Helically arranged cross struts in azhdarchid pterosaur cervical vertebrae and their biomechanical implications.

Azhdarchid pterosaurs, the largest flying vertebrates, remain poorly understood, with fundamental aspects of their palaeobiology unknown. X-ray computed tomography reveals a complex internal micro-architecture for three-dimensionally preserved, hyper-elongate cervical vertebrae of the Cretaceous azhdarchid pterosaur, Alanqa sp. Incorporation of the neural canal within the body of the vertebra and elongation of the centrum result in a "tube within a tube" supported by helically distributed trabeculae. Linear elastic static analysis and linearized buckling analysis, accompanied with a finite element model, reveal that as few as 50 trabeculae increase the buckling load by up to 90%, implying that a vertebra without the trabeculae is more prone to elastic instability due to axial loads. Subsuming the neural tube into the centrum tube adds considerable stiffness to the cervical series, permitting the uptake of heavy prey items without risking damage to the cervical series, while at the same time allowing considerable skeletal mass reduction.

Introduction

Pterosaurs, volant reptiles of the Mesozoic made their first appearance in the fossil record in the Late Triassic and survived until the end of the Cretaceous approximately 66 million years ago (Unwin, 2005; Witton, 2013; Longrich et al., 2018). Although some pterosaurs were small, with wingspans of less than 1 m, the enigmatic Azhdarchidae achieved wingspans of up to 10 m, possibly even as high as 12 m (Lawson, 1975; Frey and Martill, 1996; Buffetaut et al., 2003; Witton and Habib, 2010). These gigantic forms were globally distributed, but mainly restricted to the late Early to end Late Cretaceous (Averianov, 2010, 2013; Naish and Witton, 2017). The Azhdarchidae are notable for elongation of the neck as a result of hyper-elongation of their cervical vertebrae (Frey and Martill, 1996; Unwin and Lü, 1997; Martill et al., 1998; Company et al., 1999; Unwin, 2003; Henderson and Peterson, 2006; Watabe et al., 2009; Witton, 2013; Liu et al., 2015; Harrell et al., 2016). Their cervical vertebrae (Figure 1) display many modifications of the centrum, neural arch, and articulatory facets and processes (condyles, cotyles, and zygapophyses), many of which appear to be adaptations for holding the neck in an outstretched position (Averianov, 2013; Naish and Witton, 2017). Numerous bone locks restrict flexion in three planes, and deep ligament sockets anteriorly and posteriorly imply strong linkage between individual vertebrae. Flattening of the condyle and cotyle also limits flexion to a single plane (Averianov, 2013). However, the function and complexity of the internal structure of these highly unusual vertebrae has never previously been investigated. Previous analysis of the biomechanics of azhdarchid cervical vertebrae (e.g., Averianov, 2013; Naish and Witton, 2017) modeled them as a simple, single hollow tube, but such analyses fail to correctly determine the biomechanical properties of the pterosaur neck skeleton by ignoring its internal structure. This lack of quantifiable analysis has hampered efforts to assess fundamental aspects of azhdarchid ecology, such as their prey size and neck strength.

Figure 1

Cervical vertebra of Alanqa sp. from the Kem Kem Group of Morocco

Cervical vertebra of Alanqa sp. FSAC-KK 5077 in (A), dorsal view, (B), ventral view, (C), right lateral view, (D), anterior view, (E), posterior view. Scale bars represent 10 mm. Abbreviations: pz, prezygapophysis; ct, cotyle; ns, neural spine; su, sulci; fo, foramina; lpf, lateral pneumatic foramina (See Table S1 for measurements).

Studies of pterosaur skeletal anatomy are often limited by a shortage of high-quality specimens displaying 3D morphology, and this is especially true for the pterosaur neck skeleton. The limited amount of morphological data for Azhdarchidae contributes to our poor understanding of the biomechanics and palaeoecology of these pterosaurs. Although three-dimensionally preserved pterosaur bones are rare, and articulated material rarer still, the mid Cretaceous Kem Kem Group of Morocco is becoming increasingly important as a source of well-preserved, 3D pterosaur bones, including azhdarchid cervical vertebrae (Ibrahim et al., 2020).

