Shifts in stability and control effectiveness during evolution of Paraves support aerial maneuvering hypotheses for flight origins

Model construction

We constructed models (8 cm snout-vent length, Figs. 1–2) of four extant birds and seven fossil paravians (Xu et al., 2011), encompassing five avialans (Gauthier & Padian, 1985), Microraptor (Xu et al., 2003) and Anchiornis (Hu et al., 2009) (Fig. S1), using 3D printing. Fossils were selected to sample phylogenies available in 2011 (when the work was done), although an eighth paravian, Zhongornis (Gao et al., 2008), was later dropped due to questions about its phylogenetic position and because the specimen was identified to be a juvenile. Additional information regarding the morphology of Microraptor, Jeholornis, and Sapeornis has become available since the measurements were done; the effect of the new information is addressed in the discussion. To explore parallel evolution and for calibration, we also constructed models of three pterosaurs, two bats (Bitbucket), and two artificial test objects (sphere and weather vane) (Fig. 2). Construction methods closely followed those of Koehl, Evangelista & Yang (2011), Evangelista et al. (2014b), Evangelista (2013), Munk (2011) and Zeng (2013). Solid models were developed in Blender (The Blender Foundation, Amsterdam), closely referencing published photographs of fossils and reconstructions from the peer-reviewed literature and casts of Archaeopteryx to match long bone, axial skeleton, and body proportions. Modeling was also guided by Starling (Sturnus vulgaris) dissections, preserved specimens, and vertebrate paleontology and anatomy/functional morphology texts (Benton, 2005; Liem et al., 2000). To create the models, photos of the fossils were imported into Blender and used to guide digital sculpting of a series of 3-D meshes representing the head, torso, tail and limbs of each taxon. Each mesh was constrained to maintain left–right symmetry and stretched in the antero-posterior, dorsoventral, and lateral axes to approximately match the proportions of the fossil or reconstruction. Specific target points used included the length of all limb elements (humerus, radius/ulna, and manus; femur, tibiotarsus, tarsometatarsus, and pes), length of the skull, and distances along the axial skeleton (occipital to pectoral; pectoral to pelvic, and tail) as well as an approximate depth of the ribcage where available. In some cases, some of these targets were estimated. Meshes were provided with holes to accept a 26 gauge armature and mounts for the force sensor (discussed below). This process was used to provide more repeatable and replicable results than hand sculpting by eye with polymer clay (as used in Koehl, Evangelista & Yang, 2011; Evangelista et al., 2014b). Specific species and the corresponding specimen and references include Anchiornis (LPM B00169, Hu et al., 2009), Microraptor (IVPP V13352, Xu et al., 2003), Archaeopteryx (Berlin specimen as reconstructed in Longrich, 2006), Jeholornis (IVPP V13274 and 13553, Zhou, Zhang & Science, 2002; Zhou & Zhang, 2003b), Sapeornis (IVPP V13275, Zhou & Zhang, 2003a), Zhongjianornis (IVPP V15900, Zhou & Li, 2010), and Confuciusornis (Hou et al., 1995; Chiappe et al., 1999; Chiappe et al., 2008). The .STL files used to create the models are available for download to researchers wishing to replicate our models.

Models were printed using a 3D printer (ProJet HD3000; 3D Systems, Rock Hill, SC), then mounted on 26 gauge steel armatures with felt or polymer clay filling in gaps between printed parts where flexibility was needed for repositioning. Wings were constructed using methods described in Koehl, Evangelista & Yang (2011) and Evangelista et al. (2014b). Wings were traced from the published reconstructions in peer-reviewed publications (Hu et al., 2009; Longrich, 2006; Hou et al., 1995; Chiappe et al., 1999; Zhou, Zhang & Science, 2002; Zhou & Zhang, 2003b; Xu et al., 2003; Zhou & Zhang, 2003a; Zhou & Li, 2010), although this procedure was subject to uncertainty in preservation and reconstruction inherent even in work by acknowledged paleontological experts in peer-reviewed publications. Wings were printed on paper and cut. Monofilament stiffening was added along feather rachises and the wings were attached to 26 gauge steel limb and tail armatures (scaled as described above) using surgical tape (3M, St. Paul, MN). Surgical tape was also used where necessary to secure the proximal wing to the body and to repair light damage during testing. This procedure was found in previous work to match more laborious and less repeatable application of manually attached real bird feathers (Koehl, Evangelista & Yang, 2011) for fixed-wing tests.

