# Wing bone laminarity in Pterosaurs: insights into torsional adaptations for flight evolution

Esaú Victor De Araújo, Jorge Cubo, Mariana Valéria de Araújo Sena, Renan Alfredo Machado Bantim, Luiz Carlos Weinschütz, Alexander Wilhelm Armin Kellner, Juliana Manso Sayão

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Esaú Victor De Araújo, Jorge Cubo, Mariana Valéria de Araújo Sena, Renan Alfredo Machado Bantim, Luiz Carlos Weinschütz, et al. Wing bone laminarity in Pterosaurs: insights into torsional adaptations for flight evolution. Anais da Academia Brasileira de Ciências, 2025, 97 (suppl 1), 10.1590/0001-3765202520240540. [hal-04968318](https://hal-04968318)

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## PALEONTOLOGY

# Wing bone laminarity in Pterosaurs: insights into torsional adaptations for flight evolution

ESAÚ VICTOR DE ARAÚJO, JORGE CUBO, MARIANA VALÉRIA DE ARAÚJO SENA, RENAN ALFREDO MACHADO BANTIM, LUIZ CARLOS WEINSCHÜTZ, ALEXANDER WILHELM ARMIN KELLNER & JULIANA MANSO SAYÃO

**Abstract:** Powered flight has evolved separately in three tetrapod clades: pterosaurs, birds (avian dinosaurs), and bats. To meet the challenges of powered flight, tetrapods acquired structural, mechanical, and physiological adaptations. Circumferential vascular canals, forming laminar bone, have been proposed to be an adaptation linked to withstanding torsional loading during flight in birds. However, whether laminarity serves as an indicator of biomechanical torsion in pterosaurs, remains to be elucidated. Through a comparative statistical approach, we investigate the association between cortical bone laminarity and skeletal stress in pterosaur flight. For the first time, the presence of laminarity in pterosaur bones was analyzed to observe torsion in bones associated with flight, using thirty-five thin sections of the tapejarid Caiuajara dobruskii, Anhangueridae, and Dsungaripteroidea pterosaurs. We conclude that adaptive relationships arise between bone microstructure and biomechanical function, with forelimb elements (humerus, ulna, and wing phalanges) exhibiting higher laminarity rates compared to hindlimb bones. Additionally, the results provide insights into the possible flight style of these pterosaurs through comparison with bird groups. The presence of laminarity in pterosaurs and birds, but not in bats, highlights that this feature, once considered exclusive to birds, may have convergently evolved in pterosaurs and birds.

**Key words:** Biomechanics; bone histology; flight evolution; laminarity; pterosaur.

## INTRODUCTION

Flight has independently evolved in three tetrapod clades: pterosaurs, birds (avian dinosaurs) and bats (Rayner 1988, Tokita 2015). Structural, mechanical, and physiological adaptations were acquired linked to powered flight, allowing flying tetrapods to develop lightweight skeletons yet sufficiently rigid to withstand torsion and flexion (de Margerie 2006, Padian & Lamm 2013). Despite their distinct phylogenetic origins, powered flying tetrapods exhibit remarkable convergences in their anatomy and flight capabilities (Hazlehurst & Rayner 1992). Pterosaurs, birds, and bats share some eco-morphological correlations. However,

birds are the more appropriate analogues to large body sized pterosaurs, especially those of Late Cretaceous (Hazlehurst & Rayner 1992). The similarities between pterosaurs and birds are evident in wing shape, and features such as pneumaticity and histology (Padian 1987, Steel 2008). Considering their bone histology, pterosaurs and birds are characterized by their fast bone growth rate resulting in primary bone composed of high vascularized fibrolamellar complex (de Ricqlès et al. 1991, 2000, de Margerie 2006, Kuehn et al. 2019), with ontogenetically mature individuals showing an external fundamental system (e.g. Kellner et al. 2013). Their densely vascularized cortical bone
consists of a woven bone matrix vascularized mainly by primary osteons (de Ricqlés et al. 2000, Sayão 2003, de Margerie 2006, Steel 2008, Eleutério et al. 2015, Bantim et al. 2021, Araújo et al. 2023). These vascular canals could exhibit various orientations such as longitudinal, radial, circular, and oblique (de Ricqlés et al. 1991, Cubo et al. 2012). It has been hypothesized that differences in primary vascular canal orientation might reflect growth rate, biomechanical loads, or phylogenetic relationships (de Margerie 2002, Padian & Lamm 2013).

Previous studies on birds and bats wing mechanics have demonstrated the torsional loading experienced by the wing skeleton during flight (Pennycuick 1967, Swartz et al. 1992, Kirkpatrick 1944, Biewener & Dial 1995, de Margerie 2002, 2006). Observing bones of birds, de Margerie (2002) noted that laminar bone organization is concentrated in certain bones, namely humerus, ulna, carpometacarpus, and femur. Based on this observation, the presence of laminar tissue in the inner cortices of long bones is associated with torsional resistance during flight, at least in birds. In fact, it has been observed that laminar bone offers advantages in resisting torsional stress due to its multi-layered structure, which contains collagen fibers and osteons oriented in specific directions. These features allow the bone to distribute and absorb torsional forces more effectively (Currey 2002). The presence of empty spaces, such as Haversian canals, contributes to stress distribution and enhances resistance to crack propagation. Furthermore, it improves bone's ability to withstand twisting forces (Martin & Burr 1989).

Questions related to the functional significance of laminarity are debated, and several methods have been used to study it. Some studies in birds and bats have supported de Margerie's (2002) initial laminarity hypothesis

suggesting that laminarity is primarily present in bones subjected to higher torsional stress during flight. This idea was further explored by Skedros & Hunt (2004) using vascular area analysis and circularly polarized light (CPL), as well as by Simons & O'Connor (2012). Similarly, Lee & Simons (2015) demonstrated that bat humeri, regardless of size or phylogeny, are entirely avascular and consequently lack laminar bone. This finding suggests that laminarity may not be a necessary biomechanical feature in flying vertebrates. Later, Pratt et al. (2018) demonstrated that these 2D methods of measuring laminarity using area tend to overestimate the laminarity index compared to 3D measurements. Then, using micro-CT, they reported that the relationship between vascular channel orientation and functional load is complex and did not support the hypothesis that flight bones exhibit higher laminarity. Kuehn et al. (2019) and Skedros & Doutré (2019) confirmed that ontogenetic factors and osteon morphology do not clearly distinguish between torsional and bending loads in the bones of emus, pigeons, and bats. McGuire et al. (2020) highlighted the uncertainty regarding microstructural adaptations in avian cortical bones, suggesting that elevated laminarity may not necessarily be an adaptation for flight and may vary during ontogeny, decreasing with bone maturity, at least in pigeons.

