Allometric wing growth links parental care to pterosaur giantism

(a) . Allometric analysis

Measurements of 13 key skeletal dimensions were collected for allometric analysis: 1, skull length; 2, neck length; 3, tail length; 4, humerus length; 5, ulna or radius length; 6, wing metacarpal length; 7–10, lengths of WP1–4, respectively; 11, femur length; 12, tibia length; 13, wingspan (= combined length of humerus + ulna/radius + metacarpal IV + WP1–4) × 2.1) [26]. Measurements of Rhamphorhynchus muensteri (sensu Bennett [27]), Pterodactylus antiquus (sensu Bennett [15] and Vidovic & Martill [28]), Sinopterus dongi (sensu Pêgas et al. [29]) and Pteranodon (sensu Bennett [14]) were taken from Hone et al. [16] (88 specimens), Wellnhofer [30] (22 specimens), Pêgas et al. [29] (and references therein; 10 specimens) and Bennett [14,31] (59 specimens), respectively (see electronic supplementary material, data S1 for detailed measurements for each specimen). Measurements of Pteranodon include two species, Pteranodon sternbergi and Pteranodon longiceps, because they do not differ in their postcranial skeletal anatomy [14] and only postcranial measurements are included in this analysis.

Among the specimens with complete preservation of forelimb elements, the wingspan ranges are 0.30–1.28 m for Rhamphorhynchus, 0.19–0.74 m for Pterodactylus, 0.81–2.17 m for Sinopterus and 3.91–6.37 m for Pteranodon. Incomplete preservation of forelimb elements prevents calculation of wingspan. Based on the length of individual elements, however, the wingspan of some incomplete specimens is likely to lie beyond the stated range for each taxon above. This likely difference in wingspan between complete and incomplete specimens is particularly pronounced for Pteranodon, for which most specimens are incomplete. At least five incomplete Pteranodon specimens probably fall below the wingspan range (i.e. less than 3.91 m wingspan) and the smallest (and incomplete) specimen had an estimated wingspan of 1.76 m [31]. Although smaller specimens of Pteranodon (i.e. less than 1.76 m in wingspan) are currently unknown, the available specimens cover a broad range of sizes, allowing investigation of growth allometry.

Measurements for each taxon were subjected to allometric analysis using a multivariate approach of principal components analysis following Yang et al. [17] (see electronic supplementary material for details); skeletal dimensions with no available data were not included in the analysis. Growth allometry of anurognathids was taken from Yang et al. [17] for comparison and for subsequent ontogenetic reconstruction of wing planforms.

(b) . Ontogenetic reconstruction of wing planforms

Results on growth allometry enabled us to extrapolate skeletal dimensions at various wingspans in growth and at hypothetical larger sizes (i.e. beyond actual adult sizes), by using the following equation:

Y₁ and Y₂ are dimensions of a skeletal element (e.g. humerus length, ulna length, etc.) at wingspans Z₁ and Z₂, respectively; b_y and b_z are allometric coefficients of the skeletal dimension and wingspan, respectively. Specimen-based measurements were used for Y₁ and Z₁, based on which Y₂ was extrapolated at wingspans from 0.3 to 7 m. The specimens used were SMNS 81928 [32], Wellnhofer 1975 #20, Wellnhofer 1970 #1, IVPP V 13363 and AMNH 6158 (electronic supplementary material, data S1) for anurognathids, Rhamphorhynchus, Pterodactylus, Sinopterus and Pteranodon, respectively. In order to define trunk sizes, we extrapolated the distance between humeral head and body midline (L1), the distance between femoral head and body midline (L2) and the distance between forelimb and hindlimb attachments along the midline (L3) (figure 1); these three dimensions were calculated by assuming isometric growth. In addition, WP3–4 were treated as a single dimension (i.e. using the combined length and the average posture of the two bones) for anurognathids following Yang et al. [17], because the presence of WP4 in juvenile Anurognathus remains controversial [33].

