Comparison with Previous Studies

ASP values found in this study are within the range previously published in the literature for pterosaurs (Tables 2, 3), although important differences are discussed below. The ASP values also appear to be within the range of cervical vertebrae of sauropod dinosaurs with high ASP, although they do not exhibit the wide range seen in sauropods [20]. However, these ASP values do exhibit a higher percentage of air in the bones than do bird wing bones [21]–[23] (Table 3).

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Table 3. ASP values from previous studies.

https://doi.org/10.1371/journal.pone.0097159.t003

Values reported for Pteranodon [21] (and derived from previously published literature [1]) are higher than those found here. However, the results of Pteranodon ASP may not be accurate because the original cortical thickness values [1] have been transformed first into K [21], then additionally into ASP here. It has also been suggested that the initial transformation into K was not accurate [21]. Alternatively, as different taxa exhibit contrasting degrees of pneumaticity and wall thicknesses (see below), it may be that Pteranodon surpasses other pterosaurian taxa in its proportion of air to bone. The limited sample size and phylogenetic spread of our study combined with the crushed nature of Pteranodon remains from the Niobrara Formation limit our ability to analyze this further as few three dimensional specimens exist. Fastnacht [24] reported a lower range of ASP in dsungaripteroid pterosaurs, although it is unknown which bones or specimens his conclusions were based on. Dsungaripteroids have thick-walled bones compared to other pterosaurs [27], which explains the lower value of ASP [24]. This may be relevant to the debated taxonomic nature of Bennettazhia, the humerus studied here (USNM 11925). Although this specimen is typically referred to as an azhdarchid [28], the lack of proximal pneumatic foramina characteristic of azhdarchids suggests it may be better to consider it an indeterminate Tapejaroidea (Dsungaripteroidea + Azhdarchoidea) (M. Witton, pers. comm.). Alternatively, it may represent a different group, which is suggested by a recent phylogenetic analysis that does not support the traditional grouping of Tapejaroidea [29]. Another explanation for the difference in values may come from the method of converting K values to ASP in pterosaurs. While K² is equal to ASP for semi-circular shaft cross sections with constant wall thickness such as those seen in most birds, pterosaur wing phalanges are sub-triangular in cross section with thickness increasing towards the corners. As it is unclear which bones the dsungaripterid values came from [24], this difference could be from converting non-circular bone cross sections to ASP values which may not be accurate. Comparison with data published from SMNK PAL 3985 [17] demonstrated that the rib, femur, tibia, and cervical vertebra ASP ranges are similar to those found in this study. However, the only bone in SMNK PAL 3895 directly comparable here is a wing phalanx, and represents the smallest ASP found with only 0.27 (Table 3), notably different from wing phalanx ASP found here (Table 2). An ASP of 0.27 was determined by taking a picture of a cross section of the specimen which had the internal structure exposed, and applied the calculated ASP from this single cross section throughout the bone [17]. It may be that a more comprehensive study of this specimen using CT analysis would reveal a larger ASP more characteristic of other bones. Further analysis of this specimen is needed to determine its pneumatic properties in more detail.

When comparing the results here with those of studies estimated from K values of the long bones of birds, pterosaur ASP exhibits a narrower range than that of birds (Tables 2, 3). The pterosaur results are at the high end of the bird range, and the extreme values are greater than the highest bird ASP estimates. This adds further support to the view that pterosaurs were highly pneumatic, which may have been linked to their well developed respiratory system and possibly contributed to their ability to reach gigantic sizes [6].

In comparison with sauropod dinosaurs, the ASP of pterosaur wing bones is similar to that of the high end of the range seen in sauropod vertebrae (Tables 2, 3). As only wing elements were studied here, a direct comparison between comparable elements in sauropods and pterosaurs is not possible, and is a subject that holds promise for future study. In summary, it appears that the wing elements of pterodactyloid pterosaurs possess higher ASP values than the long bones of birds, and are comparable to the most pneumatized sauropod vertebrae.

