From our total sample of 31 pachypleurosaur specimens (Table 1), we first chose 17 specimens that have preserved five growth marks or at least four growth marks and the outer cortex. Only these specimens were passed to growth curve modeling (Dactylosaurus: MB.R. 771.5, MB.R. 801.2, MB.R. 772.3, MB.R. 776.2, MB.R. 786; Anarosaurus: Wijk07-50, Wijk07-70, Wijk09-472, Wijk09-58; aff. Neusticosaurus pusillus: SMNS 50372c, SMNS 92125; N. pusillus: PIMUZ T 4178, PIMUZ T 4211; N. edwardsii: PIMUZ phz 153, PIMUZ T 4758; Serpianosaurus: PIMUZ phz 119, PIMUZ T 4510). The number of growth marks should preferably be as high as possible for growth curve modeling to cover more than just the quasi-linear phase of growth (Klein and Griebeler, 2016; see below). We then carried out a complex model fitting procedure for each of these specimens in order to find the statistically best growth model(s) for each of them. The complete fitting procedure is described in detail in Supplement S2. Here we give only a rough outline of the procedure. Our procedure is based on Griebeler et al. (2013) and was already improved in Klein et al. (2015b) and Klein and Griebeler (2016). It is also able to tackle the technical problem that an unknown number of growth marks could be missing from the inner part of a bone. An estimation of this number had to be done for 3 out of the 17 specimens modeled (aff. Neusticosaurus pusillus: PIMUZ T 4211; Serpianosaurus: PIMUZ phz 119, PIMUZ T 4510). For all others there was no histological indication that growth marks are lost in the inner part of the cortex (Table 1). Our procedure also explicitly tackles the technical problem, which is that the growth record has no information preserved on both growth acceleration and deceleration; i.e., the record covers only the exponential, quasi-linear or asymptotic phase of growth (see discussion in Myhrvold, 2013). This information on growth is needed for establishing a reliable sigmoidal growth model on a specimen (Myhrvold, 2013; Klein et al., 2015b; Klein and Griebeler, 2016). This criterion finally failed for 4 out of the 17 specimens passed to modeling. Their growth record clearly covered only the quasi-linear phase of growth. Thus, we were finally able to establish growth model(s) for 13 pachypleurosaurs.

All models tested for pachypleurosaurs relate humerus length (cm) to age (years), because mass estimation is difficult in Pachypleurosauria (see Supplement S1) and would make our growth models less precise. We always considered four standard growth models for each specimen: von Bertalanffy (vBGM), Gompertz (GGM), logistic (LGM), and Chapman–Richards (CRGM). These standard growth models differ in the masses at which the increase in humerus length is maximal (i.e., inflection point). However, finally the CRGM could not be fitted to the growth record of any specimen studied so far (see also Klein et al., 2015b; Klein and Griebeler, 2016), presumably because of its large number of parameters that have to be estimated.

The specific equations used for the vBGM (Eq. 1), GGM (Eq. 2), and LGM (Eq. 3) (Klein et al., 2015b; Klein and Griebeler, 2016) are as follows: L(t)=Lmax⁡-(Lmax⁡-L0)exp⁡(-gt),L(t)=L0+Lmax⁡exp⁡(-exp⁡(-g(t-i))),L(t)=L0+Lmax⁡1+exp⁡(-g(t-i)). In Eqs. (1) through (3), L(t) is length at age t (where t is a real number), L0 is an initial length, Lmax⁡ is the maximum length, g the growth parameter, and i the location of the inflection point on the age axis. Please note that our formulation of the GGM and LGM allows a flexible location of the inflection point with respect to age (contrary to the other formulations of both models). Note also that only under the vBGM (formulation taken from von Bertalanffy, 1938, 1957; Pütter, 1920) the humerus length at age 0 (birth size) is L0 and asymptotic length equals Lmax⁡. By contrast, for the GGM and LGM humerus length at age 0 (birth size) is L(t) evaluated at t=0 (=L(0)) and asymptotic length is L0+Lmax⁡. Under the GGM and LGM parameter L0 allows for a non-zero length at t=0 and thus it moves the respective growth curve along the length axis.

Before applying any standard growth model to each specimen, we tested whether its growth record covers only the exponential, quasi-linear or asymptotic phase of growth (Myhrvold, 2013). We therefore fitted an exponential (Eq. 4), linear (Eq. 5) and asymptotic equation (Eq. 6) to its ontogenetic growth series on humerus length (Klein et al., 2015b; Klein and Griebeler, 2016): L(t)=L0exp⁡(gt),L(t)=L0+gt,L(t)=L0+(Ldeath-L0)(1-exp⁡(-gt)). In Eqs. (4) through (6) L0 is humerus length preserved at the first growth mark (t=0), and g the growth parameter. In Eq. (6) Ldeath is length at the last growth mark preserved or observed for the outer cortex. Equation (1) on the vBGM has three parameters (L0, Lmax⁡, g) and Eqs. (2) and (3), on the GGM and LGM, respectively, have four (L0, Lmax⁡, g, i), and that on the CRGM has five. These high numbers of parameters can become problematic in non-linear regression analysis and statistics of estimated parameters when the number of growth marks preserved in a bone is comparatively small. This is true for the majority of specimens studied herein. We therefore additionally considered simpler equations for each of the standard growth models (Eqs. 1 through 3), in which we fixed different model parameters to specific values (i.e., did not fit them, for details on this refer to Supplement S2). Thus, finally, 6 equations derived from the general equation were applied to each specimen implementing von Bertalanffy growth (Eq. 1), 11 equations implementing Gompertz growth (Eq. 2), 11 equations implementing logistic growth (Eq. 3), and 12 equations implementing Chapman-Richards growth. Thus, in total for each of the specimens under study we considered 40 equations on standard growth models and 3 equations testing whether not only one phase of growth is preserved in its growth record (exponential, quasi-linear, or asymptotic, Eqs. 4 through 6). To derive the best number of missing growth marks and the best birth size for the three humeri PIMUZ T 4211 (N. pusillus), PIMUZ T 4510, and PIMUZ T 119 (both Serpianosaurus), 40 growth equations were applied. In addition, we did a manual grid search on numbers of missing growth marks and birth sizes (for more details on this procedure refer to Supplement S2).

