Introduction

The time and energy invested by parents in post-natal care in tetrapods partly control reproduction rates and offspring survival rates, two key parameters used in models to explain population dynamics and dispersion1,2,3,4. Post-natal parental care is thus a key factor in the understanding of the biogeography of a species and its evolutionary history2,5,6. However, post-natal parental care (food provision, protection against predation, grooming) is difficult to infer in extinct tetrapods as it leaves scarce traces in the fossil record7. Post-hatching parental care has been proposed for the ornithischian dinosaur Psittacosaurus based on the exceptional discovery of an adult closely associated with 34 juveniles interpreted as its offsprings8. It was also proposed for the saurolophine hadrosaur Maiasaura peeblesorum based on the cartilaginous long bone epiphyses of the hatchlings suggesting a neonatal lack of locomotor activity7 and the exceptional discovery of 11 juveniles of a few months old that died in their nest, suggesting that there were nestlings9. More indirectly, nest building and brooding behavior identified for instance in some oviraptorid theropods10, or the coexistence of several ontogenetic stages in the same herd inferred from hadrosaurid track sites11 also supported the hypothesis of parental care in non-avian dinosaurs. On the contrary, the lambeosaurine hadrosaur Hypacrosaurus is recovered in age-segregated herds in the deposits based on long bone histology12. It was suggested that these dinosaurs were precocial and thus have been able to survive without parental care. On the other hand, intensive parental care due to the lack of mobility in M. peeblesorum has been challenged based on the fully mineralized pelvis of the neonates enhancing a neonatal locomotor capacity as well as on the absence of adult skeletal remains at nest sites13.

The classification of Nice14 for present-day birds associates the degree of post-hatching parental care with the state of the neonates in the altricial-precocial spectrum, with intensive parental care given to altricial neonates. The neonatal state could be quantitatively represented by the neonatal aerobic scope noted ΔMR value, corresponding to the difference between the maximum and the minimum rates of oxygen consumption. As they have locomotor and motor systems inactive, altricial species stay in the nest for an extended period and are characterized by a maximal metabolic rate (MMR) equal to the resting metabolic rate (RMR) (ΔMR = 0)15. On the contrary, precocial bird species are able to forage alone at hatching and consequently have a higher MMR value than their RMR one (ΔMR > 0). This rule is less true in shorebirds like the brush-tailed penguins Pygoscelis or representatives of the Scolopacidae that live in cold and windy environments inducing a very high energetic cost at rest, hence reducing their ΔMR values15,16. It does not apply to hyperprecocial ectothermic reptiles like sea turtles or crocodiles that mostly rely on anaerobic power even at peak activity, also leading to reduced or null ΔMR value17,18. Compared with altricial species, parental care is reduced or absent in precocial species. In ducks, neonates are autonomous but stay near their parents14,15. In megapodes, neonates hatch without the parents and survive alone19.

The aim of this study is to infer neonatal mass-specific RMR and MMR values of M. peeblesorum from the middle and late Campanian of the Two Medicine Formation (82–76 My20) in order to calculate its neonatal ΔMR value. This metabolic scope provides the first quantitative insight into the position of this ornithischian dinosaur in the altricial-precocial spectrum by comparing it with those of extant tetrapod species. The result allows for a qualitative hypothesis regarding the degree of dependence to parental care in Maiasaura. Analyzing this duck-billed dinosaur as a case study is appropriate as a first attempt at this method because it is represented in the fossil record by embryonic/perinatal remains, sometimes associated with nests and eggs21, enabling accurate data to be collected.

We infer the neonatal mass-specific MMR and RMR values using phylogenetic eigenvector maps (PEM)22,23,24,25,26, a statistical tool designed to build models integrating phylogeny and considering phylogenetic information as a weighted influence matrix. The models are built with metabolic rate data from extant species, their osteo-histological variables and a set of phylogenetic eigenvectors used as predictors22,23,27. We used the femoral relative density of primary osteon (RPOA) as an explanatory variable for RMR. In juveniles, the resting metabolic rate is primarily correlated with bone growth rate27, which is characterized by vascularization during mineralization represented by RPOA28,29,30,31. We used blood flow as an explanatory variable for MMR. Femoral blood flow is correlated with MMR because it is related to bone oxygen supply32 for bone remodeling due to stresses of locomotion and vary similarly to the oxygen consumption of animals running on treadmills33,34.

We then discussed the significance of the estimated ΔMR value in terms of neonatal state and its ecological implications based on present-day birds and mammals15,35,36. This novel method can subsequently be applied to other extinct tetrapod species.