Laminarity in pterosaur bones have been previously reported through osteohistological analysis in *Dimorphodon macronyx* Owen 1859 (de Ricqlés et al. 2000), while others, like *Pterodaeustro guinazui* Bonaparte 1970 exhibit a different pattern with longitudinal canals (Chinsamy et al. 2009). Despite that, the precise mechanisms that underlie torsion resistance in pterosaurs remain poorly understood (Palmer & Dyke 2010). Given these previous findings, to investigate whether pterosaur wing bones
possess structures capable of supporting
torsional loads, and whether there is convergence
in wing bone structure with birds and bats is
timely. It is important to emphasize that in
addition to pneumaticity and laminarity, other
factors should be considered as requirements
for bones that withstand the torsional stress of
flight, including the circularity of the cortex, the
thickness of the walls, and the orientation of
collagen fibers (de Margerie 2006). In this study,
due to limitations in our sample, we exclusively
focus on inferring the laminarity rate of
pterosaur bones through their vascular network.
We conducted quantitative measurements on
thin sections of the diaphysis of 35 pterosaur
bones to investigate the presence of varying
degrees of laminarity. Our analysis focused on
bones from the forelimbs (humerus, radius, ulna,
and phalanges) and hindlimbs (femur and tibia).
We hypothesize that these flying vertebrates
employ similar (analogous) musculoskeletal
adaptations, generating mechanical force
through similar aerodynamic mechanisms, as
suggested by de Margerie (2006). We expected
to find a high laminarity index in the forelimbs
of adult pterosaurs, assuming that this would
be the stage of life characterized by more active
flight. Results contradicting this hypothesis may
suggest an earlier onset of flight activity in the
ontogeny, at least for the groups analyzed here.

MATERIALS AND METHODS

Histological Sections

Here, we interpret thirty-five thin sections
taken from the midshaft of long bones from
the tapejarid *Caiuajara dobruskii*, three
Anhangueridae indet. and a Dsungaripteroidea
indet. (Table I). In the Ph2D4 (specimen MPSC
R1395), two sections were analyzed: one
from the proximal portion and one from the
medial portion. It is worth noting that due to

the preservation quality of the fossils, not all
sections presented the entire cortical portion
available for analysis, which makes it impossible
to infer adequate measures of cortical thickness
and circularity. The thin-sections were
previously prepared, and their histological
descriptions can be found in Sayão (2003), Sayão
et al. (2004), Eleutério et al. (2015), Bantim et al.
(2021) and Araújo et al. (2023).

Bone laminarity calculation

We categorized the vascular canals into four
orientation categories based on the angle
of these canals within the cortical section, as
suggested by de Margerie (2002): (1) circular
(circumferential) canals are oriented parallel (0
± 22.5°) to the periosteal surface of the bone;
(2) radial canals are orthogonal (90 ± 22.5°) to
the periosteal surface; (3) longitudinal canals
run parallel to the long axis of the bone and
have ellipses with an aspect ratio of less than
3; (4) oblique canals are all other orientations.
However, unlike de Margerie (2002) definition,
here employed a redefined approach where
laminarity, was considered as the ratio of the
number of circular canals to the total number
of vascular canals. This redefinition aligns with
the method used by Simons & O'Connor (2012),
Legendre et al. (2014), Lee & Simons (2015) and
McGuire et al. (2020).

The calculation of bone laminarity starts
with the images of wing and hindlimb elements,
divided into four anatomical octants, and
considering only the four parts corresponding
to the cardinal anatomical positions: cranial,
caudal, dorsal, and ventral. In cases where
the thin section is incomplete, preventing the
visualization of the four parts of the octant,
vascular canals were counted across the
entire available image (Fig. 1). The canals
were quantified using Fiji/ImageJ (Schindelin
et al. 2012), and each extracted octant was
<table><caption>**Table I.** Specimens selected for analysis. 33 specimens from 3 different families of pterosaurs were used: *Caiuajara dobruskii* (Tapejaridade); *Anhangueridae*; *Dsungaripteroidea*. Ph1D4: First phalanx of 4th digit; Ph2D4: Second phalanx of 4th digit; Ph3D4: Third phalanx of 4th digit; Ph4D4: Fourth phalanx of 4th digit.</caption><thead><tr><td>Species</td><td>Specimen</td><td>Bone</td></tr></thead><tbody><tr><td>Caiuajara dobruskii</td><td>CP. V 2057</td><td>Femur</td></tr><tr><td>Caiuajara dobruskii</td><td>CP. V 2058</td><td>Femur</td></tr><tr><td>Caiuajara dobruskii</td><td>CP. V 2750a</td><td>Tibia</td></tr><tr><td>Caiuajara dobruskii</td><td>CP. V 2059</td><td>Tibia</td></tr><tr><td>Caiuajara dobruskii</td><td>CP. V 5698</td><td>Humerus</td></tr><tr><td>Caiuajara dobruskii</td><td>CP. V 1032</td><td>Humerus</td></tr><tr><td>Caiuajara dobruskii</td><td>CP. V 5701</td><td>Ulna</td></tr><tr><td>Caiuajara dobruskii</td><td>CP. V 5701</td><td>Radius</td></tr><tr><td>Caiuajara dobruskii</td><td>CP. V 2301</td><td>Wing Phalanx</td></tr><tr><td>Caiuajara dobruskii</td><td>CP. V 2446</td><td>Wing Phalanx</td></tr><tr><td>Anhangueridae</td><td>MN 4809-V</td><td>Femur</td></tr><tr><td>Anhangueridae</td><td>MN 4809-V</td><td>Radius</td></tr><tr><td>Anhangueridae</td><td>MN 4809-V</td><td>IV Metacarpus</td></tr><tr><td>Anhangueridae</td><td>MN 4809-V</td><td>Ulna</td></tr><tr><td>Anhangueridae</td><td>MN 4809-V</td><td>1 Phalanx IV digit</td></tr><tr><td>Anhangueridae</td><td>MN 6527-V</td><td>Ulna</td></tr><tr><td>Anhangueridae</td><td>MN 6527-V</td><td>Radius</td></tr><tr><td>Anhangueridae</td><td>MN 6527-V</td><td>IV Metacarpus</td></tr><tr><td>Anhangueridae</td><td>MN 6527-V</td><td>Humerus</td></tr><tr><td>Anhangueridae</td><td>MPSC R 982</td><td>Radius</td></tr><tr><td>Anhangueridae</td><td>MPSC R 982</td><td>Coracoid</td></tr><tr><td>Anhangueridae</td><td>MPSC R 982</td><td>Metacarpus IV</td></tr><tr><td>Anhangueridae</td><td>MPSC R 2090</td><td>Wing Phalanx</td></tr><tr><td>Anhangueridae</td><td>MPSC R 2090</td><td>Ulna</td></tr><tr><td>Anhangueridae</td><td>MPSC R 2090</td><td>Radius</td></tr><tr><td>Anhangueridae</td><td>MPSC R1395</td><td>Humerus</td></tr><tr><td>Anhangueridae</td><td>MPSC R1395</td><td>Ph1D4</td></tr><tr><td>Anhangueridae</td><td>MPSC R1395</td><td>Ph2D4</td></tr><tr><td>Anhangueridae</td><td>MPSC R1395</td><td>Ph2D4</td></tr><tr><td>Anhangueridae</td><td>MPSC R1395</td><td>Ph3D4</td></tr><tr><td>Anhangueridae</td><td>MPSC R1395</td><td>Ph4D4</td></tr><tr><td>Dsungaripteroidea</td><td>MUCPv-358</td><td>Ulna</td></tr></tbody></table>
repositioned using the “Straighten” function. This straightening process is aimed at the periosteal tangent line, to improve the accuracy of measurements to be used for classifying vascular canals orientation (Lee & Simons 2015, Kuehn et al. 2019).

