Transitions to and from the air are critical for aerial locomotion and likely shaped the evolution of flying animals. Research on take-off demonstrates that legs generate greater body accelerations compared with wings, and thereby contribute more to initial flight velocity. Here, we explored coordination between wings and legs in two species with different wingbeat styles, and quantified force production of these modules during the final phase of landing. We used the same birds that we had previously studied during take-off: zebra finch (Taeniopygia guttata, N=4) and diamond dove (Geopelia cuneata, N=3). We measured kinematics using high-speed video, aerodynamics using particle image velocimetry, and ground-reaction forces using a perch mounted on a force plate. In contrast with the first three wingbeats of take-off, the final four wingbeats during landing featured ~2 times greater force production. Thus, wings contribute proportionally more to changes in velocity during the last phase of landing compared with the initial phase of take-off. The two species touched down at the same velocity (~1 m s−1), but they exhibited significant differences in the timing of their final wingbeat relative to touchdown. The ratio of average wing force to peak leg force was greater in diamond doves than in zebra finches. Peak ground reaction forces during landing were ~50% of those during take-off, consistent with the birds being motivated to control landing. Likewise, estimations of mechanical energy flux for both species indicate that wings produce 3–10 times more mechanical work within the final wingbeats of flight compared with the kinetic energy of the body absorbed by legs during ground contact.
Landing allows the transition from the air to the ground or other substrate. This phase is fundamental to flight, but is often overlooked in studies compared with take-off or cruising flight. Landing places a unique selective pressure upon aerial animals, because a controlled deceleration and descent must be accomplished to avoid injury (Bonser, 1999; Paskins et al., 2007). Animals that do not decelerate properly risk broken wings or legs, or damaged integument: collisions often lead to mortality (Klem, 1990). Thus, understanding this unique aspect of flight performance where legs and wings must coordinate is important in understanding how animal design relates to the ecology, evolution and biomechanics of birds, and even the engineering of autonomous flying vehicles. Herein, we explored the coordination of force production between both legs and wings during landing in birds.
Several lines of evidence indicate that birds carefully control their landing and generally seek to minimize their kinetic energy at touch-down (Warrick et al., 2002) even if some species are eminently capable of targeting in fast flight [for example, a peregrine falcon stooping on a pigeon at relatively fast speed (Alerstam, 1987)]. During landing, birds modulate both wing and tail kinematics to decelerate prior to arriving at the perch (Berg and Biewener, 2010). The distal muscles of the wing, associated with finer-control of the wing surface, show greater motor-unit recruitment during normal landing and birds are unable to coordinate landing when they cannot use these muscles (Dial, 1992a; Dial, 1992b). Landing also requires the integration of the visuomotor system to target and arrive on a landing site safely. This involves the visual system properly processing the changing distance between the bird and perch, and integrating that with the rate of deceleration (Davies and Green, 1990; Lee et al., 1993). Likewise, processing the perch type contributes to changing the landing technique (Green and Cheng, 1998). Given the need for control, we predicted that birds would land at lower velocities than they use to initiate flight even during routine, non-escape take-off (Tobalske et al., 2004; Provini et al., 2012). Consistent with this prediction, prior measurements of ground reaction forces during take-off and landing show that landing forces are ~30% lower (Bonser and Rayner, 1996). This indicates a primary deceleration is accomplished using the wings before touch-down. Here, we used flow visualization techniques to estimate aerodynamic forces during the final phase of landing and, thereby, directly tested the hypothesis about relative wing contribution.
In the light of recent understanding of the unequal contribution of legs and wings during take-off (Provini et al., 2012), we wanted to quantify the contribution of both legs and wings during landing and explore the differences in landing strategies between species with different wing morphology and body size. We used the same zebra finches (Taeniopygia guttata, Reichenbach 1862) and diamond doves [Geopelia cuneata (Latham 1801)] that we recently studied during take-off (Provini et al., 2012). Zebra finches (12 g, Passeriformes) have rounded, low-aspect ratio wings, while diamond doves (51 g, Columbiformes) have more pointed higher-aspect ratio wings. The two species differ in their wingbeat style and overall flight patterns. We used our previous methods (Provini et al., 2012) to integrate data from wing and body kinematics, ground reaction forces and aerodynamics to improve our understanding of the force transition from the air to the substrate.
