Visual guidance of forward flight in hummingbirdsreveals control based on image features insteadof pattern velocityRoslyn Dakina, Tyee K. Fellowsa, and Douglas L. Altshulera,1

aDepartment of Zoology, University of British Columbia, Vancouver, BC, Canada V6T 1Z4

Edited by John G. Hildebrand, University of Arizona, Tucson, AZ, and approved June 14, 2016 (received for review February 25, 2016)

Information about self-motion and obstacles in the environment isencoded by optic flow, the movement of images on the eye. Decadesof research have revealed that flying insects control speed, altitude,and trajectory by a simple strategy of maintaining or balancing thetranslational velocity of images on the eyes, known as patternvelocity. It has been proposed that birds may use a similar algorithmbut this hypothesis has not been tested directly. We examined theinfluence of pattern velocity on avian flight by manipulating themotion of patterns on the walls of a tunnel traversed by Anna’shummingbirds. Contrary to prediction, we found that lateral coursecontrol is not based on regulating nasal-to-temporal pattern velocity.Instead, birds closely monitored feature height in the vertical axis,and steered away from taller features even in the absence of nasal-to-temporal pattern velocity cues. For vertical course control, weobserved that birds adjusted their flight altitude in response to up-ward motion of the horizontal plane, which simulates vertical de-scent. Collectively, our results suggest that birds avoid collisionsusing visual cues in the vertical axis. Specifically, we propose thatbirds monitor the vertical extent of features in the lateral visual fieldto assess distances to the side, and vertical pattern velocity to avoidcollisions with the ground. These distinct strategies may derive fromgreater need to avoid collisions in birds, compared with small insects.

automated tracking | vision | locomotion | optic flow | optomotor

How are birds able to fly through dense forest and openspaces without colliding or crashing to the ground (1)? The

translational motion of images on the eye (hereafter referred to as“pattern velocity”) provides a rich source of information about self-motion and the surrounding environment and has been shown toplay a prominent role in the visual guidance strategies of all flyinganimals studied to date (2–5). Honey bees use pattern velocity for adiverse set of flight controls: they balance pattern velocity on theirleft and right sides to navigate narrow passageways (6); they reg-ulate pattern velocity to control their flight speed (7) and altitude(8); and they integrate pattern velocity to estimate distances toforaging sites, communicating this information to hivemates (9, 10).Pattern velocity thus represents an elegant solution to insect flightcontrol that is robust to a range of spatial frequencies and contrasts(2, 3, 6, 7).In the first study to ask whether birds also use a similar strategy,

Bhagavatula et al. (11) trained five budgerigars to fly repeatedlydown a tunnel. The authors found that like bees (6), the budgerigarssteered away from vertically oriented gratings that provided strongnasal-to-temporal (fore–aft) pattern velocity, and toward horizon-tally oriented gratings and blank walls that provided little to nonasal-to-temporal pattern velocity. However, because Bhagavatulaet al. (11) used only stationary gratings and did not manipulatepattern velocity directly, the exact mechanism used by birds remainsto be confirmed. More recent experiments demonstrate that patternvelocity does not affect the flight speed of budgerigars (12) in thesame manner as it does flying insects (3, 13). Unlike bees and flies,the budgerigars increased their speed only slightly in response tolarge decreases in nasal-to-temporal pattern velocity, and they werenot affected by large increases (12), demonstrating that birds do

not adjust their flight speed to hold nasal-to-temporal patternvelocity constant.To determine if avian visual control of steering in flight differs

from that of insects, we studied hummingbirds, agile fliers thatperform rapid cruising flight as well as extended bouts of hover (14,15). We used an automated tracking system to record more than3,100 flights of birds in free flight traversing a narrow tunnel wherethe wall patterns could be experimentally controlled (Fig. 1). Wemeasured the average lateral position of the birds as they crossedthe tunnel (Movie S1). Because hummingbirds can be trained toperform many trips to and from a feeder, we were able to explore abroad range of stimulus patterns. The results of our first twoexperiments indicate that, contrary to what had been previouslyproposed (11), birds do not steer to balance nasal-to-temporalpattern velocity like insects (Movie S2). We then performed threeadditional experiments to understand how other visual cues mayinfluence avian flight control. From our collective results, wepropose that birds use a different set of strategies based on changesin both vertical feature size and vertical pattern velocity.