Forelimb postures of anurognathids and Rhamphorhynchus were modelled using the wing reconstructions in [34]. For Pteranodon, we used the forelimb posture in [35] as the anterior sweep position is more aerodynamic whereby the centre of mass and centre of pressure coincide. To date, reconstructions of the wing of Sinopterus do not consider aerodynamics; we modelled its posture based on the tapejarid Tupuxuara [34]. Because Tupuxuara and Pterodactylus have similar positions of centre of mass and wing centroid to those in Pteranodon [34], we applied the Pteranodon forelimb posture to both Sinopterus and Pterodactylus.

Two extreme positions are proposed for hindlimbs in previous pterosaur reconstructions: (i) hindlimbs extended directly posteriorly (‘straight-legged’ model) and (ii) femur extended laterally and tibia posteriorly (‘bat-like’ model) [36]. Padian et al. [36] argued that neither model is realistic owing to the range of motion at hindlimb joints and thus intermediate hindlimb positions (as used in most recent studies) are more likely. Here we oriented the femur at 45° to the acetabulum and the tibia, parallel to the body midline (figure 1).

We used an ankle attachment for the trailing edge of the main wing membrane (i.e. the brachiopatagium; as in [37]). Since the curvature of the trailing edge remains unclear, the trailing edge was defined using the same method for all five pterosaur taxa to prevent artificially imposed variations. It was taken as a Bézier curve, which was mathematically defined by four control points (P0–P3 in figure 1). P1 and P2 define the curvature; P0 and P3 define the ends of the curve located at the distal termini of tibia and wing finger, respectively. P1 was placed at the intersection of two lines oriented at 30° to tibia and the distalmost phalanx of the wing finger, respectively; P2 was placed at the same position as P3 (figure 1). Uropatagium reconstructions for basal and pterodactyloid pterosaurs follow those of Witton [38].

Wing planform changes during growth from 0.3 to 7 m wingspan were then modelled based on the extrapolated dimensions, limb postures and wing membrane definitions. The area of the resultant wing planform was measured using the image processing freeware ImageJ (available at http://rsbweb.nih.gov/ij/); wing area was calculated as twice the measured area for a single wing. Wing aspect ratio was then calculated as wingspan²/wing area.

We also modelled the wing planforms using a neutral posture to test the effects of taxonomic variation in posture on our aerodynamic models. The neutral posture is the average limb posture of the five pterosaurs; each pterosaur has the same pose with the leading edge fundamentally perpendicular to the long axis of the body (electronic supplementary material, figure S2).

(c) . Flight performance calculations

Following the methods outlined in Venditti et al. [12], performance of powered and gliding flight at wingspans from 0.3 to 7 m was estimated for each pterosaur via an actuator-disc-based biophysical model. Unlike Venditti et al. [12], who used a modified version of Pennycuick's [39] flight model, we used the ‘afpt’ package [40] in R v. 4.1.2, because ‘afpt’ is readily accessible and it was also developed from, and provides more accurate estimations [40] than, Pennycuick's [39] flight model.

Flight performance was estimated using body mass, wingspan and wing area. There is a significant positive correlation between pterosaur body mass and wingspan, but previous studies using different approaches have yielded different scaling equations for body mass estimation. For comparison, here we used the equations recovered by two different approaches (by Witton [38] and Henderson [34], respectively) and generated two sets of body mass estimations for subsequent aerodynamic modelling. The equations are M_{non-pterodactyloid pterosaurs} = 0.681 × wingspan^2.807 and M_{pterodactyloids} = 0.519 × wingspan^2.550 [38] and M_{non-pterodactyloid pterosaurs} = 0.3 × wingspan^2.74 and M_{pterodactyloids} = 0.315 × wingspan^2.56 [34], where M is body mass (kg). Wing loading was calculated as M/wing area (kg m⁻²).