XCT scanning of a well-preserved azhdarchid cervical vertebra from the Kem Kem Group provides a rare opportunity to investigate the internal architecture of these highly derived bones to determine their mechanical properties and tolerance. We tentatively attribute these vertebrae to the taxon, Alanqa sp. Ibrahim et al. (2010), although we note, based on recently described finds that other azhdarchoid taxa were present in the Kem Kem Group (Ibrahim et al., 2020). The Kem Kem Group records a complex fluvial system dominated by red-bed strata. They are famous for the high abundance of fragmentary, but well-preserved remains of disarticulated vertebrates (Lavocat, 1954; Sereno et al., 1996; Ibrahim et al., 2010). Most pterosaur material has been collected from the Albian-Cenomanian Ifezouane Formation (Ibrahim et al., 2020).

Pterosaur bone

Pterosaur bones are typically hollow and usually thin walled with reduced internal trabeculae, except at points of articulation (Witton, 2013). Like all tetrapod bones, pterosaur bone is rich in osteocyte lacunae with dense fringes of canaliculae (de Ricqlès et al., 2000; Steel, 2008) and micro-capillaries, which may render the bone less dense than if it were solid (Supplemental information Figure S1). Thus, pneumatized pterosaur bones likely are extremely light (Witton and Habib, 2010, but see Butler et al., 2009; Dumont, 2010; Martin and Palmer, 2014 for a discussion on the effects on pneumaticity on bone density in volant tetrapods). Most Cretaceous pterosaur bones appear extremely fragile due to the highly reduced thickness of their bone walls (Bennett, 1997). Paleohistological studies reveal thin-walled pterosaur bone to be composed of microlamellar bone, with many lamellae per mm of thickness (de Ricqlès et al., 2000; Steel, 2008). Such histology is widely thought to confer stiffness and resist impact fracture (de Ricqlès et al., 2000).

Pterosaur neck skeleton

Pterodactyloid pterosaur necks are comparatively large structures with generally eight or nine cervical vertebrae, most of which are larger than individual thoracic, lumbar, sacral, and caudal vertebrae (Howse, 1986; Wellnhofer, 1991; Witton, 2013; Bennett, 2014). The neck is usually longer than the torso and often supports an extremely large but lightly constructed skull (Kellner and Langston, 1996). Individual vertebrae are usually pneumatized with enlarged lateral foramina, low, or even absent neural spines and in many cases are approximately as high as they are wide and long (approximately equant) (Butler et al., 2009; Claessens et al., 2009). They are procoelous and articulate with adjacent vertebrae via a horizontally oval condyle and cotyle, with inclined facets of the anterior and posterior zygapophyses (Howse, 1986; Witton, 2013).

In ctenochasmatid and azhdarchid pterosaurs cervical vertebrae are more elongate in the central portion (C3 to C7), and in Azhdarchidae, they are highly elongate and even hyper-elongate in the case of cervical five (C5) (the Romanian Hatzegopteryx may have secondarily shortened their neck length, but the evidence is equivocal) (Vremir et al., 2015; Naish and Witton, 2017). Most notably, the late Cretaceous azhdarchid Arambourgiania has a cervical vertebra (C5) with an estimated maximum length of 770 mm (Frey and Martill, 1996) and an estimated total neck length of ~2.5 m. Such elaborate structures have become the subject of several biomechanical and functional studies (Witton and Habib, 2010; Averianov, 2013; Naish and Witton, 2017), as such long necks are remarkable for volant animals. Besides their increased length, several other features distinguish azhdarchid cervical vertebrae from other pterosaurs. Notable is the lack of pneumatic foramina on the centrum sides, the reduction of the neural spine, and subsuming of the neural canal into the middle of the centrum to form a neural tube (Frey and Martill, 1996), although this latter feature has also been recorded for another group, the Dsungaripteridae (Buffetaut and Kuang, 2010).

In this analysis we examine the role of the internal architecture of an azhdarchid cervical vertebra to determine its biomechanical properties regarding azhdarchid pterosaur feeding behavior (see Supplemental information for methods, Figures S2 and S3).

