, wide and well-developed, stylar cusp C reduced. Paraconule not very pronounced or absent, metaconule weak. In occlusal view, M3 with a rather massive aspect (stylar line relatively long, preprotocrista – postprotocrista angle quite open). On lower molars, lingual opening of the prefossid higher than the lowest point of the entocristid. m4 longer than m3.'

**New differential diagnosis:** Differs from the other European peradectid species in being significantly larger. Further differs from *Pd. crocheti* sp. nov. in having: (i) stylar cusp C apex less ventral than stylar cusp D apex on M3; (ii) crown labial emargination on m3 and m4, and often m2; (iii) trigonid more labiolingually wide than talonid on m3; and (iv) entoconid and hypoconulid separated by a shallower notch. Differs also from *Pd. louisi* and '*Arm.' dufraingi* in having relatively wider lower molars. Further differs from *Pd. louisi* in having: (i) stylar cusp
D strictly labial to metacone apex; and (ii) stylar cusp C apex as ventral as stylar cusp D apex on M1 and M2. Further differs from ‘Arm.’ *dufraingi* notably by: (i) entoconid higher than hypoconulid on m2 and as high as hypoconulid on m3; and (ii) larger postcingulid on m2 and m3.

**Comparative description**

**Remark:** *Peradectes russelli* being similar to *Pd. crocheti* sp. nov. and *Pd. louisi*, detailed comparisons of *Pd. russelli* with North American peradectids are not proposed.

**Upper molars:** The mesiodistal length of the talon and of the centrocrista varies positively with the mesiodistal length of the specimens (e.g., MNHN.F.CB3007, Fig. 12b vs MNHN.F.CB3275, Fig. 12d for M1; MNHN.F.Av6837, Fig. 12f vs MNHN.F.CB2502, Fig. 12h for M3). The protocone of one M1 (MNHN.F.Av16024; Crochet 1980b: fig. 19b) and two M2 (MNHN.F.Mu18002, Crochet 1980b: fig.21; MNHN.F.CB850, Fig. 12j) is relatively more distally positioned than for other specimens (still mesiolingual to the midpoint of the centrocrista). The tiny paraconule preserved on molars of the holotype (Crochet 1979: fig. 2; pers. obs.) is indistinct on most other upper molars (Fig. 12b, d, f, h, j), as in *Pd. louisi*. M1 and M2 have a faint premetaconular crista in addition to the postmetaconular crista (e.g., Fig. 12b, d, j), the former being more marked on some specimens (e.g., MNHN.F.CB2501). The M3 MNHN.F.CB2502 has a doubled stylar cusp A (Fig. 12g-h). One of the two small cusps in the stylar cusp A position is directly mesial to stylar cusp B, and is connected to it by a crest; the second small A cusp is placed mesiolingually to stylar cusp B, as on other M3. Stylar cusp B is strictly labial to the paracone on the M3 of the holotype (MNHN.F.CB924; Crochet 1979: fig. 2) and mesiolabial to the paracone on the M3 MNHN.F.Mu5521, former holotype of *Pd. mutigniensis* (Crochet 1979: fig. 3). Apart from MNHN.F.CB924, only the M3
<figure><img src="image_14.png" /><figcaption>**Fig. 12** Upper and lower molars of *Peradectes russelli* from Avenay (MP8+9), Condé-en-Brie, Mutigny, Sables de Brasles and Sézanne-Broyes (~MP8+9), all in the Paris Basin. **a-b.** MNHN.F.CB3007, right M1; **a.** labial view; **b.** occlusal view. **c-d.** MNHN.F.CB3275, left M1; **c.** reversed labial view; **d.** reversed occlusal view. **e-f.** MNHN.F.Av6837, right M3; **e.** labial view; **f.** occlusal view. **g-h.** MNHN.F.CB2502, right M3; **g.** labial view; **h.** occlusal view. **i-j.** MNHN.F.CB850, left M2; **i.** reversed labial view; **j.** reversed occlusal view. **k.** UM-AV-14-SK, left m2 in reversed occlusal view. **l-m.** MNHN.F.Mu18000, right m2; **l.** occlusal view; **m.** lingual view. **n-o.** MNHN.F.SZ18002, left m1; **n.** reversed occlusal view; **o.** reversed lingual</figcaption></figure>
view. **p-q.** MNHN.F.CB928, right m2; **p.** occlusal view; **q.** lingual view. **r-t.** MNHN.F.GL410, right m3; **r.** distal view; **s.** occlusal view; **t.** lingual view. **u-v.** MNHN.F.Mu18003, right m4; **u.** occlusal view; **v.** lingual view. The arrows denoting the stylar cusp C on labial views are followed by '+' if the most ventral point on the st. C – st. D mesiodistal extension is reached on the st. C, and by '-' if this most ventral point is reached on the st. D. The segments on the occlusal views of MNHN.F.Av6837 (**f**) and MNHN.F.CB2502 (**h**) are positioned on the paracone – metacone axis and its perpendicular line. Abbreviation: **st D**, stylar cusp D. Scale bar equals 1 mm.

MNHN.F.Av4813 (Crochet 1980b: fig. 4a) has a stylar cusp B strictly labial to the paracone (2 out of 6 M3 specimens). This character state is present on all M1 and M2 as in *Pd. crocheti* sp. nov. and *Pd. louisi*. In occlusal view, stylar cusp C is closer to stylar cusp B than to stylar cusp D on 4 out of 7 M1 (MNHN.F.CB2501; MNHN.F.CB3275, Fig. 12c; MNHN.F.Mu18004; MNHN.F.Mu5532) and 2 out of 5 M2 (MNHN.F.CB5103; MNHN.F.CB850, Fig. 12i). The apices of stylar cusps C and D are equally ventral on both M1 and M2 contrary to *Pd. louisi*, except for the M1 MNHN.F.CB3007 on which stylar cusp D is more ventral than the vestigial stylar cusp C (1 out of 12 M1 to M2 specimens, Fig. 12a). The height relationships of stylar cusps of *Pd. russelli* are as follows: st. B > A = C = D for M2, and st. B > A > D > C for M3 (e.g., Fig. 12e) (Table 3). On 5 out of 18 isolated M1-M3 (MNHN.F.Mu18004 and MNHN.F.CB3275 for M1, MNHN.F.CB850 for M2, MNHN.F.CB742 and MNHN.F.CB924 for M3), stylar cusp D has a lingual crest of variable labiolingual length (e.g., Fig. 12d, j), which is unseen in *Pd. crocheti* sp. nov. and *Pd. louisi*. The ectoflexus is relatively deep on 4 out of 7 M1 (e.g., MNHN.F.CB3007, Fig. 12b), especially on UM-AV-13-SK. The M4 (MNHN.F.CB924, Crochet 1979: fig. 2) lacks stylar cusp C unlike *Pd. crocheti* sp. nov. and *Pd. louisi*, and has minute stylar cusps A and B. The M4 lacks internal conular cristae. As in *Pd. crocheti* sp. nov. and *Pd. louisi*, stylar cusp A of M4 is higher than stylar cusp B and there is a deep ectoflexus.
**Lower molars:** The m1 and m4 described here are the first reported for this species. m1 have a relatively long paracristid and a metaconid much higher than the paraconid. The m1 from Sézanne-Broyes (MNHN.F.SZ18002, Fig. 12n-o) is significantly larger than the m1 of *Pd. louisi* from the same locality (MNHN.F.SZ18003, Fig. 11c-d). As in *Pd. louisi*, m2 differ from m3 in having as labiolingually wide trigonid and talonid instead of a narrower talonid, and entoconid higher than the hypoconulid instead of equal in height (e.g., Fig. 12l-m, p-q vs Fig. 12s-t). The talonid is as labiolingually wide or wider than the trigonid on m2, except for MNHN.F.GL92, for which the talonid is slightly narrower than the trigonid (Crochet 1980b: fig. 25). The metaconid is longer than the paraconid on m1 and m2 (Fig. 12o, q), these two cuspids are subequal in length on m3 (Fig. 12t), and the paraconid is longer than the metaconid on the single available m4 (Fig. 12v). The labial emargination of the crown is present in one out of the two m1 (MNHN.F.SZ18002, Fig. 12n), slightly on 4/9 m2 (e.g., UM-AV-14-SK, Fig. 12k vs MNHN.F.Mu18000, Fig. 12l) and all m3-m4 (Fig. 12s, u). The entoconid and hypoconid are of the same height in distal view (e.g., Fig. 12r), with the exception of the m2 MNHN.F.CB928, with a hypoconid higher than the entoconid. The hypoconid is unambiguously mesiolabial instead of labial to the entoconid on some lower molars (e.g., Fig. 12k, l, n, u), as in *Pd. louisi*. On m2, the entoconid can be positioned either close to the distolingual corner of the molar (e.g., UM-AV-14-SK, Fig. 12k or MNHN.F.Mu18000, Fig. 12l) or intermediate between the distal edge of the trigonid and the distal margin of the molar (e.g., MNHN.F.CB928, Fig. 12p). The entoconid – hypoconulid notch is slightly higher than the metaconid – entoconid notch on m2 (e.g., MNHN.F.CB928, Fig. 12q) and much higher on m3 (e.g., MNHN.F.GL410, Fig. 12t). m1 and m4 have a straight postcristid, whereas it is curved on m2 and m3. The m4 has a relatively long paracristid lingual segment, a relatively high paraconid and a labiolingually narrow talonid (Fig. 12u), as in *Pd. crocheti* sp. nov. and *Pd.*
*louisi*. The mesial end of the cristid obliqua of m4 is slightly labial to the protocristid notch on the trigonid wall. There is no distinct postcingulid on m4, as in *Pd. louisi*.