Material and methods

Material

Material

This study is based on the analysis of 23 femora attributed to the saurolophine M. peeblesorum recovered from the Campanian in Montana, USA, and curated at the Museum of the Rockies (MOR) or Princeton University (YPM-PU) (listed in Table 1). They include 4embryonic long bones (2 femora, 1 tibia, and 1 humerus)21, and long bones representing a large proportion of all other postnatal ontogenetic stages as presumed based on their femoral circumference and lenght (Fig. 1, Table 1). Two other specimens (MOR 758 16-16-15-99 presented Fig. 2 and MOR PU 22400 GS400F3 presented in supplementary material 6) are mid-diaphyseal femoral thin sections that still contain embryonic bone. Fossils of M. peeblesorum were previously collected between the two bentonite levels Hadro Hill 8-9-93 dated 78.6My and L2R061517-1 dated 76.2My20.

Table 1 Maiasaura specimens used to model the evolution of femoral nutrient foramen dimensions in relation to the evolution of femoral circumference. Collection number, femoral circumference Fc, femoral length Fl (for broken bones, femoral length was estimated using a cross product based on complete femora of similar size.
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Fig. 1
figure 1

Ontogenetic evolution of the femoral nutrient foramen radius. (a–d) M. peeblesorum 3D models from the embryonic MOR 240 2024-c-238 (femur), MOR 240 2024-c-241 (tibia), and MOR 240 2024-c-239 (humerus)21, black and white arrows point to the nutrient foramen, the scale bar represents 1 cm. (a) Femur in anterior and lateral? view. (b) Femoral section of the 3D model. (c) Humerus in anterior and lateral or medial view. (d) Tibia. (e) Ontogenetic evolution of the nutrient foramen radius in mm with the mid-shaft circumference of the femur in mm (Table 1). 3D models were obtained with Avizo 3D Lite 9.2, ThermoFischer Scientific and are available upon request from the Museum of the Rockies.

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We modeled the ontogenetic evolution of the femoral nutrient foramen radius (R) in Maiasaura with the evolution of femoral mid-shaft circumference (Fc) representing the developmental stage (Table 1, Fig. 1E). The equation is a power function having the following shape: Y = aXb, accordingly to previous studies about distribution of blood flow with adult body mass, or through the ontogeny18,33,37.

We also used 14 neonates from present-day species of mammals, birds amphibians, crocodiles, turtles and lizards listed in Table 2 to build a model for neonatal mass-specific RMR inferences.

Table 2 Neonatal blood flow (Q̇) estimated based on the femoral nutrient foramen radius (R) of neonates from 14 present-day vertebrate species and associated neonatal mass-specific MMR values used to construct a model for neonatal mass-specific MMR inference.
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We obtained the necessary permissions to study each specimen from their original collections (see Data Availability for details on the scanned specimens. Rangifer tarandus: Museum National d’Histoire Naturelle, la collection des mammifères; Pygoscelis_adeliae, Anas sp.: Museum National d’Histoire Naturelle, la collection des oiseaux; Larus glaucescens: Oklahoma State University).

Methods

CT-scan and 3D models

Bones were CT-scanned with a Double Tomograph at High Energy (DTHE) from RX Solutions. Regarding the fossil material, we used a current of 103.4 µA and a voltage of 180 kV and a voxel size of 13–16 µm (supplementary material 1). Regarding the extant specimens, we tested their preservation fluid for the presence of formaldehyde using Schiff’s reagent to ensure that the tissues were properly fixed and could withstand further treatments. The specimens were then washed 3 times in baths composed of a 70%-alcohol-30%-water mixture to ensure a good contrast between bone and flesh on the slides. These specimens were scanned out of their preservation fluids with a current ranging from 80 to 263 µA and a voltage ranging from 100 to 200 kV and a voxel size ranging from 9 to 25 µm (see supplementary material 1 for details). Volume rendering, processing of scans (femur or nutrient foramen) and measurements were obtained using Avizo software (Avizo 3D Lite 9.2, ThermoFischer Scientific). The 3D models are digitally stored in their respective collections (supplementary material 1).

Phylogenetic eigenvector maps

Both maximal and resting metabolic rates were inferred using phylogenetic eigenvector maps (PEM ; supplementary material 2; e.g.23,25,26) on R (4.3.0) 38. It is a predictive modeling technique for missing data that considers phylogenetic non-independence24 (supplementary material 3). A calibrated tree for present-day taxa is coded as a matrix that is transformed to extract eigenvectors. Two parameters control the extent of the evolutionary changes along the branches: 1) “a” (0 < a < 1) representing the steepness of the evolutionary changes after each phylogenetic node that is estimated with the “PEM.fitSimple” function of the “MPSEM” R package24 and 2) “Ψ” representing the relative evolutionary rates23,24,39. We assumed that metabolic rates evolved constantly throughout the phylogeny23. We thus assigned a single pair of “a” and “Ψ” value per model. When a = 1, evolution occurs at fixed rates independently of branch lengths. When a = 0, changes occur in proportion to the square root of branch length. The values used for inferences were intermediate, with 0.425 for MMR models and 0.419 for RMR models. Regarding Ψ, we choose the default value of 1 following Molina-Venegas et al.39. n-1 eigenvectors are produced, n the number of taxa used in a model. The functions lmforwardsequentialsidak or lmforwardsequentialAICc in MPSEM performed a forward stepwise selection of these eigenvectors24. We produced two models: a first model accounting for the phylogeny and the evolution of the response variable (to be inferred in the hadrosaur species) and a second including in addition a predictor variable (a bone histological or osteological feature).