Out of all growth model equations applied to a specimen we next identified those being statistically assured (i.e., all model parameter estimates differ significantly from zero; for more details refer to the Supplement S2) and which of these models were also biologically reliable (e.g., Lbirth is not negative, inflection point is located after the birth of the individual). From the models passing all criteria, we identified the statistical best model(s) out of these for each specimen by using an Akaike information criterion (AIC) based approach (Burnham and Anderson, 2002, AIC corrected for small sample sizes, the best models are within the range ΔAIC ≤ 10, Griebeler et al., 2013; Klein et al., 2015b; Klein and Griebeler, 2016; for more details on this model selection process refer to Supplement S2).

We calculated for each specimen five life-history traits from each of its best growth curves (those passing the ΔAIC ≤ 10 criterion): humerus length at birth (Lbirth), asymptotic humerus length (AL), age at which sexual maturity is reached (ASM), humerus length of a fully grown individual (99 % AL; equals 99 % of AL), and age at which the individual is fully grown (AA; age at which 99 % of AL is reached). To estimate the age at which the individual reached sexual maturity from its growth curve (ASM), we assumed that the inflection point of the curve coincides with sexual maturation. Evidence for this concept exists in reptiles and amphibians (Kupfer et al., 2004; Lee and Werning, 2008; Reiss, 1989; Ritz et al., 2010). Under the GGM, ASM is seen at about 38 % of AL and under the LGM at 50 % of AL. As our formulation of the vBGM (Eq. 1) only has an inflection point when mass is plotted against age (at 30 % of asymptotic mass), we assumed that ASM coincides with the age at which 30 % of AL is reached (Klein et al., 2015b).

To the growth record of Anarosaurus Wijk07-70 and N. edwardsii PIMUZ T 4758 the single best growth model was finally identified. We calculated AL, ASM, 99 % AL, and AA directly from the respective curve. To find estimates on Lbirth, AL, ASM, 99 % AL, and AA for specimens for which more than one growth model worked well, we did model averaging for trait values (Burnham and Anderson, 2002). We therefore first estimated each of these five traits from all of its best growth curves. We then averaged these values based on the models' respective Akaike weights for each of the traits (Burnham and Anderson, 2002).

Maximum growth rate (MGR) was also obtained from model averaging, except for Wijk07-70 and PIMUZ T 4758. We therefore estimated the annual mass gain seen within the year of the inflection point (ages i, and i+1), and calculated body masses from humerus length at age i and (i+1) for each of the best models on the specimen's growth record.

Estimated birth to adult size ratios (LbirthToAL) of specimens were derived from averaged Lbirth and 99 % AL values, again except for Wijk07-70 and PIMUZ T 4758.

All humeral cross sections are round-oval at midshaft and more oval or elliptical towards the proximal and distal end. All samples, proximally or distally to midshaft, display a medullary region that consists of a matrix of calcified cartilage that contains some small round erosion cavities surrounded by endosteal bone (Fig. 1b). The medullary region is here surrounded by a sharp line (Fig. 1a; Table 1), which separates the periosteal from the endosteal domain. In samples close to midshaft, the amount of calcified cartilage is low and often only locally visible at the inner margin of the sharp line. At midshaft, no calcified cartilage is preserved (Fig. 1c).

Midshaft samples of Dactylosaurus have a small medullary region consisting of a small, round, and well delimited free cavity that is surrounded by endosteal bone (Fig. 1d). Bone compactness is in Dactylosaurus between 89.6 and 95.5 % (Table 1).

The medullary region in samples of aff. N. pusillus is more variable but the medullary region is also always small. SMNS 58025a and SMNS 58025b display little endosteal bone and several large, irregularly formed erosion cavities that reach into the periosteal domain (i.e., indicating some remodeling) (Fig. 1e). SMNS 50372a and SMNS 92125 were not sampled exactly at midshaft and have both a free cavity surrounded by thick endosteal bone, calcified cartilage, and a sharp line. SMNS 50372b displays a central free cavity surrounded by endosteal bone (Fig. 1f) whereas in SMNS 50372c few small erosion cavities and in SMNS 56312 few round decentral cavities are documented (Fig. 1g). In SMNS 50372a, b, and c the cavity of the nutrient foramen is visible. Bone compactness is in samples of aff. N. pusillus between 86.3 and 95.6 %.