Results

Internal architecture

The results of XCT scanning and 3D manipulation reveal a complex internal architecture of the azhdarchid cervical vertebra. Clearly visible is an approximately centrally located bony neural tube attached to the centrum wall (centrum tube) by helically arranged radial, spoke-like trabeculae (Figure 2. See also Videos S1 and S2). These are arranged as complimentary opposed helices (clockwise vs anticlockwise) and are often fused where they cross over. Superficially, looking along the length of the centrum internally the radial trabeculae resemble bicycle wheel spokes (Figures 2B and 2D). The arrangement is somewhat irregular and so the helices are not perfect, but this likely reflects changes in the stress regime along a centrum that is not a perfect cylinder. The “spokes” are inclined posteriorly or anteriorly, while still displaying the radial architecture (Figures 2B and 2D). Some “spokes” bifurcate and branch, especially toward the centrum outer wall (Figure 2A, 2C, and 2E). Toward the dorsal part of the centrum (neural arch) and the prezygapophyses the trabeculae are more densely arranged and are orientated more randomly (Figure 2A, 2C, and 2E). Trabeculae are also present along the interior wall of the vertebra, presumably providing support and increasing its strength. The “spokes” have varying diameters, with an average of 1.16 mm.

Figure 2

Images of XCT scan of cervical vertebra of Alanqa sp

Images of digital model generated from XCT scans of cervical vertebra FSAC-KK 5077 showing the internal architecture (A and B) and simplification diagrams of the internal structure (C and D), dorsal (A (above neural canal), (C and E) (cut through neural canal)) and anterior (B and D) views cut transversely through the cervical (position indicated by arrows). All views to same scale; scale bar represents 10 mm.

Biomechanical properties of a single cervical vertebra

The load multiplier associated with buckling changes with the number of trabeculae, because an increase in trabeculae creates a stronger bond between the external and internal tubes and increases the overall resistance of the structure to buckling (Figure 3A). An increase in trabeculae reinforces the structure by increasing its elastic stability (i.e. a bigger load to produce buckling); at the same time, this produces a stress transfer between the external bone wall and the internal neural tube (see Figure 4), thus reducing the safety factor with respect to tissue failure. In other words, with more trabeculae the structure is more stable but closer to the limit of fracture of the material. In this sense, an optimal trade-off in the trabecula number seems to optimize the first effect (stability) with lesser impact on the latter (safety factor with respect to fracture).

Figure 3

Graphs displaying relative buckling and relative safety factor for a simplified azhdarchid cervical vertebra modeled with varying numbers of trabeculae

(A) Relative increase of buckling load proportional factor (LPF) versus number of trabeculae (average values and standard deviation).

(B) Safety factor (SF) in tension and in compression determined via a static analysis (average values reported) averaged values rated to the no trabeculae condition. The safety factor refers to the strain level. When the number of the trabeculae increases, it increases the mechanical bonding between the external shell of the vertebra and the internal channel; this introduces an increased stress concentration (and therefore strain level) onto the wall of the internal neural tube. In fact, the internal neural tube is the area where stresses and strains are highest, as shown in Figure 4.

Figure 4

Distribution of the maximum principal strain on the finite element (FE) model; a cross-section showing the effect of the load transfer via the trabeculae

(A–C) (A) 50 trabeculae; (B) 150 trabeculae (optimum number), and (C) 450 trabeculae.

The critical load triggering the structural instability shows a highly non-linear dependence with the number of trabeculae. Assuming as reference the case of no trabeculae, the critical load able to trigger buckling is increased on average up to 90% when the first 50 trabeculae are randomly introduced on the vertebral body. Conversely, the introduction of a further 400 trabeculae increased the critical load by only 10% with respect to the initial condition. Thus, when the number of trabeculae increases, the stability of the structure also increases and is less prone to buckling (i.e., the load triggering buckling increases); at the same time, the connection between the external bone wall and the internal neural tube increases, resulting in a greater tensile strain on the wall of the neural tube. Thus, as few as 50 trabeculae produce a considerable increase in the vertebra's structural stability without generating a hazardous strain concentration on the central neural tube.

Figure 3B shows the change of safety factor related to material fracture with the number of trabeculae; the chart reports the change rate with respect to the reference condition of no trabeculae. As well as the buckling load multiplier, the safety factor (i.e., how close the structure is to localized material fracture) changed non-linearly with the number of trabeculae arranged onto the vertebral body. In particular, the overall trend is of a progressive deterioration of the safety factor in both tension and compression. For all the analyzed cases, the decay in the safety factor is overall within approximately 20% of the initial value. This change is not uniform in both trend and magnitude; a monotonic trend appears only after the level of 150 trabeculae.