Models produced in this manner provide an approximation to the general planform but do not replicate specific skeletal elements (via X-ray scanning and 3D printing) as has since become possible; neither the methods nor the fossils were available to us when the work was done. While they may not perfectly mimic real animals, they do allow examination of how shape affects stability and control. Perfect mimicry is not possible for extinct organisms reconstructed from single or a few fossils; such a limitation is inherent in all modeling studies. We suggest that, by using multiple models in a phylogenetic context, we provide more robustness than does the case of a single model (as in all prior work). Also, the use of such techniques is justified based on benchmarking against extant animals and micro air vehicles at high angles of attack (discussed below).

Body posture and appendage position

Fossil paravian models were positioned with wings spread and legs extended back (Xu et al., 2004; Evangelista et al., 2014b) (Figs. 1–3). The aim of this study was to examine maneuvering within several species rather than the posture of one; accordingly we used a legs-back posture seen in extant birds and also reasonably well supported for fossils (Xu et al., 2004; Davis, 2008), with leg feathers where present. While alternative postures have been considered (specifically in Microraptor, as reviewed in Koehl, Evangelista & Yang, 2011; Evangelista et al., 2014b), some may be infeasible, notably sprawled (Xu et al., 2003); others are not observed in extant birds, such as biplane configurations (Chatterjee & Templin, 2007; Alexander et al., 2010) or less extreme sprawled leg positions (Dyke et al., 2013); while legs-down positions (Huynh et al., 2011; Habib et al., 2012; Hall et al., 2012; Dyke et al., 2013; Evangelista et al., 2014b) appear to have very high wing loading compared to alternatives like legs-back.

For control effectiveness, we tested fixed static appendage movements previously identified as being aerodynamically effective (Evangelista et al., 2014b; Evangelista, 2013): asymmetric wing pronation and supination, wing tucking, symmetric wing protraction and retraction, and dorsoventral and lateral movements of the tail (Fig. 3). The angular extent of each movement tested is shown on Fig. 3. To avoid confusion, we present data for specimens as described with all appendages present; artificial manipulations (such as removal of tail and leg surfaces) were discussed in Evangelista et al. (2014b) and Evangelista (2013).

Models were mounted at the estimated center of mass (COM) for the baseline body posture. The estimate was formed in Blender assuming a uniform density for the posed model, as in Allen et al. (2013). While we did not duplicate the same sensitivity analyses as Allen et al. (2013), we recognize that the COM estimate could vary up to 3–5% of the body length, or by smaller amounts for the variable load associated with appendage movements; this uncertainty is usually within the bounds of coefficient estimates identified as marginally stable. All scale models were tested on a sting, zeroed before each measurement, and thus the mass of the model does not affect testing. Mass and wing loading of the organism, while important for estimating speed from lift and drag coefficients, do not directly affect the nondimensional coefficients presented here.

Wind tunnel testing

Wind tunnel testing used previous methods (Evangelista et al., 2014b), with a six-axis sensor (Nano17; ATI, Apex, NC) mounted to a 0.5 inch (12.7 mm ) damped sting exiting the model downwind at the center of mass (Fig. 2). In some measurements, a 2 mm steel extension rod or a 3 mm acrylic plate were used to avoid geometric interferences and to keep the sting several diameters away and downstream of aerodynamic surfaces. The sensor was zeroed immediately before each measurement, eliminating model deadweight effects. Models were tested in an open-circuit Eiffel-type wind tunnel with an 18 × 18 × 36 inch (45.7 × 45.7 × 91.4 cm) working section (Engineering Laboratory Design, Lake City, MN). Testing at 6 m s⁻¹ resulted in a Reynolds number of ∼32,000 for all models, matching full scale for Anchiornis, Archaeopteryx, Sapeornis, Zhongjianornis, and Confuciusornis.

