Ontogenetic analysis of Anisian (Middle Triassic) ptychitid ammonoids from Nevada, USA

Abstract. Ptychites is among the most widely distributed ammonoid genera of the Triassic and is namesake of a family and superfamily. However, representatives of the genus mostly show low-level phenotypic disparity. Furthermore, a large number of taxa are based on only a few poorly preserved specimens, creating challenges to determine ptychitid taxonomy. Consequently, a novel approach is needed to improve ptychitid diversity studies. Here, we investigate Ptychites spp. from the middle and late Anisian of Nevada. The species recorded include Ptychites embreei n. sp., which is distinguished by an average conch diameter that is much smaller and shows a more evolute coiling than most of its relatives. The new species ranges from the Gymnotoceras mimetus to the Gymnotoceras rotelliformis zones, which makes it the longest-ranging species of the genus. For the first time, the ontogenetic development of Ptychites was obtained from cross sections where possible. Cross-sectioning highlights unique ontogenetic trajectories in ptychitids. This demonstrates that, despite showing little phenotypic disparity, Ptychites was highly ontogenetically differentiated, and thus the high taxonomic diversity at the species level is justified for the species investigated.

In this paper, we describe a new species of Ptychites and discuss the taxonomic diversity and morphologic disparity of this genus during the Middle Triassic of the west coast of North America. Our study area in north-western Nevada, *Corresponding author USA, belongs to the world's most complete low-paleolatitude sequences, revealing late Anisian ammonoid faunas (Monnet and Bucher, 2005). The continuous sequences, which include a very diverse and abundant ammonoid fauna, provide a good basis for ontogenetic studies on a high-resolution scale. Due to their distinctive ontogenetic trajectories (model curves), ptychitids will act as an important cornerstone in future quantification of ontogenetic analyses.
Because Ptychites is found all over the world, this study also contributes to the worldwide correlation of Middle Triassic sediments. Representatives of this group were described from many different localities all over the world. However, most of these records originate from condensed facies, with significant uncertainty regarding the number and age of the faunas, and the composition of the populations. This makes correlative work particularly challenging. The problems of correlation and condensation are discussed by Tozer (1971) and are, for example, reported from Epidauros (Greece) by Krystyn and Mariolakos (1975) and Krystyn (1983). Furthermore, Balini (1998, p. 144) emphasized that the alpha taxonomy of Ptychites is characterized by a lack of information on the stratigraphic relationships between the type specimens. The study of ptychitid ammonoids therefore holds great potential for both biostratigraphic and paleobiological work.

Geological setting and material
The bulk of the fossil material used here was collected by members of the Geosciences Collection of the University of Bremen (Germany). It derives from the Muller and Favret Canyon of the Augusta Mountains (Pershing County), north-western Nevada, USA (see Fig. 1). A complete section of the upper portion of the late Anisian Fossil Hill Member of the Favret Formation and the lowermost part of the early Ladinian Home Station Member of the Augusta Mountain Formation was meticulously documented and measured. Furthermore, J. Jenks collected additional material in Rieber Gulch and Favret Canyon of the Augusta Mountains, Pershing County, and the Wildhorse-McCoy Mine area, Churchill County (see also Fig. 1). Since the fossil material of J. Jenks was loosely collected, no measured sections are associated with this material. However, the sites where the fossil material was found are thoroughly documented and the biostratigraphic framework is well known (Jenks et al., 2015).
Biostratigraphically, Ptychites spp. from Nevada that are the focus of this study were collected in the Balatonites shoshonensis and the Gymnotoceras mimetus-Gymnotoceras rotelliformis zones of the Fossil Hill Member (middle and late Anisian; see Fig. 2). The Fossil Hill Member consists of alternating layers of calcareous siltstone and mudstone with lenticular limestone. The rich fauna of the succession primarily consists of halobiid bivalves and ammonoids. Ceratitids are quite abundant and diverse throughout the member. The Anisian faunas of the Humboldt Range were previously described in the 19 th and early 20 th century (Gabb, 1864;Hyatt and Smith, 1905;Smith, 1914). Recently, Silberling and Nichols (1982) and Monnet and Bucher (2005) refined the original alpha taxonomy and the biostratigraphy.