The widespread lmforwardsequentialAICc function use the corrected Akaike information criterion (AICc)40 to find the best model having the lowest AICc value and the highest R2 value. It produces a model that minimizes overfitting while optimizing the balance between fitting quality and complexity. However, it has been shown that the AICc approach displayed high type I error and resulted in wrong ecological interpretation41. The lmforwardsequentialsidak function used the Holm-Sidak correction24,42,43 to find a model that controls the type I error and minimizes the risk of false significance. In this study, the authors prefer the Holm-Sidak correction selection procedure over AIC selection procedure, but we propose to compare the results of both methodologies (supplementary material 8. A. and B.).

A model was accepted only if its residuals followed a normal distribution, i.e., if the p-value obtained from the Shapiro–Wilk normality test on the residuals was greater than 0.0544.

The initial models for RMR and MMR inferences yielded residuals that did not follow a normal distribution with p-values of 0.023 and 0.014 respectively. We consequently discarded these two first models and a log-transformation was applied to both RMR and MMR values, as recommanded by23. Nonetheless, explanatory variables were not log-transformed to avoid issues with zero values. Following the transformation, the Shapiro–Wilk test yielded p-values of 0.67 and 0.38 for RMR and MMR respectively, leading to the acceptance of the models for RMR and MMR inferences. Further in this study, the results are presented in their exponential form to reverse the log transformation. We finally checked the predictive power of the model by performing a leave-one-out cross-validation test (supplementary material 8. B.).

Histological and osteological variables

Nomenclature

We followed the nomenclature of de Buffrénil and Quilhac (2021)45 to describe bone histological structures.

Relative primary osteon area

We used the relative primary osteon area (RPOA) defined as the surface occupied by the primary osteons divided by the observed surface31 as an explanatory variable for neonatal mass-specific RMR. In juveniles, RMR is primarily correlated with bone growth rate27, which is characterized by vascularization during mineralization as blood primarily supply osteocytes in oxygen28,29,30,32. RPOA is thus a proxy for the oxygen needs during bone formation31,45, and is therefore correlated with RMR31.

RPOA measurements were conducted on the two M. peeblesorum femoral sections MOR 758 16-16-15-99 and MOR PU 22400 GS400F3 exhibiting a neonatal line and therefore an innermost cortex representative of the postnatal condition (supplementary material 6). Embryonic bone is extensively resorbed in MOR PU 22400 GS400F3.

Bone sections were studied using the Nikon Optiphot2-POL microscope from the Museum of the Rockies coupled with a Nikon DS-Fi-2 camera. We used the NIS-Elements BR 5.21.03 software (Nikon Imaging Software-Elements Basic Research) to produce mosaic images of the entire femoral sections (e.g. Fig. 2A, B). Under lambda wave plate, the primary osteons are composed of birefringent lamellar or parallel-fibered bone46. The primary osteons are delimited by the isotropic woven bone presenting a higher density of osteocyte lacunae46.

The delimitation of the primary osteons and the calculation of their density were made manually using a graphic tablet (Wacom Cintiq 22) and the ImageJ 1.54 k software. Measurements were taken as close as possible to the neonatal line in order to observe the perinatal conditions.

Blood flow

Blood flow (Q̇) is the volume of blood perfusing the femur per time unit and can be computed using the Eq. (1).

$${\text{Log }}\left( {{{\dot{\text{Q}}\, {\text{ml}}}}\;{\text{min}}^{{ - {{1}}}} } \right) = - 0.20.{\text{log}}\left( {\text{r}} \right)^{{{2}}} + {{1}}.{{91}}.{\text{log}}\left( {\text{r}} \right) + {{1}}.{{82}}$$
(1)

with r the radius of the femur nutrient foramen47. Equation (1) was built using mammals but has also previously been applied to Maiasaura18. We used it as an explanatory variable for mass-specific MMR (e.g.26), because bone perfusion is related oxygen supply32 for bone remodeling upon microfractures due to exertion, and to the ability to withstand blood pressure48. In fact, blood flow and MMR covary with body mass, both following a relationship involving the same exponent33,47. Nutrient foramina are bone openings through which an artery enters from the external bone surface to supply cortical bone with blood49. In mammals, a perforating branch of the deep femoral artery passes through the nutrient foramen and fills 50–70% of the foramen50. Some bird species have pneumatized long bones with both an air sac and an artery passing through the pneumatic foramen, reducing the femoral artery space to 20% of the foramen volume51. As we do not know the space occupied by the femoral artery in dinosaur femoral nutrient foramen, we decided to use r as the radius of the nutrient foramen rather than the radius of the artery following26.