Three-dimensional kinematic data of the head and wingtip of birds engaged in descending flight and landing (Fig. 1) showed that body position changed smoothly during the last 12 and the last five wingbeats in zebra finches and diamond doves, respectively. However, the global pattern of the wingbeat trajectory differed from
List of symbols and abbreviations
loop area of wake vortex
horizontal component of the acceleration
vertical component of the acceleration
vortex added-mass coefficient
distance between shed vortices
ground reaction force vector
horizontal component of the aerodynamic force
vertical component of the aerodynamic force
particle image velocimetry
width of wake vortex
full wingbeat duration
self-convection velocity of shed vortices
work per wingbeat
work absorbed by the hindlimbs
final full wingbeat
last but one wingbeat
second to last wingbeat
third to last wingbeat
that of the third to last wingbeat (W−3) in both species; therefore, we considered landing to begin at the onset of W−3.
In both species, the velocity of the body decreased throughout landing (Fig. 2). In zebra finches, horizontal velocity (Vh) decreased from a mean (±s.d.) of 1.3±0.3 m s−1 at the beginning of W−3 to 0.82±0.1 m s−1 at touch-down (TD), whereas vertical velocity (Vv) started at −0.57±0.1 m s−1 and ended at −0.41±0.1 m s−1. Patterns were generally similar in diamond doves, where Vh went from 1.3±0.2 m s−1 at the beginning of W−3 to 0.81±0.2 m s−1 at TD while Vh started at −0.51±0.2 m s−1 and ended at −0.27±0.09 m s−1. Then, velocity decreased more rapidly after TD in both species.
The relative timing of leg extension (LE) and final full wingbeat (W0) differed between species (Fig. 3). During the landing approach, zebra finches started extending their hindlimbs 53±16 ms before TD, which corresponded to the middle of upstroke of the last but one wingbeat (W−1). In diamond doves, LE occurred 137±37 ms before TD, corresponding to the middle downstroke of W−3. In zebra finches, W0 started 19.8±13.3 ms before TD, which was significantly different from TD (t-test: d.f.=14, P<0.0005). In contrast, in doves, W0 started 8±32 ms after TD, which was not significantly different from TD (t-test: d.f.=14, P>0.3).
Differences were apparent between W0 and the preceding wingbeats although the patterns were not consistent between species. For zebra finches, wingbeats W−3 to W−1 were 35±0.6 ms in duration, whereas W0 was only 29±8 ms in duration. In contrast, for diamond doves, mean wingbeat duration for W−3 to W−1 was 70±5 ms, which was less than the duration of W0 (79±5 ms). Downstroke duration in zebra finches corresponded to 54±1.0% of the whole wingbeat duration for W−3 to W−1, whereas downstroke duration decreased to 46.0±0.8% of W0. For diamond doves, downstroke duration corresponded to 49.1±0.9% of the whole wingbeat duration for W−3 to W−1 and increased to 58.8±0.8% for W0 (Fig. 3).
Changes in body angle differed between zebra finches and diamond doves (Fig. 3). In zebra finches, during W−3, body angle was 56±10 deg and was virtually unchanged at TD (58±8 deg) (t-test: d.f.=15, P=0.9), with a peak at 65±12 deg after LE. Thereafter, a transition to lower body angles occurred; when the bird reached immobility, its body angle was 24±5 deg. A distinctly different trend was observed for diamond doves: the body angle in W−3 started at 49±9 deg, increased to 61±13 deg at TD (statistically different, t-test: d.f.=15, P=0.001) and thereafter decreased to 26±7 deg when the diamond doves were motionless.
Force production of the wings
The structure of vortices shed into the wake was complex (Fig. 4), with dispersed vorticity not clearly delineating starting and vortex cores. Moreover, there was intermingling of opposite-sign vorticity in what we interpreted to be the cores, and we consistently observed vorticity near the tail (Fig. 4).
For zebra finches, W0 produced significantly less lift (L) than the previous wingbeats (ANOVA: factor=wingbeat: F1,22=23.41, P<0.0001; factor=individuals: F1,3=0.53, P>0.5) (Fig. 5A). Therefore, L during W0 represented 0.3±0.15 times body weight, whereas it comprised 1.2±0.7 times body weight for W−1, 1.9±0.5 for W−2 and 1.9±0.9 for W−3. The aerodynamic force calculated from the particle image velocimetry (PIV) data produced during W0corresponded to 12.9±3.7% of the previous wingbeats (Fig. 5A). There was no significant difference in aerodynamic forces between W−3 and W−2 (t-test: d.f.=9.59, P=0.9); however, there was a significant difference between W−2 and W−1 (t-test: d.f.=13.4, P=0.003) and between W−3 and W−1 (t-test: d.f.=9.9, P=0.03) (Table 1, Fig. 5A).