## Results

### Quantitative comparisons

**Size and proportions of molars.** Univariate statistics based on molar measurements for the three studied peradectid species are presented in Table 4. The two complete and unworn upper molars from Palette are the M1 MHN.AIX.PV.2018.26.20, which is smaller than the M1 of the holotype, and the M3 MHN.AIX.PV.2017.6.7, which is larger than the M3 of the holotype (Online Resource 1: Table S1). In particular, the length and width of MHN.AIX.PV.2018.26.20 represent the minimum of the observed range values for M1, and the width of MHN.AIX.PV.2017.6.7 is the maximum of the observed range values for M3 (material from all localities included). Thus, most of the size variation of *Pd. crocheti* sp. nov. is represented in its type locality. The disparity of length to width ratio between the M2 and M3 (L/W M2 - L/W M3) is weak based on mean values (i.e., < 0.10) for *Pd. louisi* and *Pd. russelli* (isolated molars only). Because of the low number of specimens with calculated L/W ratios for M2 of *Pd. crocheti* sp. nov. (two specimens, including the holotype), only the disparity of M2-M3 from the type specimen is retained for comparisons of this character between *Pd. crocheti* sp. nov. and other peradectids (Table 2). The m1 of *Pd. crocheti* sp. nov. and *Pd. louisi* are a mean of 9% mesiodistally shorter than the m2, whereas this value is 12.5% for *Pd. russelli* (Table 4).

The standard deviation and coefficient of variation values for the length of the M2 of *Pd. crocheti* sp. nov. are relatively higher than for the other molar loci, probably because the M2 from Croydon (Hooker 2020) is much larger than other M2 specimens ascribed to this species. However, the normal distribution for the length of the M2 of *Pd. crocheti* sp. nov. is not
<table><caption>**Table 4** Univariate statistics associated with measurements (in mm) of upper and lower molars of *Peradectes crocheti* sp. nov., *Pd. louisi* and *Pd. russelli*. Abbreviations: **N**, number of specimens measured; **OR**, observed range; **SD**, standard deviation; **CV**, unbiased coefficient of variation (%); **W**, Shapiro-Wilk normality test (**ns**, normal distribution cannot be rejected; **s**, normal distribution is rejected; P < 0.05).</caption><thead><tr><th colspan="8">Peradectes crocheti sp. nov</th><th colspan="8">Peradectes louisi</th><th colspan="8">Peradectes russelli</th></tr><tr><th>Locus</th><th>N</th><th>OR</th><th>Mean</th><th>SD</th><th>CV</th><th>W</th><th>Locus</th><th>N</th><th>OR</th><th>Mean</th><th>SD</th><th>CV</th><th>W</th><th>Locus</th><th>N</th><th>OR</th><th>Mean</th><th>SD</th><th>CV</th><th>W</th></tr></thead><tbody><tr><td>M1</td><td>L</td><td>5</td><td>1.51-1.71</td><td>1.60</td><td>0.079</td><td>4.91</td><td>ns</td><td>M1</td><td>L</td><td>9</td><td>1.47-1.65</td><td>1.56</td><td>0.060</td><td>3.86</td><td>ns</td><td>M1</td><td>L</td><td>7</td><td>1.62-1.97</td><td>1.81</td><td>0.117</td><td>6.45</td><td>ns</td></tr><tr><td></td><td>W</td><td>6</td><td>1.40-1.59</td><td>1.49</td><td>0.093</td><td>6.27</td><td>s</td><td></td><td>W</td><td>9</td><td>1.45-1.66</td><td>1.55</td><td>0.070</td><td>4.50</td><td>ns</td><td></td><td>W</td><td>7</td><td>1.78-2.09</td><td>1.89</td><td>0.099</td><td>5.25</td><td>ns</td></tr><tr><td></td><td>L/W</td><td>5</td><td>0.97-1.21</td><td>1.06</td><td>0.092</td><td>8.67</td><td>ns</td><td></td><td>L/W</td><td>9</td><td>0.94-1.07</td><td>1.01</td><td>0.042</td><td>4.19</td><td>ns</td><td></td><td>L/W</td><td>7</td><td>0.88-1.03</td><td>0.96</td><td>0.048</td><td>5.01</td><td>ns</td></tr><tr><td>M2</td><td>L</td><td>7</td><td>1.45-1.81</td><td>1.57</td><td>0.117</td><td>7.46</td><td>ns</td><td>M2</td><td>L</td><td>6</td><td>1.52-1.71</td><td>1.61</td><td>0.068</td><td>4.23</td><td>ns</td><td>M2</td><td>L</td><td>5</td><td>1.82-2.11</td><td>1.97</td><td>0.110</td><td>5.58</td><td>ns</td></tr><tr><td></td><td>W</td><td>3</td><td>1.66-1.85</td><td>1.74</td><td></td><td></td><td></td><td></td><td>W</td><td>9</td><td>1.69-1.87</td><td>1.77</td><td>0.067</td><td>3.79</td><td>ns</td><td></td><td>W</td><td>4</td><td>2.07-2.27</td><td>2.19</td><td>0.097</td><td>4.43</td><td>ns</td></tr><tr><td></td><td>L/W</td><td>2</td><td>0.88-0.98</td><td>0.93</td><td></td><td></td><td></td><td></td><td>L/W</td><td>4</td><td>0.86-0.98</td><td>0.91</td><td>0.056</td><td>6.15</td><td>ns</td><td></td><td>L/W</td><td>4</td><td>0.85-0.92</td><td>0.88</td><td>0.030</td><td>3.38</td><td>ns</td></tr><tr><td>M3</td><td>L</td><td>5</td><td>1.40-1.60</td><td>1.53</td><td>0.078</td><td>5.10</td><td>ns</td><td>M3</td><td>L</td><td>4</td><td>1.41-1.63</td><td>1.51</td><td>0.093</td><td>6.17</td><td>ns</td><td>M3</td><td>L</td><td>6</td><td>1.78-2.02</td><td>1.92</td><td>0.096</td><td>5.01</td><td>ns</td></tr><tr><td></td><td>W</td><td>6</td><td>1.77-1.98</td><td>1.85</td><td>0.083</td><td>4.49</td><td>ns</td><td></td><td>W</td><td>4</td><td>1.72-1.92</td><td>1.83</td><td>0.083</td><td>4.53</td><td>ns</td><td></td><td>W</td><td>6</td><td>2.27-2.52</td><td>2.36</td><td>0.103</td><td>4.36</td><td>ns</td></tr><tr><td></td><td>L/W</td><td>4</td><td>0.77-0.87</td><td>0.82</td><td>0.044</td><td>5.44</td><td>ns</td><td></td><td>L/W</td><td>4</td><td>0.77-0.88</td><td>0.82</td><td>0.051</td><td>6.23</td><td>ns</td><td></td><td>L/W</td><td>6</td><td>0.78-0.86</td><td>0.81</td><td>0.030</td><td>3.74</td><td>ns</td></tr><tr><td>M4</td><td>L</td><td>2</td><td>1.12-1.26</td><td>1.19</td><td></td><td></td><td></td><td>M4</td><td>L</td><td>1</td><td>1.33</td><td></td><td></td><td></td><td></td><td>M4</td><td>L</td><td>1</td><td>1.35</td><td></td><td></td><td></td></tr><tr><td></td><td>W</td><td>1</td><td>1.79</td><td></td><td></td><td></td><td></td><td></td><td>W</td><td>1</td><td>1.88</td><td></td><td></td><td></td><td></td><td></td><td>W</td><td>1</td><td>2.36</td><td></td><td></td><td></td></tr><tr><td></td><td>L/W</td><td>1</td><td>0.70</td><td></td><td></td><td></td><td></td><td></td><td>L/W</td><td>1</td><td>0.71</td><td></td><td></td><td></td><td></td><td></td><td>L/W</td><td>1</td><td>0.57</td><td></td><td></td><td></td></tr><tr><td>m1</td><td>L</td><td>2</td><td>1.47-1.57</td><td>1.52</td><td></td><td></td><td></td><td>m1</td><td>L</td><td>8</td><td>1.40-1.56</td><td>1.50</td><td>0.063</td><td>4.19</td><td>ns</td><td>m1</td><td>L</td><td>2</td><td>1.65-1.71</td><td>1.68</td><td></td><td></td></tr><tr><td></td><td>W</td><td>3</td><td>0.86-0.94</td><td>0.91</td><td></td><td></td><td></td><td></td><td>W</td><td>8</td><td>0.76-0.85</td><td>0.81</td><td>0.038</td><td>4.73</td><td>ns</td><td></td><td>W</td><td>2</td><td>0.89-0.92</td><td>0.91</td><td></td><td></td></tr><tr><td></td><td>L/W</td><td>2</td><td>1.69-1.71</td><td>1.70</td><td></td><td></td><td></td><td></td><td>L/W</td><td>8</td><td>1.75-2.03</td><td>1.85</td><td>0.087</td><td>4.69</td><td>ns</td><td></td><td>L/W</td><td>2</td><td>1.79-1.92</td><td>1.86</td><td></td><td></td></tr><tr><td>m2</td><td>L</td><td>4</td><td>1.64-1.69</td><td>1.67</td><td>0.026</td><td>1.58</td><td>ns</td><td>m2</td><td>L</td><td>13</td><td>1.54-1.73</td><td>1.65</td><td>0.060</td><td>3.66</td><td>ns</td><td>m2</td><td>L</td><td>9</td><td>1.75-2.05</td><td>1.92</td><td>0.114</td><td>5.94</td><td>ns</td></tr><tr><td></td><td>W</td><td>3</td><td>0.99-1.04</td><td>1.02</td><td></td><td></td><td></td><td></td><td>W</td><td>14</td><td>0.87-1.00</td><td>0.94</td><td>0.044</td><td>4.62</td><td>ns</td><td></td><td>W</td><td>9</td><td>1.04-1.25</td><td>1.14</td><td>0.074</td><td>6.49</td><td>ns</td></tr><tr><td></td><td>L/W</td><td>3</td><td>1.59-1.71</td><td>1.63</td><td></td><td></td><td></td><td></td><td>L/W</td><td>13</td><td>1.61-1.83</td><td>1.74</td><td>0.060</td><td>3.45</td><td>ns</td><td></td><td>L/W</td><td>9</td><td>1.62-1.79</td><td>1.69</td><td>0.053</td><td>3.14</td><td>ns</td></tr><tr><td>m3</td><td>L</td><td>5</td><td>1.53-1.66</td><td>1.60</td><td>0.068</td><td>4.24</td><td>ns</td><td>m3</td><td>L</td><td>18</td><td>1.47-1.66</td><td>1.57</td><td>0.050</td><td>3.20</td><td>ns</td><td>m3</td><td>L</td><td>2</td><td>1.74-1.85</td><td>1.80</td><td></td><td></td></tr><tr><td></td><td>W</td><td>5</td><td>0.87-1.06</td><td>0.97</td><td>0.078</td><td>8.02</td><td>ns</td><td></td><td>W</td><td>16</td><td>0.84-0.95</td><td>0.89</td><td>0.036</td><td>4.02</td><td>ns</td><td></td><td>W</td><td>2</td><td>1.05-1.11</td><td>1.08</td><td></td><td></td></tr><tr><td></td><td>L/W</td><td>5</td><td>1.58-1.77</td><td>1.65</td><td>0.077</td><td>4.66</td><td>ns</td><td></td><td>L/W</td><td>16</td><td>1.62-1.87</td><td>1.77</td><td>0.063</td><td>3.58</td><td>ns</td><td></td><td>L/W</td><td>2</td><td>1.66-1.67</td><td></td><td></td><td></td></tr><tr><td>m4</td><td>L</td><td>1</td><td>1.55</td><td></td><td></td><td></td><td></td><td>m4</td><td>L</td><td>3</td><td>1.44-1.53</td><td>1.48</td><td></td><td></td><td></td><td>m4</td><td>L</td><td>1</td><td>1.75</td><td></td><td></td><td></td></tr><tr><td></td><td>W</td><td>1</td><td>0.92</td><td></td><td></td><td></td><td></td><td></td><td>W</td><td>3</td><td>0.78-0.85</td><td>0.83</td><td></td><td></td><td></td><td></td><td>W</td><td>1</td><td>1.00</td><td></td><td></td><td></td></tr><tr><td></td><td>L/W</td><td>1</td><td>1.68</td><td></td><td></td><td></td><td></td><td></td><td>L/W</td><td>3</td><td>1.74-1.85</td><td>1.80</td><td></td><td></td><td></td><td></td><td>L/W</td><td>1</td><td>1.75</td><td></td><td></td><td></td></tr></tbody></table>
rejected. The low standard deviation value for the length of the m2 of *Pd. crocheti* sp. nov. is most likely because two out of the four specimens included probably represent the same individual (MHN.AIX.PV.2017.6.8 and MHN.AIX.PV.2017.6.9). The normal distribution is rejected for the width of M1 of *Pd. crocheti* sp. nov. (Table 4). This is most likely because no size continuum is recorded between the six M1 forming two clusters for *Pd. crocheti* sp. nov. (Online Resource 1: Table S1). For all other molar measurements, the normal distribution is not rejected (see Table 4).