The model produced a U-shaped power-to-airspeed relationship from which a minimum power speed (V_mp) can be calculated, that is, the least energetically expensive flight speed. The model also estimated the total aerodynamic drag (D), resulting from the addition of the induced, parasite and profile drags. Following Venditti et al. [12], two indices of flight performance were calculated. The first index is the efficiency of flight (kg m J⁻¹), which is the inverse of the cost of transport (COT⁻¹); the COT is the metabolic energy required to move a unit mass a unit distance at the least energetically expensive travel speed. The efficiency of flight index was calculated as (V_mp × M)/P_BMR, where P_BMR was estimated as 3.277M^0.624 (J s⁻¹). The second index is the sinking rate V_z (m s^–1), which is the speed of altitude loss during gliding; it was calculated as D × V_mp/M × g, where g is the gravitational acceleration, equal to 9.81 m s⁻². An additional index, glide ratio, was calculated as the ratio of forward speed to sinking rate; it is a measure of the gain in forward advance given the loss in altitude [39] and therefore was used here as an indicator for gliding performance.

To test whether the ontogenies of the five pterosaur taxa are significantly different in terms of powered and gliding flight performance, a pair-wise permutation test was performed for COT⁻¹ and glide ratio, respectively. We used the symmetry_test function in the R package ‘coin’ [41], which treats the index values, at each wingspan, and for both of the paired pterosaur taxa, as paired data. Flight performance between taxa was considered as different at the 0.05 significance level; otherwise, a comparable level of performance was assumed.

(a) . Growth allometry of limb elements

Allometric analysis reveals a unique growth pattern for each pterosaur (figure 2 and table 1; electronic supplementary material, table S1). Despite this, there are common growth trajectories shared by the smaller-bodied pterosaurs (i.e. anurognathids, Rhamphorhynchus, Pterodactylus and Sinopterus) that contrast with Pteranodon. Among the smaller-bodied pterosaurs, the proximal portion of the forelimb shows overall negative allometric growth, which is the combined effect of negative allometry in the humerus and ulna/radius and negative allometry or isometry in metacarpal IV; on the other hand, Pteranodon shows positive allometry in all of these elements. A similar contrast is also seen in the hindlimb, where the femur shows either negative allometry or isometry in most smaller-bodied pterosaurs but positive allometry in Pteranodon; the only exception of the smaller-bodied pterosaurs is Sinopterus, which also shows positive allometry in the femur.

The allometric growth patterns (figure 2 and table 1; electronic supplementary material, table S1) recovered by our multivariate approach are consistent with previous reports of allometry that used bivariate methods. These reports conclude that: (i) the ontogeny of Rhamphorhynchus shows near-isometry in wingspan, negative allometry in humerus, radius and metacarpal IV and positive allometry in WP2–3 relative to body length [16]; (ii) large specimens of Pterodactylus have significantly longer necks and skulls, and the metacarpal IV and proximal wing phalanges show positive allometry relative to the antebrachium and to distal wing phalanges [15]; (iii) sinopterine pterosaurs share isometry in the ulna, metacarpal IV and WP1–2, and positive allometry in the femur [29]; and (iv) Pteranodon shows negative allometry in tibia relative to femur and positive allometry in metacarpal IV relative to radius/ulna and to WP1 [14].

(b) . Ontogeny of wing planforms

Based on the recovered allometric growth patterns, wing planforms were reconstructed for each pterosaur during growth from an early juvenile of 0.3 m wingspan to a (hypothetical for non-pterodactyloid pterosaurs, Pterodactylus and Sinopterus) giant adult of 7 m wingspan. Using taxon-specific postures (see electronic supplementary material, figure S1 for individual wing planforms reconstructed), Pteranodon shows the greatest change in wing shape, with aspect ratio increasing from 10.40 to 16.67 (figure 3a; electronic supplementary material, table S2). Sinopterus also shows striking change in wing shape, but with an overall decrease (from 14.75 to 10.23) in wing aspect ratio. The other smaller-bodied pterosaurs, in contrast, show smaller changes in wing aspect ratio during growth, including relatively consistent values in anurognathids and Rhamphorhynchus (with ranges of 8.70–9.51 and 11.36–11.82, respectively) and a decrease (from 9.30 to 6.74) in Pterodactylus. Wing areas for all five taxa are similar at small wingspans, but diverge during growth, with Pteranodon showing the smallest increase in wing area (figure 3b). Wing planform reconstructions using the neutral posture (electronic supplementary material, figure S2) yielded different results, but show similar trends of ontogenetic changes in both wing aspect ratio and area (electronic supplementary material, figure S3a,b and table S3).