We measured the nutrient foramen in 19 M. peeblesorum femora of different ontogenetic stages, including the two M. peeblesorum embryos MOR 240 2024-c-243 and MOR 240 2024-c-238 (Table 1, Fig. 1E). The nutrient foramen is funnel-shaped and measurements were taken using ImageJ software following the methodology proposed in33. Measurements of embryos were taken on 3D models (Fig. 1A,B). The foramen radius was turned into Q̇ following the polynomial Eq. (1) of47 for apneumatic femora that was calibrated on 20 species of present-day mammals. We also studied the two 3D models of embryonic M. peeblesorum MOR 240 2024-c-241 (tibia) and MOR 240 2024-c-239 (humerus) in order to compare the dimensions of their nutrient foramen with those of the two M. peeblesorum embryonic femora (Fig. 1A–D).

Models for neonatal metabolic rate inference

The model for neonatal resting metabolic rates inference

Mass-specific RMR is very dynamic through ontogeny, especially during early development with body mass increasing asymptotically (e.g.15). To avoid possible ontogenetic biases, we built a new dataset that represents as much as possible neonatal conditions for inferring neonatal metabolic rates. The dataset was built based on the present-day species previously used in22 which complements the dataset proposed in27. Age of the growing specimens were estimated based on their body mass and their specific growth rate provided in27. We estimated ages ranging from 5 to more than 100 days. To better fit with neonatal conditions, we replaced when possible RMR values measured in27 with neonatal RMR values (0–4 days) available in the research literature (See supplementary material 5 A. and B. for details). As expected due to the stresses associated with birth or hatching, we observed resting metabolic rate in neonates higher than those of juveniles (e.g.16,38). No age estimation could have been made on Alligator mississippiensis and Caiman crocodilus, and ages higher than a month were estimated for the species Chelodina oblonga, Pelodiscus sinensis. As no neonatal RMR value were available in the literature for these four species, they were consequently discarded from the dataset. Finally, the 15 remaining species (See Table 3) have RMR values corresponding to 0–10 days (see Table 3). Despite the fact that ontogenetic temporality differs from one species to an other, we estimated that such dataset yet offers the best balance between the number of taxa and the accurate representation of neonatal conditions. We used the RPOA measurements from24, taken from the innermost cortical region of juvenile specimens, as these are the most representative of postnatal conditions in the available research literature. The model finally includes: 1 amphibian, 1 turtle, 2 birds, 6 mammals, 1 crocodile, and 4 lizards (Table 3, supplementary material 5).

Table 3 RPOA and neonatal mass-specific RMR values of 15 present-day species used to construct a model of mass-specific RMR inference. RPOA values come from24.
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The model for maximal metabolic rate inference

No dataset for neonatal maximal metabolic rate inferences was available before this study, or for neonatal blood flow estimation based on femoral nutrient foramen radius. The existing data were acquired from adults26 and their use for neonatal estimation could be skewed by ontogeny. We therefore established a dataset that is limited by the availability of neonatal MMR values (within the 5 first days of life) in the litterature and the number of neonate species available in museum collections. The final dataset includes neonates from 16 present-day species (Table 2, supplementary material 4 and 7 for the references). The dataset also excluded all bird species having air sacs in their femora which skewed the estimations of the dimension of the foramen52,53,54. The nutrient foramen radius was calculated from nutrient foramen area measurements. The dataset for MMR finally includes: 1 crocodilian, 1 mammal, 1 varanid, 2 turtles, and 11 birds (Table 2, supplementary material 4 and 7).

Unit

Previous studies using the PEM expressed metabolic rates in mL(O2) h−1 g−0.6722,25,26. The allometric mass scaling exponent 0.67 accounts for the caloric losses linked to the decrease of the ratio surface/volume with increasing body mass. It was first determined theoretically by euclidean surface-area-to-volume considerations64. Empirical studies show that the theoretical 0.67 exponent does not fit current observations (e.g.65). The empirical allometric exponent may vary from 0.67 to 1 depending on the group, the thermophysiology, the ontogenetic stage, the activity (rest, activity, stress, etc.) and the environment (temperature, food, etc.) (e.g.37,66,67). As we cannot use different exponents for different taxonomic groups in a given analysis, we expressed in this study the metabolic rates using the allometric exponent of 0.67 so that (1) the units are homogeneous despite the type of organism and (2) the inferred metabolic rates are comparable with previous data resulting from PEM analysis. The error associated with environmental factors may be minimized, as metabolic rate values were obtained from laboratory measurements conducted under standardized environmental conditions15,17,27,60,68.