ResultsWe first asked if birds, like insects, steer by balancing patternvelocity. Our first experiment manipulated the motion of verticalgrating patterns on the left and right sides of the 59-cm-wide tunnel(Fig. 2A) (n = 297 flights by 6 birds). The grating pattern on onewall was moved at a rate of 0.34 m/s either toward or away fromthe feeder while the pattern on the other wall was held stationary.The control treatment had stationary gratings on both sides. Theexperimental manipulations would have resulted in a ±17%change in nasal-to-temporal pattern velocity on one side for abird flying at the average forward flight speed of 2.0 m/s [95%confidence interval (CI) 1.8, 2.2] along the midline of the

Significance

Birds can steer a precise course at high speed, but little is knownabout how they avoid collisions with surrounding objects and theground. We manipulated the visual environment of hummingbirdsas they flew across a long chamber to evaluate how they use visualinformation for course control. We found that lateral course controlis based on the vertical size of features, rather than the strategyobserved in insects of regulating fore–aft image velocity. However,like insects, birds use image velocity in the vertical axis for altitudecontrol. Our results suggest that in natural settings, birds may avoidcollisions by monitoring the vertical size, expansion, and relativeposition of obstacles.

Author contributions: R.D., T.K.F., and D.L.A. designed research; R.D., T.K.F., and D.L.A.performed research; R.D. analyzed data; and R.D. and D.L.A. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

Data deposition: The data reported in this paper have been deposited in the Figshare datarepository (https://figshare.com/articles/statistical_supplement_flight_course_control_R/3382759).1To whom correspondence should be addressed. Email: doug@zoology.ubc.ca.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1603221113/-/DCSupplemental.

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chamber. Birds using a strategy of balancing nasal-to-temporalpattern velocity are predicted to remain centered on the midlinein the control condition, and to deviate laterally by about 2.5 cmin the motion treatments (SI Appendix). Contrary to prediction,there was no significant difference in average lateral positionwhen comparing the treatments to the controls (all P > 0.25),even though we had sufficient statistical power to detect thepredicted deviation (see CIs in Fig. 2A).We selected a vertical stripe grating for our first experiment

because it is a salient pattern for other flying animals (3, 6, 11).However, it is possible that this grating pattern may have inhibiteda response. To address this possibility, we conducted a secondexperiment where we manipulated the pattern velocity of dot fields(Fig. 2B) (n = 860 flights by 10 birds). Treatments had dot patternsthat moved 0.26 m/s in opposing axial directions on the left andright sides, to achieve an even greater imbalance in pattern velocitythan in our first experiment. Stationary dot-field patterns were usedas the controls. These treatments resulted in an 11% increase inpattern velocity on one side and an 11% decrease on the other sidefor a bird flying at the average forward speed of 2.2 m/s (95% CI1.9, 2.5) on the midline. We tested three dot densities: 0.47, 0.95,and 1.89 dots/cm2, using 0.29-cm-wide dots. None of these motiontreatments significantly affected the birds’ lateral position aspredicted (Fig. 2B) (comparisons with controls, all P > 0.50),even though we had sufficient power to detect the predicteddeviation of 3.5 cm on average (SI Appendix).The results of our first two experiments did not support the

hypothesis that birds steer to regulate nasal-to-temporal patternvelocity (11). We next asked whether the hummingbirds wouldrespond to other types of visual motion during forward flight, asthey do during hover (14). To address this question, we conducteda third experiment in which birds were presented with horizontal

gratings that moved up on both side walls, or down on both sidewalls, synchronously at 0.34 m/s (Fig. 2C) (n = 148 flights by 5birds). When the patterns moved upward, the hummingbirds flewabout 4.2 cm (95% CI 0.9, 7.6) higher in the tunnel, on average,relative to stationary controls (P = 0.02). The birds flew about2.8 cm (95% CI –0.8, 6.4 cm) lower than stationary controls whenpatterns moved downward, although this effect was not significant(P = 0.21). These results indicate that birds steer upward in re-sponse to pattern velocities that simulate descent, similar toDrosophila (16).

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Fig. 1. Birds were video-recorded in a 5.5-m-long flight tunnel to study theircourse control strategies (Movie S1). An automated tracking system determined 3Dflight trajectories from eight camera views (A). Sample trajectories are shown for abird flying to the feeder and then back to the perch when both walls presentedvertical gratings (B). Trajectories were analyzed between meters 1 and 5 withinthe tunnel to exclude the take-off, feeder approach, and landing phases. Forillustration purposes, the bird, perch, and stimulus features are not to scale.

