Side-slip manoeuvre of Drosophila and body orientation. (A) Sequence of video images showing a side-slip manoeuvre of a flying fruit fly in front of the rotating pattern. The red arrow indicates body orientation that is derived from the length and width ratio of the fly's image (grey blob). The small red dot indicates the position of the fly's head. Sampling rate, 62.5 Hz; rotational speed of environment, 180° s^–1. (B) Data of a single fly showing the relationship between body orientation derived from blob analysis (x-scale, orientation I, b/a ratio <0.8, where b is the lateral and a the longitudinal extension of the blob ellipsis, inset) and body orientation reconstructed from the position of the fly on two successive video frames (y-scale, orientation II). In the experiment, the fly responded to an optomotor pattern rotating at 500° s^–1. Flight time was 7.54 s. Linear regression fit (reduced major axis, model II regression, y=0.995x–2.12, R²=0.94, N=775 sample points, P<0.001, red) shows a high degree of conformance between the two methods, suggesting that side-slip manoeuvres are rare in freely flying Drosophila. See text for details.

Mean position probability of freely flying fruit flies at various rotational velocities of the flight arena (bin width, 4 mm×4 mm). (A) Stationary pattern. (B) 100, (C) 300, (D) 500, (E) 700 and (F) 900° s^–1 arena velocity. The outer rings represent the random-square pattern while the white line marks the position of the immovable translucent inner cylinder. All position histograms are normalized to the same data sum and position probability is plotted in pseudo-colour.

Distance between the animal and the arena centre, and turning angles at various experimental conditions. (A) Probability histograms and medians (dotted white lines) of the distributions obtained for flies responding to six different arena velocities. Means ± s.e.m. (B) Mean distance of the flying animal from the arena centre plotted against the fly's horizontal (forward) velocity (bin width, 0.1 m s^–1). Linear regression fit is plotted in red (y=0.016x+35.8, R²=0.88, N=13 horizontal velocity bins, P<0.001). (C) Total turning angle within a flight saccade (grey) and between two saccades (open) shown as a function of arena velocity. (D) Ratio of total turning angle during saccadic flight style and smooth turning between two subsequent saccades. Data show a minimum contribution of saccades to turning angle at 500° s^–1 arena velocity. SMT, time between two flight saccades; SAT, duration of a saccade. Means ± s.d., N=131 flies.

Mean flight velocities at various rotational velocities of the flight arena. Mean horizontal (black, left scale), turning (blue, right scale) and vertical (red, left scale) velocity of the animals in response to the changes in stimulus conditions. The fly may fully achieve retinal slip compensation (grey area) when angular velocity, which is the rate of change in gaze, is equal to the angular speed of the rotating environment at a given horizontal velocity (slope=1, dotted blue). Positive turning and vertical values mean counter-clockwise turns and climbing flight, respectively; N=22 (0° s^–1), 23 (100° s^–1), 20 (300° s^–1), 20 (500° s^–1), 21 (700° s^–1) and 26 flies (900° s^–1). Means ± s.e.m.

Saccadic flight style of Drosophila flying freely in a non-rotating random-dot arena. (A–C) Three flight paths of single fruit flies voluntarily starting from rest (top view). Flight is characterized by sequences of straight flight interspaced by 130 ms short, approximately 90–180° saccadic turns. Horizontal forward velocity is plotted in pseudo-colour. Red cross, arena centre. (D) Angular velocity during flight saccades elicited at various forward velocities in response to optomotor stimulation. Each data point of a curve represents the averaged value derived from the mean saccadic velocity of each of the 131 tested fruit flies. The mean standard deviations over all data points of each curve amount to 546 (black), 425 (red), 347 (green), 263 (blue), 287 (cyan) and 513° s^–1 (purple). (E) Modulation in horizontal velocity during flight saccades. The standard deviations averaged over all data points of a curve amount to 0.12 (black), 0.12 (red), 0.15 (green), 0.10 (blue), 0.13 (cyan) and 0.17 m s^–1 (purple). (F) Frequency of saccades slightly increases with increasing horizontal velocity estimated from flight sequences between saccades (intersaccade velocity). The black line represents the linear regression fit on the data set (y=1.31x+2.55, R²=0.04, N=131 saccades, P=0.024). Colour coding in D–F: 0° s^–1, 0.26±0.08 m s^–1, 22 (black); 100° s^–1, 0.27±0.08 m s^–1, 23 (red); 300° s^–1, 0.33±0.07 m s^–1, 20 (green); 500° s^–1, 0.45±0.06 m s^–1, 20 (blue); 700° s^–1, 0.49±0.09 m s^–1, 21 (cyan); and 900° s^–1, 0.45±0.09 m s^–1, 26 (purple); for arena velocity, mean forward flight velocity and number of flies, respectively.

