Drosophila strains

Flies were raised at 25 °C on standard Drosophila cornmeal-molasses medium. RNAi lines directed against the CG43146 locus, corresponding to narrow, were obtained from the Vienna Drosophila RNAi Centre (VDRC). The three lines used in this study (v12800, v50712 and v49678, corresponding to the genotypes N800, N512 and N678, respectively) were driven with the Gal4/UAS system33, and expression was restricted to the developing wing with the nubbin-Gal4 (nub-Gal4) driver20. The UAS-His2ADsRed reporter used to analyse the expression pattern of nub-Gal4 was obtained from the Bloomington Stock Center.

Because the Gal4-UAS system is bipartite and requires a cross to unite the Gal4 and UAS constructs in a single fly, rather than performing the experiments in a pure isogenic background, we opted for a heterozygote between two isogenic strains. The RNAi lines were generated in an isogenic w1118 background34, and the nub-Gal4 insertion was introgressed into an isogenic Oregon R background. To generate the flies with different wing planforms, the nub-Gal4 strain was crossed to each of the three RNAi lines of the genotype w1118; UAS=CG*RNAi, and females of the genotype w1118/+; nub-Gal4/UAS=CG*RNAi, fully heterozygous for all chromosomes, were used in the experiment.

To control for the health and age of the flies, five independent crosses of five w1118; UAS=RNAi* males to eight nub-Gal4 virgin females were made in vials and transferred daily to prevent crowding. Two days after the first flies had begun to eclose, the female progeny of the appropriate genotype were collected and placed into clean vials sprinkled with yeast. Flies were transferred daily into new vials until they were flight tested. All flights were made between 4 and 12 days after eclosion.

Wing mounting

After completion of the flight experiments, flies were preserved in Isopropanol (Fisher). The wings were then dissected from the body and mounted in DPX mounting medium (Fisher) and photographed (Zeiss Axiophot: 2,592 × 1,944 pixels). Wing images were then analysed using two methods to describe variation in their shapes.

Traditional morphometrics

We used custom written software (Matlab, Mathworks, MA, USA) to determine gross morphological variables using the wing margin. The start point was the anterior end of the humeral cross vein; the end point was identified as the junction between the alula and the posterior margin. Finally, the wing tip was identified as the terminus of radial vein L3. The wing outline was used to estimate wing area and aspect ratio. In this standardized procedure, the alula was not included in wing area estimates.

Geometric morphometrics

Fifteen landmarks were digitized from wing images using the Fly Wing Kit plug-in for ImageJ provided by C. Klingenberg (Fig. 1) and geometric morphometric analyses were performed using MorphoJ35. Shape information for each genotype was extracted by Procrustes superimposition and outliers removed. Data for the different genotypes were then combined and a covariance matrix was generated that was used in a principal component analysis to quantify shape change.

Trajectory data acquisition

We recorded self-motivated flights in a calibrated arena measuring 2 × 2 × 1.8 m (c.1,000 body lengths in each dimension) with a pair of synchronized, high-speed, CMOS cameras operating at 500 fps (Photron Fastcam SA3, Photron Europe Ltd, Bucks, UK). The flies were chilled on ice for ∼20 s then weighed (UMX2 ultra-microbalance; Mettler-Toledo, Leicester, UK) and allowed 30 min to recover. The arena was illuminated with DC lights (Arri CT limited, Middlesex, UK; Unomat International, Germany) and one netted wall provided camera access and visual cues for the flies in the form of equipment and furniture. Additional high contrast visual information came from a monochrome calibration grid (14 × 14 large dots; 59 mm spacing) laid on the floor.

The vials were opened 0.1 m above the grid; the flies then climbed to the rim and took off voluntarily. Flies tended towards the side of the arena with the greatest visual information so, to maximize the length of recorded sequences, take-off location was close to the back of the arena. Thus, flight trajectories tend to be largely upward and forward within the arena although we also captured downward flight and many turns. For each genotype, we aimed to record five flights from at least 20 flies of each phenotype. Flies that did not reach the top of the vial or who failed to take off after five minutes on two successive trials were discarded. In total we gathered c. 8.8 min of flight, which sampled the fly genotypes sufficiently for subsequent analysis (see Supplementary Fig. 4 for example histograms).

Trajectory data processing

We used photogrammetry to reconstruct 3D trajectories as described elsewhere14,36. The following describes the salient features of the method and any modifications. The reader is referred to ref. 14 for further detail. First, we calibrated the volume with multiple images (c. 35) of a grid of known dimensions to minimize the reprojected pixel error using a bundle adjustment nonlinear least squares optimization routine14,36. The modal reprojected pixel error of the calibrations averaged 0.76 pixels. This resulted in a calibration matrix required for the next stage. The next step in the procedure used custom point tracking code (Matlab, Mathworks, MA, USA) to identify the two-dimensional co-ordinates of the fly in each camera view. These data were used in conjunction with the calibration matrix to reconstruct the 3D fly positions at each time interval. A quintic spline was fitted to the x, y and z co-ordinates so that differentiation would yield an analytical solution for velocity and acceleration. The smoothing tolerance was calculated from the residuals of a third-order Butterworth filter. The tolerance factor for SPAPS was 1.1 × the sum of the filter residuals squared. The initial Butterworth cut off frequency of 30 Hz was selected by an autocorrelation method described previously that evaluates autocorrelation in the residuals compared with autocorrelation of the residuals from white noise filtered in the same way14. The data were padded at the start and end points using reflection around the boundary point to reduce errors at the start and end of the data series. We tested the procedure by dropping an object of comparable dimensions to the fly in the centre and at four extremities of the calibrated volume and subsequently compared the calculated acceleration with standard gravity, g. The mean acceleration of the ball immediately after release was calculated to be 9.730 ±0.070 ms−2: an error of 0.78%.