## Beta Analysis

Statistical analysis was performed using the R software, applying the Beta regression model to assess the laminarity index across different bone elements and ontogenetic stages. The Beta regression model (Cribari-Neto & Zeileis 2010) was chosen due to the proportional nature of the laminarity index data, which ranges between 0 and 1. The laminarity index was considered the dependent variable, while bone elements and ontogenetic stages were treated as explanatory variables. First, the data were organized into an appropriate format for analysis, grouping them according to the factors of interest. Subsequently, the Beta regression model was fitted to identify significant differences in laminarity between the groups. The validity of the model was assessed

by checking the normality of the residuals and the appropriateness of the precision model. The normality of the residuals was tested using the Shapiro-Wilk test, and the adequacy of the precision model was evaluated based on the obtained coefficients. This approach allowed for a detailed examination of variations in the laminarity index in relation to taxonomic groups and ontogenetic stages, providing insights into potential significant differences.

## RESULTS

### Laminarity

The majority sections exhibited a partially laminar bone. The Laminarity Index (LI) for all sampled species ranged from 0 (no circular canals) to 0.72 (over 72% circular canals) (Fig. 2). Data on laminarity variation throughout ontogeny were compared using specimens previously described and categorized by ontogenetic stages (Sayão 2003, Sayão et al. 2004, Eleutério et al. 2015, Bantim et al. 2021, Araújo et al. 2023) (see Table II). The highest values of laminarity were found in forelimbs,

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

**Figure 1.** Demonstration of the calculation of vascular canal orientation, defined by the ratio between the area of circular canals and the total vascular area (according to de Margerie, 2002), a - Identification of the octants marked in red dashed areas. b - Graphic scheme defining the areas of the octants where they are represented in C (Red), circular vascular canals; O (Yellow), oblique vascular canals; R (Blue), radial vascular canals; L (Orange), longitudinal vascular canals. c - Detail of an octant with the respective markings of the orientations of the vascular canals.
as the ulnae (See Table II), stated as subadults (MUCPv-358; MPSC 2090) and early juvenile (CP. V 5701).

For *Caiuajara*, the highest values of laminarity were observed in the ulna (CP. V 5701), Tibia (CP. V 2059) and humeri (CP. V 1032) respectively (Fig. 3), these specimens are

<figure><img src="image_4.png" /><figcaption>**Figure 2.** Microstructure of bones in thin sections to depict the range in vascular canal organization. Abbreviations: a) Humerus (CP. V 1032); b) Humerus (CP. V 5698); c) Humerus (MN 6527-V); d, e) Humerus (MPSC R1395); f, g) Radius (CP. V 5701); h) Radius (MN 4809-V); i) Radius (MPSC R982); j) Radius (MPSC R2090); k) Ulna (CP. V 5701); l) Ulna (MN 4809); m) Ulna (MN 6527-V); n) Ulna (MPSC R2090); o) Ulna (MUCPv-358); p) Ph1D4 (CP. V 2301); q) Ph1D4 (CP. V 2446); r) Ph1D4 (MN 4809-V); s) Ph3D4 (MN 4809-V); t) Ph1D4 (MPSC R1395); u, v) Femur (CP. V 2057); w, x) Femur (CP. V 2058); y) Femur (MN 4809-V); z, z1) Tibia (CP. V 2058); z2, z3, z4) Tibia (CP. V 2750a).</figcaption></figure>
identified as early juveniles (Araújo et al. 2023). In *Caiuajara* thin sections exhibit complete cortical sections, the laminarity index was also observed in each quadrant (ventral, caudal, dorsal, and cranial). It was noted that in most specimens, the highest laminarity index was present in the ventral portion of the bone, except for ulna CP. V 5701, which exhibited the highest index in the dorsal region.

Comparing the laminarity index across the anhanguerid wing bones specimen (MPSC R1395), we observed that the LI is higher in proximal bones such as the humerus (0.43) and Ph1D4 (0.33), while distal bones such as

Ph2D4 (0.13), Ph3D4 and Ph4D4, exhibit lower values (see Fig. 4). Two portions of the Ph2D4 were analyzed: the proximal portion and the diaphyseal portion, while for other samples only the diaphyseal portion was visualized. Different LI values were observed in each portion, with the proximal portion having an LI of 0.37 and the medial portion having an LI of 0.13.

The LI found in the radii seems don't exhibit a pattern, a low value (LI = 0%) was recorded in the Anhangueridae MPSC R 2090, a late juvenile specimen. While in other specimens there's a variance, such as in MN 6527-V (subadult) which has high value (69%), when compared to the