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Fig. 2. Unlike insects, birds did not steer to balance nasal-to-temporal patternvelocity on their left and right sides. Motion of vertical stripes (A) and dot fields (B)did not affect flight trajectories as predicted if birds control flight usingnasal-to-temporal pattern velocities (Movie S2). However, when horizontal stripesmoved upward, simulating descent, the birds steered upward (C). Data points inthemiddle column show grandmeans for individual birds connected by solid lines(lateral position in A and B; altitudinal position in C). Pink and blue are used torepresent the motion treatments and white represents the controls. To allowfurther comparison of the treatments, the shaded curves show the estimatedprobability densities for all of the flight averages. The area under each curve sumsto a probability of one. Note that the tunnel midline has a lateral position of0 and the walls are at lateral positions of ±29.5 cm (the axis range of ±30 cm in Aand B is used for illustration only). Effect sizes, calculated as the average differencebetween each treatment and the control, are plotted in the rightmost column,with a separate effect size shown for each bird (small gray dots) and the overalleffect size relative to the control and its 95% CI below. The analyses in A and Bdefine left and right using the bird’s frame of reference. The gratings in A and Chad a spatial period size of 18.4 cm. Statistical significance: ***P < 0.001; **P <0.01; *P < 0.05; ns P > 0.05.

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The conclusion that birds respond to vertical but not nasal-to-temporal pattern velocity seems to conflict with the results ofBhagavatula et al. (11). In this pioneering study of avian visualguidance, Bhagavatula et al. (11) found that budgerigars consis-tently steered away from a stationary vertical grating that generatedstrong nasal-to-temporal pattern velocity. To determine if there is afundamental difference between the visual guidance strategies ofbudgerigars and hummingbirds, we performed a fourth experimentwith stationary horizontal and vertical gratings. We took advantageof hummingbirds’ tendency to perform many trips to the feeder totest a broad range of spatial period sizes of the gratings (Fig. 3A)(n = 1,180 flights by 10 birds). This approach allowed us to explorethe hypothesis that birds might be sensitive to expansion (17, 18).Larger features expand faster for a given distance and approachrate (19), and thus we predicted that birds may steer further awayfrom gratings with larger period sizes.Like Bhagavatula et al. (11), we found that the hummingbirds

steered toward horizontal gratings and away from vertical gratings,but only when the gratings had spatial period sizes of 1.15 and2.3 cm (all P < 0.004). Treatments with smaller (0.58 cm) and larger(4.6, 9.2, and 18.4 cm) grating period sizes did not cause any sig-nificant deviation away from the vertical stripes (all P > 0.29). Thelack of effect of the smallest period size may be because the birdsflew fast enough for the vertical stripes in this treatment to fuse as aresult of motion blur, such that the vertical grating could not beresolved (Fig. 3B; also see SI Appendix and ref. 20). Vertical grat-ings with a spatial period smaller than 3 cm may have fused for aconsiderable proportion of the trip, depending on a bird’s forwardflight speed. In contrast, birds never flew fast enough for the verticalstripes to fuse with the largest grating period sizes (Fig. 3B). Thelack of effect in these treatments must therefore be because thebirds steered away from the large-period horizontal gratings, orbecause they were less repelled by the large-period vertical gratings[which have a lower spatial frequency (3, 6)].To test these two visual guidance strategies, we conducted a fifth

experiment examining all possible combinations of horizontal andvertical stripe gratings with intermediate (2.3 cm) and large (18.4cm) period sizes (Fig. 4). The results revealed a strong influence ofthe period size of the horizontal grating (Fig. 4A and Movie S2)(n = 474 flights by 6 birds). Specifically, we observed a strongsteering response when the horizontal grating had a 2.3-cm period(all P < 0.0001), but this effect was diminished when the horizontalgrating had an 18.4-cm period (P = 0.02 and P > 0.99 for verticalperiod sizes 18.4 and 2.3 cm, respectively). Importantly, the dif-ference between the two horizontal gratings was highly significant(P < 0.0001). In contrast, there was no significant difference be-tween the two vertical gratings (P = 0.06), and if anything, the birdswere more repelled by the vertical grating with the larger periodsize (Fig. 4A). Overall, this experiment demonstrated that birdssteer away from horizontal gratings with larger period sizes. Thisbehavior was confirmed in additional treatments with gratings thathad the same orientation on both sides (Fig. 4B) (n = 236 flights by6 birds). Again, we observed that hummingbirds steered away fromhorizontal gratings with a larger period size (Fig. 4B) (P < 0.001),even in the absence of nasal-to-temporal pattern velocity (Movie S2).Consistent with our other results, there was no significant tendencyto steer toward either of the vertical gratings tested (Fig. 4B)(P = 0.08).