Implications for azhdarchid feeding

It has been widely assumed that azhdarchids were either piscivores or generalist feeders taking perhaps small mammals and reptiles (Witton and Naish, 2008). Alternative feeding strategies have been proposed, including skim feeding for surface plankton and probe feeding for molluscs and infaunal arthropods (Lehman and Langston, 1996; Bestwick et al., 2018). There seems to be a consensus that small tetrapods and fish were the likely prey (Averianov, 2013). Thus, based on the structural constraints imposed by the cervical vertebrae, it is pertinent to ask the question, what is a reasonable maximum prey animal mass the pterosaurs were able to catch, lift (with its head and neck), and process?

Adopting for the variables in Equation (5) the values reported above and assuming the elastic modulus for the bone ranging from 15 GPa to 22 GPa, the corresponding maximum mass of the prey ranges between 18 kg and 27 kg. In order to consider dynamical effects related to the flying dynamics and to an expected fast action of prey catching, the values related to both the head mass and the prey mass should be multiplied by a magnification factor MF. Equation (5) then becomes:

In the absence of detailed information about pterosaur feeding strategies, it is hard to identify a reliable value for this load multiplier. Nonetheless, it appears reasonable to consider the same value of the dynamic amplification factor associated with a dynamic system with a suddenly applied load, i.e., 2 (Chao et al., 2020). In this condition, Equation (6) gives a maximum mass for the prey ranging between 9 kg and 13 kg.

Discussion

Previous analyses

Averianov (2013) was first to attempt a biomechanical analysis of the neck of azhdarchid pterosaurs, determining that the neck was held outstretched in a sub-horizontal pose (not straight) and was somewhat “S” shaped at the posterior-most four cervical vertebrae, although the degree of flexion between vertebrae was no more than 20°. Averianov (2013) considered azhdarchids essentially volant animals feeding on the wing.

Later biomechanical models to determine the “strength” of the azhdarchid neck assumed each vertebra to represent a simple hollow tube (Witton and Habib, 2010: Naish and Witton, 2017). Adoption of a hollow tube proxy is not unreasonable but fails to recognize the role of some of the complexities seen on the external surface and ignores entirely the internal architecture of the vertebrae.

Naish and Witton (2017) concluded that the azhdarchid Hatzegopteryx neck vertebrae are substantially stronger than those of Arambourgiania, with relative failure forces (RFFs) of 5.26 and 0.38 in coronal plane, respectively when loaded by 2,452 N. They suggested that the relatively thick wall of the vertebrae of Hatzegopteryx enhanced buckling strength without altering bending strength. They acknowledged that other internal features also needed to be considered—camellate bone and trabeculae. However, these features were not considered in their analyses. They concluded that Hatzegopteryx was a robust form of azhdarchid, whereas Arambourgiania was more gracile, occupying distinct ecological niches and perhaps diets. Unfortunately, the comparison is flawed, as the two vertebrae compared are from different parts of the cervical series (Naish and Witton, 2017) and likely would have distinct biomechanical properties in any case.

Vertebral internal architecture

The functional capabilities for any bone result from the combination/interaction of all its structural components. Thus, the internal structure as well as the external components and their mechanical properties must be considered in any analysis of its form and function. This can be extended to its histology, microstructure, and even molecular composition of the bone material itself (e.g., Huiskes, 2000; Rayfield, 2007). XCT scanning revealed an internal structure of a generally thin-walled cylindrical vertebra dominated internally by an axially located bony neural tube supported by a cross-helical arrangement of thin trabeculae along the entire length of the vertebral cylinder.

Additional resistance to buckling could have been achieved by thickening the external walls of the vertebral body; however, such thickening would considerably increase the mass of the vertebra, something that is detrimental for a flying vertebrate. The evolution of a spirally arranged system of thin trabeculae as an alternative allowed for a reduced wall thickness and thus a reduction in the mass of the vertebra along with increased resistance to torsion and compression, i.e., the system was both lighter and stronger and energetically cheaper to construct.