<table><caption>Table II. Specimens analyzed and their respective attributed ontogenetic stages.</caption><thead><tr><td>Specie</td><td>Specimen</td><td>Bone</td><td>OS</td><td>LI</td><td>Cortex Thickness</td></tr></thead><tbody><tr><td>Caiuajara dobruskii</td><td>CP. V 2057</td><td>Femur</td><td>Adult (Araújo et al. 2023)</td><td>0,10</td><td>621,38 µm</td></tr><tr><td>Caiuajara dobruskii</td><td>CP. V 2058</td><td>Femur</td><td>Late Juvenile (Araújo et al. 2023)</td><td>0</td><td>490,12 µm</td></tr><tr><td>Caiuajara dobruskii</td><td>CP. 2750a</td><td>Tibia</td><td>Adult (Araújo et al. 2023)</td><td>0,25</td><td>1053,60 µm</td></tr><tr><td>Caiuajara dobruskii</td><td>CP. V 2059</td><td>Tibia</td><td>Early Juvenile (Araújo et al. 2023)</td><td>0,44</td><td>666,44 µm</td></tr><tr><td>Caiuajara dobruskii</td><td>CP. V 5698</td><td>Humerus</td><td>Subadult (Araújo et al. 2023)</td><td>0,25</td><td>700,33 µm</td></tr><tr><td>Caiuajara dobruskii</td><td>CP. V 1032</td><td>Humerus</td><td>Early Juvenile (Araújo et al. 2023)</td><td>0,32</td><td>859,2 µm</td></tr><tr><td>Caiuajara dobruskii</td><td>CP. V 5701</td><td>Ulna</td><td>Early Juvenile (Araújo et al. 2023)</td><td>0,69</td><td>509,48 µm</td></tr><tr><td>Caiuajara dobruskii</td><td>CP. V 5701</td><td>Radius</td><td>Early Juvenile (Araújo et al. 2023)</td><td>0,23</td><td>327,57 µm</td></tr><tr><td>Caiuajara dobruskii</td><td>CP. V 2301</td><td>Ph1D4</td><td>Adult (Araújo et al. 2023)</td><td>0,04</td><td>1451,2 µm</td></tr><tr><td>Caiuajara dobruskii</td><td>CP. V 2446</td><td>Ph1D4</td><td>Subadult (Araújo et al. 2023)</td><td>0,11</td><td>904,70 µm</td></tr><tr><td>Caiuajara dobruskii</td><td>CP. V 2056</td><td>Metacarpus IV</td><td>Subadult (Araújo et al. 2023)</td><td>0,30</td><td>690,27 µm</td></tr><tr><td>Caiuajara dobruskii</td><td>CP. V 2061</td><td>Metacarpus IV</td><td>Subadult (Araújo et al. 2023)</td><td>0,50</td><td>725 µm</td></tr><tr><td>Anhangueridae</td><td>MN 4809-V</td><td>Femur</td><td>Adult (Sayão 2003)</td><td>0,32</td><td>816,44 µm</td></tr></tbody></table>
<table><caption>Table II. Continuation.</caption><tr><td>Anhangueridae</td><td>MN 4809-V</td><td>Radius</td><td>Adult (Sayão 2003)</td><td>0,20</td><td>343,14 µm</td></tr><tr><td>Anhangueridae</td><td>MN 4809-V</td><td>Metacarpus IV</td><td>Adult (Sayão 2003)</td><td>0,30</td><td>1333,99 µm</td></tr><tr><td>Anhangueridae</td><td>MN 4809-V</td><td>Ulna</td><td>Adult (Sayão 2003)</td><td>0,19</td><td>1162,54 µm</td></tr><tr><td>Anhangueridae</td><td>MN 4809-V</td><td>Ph1D4</td><td>Adult (Sayão 2003)</td><td>0,37</td><td>1034,03 µm</td></tr><tr><td>Anhangueridae</td><td>MN 6527-V</td><td>Ulna</td><td>Subadult (Sayão 2003)</td><td>0,68</td><td>934,3 µm</td></tr><tr><td>Anhangueridae</td><td>MN 6527-V</td><td>Radius</td><td>Subadult (Sayão 2003)</td><td>0,69</td><td>190,2 µm</td></tr><tr><td>Anhangueridae</td><td>MN 6527-V</td><td>Metacarpus IV</td><td>Subadult (Sayão 2003)</td><td>0,26</td><td>1163,8 µm</td></tr><tr><td>Anhangueridae</td><td>MN 6527-V</td><td>Humerus</td><td>Subadult (Sayão 2003)</td><td>0,69</td><td>1084,9 µm</td></tr><tr><td>Anhangueridae</td><td>MPSC R 982</td><td>Radius</td><td>unknown</td><td>0,25</td><td>372,8 µm</td></tr><tr><td>Anhangueridae</td><td>MPSC R 982</td><td>Coracoid</td><td>unknown</td><td>0</td><td>749,42 µm</td></tr><tr><td>Anhangueridae</td><td>MPSC R 982</td><td>Metacarpus IV</td><td>unknown</td><td>0,29</td><td>1486,18 µm</td></tr><tr><td>Anhangueridae</td><td>MPSC R 2090</td><td>Ph1D4</td><td>Late Juvenile (Eleutério et al. 2015)</td><td>0,47</td><td>781,35 µm</td></tr><tr><td>Anhangueridae</td><td>MPSC R 2090</td><td>Ulna</td><td>Late Juvenile (Eleutério et al. 2015)</td><td>0,43</td><td>957,21 µm</td></tr><tr><td>Anhangueridae</td><td>MPSC R 2090</td><td>Radius</td><td>Late Juvenile (Eleutério et al. 2015)</td><td>0</td><td>192,10 µm</td></tr><tr><td>Anhangueridae</td><td>MPSC R1395</td><td>Humerus</td><td>Late Juvenile (Bantim et al. 2021)</td><td>0,43</td><td>797,4 µm</td></tr><tr><td>Anhangueridae</td><td>MPSC R1395</td><td>Ph1D4</td><td>Late Juvenile (Bantim et al. 2021)</td><td>0,33</td><td>850,43 µm</td></tr><tr><td>Anhangueridae</td><td>MPSC R1395</td><td>Ph2D4 (proximal – metaphysis portion)</td><td>Late Juvenile (Bantim et al. 2021)</td><td>0,37</td><td>885,75 µm</td></tr><tr><td>Anhangueridae</td><td>MPSC R1395</td><td>Ph2D4 (medial – diaphysis)</td><td>Late Juvenile (Bantim et al. 2021)</td><td>0,13</td><td>885,75 µm</td></tr><tr><td>Anhangueridae</td><td>MPSC R1395</td><td>Ph3D4</td><td>Late Juvenile (Bantim et al. 2021)</td><td>0</td><td>583,26 µm</td></tr><tr><td>Anhangueridae</td><td>MPSC R1395</td><td>Ph4D4</td><td>Late Juvenile (Bantim et al. 2021)</td><td>0</td><td>445,86 µm</td></tr><tr><td>Dsungaripteroidea</td><td>MUCPv-358</td><td>Ulna</td><td>Subadult (Kellner et al. 2006)</td><td>0,72</td><td></td></tr></table>
ulna of the same individual, that exhibit LI of 68%. In the radius CP. V 5701 of *Caiuajara* the observed laminarity was 23%.

Concerning the forelimbs, in contrast to the high laminarity identified in the hindlimbs, the *Caiuajara's* femur of a late juvenile (CP. V 2058)

presented the lowest laminarity of the entire sample, 0% (Table II), however, a femur of an adult (CP. V 2057) exhibited 10% LI. Likely, for the tibiae was observed different rates according to the ontogenetic stage, in the tibia CP. V 2059 considered an early juvenile, was observed a high laminarity index (44%), while in the adult tibia (CP. V 2750) it corresponds to a lower value (25%). The anhanguerid femur MN 4809-V has a laminarity rate of 32%, while the femora (CP. V 2057; CP. V 2058) of *Caiuajara* had 10% and 0%. respectively.

<figure><img src="image_5.png" /><figcaption>**Figure 3.** Diagram demonstrating variable laminarity in different long bone categories of *Caiuajara dobrushkii*. Note the high laminarity values in bones as *Humerus* and *Ulna*. Black circles: individual values. **H:** *Humerus*; **R:** *Radius*; **U:** *Ulna*; **Ph1D4:** First phalanx of 4th digit; **F:** *Femur*; **T:** *Tibia*.</figcaption></figure>

## Beta Analysis

Considering bone elements, the analysis of the beta regression model, using the coefficients from the mean model with the logit link, indicated a significant influence relation of the bone type on the laminarity index (Table III). The quantile residuals, ranging from -2.7094 to 2.6877, indicate a relatively symmetric distribution around zero, suggesting a generally adequate model fit.