The observed ranges for dental measurements of *Pd. crocheti* sp. nov. and *Pd. louisi* are alike, except for the labiolingual width values of the lower molars, which are lower in the latter (Table 4). There is a statistically significant difference between the L/W ratios of lower molars of the coeval *Pd. louisi* and *Pd. russelli*, either when m1 to m4, m2 to m3 or only m2 are taken into account (Table 5). However, the mean L/W ratio for lower molars of *Pd. russelli* and *Pd. crocheti* sp. nov. do not differ significantly (Table 5). Similarly to *Pd. crocheti* sp. nov., the lower molars of *Pd. russelli* are relatively labiolingually wider than those of *Pd. louisi*, except for m1 (Table 4). For the three species studied, the m2 are larger than the m3 in mean (Table 4, Fig. 13). The m2 to m4 of *Pd. louisi* are larger than equivalent loci in 'Arm.' *dufraingi* (Table 4 vs Smith and Smith 2013: p. 304).

Taking into account all molar loci, the size distributions of *Pd. louisi* and *Pd. russelli* show almost no overlap (Fig. 13a-b). Only one M1 of *Pd. russelli* (MNHN.F.CB3007) is similar in size to M2 and M3 of the smaller *Pd. louisi* (Online Resource 1: Table S3). In the same way, the two m1 of *Pd. russelli* (MNHN.F.CB3021 and MNHN.F.SZ18002) are closer in size to both m2 and the largest m3 of *Pd. louisi* (Fig. 13b). However, M1 and m1 of *Pd. louisi* and *Pd. russelli* form two distinct size clusters. MNHN.F.SZ18004, the single M4 of *Pd. louisi*, is
attributed to this species in part because it is closer in width to the M3 of *Pd. louisi* than to the M3 of *Pd. russelli* (Fig. 13a).

**Table 5** Results of Welch's *t*-test for comparisons of mean length to width ratio values between lower molars of *Peradectes louisi* and *Peradectes russelli*. The equality of mean L/W ratios is rejected for the three subsamples (which differ in the molar loci included) comparing lower molars of *Pd. louisi* and *Pd. russelli*, but not for the sample comparing lower molars of *Pd. crocheti* sp. nov. and *Pd. russelli*. Abbreviations: **d.f.**, degree of freedom; **L**, length; **N**, number of lower molars; **P**, p-value; **ns**, mean values not significantly different; **s**, mean values significantly different, *P* < 0.05; **t**, Welch Two Sample *t*-test value; **W**, width.

<table><thead><tr><th>Compared samples for L / W ratio</th><th>Result of Welch's t-test</th></tr></thead><tbody><tr><td>m1-4 <i>Pd. louisi</i> (N = 40) vs <i>Pd. russelli</i> (N = 14)</td><td>s (t = 2.58, d.f. = 21.79, P = 0.017)</td></tr><tr><td>m2-3 <i>Pd. louisi</i> (N = 29) vs <i>Pd. russelli</i> (N = 11)</td><td>s (t = 3.79, d.f. = 23.32, P = 0.001)</td></tr><tr><td>m2 <i>Pd. louisi</i> (N = 13) vs <i>Pd. russelli</i> (N = 9)</td><td>s (t = 2.11, d.f. = 18.68, P = 0.049)</td></tr><tr><td>m1-4 <i>Pd. crocheti</i> sp. nov. (N = 11) vs <i>Pd. russelli</i> (N = 14)</td><td>ns (t = 1.88, d.f. = 22.99, P = 0.073)</td></tr></tbody></table>

MNHN.F.Mu5521, former holotype of *Pd. 'mutigniensis'*; is the M3 of *Pd. russelli* with the lowest length and width, whereas the M3 of the holotype of *Pd. russelli* (MNHN.F.CB924) has the highest width value of the sample (Fig. 13a). *Peradectes russelli* occupies a larger length x width space than *Pd. louisi* (Fig. 13a-b), probably due to its larger size. In particular, the M3 and M4 of the holotype MNHN.F.CB924 differ greatly in length, more than what would be expected for the same molar loci in *Pd. louisi* based on available M3 and M4 specimens (Fig. 13a). The M2 and M3 overlap more in width in *Pd. louisi* than in *Pd. russelli*. Conversely, the M2 and M3 overlap more in length in *Pd. russelli* than in *Pd. louisi*.

**Absolute basal heights of stylar cusps C and D.** In the whole sample, the values of the absolute basal height of stylar cusp C to the absolute basal height of stylar cusp D are comprised in a range from 0.215 (i.e., the absolute basal height value of stylar cusp C is more than four times lower than for stylar cusp D; M1 MNHN.F.CB3007 of *Pd. russelli*) to 1,939 (i.e., the absolute basal height value of stylar cusp C is almost two times higher than for stylar cusp D;
a

<figure><img src="image_15.png" /></figure>

b

<figure><img src="image_16.png" /></figure>

**Fig. 13** Bivariate graphs (length x width) of upper molars (**a**) and lower molars (**b**) of the two species of *Peradectes* (*Pd. louisi* and *Pd. russelli*) from MP8+9, ~MP8+9 and MP8+9-MP10 interval localities of the Paris Basin. For upper molars (**a**), specimen numbers indicate the holotype of *Pd. russelli* (MNHN.F.CB924), the former holotype of *Pd. mutigniensis* chosen by Crochet (1979) (MNHN.F.Mu5521) and the M4 of *Pd. louisi* (MNHN.F.SZ18004). For lower molars (**b**) the m4 specimen representing *Peradectes cf. louisi* is plotted in red. All measurements are from isolated molars with the exception of MNHN.F.CB924.