Bone tissue in Dactylosaurus and aff. N. pusillus is dominated by parallel-fibered bone with an increase of highly organized tissue towards the outer cortex. Some samples have woven bone deposited in the inner cortex. Please note that we follow the definition of Francillon-Vieillot et al. (1990: 206) for woven bone but see Stein and Prondvai (2013) for more information on the problem of identifying true woven bone tissue. The bone tissue type can be summarized as lamellar-zonal bone. Midshaft samples of Dactylosaurus and aff. N. pusillus have a loosely organized bone tissue (woven bone and/or loosely organized parallel-fibered bone) preserved in their innermost cortex, which we interpret as (pre-)hatchling bone tissue (Fig. 1; Table 1). In some samples this tissue is surrounded by a distinct layer formed by highly organized, and perpendicularly oriented fine fibers (Figs. 1h, 2e). The tissue appears very bright in normal light and shows the extinction pattern of lamellar bone in polarized light. Only one humerus of Dactylosaurus (MB.R. 776.2) but several humeri of aff. N. pusillus (SMNS 58025-2, SMNS 50372b, c, SMNS 92125) show this distinct layer of highly organized and perpendicularly oriented fine fibers around the (pre-)hatchling tissue (Table 1).

Vascularization is dominated by radial vascular canals but longitudinal canals also occur (Figs. 1, 2). Some vascular canals are lined by lamellar bone and thus started being transformed into primary osteons. Some samples show a funnel-shaped arrangement of the crystallites around the simple, mainly radial vascular canals, which may be a precursor of an alignment by lamellar bone of true primary osteons. Vascular density is low, although in some samples long radial vascular canals occur that reach over several growth layers and open into the outer surface (Fig. 1d). One aff. N. pusillus humerus (SMNS 50372b) has longitudinal primary osteons developed, which are well sheathed by lamellar bone (Fig. 1c). These primary osteons are similar to what was described for some placodonts (Klein et al., 2015a, b).

Growth marks occur in form of zones, annuli, and LAGs (lines of arrested growth). Subcycles, in the form of thin layers of highly organized bone tissue, which cannot be followed all around the cross section, are common as well. Histological onset of sexual maturation (Table 1) was estimated on the basis of the clearest growth mark in the inner or middle cortex, accompanied by a general increase in bone tissue organization in the following cycles. Midshaft samples of Dactylosaurus and aff. N. pusillus display an inner ring of (pre-)hatchling bone, implying that the growth record is complete. However, this inner tissue is not separated by an annual growth mark. Some samples show distinct LAGs well visible in normal light, whereas others display a more diffuse growth pattern, consisting of alternating zones and annuli, best visible in polarized light. In some humeri, the inner tissue is made of a bone tissue suggesting very fast growth (woven bone, loosely organized parallel-fibered bone, and high vascular density) whereas others have here a tissue suggesting slow growth (highly organized parallel-fibered bone and low vascular density).

Life-history traits Lbirth, AL, ASM, 99 %AL, AA, and AD derived from growth models differed between the five pachypleurosaur taxa. They also showed a low up to high variability within each of the five taxa (Table 2, Fig. 4). Estimated Lbirth were lowest in Serpianosaurus (range in Lbirth: 0.152–0.402 cm) and highest in Anarosaurus (1.389–1.706). Dactylosaurus (0.913–1.210), N. edwardsii, (0.877–0.933), N. pusillus (0.360–0.829), and aff. N. pusillus (0.500–0.571) had intermediary Lbirth. Neusticosaurus pusillus (the largest Lbirth is 2.3 times higher than that of the smallest) and Serpianosaurus (2.6 times) showed the strongest within-taxon variability in Lbirth and N. edwardsii (1.1 times) the lowest. In Dactylosaurus (1.3 times) and Anarosaurus (1.2 times) within-taxon variability was somewhat higher than in N. edwardsii. AL and 99%AL were lowest in N. pusillus (AL: 1.658–1.783 cm; %99AL: 1.662–1820 cm) and in aff. N. pusillus (AL: 1.797–1.838; %99AL: 1.662–1.820). AL and 99 %AL showed the highest variability within N. edwardsii (AL: 2.804–6.518, 2.3 times; %99AL: 2.776–6.477, 2.3 times), and the lowest within Anarosaurus (AL: 4.409–5.002, 1.1 times; %99AL: 4.365–4.951, 1.1 times). Within-taxon variability in AL and 99%AL was lower in Anarosaurus than in Dactylosaurus (AL: 4.479–5.444, 1.2 times; %99AL: 4.434–5.390, 1.2 times) and Serpianosaurus (AL: 2.185–4.457, 2.0 times; %99AL: 2.163–4.413, 2.0 times). Estimated AA values were highest in Serpianosaurus (15.824–57.547 years) and lowest in Anarosaurus (5.287–6.331). Within taxon variability AA was considerably larger in N. edwardsii (9.638–43.022, 4.5 times) and Serpianosaurus (5.824–57.549, 3.6 times) than in the three other pachypleurosaur taxa (Dactylosaurus: 9.149–13.548, 1.5 times; Anarosaurus: 5.287–6.331, 1.2 times; N. pusillus: 4.589–13.418, 2.9 times). Except for three specimens, for which models estimated that growth marks are missing in the inner part of the bone (PIMUZ T 4211 N. pusillus; PIMUZ T 4510 and PIMUZ T119, Serpianosaurus) AD coincided with the numbers of growth marks preserved, and thus life spans documented in the growth record of specimens.