Phylogenetic relationships

Phylogenetic relationships were coded as typology and branch lengths, with branch lengths being the age separating two successive nodes or node and terminal taxon.

The phylogeny of extant species used to build models for RMR inferences was taken up from25,69,70,71 to build models for RMR inferences (supplementary material 3). We used the same phylogeny as much as possible to build models for MMR inferences and we detailed turtle phylogeny following72, and bird phylogeny following73,74 (supplementary material 3)..

The phylogenetic relationship between M. peeblesorum and the present day species was taken in Langer et al.75, and the datation of Maiasaura was taken from Rogers et al.20.

Results

Neonatal relative primary osteon area measurements

We found a RPOA value of 0.74 ± 0.07 (MOR PU 22400 GS400F3) and of 0.76 ± 0.05 (MOR 758 16-16-15-99) with a mean value of 0.75 ± 0.05 for the innermost cortex of the two hatchling M. peeblesorum (Table 4). The uncertainties are standard deviations calculated with RPOA values measured in the anterior, posterior, lateral and medial parts of the thin sections.

Table 4 RPOA values measured on mid-diaphysis femoral sections.
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Neonatal blood flow estimation

Femoral circumference, length, nutrient foramen area measurements, and blood flow estimations are listed in Table 1 for 19 M. peeblesorum specimens (We have not included the embryonic tibia and humerus in the model). Data for one M. peeblesorum tibia and humerus perinatal/embryonic specimens are also given.

We modeled the ontogenetic evolution of the femoral nutrient foramen radius (R) with the evolution of femoral mid-shaft circumference (Fc) representing the developmental stage (Table 1, Fig. 1E). We obtained the Eq. (2).

$${\text{R}} = 0.0056 \pm {\text{1}}.{\text{13974 }}*{\text{ Fc}}^{{{\text{1}}.0{\text{7}}0{\text{9}} \pm 0.0{\text{688}}}} \left( {{\text{n}} = {\text{21}}} \right).$$
(2)

We estimated M. peeblesorum embryonic femoral circumference based on measurements of the embryonic region of its mid-diaphysis femoral sections (MOR PU 22400 GS400F3 and MOR 758 16-16-15-99) using the software ImageJ (Fig. 2A). Following the neonatal line, we estimated a maximal mean embryonic femoral circumference of about 25.53 mm.

Applying the Eq. (2) (Fig. 1E), we determined nutrient foramen radii of 0.180 for M. peeblesorum corresponding to blood flows of 0.007564 using Eq. (1).

Inferred neonatal metabolic rates

Results are presented in Table 5.

With the Holm–Sidak selection procedure, we obtained a neonatal mass-specific RMR value of 5.22→12 mL(O2) h−1 g−0.67 for M. peeblesorum using RPOA as an explanatory variable (Fig. 2, Table 5). We used the default alpha value of 0.05 of lmforwardsequentialsidak for the selection procedure. This model including the RPOA as a predictor variable has a R2 of 0.90, a p-value of 3.97*10–7.. It has a better fit than a model built without the additional explanatory variable (R2 = 0.53).

Neonatal mass-specific MMR value were determined for M. peeblesorum integrating blood flow as a predictor variable. The default sidak selection procedure (alpha = 0.05) was too restrictive and produced a model with an insufficient fitting (with alpha = 0.05, R2 = 0.33). We used an alpha-value of 0.20 instead of 0.05, allowing the selection of an additional eigenvector to build the model. The risk of type I error increased to 20% instead of 5%, which is still lower than the risks of 100% produced with an AIC selection procedure41.

Neonatal mass-specific MMR values of 6.04→9 mL(O2) h−1 g−0.67 were determined for M. peeblesorum (Fig. 3, Table 5). This model (R2 = 0.77, p-value = 9.672*10–5) has a better fit than the one built without the additionnal explanatory variable (R2 = 0.37).

Fig. 2
figure 2

Neonatal RMR inferences using PEM and the neonatal RPOA value as co-predictor. (a) Results of the PEM analysis using RPAO as a predictor variable for RMR inferences in mL(O2) h−1 g−0.67. Fitted values are available in the supplementary material 8. B. The black dots are the osteocytes lacunae. The RPOA value of 0.74 equals the area delimited by the green outlines divided by the total area delimited with the black rectangle. (b) Femoral thin section under natural light of the hatchling MOR 758 16-16-15-99 (right) that has been slightly crushed anteroposteriorly during diagenesis. The area delimited in blue corresponds to the embryonic area. A and P the anterior and posterior parts. The blue dashed lines indicate the neonatal line. The black dots are the osteocytes lacunae. The RPOA value of 0.74 equal the area in green divided by the total area delimited with the black rectangle. (c) Zoom under natural light in the black rectangle in b to show the neonatal line (blue arrow) delimited by drastic change of vascularization. Embryonic bone to the Left, cortex to the right. (d) RPOA measurement on the cortex area with lambda wave plate. The calcite in white fills the primary osteon delimited in green46. The black dots are the osteocytes lacunae. The RPOA value of 0.74 equal the area in green divided by the total area delimited with the black rectangle.