Wingbeat frequency acquisition

We filmed fly lines in a smaller chamber measuring 220 × 180 × 300 mm to assess wingbeat frequency. Flies performed self-motivated flights from a vial and were recorded using a single Phantom SA3 camera operating at 4,000 fps until they left the field of view. The first 10 wingbeats following take off were ignored and the remaining complete wingbeats counted, beginning and ending at dorsal stroke reversal (pronation). We recorded 10 flies per genotype, aiming to capture a minimum of 50 wingbeats per fly; the mean number was 114 ±38.6. Wingbeat frequency for each fly was then normalized by its mass for inter-genotype comparison. Flights were recorded in a constant temperature room at 29° (Supplementary Table 1).

Geometric morphometrics using principal component analysis

We chose to describe the RNAi-induced wing shapes using traditional morphological measurements as well as landmark-based, geometric morphometrics35. The former yields data that are fundamental to well-established aerodynamic theory, such as span length, chord length and aspect ratio. For those aerodynamic analyses, the detail of the wing vein architecture that supports the planform is inconsequential. The latter yields the main features of shape variation described by orthogonal principal components, or shape warps. The landmark-based approach is indispensable if we are to reveal the developmental mechanism underpinning the resultant wing phenotype. Furthermore, noting the proximal direction of movement of the relatively heavy wing veins, and the junctions between them, supports the notion that our estimate of the decreasing moment of inertia is a conservative one. Wing shape is governed by the expression of a number of genes, the modulation of which leads to phenotypic variation. The results of changing the balance of expression bears little relation to the independent parameters engineers vary when designing aircraft wings, yet these are the gene expression-driven shape warps upon which natural selection acts.

Calculating the second moment of wing area

We calculated the second moment of wing area for a single wing from each individual. The nth moment of wing area, S n , is defined by

where R is wing length, c is local chord length and r is radial position along the wing28. If we assume uniform density and thickness, the moment of inertia of wings I w is given by

where ρ A is the wing mass per unit wing area, estimated to be 1.31 μg mm−2 according to the wing area and mass measured by Bergou et al.13. The wing’s contribution to the moment of inertia about the body axis (and to the flight dynamics) is noticeable in insects such as the dronefly, in which the moment of inertia of the wings is about 30% of that of the body37. As the body’s moment of inertia around the roll axis in Drosophila38 is 1.1 × 10−13 N m s2, the wings’ moment of inertia reaches up to 10% of that of the body.

Here, in order to isolate the shape effect, the S 2 , and hence I w , are normalized by wing area S and wing length as follows28:

The decreases when transitioning between the CONT and N800, and between N712 and N678, which can lead the enhancement of turning performance N800 and N712. It should be noted that, considering the shift of cross-veins towards the wing base and the distal tapering of veins, the estimated differences in the non-dimensional moment of inertia are a minimum bracket owing to our assumption of uniform density and constant thickness.

Quasi-steady estimates of aerodynamic performance

The aerodynamic performance of a single wing from each individual during flapping flight is estimated using a blade element model under the quasi-steady assumption. A blade element model calculates aerodynamic force by integrating the forces on virtual chordwise blades. Translational force can be calculated by:

where ρ, C Lt , U, φ, and dS are density of air, the translational lift coefficient, velocity of the blade, wing’s positional angle and the area of the blade, respectively; the aerodynamic force is proportional to the second moment of wing area10.

To isolate the effect of wing shape, all of the wings are evaluated with the same wing kinematics during hovering flight as measured by Fry et al.39. The time series of positional angle and angle of attack (feathering angle) are interpolated by 3rd order Fourier series. Wingbeat frequency f is set to 272 Hz. Mean vertical force is represented as two force components: translational force F L,trans , and rotational force F L,rot , which are calculated as follows:

where C Lt is given by Dickinson et al.4 as a function of angle of attack α. The single value 1.55 is used as the rotational force coefficient C Lr (ref. 40). The effect of added mass is neglected here because its contribution to net force is quite small41. As expected from the changes in second moment of wing area, the aerodynamic force generation is significantly decreased when transitioning between the CONT and N800 strains and the N712 and N678 strains.

Aerodynamic efficiency is also estimated by the blade element analysis with Rankine–Froude momentum theory. Rankine–Froude estimates of induced power P RF , which is the minimum power required to generate the lift F L (ref. 5), is given by:

The induced power P ind , which depends on the induced velocities of the wake in association with lift, is given with a correction factor, k, which takes into account the spatial and temporal distribution of the wake10:

The power required to overcome skin friction and pressure drag, the profile drag P pro , is given by:

For the mean profile drag coefficient, C D,pro , we used the published constant value of 1.46 (ref. 39). The inertial power P acc required to accelerate the wing in air is10:

The ratio between Rankin–Froude power and the mechanical power given as the sum of the induced, profile and inertial power is used as the measure of mechanical efficiency η:

Aerodynamic efficiency is significantly decreased with increasing knockdown, despite the increase in aspect ratio that can enhance the span efficiency, because of the high profile drag compared with induced drag at the low Re (<200). The decrease in lift-generating capacity in stronger phenotypes must lead to modulation of wing kinematics to generate enough aerodynamic force to support their weight and to accelerate; this is a focus of future work.

To compare the aerodynamic torque T a during turns with equivalent aerodynamic force F a the position of the centre of pressure (that is, the length of moment arm) x m is also approximated using the blade element method: