Anticipatory Manoeuvres in Bird Flight

It is essential for birds to be agile and aware of their immediate environment, especially when flying through dense foliage. To investigate the type of visual signals and strategies used by birds while negotiating cluttered environments, we presented budgerigars with vertically oriented apertures of different widths. We find that, when flying through narrow apertures, birds execute their maneuvers in an anticipatory fashion, with wing closures, if necessary, occurring well in advance of the aperture. When passing through an aperture that is narrower than the wingspan, the birds close their wings at a specific, constant distance before the aperture, which is independent of aperture width. In these cases, the birds also fly significantly higher, possibly pre-compensating for the drop in altitude. The speed of approach is largely constant, and independent of the width of the aperture. The constancy of the approach speed suggests a simple means by which optic flow can be used to gauge the distance and width of the aperture, and guide wing closure.

b) The pixel positions of the grid locations are then determined in the camera image, to obtain a one-to-one mapping between the real co-ordinates of the grid locations on the floor and their corresponding pixel coordinates in the image. h) The position of the centroid of the image of the bird in each video frame [as computed in (c)] is projected on to the floor by using a process of 2D interpolation, as described in (e). The (X,Y) position of the bird in the tunnel at each frame instant is then computed by combining the projected floor position of the image centroid at with the corresponding height and using the geometry of similar triangles, in a process analogous to that described in (f).
i) The final result is an estimate of the (X,Y,Z) co-ordinates of the bird for each frame of the video sequence.
The calibration grid on the floor was used only during the camera calibration, and was not present in the experiments. The precision of the 3D trajectory reconstruction procedure was evaluated by placing a small test target -a model bird with with a calibrated wingspan of 30 cm -at 44 different, known 3D locations within the tunnel, of which 39 were within the boundary of the grid. The results are shown in Table S1, below. The standard deviations of the errors along the x, y and H directions were 21 mm (x), 6.1 mm (y) and 25.4 mm (H).

Supplementary Table S1
: Test of accuracy of 3D position measurements. X, Y and H represent (in cm) the true co-ordinates of a test target along the axial (length), width and height of the tunnel, respectively. X calc, Y calc and H calc are the calculated values of these co-ordinates, and X error, Y error and H error represent the respective errors.
The standard deviation of the errors (SD) are given at the end of the table. The 5 missing measurements pertain to target positions whose floor projections fell outside the grid.

FLIGHT TRACKING PERFORMANCE: COMPARISON OF AUTOMATIC AND MANUAL TRACKING METHODS
To reduce the intensive labour of manual tracking, we created a purposed-written

SUPPLEMENTARY VIDEOS
Four examples of the flights of one bird (bird Four) are shown in videos SV1, SV2, SV3 and SV4. Clip SV1 depicts the flight of the bird in the tunnel when there is no intervening aperture. In SV2, the bird passes through an aperture that is 5 cm wider than its wingspan (+5 cm) without closing its wings. In SV3, the bird passes through an aperture that is 5cm narrower than its wingspan (-5 cm), and closes its wings before entering the aperture. Clip SV4 shows a side view of the same bird while landing on a perch, illustrating its behaviour during active braking.
A reliable and easily detected indication of active braking before entering the aperture is an increase in the pitch of the body (a lowering of the abdomen and the tail). This is clearly evident in the landing video SV4. In downward-looking views of bird flight, the increased pitch would up as a shortening of the projected body length. By this criterion, there is no evidence of active braking in any of the videos SV1-SV3.

Video SV1: Video of a bird (Four) flying in an aperture-free tunnel
Video SV2: Video of Four passing through an aperture that is 5 cm wider than his wingspan.
Video SV3: Video of Four passing through an aperture that is 5 cm narrower than his wingspan.
Video SV4: Video (side view) of Four while landing on a perch.

Relationship between the coefficients of variation of distance and time to initiation of wing closure
If the birds approach the aperture at a constant speed V, then wing closure will be initiated at a distance D that is inversely proportional to the time T to the aperture. That is, Which can be rearranged to read where V is a constant. We use perturbation analysis to determine the relationship between small variations in D and T. These variations reflect noise in the behavioural response, which can arise from noise at several levels of the sensorimotor pathway.
Perturbing equn (2), we obtain Dividing both sides of (3) by D.T and rearranging, we obtain If we consider only the magnitudes of the perturbations, we can drop the (-) sign and We observe that the left hand side of (5) is a measure of the coefficient of variation of D, while the right hand side is a measure of the coefficient of variation of T. Thus, when the approach speed is constant, we would expect the CV of distance to be equal to the CV of time. This is exactly what we find in our experiments, which reinforces our observation that the approach speed is constant.