The reference bone (likely coracoid) has a logit of the mean laminarity index of -3.355. Compared to this value, femur, humerus, metacarpus IV, Ph1D4, Ph2D4, tibia, and ulna exhibit significant positive effects on the laminarity index, with p-values less than 0.05 for most of these bones, except for Ph3D4 and Ph4D4, which did not show significant effects (Fig. 5). The radius also showed a marginally significant effect. The phi coefficient, with a value of 5.980 and p < 0.001, indicates a high precision of the model, suggesting that the data are well concentrated around the predicted mean. The red line represents the predicted laminarity index values for each bone type based on the beta regression model, which accounts for the categorical nature of the bone types. This line illustrates the average predicted laminarity index across different bone types, reflecting how each type deviates from the reference category.
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Diagram representing the anhanguerid wing and its respective histological sections. All the images belong to bones of specimen MPSC R1395. hu - Humerus shows the highest laminarity index (0.43); Ph1D4 - First phalanx of fourth digit LI (0.33); Ph2D4 - second phalanx of fourth digit (medial portion), showing low LI (0.13); Ph3D4 - third phalanx of fourth digit LI (0); Ph4D4 - fourth phalanx of fourth digit LI (0). Note that the most distal bones exhibit the lowest LI.</figcaption></figure>

The pseudo R-squared of 0.6568 indicates that approximately 65.68% of the variability in the laminarity index is explained by the model, reflecting a good explanatory capacity. The model converged after 35 iterations of the BFGS method and 2 iterations of the Fisher scoring method, indicating the stability of the fitting process.

In the analysis considering ontogenetic stages, the results reveal that the model's intercept, estimated at -0.8495, is statistically significant (p = 0.014). This suggests that the laminarity index for the reference ontogenetic stage differs significantly from zero, establishing a baseline for comparison. For the different ontogenetic stages, the early juvenile stage has a positive coefficient of 0.6052, indicating a higher laminarity index compared to the reference stage. However, this difference is not statistically significant (p = 0.316). The late juvenile stage

exhibits a negative coefficient of -0.6780, suggesting a lower laminarity index relative to the reference stage, but this difference is also not statistically significant (p = 0.153). The subadult shows a positive coefficient of 0.3171, reflecting a higher laminarity index, though this difference is not statistically significant either (p = 0.477). The phi coefficient, estimated at 2.830 with a highly significant p-value (p = 0.000), indicates substantial variability in model precision. This high phi value suggests that the model fits the data well, capturing the variability around the predicted mean effectively. Therefore, while the intercept is significant, the laminarity index differences among ontogenetic stages do not achieve statistical significance compared to the reference stage.

Additionally, considering the proportion of canals by ontogenetic stage (Table IV), the distribution of different types of vascular canals
<table><caption>**Table III.** Beta regression analysis results for laminarity index. Results of a beta regression analysis examining the effects of different bones on the laminarity index. The estimates represent the effect sizes of each bone relative to the reference bone (coracoid), with their corresponding standard errors, Z values, and p-values.</caption><thead><tr><td>Parameter</td><td>Estimate</td><td>Standard Error</td><td>Z value</td><td>Pr(&gt;|z|)</td><td>Notes</td></tr></thead><tbody><tr><td>Intercept</td><td>-3,35E+06</td><td>1.023.269</td><td>-3,28E+06</td><td>0.0010445836</td><td>Logit of the mean laminarity index for the reference bone (Coracoid).</td></tr><tr><td>Femur</td><td>2,28E+06</td><td>1.119.155</td><td>2,04E+06</td><td>0.0412157291</td><td>Significant positive effect compared to the reference bone.</td></tr><tr><td>Humerus</td><td>3,07E+06</td><td>1.088.927</td><td>2,82E+06</td><td>0.0047605253</td><td>Significant positive effect.</td></tr><tr><td>Metacarpus IV</td><td>2,75E+06</td><td>1.075.921</td><td>2,55E+06</td><td>0.0106492401</td><td>Significant positive effect.</td></tr><tr><td>Ph1D4</td><td>2,28E+06</td><td>1.078.949</td><td>2,11E+06</td><td>0.0348613245</td><td>Significant positive effect.</td></tr><tr><td>Ph2D4</td><td>2,36E+06</td><td>1.165.274</td><td>2,02E+06</td><td>0.0428676490</td><td>Significant positive effect.</td></tr><tr><td>Ph3D4</td><td>9,92E-12</td><td>1.422.113</td><td>6,97E-12</td><td>1.000.000.000</td><td>No significant effect</td></tr><tr><td>Ph4D4</td><td>-4,34E-10</td><td>1.422.113</td><td>-3,05E-10</td><td>1.000.000.000</td><td>No significant effect</td></tr><tr><td>Radius</td><td>1,83E+06</td><td>1.084.091</td><td>1,68E+06</td><td>0.0919924211</td><td>Marginally significant effect</td></tr><tr><td>Tibia</td><td>2,79E+06</td><td>1.155.442</td><td>2,42E+06</td><td>0.0155725855</td><td>Significant positive effect</td></tr><tr><td>Ulna</td><td>3,66E+06</td><td>1.071.100</td><td>3,41E+06</td><td>0.0006409921</td><td>Significant positive effect</td></tr></tbody></table>

**Figure 5.** Dispersion of laminarity index by bone type. The red line shows the average predicted laminarity index across different bone types, reflecting how each type deviates from the reference category. C: Coracoid; F: Femur; H: Humerus; MIV: Metacarpus IV; Ph1D4: First phalanx of the fourth digit; Ph2D4: Second phalanx of the fourth digit; Ph3D4: Third phalanx of the fourth digit; Ph4D4: Fourth phalanx of the fourth digit; R: Radius; T: Tibia; U: Ulna.

<figure><img src="image_7.png" /></figure>

in bones (circular, longitudinal, radial, and oblique) varies significantly. Circular canals are prevalent in juveniles and subadults, such as in the tibia (54% in early juveniles) and the humerus (50% in subadults and 48% in early juveniles). Conversely, longitudinal canals are