DiscussionBased on previous studies of insects and budgerigars, we hypoth-esized that pattern velocity would influence how birds steer duringforward flight. The results of our first two experiments did notsupport this hypothesis or the specific prediction that humming-birds would steer to regulate nasal-to-temporal pattern velocity(Fig. 2 A and B and Movie S2). However, we did find that the birdsresponded to pattern velocity in the vertical axis, indicating thatpattern velocity may be used for altitude control to avoid collisionswith the ground (Fig. 2C) (16). Our fourth and fifth experimentsrevealed that lateral steering is instead guided by a mechanism thatappears to be based on feature size: the birds steered away from

features that had a greater vertical extent (i.e., height), includingvertical stripe gratings and horizontal gratings that had a largeperiod size (Figs. 3 and 4 and Movie S2).What visual response mechanism could lead to this strategy for

lateral course control? One possibility is that birds use visual ex-pansion for distance estimation (18, 21, 22). Expansion, anothertype of optic flow, is defined as the change in image size as anobject or feature is approached, and the rate of expansion in-creases more rapidly for larger features (Fig. 5 A and B). It isthought that birds use expansion is used for a variety of deceler-ation and interception behaviors (23–26), and it has been experi-mentally shown that expansion influences the ability of hoveringbirds to hold station (14). In our experiments, the birds may haveevaluated expansion of features on the side walls during slightlateral oscillations in flight: for example, when they were halfwayto the feeder, the hummingbirds moved laterally at up to ±0.1 m/son average (SI Appendix, Table S10). Neurons that compute ex-pansion have been identified in the nucleus rotundus of the

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Fig. 3. Course control depends on the grating period size. Birds were predictedto steer away from vertical stripe gratings (and toward horizontal stripes) (A),but this was only observed when the stripe gratings had period sizes of 2.3 cmand 1.15 cm. Vertical stripe gratings with a period size <1 cm nearly always fusedas a result of motion blur, although fusion cannot explain the diminished effectof the gratings with a large period (B). Pink is used to represent treatments withthe horizontal grating on the left, whereas blue treatments have the horizontalgrating on the right. The middle column shows grand means for the individualbirds and probability densities for the flight averages, as in Fig. 2. Effect sizes arecalculated as the average difference between the pink and blue treatments.Note that this analysis uses the tunnel frame of reference, because birds wereexpected to steer away from vertical gratings regardless of heading. Stimulusfeatures are not drawn to scale. See SI Appendix for details of fusion calculations.Statistical significance: ***P < 0.001; **P < 0.01; ns P > 0.05.

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pigeon brain, part of the tectofugal pathway (19). This samenucleus also contains cells that respond to expansion scaled byapparent size (equal to 1/τ, where τ is the time-to-collision) andexpansion scaled by an exponential function of apparent size(known as η) (19). These cues can inform an animal about thenearness in time of an impending collision, triggering an ap-propriately timed response without knowledge of the true sizeor distance of the approaching object (27, 28). It was recentlydiscovered that the zebra finch nucleus rotundus also containscells that respond during simulated flight if an approachingfeature is located at the point of expansion, suggesting that thetectofugal pathway may also be involved in flight control (22).

In this study, the birds steered toward positions that wouldhave reduced feature expansion, ρ, in the vertical axis resultingfrom any additional lateral deviation (Fig. 5C). In treatmentswith the same pattern on both sides, the birds remained on averagecentered over the midline (Fig. 5D; see the SI Appendix for details).This finding indicates that the birds were not necessarily attractedto the fine horizontal gratings, suggesting instead that they mayhave been less repelled by them. Additional experiments areneeded to test whether lateral course control is indeed based onour proposed mechanism of expansion reduction (becausesmaller features do not expand as rapidly) (Fig. 5), as opposed toan attraction effect or an effect of feature size independent ofexpansion. For example, the avian visual system may be tuned toparticular feature sizes or spatial frequencies that may be easy toresolve visually and track (5, 18, 29, 30). Additional studies thatdirectly manipulate expansion are needed to test these alterna-tives. Another question is whether this differs across bird specieswith diverse visual systems and flight styles.Our results do not rule out the use of pattern velocity altogether.