Models estimated ASM within the first year of life for all specimens from N. pusillus, within the first or the second year of life for Anarosaurus, within the second or third year of life for N. edwardsii, within the second and the fourth year of life in Dactylosaurus, and within the fourth year of life for Serpianosaurus. When ASM was related to AA and AD (relative onset of maturation within maximum life time) this ranking in ASM of taxa disappeared due to the large within-taxon variability in AA and AD, and also because for most of our specimens modeled AD were considerably smaller than AA (Table 2). Nevertheless, when relating ASM to AA, all specimens were sexually mature within the first third of their life, whereas N. pusillus and aff. N. pusillus even reached maturation within the first tenth of life.

Modeled LbirthToAL of pachypleurosaurs ranged between 0.064 and 0.465 (Table 2). The lowest ratios were seen in Serpianosaurus (0.064, 0.091). When using humerus lengths at the first growth mark preserved and humerus length at death length ratios L1gmToLlastgm ranged from 0.177 to 0.630 (Table 2).

Estimated MGR values were lowest in Serpianosaurus (0.044–0.047 g day-1) and highest in Anarosaurus (1.030–2.306 g day-1). Dactylosaurus (0.672–0.882 g day-1), N. pusillus (0.278–0.401 g day-1), N. edwardsii (0.159–0.265 g day-1), and aff. N. pusillus from the Germanic Basin had intermediary MGR values. MGR values varied considerably within Anarosaurus (the largest MGR is 2.2 times higher than that of the smallest), N. pusillus (3.3 times), and aff. N. pusillus (1.4 times). For mass-specific maximum growth rate (MGR / asymptotic mass or MGR / mass at death, Table 3) this clear ranking in maximum growth increment disappeared, except for Serpianosaurus having again the lowest values.

Two different growth and maturation strategies (please note that the inflection point of the growth curve sets ASM and thus the maturation strategy is implicitly given by the growth strategy) were observed within pachypleurosaur taxa (Figs. 3, 5). These different growth strategies coincide with the above described differences between life history traits, birth-to-adult size ratios, and maximum mass gain during life seen between and within taxa. Different growth strategies could indicate a sexual dimorphism in size and maturation in these taxa (Stamps, 1993; Stamps and Krishnan, 1997; see below).

In Dactylosaurus, both sexes start from rather similar Lbirth but the putative sex with the higher asymptotic size (MB.R. 776.2) matures later than that with the lower size (MB.R. 786). This in turn implies an earlier onset of maturation within life (absolute ASM, and relative ASM / AA, ASM / AD, Fig. 5) in MB.R. 786 than in MB. R. 776.2. Contrary, in Anarosaurus the specimens Wijk 09-472 and Wijk 07-70 have very similar Lbirth and AL, but Wijk 09-472 matures one year earlier in life than Wijk 07-70, and shows a much earlier onset of maturation when ASM is compared to AA and AD (Fig. 5). The pattern in growth and maturation documented in Dactylosaurus is also seen in aff. N. pusillus (Fig. 5). SMNS 92125 and SMNS 50372c have rather similar Lbirth, but SMNS 92125 has a smaller AL than SMNS 50372c, and sexual maturation is much earlier (absolute and relative) reached in SMNS 50372c than in SMNS 92125. Contrary, N. pusillus from the Alpine Triassic (PIMUZ T 4178 and PIMUZ T 4211) reach rather similar AL, but their Lbirth differ more strongly than between SMNS 92125 and SMNS 50372c, and they show no clear differences in ASM, ASM / AA, and ASM / AD (Fig. 5). Neusticosaurus edwardsii resembled the growth strategies and maturation patterns seen in aff. N. pusillus (Fig. 5). The N. edwardsii specimens PIMUZ phz 153 and PIMUZ T 4758 have rather similar Lbirth, but reach considerably differing AL and also differ in onset of maturation (absolute and relative). The two specimens PIMUZ T 4510 and PIMUZ T 119 of Serpianosaurus have differing Lbirth and AL, and show differences within their life history only in the onset of sexual maturation for ASM / AA (Fig. 5).

Microanatomy indicates osteosclerosis as typical secondary aquatic adaptation in all studied pachypleurosaurs, except for Anarosaurus. Contrary to the other pachypleurosaurs, Anarosaurus retained a large free central medullary cavity and is in this aspect plesiomorphic (i.e., closer to the ancestral terrestrial condition). It is thus less adapted to an aquatic environment. The stratigraphically older Dactylosaurus, which inhabited the Germanic Basin as well, has (as with Neusticosaurus spp. and Serpianosaurus from the Alpine Triassic) an already reduced free medullary cavity and thus displays osteosclerosis. Microanatomical differences might result from the near coastal environment documented for Winterswijk vs. the shallow marine conditions during the deposition of the Gogolin Formation. However, microanatomy of Dactylosaurus and of aff. N. pusillus also differs slightly from pachypleurosaurs from the Alpine Triassic in retaining a very small free cavity at midshaft whereas the taxa from the Alpine Triassic have filled nearly all cavities by endosteal bone.