Methods and conventions
In order to underpin the description of Ptychites embreei new species, we performed an ontogenetic analysis of selected specimens of Ptychites. The methods introduced by Korn (2010) and Klug et al. (2015) were used. All samples used for ontogenetic analysis were first removed from the rock matrix by mechanical preparation and were then measured along the longest axis. The conch dimensions of the growth stages were obtained from digitized sketches of high-precision cross-sections intersecting the protoconch. In order to find a non-destructive method, a CT scan of selected specimens with a GE Phoenix v device, tome, x s 240 with a nanoray tube NF 180 kV was performed at the University of Erlangen, Germany. Unfortunately, the differences in density were marginal, and therefore the contrast of the internal structures on the scan images were not sufficient for further analysis.
The basic conch parameters (dm: diameter; ww: whorl width; wh: whorl height) for all available specimens were measured at every distinct growth stage (i.e., half whorl), starting at the protoconch. For the ontogenetic analysis, the growth parameters whorl expansion rate (WER n = [dm n /dm n-0.5 ] 2 ), whorl width index (WWI n = ww n /wh n ), umbilical width index (UWI n = uw n /dm n ), and the conch width index (CWI n = ww n / dm n ) were calculated (for further explanations see Korn, 2010;Klug et al., 2015).
Ontogenetic morphospace.-The growth parameters WER, UWI, and CWI were also analyzed in a principal component analysis (PCA). The dataset comprises the values for all distinct growth stages of an individual. In contrast to most other ontogenetic studies using ternary plots or multivariate statistics (e.g., Korn and Klug, 2007;Klug et al., 2016;Korn, 2017, 2018), herein every individual is defined by the sum of all parameters of all ontogenetic stages. In order to omit missing values in the analysis, the PCA data set was limited to the last growth stage of the specimen with the fewest number of half whorls (here growth stage number 5.0; see Appendix). All parameters are numbered consecutively, starting with the first half whorl (i.e., WER 0.5 , CWI 0.5 , UWI 1.0 ) to the last one of the analysis (i.e., WER 5.0 , CWI 5.0 , UWI 5.0 ). Therefore, the space opened up by this analysis is not a classical morphospace showing the morphology of an individual at a specific growth stage, but in an artificial state of combined morphologies of different ontogenetic stages. It illustrates how the ontogeny of the groups differ. To prevent confusion, we introduce the term "ontogenetic morphospace." The PCA with correlation matrix was run using PAST (version 3.25;Hammer et al., 2001).
to letter L of the traditional nomenclature); U: umbilical lobe; I: internal lobe; E/A (that is E/L of traditional nomenclature) is the saddle between E and A; A/U (that is L/U of traditional nomenclature) corresponds to the saddle between A and U.  Bischof and Lehmann-Middle Triassic ptychitid ammonoids from Nevada, USA 831 USA. The abbreviation JJ refers to localities of J. Jenks, Salt Lake City, Utah, USA, and HB refers to localities of H. Bucher, Zurich, Switzerland. In the synonymy list we used '[n.s.]' for publications we have not seen, because we could not get hold of a copy of that paper.

Systematic paleontology
Order Ceratitida Hyatt, 1884 Superfamily Ptychitoidea Mojsisovics, 1882 Family Ptychitidae Mojsisovics, 1882 Genus Ptychites Mojsisovics in Neumayr, 1875 Type species.-Ammonites rugifer Oppel, 1863(designated by Tozer, 1994, see discussion on p. 133). Tozer (1981, p. 94) was used as reference for the family-group taxonomy.  imprints on the steinkern however reveal that the shell was smooth, bearing some fine growth striae. The major elements of the suture line of specimen GSUB C13194 ( Fig. 4.1) are uniformly large, namely with an U3/ U2, U2, A/U2, and an A that are of a similar extent. The A lobe is bifid, with the endings slightly less incised compared to the other major sutural elements. The U2/A tapers towards the aperture. The E/A is slender and less strongly denticulate. The U1/U4 shows a prominent, slender spur. The suture line of GSUB C13194 shows only minor differences to the sutures redrawn from Tozer (1994) (Fig. 4.2). The latter differs by a trifid A lobe that is slightly smaller, a U2/A that is not tapering, and the U1/U4 that lacks a spur.
Remarks.-Köhler-Lopez and Lehmann (1984) illustrated the ontogenetic development of the suture line of Aristoptychites, and thus demonstrated that the traditional nomenclature should be modified in Ptychitidae. In this respect, Tozer (1994, p. 133) refers to "four lateral saddles," these are the U2/A, U3/ U2, U4/U3, and U1/U4 of the ontogenetic nomenclature used herein. The diagnosis of the suture line of P. guloensis given by Tozer (1994, p. 133) is as follows: "[…] with four lateral saddles, the outer two large and the inner two small. The inner two are depressed in relation to the large saddles. The outer large saddles are not bifid; the inner small saddles weakly bifid." However, this does not characterize the species because the features can be found in other species of Ptychites as well.