Under the test conditions, the aerodynamic coefficients of interest are reasonably constant with Reynolds number, Re = UL/ν, where L here is the snout-vent length and ν is the kinematic viscosity of air (Evangelista et al., 2014b; Evangelista, 2013). Early in the evolution of animal flight, organisms likely flew at moderate speeds and high angles of attack (Evangelista et al., 2014b; Dyke et al., 2013) where flows appear like bluff body turbulent flows (in which coefficients are largely independent of Re, for 10³ < Re < 10⁶). In previous work (Koehl, Evangelista & Yang, 2011; Evangelista et al., 2014b), we performed a sweep of wind tunnel speed, to examine Re from 30,000 to 70,000, to validate that scale effects were not present.

As additional support for this approach, tests for maneuvering bodies are nearly always tested at well below full scale Re, e.g. the largest US Navy freely-maneuvering model tests are well below $\frac{1}{3}$-scale. Our methods were also previously benchmarked using model tests at full scale Re of gliding frogs (Emerson, Travis & Koehl, 1990; McCay, 2001) (repeated for comparison), Draco lizards, Anna’s Hummingbirds (Calypte anna) in glide and extreme dive pullout maneuvers, hummingbird body shapes in hovering (Sapir & Dudley, 2012), and reduced-scale tests of human skydivers compared to actual data (Cardona et al., 2011; Evangelista et al., 2012); while at Re ∼ 1000, our modeling methods have been benchmarked against extant winged seeds. Perching aerial robots, developed to test control algorithms, have shown good agreement between fully 3D robots and flat plate models with the same planform (Roberts, Cory & Tedrake, 2009; Hoburg & Tedrake, 2009; Tangler & Kucurek, 2005). Results (Evangelista et al., 2014b) for lift and drag coefficients using our method agreed with those for full-scale Microraptor models in the other modeling tests (Dyke et al., 2013; Alexander et al., 2010); our Jeholornis model was at lower Re than Microraptor and is of similar shape.

Sensor readings were recorded at 1000 Hz using a data acquisition card (National Instruments, Austin, TX) (Evangelista et al., 2014b). The sting was mounted to a servo (Hitec USA, Poway, CA) interfaced to a data acquisition computer, using an Arduino microcontroller (SparkFun, Boulder, CO) and specially written code in Python and R (R Core Team, 2014), to automate positioning and measurement of windspeed and whole-body force/torque. Raw measurements were rotated to a frame aligned with the wind tunnel and flow using the combined roll, pitch, and yaw angles by multiplication with three Euler rotation matrices; translation from the sensor to the model COM was also included. Transformed measurements were averaged over a one-minute recording. We then computed non-dimensional force and moment coefficients, static stability coefficients, and control effectiveness (McCay, 2001; Evangelista et al., 2014b; McCormick, 1995). Three series, varying pitch, roll, and yaw, were conducted at 5° increments. Using the automatic sting, we obtained 13,792 measurements, with at least five replicates for 18 models in 247 total positions: generally 5 each in pitch (88 total), 2 each in roll for two angles of attack (69 total), and 3 each in yaw for two angles of attack (92 total). Test positions are indicated in Fig. 3.

Static stability was measured by examining the sign of the slope ∂C_m/∂α (positive slope is unstable, negative stable, zero marginally stable, see Figs. 2B and 5) of the non-dimensional pitching moment coefficient C_m near fixed points as the body was subjected to small deflections dα (Evangelista et al., 2014b; McCay, 2001; McCormick, 1995): (1)${\displaystyle \text{pitching moment }M=0.5\rho U^2{C}_m\lambda S}$ where U is tunnel speed, λ is the snout-vent length, and S is planform area. S accounts for the overall area of the shape (as in lift and drag coefficients), while λ is a length scale needed dimensionally to obtain moments; use of snout-vent length is consistent with other previous work (McCay, 2001; Koehl, Evangelista & Yang, 2011; Evangelista et al., 2014b). Control effectiveness (∂C_m/∂δ, (Etkin & Reid, 1996; McCay, 2001; Evangelista et al., 2014b)) was measured by deflecting appendages (Fig. 3) by an amount dδ and examining the change in pitching moment coefficient. Both are unitless (rad⁻¹). Roll and yaw were similarly calculated from series of varying roll angles or headings, respectively, with the static stability and control effectiveness partial derivatives taken for the roll (0.5ρU²C_rλS) and yaw (0.5ρU²C_yλS) moment coefficients. Stability (eight quantities) was computed for three axes (pitch, roll, and yaw) at low (15°) and high (75°) angle of attack as well as (for pitch only) at 0° and at pitching equilibrium. Control effectiveness (12 quantities) was similarly computed for three axes and at low and high angle of attack for the movements depicted in Fig. 3.