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Fig. 3
figure 3

Neonatal MMR inferences using PEM and the neonatal blood flow as co-predictor. (a–e) Localization of the nutrient foramen in present-day neonates, the arrows point to the foramen. Epiphyses are not always mineralized. (a) 3D model of a femur of the neonate Chelonia mydas ENS-AgSVSTUA022002. (b) 3D model of a femur of the neonate Procellaria aequinoctialis MNHN-ZO-2021-3036. (c) Photograph of a femur of the neonate Rangifer tarandus MNHN-1940–172. (d) 3D model of the femur of a neonate Varanus niloticus MNHN-Va.0012-80. (e) 3D model of a femur of the neonate Crocodilus niloticus MNHN-Cr.0056-107. (f) Results of the PEM analysis using blood flow as a predictor variable for MMR inferences in mL(O2).h−1.g−0.6722,23,25. Fitted values are available in the supplementary material 8. B.

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Table 5 Metabolic rate inferences using the forward stepwise eigenvector selection using Holm–Sidak correction (sidak)42,43 and the corrected Akaike Information criterion (AICc)40 with the MPSEM R package24,38.
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With the AIC selection procedure, we obtained a neonatal mass-specific RMR value of 6.33→13 mL(O2) h−1 g−0.67 for M. peeblesorum (Table 5). This model including the RPOA as a predictor variable has a R2 of 0.93, an AIC of 30, and a p-value of 3.306e−07. It has a better fit than a model built without the additionnal explanatory variable (R2 = 0.53, AIC = 40).

Neonatal mass-specific MMR values of 7.05→10 mL(O2) h−1 g−0.67 were determined for M. peeblesorum integrating blood flow as a predictor variable (Table 5). This model (R2 = 0.99, AIC = 2, 1.554e−08) has a better fit than the one using the phylogeny built without the additionnal explanatory variable (R2 = 0.98, AIC = 17).

Difference between neonatal maximum and resting metabolic rates (ΔMR)

Neonatal ΔMR values for present day species were calculated in this study using data available from the literature (Fig. 4, Table 6). The mean neonatal M. peeblesorum ΔMR value is of 10 → 9 mL(O2) h−1 g−0.67 (X0 → uncertainty is a notation to avoid impossible negative ΔMR values) whether the eigenvector selection method used is AICc or sidak selection procedure. This mean ΔMR value falls within the range of altricial birds and hyperprecocial ectotherms.

Table 6 Neonatal ΔMR values calculated in this study using data available from the literature.
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Discussion

Selecting the eigenvectors

We compared models obtained using forward stepwise selection of eigenvectors of the MPSEM R package24. The criteria of selection of the eigenvectors could be based on AICc40 or Holm-Sidak correction42,43. AICc is routinely used in Phylogenetic Eigenvector Maps (PEM) e.g.22,23,25,26, and is a method minimizing overfitting and optimizing fitting and complexity. However, it has been shown that this methodology is sensitive to Type I error41. Consequently, the selection can be skewed, as well as the physiological interpretation resulting from the model. A selection with the Holm-Sidak correction focuses on significance and controls the type I error. In this study, we therefore place more confidence in the Holm-Sidak correction selection.

Comparing the results, metabolic rates inferences are 1 mL(O2) h−1 g−0.67 higher utilizing the AICc selection (Table 5). In our case, this difference does not lead to major changes in the interpretations and remains smaller than the uncertainties (0→9 mL(O2) h−1 g−0.67). Furthermore, no differences in ΔMR values are observed (Table 5). We conclude that the mode of selection does not affect our results in our case, but this result cannot be generalized at this time. A more general and detailed comparison of these two selection methods would be necessary for further metabolic rate inferences, but it exceeds the scope of the present study.

Neonatal hadrosaur physiology

Although widespread endothermy has been proposed for Cretaceous dinosaurs including hadrosaurs from apatite oxygen isotopes77 and diverse other proxies78, ectothermy or low metabolic rate was proposed for hadrosaurs (1.6 mL(O2).h−1 g−1) from the study of fossil biomolecules derived from respiration79. A very low RMR value of about 0.8 mL(O2) h−1 g−0.67 was also estimated in25 using the PEM with the vascular canal density as a predictor variable.