For diamond doves, W0 also produced significantly less L than the previous wingbeats (ANOVA: factor=wingbeat: F1,32=19.7, P<0.0001; factor=individuals: F1,2=1.6, P>0.1). Therefore, L during W0 represented 0.2±0.2 times body weight, whereas it comprised 0.6±0.5 times body weight for W−1, 1.1±0.6 for W−2 and 1.2±0.4 for W−3. The aerodynamic force produced during W0 corresponded to 15±3% of the previous wingbeats (Fig. 5B). There was no significant difference between the forces calculated from the PIV data between W−3 and W−2 (t-test: d.f.=9.1, P=0.5) whereas there was a significant difference between W−2 and W−1 (t-test: d.f.=10.7, P=0.01) and between W−3 and W−1 (t-test: d.f.=21.6, P<0.001). The whole-body acceleration was fully supported by the wing forces from W−3 to W−1. At W−1, this whole-body acceleration was no longer constant; instead it started to decrease and was no longer supported by the wing production of lift.
Considering the relevant variables for estimating L (Eqn 1, see Materials and methods; Table 1) the differences distinguishing W0 from the other wingbeats in both species were due to lower circulation (Γ) and smaller area (A) swept by the wings (Table 1). Also, in zebra finches, but not in diamond doves, W0 was relatively shorter in duration (Table 1).
The angle of induced velocity was ~80 deg through landing and did not vary significantly among wingbeats (Table 1; ANOVA: zebra finches: factor=wingbeat: F3,43=0.96, P>0.4; factor=individuals: F1,43=4.8, P>0.3; for diamond doves: factor=wingbeat: F3,58=0.76, P>0.5; factor=individuals: F1,58=1.4, P>0.2). The magnitude of the induced velocity decreased with each wingbeat in zebra finches, from 4.7 m s−1 in W−3 to 2.3 m s−1 in W0; the induced velocity was greatest during W−2 in diamond doves, and decreased with subsequent wingbeats to 3.4 m s−1 in W0.
Our 3D kinematic data allowed the calculation of aerodynamic forces during the approach to calculate the resultant aerodynamic forces (Fig. 5). There were no significant differences between the lift forces calculated from the PIV technique (Fig. 5, yellow) and the resultant aerodynamic forces calculated from the Newton equation using kinematic data (Fig. 5, blue), for W−3 (t-test: zebra finches: d.f.=21.18, P=0.07; diamond doves: d.f.=15, P=0.05), W−2 (t-test: zebra finches: d.f.=10.1, P=0.1; diamond doves: d.f.=23, P=0.05) and W−1 (t-test: zebra finches: d.f.=26.4, P=0.08; diamond doves: d.f.=22, P=0.06). However, there was a difference for W0 (t-test: zebra finches: d.f.=15.6, P=0.04; diamond doves: d.f.=8.1, P<0.01).
Force production of legs
We observed a force peak after TD in both species (Fig. 5), but significant differences occurred between species, in both magnitude and timing. The peak force produced during landing was 0.34±0.1 N on the horizontal component and 0.31±0.1 N on the vertical component in zebra finches and occurred 12±1 ms after TD, compared with 0.56±0.2 N on the horizontal component and 0.72±0.3 N on the vertical component, 22.0±0.9 ms after TD in diamond doves.
There were no significant differences between the forces measured by the force plate (Fig. 5, pink) and the forces deduced from the kinematic data (Fig. 5, blue) (t-test: zebra finches: d.f.=29.4, P=0.8; diamond doves: d.f.=79, P=0.06).