A first-order estimate of maneuvering is obtained from considering the two together and a biomechanical trade-off is apparent: a stable object can resist perturbations from the environment with minimal control effort but will also have difficulty in changing direction (which might be necessary to accomplish aerial righting, navigate in cluttered forests, seek resources or avoid predators) (Smith, 1952; Dudley & Yanoviak, 2011; Taylor & Thomas, 2002). The metrics underestimate maneuvering in very dynamic cases (high advance ratio flapping or where second-order damping terms become important; Sachs, 2005), but are adequate for quasi-static maneuvers. Locomotion is a complex task, and passive stability is often exploited where possible to reduce control effort (Jindrich & Full, 2002; Kubow & Full, 1999; Ting, Blickhan & Full, 1994); conversely, passive instability may be exploited in extreme (and likely elective) maneuvers. The absence of stability, coupled with the presence of large control effectiveness, would suggest the presence of strong closed-loop neuromuscular control. The absence of control effectiveness would suggest a lack of control, as even with feedback an ineffective surface cannot generate the necessary forces and torques. Thus, while the full control abilities of an extinct form are difficult if not impossible to fully enumerate, the simple metrics here provide a useful proxy.

Phylogenetic comparisons

We used the phylogeny shown in Fig. 4A. A Nexus file without branch lengths (bitbucket.org/devangel77b/comparative-peerj-supplemental) was assembled from published phylogenies of the study taxa. For paravians, the strict consensus of Zhou & Li (2010), Li et al. (2010) and O’Connor, Chiappe & Bell (2011) was used, with the family relationships of Cracraft et al. (2004) used to fill in the extant birds. Multiple sources were used because of differences in single species being included, but otherwise sources showed the same topology (reviewed in Turner, Mackovicky & Norell, 2012). While further revisions to the phylogenetic relationships have been discussed (depicted in Fig. 4B), (see Xu et al., 2011; Godefroit et al., 2013; Turner, Mackovicky & Norell, 2012; O’Connor et al., 2013), they do not appear to alter the patterns in stability and control effectiveness; trees from Xu et al. (2011), Godefroit et al. (2013), Turner, Mackovicky & Norell (2012) and O’Connor et al. (2013) are in the .nex file available at bitbucket.org/devangel77b/comparative-peerj-supplemental. Mapping, as outlined in Padian (2001), of discrete maneuvering traits was performed in Mesquite (Maddison & Maddison, 2010) with the built-in ancestral state reconstruction routines using unordered parsimony. The aerodynamic measurements were coded into a matrix giving the aforementioned eight discretized stability values and 12 discretized control effectiveness values. Stability values were coded as stable (slope < 0), marginal (slope = 0), or unstable (slope > 0) based on whether the 75% confidence interval of ∂C/∂α measurements included zero or not. The discretized control effectiveness values were obtained from the measurements by thresholding based on the moment necessary to overcome measured weather vane stability (dC/dδ > 0.09 was coded as effective; <0.09 coded as ineffective), or equivalently, to cause a displacement of the center of aerodynamic pressure of about 10% of total length.