Nevertheless, the Canadian specimen shows typical features of Ptychites, such as the rather broad and rounded outline of the U3/U2 and U2/A and the multi point indentations of the lobes. Although we consider the preservation of GSUB C13194 as good, we cannot rule out that the slightly more slender and irregular indentations of the U3/U2 and U2/A and the different shape of the lowermost tip of the A lobe with fairly broad and simple indentations are a matter of preservation. Diagnosis.-Small to moderately sized species of Ptychites with a rounded to subtriangular venter and a rather narrow umbilicus with an abrupt umbilical shoulder. The conch bears very weak folds and ribs.
Description.-Measurements of the selected specimen are provided in Table 2. Specimen NMMNH 80882 ( Fig. 3.1-3.4) is a complete conch with a maximum diameter of 38.74 mm. The pachyconic shell (ww/dm = 0.74) is subinvolute (uw/dm = 0.26) revealing a deeply incised umbilicus ( Fig. 3.3) and an abrupt umbilical shoulder. Rounded to subtriangular shoulder. The flanks are covered with very weak, irregular and slightly rursiradiate ribs and folds. The length of the body chamber exceeds one whorl.
Remarks.-The diagnosis for this species is newly established here, due to a lack of a former diagnosis. The occurrence of this species seems to be restricted to the open water fauna of the Panthalassic Ocean. The available material does not allow an ontogenetic analysis. The suture line published in McLearn (1969) shows that the sutural elements of this species are     Holotype.-The holotype USNM 448264, the paratypes USNM 448262, USNM 448265-448267, and the plesiotype USNM 448263 are all stored in the collection of the National Museum of Natural History in Washington D.C, USA (Bucher, 1992).
Diagnosis.-Rather large species of Ptychites reaching a diameter of 90 mm and in rare cases more than 250 mm (see Bucher, 1992, p. 440). The conch of juvenile specimens is mostly pachyconic. The later ontogenetic stages, however, show two different morphotypes: pachyconic-subevolute (ww/ dm ∼0.70; uw/dm ∼0.40) and discoidal-subinvolute (ww/dm ∼0.50; uw/dm ∼0.30). Furthermore, the conch bears a smooth ornament of irregular, rectiradiate to slightly falcoid ribs and growth striae. The internal mold of juvenile specimens shows growth constriction. Description.-Measurements of the selected specimens are provided in Table 3. The largest pachyconic (ww/dm = 0.76) and robust specimen (NMMNH 80879;) has a diameter of dm = 66.66 mm. The subevolute to evolute umbilicus (uw/dm = 0.44) is very deeply incised with a steep umbilical wall and a very abrupt umbilical shoulder. The venter is subtriangular. The ornamentation of the conch consists of smooth and irregular, rectiradiate to slightly falcoid ribs, and very fine growth striae. The partly preserved shell of the largest specimen (GSUB C13196; Fig. 3.8-3.10) is very thick (1.5 mm at the venter and >3 mm along the umbilical shoulder).
The partially preserved suture line of GSUB C13196 is illustrated in Figure 7. The umbilical part of the line is missing. The widths of U3/U2, U2, A/U2, A, and A/E of the herein described specimen (Fig. 7.1, 7.2) are comparable to those of the specimen published in Bucher, 1992 (Fig. 7.3 herein). The A lobe is trifid. As with the E/A illustrated in Bucher, 1992, this saddle is slender and less strongly denticulate than the others are. Bucher (1992) did not illustrate the conch of the specimen he analyzed. However, since the whorl height of the specimen indicated is ∼80 mm, the specimen must have had a similar conch size to the specimen of this study (whorl height of specimen GSUB C13196: 88.30 mm).
The largest discoidal (ww/dm = 0.46) specimen used for the ontogenetic analysis (GSUB C11443; Fig. 5.7-5.10), has a diameter of dm = 85.62 mm. The subinvolute umbilicus (uw/ dm = 0.27) is also very deeply incised (Fig. 5.9). The umbilical wall is a little bit less steep than that of their more robust conspecifics. The venter of the discoidal specimen is subtriangular. The ornamentation, however, equals the robust specimens.