Determining whether to close the wings, and if so where (or when)
Consider a bird, flying at a speed V, approaching an aperture of width W (Inset, Fig. S3).
In this analysis we assume that the flight speed is constant over aperture distances that ranges from 2 m (well ahead of the point of judgement of aperture width, estimated to be at 1.2 m) to 0 m (beyond the point of initiation of wing closure), This is a reasonable approximation (see Figs. 3a, 4a). For a constant flight velocity, it can be shown that the angular velocity ω of the image of an edge of the aperture in the eye will be: where θ is the viewing direction of the edge. It can also be shown that, when the bird is at a distance D from the aperture, the angular velocity of the image of edge of the aperture in the eye will be: If wing closure is required, the relationship in equation (2) can also be used to ensure that this occurs at a prescribed distance D0 from the aperture. When the bird is at a distance D0 from the aperture, the expected angular velocity ω of the image of the edge (as a function of the direction in which the edge is viewed) would be given by The black curve in Fig. S3 shows the profile of the expected value of ω for various viewing directions θ when the bird is at a distance D0 = 0.37 m from the aperture. When the measured value of ω exceeds the expected value for the current direction θ of the edge, the distance to the aperture has dropped below 0.37 m.
An alternative strategy would be to initiate wing closure at a specific time T0 before reaching the aperture. For an approach velocity V, the time T to reach the aperture would be D/V when the bird is at a distance D from it. Setting T=D/V, we may rewrite ( when ω in the direction of the edge θ exceeds the expected value for that direction for the prescribed value of D0, as specified by equation (3).
This strategy would ensure that wing closure occurs only when the aperture is narrower than the wingspan, and that the closure, if it occurs, is initiated at a constant, prescribed distance from the aperture. In effect, the wing closure, if required, is triggered at the point where the black curve intersects the blue curve corresponding to the relevant aperture width in Fig. S3.
A schematic description of a neural circuit for performing these computations is proposed in Fig. S4. The upper part of Fig. S4 illustrates a circuit for determining whether an aperture that the bird is approaching is narrower than the bird's wingspan, W. As the bird approaches the aperture, the edge of the aperture successively stimulates angular velocity sensors 1,2, …n, which generate responses proportional to the angular velocities ω 1 ,ω 2 , ... ω n . The angular velocity of the edge will depend upon the width of the aperture, and upon the viewing direction θ of the edge. Accordingly, the outputs of the angular velocity sensors are compared with the expected values for an aperture of width W for various viewing directions, as specified in equation (1). When any of these sensors registers an angular velocity that matches or exceeds the expected value, the output of the associated comparator will be set to 1, indicating that the aperture is narrower than the bird's wingspan W. Thus, switching of the output of any of the comparators from 0 to 1 indicates that wing closure will be necessary. In the presence of noise, the reliability of this decision can be improved by monitoring the outputs of several comparators. As the edge moves across the visual fields of successive angular velocity sensors, each comparator will switch to 1 if the aperture is narrower than the wingspan. Summation of the outputs of the comparators, and comparison with a preselected threshold (say, n/2, where n is the number of angular velocity sensors that have responded so far) will improve the reliability of the decision by ensuring that the aperture is deemed to be narrower than the wingspan only if at least half the number of comparators has switched to 1. The quality of this decision can be adjusted by varying the threshold. A threshold value lower than n/2 will lead to detection that has greater sensitivity but is more prone to false alarms, whereas a value threshold value that is greater than n/2 will have the opposite effect. The summation for determining whether wing closure is necessary can, of course, progress only until the bird has reached the critical distance D0, at which point wing closure must be initiated if it is deemed necessary. Thus, the circuit can maintain a running total of n as well as the number of switched comparators until the critical distance D0 is reached, to provide the most reliable decision about wing closure.
Supplementary Figure S4. Schematic description of neural circuits for (a) mediating a decision on wing closure, and (b) determining the distance to the aperture.
A circuit that ensures that wing closure, if necessary, is initiated at a prescribed distance D0 from the aperture, is illustrated in the lower half of Fig. S4. This circuit receives its inputs from the same set of angular velocity sensors. However, it compares the measured angular velocities against a different set of expected values, as prescribed in equation (3). The angular velocity of the edge when the bird is at a distance D0 from the aperture will depend upon the width of the aperture, and upon the viewing direction θ of the edge. Accordingly, the outputs of the angular velocity sensors are compared with the expected values for an aperture distance D0 for various viewing directions, as specified in equation (3). When any of these sensors registers an angular velocity that matches or exceeds the expected value, the output of the associated comparator will be set to 1, indicating that the aperture is at the critical distance D0. The output of the inclusive OR operator at the final stage of the circuit will switch to 1 when any of the angular velocity sensors has exceeded its prescribed threshold, indicating that the distance to the aperture is now D0.
The motor command to initiate wing closure is issued when two conditions are met: (a) the aperture is narrower than the wingspan, as determined by the upper circuit, and (b) the bird is at the critical distance D0 from the aperture, as determined by the lower circuit. Accordingly, the motor command is derived by performing an 'AND' operation on the outputs of the two circuits.
Although the circuits described above have the flavour of electronic circuitry rather than neuronal circuitry, there is now evidence that computations such as the measurement of image angular velocity, and operations that involve thresholding, summation, and executing Boolean operations such as OR and AND can be performed by neural circuits 2,3 .
We have seen above that constancy of the approach speed enables the calibration of distances and apertures directly in terms of optic flow magnitude, leading to a simple and robust scheme for controlling wing closure, as described above. In an earlier study, based on more limited information about the birds' behaviour when flying through narrow apertures 4 , we had proposed that wing closure occurs when the angular velocity of the edge exceeds a threshold value. That model predicted that narrower apertures would elicit wing closure at larger distances from the aperture. In that study there was no information about birds' flight speeds, or about where they closed their wings in relation to the aperture. We now have this information, and our present data shows that wing closure, if it occurs, takes place at a constant distance from the aperture, irrespective of the width of the aperture.