more frequent in adult bones, particularly in tibias (62%). Instead, radial canals are abundant in young specimens, notably in the humerus of early juveniles (53%). Oblique canals are also prevalent in juveniles and subadults, indicating
<table><caption>**Table IV.** Percentage distribution of vascular channels (circular/laminar, longitudinal, radial and oblique) in different ontogenetic stages.</caption><thead><tr><th>Bone Type</th><th>Specimen</th><th>Ontogenetic stage</th><th>Circular (%)</th><th>Longitudinal (%)</th><th>Radial (%)</th><th>Oblique (%)</th></tr></thead><tbody><tr><td>Femur</td><td>CP. V 2057</td><td>Adult</td><td>7</td><td>16</td><td>19</td><td>32</td></tr><tr><td>Femur</td><td>CP. V 2058</td><td>Late Juvenile</td><td>19</td><td>22</td><td>13</td><td>18</td></tr><tr><td>Tibia</td><td>CP. V 2750a</td><td>Adult</td><td>24</td><td>62</td><td>10</td><td>19</td></tr><tr><td>Tibia</td><td>CP. V 2059</td><td>Early Juvenile</td><td>54</td><td>23</td><td>38</td><td>32</td></tr><tr><td>Humerus</td><td>CP. V 5698</td><td>Subadult</td><td>50</td><td>12</td><td>31</td><td>41</td></tr><tr><td>Humerus</td><td>CP. V 1032</td><td>Early juvenile</td><td>48</td><td>0</td><td>53</td><td>50</td></tr><tr><td>Ulna</td><td>CP. V 5701</td><td>Early juvenile</td><td>64</td><td>3</td><td>12</td><td>13</td></tr><tr><td>Wing ph.</td><td>CP. V 2301</td><td>Adult</td><td>14</td><td>22</td><td>13</td><td>9</td></tr><tr><td>Wing ph.</td><td>CP. V 2446</td><td>Subadult</td><td>10</td><td>17</td><td>9</td><td>15</td></tr><tr><td>Metacarpus</td><td>CP. V 2061</td><td>Adult</td><td>8</td><td>8</td><td>0</td><td>0</td></tr><tr><td>Metacarpus</td><td>CP. V 2056</td><td>Subadult</td><td>14</td><td>13</td><td>2</td><td>12</td></tr></tbody></table>

that these bones experience more complex forces during growth.

# DISCUSSION

## Comparing Pterosaur, Bird, and Bat Laminarity

The initial hypotheses connecting laminarity with torsional strength were introduced by de Margerie in 2002. He studied the bones of the mallard, *Anas platyrhynchos* Linnaeus, 1758, which are primarily subjected to torsional stress, such as the humerus, ulna, and femur, and found that these bones exhibit a laminar microstructure. Subsequent studies involving various species have consistently supported this pattern (de Margerie et al. 2005).

The results presented here indicate that there is a significant influence of laminar bone structure in the wing-associated bones of Pterosauria. In particular, the ones more proximally located, which is consistent with de Margerie (2002) hypothesis. However, it is interesting to note that none of the analyzed bones exhibited a LI as high as that established by de Margerie et al. (2002). For example, in

the case of *Caiuajara dobruskii* femora, we observed laminarity index values of 0.10 and 0 (CP. V 2057 and CP. V 2058) and 0.32 (MN 4809-V), for Anhangueridae. In contrast, de Margerie et al. (2005) inferred an LI of 0.563 for the femur. Furthermore, according to de Margerie (2002), high laminarity in the femur of birds is expected, associated with bipedalism. Considering a bird from the dorsal view, the femur is oriented not in a parasagittal plane but rather in an oblique plane. This angulation induces torque in the femur. When viewed dorsally, pterosaurs have a similar angulation of the femur, approximately 20° (Chatterjee & Templin 2004, Costa et al. 2014), which would also induce torque. However, our LI in the femur is not clear enough to explain this phenomenon and seems to be influenced not only by the torque but also by the ontogenetic stage.

An unexpected pattern of high laminarity was observed in the tibia (CP. V 2059); it was the only hindlimb among all our samples with a high LI. This phenomenon resembles the high laminarity pattern observed by de Margerie (2002) in the femur of birds. However, the femur
as a proximal bone that is supposed to be subjected to a higher mechanical stress than the tibia, we hypothesize that this discrepancy may be attributed to the early ontogenetic stage of CP. V 2059, which is the youngest specimen analyzed according to Araújo et al. (2023). It is not entirely clear, but it is plausible that the hindlimbs of early juvenile pterosaurs could exhibit high laminarity, different from that of adults, which typically show low LI in the posterior elements. It could be associated with the high rates of bone deposition, and likely allometry of the bones as shown by Yang et al. (2023). Moreover, it was reported that altricial birds exhibit higher rates of bone deposition in the early ontogenetic stages (Starck & Sutter 2000, Erickson et al. 2001, Prondvai et al. 2020). Additionally, we hypothesize that if pterosaurs were altricial, we could find laminar bone and high rates of bone deposition in both forelimbs and hindlimbs during early ontogenetic stages.

For the humerus, the LI ranged from 0.25 (CP. V 5698) to 0.32 (CP. V 1032), still below the values reported by de Margerie et al. (2005), who obtained an LI of 0.625. Additionally, the laminarity values for other pterosaur bones, such as ulna, radius, and wing phalanges, are also lower than the values reported in previous studies (de Margerie 2002, de Margerie et al. 2005). For instance, for the ulna of *Caiuajara dobruskii* (CP. V 5701), we observed a value of 0.69, while for the wing phalanges (CP. V 2301 and CP. V 2446), the values ranged from 0.04 to 0.11 respectively. Regarding Anhangueridae, the LI of the ulna ranged from 0.19 (MN 40809-V) to 0.43 (MPSC R 2090). Despite being a forelimb, all the sampled radii exhibit a low LI, also observed in birds (de Margerie 2002). This may occur due to the radius being associated with and supported by the ulna, which may undergo all the mechanical impact.

The disparities in LI observed between the pterosaurs examined in this study and the LI values reported for birds by de Margerie et al. (2005) suggest that flying reptiles likely employed distinct flight strategies. This could imply a reduced reliance on the intensive use of their forelimbs for flight, favoring instead the utilization of wing membrane and other aerodynamic adaptations to sustain flight. Additionally, the variations in bone laminarity may signify the independent evolution of bone structure and torsional resistances within these two groups of flying tetrapods.

The LI of pterosaurs appears larger than that presented by bats. Although these groups also share convergent characteristics with birds related to powered flight, bones with relatively thin cortical walls (Swartz et al. 1992), bone mineral density (Dumont 2010) and metabolic rate (Maina 2000), bats completely lack bone laminar (Lee & Simons 2015, Pratt et al. 2018, Skedros & Doutré 2019). Furthermore, according to Lee & Simons (2015) bats do not grow fast enough to form laminar bone. Due to the absence of laminarity in bat wings, it has been proposed so far that this feature would probably be an exclusive feature of birds (de Margerie 2006). However, our new findings suggest that pterosaurs also developed laminarity, showing that pterosaurs and birds have much more convergence than previously thought.

## Relationship between flight modes and bone laminarity

Pterosaurs, much like birds, likely occupied a variety of ecological niches, ranging from forms that fed on water to those specialized in flying in terrestrial environments (Witton & Habib 2010). Based on morphological features of *Pteranodon* and correlated species, pterosaurs were interpreted as being capable only of gliding and soaring performance (Hazlehursts & Rayner
1992). Like large birds, large pterosaurs would have been particularly proficient, comparable to the best soarers (Rayner 1988, Hazlerhursts & Rayner 1992). Therefore, we believe that an association between the laminarity index of pterosaur bones and their flight habits can be compared to the different types of bird flight and their respective LI, to better understand the issues related to the type of flight and the pterosaur's capabilities.