Ontogenetic description.-The ontogenetic development of P. gradinarui is illustrated in Figure 8, and the raw data of the analysis are supplied in the Appendix. The whorl expansion rate (WER; Fig. 8.2) shows a triphasic behavior with a strong decrease in the earliest stages and a rather stable intermediate phase. In phase III, the WER increases again, indicating an acceleration of growth.
The values for the whorl width index (WWI) are more scattered than the other series ( Fig. 8.3). Nevertheless, a triphasic development of the growth trajectories can be observed. In phase I and II, the conch width index (CWI) and the umbilical width index (UWI) describe opposing parabolas (Fig. 8.4). Ptychites gradinarui shows a trend of developing a slightly more pachyconic and less evolute conch in their early stages, resulting in a clock-wise progression (Fig. 8.5). In contrast to UWI, the CWI is a triphasic trajectory. Therefore, at growth stage 8.0, the two indices decouple. Whereas the UWI sticks to the parabolic curve progression, CWI quite abruptly decreases after Bischof and Lehmann-Middle Triassic ptychitid ammonoids from Nevada, USA 837 whorl 8.0, causing a distinct buckle in the growth trajectories ( Fig. 8.5). This means that in later ontogenetic stages, the species develops more discoidal and less evolute conches. Following the notation of Walton and Korn (2017), the morphologic development of P. gradinarui is characterized by a C-mode ontogeny.
In general, all the trajectories shown in Figure 8.2-8.5 show a change in direction towards the end of the phase II (growth stage 5.0 to 8.0; roughly corresponds to growth size of 9-27 mm; see also Appendix). These changes in the progression of the trajectories are interpreted to mark the transition from juvenile to adult stages. The analysis of a large pachyconic specimen would allow testing whether the two morphotypes (discoidal and pachyconic, see above) could be explained by sexual dimorphism. If more globous variants of this species show the same ontogenetic trends, at around the same growth stage, this would underpin the hypothesis of sexual dimorphism. However, no appropriate specimen was available.
Remarks.-The diagnosis for this species is newly established here, due to a lack of a former diagnosis. This species appears to be endemic to Nevada, with its closest ally, P. sahadeva Diener, 1895a, from the Himalayan region according to Bucher (1992). Among the material herein, two different morphotypes can be distinguished-a more depressed type with a subtriangular venter and a slightly narrower umbilicus, and a robust variant with very abrupt umbilical shoulders. However, the ornamentation with irregular fine ribs, growth striae, and weak depressions are very similar. Furthermore, smaller specimens herein and the specimens illustrated in Bucher (1992) seem to be intermediate to these two morphotypes. Because the biostratigraphic and geographic ranges of both morphotypes are also overlapping, the two morphotypes were assigned to one species, dimorphism cannot be excluded. Bucher, 1992 Figures 6.12-6.14, 9.1-9.3 1992 Ptychites densistriatus; Bucher, p. 441, pl. 9, figs. 1-10.
Diagnosis.-Moderately sized species of Ptychites with a subinvolute (uw/dm ∼0.25) and discoidal to pachyconic conch (2-4) Ontogenetic development of the whorl expansion rate (WER n = (dm n /dm n-0.5 ) 2 ), whorl width index (WWI n = ww n /wh n ), umbilical width index (UWI n = uw n /dm n ), and the conch width index (CWI n = ww n /dm n ) plotted against number of half whorls (ontogenetic stages). (5) Ratio between UWI and CWI of the available specimens. Bubble size refers to number of half whorl; the picture in the background shows the shape of the last complete whorl (developed by Korn, 2010). Roman numbers refer to interpretation of different life phases; I: Hatchling, II: Juvenile; III: Subadult-adult; for more detailed explanations see Walton and Korn (2017, p. 713). Description.-Measurements of the selected specimens are provided in Table 4. Specimen NMMNH 80881 (Fig. 6.12-6.14) is a complete conch with a maximum diameter of 53.49 mm. The discoidal to pachyconic shell (ww/dm = 0.60) is subinvolute (uw/dm = 0.24), revealing a deeply incised umbilicus with a steep umbilical wall and a narrowly rounded umbilical shoulder. The specimen is slightly ovoid. Furthermore, the almost smooth surface of the conch only bears smooth growth striae. Materials.-Two specimens (NMMNH 80881, GSUB C11439).
Remarks.-The diagnosis for this species is newly established here, due to a lack of a former diagnosis. To our knowledge, this species in endemic to Nevada. Preservation of the available material did not allow a sutural and ontogenetic analysis.