Additional information and new reconstructions

The aerodynamic tests described here were performed in the fall of 2011; since then, more information has become available leading to more detailed reconstructions and phylogenies being proposed (Li et al., 2012; O’Connor et al., 2012; O’Connor et al., 2013; Zheng et al., 2013; Foth, Tischlinger & Rauhut, 2014). While we are not able to perform new measurements, we can theorize about the effect of these newer reconstructions. Foth, Tischlinger & Rauhut (2014) confirmed Longrich’s (2006) finding of leg feathers and does not alter our results. Li et al. (2012) provide a detailed tail reconstruction of Microraptor tail plumage including a graduated tail shape with long, midline feathers; we estimate that this tail morphology may have slightly different values for stability and control effectiveness but the overall presence/absence pattern we observed here would be unchanged. O’Connor et al. (2012) and O’Connor et al. (2013) provide further information on plumage for Jeholornis; while our forewing reconstruction appears adequate, we lack the proximal fan of the “two-tailed” morphology identified in newer specimens. The additional contribution of the proximal fan is hard to estimate and should be considered in future work; however, its forward position suggests a small moment arm and therefore a small effect. This is further supported by the marginal stability and small control effectiveness of unrealistically sprawled legs, which were also near the center of mass, observed in Microraptor models (Evangelista et al., 2014b). Zheng et al. (2013) identify distal leg feathers and a long/broad tail in new specimens of Sapeornis, while Turner, Mackovicky & Norell (2012) revise the position of Sapeornis to be more basal than Jeholornis (see Fig. 4B). As tested, a more basal position for Sapeornis complicates the interpretation of our findings, thus we include a mapping onto such a tree in the .nex file at bitbucket.org/devangel77b/comparative-peerj-supplemental. However, taken together, the additional leg and tail plumage described in Zheng et al. (2013) and the more basal position proposed in Turner, Mackovicky & Norell (2012) and O’Connor et al. (2013) would maintain the patterns we see here, shifting one node earlier in the case of pitch (from node 2 to node 1).

Patterns in longitudinal stability and control

Long-tailed taxa (Fig. 5A) show a stable equilibrium point and the tail is effective in generating pitching moments, whereas short-tailed taxa (Fig. 5B) were unstable and had reduced control effectiveness of the tail. Notably, the same pattern (i.e., downward sloping C_m versus α) is seen consistently in two early representatives of the Avialae, in a long-tailed pterosaur (Rhamphorhynchus), and in the paravian Early Cretaceous dromaeosaur Microraptor, suggesting that these patterns more likely derive from shape and aerodynamics than from immediate ancestry. Similarly, the humped curves of Fig. 5B are consistent between paravians and a short-tailed pterosaur (Pteranodon).

The study taxa show progressive tail loss as well as loss of leg-associated control surfaces along with a concomitant increase in forewing size. Changes in stability and control effectiveness here (as well as manipulations in which appendage surfaces were removed with all else held constant Evangelista et al., 2014b) reflect these morphological changes. In pitch (Fig. 6), taxa shift from being statically stable ancestrally to subsequently being unstable (and thus requiring active control, or possibly damping from flapping counter-torques; Fig. 6A, red line in 6D). Control effectiveness concomitantly migrates from the ancestrally large and feathered tail (Fig. 6B, orange line in 6D) and legs to the increasingly capable forewings (Fig. 6C, yellow line in 6D), which become relatively larger, gain larger muscle attachments and gain skeletal features and stiffness proximally (Benton, 2005; Liem et al., 2000) that would improve production of left–right and fore-aft kinematic asymmetries needed for control. Distally, bone loss, joint fusion and use of ligaments to reduce degrees of freedom (Benton, 2005; Liem et al., 2000) would have enabled mechanical feedback and tuned mechanisms as flapping developed, enabling neuromuscular control effort to be focused on dealing with increasing overall flight instability and active control. Comparative forelimb myology examining extant organisms as well as a basal theropod also support the early presence of limb control via scapular protraction/retraction and pronation/supination (Burch, 2014).