Comparison of wings and legs contribution during landing
Comparison of the aerodynamic forces with the ground reaction forces revealed that there was a significant difference between the forces generated during W−3 to W0 and the forces generated on the force plate during the peak force (t-test: W−3 zebra finches: d.f.=31, P<0.001; diamond doves: d.f.=35.9, P=0.001; W−2 zebra finches: t-test: d.f.=33.0, P<0.001; diamond doves: d.f.=37.7, P<0.001; W−1 zebra finches: t-test: d.f.=31.2, P<0.001; diamond doves: d.f.=35.5, P<0.001; W0 zebra finches: t-test: d.f.=35.2, P<0.001; diamond doves: d.f.=45.3, P<0.001) (Fig. 5).
Mechanical work output per wingbeat was ~37 mJ for W−3 and W−2 in zebra finches and decreased to 16 mJ for W−1. For diamond doves, mechanical work for W−3, W−2 and W−1, respectively, was 223, 258 and 128 mJ. Kinetic energy absorbed by the legs was 6 mJ in zebra finches and 26 mJ in diamond doves. The energy absorbed by the legs was therefore 5±2 times less than the per-wingbeat work performed during W−3 to W−1 in zebra finches and 8±3 times less for the legs compared with the wings in diamond doves.
Our results provide new insight into the transition between the air and land in birds by quantifying the transition from wing forces to leg forces through landing in two species of birds with very different landing strategies. In general, the aerodynamic forces produced by the wings were greater during the final phase of landing compared with the initial phase of take-off, and peak ground reaction forces during landing were lower than during take-off (Provini et al., 2012) (Fig. 5). The pattern of lower ground reaction forces during landing than during take-off has also been reported for starlings (Bonser and Rayner, 1996). Therefore, legs did not dominate changes in velocity during the late phase of landing to the same extent that they did during the beginning of take-off. In landing, the hindlimbs reduced velocity by ~60%, whereas in take-off, the hindlimb contribution was ~95% over similar time scales (three wingbeats) (Provini et al., 2012). Coupled with slightly slower velocity at touchdown during landing compared with take-off velocity at the third wingbeat, these results are consistent with the hypothesis that birds are motivated by safety to carefully control landing (Bonser, 1999; Paskins et al., 2007).
Alternative explanations for the greater relative contribution of wings to landing compared with take-off include (1) the prediction that the diminutive mass of the leg musculature would, in the absence of wing activity, not be capable of absorbing the kinetic energy of the body and (2) the possibility that mechanical work contributing to deceleration for the body requires less metabolic energy from the wing muscles compared with the energy required from the leg muscles during the phase of landing featuring ground contact. We discount both of these alternatives, but they certainly merit further study. First, the kinetic energy at take-off [about 0.023 J for zebra finches and 0.042 J for diamond doves (Provini et al., 2012)] is greater than the kinetic energy at touchdown (about 0.005 J for zebra finches and 0.018 J for diamond doves), and vertebrate muscle is capable of producing more force during active lengthening than during shortening, and is capable of absorbing more negative than positive work (Hill, 1953; LaStayo et al., 2014). Second, we estimate that the rate of change of kinetic energy within a wingbeat in zebra finches varied from about 0.01 to 0.0017 J from W−3 to W−1 and was 0.046 J during ground contact from touch-down to the return to support of body weight, while for diamond doves it was 0.0056 to 0.03 J from W−3 to W−1, and 0.042 J during ground contact from touchdown to the return to support of body weight. Assuming the metabolic efficiency of vertebrate muscle is 25% and −120% during positive and negative work, respectively (Margaria and Margaria, 1976), the metabolic energy devoted to deceleration per wingbeat varied from 18 to 104% of the energy output during ground contact for zebra finches and between 64 and 342% for diamond doves. Thus, the energy can be dissipated more physiologically economically with some but not all wingbeats prior to touch-down.
As in the present effort, our study of take-off (Provini et al., 2012) involved relaxed, volitional flight generally motivated by the wave of a hand in the vicinity of the bird. Motivational state alters the relative contribution of the hindlimbs to take-off velocity in hummingbirds (Tobalske et al., 2004); thus, we anticipate differences in aerodynamic forces in take-off in zebra finches and diamond doves would be more dramatic if escape or agonistic take-off was included for comparison (Tobalske et al., 2004; Jackson and Dial, 2011).
Interestingly, our data have revealed a stereotyped succession of the forelimb and hindlimb use through landing that differs between species. In zebra finches, TD happens after W0. This implies a functional separation between the wings and the legs, with the latter entering into locomotion after the wings are inactive. This observation may be related to the concept of modules (Gatesy and Dial, 1996), with a morphological and functional separation of wings and legs in birds. However, in diamond doves, the bird has already reached the perch when W0 starts. This interesting overlap in the timing of leg extension and wing beating in flight implies that the two modules are not as fully separated in diamond doves as they are in zebra finches. Our two-species comparison is not adequate for testing this idea (Garland and Adolph, 1994), but given the differences in upstroke between zebra finches and diamond doves, future comparative work should seek to explore integration of hindlimb and forelimb modules within phylogenies that include these species (Passeriformes, Columbiformes).
As highlighted above as a major result of our study, wing forces estimated using PIV were greater during landing than during take-off. This was a function of more circulation shed by the wings into the wake rather than aspects of the assumed geometry of the wake, which we made using 3D wing kinematics. Comparing fully airborne wingbeats in landing with those of take-off, circulation was ~1.2 times greater in zebra finches and ~1.3 times greater in diamond doves (Table 1) (Provini et al., 2012). We observed reasonable congruence between aerodynamic forces calculated from the centre of mass kinematics and PIV data for wingbeats other than W0, where estimated forces from PIV was only 30–40% of acceleration measured using kinematics (Fig. 5). The reason for the discrepancy between the two data sets is linked to the overlap of W0 with TD and thus to the transition from aerodynamic forces to ground reaction forces (Eqn 3, Materials and methods).
Comparing landing with take-off (Provini et al., 2012), changes in body angle and the angle of induced velocity were consistent with a ‘body reorientation’ hypothesis wherein induced-velocity (downwash) angles during manoeuvres tracks variations as body angle (Berg and Biewener, 2008; Berg and Biewener, 2010; Ros et al., 2011). During the aerial phase of landing, body angle varied from 50 to 65 deg (Fig. 3) and the angle of induced velocity approached perpendicular to horizontal at ~80 deg. During take-off, both angles were smaller: body angle varied from 20 deg relative to the horizontal at lift-off to 35 deg at W3, and the angle of induced velocity was 60–70 deg in both species during take-off (Provini et al., 2012).
Current understanding of the relative contributions of the forelimb and hindlimb modules to velocity during take-off and landing needs to be placed in the broader context of avian flight. The existing studies of take-off interpret that the legs dominate, and have also focused on at most three wingbeats (Earls, 2000; Tobalske et al., 2004; Provini et al., 2012). Once in the air, changes in velocity are the exclusive domain of the wings, rather than the legs. Exceptions may include birds modulating drag using their legs in some circumstances; for example, for stability in turbulence (Combes and Dudley, 2009). Birds of similar size and phylogeny as the species in our study routinely fly at around 15 m s−1 during migratory flights (Bruderer and Boldt, 2001). Flight speeds between foraging substrates in small woodpeckers (Piciformes, birds that routinely use flap-bounding like the finches) is ~10 m s−1 (Tobalske, 1996). Therefore, the potentially overlooked – yet obvious – conclusion is that, overall, the forelimbs dominate the modulation of velocity in flying birds, and the relative contribution of the legs to transitions between substrates is partly a function of the arbitrary time scale researchers use to delineate the end of take-off or the beginning of landing (Fig. 1). Underscoring this, and helping to account for the significant mass difference between the wing muscles and those of the legs of flying birds, our estimates of mechanical work per wingbeat during W−3 to W−1 of landing were 3–10 times greater than energy absorption by the legs during ground contact.
This study integrates for the first time aerodynamics with kinematics and ground reaction force measurements during the final phase of landing, and revealed that birds appear to control their landing by producing larger wing forces in the final wingbeats prior to touchdown compared with the initial wingbeats during take-off. The hindlimbs nevertheless function significantly in changing velocity during the final phase of landing and are, therefore, critical to the absorption of kinetic energy after touchdown. To improve understanding of how birds modulate velocity when moving in the three vastly different substrates on earth (air, land and water), it will remain important to frame transitions between substrates in the context of sustained locomotion within substrates. In this way, our results will inform future efforts to understand the ecology and evolution of transitions to and from the air.
MATERIALS AND METHODS
Four zebra finches (T. guttata; mean ± s.d. body mass 12.3±0.21 g) and three diamond doves (G. cuneata; 51.0±5.1 g) were purchased from commercial dealers, housed in flight cages, and provided with food and water ad libitum.