Paratypes.-Five specimens GSUB C8273 ( Fig. 9.4), C8287 ( Fig. 9.8-9.10), C8289 ( Fig. 10.7-10.9), C8280 ( Fig. 11.1-11.3), and C9458 ( Fig. 11.7-11.9), Fossil Description.-Measurements of the selected specimens are provided in Table 5. The holotype (GSUB C9453; Fig. 12) is a complete specimen with a maximum diameter of 29.77 mm. Because of its large size, compared to other representatives of this new species, it is interpreted as an adult specimen; there are no other criteria for maturity. The pachyconic (ww/dm = 0.61) shell is subevolute (uw/dm = 0.37) and reveals a deeply incised umbilicus with a steep umbilical wall and a distinctive umbilical shoulder. The surface of the shell is smooth and bears a very fine ornament of striae. The venter is perfectly rounded and smooth.
Ontogenetic description.-The ontogenetic development of P. embreei n. sp. is illustrated in Figure 13, and the raw data of the analysis are supplied in the Appendix. The whorl expansion rate (WER; Fig. 13.2) shows a regular behavior with a strong decrease in the earliest stages, followed by more stable state towards the end of phase II. The slightly higher values of half whorl 7.5 and 8.5 suggest a possible acceleration of growth in later ontogenetic stages.
The values for the whorl width index (WWI; Fig. 13.3) are more scattered than the other series. However, considering the shape of the CWI trajectory ( Fig. 13.4) and the more regular WWI of P. gradinarui (Fig. 8.3), it can be assumed that the progression of WWI is at least triphasic.
During phase I and II, the trajectories for the conch width index (CWI) and the umbilical width index (UWI) are inverse ( Fig. 13.4), indicating a close relationship between these two indices. The development of UWI and CWI is similar to the C-mode ontogeny introduced by Walton and Korn (2017). However, towards later ontogenetic stages, the UWI and CWI are decoupled, which distinguishes P. embreei n. sp. from regular C-mode ontogeny. Whereas the conches of early stage P. embreei n. sp. are more globous and more involute, in the course of their growth they build slightly more discoidal and more evolute conches, resulting in a counterclockwise progression (Fig. 13.5). The decoupling of the CWI and UWI results in a distinct buckle in the progression. In general, all the trajectories (Fig. 13.2-13.5) that are long enough show a change towards the end of the second phase (growth stage 5.0 to 8.0; roughly corresponds to a growth size of 12-19 mm). These changes in the progression of the trajectories most probably mark the transition from the juvenile to the adult stage.
Etymology.-The species was named in honor of geologist Patrick G. Embree (Orangevale, CA, USA) for his contributions and broad support of the research on the Triassic of Nevada.
Remarks.-Specimen PIMUZ 25361, referred to as Ptychites sp. indet. by Monnet and Bucher (2005), is regarded as    (2-4): Ontogenetic development of the whorl expansion rate (WER n = (dm n /dm n-0.5 ) 2 ), whorl width index (WWI n = ww n /wh n ), umbilical width index (UWI n = uw n /dm n ) and the conch width index (CWI n = ww n /dm n ) plotted against number of half whorls (ontogenetic stages). (5) Ratio between UWI and CWI of the available specimens. Bubble size refers to number of half whorl; the picture in the background shows the shape of the last complete whorl (developed by Korn, 2010). Roman numbers refer to interpretation of different life phases; I: Hatchling, II: Juvenile; III: Subadult-adult; for more detailed explanations see Walton and Korn (2017). conspecific with P. embreei n. sp. Among the ptychitids of Nevada, P. embreei n. sp. covers by far the largest time span. It remains to be clarified whether this is due to biological processes or reflects a bias caused by more intensive sampling associated with this study relative to prior work. There are two more globular genera occurring in sediments of the same age in Nevada: Humboldtites Nichols, 1982 andProarcestes Mojsisovics, 1893. Both genera differ from representatives of P. embreei n. sp. through their very involute to closed umbilicus and the more compressed shape. Furthermore, their suture lines have much narrower main saddles and a more constricted base. Mojsisovics (1882, p. 244) divided all species of Ptychites in five different groups: P. rugiferi, P. megalodisci, P. subflexuosi, P. opulenti, and P. flexuosi. Ptychites embreei n. sp. is included into the group of P. opulenti because it agrees in being predominantly globular. The distinguishing morphologic features of different species of this group are given in Table 6. In summary, representatives of P. embreei n sp. differ from other Ptychites species mainly in having smaller growth size, the absence of ribs, and the more rounded umbilical shoulder.