M3 UM-FDN-23 of *Pd. crocheti* sp. nov.) (Fig. 14; Online Resource 1: Table S4). The values equal or lower than the first quartile are only those of some M1 or M2 for *Pd. crocheti* sp. nov., whereas it concerns also some M3 specimens for the distributions of the values of *Pd. louisi* (MNHN.F.Mu18001) and *Pd. russelli* (MNHN.F.Av6837; MNHN.F.CB742). Conversely, the values equal or higher than the third quartile concern only M3 (five specimens) for *Pd. crocheti* sp. nov.; M1 (one specimen), M2 (three specimens) and M3 (one specimen) for *Pd. louisi*, with only M2 specimens as outlier values; and M1 (one specimen) and mostly M2 (four specimens)
for *Pd. russelli* (Fig. 14). It is worth noting that fewer M3 specimens are known for *Pd. louisi*
(five specimens) than for the two other species. Among these specimens, two lack stylar cusp
C (MNHN.F.GL197 and MNHN.F.CB4182), one is damaged in the stylar cusp C area, and only
two have measurable absolute basal heights for stylar cusps C and D (MNHN.F.Mu18001 and
MNHN.F.SZ18005; Online Resource 1: Table S4). *Peradectes russelli* differs from *Pd.
crocheti* sp. nov. and *Pd. louisi* in having a lower value for the interquartile range, almost equal
mean and median values, and the lowest ratio values of the whole sample (the M1
MNHN.F.CB2501 and MNHN.F.CB3007, and the M3 MNHN.F.CB742; Online Resource 1:
Table S4).

There is a statistically significant difference between the rank sum of the absolute basal height
of stylar cusp C to the absolute basal height of stylar cusp D of *Pd. crocheti* sp. nov. and *Pd.
louisi* (Fig. 14; Wilcoxon-Mann-Whitney test; W = 226, P = 0.043), and *Pd. crocheti* sp. nov.
and *Pd. russelli* (Wilcoxon-Mann-Whitney test; W = 256, P = 0.0004). We should mention that
without including the *Pd. crocheti* sp. nov. M3 UM-FDN-23, which has a high value for the
calculated ratio (Online Resource 1: Table S4), there is no statistically significant difference
between *Pd. crocheti* sp. nov. and *Pd. louisi* for this character (Wilcoxon-Mann-Whitney test;
W = 208, P = 0.072), and the statistical difference still occurs between *Pd. crocheti* sp. nov. and
*Pd. russelli* (Wilcoxon-Mann-Whitney test; W = 239, P = 0.0007). There is no statistically
significant difference between the rank sum of the calculated ratios of *Pd. louisi* and *Pd. russelli*
(Wilcoxon-Mann-Whitney test; W = 204, P = 0.096). Noteworthy, a statistically significant
difference is recovered between *Pd. louisi* and *Pd. russelli* using a parametric instead of a non-
parametric test (Welch's *t*-test; t = 2.11, d.f. = 28.49, P = 0.044). Finally, the range of variation
for the absolute basal height of the stylar cusp C for *Pd. russelli* (0.033 mm – 0.123 mm) is
included in the one of *Pd. crocheti* sp. nov. (0.030 mm – 0.131 mm) (Online Resource 1: Table
S4), although the former species is larger than the latter.
<figure><img src="image_17.png" /><figcaption>**Fig. 14** Boxplots showing the distribution of the ratio values of the absolute basal height of stylar cusp C to the absolute basal height of stylar cusp D for *Peradectes crocheti* sp. nov. (MP7-MP8+9 interval), *Pd. louisi* and *Pd. russelli* (MP8+9 and ~MP8+9). M1 to M3 loci are considered. The value of the calculated ratio for each specimen is displayed for each box. The rank sum of ratio values of *Pd. crocheti* sp. nov. statistically significantly differs (letter 'a' above the box) from those of *Pd. louisi* and *Pd. russelli* (letter 'b') (non-parametric Wilcoxon-Mann-Whitney tests, P < 0.05; see main text). Abbreviation: [MP7-MP8+9], time interval between MP7 and MP8+9 reference levels.</figcaption></figure>

**Height of the dentary.** The dentary of MNHN.F.CB226 (*Pd. louisi*) is relatively higher below m2-m3 than those of MHN.AIX.PV.2017.6.8 (*Pd. crocheti* sp. nov.) and MNHN.F.CB925 (*Pd. russelli*) (Online Resource 1: Table S5). In turn, the dentary of *Pd. crocheti* sp. nov. is relatively
lower than the one of *Pd. russelli*. No conclusion can be made out of these height data, because of the small number of specimens, and because the height of the dentary and its elongation in opossum and 'opossum-like' metatherians may vary depending on the age and sex of the individuals (e.g., Hough 1961; Crochet 1980b: p. 35, fig. 5).

**Intrafamilial phylogenetic analysis**

**Main cladistic analysis.** The heuristic search yielded a single most-parsimonious tree (MPT) of 103 steps (Fig. 15), with a consistency index (CI) of 0.563 and a retention index (RI) of 0.526, which are indicative of high level of homoplasy in the dental characters used. A value of RI just above 0.5 indeed indicates that almost half of the similarities coded in the data matrix correspond to homoplasy (Farris 1989a, 1989b). The single MPT supports the monophyly of the ingroup, the Peradectidae, with a Bremer value of 4.7 out of 37 (= 19%) characters are not parsimony informative for resolving relationships between the ingroup taxa. Within the ingroup (late Paleocene – middle Eocene peradectids), *Pd. elegans* is the earliest diverging offshoot of the branching sequence formed with *Pd. protinnominatus* and its sister-clade, which includes strictly Eocene *Peradectes* species as well as *Armintodelphys* and *Mimoperadectes* (hereafter designated as the 'Eocene' peradectid clade; Fig. 15). All late Paleocene – middle Eocene species distinct from *Pd. elegans* form a clade (Bremer index [BI] = 2, relatively to the mean Bremer value of 2.1) and share the following non-ambiguous synapomorphies: m1 slightly shorter (< 10%) than the m2 (4'), postcingulids that attenuate labially to the hypoconulid (16'), and stylar cusp A distinctly smaller than stylar cusp B on M3 (32').

The 'Eocene' clade is supported (BI = 2) by three non-ambiguous synapomorphies: p3 higher than m1 (3'), the low disparity between the L/W ratios of M2 and M3 (22'), and stylar cusp D placed distolabially to the metacone apex on M1 (35'); two of these are non-homoplasic (3',
35¹). The four European species (*Pd. crocheti* sp. nov., *Pd. russelli*, *Pd. louisi* and *'Armintodelphys' dufraingi*) are clustered in a clade that is unambiguously supported (BI = 2) by four synapomorphies: the entoconid has an intermediate position, between the distal edge of the trigonid and the distal margin of m2 and m3 (21¹, non-homoplasic), stylar cusp A most frequently positioned mesiolingually to stylar cusp B on M2 or M3 (31¹, convergent), stylar cusp B positioned strictly labially to the apex of the paracone, at least on M1 and M2 (33¹, non-homoplasic), and the ectoflexus of their M3 is asymmetric (37¹, convergent). The relationships within the European clade are well-resolved despite the high amount of missing data for *'Arm.' dufraingi* (17 out of 37 [= 46%] scored characters). Within this clade, *Pd. crocheti* sp. nov. is the earliest diverging species. The clade comprising *Pd. russelli*, *Pd. louisi*, and *'Arm.' dufraingi* is supported (BI = 2) by two non-ambiguous synapomorphies: the presence of a straight postcristid at least on one m2-m4 locus (15⁰, convergent) and the relatively small stylar cusp C compared to stylar cusps B and D (34¹, convergent). The less inclusive clade *Pd. louisi* + *'Arm.' dufraingi* is also supported (BI = 2) by two non-ambiguous synapomorphies: relatively long m2 or m3 with a L/W ratio equal to or higher than 1.75 (5¹, convergent) and the mesial end of the cristid obliqua sometimes ventral to the protocristid notch on m4 (11¹, convergent).

The sister group of the European peradectids is formed by a clade that includes the strictly Eocene North American peradectids (*Mimoperadectes labrus*, *Armintodelphys blacki* Krishtalka & Stucky, 1983a, *Armintodelphys dawsoni* Krishtalka & Stucky, 1983a, *Pd. chesteri*, *Pd. gulottai* and *Pd. californicus*). This clade is supported (BI = 2) by the following non-ambiguous synapomorphies: small distal heel on lower premolars (1¹, non-homoplasic), hypoconulid higher than the entoconid on m3 and m4 (19¹, convergent with *'Arm.' dufraingi*), and postmetacrista subequal in length or shorter than the preparacrista on M2 or M3 (29⁰, with intraclade reversion). North American *Armintodelphys* species are more closely related to the strictly Eocene North American *Peradectes* species than to *Mimoperadectes labrus* based on
the absence of internal cristae on the conules (26º, with intraclade reversion). The p3 lower than
the m1 (3²) is an ambiguous non-homoplasic character which supports the latter clade with the
accelerated transformation (Acctran) optimization, or only the Eocene North American
*Peradectes* clade with the delayed transformation (Deltran) optimization. The genus
*Armintodelphys* is recovered as monophyletic based on two non-ambiguous synapomorphies
not observed in *'Arm.' dufraingi*, namely a trigonid as wide as the talonid on m3 (7¹) and a
talonid as long as the trigonid on m4 (8¹, non-homoplasic within the ingroup). In this topology,
the genus *Peradectes* is not monophyletic, because a subclade of three *Peradectes* species is
well nested (BI = 2) within the 'Eocene' North American clade that also includes
*Mimoperadectes* and *Armintodelphys*. One of the most strongly supported clades of the ingroup
is *Pd. gulottai* + *Pd. californicus* (BI = 3), although *Pd. gulottai* is the taxon with the least
complete scoring (15 out of 37 [~ 41%] scored characters).