The data were obtained with the same experimental protocol as described previously (Provini et al., 2012) other than the direction of bird flight, so we abbreviate our description of our methods here. Kinematics, force and PIV data collection were performed at the Field Research Station in Missoula, MT, USA. The animals were trained to land on a perch at a descent angle of about 45 deg, with a 1 m flight path distance between their take-off and landing perches. All care and experimental procedures were approved by the University of Montana IACUC.
We used four digital high-speed video cameras, including two Photron 1024 PCI, one Photron SA-3 (Photron, Inc., San Diego, CA, USA) and one Phantom MiroEx4 (Vision Research Inc., Wayne, NJ, USA) sampling at 500 Hz with a shutter speed of 200 μs. We focused our analysis upon the final four wingbeats of landing that ended with the bird motionless on the perch. Three-dimensional motion of the wings was used to estimate average aerodynamic force per wingbeat (see below). Measures of whole-body velocity and acceleration were computed using 2D, lateral-view videos obtained from one Photron 1024 PCI camera.
We used a conventional frame of reference (vertical axis pointing upward, horizontal axis in the direction of the forward movement of the animal). The vertical trajectory of tip of the ninth primary was used to define flight phases as it describes a succession of local maxima and minima that match the upstroke/downstroke transition (USDS) and downstroke/upstroke transition (DSUS), respectively.
We classified the wingbeats of landing as described elsewhere (Berg and Biewener, 2010). The last wingbeat amplitude was usually lower than that during the preceding wingbeats and this final wingbeat (W0) led directly to the final repositioning of the wings during perching. The previous three wingbeats were numbered backwards. We measured the onset of leg extension (LE) during flight. Touch-down (TD) was defined as the first contact of the perch by the feet.
Ground reaction forces
The force perch was the same as that used previously (Provini et al., 2012), mounted to a custom-designed Bertec force plate (15×15 cm platform, 200 Hz resonant frequency; Bertec Corp., Columbus, OH, USA). Forces on the Bertec plate were digitally amplified 10 times (Bertec AM6800) and recorded at 500 Hz using Chart software v4.5 (ADInstruments Inc., Colorado Springs, CO, USA) and a Powerlab 8 SP A/D converter (ADInstruments Inc.).
Forces were filtered using a zero phase shift low-pass (50 Hz) Butterworth filter. Because landing implied forces in both directions as well as acceleration and deceleration, it was clearer to work with forces, instead of accelerations. Therefore, unlike in our previous study (Provini et al., 2012), we did not subtract body weight [=body mass (m) × gravitational acceleration (g)] from the force recordings but we used the equation of Newton and included body weight in the equation (see below).
To compare aerodynamics with associated wingbeat kinematics, we used a synchronized high-speed video camera (Photron 1024 PCI) sampling at 500 Hz, located lateral to the animal. Data acquisition and analysis of PIV were performed using a LaVison GmBH (Goettingen, Germany) PIV system running DaVis 7.1 software. See our previous study (Provini et al., 2012) for additional details.
Comparison between data sets
Because of the many simplifying assumptions intrinsic to our estimates of aerodynamic work, and the mixed contribution of W0 and the legs to energy flux during the initial phase of ground contact, the values we report should be interpreted with caution and used only as a general index.
To test for differences in the timing of last downstroke and TD, we used two-way repeated measures ANOVA with time and individual as factors and taking into account the trial repetition and species. We also used two-way repeated measures ANOVA to test for a statistically significant difference between wingbeats (W−3 to W0) for L, the angle magnitude of induced velocity in the wake. Wingbeat and individual were used as factors and the trial repetition was also taken into account for both species. Lastly, t-tests were used to compare data sets coming from kinematic analysis with data sets coming from ground reaction force or aerodynamic analyses. All statistical tests were performed using R package stats version 2.15.0 (R Development Core Team, 2010). Throughout, we report means ± s.d.
We are grateful to Brandon Jackson for his help during the experiments. Thanks to the two anonymous reviewers for their insights and their help in clarification of the manuscript.
This research was supported by grants from the UMR 7179, l'Action Transversale du Muséum National d'Histoire Naturelle formes possibles, formes réalisées and from Ecole Doctorale Frontières du Vivant and Bettencourt-Schueller foundation fellowships as well as the National Science Foundation [grant nos IOS-0923606 and IOS-0919799].
The authors declare no competing financial interests.