The range of intraspecific variability among the material described herein is rather small. The largest differences seem to result from ontogenetic processes, which is also the case with certain Paleozoic ammonoids (e.g., Korn, 2017;Korn et al., 2018), in which the trajectories for CWI and UWI are inverses (Fig. 13.4), indicating a close relationship between these two indices. This means that, in agreement with Buckman's first Rule of Covariation (Westermann, 1966), compression co-occurs with less evolute conches.

Morphospace
In order to analyze the ontogenetic morphospaces of Ptychites gradinarui and P. embreei n. sp., a principal component analysis was performed (Fig. 14). Despite the low number of available specimens, the ontogenetic morphospaces of the two species are clearly separated in the PCA plot. The first two principal components of the PCA explain ∼81.52% (PC 1: 73.76%; PC 2: 7.76%) of the observed variation. The raw data for the analysis are provided in the Appendix.
The first principal component (PC1) is mainly dominated by values of the umbilical width index (UWI) and the conch width index (CWI), which have similar loadings. On principal component 2 (PC2), however, values for the whorl expansion rate (WER) alone feature dominantly. Therefore, the axes of the analysis reflect the following: (1) high PC 1 values express a more depressed and lower values a more compressed conch shape, and (2) high PC 2 values mainly coincide with a higher WER. The right part of the morphospace is thus occupied by more pachyconic, and the left part with rather discoidal conches. Most of the ontogenetic changes are captured within changes of the umbilical diameter and the conch width. Even though P. gradinarui generally reaches a much larger growth size, the whorl expansion rate seems to be of minor importance for the distinction of the ontogenetic pathways of these species.

Geographic and stratigraphic occurrence of ptychitids
During the Middle Triassic, representatives of Ptychites were widely distributed in the Panthalassic as well as the Tethys Ocean. Here we present a summary of the biostratigraphic distribution of Ptychites spp. in the most significant domains (Fig. 15). The different biostratigraphic occurrences of P. guloensis in Nevada and British Columbia are possibly biased by a low number of specimens. However, it is apparent that the faunas of Nevada and British Columbia are similar in composition to a certain degree.
Representatives of Flexoptychites, closely allied to Ptychites, were also described from the isolated Germanic Muschelkalk Sea (e.g., Claus, 1921Claus, , 1955Urlichs and Kurzweil, 1977), which is characterized by an endemic ammonoid fauna. In fact, ptychitids are known from the Lower and the Upper Muschelkalk, probably reflecting that the endemism is higher in the Upper Muschelkalk (see Urlichs and Mundlos, 1985;Kaim and Niedźwiedzki, 1999). However, based on the description and illustrations in the former, it cannot be verified with certainty whether the described specimens really belong to Ptychites or closely allied forms. Furthermore, Urlichs and Mundlos (1985) and Balini (1998) doubted that those occurrences were part of a living population and suggested a postmortem drift of the shells from the Tethys. For those reasons, the Germanic Muschelkalk Basin was not considered in the summary of the biostratigraphical occurrences of ptychitids during the Anisian stage (Fig. 15).

Discussion
Representatives of Ptychites can be found in sediments that were deposited in the Panthalassic (e.g., Smith, 1914;McLearn, 1948;Tozer, 1994;Monnet and Bucher, 2005) and Tethyan Oceans (e.g., Diener, 1913;Waterhouse, 1994Waterhouse, , 1999Waterhouse, , 2002a. Due to its almost global distribution, the genus Ptychites has been broadly discussed in the literature, but limited research has been done in recent years. Especially the correlation between the Tethyan and Panthalassic faunas still demands further attention. In the Panthalassic realm, the co-occurrence of ptychitids in Table 5. Measurements in mm of selected specimen of Ptychites embreei n. sp. collected in the Fossil Hill Member of the Favret Formation at the Muller Canyon locality in the Augusta Mountains. Pershing County. Nevada. USA. Further details on the bed number see Figure 2 ("Bed No."). uw: maximum umbilical width; ww: Maximum whorl width; dm: maximum diameter of shell; (): fragmented specimen, estimated value; *: specimens used for ontogenetic analysis, cast present; **: specimen used for ontogenetic analysis, preservation not sufficient, cast present; H: holotype. Journal of Paleontology 94(5):829-851 Table 6. Morphologic comparison of different species of Ptychites of the P. opulentus group to the newly introduced species P. embreei n. sp. For biostratigraphic and geographic distribution, see Figure 15. U and uw: maximum umbilical width; D and dm: maximum diameter of conch; S.s.: Small specimens; L.s.: Large specimens.  (Lindström, 1865) Umbilical shoulder angular Unknown P. hamatus Tozer, 1994 (p. 134, pl. 65, figs. 13, 14, pl. 67, fis. 1-4 pl. 71, fig. 2a (2018) that low-and mid-paleolatitude regions were well connected during the Middle Triassic. This stresses the importance of re-evaluation of the alpha taxonomy of ptychitid species by novel or underexplored methods, as performed in this study.