In this study, we observed in Maiasaura femoral sections a highly vascularized cortex suggesting a high oxygen supply at rest (e.g. Fig. 2A)23,27,31. The associated RPOA value of 0.76 ± 0.03 is similar or higher than the RPOA values of present-day birds and mammals (0.68 in Gallus gallus, 0.74 in Capreolus capreolus and 0.81 in Lepus europaneus) and differs from the avascular or almost avascular bone of present-day slow-growing ectotherms having RPOA values averaging 0.015 for the two Varanus and 0.05 in Crocodylus niloticus. We inferred a neonatal RMR value for M. peeblesorum from 5.22→12 mL(O2) h−1 g−0.67. This value is higher than that obtained in25 for adult M. peeblesorum and may be explained by the difference in ontogenetic stage. Mass-specific metabolic rates are expected to decrease with ontogeny, for instance with the slowing of growth or the increasing body mass (e.g.15). However, comparing mass-specific RMR values of specimens having the same ontogenetic stage reduces such bias and may avoid misintinpretation of their thermophysiology. Other parameters explain the observed differences, namely: (1) the choice of the explanatory variable and (2) a different mode of eigenvector selection (Sidak method instead of AICc). This RMR value of 5.22→12 mL(O2) h−1 g−0.67 is above the range of birds used in the PEM (3.8 ± 0.2 mL(O2) h−1 g−0.67, n = 2, Table 6) and within the range of RMR values of mammals ranging from 1.5 to 15 mL(O2) h−1 g−0.67 (n = 7, Table 6), and is higher than those of ectotherms (0.2 ± 0.2 mL(O2) h−1 g−0.67, n = 6, Table 6). These results show that neonate Maiasaura rely on aerobic power at rest for growth and maintenance like extant fast-growing endotherms (Fig. 2C). It is also consistent with previous histological studies that estimated a bird-like bone apposition rate of 86.4 µm/day in nestling M. peeblesorum80 and of 24 µm/day in the juvenile lambeosaurine hadrosaur Hypacrosaurus stebingeri81. Bone apposition rate of ecthotherm reptiles ranges between 0.6 and 3.5 µm/day for the lizard Podarcis muralis and the Nile crocodile Crocodylus niloticus27. These results also reject a varanid-like intermediate thermophysiology for hadrosaurs because monitors have relatively low bone vascularization (RPOA = 0.015) associated with low oxygen consumption rate at rest60,82. It is therefore more relevant to compare the Maiasaura ΔMR values with the endotherm ΔMR values than with the ectotherm ΔMR values for inferring their neonatal state in the altricial-precocial spectrum.

Environmental biases in the interpretation of ΔMR values

The inferred mean ΔMR value could be interpreted in terms of reproductive strategies (based on the data from15) or living environments because cold environments for instance increase the RMR due to higher energetic costs associated with thermoregulation, reducing ΔMR15,16. A continental mean annual air temperature of 16 ± 4 °C83,84 has been determined based on a Late Cretaceous latitudinal temperature gradients reconstructed from multiple North American fossil leaf assemblages using leaf margin analysis. It is unlikely that such temperate living environment conditions could significantly affect neonatal energetic costs for thermoregulation and thermogenesis that could have increase Maiasaura neonatal resting metabolic rate.

Furthermore, Maiasaura remains and egg sites are located in the non-marine Two Medecine Formation. This 600 m-thick formation is dominated by mudstones intercalated with sandstone lenses interpreted as a vast plain, several hundred kilometers wide, situated between the Cordilleran Highlands to the west and the Interior Seaway to the east20,85. Such a plain does not feature environments that would require a particularly high RMR due to thermoregulation and heat production, such as cold high-altitude environments or windy coastal environments.

We reasonably assume in this study that our inferences could be interpreted in terms of reproductive strategies with negligible effect of local climatic conditions.

Since metabolic rates change throughout ontogeny (e.g.15), the ontogenetic stage of the specimens is also a potential source of bias, which we strive to minimize as much as possible. Regarding the present-day species used for the construction of the model inference, specimens were selected based on their age (− 1 to 4 days old, plus Anas sp. at 10 days old) to ensure an ontogenetic homogeneity of the datasets. Regarding M. peeblesorum, the ontogenetic model of the nutrient foramen presented in Fig. 1 allows for the selection of values at hatching and histology also provides access to post-hatching conditions. All these precautions ensure reliable inferences of neonatal metabolic rates.

Maiasaura neonatal state and parental care

Our novel methodology allows us to provide the first estimation of an average neonatal aerobic scope of 1 mL(O2) h−1 g−0.67 for M. peeblesorum. It corresponds to the aerobic scope measured today in altricial bird neonates (Fig. 4). It can therefore be inferred that M. peeblesorum was altricial or semi-altricial, which means it had poor or no locomotor capacities at hatch and was dependent on parental care for feeding. This consequently suggests that it might spend its first days of life staying in the nest and that parental care was a necessity for this species.