Indeed, we suggest that birds use vertical pattern velocity tomaintain flight altitude, similar to Drosophila (16). It is possible thatwe might have been able to observe an effect of nasal-to-temporalpattern velocity on lateral course control with much larger manip-ulations, or manipulations in other parts of the visual field [e.g.,ventral (8)]. It is important to note that like the hummingbirds inour study, the budgerigars and honey bees in other studies also hadextensive experience in the flight chamber (6, 11, 12), and bothbirds and bees are capable of sophisticated spatial memory andmapping (10, 31–33). Unlike previous studies, our results conclu-sively demonstrate that birds use the vertical extent (i.e., height) offeatures in the lateral visual field to guide flight, even in theabsence of strong nasal-to-temporal pattern velocity cues (Fig. 4and Movie S2). This finding has implications for studies acrossother taxa: a tendency to steer away from vertical gratings does notnecessarily imply a response to nasal-to-temporal pattern velocity(e.g., refs. 4, 34, 35).Collectively, our findings suggest that birds control forward

flight by monitoring changes in the vertical axis: specifically, theheight of features and vertical pattern velocity. This finding isconsistent with other laboratory studies showing that flying birdsrapidly stabilize key features in their visual field (36). In nature,collisions may be avoided by monitoring changes in the apparentsize of features (22), such as trees and branches, as well aschanges in the vertical position of those features. Although ourexperiments focused on manipulating a limited number of cues,we do not suggest that these represent the only visual guidancestrategies used by birds. Indeed, the birds in our study and inprevious studies could avoid collisions despite a variety of visualpatterns (Movie S2) (11). The birds may also monitor and sta-bilize features in the frontal optic flow field (1, 22, 26, 36), whichin our study would have included features such as the perch,feeder, and edges of the rectangular end walls of the chamber.Natural scenes provide an even richer mosaic of optic flow cuesfor distance estimation. Expansion may be especially useful inthis context (27), because most natural objects are large enoughthat the expansion rate rises very rapidly even at slow approachvelocities (e.g., 0.1 m/s in Fig. 5).The discovery of a visual guidance algorithm based on the

vertical extent of features in the lateral visual field leads to excitingnew questions. Although there have been multiple experimentswith insects that demonstrate different mechanisms of forwardflight control, the manipulations presented here represent a uniqueset. To our knowledge, an experiment comparing horizontal grat-ing period sizes (Fig. 4) has not been performed with insects. Thus,we do not know if their visual guidance of forward flight is alsoinfluenced by the vertical extent of features. A key distinction be-tween fruit flies (∼1 mg), honey bees (∼100 mg), and especiallyhummingbirds (∼4,000 mg) is that the magnitude of change inmomentum during a collision is much greater for birds, because oftheir larger body mass. This, explains why bumblebees and otherinsects often collide with vegetation (37, 38), whereas collisions are

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Fig. 4. Lateral course control is based on the size of horizontal features,even in the absence of nasal-to-temporal pattern velocity. Hummingbirdshad a strong tendency to steer away from vertical stripe gratings and towardhorizontal gratings, but only when the horizontal stripes were relativelysmall (2.3-cm period size; top two rows of A). This steering response wasdiminished by the presence of large horizontal stripes (18.4-cm period size;bottom two rows of A). Additional tests confirmed that birds steered awayfrom horizontal gratings with a larger period size even in the absence ofvertical stripes that generate nasal-to-temporal pattern velocity (B) (MovieS2). The middle column shows grand means for individual birds and prob-ability densities, as in Fig. 2. Effect sizes are calculated as the average dif-ference between the pink and blue treatments. Stimulus features are notdrawn to scale. Statistical significance: ***P < 0.001; *P < 0.05; ns P > 0.05.

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a major source of mortality in birds (39). These differences in therisk of damage may lead to different visual guidance strategies, inaddition to divergent sensory and neurobiological systems.One of the most intriguing results across visual guidance studies

in insects is that different algorithms are used to control differentflight modes (e.g., refs. 16 and 18). Because hummingbird flight isvery amenable to study in the laboratory, this presents a powerfulopportunity to determine if feature size in general and image ex-pansion in particular are used for guiding different flight modes orrestricted to only some aspects of forward flight control. We hopethat these questions about visual guidance behavior will alsostimulate further research in systems neuroscience that can confirmthe proposed mechanisms at a cellular level (22).

Materials and MethodsAnimals. Eighteen adult male Anna’s hummingbirds (Calypte anna) werecaught in Vancouver, BC, Canada between March 2014 and April 2015 andhoused individually (14). All procedures were approved by the University ofBritish Columbia Animal Care Committee.