<figure><img src="image_18.png" /></figure>

**Fig. 15** Single most-parsimonious tree of 103 steps (CI = 0.563, RI = 0.526) from the first cladistics analysis (non-polymorphic characters 11, 31, 36 and 37; all characters unweighted and unordered). Underlined values under the branches at nodes are Bremer indices (BI) when > 1. The non-ambiguous synapomorphies are figured at the nodes of interest in this work, within
the ingroup. The character states in superscript are summarized in *Online Resource 3*. The non-ambiguous and non-homoplastic synapomorphies (CI = RI = 1) are in bold.

**Subsequent cladistic analyses dealing with more characters concerned by polymorphic coding, implied weighting or ordered characters.** A single MPT with the same topology is recovered from the second analysis (111 steps, CI = 0.604, RI = 0.517), for which the frequencies of observation were replaced by polymorphisms in the scoring of the characters 11, 31 and 36 (Online Resource 5: Fig. S1 and text). The differences with the first analysis concern notably (but not exclusively) two non-ambiguous synapomorphies of the first analysis that become ambiguous synapomorphies at their respective node with the accelerated transformation optimization, which are: stylar cusp A positioned mesiolingually to the stylar cusp B on the M2 or M3 (31') for the European peradectid clade, and the presence of a mesial end of the cristid obliqua ventral to the protocristid notch on the m4 (11') for the clade *Pd. louisi* + ‘Arm.’ *dufraingi*. Numerous clades have a value of Bremer index decreasing from BI = 2 to BI = 1, namely the European clade, the *Pd. russelli* + *Pd. louisi* + ‘Arm.’ *dufraingi* clade, the *Pd. louisi* + ‘Arm.’ *dufraingi* clade, the strictly Eocene North American peradectid clade and the strictly Eocene North American *Peradectes* clade. The value of the Bremer index of the clade *Pd. gulottai* + *Pd. californicus* also decreases from 3 to 2.

As for the third analysis (addition of a polymorphic scoring for the character 37 to changes of the second analysis; see Online Resource 5), two different MPTs of 112 steps each (CI = 0.607, RI = 0.511) are obtained, and the strict consensus tree is weakly resolved, with no Bremer index values higher than BI = 1 within the ingroup (Online Resource 5: Fig. S2), and a large polytomy at the base of the ‘Eocene’ clade. *Peradectes crocheti* sp. nov. branches at this polytomy with other strictly Eocene peradectids, and thus does not form a clade with the other European species. *Peradectes louisi*, *Pd. russelli* and ‘Arm.’ *dufraingi* still form a clade on the strict
consensus tree, but its internal topology is also unresolved. A monophyletic North American *Armintodelphys* is retained. One of the two MPTs has the same topology as the single MPT found in the previous analyses.

The fourth analysis of identical parameters and scoring as the previous one (which has the highest frequency of polymorphisms in its scoring), but with downweighted homoplasic characters instead of unweighted characters, resulted in a single MPT. The topology obtained is the same as in the main and second analyses (Fig. 15), and is that of one of the two trees of the third analysis; it is here favored for this reason. The same tree length, CI and RI scores as those of the third analysis are recovered. Finally, the fifth analysis with characters 3 and 34 ordered recovered a single MPT (105 steps, CI = 0.552, RI = 0.505), again with the favored topology. The only differences with the first analysis are as follows: i) the p3 higher than m1 (3⁰) becomes homoplasic, and an ambiguous instead of non-ambiguous synapomorphy (Acctran optimization) supporting the ‘Eocene’ clade (for which BI = 1 instead of BI = 2); ii) the Bremer value of the ‘Eocene’ North American clade decreases from BI = 2 to BI = 1; iii) the acquisitions of a well-developed stylar cusp C (34²) in the ingroup (still non-ambiguous) and of a p3 lower than m1 (3²) in the *Armintodelphys* + ‘Eocene’ North American *Peradectes* clade (still ambiguous with Acctran optimization) take two steps instead of one each.

**Discussion**

**Characters and spatiotemporal distribution of the earliest European peradectid species, *Peradectes crocheti* sp. nov.**

**The earliest occurrence of Peradectidae in Europe.** Two *Peradectes* species were recognized in the Sotteville-sur-Mer fauna from the Mortemer Formation (~MP7, Normandie, Paris Basin;
Smith et al. 2011), each represented by a single specimen. The Sotteville-sur-Mer locality being considered as intermediate in age between Dormaal and both Soissons and Meudon (Smith et al. 2011; Marandat et al. 2012; Hooker 2015), both of these *Peradectes* species were proposed as the first European peradectids. *Peradectes* sp. 1 was identified after a fragment of a small left dentary, preserving a complete worn molar and a worn talonid (Smith et al. 2011: fig. 5.17), and would be the smallest peradectid recorded so far in Europe (Smith et al. 2011). On the molar designated as m3, the trigonid is mesiodistally narrow, much shorter than the talonid, the small protoconid is almost strictly labial to the metaconid, and the preprotocristid is rectilinear in mesiolabial view. On the putative m3 and better-preserved talonid of m2, the hypoconid is distolabial to the entoconid on the anteroposterior axis of the molar. The hypoconulid, though worn, is much lower than the entoconid, and these cuspids are not connected. Here, we rule out the attribution of this specimen to *Peradectes* because of the absence of the aforementioned characters in peradectids (Table 6). Furthermore, the low and mesiodistally pinched paraconid lacks the mesiolingual paraconid keel, a distinctive feature of metatherian mammals and of some basal therians and eutherians (Averianov et al. 2013; Averianov 2015: p. 175). The metaconid is subequal in height to the protoconid, but to our knowledge, no Laurasian metatherian with a metaconid subequal to or higher than the protoconid on lower molars exists. This feature occurs in, for example, some Paleocene South American metatherians from Tiupampa (e.g., Goin et al. 2003: p. 873; Muizon and Ladevèze 2022: p. 631-632), and is a synapomorphy of Eutheria (O'Leary et al. 2013). Finally, the entoconid and hypoconulid are not as twinned as in metatherians on the most anterior molar, and the postcingulid is absent, as seen in earliest marsupialiforms (e.g., Vullo et al. 2009) and eutherians, which also indicate the eutherian nature of this material.

Regarding the upper molar with a rectilinear centrocrista referred to as *Peradectes* sp. 2 (Smith et al. 2011: fig. 5.18), the depth of the ectoflexus and the relative length of the preparacrista
indicate it is a M3 rather than a M2. According to the authors, this molar is comparable in size
and morphology to both *Pd. 'mutigniensis'* (= *Pd. russelli*; MP8+9 and ~MP8+9 localities of
the Paris Basin) and *Pd. protinnominatus* (Clarkforkian and early Wasatchian of the Bighorn
Basin). However, among European peradectids, *Peradectes* sp. 2 from Sotteville-sur-Mer (L =
1.58 mm, W= 1.91 mm) is smaller than M2 and M3 of *Pd. 'mutigniensis'* , and closer in size to
the holotype of *Pd. louisi*, as stated by Hooker (2020), and to the M3 of *Pd. crocheti* sp. nov.
As in *Pd. crocheti* sp. nov. and *Pd. protinnominatus*, and contrary to *Pd. louisi*, stylar cusp D
is labial instead of distolabial to the metacone apex, and stylar cusp C is much higher instead
of subequal or lower than stylar cusp D. Although *Peradectes* sp. 2 and *Pd. protinnominatus*
are almost the same size, *Peradectes* sp. 2 has a stylar cusp B positioned labially to the apex of
the paracone on the stylar shelf, and the ectoflexus is asymmetric, as seen on M3 of *Pd. crocheti*
sp. nov. from Palette. On the holotype of *Pd. protinnominatus* (UCMP 44077; McKenna 1960:
fig. 17a) and on M3 from the Bighorn Basin (Bown 1979: fig. 40a right) attributed to *Pd.
protinnominatus* in the last comprehensive revision of the species (Krishtalka and Stucky
1983b: p. 246-247), stylar cusp B is located mesiolabially to the paracone, and the ectoflexus
has a symmetric shape (Fig. 4). It is worth mentioning that Gingerich and Smith (2006) did not
report ascertained M3 of *Pd. protinnominatus* from the Bighorn Basin localities they studied.
Considering its size and morphology, *Peradectes* sp. 2 is consequently better assigned to *Pd.
crocheti* sp. nov., and it represents the earliest occurrence of this species. Therefore, *Pd.
crocheti* sp. nov. is definitely the oldest European peradectid currently known (see Smith et al.
2011).

**Recognition of other synonyms of *Peradectes crocheti* sp. nov.** All other here proven peradectid dental material of MP7-MP8+9 interval localities attributed to *Peradectes* sp. (Russell et al. 1988; Marandat 1991; Hooker 2010) and *Pd. louisi* (Godinot 1981; Hooker 2020) have been allocated to *Pd. crocheti* sp. nov. in this study. These specimens conform to the size
range and morphological variation observed in *Pd. crocheti* sp. nov. from Palette. In Hooker's view, the labial fragment of upper molar from Abbey Wood (London, Blackheath Formation) he considered as *Peradectes* sp. (Hooker 2010: p. 17, fig. 8a-b) differs from all upper molars of the French *Peradectes* species in its much weaker stylar cusps and its more gracile metacone.