The sharp line described herein as well as by several authors having studied long bone histology of Triassic sauropterygians (Sander, 1990; Klein, 2010; Hugi et al., 2011; Klein et al., 2015a, b, 2016) is similar to the Kastschenko's line described in long bones of amphibians (e.g., Castanet and Smirina, 1990; Francillon-Vielleit et al., 1990) and might be homologous to this. Kastschenko's line corresponds to thin remains of the embryonic cartilage matrix at the border of the medullary cavity and separates the endosteal from the periosteal region. In amphibians it is considered as evidence that the growth record is complete because it indicates that endosteal bone resorption and remodeling have not removed the first periosteal deposition yet (Castanet and Smirina, 1990; Francillon-Vielleit et al., 1990). However, in Sauropterygia the sharp line occurs only in non-midshaft samples and the destruction of inner cycles is here likely because loss of inner cycles in non-midshaft samples is documented in some specimens for which a midshaft and a more proximal or distal sample does exist.

Dactylosaurus, Anarosaurus, and aff. N. pusillus all from the Germanic Basin display a distinct change in tissue in their innermost cortex; here interpreted as a transition from prehatchling or hatchling bone tissue to “normal” periosteal bone growth. It only occurs in midshaft samples (Table 1). We hypothesize that this change in tissue indicates an important event in the individual's life history such as hatching (prehatching tissue) or a switch in the hatchling's diet (resorbing the yolk, hatchling tissue vs. foraging start of “normal” periosteal bone growth). This inner bone tissue is usually not documented in pachypleurosaur samples from the Alpine Triassic (Hugi et al., 2011; Nicole Klein, personal observation, 2017). However, it is also less clear in Anarosaurus.

Some individuals that exhibit this tissue start growth fast (i.e., with a zone) and others slowly (i.e., with an annulus). This might indicate two breeding, egg laying, and hatchling periods during a season or year, giving rise to two sub cohorts a year. Producing several clutches a season is known for many reptiles. However, to our knowledge no histological study of a population had ever focused on differences in the inner tissue. Thus, our hypothesis remains quite hypothetical until this is studied in modern reptiles. In addition, one has to consider that our sample does not represent a single population but consists of individual specimens, of which many were found in different localities (= environments) and which had not lived at the same time. Therefore, climatic and environmental differences between localities as well as in time must be considered as well.

In some samples the inner remains of (pre-)hatchling tissue are surrounded by a distinct layer of highly organized, and perpendicularly oriented fine fibers, which are very distinct in polarized and in normal light. Although this layer is very distinct we do not interpret it as 1st annual growth mark because it does not occur in all samples that have (pre-)hatchling tissue and the tissue is very different from the tissue usually forming typical annuli or LAGs. This layer might indicate a period of rest after hatching (resorbing the rest of the yolk, although already hatched) or biomechanical changes (e.g., locomotion, skin attachment). The distinct layer of highly organized and perpendicularly oriented fine fibers is usually not documented in pachypleurosaurs from the Alpine Triassic.

Bone tissue and growth rate strongly underlie individual variation, i.e., developmental plasticity in all Triassic Sauropterygia studied so far (Klein, 2010; Hugi et al., 2011; Klein et al., 2015a, b, 2016; Klein and Griebeler, 2016). Differences related to environmental conditions experienced by taxa under study are obvious as well. They originate from different localities and most likely lived at different times besides overall different stratigraphic origins. Only the sample of Anarosaurus originates from the same locality and horizon. Even here differences in bone tissue, vascularization, vascular density, and microanatomy exist. The length of the time period during which the bones of Anarosaurus accumulated is unclear and could have lasted decades to thousands of years. Moreover, at the same locality even within a year exogenous condition can vary greatly. The four different pachypleurosaurs taxa from the Alpine Triassic occur subsequently in four different horizons (summarized in Hugi et al., 2011). All other samples originate from different localities and horizons. Thus, climate as well as other exogenous conditions (e.g., sea level, food availability) have varied considerably. Besides exogenous factors endogenous conditions (e.g., fitness of female and individual) must be considered.

Also, as a result of the above mentioned factors, the sequences of growth marks are very variable in pachypleurosaurs. They rather seem to indicate individual and environmental variability than taxonomy, as does the presence of subcycles and double LAGs. Sexual dimorphism as a further source of within-taxon variability is also a likely factor for high variability (Sander, 1989; Lin and Rieppel, 1998; Cheng et al., 2004, 2009; Xue et al., 2015; discussed below).

Dactylosaurus and aff. N. pusillus were small pachypleurosaurs (∼ 50 cm body length) with a relatively short life span. Based on their preserved growth record, both taxa reached sexual maturity early in life, after the 1st or 2nd year. Maturation is marked by a distinct LAG accompanied by an increase in tissue organization and a decrease in vascular density. After the 4th year of life, growth rate increases again because growth marks become closely spaced and mark attainment of maximum size. While growth models resembled ages at which sexual maturity is documented in the growth record for Dactylosaurus (within the 2nd or 4th year of life), they indicated sexual maturation already within the first year of life in aff. N. pusillus. Given the short life span in aff. N. pusillus this difference in onset of maturation is large (the preserved growth record indicates it after two years and the models within the 1st year of life). Overall, life-history traits derived from models on aff. N. pusillus and N. pusillus were rather similar and comprised a similar amount of variability within both taxa. This supports the hypothesis that both groups belong to the same taxon.