Species
Ontogenetic analysis.-Ammonoid generic diversity reached its maximum during the Triassic Period (Brayard et al., 2009). At present, few studies have investigated trends in morphological disparity of Triassic ammonoids . McGowan (2004McGowan ( , 2005 and Brosse et al. (2013) carried out important foundational research in this field. Although the background data of both studies differ significantly, both come to the same conclusion: the taxonomic diversity and morphologic disparity of Triassic ammonoids are decoupled. However, it is open to debate whether the high diversity is also biased by taxonomic over-splitting (Forey et al., 2004;De Baets et al., 2013) of the ammonoid faunas. A method, whose potential is far from being fully exploited, is the analysis of ontogenetic trajectories obtained from longitudinal cross-sections. The accretionary growth of ammonoids with conservation of juvenile stages allows the investigation of complete ontogenetic transformations of a set of traits, such as the conch geometry and septal characters (Korn, 2012). Therefore, ontogenetic analyses are an ideal tool to unravel phylogenetic and taxonomic relationships between ammonoid groups (Rieber, 1962). This makes them ideal for the study of evolutionary change in ontogeny through time . Walton and Korn (2017) carried out an extensive comparative ontogenetic analysis of ammonoids within the pachyconic to globular morphospace. They introduced the term C-mode ontogeny, which is by far the most common ontogeny of pachyconic to globular ammonoids. Whereas the herein discussed species P. gradinarui shows a C-mode ontogeny, P. embreei n. sp. has a different development. In phase I and II, P. embreei n. sp. and P. gradinarui have opposing trends in their relationships of the CWI and UWI (Figs. 8.5,13.5). However, both trajectories show a distinct buckle in the curve that marks the decoupling of the UWI and CWI, which is approximately located at an UWI of 0.35 and CWI of 0.70. The change in the direction of the progression marks the onset of the third phase, during which both  Walton and Korn (2017), the change in conch morphologies during ontogeny could be caused by the adaptation to different niche types in the different life phases. It is questionable, whether the disparity of these two groups is significant enough to suggest two different modes of life during the earliest life phases. Nevertheless, it is very interesting to note that ptychitids have very distinct ontogenetic developments even at the species level.
In general, there is limited literature on ontogenetic analysis of individual species. However, in their study of heteromorph ammonites of the Early Cretaceous, Hoffmann et al. (2019) used similar multivariate methods as described in this study. Their study proved that the statistical evaluation of ontogenetic trajectories of ammonoids provides useful information about diversity and disparity at species level. Our study verifies that the statistical evaluation of ontogenetic processes is applicable to normally coiled planispiral ammonoid species from the Middle Triassic. Important ontogenetic changes can be visualized using univariate (Figs. 8, 13) and multivariate (Fig. 14) methods.
Despite a low number of available specimens, the principal component analysis succeeded in separating the two ontogenetic morphospaces of the two ammonoid groups. This highlights the uniqueness of the ontogenetic trajectories and morphospaces that representatives of this group occupy.