The relative heights of the stylar cusps have been used here instead of the absolute height of the stylar line as diagnosic features of European peradectid species. Although both stylar cusps C and D are low on the M2 from Abbey Wood (e.g., compared to stylar cusp B), as on most upper molars of *Pd. crocheti* sp. nov. and *Pd. louisi* (Figs. 5, 9-10), the most ventral point of the stylar cusp C – D mesiodistal extension in labial view is on stylar cusp C, which is consequently higher than stylar cusp D, as in almost all specimens of *Pd. crocheti* sp. nov. (Fig. 5) and unlike *Pd. louisi* (Figs. 9-10). It is worth noting that Hooker (2020: p. 461) made the same observation for the relative heights of the stylar cusps of the M2 from Croydon (here re-referred as *Pd. crocheti* sp. nov.), which was however attributed to *Pd. louisi*. Furthermore, the metacone of the specimen from Abbey Wood is not significantly more gracile when compared with other unworn M2 of *Pd. crocheti* sp. nov. (e.g., MNHN.F.Me15975, Fig. 5o-p); thus, the shape of this cusp on the specimen from Abbey Wood is not exclusively shared with *Pd. protinnominatus* (contra Hooker 2010). Peradectid upper molars from Fordones (UM-FDN-1 and UM-FDN-23) were first found to be more similar to *Peradectes* sp. from MP8+9 and ~MP8+9 localities of the Paris Basin (= *Pd. louisi* in part, see below) than to any other peradectids then known, because, as on the M1 from Mutigny (MNHN.F.Mu18006; Fig. 10d), they are mesiodistally pinched at the base of the main cusps (Marandat 1991: p. 67, pl. 1, figs. 1-2), i.e., the distal edge of these upper molars is emarginated. The shape of the distal edge or mesiodistal constriction of the upper molars is here regarded as variable within the European *Peradectes* species. For example, the M1 UM-FDN-2 (Fig. 5e) of *Pd. crocheti* sp. nov., first assigned to a herpetotheriid by Marandat (1991: p. 71), shows a relatively long talon and a weak
distal emargination, which is the opposite condition to UM-FDN-1. Since this character varies substantially in the European peradectid species, its use to diagnose peradectid species (e.g., Horovitz et al. 2009) may be doubtful.

The two lower molars from Fordones would also be similar to the MP8+9 and ~MP8+9 *Peradectes* sp. due to the lingual position of the hypoconulid (Marandat 1991: p. 67, pl. 1, fig. 18). However, in addition to this character, the distolingual orientation of the hypoconulid, the entoconid higher than the hypoconid in distal view, the hypoconid positioned distolabially to the entoconid, and the pronounced labial emargination of the crown are more evocative of a herpetotheriid species. The presence of subequally-sized entoconid and hypoconulid as seen on these specimens is known to be not exclusive to Peradectidae (it also occurs in e.g., Herpetotheriidae [Crochet 1980b: p. 149, fig. 162] and ‘Alphadontidae’ [Johanson 1996: p. 1028]), and thus does not prevent the attribution of the lower molars from Fordones to herpetotheriids (*contra* Marandat 1991). Fragmentary lower molars of peradectids and herpetotheriids may be particularly difficult to distinguish in occlusal view. For example, a fragmentary lower molar from Fordones, lacking the paraconid and ascribed to the herpetotheriid *Pt. constans* (UM-FDN-18, Fig. 7d; Marandat 1991: p. 68) exhibits a curved lingual edge of the talonid with a relatively labiolingually wide hypoconulid, which may be superficially evocative of peradectids. If the metaconid and entoconid apex are considered aligned as on, for example, MNHN.F.Me16101 (Fig. 7i), the lingual edge of the talonid appears straight between the entoconid and metaconid (i.e., not fully curved) on UM-FDN-18, and its hypoconid is distolabial instead of labial or mesiolabial to its entoconid. In labial and lingual views, the entoconid is relatively higher and the entoconid – hypoconulid notch is deeper than in m2 of *Pd. crocheti* sp. nov. (Figs. 6, 7) and some m2 of *Pd. protinnominatus* (Gingerich and Smith 2006: fig. 26A-C). The postcingulid is also less convex than on figured peradectid m2 on which this cingulid is entirely preserved. These subtle differences probably led to confusion
<table><caption>**Table 6** Summary of the main morphological differences between cheek teeth of ascertained late Paleocene – middle Eocene Peradectidae and Eocene Herpetotheriidae (and *Herpetotherium fugax*), deduced from comparisons of peradectid material described in this study. The character states in bold are documented absent in one or more species of the concerned group. Comparative data for *Herpetotherium fugax*: Korth (1994: fig. 8.1) for lower premolars, cast of AMNH 5254 (holotype) and Korth (2018: fig. 6b) for lower molars, Sánchez-Villagra et al. (2007: fig. 1c; *Herpetotherium cf. fugax*) for upper premolars, e.g., Green and Martin (1976: fig. 2), Fox (1983) and Korth (2018: fig. 6a) for upper molars.</caption><thead><tr><th></th><th>late Paleocene – middle Eocene Peradectidae</th><th>Eocene Herpetotheriidae + Herpetotherium<br/>fugax</th></tr></thead><tbody><tr><td colspan="3"><strong>Lower premolars</strong></td></tr><tr><td>Shape of mesial edge in labial or lingual view</td><td>curved</td><td>V-shaped, at least on one locus</td></tr><tr><td>Shape of roots</td><td>curved</td><td>straight</td></tr><tr><td colspan="3"><strong>Upper premolars (P2-P3)</strong></td></tr><tr><td>Distal crista and accessory cusp configuration</td><td><strong>separated by a notch</strong></td><td>highly connected</td></tr><tr><td colspan="3"><strong>Lower molars</strong></td></tr><tr><td>Preprotocristid shape on m1-3</td><td>fully convex</td><td>almost vertical</td></tr><tr><td>Metaconid most frequent position</td><td><strong>distolingual to protoconid</strong></td><td>almost strictly lingual to protoconid</td></tr><tr><td>Lingual opening of trigonid basin on m2</td><td>higher than metaconid-entoconid notch</td><td>as high as metaconid-entoconid notch</td></tr><tr><td>Entoconid vs hypoconid height in distal view</td><td>subequal</td><td>entoconid higher</td></tr><tr><td>Hypoconid position compared to entoconid on<br/>m2 or m3</td><td>mesiolabial to labial</td><td>labial to distolabial</td></tr><tr><td>Lingual edge of talonid on m2 or m3</td><td>curved, with oblique entoconid</td><td>straight, without oblique entoconid</td></tr><tr><td>Postcingulid lingual shape on m1-3</td><td><strong>attenuates labially to the hypoconulid</strong></td><td><strong>extends lingually towards hypoconulid tip</strong></td></tr><tr><td colspan="3"><strong>Upper molars</strong></td></tr><tr><td>Protocone relative height on M1-M3</td><td>lower than paracone</td><td>subequal to higher than paracone</td></tr><tr><td>Conules relative size and structure</td><td>small, with rare internal cristae</td><td>larger, with frequent internal cristae</td></tr><tr><td>Paracone and metacone shape</td><td>conical, convex labial edge</td><td>triangular, flat labial edge</td></tr><tr><td>Centrocrista</td><td>rectilinear</td><td>strongly ‘v’-shaped</td></tr><tr><td>Doubling of stylar cusp C or D</td><td><strong>rare</strong></td><td><strong>frequent</strong></td></tr><tr><td>Stylar cusp D position on M1</td><td><strong>distolabial to metacone</strong></td><td>labial or mesiolabial to metacone</td></tr><tr><td>Ectoflexus on M4</td><td>present and deep</td><td>absent or weak</td></tr></tbody></table>
with herpetotheriids. As a matter of fact, the difficulty in differentiating early peradectids from early herpetotheriids, based on lower molars with subtle differences, has often been pointed out (Johanson 1996: p. 1030; Williamson and Lofgren 2014; but see Rose et al. [2012: p. 17] for an opposing view). In an attempt to overcome this issue, we summarize here (Table 6) the morphological differences between the cheek teeth of European Peradectidae and Herpetotheriidae, deduced from our comparisons of the peradectid material here described. Among the late Paleocene – Eocene peradectids, *Pd. crocheti* sp. nov. displays a combination of both derived features, mainly on upper molars, and primitive features, mostly but not exclusively on lower molars.