Growth models corroborated that Serpianosaurus reached sexual maturity in its 2nd or 3rd year of life (Hugi et al., 2011) as they predict maturation in the fourth year of life. Model estimates on ages at death were lower than 14 years for our two specimens modeled, which is consistent with Hugi et al. (2011). Compared to the observation of Hugi et al. (2011) that the onset of sexual maturity started in N. edwardsii between the 4th and 7th year, our growth models suggested a much earlier maturation after the 1st or 2nd year of life. However, our asymptotic ages derived from models (maximum life span) corroborate that an individual from this taxon could have lived longer than 15 years (Hugi et al., 2011). Overall, ages at onset of maturation derived from the growth record and estimated from growth curves of pachypleurosaurs were more or less consistent. They also agree with the overall range of values seen in extant squamates (within the first year of life up to 12 years, Fig. 4). When compared to similar-sized extant squamates, pachypleurosaur maturation ages are among the smallest seen in extant species or even smaller. Maturation in Simosaurus is also earlier than in a modeled similar-sized extant squamates (Klein and Griebeler, 2016; Fig. 4).

Except for the aff. N. pusillus specimen SMNS 92125, estimated asymptotic ages (i.e., when maximal size is reached) did considerably exceed estimated ages at death. This pattern was also observed in Placodontia and Simosaurus as was the early onset of sexual maturity (Klein et al., 2015b; Klein and Griebeler, 2016). All of this could indicate a large predation pressure on these taxa, preventing animals from reaching asymptotic age and size and favoring an early onset of maturation within their life in order to enable a successful reproduction before death (Sinclair et al., 2003; Owen-Smith and Mills, 2008). Estimated asymptotic ages of pachypleurosaurs are not only consistent within the range seen in extant squamates (0.5–91.0 years, N=1014). They also resemble those seen in similar-sized extant squamates (Fig. 4). Compared to the other pachypleurosaurs studied and to the larger-bodied Placodontia and Simosaurus, the estimated asymptotic age of one Serpianosaurus specimen (PIMUZ T 4510, 57.5 years) and of one N. edwardsii specimen (PIMUZ phz 153, 43.0 years) was very high. However, AIC values of growth models on the two N. edwardsii specimens did not pass or only tightly passed (Serpianosaurus) our ΔAIC ≥ 10 criterion to assure that the growth record does not only cover the quasi-linear phase of growth (Table S1).

Compared to similar-sized extant squamates, all pachypleurosaurs studied and also Simosaurus have larger masses at birth (Klein and Griebeler 2016; Fig. 4). This could indicate a smaller clutch size in these Sauropterygia than in similar-sized extant reptiles (Meiri et al., 2015).

Overall, a comparison of life-history strategies of pachypleurosaurs and Simosaurus to similar-sized extant reptiles (Fig. 4) indicates a similar asymptotic age, but an earlier onset of maturation within their life. The latter might compensate their lower clutch sizes due to larger birth sizes than in similar-sized extant squamates. Maximum growth rates of all pachypleurosaurs and of Simosaurus are again consistent with those seen in similar-sized extant reptiles (Fig. 4).

Humeral morphology of Dactylosaurus and aff. N. pusillus is variable. Nevertheless, a clear separation into a simple and a more complex morphology, reflecting sexual dimorphism between females and males as is known for Neusticosaurus spp. (Sander, 1989; Rieppel, 1989) and for Keichousaurus (Lin and Rieppel, 1998; Cheng et al., 2004, 2009; Xue et al., 2015) is not possible due to the low sample size studied on Dactylosaurus and aff. N. pusillus (< 10 specimens' in this study vs. hundreds of specimens of pachypleurosaurs from the Alpine Triassic and China).

Pachypleurosaurs studied by us showed differences in the appearance and clarity and distinctness of growth marks within taxa (see Hugi and Sánchez-Villagra, 2012, for differences in growth marks in modern iguanids), and different growth and maturation strategies were identified by modeling. All these differences could indicate sexual dimorphism (Stamps, 1993; Stamps and Krishnan, 1997). However, environmental and individual variability could also generate these patterns, especially as sampled humeri do not originate from the same localities or horizons. That humeri studied might belong to different species would be a further explanation for the high variability in growth and maturation patterns but this problem is always present when studying extinct taxa.

Modeled birth sizes in Dactylosaurus and N. edwardsii differ among specimens. The putative sex with the higher asymptotic size matures later than that with the lower size, whereas the sex with the lower asymptotic size has an earlier onset of maturation within life (absolute and relative, Fig. 5). The aff. N. pusillus specimens had the same growth and maturation strategy as seen in Dactylosaurus and N. edwardsii (Fig. 5). Contrary, the N. pusillus specimens reach rather similar asymptotic sizes. The variability in size at birth was larger in N. pusillus than in aff. N. pusillus, whereas onset of sexual maturation shows a low variability within both taxa. Anarosaurus has very similar lengths at birth and similar asymptotic lengths, but show a strong difference in the onset of maturation (absolute and relative, Fig. 5). The two specimens from Serpianosaurus have differing lengths at birth and asymptotic sizes, and show large differences in the onset of sexual maturation within their life (only ASM / AD, Fig. 5). Thus, overall no uniform growth and maturation strategy is seen in the taxa from the Germanic Basin or from that from the Alpine Triassic. This suggests a high variability in growth and maturation strategies within pachypleurosaurs in space and in evolutionary time. Different environmental conditions and evolutionary history could had shaped differences in growth and maturation patterns seen between (putative) sexes.