Studies involving birds with distinct flight and habits observed that different flight strategies result in varying LI rates (de Margerie 2002, Skedros & Hunt 2004, de Margerie 2006, Simons & O'Connor 2012, Kuehn et al. 2019, McGuire et al. 2020). Birds can be categorized into various flight categories, such as: continuous flappers, static soarers, dynamic soarers, and cursorial species (del Hoyo et al. 2004). Continuous flappers, exemplified by species like *Phalacrocorax auritus* (Lesson 1831) and *Anas platyrhynchos*, and dynamic soarers, including Falconidae and Strigidae, exhibit laminarity associated with posterior bones such as the humerus and ulna (de Margerie 2002, 2005, de Margerie et al. 2004, Simons & O'Connor 2012). Conversely, static soarers like Procellariformes and Pelicaniformes show no evidence of torsional adaptation in the humerus and ulna (de Margerie 2006, Simons & O'Connor 2012).

Cursorial birds like Galliformes and Columbidae also had their LI inferred. For Galliformes, analysis of turkey and pheasant demonstrates high laminarity, indicating torsional optimization in the humerus and ulna despite their predominantly terrestrial lifestyle (Skedros & Hunt 2004, de Margerie 2006). In contrast, Columbidae shows that LI decreases with maturity, suggesting elevated laminarity is not an adaptation for flight, particularly in pigeons (McGuire et al. 2020). Additionally, Ratites, exclusively terrestrial birds like the emu,

present age and growth rates as main factors that significantly affect vascular canal orientation, suggesting that laminarity may not be indicative of torsion in their leg bones (Kuehn et al. 2019).

Although our sample included only Pterodactyloidea taxons, the Tapejaridae, Anhangueridae and Dsungaripteroidea, exhibit significant differences in terms of size and distinct anatomical features. It is not clear whether laminarity is directly influenced by wing morphology or temporal parameters, such as flight duration. Our statistical results indicate significant difference among the laminarity index of these pterosaurs, especially when compared *Caiuajara* and Dsugaripteroidea, which correspond to larger pterosaurs, with wingspan of six meters, making it some of the largest pterosaurs known from Argentina (Kellner et al. 2006).

Osteohistological analyses of *Pterodaustro guinazui*, show a predominance of longitudinal canals with low laminarity (Chinsamy et al. 2009), a pattern similar to that of de Margerie (2005) for Procellariiformes. It seems that the longitudinal organization of bone tissues in *Pterodaustro* and Procellariiformes may have been an adaptation to longitudinal stresses caused by compression, tension, or bending loads (Chinsamy et al. 2009). Therefore, although it has been proposed that the wing bones of *Pterodaustro* did not experience large torsional loads during flight and may have had a flight mode similar to that of Procellariiformes, they would still have experienced torque. The wing bones are closer to the leading edge of the wing, so most of the lift forces would act caudally to the wing skeleton. In this orientation, lift forces would generate substantial torque in the wing bones, even in the absence of flapping flight (Biewener & Dial 1995).

Unlike what was observed in *Pterodaustro*, our *Tapejaridae*, *Anhangueridae* and
Dsungaripteroidea samples showed a high laminarity index in the humerus and ulna. These differences can be attributed to a variety of factors, including wingspan and wing shape, foraging strategy, and even habitat.

The cranial morphology and presence of filaments in the jaw of *Pterodaustro* suggest that this pterosaur was a filter-feeder of plankton and small organisms while gliding over water (Bonaparte 1970, Chinsamy et al. 2009, Cerda & Codorniú 2023). Given this, it's plausible that *Pterodaustro* had a flight style similar to static soarers, favoring bending rather than torsion in the wing bones (Chinsamy et al. 2009). Conversely, Anhangueridae were considered piscivorous (Wellnhofer 1987, Veldmeijer et al. 2007). However, their feeding strategies could be different from those of *Pterodaustro*, and Anhangueridae might not have relied on gliding over water to feed. Instead, they likely adopted a flight strategy less oriented towards gliding, with dynamic soaring, performing maneuvers that generated greater mechanical stress on the wing bones. This could explain the higher laminarity in bones of Anhangueridae pterosaurs, reflecting an adaptation to withstand the physical demands associated with these aerial maneuvers.

Dsungaripteroidea, the largest specimen in our sample, belongs to a group of pterosaurs characterized by a robust skeleton with thick walls and stout bodily proportions, suggesting a primarily terrestrial lifestyle (Chatterjee & Templin 2004). However, more recent evaluations of proportions, scaling, morphology, and bone strength in pterosaurs have shown that, in addition to planar gliding performance, giant pterosaurs were capable of generating sufficient lift and thrust for active flight, as well as resisting flight-related stresses (Witton & Habib 2010, Pittman et al. 2021). The proposed abrupt landings and extensive flapping may have resulted in significant torsion, which is

consistent with the observed laminarity index in its ulna. This suggests that these pterosaurs may have engaged in an intense flapping flight style.

The tapejarid *Caiuajara dobruskii* exhibited very similar laminarity values, but lower than those observed in Anhangueridae. *Caiuajara* is a toothless pterosaur and has distinct cranial morphology, with a well-developed crest, suggesting a possible adaptation for a frugivorous diet, as suggested for *Tapejara wellnhoferi* Kellner 1989 (Wellnhofer & Kellner 1991, Manzig et al. 2014). We presume that *Caiuajara* would adopt a dynamic soaring flight strategy, similar to that observed in Falconidae and Strigidae (de Margerie 2006).

The elongated wing morphology, in addition to the flapping frequency, may have a significant influence on the torsion degree experienced by the bones, as suggested by de Margerie (2005). This morphological influence could explain the differences in laminarity observed among pterosaur species.

## Laminarity and ontogeny

In some birds, it has been observed that laminarity may be influenced by ontogeny (Kuehn et al. 2019). An analysis of turkey's samples, exhibit a significant difference in the mean LI between subadult (40.0% ± 10.7%) and adult (50.9% ± 10.4%), suggesting that adults were more subject to torsion or that these differences reflect variations in growth rates (Skedros & Hunt 2004). In a study with king penguins, *Aptenodytes patagonicus*, higher laminarity rates were also observed in adults with more modest growth rates (de Margerie et al. 2004). The same condition was observed in emus (Kuehn et al. 2019). In pigeons, on the other hand, the opposite was observed, decreasing in laminarity with maturity (McGuire et al. 2020).

As seen previously, it appears that laminarity is susceptible to different factors beyond those
related to biomechanics and torsion, such as ontogeny and growth rates. Based on the ontogenetic classification previously conducted by (Sayão et al. (2004, 2003), Eleutério et al. (2015), Bantim et al. (2021) and Araújo et al. (2023), we observed the same laminarity index between juvenile and adult specimens of *Caiuajara dobruskii*, Anhangueridae and Dsungaripteroidea. For *C. dobruskii*, adult specimens (CP. V 2057, CP. 2750a, CP. V 2301, and CP. V 2446) the laminarity index values ranging from 0 to 0.165. Conversely, the juvenile specimens (CP. V 2058, CP. V 2059, CP. V 1032, and CP. V 5701), shows low laminarity values, ranging from 0 to 0.52. The highest laminarity value was observed in the youngest juvenile specimen, the tibia (CP. V 2059), indicating that there may be variation within ontogenetic stages.