ASP Patterns in Pterosaur Wing Bones

Although not statistically significant due to the small number of samples, it appears that ASP decreases (and therefore the proportion of bone volume increases) distally along the phalanges (Table 2, Fig. 2). UP WP1 and NHMUK PV OR39411 show higher ASP values throughout the bone than that of UP WP2. NHMUK PV OR41637 has a similar distribution throughout the shaft of the bone to UP WP2, but has a higher ASP in the proximal head. However, UP WP3 has lower ASP than all other specimens, barely overlapping with any other specimens, while still sharing the general pattern of highest ASP at the ends. This suggests that the pterosaur wing phalanges are more highly pneumatized proximally, and decrease in pneumatisation distally. However, while UP WP2 and WP3 are from the same individual, UP WP1 is not. Further investigation is required to determine if pneumaticity does actually decrease distally, or if the results reported here represent individual variation.

Implications of ASP Variation within Bones

Although comparison of degrees of pneumaticity within taxa is valuable, the more important finding of this study is the degree of variation of ASP within individual bones (Fig. 2). Previous studies have reported ASP or K values from a single cross section through the bone that is generally in the shaft, either from the specimen itself, an image, or in rare cases from a single CT scan slice [17], [20]–[24]. This study shows that ASP is not constant throughout a bone: ASP is higher in the heads than in the shafts. This was not expected as the heads of the bones are filled with spongy trabecular bone, but the very thin walls of the trabeculae mean that there is a large proportion of air space. Also, increased diameter in the heads is coupled with decreased cortical thickness towards the heads (as much as 50% decrease [30]).

The difference between the average ASP and the smallest ASP measured in each specimen is 5–19%, while the difference between the highest and lowest measurements is 10–29% (table 2). These differences highlight the problem of using a single section to quantify pneumaticity within a bone since the shaft consistently shows a lower ASP than the heads. Although this trend is clear for pterosaur wing phalanges, it is not in the humerus USNM 11925 (Table 2). It is unknown if this is a general feature of humeri, or this single taxon and more investigation is needed.

It is also unknown if variation of ASP throughout a bone is solely characteristic of pterosaurs, or if it is present in other animals with pneumaticity, such as birds and sauropods. Further work must therefore be done on both sauropods and birds to determine if the variation is present within these groups as well as pterosaurs, and to what extent ASP may have been underestimated in these taxa. As biomechanical studies are often based on shaft cross-sections, this has implications for the use of a shaft cross-section to determine the bone-to-air ratio. This result may also apply to apneumatic bones, those that are filled with marrow, which were not studied here, and require more study.

Variation of Pneumaticity in Larger Flying Animals

Larger flying birds consistently have higher pneumaticity than smaller flying birds, and in groups with variable pneumaticity, the largest species always show higher pneumaticity [12], [19]. ASP is also higher in larger animals, as shown by large pterosaurs consistently having higher ASP than birds. This reveals a general trend in flying animals to increase ASP as they become larger. Traditionally, pneumaticity in birds has been attributed to reducing mass by hollowing out the bones, but this is likely to be only one of several possibly entangled factors. Another plausible driver is proposed here. Geometric considerations show that as ASP increases, specific stiffness (stiffness per unit mass) also increases. Young’s Modulus (material stiffness) of bone also increases with increasing density [31] implying that bones with higher density are also more stiff in bending. As bird and bat wing bones may be more dense than equivalent mammal bones (without taking into account the added density from marrow in apneumatic bones) [32], this suggests an evolutionary pressure to increase the stiffness of bones in flying animals. The stiffness of a bone is the result of the Young’s Modulus of the bone, and the shape of its cross-section, with bending stiffness increasing rapidly as the diameter of a bone increases. This leads to a strong new hypothesis: ASP increases with size in flying animals as an adaptation to increase bone bending stiffness related to the pressures of flight. The resulting decrease in bone mass may be a beneficial by-product caused by the decrease in bone volume and loss of marrow that come with pneumaticity.