**Intra-European paleobiogeographic and biostratigraphic implications.** A biotic provincialism between northwestern European (Anglo-Belgian and Paris Basins) and southwestern European (south of France and Iberian Peninsula) mammal faunas was proposed based on occurrences of most of the eutherian taxa around the reference level ~MP7 (Marandat 1997; Smith 2000; Solé et al. 2011, 2013, 2018; Marandat et al. 2012). Exceptions are limited to two cases when considering only recent taxonomic revisions. The teeth of the artiodactyl *Diacodexis* from Dormaal (Belgium) and Palette (Provence) show strong similarities (Boivin et al. 2018), and the three plesiadapiform species *Arcius fuscus* Russell, Louis & Savage, 1967, *Arcius lapparenti* Russell, Louis & Savage, 1967, and *Arcius zbyszewskii* Estravís, 2000, have been documented in several deposits in northwestern and southwestern Europe (e.g., López-Torres and Silcox 2018). As for metatherians, *Peradectes crocheti* is newly recorded from localities closer in age to MP7 than to MP8+9, which are located in both northwestern Europe (Abbey Wood, Croydon, Meudon, Soissons and Sotteville-sur-Mer) and southwestern Europe (Fordones and Palette) (Fig. 1a). The herpetotheriid *Peratherium constans* also probably did not follow this dispersal pattern if both earliest Eocene (MP7) and MP7-MP8+9 interval occurrences are considered (Godinot et al. 1987; Marandat 1991; Estravís 2000; Ladevèze et
al. 2012). *Amphiperatherium* cf. *maximum*, smaller than the typical MP8+9 and ~MP8+9 species *A. maximum* (Crochet 1979, 1980b), is also found in the MP7-MP8+9 interval localities of Soissons in the northwestern European province (Louis 1996) and Fournes and Rians in the southwestern European province (Godinot 1981; Marandat 1991). Whether the northern form from Soissons represents the same species as the southern form from Fournes and Rians has yet to be thoroughly tested. Note that *Amphiperatherium* cf. *maximum* represents one of the earliest occurrences of *Amphiperatherium* since *A. brabantense* Crochet, 1979 (Dormaal), was synonymized with *Pt. constans* (Ladevèze et al. 2012). Altogether, the definition of *Pd. crocheti* sp. nov. reveals that none of the earliest species of the three metatherian genera present in Europe from the MP7 reference level to slightly after (*Peradectes crocheti* sp. nov. in Peradectidae, *Peratherium constans*, and *Amphiperatherium* cf. *maximum*, if indeed a single species, in Herpetotheriidae) seems to be affected by biotic provincialism, a conclusion challenging the bioprovinces scheme of Marandat et al. (2012), at least for metatherian mammals. Three herpetotheriid species have recently been demonstrated to be widespread between western and southeastern European assemblages, as early as the latest Eocene based on the occurrences of *Amphiperatherium exile* (Gervais, 1848-1852), contrary to coeval rodents which are mainly represented by distinct species from these two parts of Europe (Wessels et al. 2024). This reinforces the originality of the dispersal patterns of Laurasian metatherians compared to most coeval eutherians, as supported here.

*Peradectes crocheti* sp. nov. is the only peradectid documented in the MP7-MP8+9 localities where the family is present. It is unrecorded from younger localities from the Paris Basin (MP8+9 and ~MP8+9) that yielded exclusively *Pd. louisi* and *Pd. russelli*, the last occurrences of *Pd. crocheti* sp. nov. being from Fournes and Rians, after the ETM2 (see Material and methods). This documents the first well-supported species turnover for an early European metatherian lineage during the early Ypresian, as it is known at the same period for some
eutherian groups, but at the generic level (e.g., Solé 2014: fig. 3; Solé et al. 2018: table 10; Bronnert and Métais 2023: table 1). This peradectid species turnover is characterized, among other morphological characters, by a clear decrease of the mean absolute basal height of stylar cusp C relative to the mean absolute basal height of stylar cusp D during the early to middle early Eocene (MP7-MP8+9 interval to ~MP8+9) (Fig. 14).

**Phylogenetic relationships between late Paleocene – middle Eocene peradectids**

**Origin and endemism of European peradectids.** An apparent lack of support for the monophyly of European peradectids has been a consequence of previous studies regarding their taxonomic status (Crochet 1980b; Smith and Smith 2013). Crochet (1980b: p. 54, fig. 33), based on the morphology of upper molars only, suggested stronger affinities between *Peradectes elegans*, *Pd. louisi* and *Pd. russelli* on the one hand, and between *Pd. protinnominatus* and *Pd. 'mutigniensis'* on the other hand. The conclusions of Crochet (1980b) hence involved at least two independent peradectid dispersals of unspecified direction between North America and Europe. Smith and Smith (2013) described a new peradectid species from Egem (Belgium, ~MP8+9, 51-52 Ma, during the Early Eocene Climatic Optimum [EECO]) attributed to the North American genus *Armintodelphys* ('*Arm.* ' *dufraingi*), and thus argued for an *Armintodelphys* dispersal from North America to Europe around the Early Eocene Climatic Optimum. However, most of our phylogenetic analyses have recovered the four European species *Pd. crocheti* sp. nov., *Pd. louisi*, *Pd. russelli* and '*Arm.* ' *dufraingi* forming a clade nested within other late Paleocene to middle Eocene peradectids, with *Pd. crocheti* sp. nov. as the earliest diverging species (Fig. 16). Even in the less resolved third analysis, '*Arm.* ' *dufraingi* forms a clade with *Pd. louisi* and *Pd. russelli*, rather than being included in the North American *Armintodelphys* clade. These results suggest that *Armintodelphys* did not disperse between
North America and Europe (contra Smith and Smith 2013), and that late Paleocene to Eocene peradectids have experienced a unique dispersal from North America to Europe during their evolutionary history (contra Crochet 1980b; Smith and Smith 2013). These conclusions imply that European peradectids certainly evolved as an endemic group until their extinction on this continent (the putative South American record of *Armintodelphys* compared with ‘Arm.’ *dufraingi* [see Carneiro and Oliveira 2023: p. 37-38, fig. 15] has been reinterpreted as a putative herpetotheriid taxon; Carneiro et al. 2024), as European herpetotheriids probably also did (Ladevèze et al. 2012, 2020), at least until the middle early Eocene (MP8+9 or close in age, to MP8+9-MP10 interval). New dental material of late early Eocene (MP10 to MP11 reference levels) peradectids is further needed to definitely verify this hypothesis, because paleobiogeographic analyses of nyctitheriids show that dispersal events of small mammals from North America to Europe may have occurred multiple times and later than the middle early Eocene (Manz and Bloch 2015: p. 27-28, fig. 7).

The dispersal of peradectids perhaps occurred later than the arrival of herpetotheriid metatherians in Europe from North America, so far envisioned during the Paleocene-Eocene Thermal Maximum (PETM) for the latter, because peradectids are still unknown in the MP7 localities of Erquelinnes (Missiaen et al. 2013), Dormaal (Ladevèze et al. 2012), Le Quesnoy (Nel et al. 1999; pers. obs.) and Silveirinha (Estravis 2000), the last three having yielded the earliest herpetotheriid metatherians of Europe to date. According to the known fossil record, a putative dispersal event including peradectids by the Thulean route (a land bridge connecting North America and Europe via Greenland; Brikiatis 2014), probably followed (and was triggered by) the PETM, and took place between the PETM and ETM2, as has been established so far for paromomyid plesiadapiforms and the mesonychid *Pachyaena* (Fig. 16; Smith et al. 2011; Hooker 2015; Solé et al. 2018: p. 31). The finding of a peradectid astragalus in Palette (Fig. 8), with a nearly ungrooved trochlea (Fig. 8b) and a sloping medial tibial facet (Fig. 8d)
suggesting tibioastragalar mobility (Rose 2012), shows that the first European peradectids were
probably already arboreally adapted, like their small (the body mass of *Pd. crocheti* is estimated
between approximately 26-30 g, using the lengths of the four available unworn M3 [Online
Resource 1: Table S1] in the appropriate predictive equation of Gordon [2003: fig. 7]), similarly
sized, contemporaneous North American counterparts during the late Paleocene – early Eocene
(Szalay 1994; Rose 2012), and like possible peradectid specimens from Messel (Kurz 2005).

The Palette astragalus is very similar to astragali of small earliest Eocene North American peradectids (Rose et al. 2012), which provide further support to the close phylogenetic affinities between North American and European peradectids. A dispersal of peradectids from North America to Europe during the PETM or slightly later is also congruent with our phylogenetic framework, since the earliest offshoots of the European and strictly Eocene North American peradectid clades, namely *Pd. crocheti* sp. nov. and *M. labrus* respectively, together with the more basal *Pd. protinnominatus*, are recovered from early Eocene localities of similar age (Fig. 16). In particular, *Pd. crocheti* sp. nov. and *M. labrus* are not formally documented earlier than the early Eocene (Fig. 16; but see Rose 1981: p. 36), which supports the occurrence of a global cladogenesis event during or immediately after, and thus potentially driven by, the PETM in the evolutionary history of peradectids.