Analyzing the canals type proportion by ontogenetic stages, in fact, the higher prevalence of circular canals in juveniles and subadults may indicate an adaptive response to the rapid growth and increased the metabolic activity typical of these stages. This enhanced laminar organization could provide greater structural support as these individuals undergo significant physical changes. In contrast, the increased presence of longitudinal canals in adult bones, particularly in the tibia, may reflect the need for enhanced resistance to bending and tensile forces, especially in posterior bones. The abundance of radial canals in early juvenile specimens further supports the idea that vascularization is heightened during early development, likely associated with high rates of deposition.

The comparison between paired samples reveals a disparity in the LI, indicating that ontogeny may significantly influence the LI of pterosaur hindlimbs. Specifically, the humerus of an early juvenile (CP. V 1032) compared to that of a subadult (CP. V 5690), and the tibiae

of the adult (CP. V 2750a) compared to early juvenile (CP. V 2059), show differences in their laminarity index. Is evident in the observation of high LI values in early stages and low LI values in later stages, resembling patterns observed in certain bird species (Kuehn et al. 2019, McGuire et al. 2020). Interestingly, there appears to be a consistent trend where juvenile specimens of both species exhibit higher laminarity than adults, contradicting findings from previous avian studies (Skedros & Hunt 2004, de Margerie et al. 2004, Kuehn et al. 2019). This elevated laminarity in juveniles may be associated with the altricial nature of these pterosaurs, as well as with rapid rates of bone deposition during early ontogeny. Additionally, the number of vascular canals with orientations in various radial and oblique axes appear to be notably more abundant in juveniles (Araújo et al. 2023). However, it's important to note that the precise influence of ontogeny on pterosaur laminarity remains unclear. Our findings indicate that there is no significant variation in the laminarity index across different bone elements, nor between the ontogenetic stages. This lack of significant variation may be attributed to the small sample size in this study. Further research is needed to confirm this trend and to gain a deeper understanding of the differences in laminarity between juvenile and adult pterosaurs.

## CONCLUSIONS

The present study analyzed, for the first time, data related to the arrangement of circular vascular canals in pterosaur bones, to attribute their laminarity index (LI). Then assessed whether pterosaurs possess laminarity as an adaptation to the torsion of flight. In all analyzed pterosaurs, the presence of laminar bone was observed, with high laminarity indexes, especially in juvenile. This laminarity was
associated with a biomechanical adaptation for torsion in the microstructure of pterosaur limb bones. Additionally, beyond ontogenetic factors, it appears that the LI in these flying reptiles may be influenced by the type of flight adopted, as well as by the shape and size of the wingspan. Anhangueridae and *Caiuajara* were associated with a flight habit like that of birds, possessing dynamic soaring flight. Although they may occupy different niches, with Anhangueridae possibly associated with coastal areas and *Caiuajara* with regions further inland, assuming a frugivorous diet. Dsungaripteroidea was associated with flapping flight and probably punctuated by abrupt landings and extensive flapping. The presence of laminarity in pterosaurs as well as in birds, and its absence in bats, highlights that this feature, once considered exclusive to birds, is also present in pterosaurs, showing another feature that may have convergently evolved in both groups.

## Acknowledgments

We would like to thank the authors of previous osteohistological descriptions used in this work, for accessing the original thin sections and their respective pictures. EVA acknowledges the PPGZoo for their grant support, as well as CP2RP - Sorbonne University for the internship that contributed to this research. This study was funded by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) #141138/2022-0 to EVA; #314222/2020-0; #309245/2023-0 to JMS and # 308707/2023-0, #406779/2021-0, #406902/2022-4 - INCT PALEOVERT to AWAK, and Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ) #E-26/201.095/2022 to AWAK; and E-26/210.066/2023 to JMS. This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101107135 to MVAS.

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**How to cite**

ARAÚJO EV, CUBO J, SENA MVA, BANTIM RAM, WEINSCHÜTZ LC, KELLNER AWA & SAYÃO JM. 2025. Wing bone laminarity in Pterosaurs: insights into torsional adaptations for flight evolution. *An Acad Bras Cienc* 97: e20240540. DOI 10.1590/0001-3765202520240540.

Manuscript received on June 3, 2024;
accepted for publication on October 7, 2024

ESAÚ VICTOR DE ARAÚJO<fnref n="1" />,<fnref n="2" />
https://orcid.org/0000-0003-3459-4495

JORGE CUBO³
https://orcid.org/0000-0002-8160-779X

MARIANA VALÉRIA DE ARAÚJO SENA³
https://orcid.org/0000-0003-4708-999X

RENAN ALFREDO MACHADO BANTIM⁴
https://orcid.org/0000-0003-4576-0989

LUIZ CARLOS WEINSCHÜTZ⁵
https://orcid.org/0000-0002-8978-6120

ALEXANDER WILHELM ARMIN KELLNER<fnref n="1" />,<fnref n="2" />
https://orcid.org/0000-0001-7174-9447

JULIANA MANSO SAYÃO<fnref n="1" />,<fnref n="2" />
https://orcid.org/0000-0002-3619-0323

<footnote n="1">¹Universidade Federal do Rio de Janeiro, Museu Nacional, Laboratório de Sistemática e Paleontologia de Vertebrados (LAPUG), Departamento de Geologia e Paleontologia, Campus de Ensino e Pesquisa, Av. Bartolomeu de Gusmão, 875, 20941-160 São Cristóvão, RJ, Brazil</footnote>

<footnote n="2">²Universidade Federal do Rio de Janeiro, Museu Nacional, Programa de Pós-Graduação em Zoologia, Quinta da Boa Vista, s/n, 20940-040 São Cristóvão, RJ, Brazil</footnote>
<sup>3</sup>Sorbonne Université, Muséum National d'Histoire Naturelle, CNRS, Centre de Recherche en Paléontologie—Paris (CR2P, UMR 7207), 4 Place Jussieu, 104, 75005 Paris, BC, France

‘Museu de Paleontologia Plácido Cidade Nuvens, Rua Plácido Cidade Nuvens, 326, 63190-000 Santana do Cariri, CE, Brazil

⁵Universidade do Contestado, Centro Paleontológico (CENPALEO), Campus Mafra, Av. Nereu Ramos, 1071, Jardim do Moinho, 89306-076 Mafra, SC, Brazil

Correspondence to: **Esaú Victor De Araújo**

E-mail: esauvictor13@gmail.com

**Author contributions**

Esaú Araújo: Conceptualization; data curation; formal analysis; investigation; methodology; writing-original draft and figures editing. Jorge Cubo: Conceptualization; methodology; data curation; formal analysis; writing-review; validation; supervision. Mariana Sena, Luiz Weinschütz and Renan Bantim: Conceptualization; methodology; data curation; formal analysis; writing-review: Alexander W. A. Kellner: Funding acquisition; supervision; validation; writing-review and editing. Juliana Sayão: Conceptualization; methodology; data curation; formal analysis; writing-review; editing; funding acquisition; supervision.

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