Transition to forewing control co-occurs with a significantly enlarged humeral deltopectoral crest (Zhou & Li, 2010) and occurs amid progressive acquisition of a fully “avian” shoulder morphology (Turner, Mackovicky & Norell, 2012). In addition, the sternum is changing from ossified in Microraptor  through varying degrees of loss (Anchiornis and potentially Archaeopteryx) or ossification without fusion (around nodes 1–2), to ossification, with later fusion (node 3) and development of a carinate keel (node 4) (Zheng et al., in press). Concomitantly, the tail becomes much reduced into a pygostyle (Fig. 6, node 2) with increased mechanical stiffness (Pittman et al., 2013), which, combined would have decreased the moments the tail could produce and eliminated inertial mechanisms. Other synapomorphies appear at node 4 (Fig. 6), including a strut-like coracoid and triosseal canal (Benton, 2005, p 216). Whereas the latter features (node 4) feature in power production, the timing of the former features (nodes 1–2) appears more consistent with enhanced forewing control effectiveness. Ontogenetic tests (Evangelista, 2013; Evangelista et al., 2014a) show 4-day post hatching Chukar Partridge (Alectoris chukar) are capable of extreme maneuvers (rolling and pitching 180°) before strong development of a carinate sternum and before symmetric wingstrokes for WAIR, suggesting this interpretation is correct.

Roll and yaw control at high angle of attack is present early in the lineage

In roll (Fig. 7), taxa were stable at high angles of attack (Fig. 7B), but either unstable or marginally stable at low angles of attack (Fig. 7A). Large asymmetric wing movements (i.e., wing tucking) were always effective in creating substantial rolling moments early, well before development of a power stroke (Fig. 7C). Also, as animals developed the ability to fly at lower angles of attack, active control of roll would have become necessary, perhaps via inertial modes of the tail (only available before node 2) or legs, and later augmented with the forewings as they became larger and more capable of left–right asymmetry during full force production (carinate sternum, node 4). In all axes, the presence of control effectiveness early is contrary to assertions that aerodynamic functions in early and potentially aerial paravians are unimportant (Foth, Tischlinger & Rauhut, 2014). Wing movements with high control effectiveness change during evolution in a manner consistent with predicted shoulder joint mobility (criterion 1 of Gatesy & Baier, 2005). The high control effectiveness of asymmetric wing motions in roll and large inertia of ancestrally long tails echo ontogenetic changes in righting ability observed in young birds (Evangelista et al., 2014a). In maneuvering baby birds, asymmetric wing use occurs before symmetric wing use and precedes wing-assisted incline running (WAIR); the shift echoes the later evolution of symmetric wing protraction control effectiveness, although extant avian ontogenies are not necessarily linked to phylogenetic patterns in maneuvering and control.

In yaw (Fig. 8), most taxa at high angles of attack (Fig. 8A, green line in 8C) were marginally stable as might be expected from symmetry when falling near vertical. Taxa with long tails were also stable at low angle of attack (Fig. 8D, dark blue line in 8G), in agreement with computational predictions for similar shapes (Sachs, 2007). As tails are reduced, yaw stability becomes marginal and control migrates from the tail (Fig. 8E, violet line in 8G) to the wings (Fig. 8F, gray line in 8G). This is similar to what was observed in the pitch axis. Asymmetric wing pronation and supination (Figs. 8B and 8F) was effective in generating yawing moments in all taxa and at high and low angle of attack, suggesting maneuverability in yaw was present ancestrally. As the tail becomes shorter, the yaw axis becomes marginally stable or unstable (node 3), and control effectiveness must migrate (as in pitch control) from the shortening tail to the enlarging forewings. In yaw as in roll, it is possible that a carinate sternum (node 4) enables more capable left–right asymmetry during full force production in extant birds. Increased stiffness of the shortening tail (Pittman et al., 2013) would still have permitted high force production at occasional, critical moments of high angle of attack flight (Fig. 8B), such as during landing.