As many situations exist that can lead to a sexual dimorphism in size and maturation it is difficult to assign a sex to a growth strategy for pachypleurosaurs and for fossils in general (where we have in addition the problem of unambiguous taxonomical assignment). For example, selection for larger male size and later onset of reproduction could be driven by male–male competition, i.e., by competition for mating opportunities, larger males have more reproductive success than smaller. This selection scenario seems to be applicable to a number of extant lizards (reviewed in Cox et al., 2003), in which males are larger than females. It would indicate that the larger pachypleurosaur specimens with the delayed maturity are indeed males. Territorial behavior that could lead to competition for mating opportunities has already been suggested to explain why males are larger than females in the Chinese pachypleurosaur Keichousaurus (Lin and Rieppel, 1998). Males can become double the size of the smallest pregnant female (Nicole Klein, personal observation, 2006, on Keichousaurus specimens in Yichang collection). However, extant lizard species in which females are larger than males also exist (reviewed in Cox et al., 2003) and thus both situations could have also existed in pachypleurosaurs. Fecundity selection favors large size and an earlier onset of maturation in females than in males, i.e., larger and earlier reproducing females can have more offspring during their life. However, the scenario that females are larger than males is not supported by our growth models. All specimens with a larger asymptotic size show a delayed (and not an earlier) sexual maturity compared to those with the other growth strategy (Fig. 5). For our pachypleurosaur sample selection for higher fecundity is only conceivable for Anarosaurus, in which onset of maturation but not birth size and asymptotic size differs between the putative sexes. In this case, Wijk 09-472 would correspond to a female, because it has the earliest onset of maturation seen within our sample on this taxon. Finally, environmental conditions could also select for a sexual size dimorphism in order to reduce intraspecific competition between sexes for food (prey, dietary partitioning) or more generally lead to niche divergence of sexes (reviewed in Shine, 1989; Cox et al., 2007).

Differences in size and age at maturation of sexes are known for extant reptiles. They corroborate differences in asymptotic sizes and ages at which sexual maturation used by us to evidence sexes in pachypleurosaur taxa (Fig. 5, Tables 2 and 3). Males are larger than females in the majority of lizards, but species in which females are larger than males also exist. In some species of Anolis, Tropidurus, Amblyrhynchus, and Varanus males are on average 50 % larger than females. By contrast, females exceed only males by as much as 20 % in Polychrus, Mabuya, and Aprasia (reviewed in Cox et al., 2007). In snakes males are also more often larger than females. In large pythons (Morelia, Python) and boas (Eunectes) male body mass can even be an order of magnitude larger than female mass. In turtles, females are most frequently larger than males. This situation is seen in 50–60 % of all turtle species. Size differences in turtles can be very impressive, e.g., in Kachuga and Graptemys females average two up to three times the length of males (reviewed in Cox et al., 2007). In large Alligator, Caiman, and Crocodylus species, males exceed females in length by 20 up to 40 % (reviewed in Cox et al., 2007). However, unfortunately the majority of comparative studies on sexual dimorphism in extant reptiles have only focused on size differences between sexes, whereas much less is known in reptiles about differences in the onset of maturation between sexes. Nevertheless, several authors have shown differences in the relationship between size at maturation and asymptotic size in Anolis lizards, the rattlesnake Crotalus viridis, the lizards Sceloporus merriami and Ctenotus pantherinus, and the slider turtle Pseudemys scripta (reviewed in Stamps and Krishnam, 1997). An evaluation of the database AnAge (de Magalhães and Costa, 2009) yields a total of 14 reptile species (11 turtles, 3 squamates) in which females mature later than males. The female turtle species (Chelydra serpentina, Chrysemys picta, Deirochelys reticularia, Emydoidea blandingii, Malaclemys terrapin, Pseudemys concinna, Trachemys scripta, Kinosternon baurii, Kinosternon subrubrum, Stenotherus minor, Apalone mutica) are 1.2 up to 2.4 times later sexually mature than males, and female squamates (Lacerta vivipara, Virginia striatula, Crotalus horridus) are 1.3 up to 2.0 times later sexually mature than males.

The distinct layer of highly organized, and perpendicularly oriented fine fibers might be related to viviparity and indicate a period of rest after hatching or being born and before starting foraging by the individual. Viviparity in Sauropterygia was clearly documented for Keichousaurus (Cheng et al., 2004) and is very likely for Neusticosaurus spp. (Sander, 1988, 1989; Rieppel, 1989). It is also documented in plesiosaurs (O'Keefe and Chiappe, 2011), the descendants of Triassic Eosauropterygia. However, O'Keefe and Chiappe (2011) argued that the small specimen located within the larger specimen must be an embryo (and not prey) due to the high ratio in humeri length of the (putative) embryo and mother, which is always considered as being indicative for viviparity in extinct taxa.