Biomechanical properties of a single vertebra

Our results identify a crucial role of the trabeculae in stabilizing the vertebral structure. As soon as the internal space is populated with trabeculae radially arranged between the neural tube and the external wall, the structure's capability to sustain loads increases; the non-linear nature of this change seems to suggest the existence of an optimal number (approximately 150 trabeculae) of trabeculae able to bring the most relevant benefit to the structural stability without impacting on both mass and stress distribution. When the number of trabeculae increases, the structure is increasingly more stable. Meanwhile, the mechanical connection between the external wall and the internal neural tube also increases. This linkage is responsible for the stabilization process, which is mediated by radial trabeculae: when the number of trabeculae increases, the wall of the internal neural tube is subjected to an increased level of strain (Figure 4). As the stabilization induced by the trabeculae is non-linearly dependent on the number of trabeculae, the increase in stress on the neural tube is also non-linear. The increased level of strain reduces the safety of the structure with respect to any local fracture. Nonetheless, the numerical models suggest this change in the safety factor is marginal and does not change significantly when the number of trabeculae increases.

The numerical analyses provide an insight into the role of the internal bone structure and specifically the role of trabeculae that extend the load-bearing ability by stabilizing the structure without making it significantly heavier. This enhances the mechanical performance of the vertebral structure, preserving its biological integrity while increasing the magnitude of the force that can be applied to a bone segment. These characteristics are of key importance for a predatory flying animal equipped with a long neck used as the main tool to capture and lift prey.

This model may also explain the radial arrangement of the trabecular structure. Although some limited areas of a more isotropic spongy bone can be envisaged locally, the most relevant part of the trabecular structure is distinct from that of the spongy bone of a typical mammalian vertebra, where trabeculae appear predominantly aligned with the vertebral axis. One possible explanation, corroborated by the above-discussed analysis, is related to the extremely slender nature of the vertebral body geometry. The particular combination of aspect ratio and wall thicknesses suggests buckling as the most relevant critical scenario to produce bone fracture. Thus, it is possible that the evolutionary process encouraged and drove the specialization of a trabecular structure able to mitigate as much as possible the risk of buckling instability. If so, this would be in the direction of an optimization process where the maximum load-bearing ability of the skeleton is increased without impacting on the overall mass.

Azhdarchid necks

Hyper-elongate necks are unusual in tetrapods outside of Dinosauria, and animals that possess them are highly distinctive. Giraffa and Tannystropheus (Nosotti, 2007; Badlangana et al., 2009; Rieppel et al., 2010) are two examples where hyper-elongation involved lengthening of the individual vertebrae rather than an increase in cervical number (Nosotti, 2007; Rieppel et al., 2010), as occurred in plesiosaurs and many avians (some animals, notably sauropod dinosaurs, achieved hyper-elongate necks by adopting both approaches) (O'Keefe and Hiller, 2006; Christian and Dzemski, 2007; Taylor and Wedel, 2013).

In animals with long necks the structure functions either as a mast (brachiosaurid dinosaurs, giraffe, ostrich) raising the head significantly above the ground or as a beam, extending the neck forwards and perhaps laterally also (Martin et al., 1998) (e.g., diplodocid sauropods, plesiosaurs, Tannystropheus, and azhdarchid pterosaurs perhaps) (Martin et al., 1998; Nosotti, 2007; Badlangana et al., 2009; Averianov, 2013; Noè et al., 2017). In those animals where the neck functions as a mast the animal is not obliged to feed in the trees as do giraffes. Ostriches are largely ground-feeding birds (Folch, 1992), whereas swans use their long necks to garner food from deeper water than their short-necked cousins, the ducks. The modus operandi of the elongate azhdarchid neck has for a long time been problematic. The analysis of Averianov (2013) showed only limited flexibility in the neck of azhdarchids, whereas Naish and Witton (2017) suggested that it had very limited resistance to buckling.

In those azhdarchids where the head and neck skeleton is known (Quetzalcoatlus, Zhejiangopterus) the skull is proportionally large (perhaps as long as >1 m for a neck 3 m in length) (Kellner and Langston, 1996; Naish and Witton, 2017), a morphology not seen in any other animal except birds such as pelicans and storks. Such a morphology poses questions for diet and mode of feeding in azhdarchid pterosaurs. A stork-like feeding strategy of terrestrial foraging (Witton and Naish, 2008) and a probe-feeding mode of foraging were proposed for Quetzalcoatlus, although the latter hypothesis was based solely on the association of invertebrate trace fossils, rather than any biomechanical analysis (Lehman and Langston, 1996).

Size of prey?