Stability in roll and yaw change between high and low angles of attack (Figs. 7A and 7B for roll, Figs. 8A and 8D for yaw). At high angle of attack, roll is more stable while at low angle of attack, yaw is initially stable but becomes marginal. As discussed, the control effectiveness of tail and wings also change; asymmetric wing movements are generally effective while the tail’s ability to generate aerodynamic and inertial yawing or rolling moments becomes reduced as tails are lost. The stability and control effectiveness patterns we observed illustrate a control system that works at steep angles in ancestral taxa (it is stable, but with large control effectiveness and tail inertia available), shifting to one optimized for low angles in derived taxa including extant birds (marginal, but with large control effectiveness in wings). The presence of such shifts in all axes is consistent with a transition from high glide angles to lower glide angles, as predicted by an aerial maneuvering hypothesis (Dudley & Yanoviak, 2011); it is inconsistent with a fundamental wing stroke with fixed orientation to gravity, in which angle should not matter.

Maneuvering and the evolution of flight

The findings suggest that the capacity for maneuvering characterized the early stages of flight evolution (Dudley & Yanoviak, 2011), before forewings with a power stroke fully evolved. Although early paravians may have been limited to tight coupling of vertebral and retricial movement (Gatesy & Dial, 1996), overall gross movement of the large tail of early paravians yielded high aerodynamic control effectiveness and the body possessed some degree of stability. Combined with likely dynamic forces and torques generated by either tail whipping at the root (Jusufi et al., 2008; Jusufi et al., 2011; Pittman et al., 2013) or mild asymmetric (Evangelista et al., 2014a) or symmetric forewing flapping (flapping limited by less robust skeletal and feather morphology or porosity), this suggests that early avialans and their ancestors were still capable of controlled aerial behaviors at high angles of attack (Figs. 6–8). Gradual evolution of improved maneuvering ability (increased control effectiveness, reduced stability) via consistent aerodynamic mechanisms is consistent with a continuum of aerial behaviors ranging to full aerial (Dudley & Yanoviak, 2011; criteria 3 and 4 of Gatesy & Baier, 2005). The staggered acquisition of certain morphological characters (e.g., sternum ossification; pygostyle) is consistent with aerial maneuvering evolving in an incremental and continuous manner. Subsequent shifts in control would be consistent with more shallow glides facilitated by incipient wing flapping, which may have served initially in control but then ultimately became the power stroke characteristic of modern birds. Incipient flapping may thus have become elaborated as a control response (Smith, 1952) to instabilities (Fig. 6, node 1; Fig. 8A, node 3; Fig. 8B, node 2) demonstrated here. Body center of mass was migrating forward (Allen et al., 2013), but this is coupled with loss of large posterior surfaces (long tail and leg flight feathers) and coincidence of the wing center with the COM. Active control was thus required as static stability was reduced and eventually lost (Smith, 1952), and associated forewing movements would also have enhanced aerodynamic force production and provided a means for inertial attitude adjustment. Once the transition to wing-mediated maneuverability and control began, larger surfaces and increased musculature would have facilitated dynamic force production for weight offset via the power stroke characteristic of modern birds.

Additional support for maneuvering hypotheses comes from examination of phylogenetically distant taxa. Similar trends may be present in pterosaurs (in pitch, see Fig. 5, Supplemental Information 1; bitbucket.org/devangel77b/comparative-peerj-supplemental), although we only sampled three pterosaurs here. We also tested two bats, but both appeared similar to short-tailed and extant birds (Supplemental Information 1; bitbucket.org/devangel77b/comparative-peerj-supplemental). In planform, Onychonycteris appears superficially similar to extant bats but with a slightly longer tail, and may not be a sufficiently transitional form to observe the same changes seen here. We would predict that an as-yet-undiscovered bat ancestor should possess means of effecting maneuvers such as limb inertias, enlarged tails, patagia with measurable control effectiveness, and some degree of stability at higher angles of attack; we would also predict that baby bats perform aerial maneuvers such as righting via asymmetric wing uses (which were generally effective in roll at high angle of attack), possibly in a manner similar to baby birds (Evangelista et al., 2014a). Beyond birds, bats, and pterosaurs (vertebrate fliers in a very narrow sense), the presence of highly capable aerial control systems in all the other vertebrates that “just glide”, as well as in volant invertebrates such as ants, bristletails, and stick insects, provides further support (Dudley & Yanoviak, 2011; Munk, 2011; Zeng, 2013).