Gaze and response of a rotation-sensitive elementary motion detector (EMD) system for two single flies flying in a stationary random-dot environment (A–E) and under optomotor stimulation due to the rotating arena (500° s^–1 counter-clockwise rotation, F–J). The time traces in B–E and G–J are subsets of the flight sequences in A and F. (A,F) Flight path and EMD response (left-minus-right eye) plotted in pseudo-colour for both stimulus conditions. Red cross, arena centre. (B,G) The fly's gaze was derived according to the procedure shown in Fig. 1D. The movement of the cylinder panorama (infrared light marker) is shown in red (right scale). (C,H) EMD response of left (blue) and right (red) eye derived according to the position and speed of the fly inside the arena and the visual panorama. (D,I) Left-minus-right eye EMD response (black) and turning velocity (red), and (E,J) left-plus-right eye EMD response (black) and horizontal velocity (red) are plotted for both stimulus conditions. Upper dotted line in D and I indicates the threshold used to identify flight saccades (>1000° s^–1). Grey dots indicate times at which flight saccades occur. Black, left scale; red, right scale.

Close-up of the flight sequence in a stationary arena cylinder (left turn). (A) The fly's gaze calculated from body orientation. (B) Inverse relationship between horizontal (blue, right scale) and turning (red, right scale) velocity, and output of a rotation-sensitive EMD system (left-minus-right eye, black, left scale).The sum of EMD responses of the two eyes is plotted in grey (left scale). Light grey area indicates times at which the fly exhibits approximately constant gaze in A and saccades in B.

Histograms of responses of a rotation-sensitive EMD system for flight sequences produced by flies flying in a stationary environment and during optomotor stimulation. (A) Distribution of the mean value bins (grey) and standard errors of left-minus-right eye EMD output of flies responding to various arena velocities. (B) Histograms show the sum of EMD output (left-plus-right eye) derived from the same flight data as shown in A. Gaussian fits to each histogram are shown as solid red lines. All histograms are normalized to the same area under the curve.

Outputs of two EMD system types in freely flying fruit flies. (A) According to previous findings on yaw torque production in tethered flies, we simulated a rotation-sensitive EMD system (upper pictogram) and an expansion-sensitive system with a lateral focus of expansion (lower pictogram). (B,C) Relative mean EMD output of the rotation system estimated from the Gaussian fit to the histograms shown in Fig. 9A and B, respectively. Errors represent the standard deviation of the fit, which is 0.5 the width of the Gaussian curve at half-peak height. Data in B and C show the mean difference (left-minus-right eye) and sum (left-plus-right eye) of the EMD response between the two eyes, respectively. (D) Relative mean EMD output (left-minus-right eye) of an expansion-sensitive system estimated from Gaussian fits similar to those shown in Fig. 9A,B. (E,F) EMD response of the rotation (black)- and expansion (red)-sensitive EMD system in flight sequences derived from two flies flying in a stationary environment in E and during 300° s^–1 arena velocity in F. See text for details. cw, clockwise turning (grey area); cww, counter clockwise turning.

Relationships between flight path curvature, horizontal and turning velocity in freely flying fruit flies. (A) The variance in flight path curvature decreases with increasing horizontal velocity. At maximum forward velocity of approximately 1.0 m s^–1, flight path curvature is apparently constrained to a unique value of approximately 0.016 mm^–1. (B) Relationship between flight path curvature and turning velocity. (C) Data distribution between horizontal and angular velocity. Each data point represents an 8 ms position measurement of each of the tested flies. The vertical line in C indicates maximum horizontal velocity of 0.49 m s^–1 averaged over all flies. Normalized relative frequencies are plotted in pseudo-colour.

Numerical model for force balance in freely flying fruit flies. (A) Forces produced by the flying insect and forces acting on the fly body during flight on a curved path. Total flight force F_t is equal to the vector sum of horizontal (F_h), vertical (F_v) and lateral forces (F_l). (B) Total force of each fly and the corresponding force components within the flight recordings that fell within the top 10% maximum of total force. Data are sorted after F_t for all 131 tested animals. (C) Minimum flight path radius at a given forward velocity and level flight, shown for four estimates of total flight force. (D) Alterations in vertical climbing velocity when horizontal flight velocity is kept constant at 0.6 m s^–1. Grey indicates path radii at which the fly loses flight altitude while turning. The numerical model predicts that at 0.6 m s^–1 forward speed fruit flies may only support their body weight when the flight path radius exceeds 50 mm (dotted line). F_g, gravitational force (body weight); CoR, centre of radius of a flight turn; r, radius of the flight path; u_l, lateral (side-slip) velocity; u_h, horizontal velocity; u_v,max, maximum vertical velocity.

Force components and body velocities of single flies flying freely in a stationary (left) and rotating (500° s^–1, right) random-dot flight arena. (A,F) Flight paths of the two animals lasting 2.4 s each. Horizontal (B,G), vertical (C,H), centripetal (D,I) and total (E,J) forces (black, left scale) and velocities (red, right scale), measured from the fly's body motion inside the arena and calculated from the equations given in the text, respectively. Total velocity is the vector sum of horizontal, vertical and turning velocity. Grey dots indicate saccades in which turning velocity exceeds 1000° s^–1 angular speed. Red cross, centre of flight arena.

Relationship between horizontal velocity and lateral force during turning in freely manoeuvring Drosophila. Data points for horizontal velocity (A) and lateral force (B) are plotted against flight path radius, whereas relative frequency is shown in pseudo-colour. Graphs show superimposed data derived from all tested flies. (C) Binned means for horizontal velocity (black, left scale) and lateral (centripetal) force (blue, right scale) derived from the data shown in A and B. N=131 flies. Means ± s.d. Radius of the inner cylinder of the arena was 70 mm.