(c) . Ontogeny of flight performance

Based on the scaling equations of wingspan and body mass by Witton [38] and those by Henderson [34], two sets of body mass estimation were generated (figure 3c,d; electronic supplementary material, tables S4 and S7). Both methods predict that non-pterodactyloid pterosaurs were heavier than pterodactyloids for a given body size and that this difference becomes progressively more pronounced during growth (figure 3c,d). Equations by Witton [38], however, predict greater values for, and greater differences between, body masses for the two pterosaur groups. As a result, there is little overlap between the two pterosaur groups in wing loading at wingspans >2 m, with non-pterodactyloid pterosaurs being generally more heavy-loaded, irrespective of limb postures (figure 3e; electronic supplementary material, figure S3c). Estimations based on Henderson [34], however, place the non-pterodactyloid pterosaurs in the wing loading range of the pterodactyloids at wingspans >2 m (using taxon-specific postures; figure 3f) or nearly so (using the neutral posture; electronic supplementary material, figure S3d). Nevertheless, all models indicate increasing wing loading during growth for all five pterosaurs, caused by (near-)isometry or negative allometry in many wing elements (figure 2) and therefore a slower increase of wing area than the cubic increase of body mass.

Aerodynamic modelling based on taxon-specific postures reveals increasing flight efficiency (COT⁻¹) and better gliding performance (based on the increasing glide ratio) during growth for all five pterosaurs (figure 3g–l; electronic supplementary material, table S4). The somewhat counterintuitive increase in glide ratio despite an increase in sinking rate reflects a faster rate of increase for forward gliding speed than sinking rate, although they both increase with wing loading [39]. As a result, although a gliding adult loses height more rapidly than a juvenile, it glides at a faster speed and therefore can travel a greater distance (i.e. better gliding performance) than the latter. The estimated glide ratios are higher than those for extant tetrapod gliders (glide ratio ca 2–4.7) [25]: young pterosaur juveniles are similar to birds of prey (glide ratio ca 10–15) [43], but during growth pterosaurs become more comparable to oceanic birds (glide ratio ca 13.8–25.1) [44].

These models did not indicate superior flight performance in Pteranodon compared with the smaller-bodied pterosaurs in either flight efficiency or gliding performance, irrespective of body mass estimation method. Rather, the models predict a flight efficiency for Pteranodon lower than or comparable to those of non-pterodactyloid pterosaurs (figure 3g,h; electronic supplementary material, table S5). In particular, for small wingspans (where wing planform is not hypothetical for each of the smaller-bodied pterosaurs), flight efficiencies are similar for all five taxa. In terms of gliding performance, the model based on Witton [38] estimates Pteranodon having a glide ratio higher than Rhamphorhynchus but lower than Pterodactylus at all wingspans, lower than Sinopterus at wingspans >2 m (figure 3k) and comparable to anurognathids (electronic supplementary material, table S6). By contrast, the model based on Henderson [34] estimates a comparable glide ratio for Pteranodon and smaller-bodied pterosaurs (figure 3l; electronic supplementary material, table S6).

Aerodynamic modelling using the neutral posture produced consistent results. All aerodynamic indices are associated with similar ontogenetic trends to those based on taxon-specific postures (electronic supplementary material, figure S3). Critically, for both flight efficiency and glide ratio, Pteranodon either falls in the range for the smaller taxa or is not significantly different from any of the latter (electronic supplementary material, figure S3 and tables S7–S9).

(a) . No support for linking the giant size of Pteranodon with its wing aerodynamics

Based on the allometric growth patterns (figure 2), we reconstructed wing planforms and tested the hypothesis that juvenile Pteranodon had an aerodynamically superior wing planform and thus higher flight efficiency and/or better gliding performance that allowed further growth than taxa with smaller adult sizes. Our results do not support this hypothesis. For both flight efficiency and glide ratio, Pteranodon either falls in the range for the smaller taxa or is not significantly different from members of the latter at the same wingspans, regardless of body mass estimation method and (taxon-specific versus neutral) limb posture. Further, our aerodynamic models reveal similar ontogenetic changes in all five taxa, i.e. increasing flight efficiency and gliding performance with growth. Increasing flight efficiency with growth is expected, because COT⁻¹ correlates with mass for various types of locomotion (including running, flight and swimming), and it is energetically cheaper for a large animal to move a given mass over a particular distance than for a small animal to travel the same distance [45,46]. In terms of gliding performance, all five pterosaurs show increasing glide ratio despite an increasing sinking rate. This indicates that adults lose height more rapidly than juveniles during gliding, but the adults glide at a much faster forward speed and thereby travel further than juveniles.

Body mass estimation for pterosaurs has been notoriously problematic (see [34] for a detailed review) and we show that different body mass estimates can alter various aerodynamic indices (figure 3e–l; electronic supplementary material, figure S3c–f). Critically, while both Witton [38] and Henderson [34] predict that non-pterodactyloid pterosaurs were heavier than pterodactyloids of the same sizes, which is sensible given the more extensive pneumatization and tail reduction in the latter group [47,48], the two methods differ considerably in predicting mass differences. This appears to have a broad impact on the estimation of flight performance—a smaller body mass difference (predicted by Henderson [34]) results in less ontogenetic divergence among the five taxa in flight efficiency, sinking rate and glide ratio (figure 3; electronic supplementary material, figure S3). This uncertainty in body mass estimation, however, probably has limited impact on our conclusion that Pteranodon had a comparable level of aerodynamic performance to the smaller taxa. This is because (i) our models using either body mass estimation method yielded consistent results, (ii) it is unlikely for the body mass difference between non-pterodactyloid pterosaurs and pterodactyloids to be larger than that predicted by Witton [38] (who predicts that non-pterodactyloid pterosaurs were more than twice as heavy as pterodactyloids at 7 m wingspan), and (iii) if the actual body mass difference between the two pterosaur groups was smaller than predicted by Henderson [34], the ontogenetic divergence in flight performance should be even less between Pteranodon and other pterosaurs.

Different limb postures can also alter aerodynamics by changing wing morphology [35,36], as demonstrated by the differences in wing planforms (electronic supplementary material, figures S1 and S2) and aerodynamic estimations (figure 3; electronic supplementary material, figure S3) between the models using taxon-specific and neutral postures. Given that the taxon-specific postures are more accurate/natural as they are aerodynamically more balanced (see Material and methods) than the neutral posture, the consistency between the models suggests that deviation from the natural postures may have a limited impact on our conclusion.

It should be noted that our aerodynamic models were simplified by design to accommodate available fossil data, as in previous studies on pterosaur flight (e.g. [12,25]). We advise caution in interpreting these results because many aspects of pterosaur anatomy remain unclear. These include (but are not limited to) plumage [49,50], muscular wing–body junctions [51], trailing edges of the wing membranes, and the morphology and function of the pro- and uropatagium [37], material properties that relate to shape changes under load [35], and metrics that relate to three-dimensional wing morphology, such as camber of the wing membrane and of the wing bone [52], location of the wing bone relative to the lifting surface [52] and skeletal–muscular configuration of the shoulder girdle [53]. These aspects, however, either are rarely preserved or cannot be determined for fossils and may vary between taxa (e.g. anurognathids had distinct wing fingers capable of flexion at all joints [33]) and even within an individual over its ontogeny (e.g. use of different gaits at different body sizes). These unknowns also prevent further quantification of many other aerodynamic indices than studied here; for instance, quantification of agility and manoeuvrability would require a detailed characterization of inertial properties [54]. In addition, wing planform and flight performance could be highly dynamic, as modern birds use in-flight wing morphing for transition between stable and unstable states and thereby dynamically trade between flight efficiency and manoeuvrability [54]. This would certainly have been possible in pterosaurs given the muscle fascia layer in the wing membranes and the ability to move both the fore- and hindlimbs at various joints [1,55].

Nevertheless, we argue that the available evidence suggests that Pteranodon had comparable level of aerodynamic performance to the small taxa at similar wingspans. The dramatic increase in wing loading with growth, observed here in pterosaurs representing diverse lineages and wing planforms, was likely a universal theme for pterosaur ontogeny. Indeed, similar wing shapes between juveniles and adults have been reported in many pterosaurs (e.g. [7,8,16,17,25]), suggesting (near-)isometric wing growth that is much slower than the cubic growth of body mass. Consequently, juveniles would have had low wing loadings that promoted slow, manoeuvrable flapping flight, whereas the heavier adults would have had improved gliding performance (via higher glide speed and stability in high wind conditions) and higher flight efficiency [11,39,45,46]. This confirms previous inferences of different flight behaviours in juveniles and adults of Rhamphorhynchus [16]; similar flight performance changes during growth have also been inferred for the pterodactyloids Sinopterus and Pterodaustro [25].

(b) . Precocial–altricial growth strategy and its link to pterosaur body size

Pteranodon shows a unique growth pattern that hints at a different developmental strategy from that of the smaller-bodied pterosaurs. Among the smaller-bodied pterosaurs, all four taxa show negative allometry or isometry in the proximal elements of forelimbs and three taxa show this feature in hindlimbs, whereas positive allometry was detected in the proximal elements of both fore- and hindlimbs of Pteranodon (figure 2). This indicates differential growth rates in these limb elements and possibly the associated major muscle groups, as observed in developing birds [23,24]. In modern endotherms (birds and mammals), there is a physiological trade-off between growth rate and functional maturity of tissues owing to their overall high growth rate [21,56,57]. This leads to the precocial–altricial developmental spectrum, that is, the high–low degree of functional maturity at hatching (or birth) coupled with low–high postnatal growth rates and negative/isometric–positive growth allometry in locomotors [21–23].

Similar trade-offs between growth rate and functional maturity may have also regulated pterosaur ontogeny, since several independent lines of evidence indicate that pterosaurs had high growth rates that were comparable to those of known endotherms [58–60]. The observed divergent growth trajectories in the proximal elements of both forelimbs and hindlimbs, which are critical elements for powering both flight and terrestrial locomotion, may thus reflect precocial development in the smaller-bodied pterosaurs and more altricial development in Pteranodon. Indeed, in line with the interpreted precociality, early juveniles of anurognathids and hatchlings of Sinopterus had considerably high bone strength for the humerus [25,61]; ontogenetic changes in the food-gathering apparatus of Rhamphorhynchus and Pterodactylus, including changing tooth morphology in the former and positive allometric growth in the skull and neck length in both taxa (electronic supplementary material, table S2), suggest that precocial juveniles may have fed on prey different from that of adults [1,15].

The interpreted altricial development of Pteranodon is consistent with our finding that its wing planform is not aerodynamically superior in growth to the smaller-bodied pterosaurs. If the reverse is true, that is, early juveniles of Pteranodon had an aerodynamically superior wing planform, it would be reasonable to expect their wings to be as functional, with a similar (if not higher) degree of precociality, as in the smaller-bodied pterosaurs; instead, Pteranodon is more altricial. The detected altricial signal for Pteranodon, however, does not necessarily preclude its flight capability relatively early in growth. Indeed, the elongated wing morphology is evidently present in the smallest specimen, with an estimated wingspan of 1.76 m [31], and according to our results (figure 2; electronic supplementary material, figure S1), may have also been present in smaller individuals, possibly a remnant heritage from its precocial ancestors. This contrasts with altricial birds and bats, which attain their large, functional wings only at, or close to, adult sizes [23,62,63]. Further, given the low wing loading of early juveniles, their bone density would need to be considerably lower to reduce wing bone strength to levels impossible for flight [25,64]. Early juveniles of Pteranodon therefore may have been facultative flyers that employed only occasional flights to maintain a low tissue maturity and a high growth rate, as seen in some juvenile birds today [65].

It should be noted that the interpreted altricial development of Pteranodon is based on the assumption that the recovered positive allometric growth in Pteranodon can be extrapolated to smaller juveniles (less than 1.76 m wingspan) for which no fossils are currently available. The alternative to this assumption is that small juveniles of Pteranodon grew differently from their older counterparts; they might have been precocial like the smaller taxa, having well-developed (and functional) limbs at hatching with isometric/negative allometric growth in early ontogenetic stages and then shifted to the observed positive allometric growth at later stages. This, however, would have required a physiological switch from high to low tissue maturity in the proximal elements of both forelimbs and hindlimbs, which is currently unknown in modern animals [57], and it is unclear whether it is physiologically possible. We therefore consider it more likely that the detected altricial signal can be extrapolated to early ontogenetic stages of Pteranodon, although growth rates (and coefficients of growth allometry) may have been heterochronic, possibly with the fastest growth occurring in early ontogenetic stages.

(Super-)precocial flight has been suggested for many pterosaurs of diverse clades [1,7,8,25] and may represent the plesiomorphic condition in pterosaurs. This condition in turn may have posed constraining effects on adult sizes of early pterosaurs. Precocial locomotion has often evolved in response to high predation rates on relatively vulnerable juveniles [66–68]; for pterosaurs, the juveniles may have also suffered from high rates of flight accidents [69]. The high risk of mortality in juveniles might have favoured selection for a shortened period of this vulnerable stage and early termination of growth and thereby constrained adult sizes [21,70]. Also, given the physiological trade-off between growth rate and maturity, precocial development could have induced ontogenetic canalization, that is, retention of juvenile phenotypes into adulthood [23,71], including a relatively small body size.

By contrast, post-hatching parental care in altricial species would reduce the risk of mortality in juveniles [72]; it would also relieve the mechanical demand in juveniles by providing protection and/or food, and thereby facilitate bypassing the potential effects of ontogenetic canalization [23]. Although evidence for specific modes of parental care in pterosaurs is lacking, the detection of an altricial signal in the development of the limb elements that were critical for powering both flight and terrestrial locomotion implies an enhanced level of parental care in Pteranodon compared with the smaller-bodied pterosaurs. This may have been the key innovation by Pteranodon, and by extension, perhaps other giant pterosaurs, to break the body size constraints on their precocial counterparts. By allowing further morphological departure from the juvenile condition [23], altriciality might have enabled development of the derived flight anatomies seen in giant pterosaurs, such as enlarged developed notaria, enlarged deltopectoral crest, robust joints and more extensive pneumatization and lightening of the skeleton [10,47,48,73].

Our proposed altricial developmental strategy for giant pterosaurs is an intrinsic factor that can explain growth to larger sizes. The extrinsic factor, i.e. the availability of ecological niches suitable for large-bodied pterosaurs, is also critical. All giant pterosaurs probably preferred soaring conditions where atmospheric movements can be exploited [10]. For instance, it is widely accepted that Pteranodon was a dynamic soarer living in open marine settings, gliding long distances through exploitation of updrafts and wind currents [10,38], whereas Quetzalcoatlus was likely a static soarer adapted for thermal soaring in terrestrial environments [10]. Giant pterosaurs would have also preferred open environments (e.g. coastal, pelagic environments or inland but without dense forests), given their large sizes (even on the ground with wings folded), thin-walled wing bones vulnerable to impacts [1,5,74] and overall high flight speed and low manoeuvrability due to their high wing loading [11,39]. Critically, there seems to be a general lack of competition with and/or predation on the giant pterosaurs in these environments [1–3,75]; this vacancy would have set the stage for the emergence of giant pterosaurs, expediting their invasion to large-bodied niches.