LbirthToAL ratios derived from growth models for pachypleurosaurs studied ranged between 0.064 and 0.465 (Table 2). When using humerus lengths corresponding to the first growth mark and humerus length at death preserved in the growth record, L1gmToLlastgm values ranged from 0.177 to 0.630 (Table 2). When the first growth mark coincides with the individual's birth L1gmToLlastgm, the birth-to-adult ratio is preserved in the individual itself. When the first growth mark was laid down after birth and thus later in ontogeny, L1gmToLlastgm overestimates the true value. Thus, overestimation is expected for specimens PIMUZ T 4211, PIMUZ T 4510, and PIMUZ T 119 in which growth marks could be missing (Table S1). Nevertheless, ranges obtained from different methods still match those observed for other viviparous fossils and Sauropterygia (please note that birth size in these fossils is most probably underestimated as embryos have not finished development) as well as those of extant viviparous reptiles. Specimens of Neusticosaurus in Sander (1988, 1989) show birth-to-adult ratios between 0.25 and 0.52. These ratios match LbirthToAL ratios of PIMUZ T 4211 (0.272) and PIMUZ T 4178 (0.465), but not that obtained from the length corresponding to the first growth mark for PIMUZ T 4211 (0.639) as the growth models suggest for this specimen that two growth marks are missing. They also fit to those estimated for the N. edwardsii specimen PIMUZ T 4758 (0.333 and 0.302), but not to PIMUZ phz 153 (0.135 and 0.205). For the nothosaur Lariosaurus, Renesto et al. (2003) report a presumably birth-to-adult humerus ratio of 0.26 consistent with both ranges. While the cited studies on Neusticosaurus and Lariosaurus estimated lengths of hatchlings from isolated embryos, Cheng et al. (2004) and O'Keefe and Chiappe (2011) had pregnant females providing direct evidence of viviparity. Based on figures in Cheng et al. (2004) a ratio of 0.27 and 0.33 for two pregnant females of Keichousaurus was calculated, in this study. O'Keefe and Chiappe (2011) gave ratios between 0.4 and 0.67 for their pregnant plesiosaur. The scincid Egernia group (Egernia stokesii: ratio = 0.46, Tiliqua rugosa: ratio > 0.5, Corucia zebrata: ratio = 0.56) listed in O'Keefe and Chiappe (2011) corroborates the high birth-to-mother ratios in the plesiosaur studied by these authors. They are also consistent with the high L1gmToLlastgm of the pachypleurosaurs studied here.

The selective pressures favoring viviparity over oviparity in the evolutionary history of vertebrates are diverse and highly discussed (Blackburn and Sidor, 2014). For pachypleurosaurs a selective advantage of viviparity could be that a female is able to reduce mortality within embryonal development in order to increase her reproductive success under high predation pressure. Alternatively, viviparity is the ancestral state for this taxon or even the entire group.

In all pachypleurosaurs, bone tissue type is lamellar-zonal, implying relatively low growth rates, except for Anarosaurus. Anarosaurus grew with incipient fibro-lamellar bone tissue type, combined with a higher vascular density, resulting in an increased growth rate. Compared to other Triassic Sauropterygia, Dactylosaurus and the Neusticosaurus–Serpianosaurus clade display the lowest growth rates based on tissue organization and vascular pattern and density (Klein et al., 2015a, b; Klein and Griebeler, 2016; Klein et al., 2016). MGR values obtained from growth models corroborate these histological findings (Tables 2 and 3). Serpianosaurus has the lowest mass-specific growth rate (MGR / asymptotic mass, MGR / mass at death, Table 3) of all pachypleurosaurs studied and compared to similar-sized extant reptiles its MGR is even lower (Fig. 4, Table 3). Neusticosaurus edwardsii has the second lowest mass-specific maximum growth rates in our sample. Rates of N. pusillus and that of Dactylosaurus are only slightly higher than those of N. edwardsii. MGR values and mass-specific growth rate of aff. N. pusillus show a higher variability than those of N. pusillus. This could indicate that the two taxa experienced different environmental conditions during growth (Alpine Triassic vs. Germanic Basin). Except for Anarosaurus, all MGR values of studied pachypleurosaurs are lower than that expected for a similar-sized extant reptile (Fig. 4). Our growth models corroborate that Anarosaurus specimens have the highest MGRs in the pachypleurosaurs sample. Histological studies suggest that growth rates in Anarosaurus are somewhat higher than the observed range in nothosaurs and that they are comparable to rates of pistosauroids (Klein, 2010; Klein et al., 2016). However, MGR values of Simosaurus are somewhat higher than those seen in modern similar-sized reptiles, and they are thus considerably higher than in Anarosaurus (scaled up to this size). Differences in growth rates could reflect differences between food availability and quality in Triassic marine ecosystems and today's terrestrial ecosystems.

In Placodontia, taxa studied from the Alpine Triassic showed lamellar-zonal bone tissue but taxa that lived within the Germanic Basin all displayed fibro-lamellar bone (Klein et al., 2015a, b). However, this might be related to taxonomical differences, low sample size, or simply may not reflect a true pattern. Nothosaurs all grew with lamellar-zonal bone but were so far only sampled from the Germanic Basin. Dactylosaurus from the Germanic Basin grew with lamellar-zonal bone tissue, whereas Anarosaurus, also from the Germanic Basin, grew with incipient fibro-lamellar bone tissue (Klein, 2010). All pachypleurosaurs from the Alpine Triassic i.e., the Neusticosaurus–Serpianosaurus clade (including aff. N. pusillus from the Germanic Basin) also grew with lamellar-zonal bone tissue. It is not clear whether microanatomical and histological differences of Anarosaurus are solely related to the environmental settings or whether phylogenetic relationships of Anarosaurus should be re-thought.