**Definitions of *Peradectes*, *Armintodelphys*, and *Peradectidae***. The intrafamilial phylogenetic analysis highlighted disentangles relationships between all late Paleocene – middle Eocene peradectids. First, we concur with Williamson et al. (2012, 2014) in evidencing a lack of support for the monophyly of the genus *Peradectes*. It was recovered as polyphyletic in their phylogenetic analyses, including all valid North American *Peradectes* species, whereas it is paraphyletic in the analysis here performed, which does not include the earliest North American *Peradectes* species (early Paleocene, Danian), *Pd. minor* and *Pd. coprexeches* (Clemens 2006; Williamson and Taylor 2011; Williamson et al. 2012). The paraphyletic status of *Peradectes*,
<figure><img src="image_19.png" /></figure>

**Fig. 16** Favored topology of the peradectid ingroup, recovered from four out of the five analyses, mapped on the Paleogene time scale (Speijer et al. 2020) and with the geographic distribution of species and selected thermal maxima of the early Eocene (PETM and ETM2). The European peradectid clade probably differentiated immediately after the PETM. *Peradectes* appears paraphyletic with the generic attributions here retained. Temporal extensions of taxa are detailed in Online Resource 2.

the genus being here valid if monospecific (i.e., restricted to *Pd. elegans*) or alternatively if it
includes the species of the genera *Mimoperadectes* and *Armintodelphys* (and potentially
*Didelphidectes* and *Nanodelphys*, which have not been included in our analyses), has long been
suggested by an early diagram of the probable relationships between peradectid species
(Krishtalka and Stucky 1983b: fig. 6), in the same way as in the topology obtained from most
of our analyses. Second, Williamson et al. (2012: p. 629) proposed a phylogenetic definition of
Peradectidae, as 'the most inclusive clade containing *Peradectes elegans*, but not
*Herpetotherium fugax*, *Pediomys elegans* or *Didelphis virginiana*. Contrary to the
phylogenetic analyses of Williamson et al. (2012, 2014), our topology recovering only
relationships among peradectids is fully resolved, and *Peradectes elegans* and *Pd. californicus*
(which form the clade Peradectidae in Williamson et al. [2012, 2014], according to the
definition of Williamson et al. [2012]) are not found as sister taxa. This implies that a
Peradectidae clade as originally conceived (e.g., Krishtalka and Stucky 1983b: fig. 6) or similar
to that recovered in this study (Fig. 16), more inclusive than *Pd. elegans* + *Pd. californicus* as
found by Williamson et al. (2012, 2014), could effectively exist, as Williamson et al. (2012: p.
632) suggested themselves. For these reasons, a broader phylogenetic analysis encompassing
all *Peradectes* species nested in the whole Metatheria will be needed, but it is beyond the scope
of this paper. Pending further study, we take a conservative and convenient approach in
maintaining the use of the genus name *Peradectes*, even for European species. This
encompasses ‘Arm.’ *dufraingi*, here rereferred to *Peradectes* (*Pd. dufraingi*; see below).

*Armintodelphys* appears polyphyletic if the species *dufraingi* is included, but is monophyletic when this European species is not considered (as in Williamson et al. [2012, 2014]), or not included in the genus (this study). The lower molars of *Pd. dufraingi* and *Pd. louisi* are relatively more elongated than any late Paleocene to middle Eocene peradectid, *Armintodelphys* included (L/W of m3 > 1.75, see Table 4 for *Pd. louisi*), and the two European species share a labial emargination of lower molars that is absent in m3 of *Arm. blacki* and *Arm. dawsoni* (pers. obs., *contra* Krishtalka and Stucky 1983a). A relatively minute entoconid, lower than the hypoconulid on molar loci more anterior than m4, that has been proposed as a diagnostic character of *Armintodelphys* (Krishtalka and Stucky 1983a), is not only present in the *Armintodelphys* species and *Pd. dufraingi*, but also in other Eocene peradectids such as *Mimoperadectes labrus* (Bown and Rose 1979: fig. 1B; Rose et al. 2012: fig. 12H), *Pd. californicus* (Lillegraven 1976: pl. 9, fig. 2b) and *Didelphidectes* (Korth 1994). In turn, the characters here supporting the monophyly of North American *Armintodelphys* were not
mentioned in the diagnosis of the genus by Krishtalka and Stucky (1983a). The morphological
similarities pointed out between *Pd. louisi* and *Pd. dufraingi*, in addition to the subtle
differences of their lower molars (see diagnosis of *Pd. louisi*), do not justify assigning the
species *Pd. dufraingi* to a genus other than that of the species *Pd. louisi* (hence *Peradectes*).

**Limits of phylogenetics analyses.** A caveat is in order on the phylogenetic analyses of peradectids, which are only based on dental characters due to the current lack of cranial and postcranial material for the group. Past research has shown that the dominance of dental characters in matrices may lead to inaccurate phylogenies, potentially due to higher levels of homoplasy in this anatomical partition (Sansom et al. 2017; Brocklehurst and Benevento 2020). The high homoplasy levels detected in our analyses (RI~0.5) do not contradict these cautionary statements. In addition, small cusps were mentioned to be possibly poorly reliable for reconstructing phylogenies due to their late occurrence in the patterning cascade of cusp development (Jernvall and Jung 2000). Whether this can apply to the stylar cusps present on upper molars of peradectids remains to be investigated, but our observations in the present study are suggestive of the presence of some phylogenetic signal in the subtle variation of these structures, for their relative position (representing 3 out of 37 characters used in the phylogenetic analyses), length and width (1 out of 37 characters), and height (1 out of 37 characters). In particular, the two methods employed to evaluate the relative height of the stylar cusps C and D produced an identical main result (the relative shrinking of the stylar cusp C between the MP7-MP8+9 interval and ~MP8+9). Meanwhile, the difficulty of accurately scoring complex dental variation (e.g., Billet and Bardin 2019) and the presence of high levels of homoplasy urge caution when interpreting current phylogenetic results on peradectids. The discovery of more complete fossils (like the material from Palette), and the use of geometric morphometric methods to characterize dental variation within peradectids, would allow to propose more robust characters in further studies.
Diagnostic characters and taxonomic status of the middle early Eocene European
peradectids, *Peradectes louisi* and *Peradectes russelli*.

Systematics of *Peradectes louisi*. Crochet (1979) chose the left M3 MNHN.F.GL197 as the holotype of *Pd. louisi*, which was then the sole available M3 for this species (Crochet 1980b). An isolated M3 from Avenay (MNHN.F.Av4813) was referred to *Pd. louisi* earlier in his work (Crochet 1980b: fig. 4a) but was not included in the material referred to this species (Crochet 1980b: table 3). MNHN.F.Av4813 is of the size of the larger *Pd. russelli*, and is here allocated to this species. The original diagnostic characters of the upper molars of *Pd. louisi* were thus explicitly based on MNHN.F.GL197 alone (Crochet 1979, 1980b: p. 39). We have proposed a new description and figuration of the holotype (Fig. 9f). On a drawing of MNHN.F.GL197 in labial view from Crochet (1980b: fig. 9a), the stylar cusps B, C and D are subequal in height. Contrary to the original diagnosis and figure of Crochet (1980b), and although the stylar shelf of this M3 is worn, its stylar cusp B is clearly dominant in height over stylar cusp D, and stylar cusp C is absent or entirely worn (Fig. 9e-g). The slightly elevated surface interpreted as the summit of stylar cusp C of MNHN.F.GL197 by Crochet (1980b) is actually lingual to the stylar line. Moreover, the M3 of *Pd. louisi* MNHN.F.CB4182 also lacks stylar cusp C (Fig. 10p). The relative heights of the stylar cusps of MNHN.F.GL197 are similar on all the upper molars here attributed to *Pd. louisi* (Fig. 10), stylar cusp B being the highest, and stylar cusp C being most often lower than stylar cusp D or absent. As mentioned by Crochet (1979) in the diagnosis, the ectoflexus of MNHN.F.GL197 is weakly developed, but the newly reported M3 of *Pd. louisi* from Condé-en-Brie (MNHN.F.CB4182, Fig. 10p) and Sézanne-Broyes (MNHN.F.SZ18000, MNHN.F.SZ18005, Fig. 10o) have deeper ectoflexi. A similar variation of this trait is here noted on the M3 of *Pd. crocheti* sp. nov. from Palette and Fordones. The ectoflexus was also considered symmetric on M3 of *Pd. louisi* (Crochet 1979, 1980b). Here again, the new
description of the holotype and a more comprehensive sampling of M3, all properly oriented, show that the ectoflexus of this dental locus is asymmetric in *Pd. louisi* (Figs. 9f, 10p, o), although this asymmetry is, on average, less pronounced than in *Pd. crocheti* sp. nov. The relative weakness of the conules of the upper molars described by Crochet (1979, 1980b) was interpreted as a synapomorphy of peradectids by various authors (e.g., Krishtalka and Stucky 1983b; Korth 2008), rather than a diagnostic character at the species level. Finally, the M3 is not relatively longer than other upper molar loci of *Pd. louisi*, or M3 of other European *Peradectes* species (Table 4) (contra Crochet 1979, 1980b).

As for lower molars, a lingual opening of the trigonid basin higher than the lingual opening of the talonid basin was also proposed as a specific feature of *Pd. louisi* (Crochet 1979, 1980b). However, this character is also present in *Pd. crocheti* sp. nov. and *Pd. russelli*, and consequently the relative heights of the lingual opening of the trigonid versus talonid basin cannot be used to discriminate between European *Peradectes* species. Moreover, since only (at least) some ascertained herpetotheriids (i.e., from the earliest Eocene; Ladevèze et al. 2012), such as *Peratherium* and *Herpetotherium*, exhibit the reverse condition of this character (the trigonid and talonid basin open lingually at the same level), the character state of *Pd. louisi* is rather interpreted as a symplesiomorphy for the whole of Metatheria. According to Crochet (1979, 1980b), the hypoconid is mesiodistally pinched and the cristid obliqua is curved on the lower molars of *Pd. louisi*, except on m4. Nonetheless, we did not make the same observation based on the two m4 from the original hypodigm we consulted (MNHN.F.Av16032 and MNHN.F.Av16037). In particular, on MNHN.F.Av16037 the cristid obliqua is curved near the distal edge of the trigonid contrary to the drawing of Crochet (1980b: fig. 13). Characters of the talonid of m4 of *Pd. louisi* are probably highly impacted by polymorphism, as for m4 of other metatherians (e.g., Martin 2005: fig. 4). Moreover, the shape of the cristid obliqua varies among the m3 of *Pd. louisi*. Finally, as noted by Crochet (1979, 1980b), the m4 of *Pd. louisi* are smaller