Sutures.-The tapering U2/A saddle and the U1/U4 with a slender spur appear to be unique sutural features among ptychitids. However, due to the lack of specimens for comparison, it remains unclear if this is significant. No further features of the suture line of GSUB C13194, P. guloensis, seem to be unique (e.g., bifid endings in the A lobe occur in our material as well as in other specimens referred to the genus; sutures of P. opulentus Mojsisovics, 1882 [Qingge et al., 1980]; Flexoptychites cf. cochleatus [Oppel, 1863] and P. cf. asura Diener, 1895b [Win, 1991]). Our examination of published suture lines in ptychitids underlines the opinion of Köhler-Lopez and Lehmann (1984, p. 63) that suture lines of ptychitids vary significantly, "much in degree of incision," but  Jenks et al. (2015). For the correlation of Spitsbergen, Harland and Geddes (1997) and Weitschat and Lehmann (1983) were used. Only representatives of Ptychites discussed in this publication are listed in this table. Therefore, empty boxes do not necessarily indicate the absence of all Ptychites spp. * Indicates location of the "Ptychiten Kalke-Ptychites layers" (e.g., Mojsisovics, 1886;Spath, 1921;Gugenberger, 1927;Rosenberg, 1952;Harland and Geddes, 1997). Paleogeographic locations of the localities are provided in Figure 1. ** According to Weitschat (1986, p. 253), the preservation of middle Anisian ammonoids of Spitsbergen is not sufficient for a successful zonation of the area. Crosses mark gaps in the ammonoid biostratigraphic framework.
"not in the number of elements." These authors state that the lateral saddle of the very well-investigated species Aristoptychites kolymensis Kiparisova, 1937 is always extremely small and narrow. This is true for many specimens of closely related genera and their species as well, but there are exceptions to this rule and thus this cannot be generalized for this group (e.g., P. cf. cochleatus in Win, 1991). We see no clear relation of sutural features to the conch morphology of ptychitid genera. The suture lines are highly dependent on the growth stage. The very large specimen GSUB C13196 (P. gradinarui, Figs. 3.8-3.10, 8) shows clearly more incisions of lobes and saddles than specimens in earlier stages. Specimen GSUB C13194 (P. guloensis, Figs. 3.5-3.7, 4) does not show the sutural development and thus we cannot discuss the ontogeny of the suture line of the species based on our material. Nevertheless, the high number of sutural elements at the umbilical seam might indicate a multiplication of elements of the U3 as recorded by Kullmann and Wiedmann (1970). The latter was called a sutural lobe due to its position at the umbilical seam (Wedekind, 1916; "sutural" means umbilical seam in this respect); this term is problematic, though, because it only refers to the position on the shell. Köhler-Lopez and Lehmann (1984) nicely show that the U1 (with multiple subdivisions) can be located at this position as well. Therefore, we agree with Köhler-Lopez and Lehmann (1984) that a U3 developed as a sutural lobe does not characterize Ptychitidae. In fact, the sutures of many species of Ptychites and closely allied genera do not show this feature, including P. compressus Yabe and Shimizu, 1927; P. guloensis; P. opulentus; P. wrighti; Discoptychites megalodiscus (Beyrich, 1967); Flexoptychites flexuosus (Mojsisovics, 1882); and Malletoptychites malletianus (see Diener, 1895a;Onuki and Bando, 1959;McLearn, 1969;Qingge et al., 1980).

Conclusions
Here we enhance the taxonomic understanding of ptychitids, including a description of Ptychites embreei n. sp. from the late Anisian of Nevada. According to the state of the art, this species is the longest-ranging within the group. Furthermore, it fills a gap in the otherwise intensively studied ammonoid fauna of north-western Nevada, USA.
After the Permian/Triassic boundary, Ptychitoidea, Megaphyllitoidea, and Arcestoidea filled the cadicone morphospace (Brosse et al., 2013;De Baets et al., 2016, fig. 7). Despite the wide geographic distribution of ptychitids, they exhibit a remarkably low level of morphological variation within their morphospace. Since all ptychitids have an almost smooth shell, with a subordinate ornamentation only, one of the most important morphological descriptive features of ammonoids  is not applicable to the group. This means there are narrow limits regarding the shell variability in the cadicone morphospace in the Anisian, with mostly leiostracan forms (smooth shelled ammonoids; Westermann, 1996). However, some features characterizing the species seem to be hidden in a distinct ontogeny (Figs. 8,13,14). We emphasize the ontogenetic differences of ptychitids to other Middle Triassic ammonoids of Nevada. Ptychitids, despite their similar morphologies, have unique ontogenetic trajectories, as demonstrated above (Figs. 8, 13). Ontogenetic analyses are therefore an ideal tool to improve the alpha taxonomy of ptychitids.
Since the evaluation of ontogenetic trajectories is a rather descriptive and therefore, to some extent, subjective process, a great potential of this method lies within their statistical quantification and interpretation. This study includes one of the first attempts to quantify the ontogenetic development of individuals using statistical methods. The analysis of the very distinct ontogenetic pathways of ptychitids will serve as an important cornerstone in future studies on the statistical quantification of ontogenetic analyses of ammonoids.