Fig. 4
figure 4

Quantitative inference of the neonatal condition of Maiasaura comparing its ΔMR with present day tetrapods. ΔMR values is expressed in mL(O2).h−1 g−0.67 for different neonatal state of endotherms and ectotherms (Table 6).

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These findings based on quantitative data are consistent with previous qualitative studies performed on poorly mineralized skeleton suggesting altriciality in M. peeblesorum as well as a lack of mobility. Death assemblages of Maiasaura individuals also suggested that the young remained in the nest for some time after hatching9,21. The co-occurrence of adults and juveniles at nesting sites is also supported by the occurrence of both large coprolites attributed to adults and smaller ones attributed to nestlings86,87. Altriciality is also consistent with the elevated growth rate of Maiasaura neonates, illustrated for example with a neonatal femoral apposition rate of 86.4 ± 7.9 µm/day determined from tibiae in80. In fact, precocial present-day birds have lower maximal growth rates than altricial birds for the same body mass at maximal growth36. This altricial higher growth rate might relate to parental care, which allows neonates to allocate most of their energy to growth.

Parental care is diverse, and widespread among both present-day ectothermic and endothermic terrestrial vertebrates7,88 but it is not ubiquitous among all vertebrate species. Pre-hatching parental care in the saurolophine Maiasaura is evident through its nests9, and might be widespread in hadrosaurs as we also have evidence of nesting behaviour in lambeosaurines (e.g.21). However, pre-hatching parental care do not necessarily induces post-hatching parental care: such behavior is observed in species of super-precocious present-day megapodes that have complex nesting strategies but do not provide parental care to neonates89,90. Indeed, the hadrosaur lambeosaurine Hypacrosaurus stebingeri also coming from the Campanian Two Medecine Formation shows differences in terms of early growth dynamics compared to M. peeblesorum80,81 that might point to a different post-hatching reproductive strategy. The hypothesis of widespread post-hatching parental care in hadrosaurs deserves to be further tested and can not been confirmed yet.

Parental care duration estimate in M. peeblesorum

The biggest known M. peeblesorum specimen found in a nest has a femoral length of 130 mm (PU 22400) corresponding to a femoral mid-shaft section radius of 7.9 mm9. We measured its cortex thickness of 3.8 mm excluding the embryonic bone having a 4.1 mm thick radius (this study, Fig. 2A). Assuming a neonatal femoral apposition rate of 86.4 ± 7.9 µm/day determined for the tibia in Woodward et al.80, we calculated a minimum age of 45 ± 5 days at which juveniles remain in the nest and still require parental care9.

The youngest M. peeblesorum found in a non-nesting site associated with adults is a 166.4 mm-long femur (MOR 758 # 2017-04). It has a mid-shaft section radius of 10.1 mm and a cortex thickness of 6 mm corresponding to a 70-day-old juvenile with an associated uncertainty of about 5 days. We therefore estimated a nidicolous period with intensive parental care extending between 40 and 75 days for M. peeblesorum. M. peeblesorum remains longer in the nest compared to most Passeriformes that leave the nest after 2 or 3 weeks, but this duration is not aberrant compared to Accipitriformes that could remain 50 or 70 days in the nest.

Concluding remarks

We inferred the neonatal RMR and MMR values of M. peeblesorum from the Two Medicine Formation to evaluate its neonatal state within the altricial-precocial spectrum and the necessity of parental care after hatching. The following results are emphasized:

  • Comparing the metabolic rates of specimens of different ontogenetic stages could biase interpretations because it evolves through ontogeny.

  • Maiasaura peeblesorum mainly rely on aerobic power at rest for growth and maintenance like present-day fast-growing endotherms, distinguishing their physiology from that of ectothermic reptiles relying mostly on anaerobic power, or varanids and the leatherback turtle that use aerobic power at activity only.

  • Maiasaura peeblesorum was most likely altricial and needed intensive parental care such as feeding and protection that long from 40 to 75 days.

Maiasaura provides a useful ecological baseline from which to infer neonatal states in other hadrosaurs of similar adult size—such as the lambeosaurine Hypacrosaurus stebingeri.

Indeed, this hadrosaur also coming from the Campanian Two Medecine Formation shows differences in terms of early growth dynamics compared to M. peeblesorum81 that might point to a relatively more precocial condition, as inferred from differences in growth dynamics distinguishing precocial and altricial extant birds of similar adult size 36. Overall, hadrosaur worldwide distribution and evolutionary success might be partly explained by a diversity of reproductive strategies allowing them to live and reproduce in contrasted environments during the Cretaceous.