Our analysis allows us to speculate on the maximum mass of prey compatible with the average bony structure identified in the neck of the pterosaur. The limiting factor considered was the prey mass at which the bone component of the vertebrae would fail. We cannot factor in the complexity of the intervertebral joints, connective tissue, and neck musculature, as these remain unknown for Pterosauria. This analysis, based on a simplified cantilever continuous beam model, is affected by many limitations: (1) a static model was assumed; (2) the neck was assumed as a homogeneous structure where only the bony structure is reacting to loads (i.e. the muscular and connective tissue contributions in loading tensional stresses are neglected); (3) either material properties (i.e. density and elastic modulus) or failure criteria for the bone tissue were assumed matching those usually valid for bird bone; and (4) the model assumed for each vertebra was extremely simplified in both the overall geometry and the internal structure. On the other hand, the model appears to be simple and parametric, able to assess the impact of the uncertainties associated with each one of its parameters in a straightforward and clear way. The absence of detailed information about the muscular structure and the flight dynamics would make pointless the elaboration of more complex models involving a more accurate skeletal structure for the purposes of a first rough assessment aimed to identify mostly the order of magnitude of the prey mass.

The values this model produced (9-13 kg) appear reasonable when correlated with the assessed total mass of the animal with a mass estimated to be between ~16 kg and 37 kg for a wingspan of approximately 6 m (Humphries et al., 2007; Witton, 2008).

Concluding remarks

XCT imaging of an azhdarchid pterosaur cervical vertebra reveals a complex internal architecture of radial, spoke-like support structures maintaining the integrity of a centrally located bony neural tube through which passed the main spinal cord. Linear elastic static analysis and linearized buckling analysis reveal that as few as 50 trabeculae increases the buckling load by up to 90%, implying that a cervical vertebra without the trabeculae is considerably more prone to elastic instability due to axial loads. Subsuming the neural tube into the centrum tube and supporting it with an optimum number of fine-spoke-like trabeculae adds considerable resistance to buckling to the cervical series, potentially permitting the uptake of heavy prey items without risking damage to the cervical skeleton, while at the same time without significant mass increase of the skeleton. Calculations applied to the entire neck indicate a prey size lift capability without failure of between 9 kg and 13 kg. Our results are consistent with large prey capture by azhdarchids, including giant forms like Quetzalcoatlus, with a wingspan of 10 m or more (Lawson, 1975). Prey size was likely limited by skull and gullet size, rather than neck lifting capacity. We also acknowledge that the neck strength may have been utilized for another function, such as neck “bashing,” an inter-male rivalry behavior seen in giraffes. Alternatively, the seemingly overengineered cervical vertebrae could be related to shearing forces associated with large skulls being buffeted by strong winds during flight or while on the ground.

Limitations of the study

Despite their popular appeal, azhdarchid pterosaurs are poorly understood. Their remains are incredibly rare, mostly fragmentary and usually crushed. The cervical vertebral series is only known for three taxa, Phosphatodraco, Zhejiangopterus, and Quetzalcoatlus, all of which are crushed to varying degrees. The specimen described here is remarkable for its 3-dimensionality with internal structure intact and is almost unique.

The model assumed for each vertebra was highly simplified in both the overall geometry and the internal structure. A hollow cylinder within a hollow cylinder mimics the overall structure of the living system. We did not consider the complexities of the articulatory surfaces, processes, and structural features at the anterior and posterior terminations of the vertebra. Similarly, our mass calculations are based on a simplified model of the vertebra.

Our mathematical analysis is based on a cantilever continuous beam model affected by several limitations: (1) a static model was assumed; (2) the neck was assumed as a homogeneous structure where only the bony structure is reacting to loads (i.e. the muscular and connective tissue contributions in loading tensional stresses are disregarded); (3) either material properties (i.e. density and elastic modulus) or failure criteria for the bone tissue were assumed to match those valid for bird bone.

Resource availability

Lead contact

Further information and requests for resources should be directed to and will be fulfilled by the lead contact, Miss Cariad J. Williams, cariad.williams1996@gmail.com.

Material availability

The original specimen is accessioned in the collection of FSAC. Digital scans and videos are available on request. The thin section of Figure S1 is accessioned in the collection of the SEGG, University of Portsmouth, UK.

Data and code availability

All data are included in this submission.

Methods

All methods can be found in the accompanying transparent methods supplemental file.