Experimental Rig. The flight tunnel consisted of an aluminum frame withacrylic side walls (Fig. 1A). The interior acrylic surface was coated in a frostedwindow covering (14). Stimulus images were back-projected by six ultrashort-throwDLP projectors (NECU310w; 120-Hz refresh rate) outside the tunnel (Fig. 1B).Two separate video cards (2GB MSI GeForce GT 640) and splitters (360 MHz VGA)were used to link three projectors on each side. These displays were synchronizedby Psychtoolbox-3 (40) for Matlab (Mathworks R2013b). The floor of the tunnelwas gray linoleum and the ceiling was nylon netting to permit filming from above.The walls at each end were covered in white paper.

We positioned the feeder and a 10-cm-wide perch 15 cm below the ceiling ofthe tunnel at either end (Fig. 1A) on the midline. Pilot studies indicated thatbirds would not descend much lower, as hummingbirds prefer to fly and perchseveral meters above the ground. Stimulus animations were projected over adepth of 37 cm (Fig. 1A). The walls were blank below the stimulus to facilitatetracking by overhead cameras. For a bird at the average cruising altitude of

1.5 m on the midline, the stimulus subtended 57° vertically on each side. Birdsnever collided with the walls of the chamber during experiments.

Experimental Stimuli. Stimulus animations were controlled using Psychtoolbox-3 (40). We used red because the DLP projectors produce white by sequentiallyflashing each of the red-green-blue (RGB) primaries at 120-Hz intervals,and at the outset of this study we did not know that the temporal reso-lution of Anna’s hummingbird vision is below 70 Hz (20). Red was chosento stimulate the long-wavelength and double-cone photoreceptors in-volved in motion processing (41) and avian flight behavior (42). For stripegratings (50% red and 50% black), the average luminance of red featureswas 8.7 cd/m2 (95% CI 8.4, 9.0) and the average luminance of black fea-tures was 1.5 cd/m2 (95% CI 1.46, 1.54) (Minolta LS-110 photometer). Asmall incandescent lamp (40 W, 120 Hz) was positioned 1.5 m above theperch to provide additional light and encourage perching at that end.To facilitate filming, near-infrared LED strips (850-nm 5050 lights,environmentallights.com) were affixed along the top of each side of thetunnel, facing the midline. This near-infrared light was detected by ourcameras but not the birds because the retinal cones of hummingbirds arenot stimulated by wavelengths > 700 nm (41).

For stimuli consisting of stationary horizontal stripes, the color of thetopmost stripe was matched for the twowalls andwas determined randomly,so that birds were sometimes exposed to red on top and sometimes to blackon top, depending on the treatment. We verified that the color of the topstripe did not significantly affect the birds’ lateral position for treatmentswith 18.4-cm period horizontal gratings (all P > 0.27).

Procedure. Birds in the tunnel were fed ad libitum from a syringe containing7.5 g/100 mL (wt/vol) sucrose solution. Before an experiment, birds wereallowed to explore the stimulus-free tunnel with overhead fluorescentlighting, similar to their aviary housing. A training stimulus consisted ofstationary red and black vertical stripe gratings on both side walls. At 10-minintervals, the grating period size was changed (using period sizes 0.58, 1.15,2.3, 4.6, 9.2, and 18.4 cm, in a different randomly selected order for each bird),with the cycle repeating after 60 min to ensure that birds would be familiarwith all sizes. Once birds had begun to feed at regular intervals, the fluo-rescent lights were turned off. The 60-min training period was repeated at

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Fig. 5. We propose that expansion may govern lateral course control in birds. Vertical expansion, ρv, is defined as the change in the angle, θ, subtended by afeature in the vertical axis (A). The rate of expansion increases much more rapidly for features with a greater vertical extent (i.e., height) (B). Expansion maybe perceived as the birds move laterally; this is shown by the green and magenta lines in C and D, which indicate ρv at the point of expansion (±90° azimuth,0° elevation) for a bird moving to the left (green) or right (magenta) at 0.1 m/s (which is typical of the maximum lateral flight speeds observed) (SI Appendix,Table S10). The dashed lines in C and D are the grand mean (average) lateral positions observed for birds that were halfway to the feeder. The shaded regionsare the grand mean (average) extremes. Note that all flights started and ended on the midline of the flight tunnel, where lateral position = 0. In our ex-periments, the birds steered toward a position that would have reduced ρv relative to their starting position on the midline (C). When the features on bothsides of the tunnel had the same vertical extent (height), the birds remained on average centered on the midline (D). See text in SI Appendix and SI Appendix,Table S10 for details.

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the beginning of each day to ensure motivation. For experiments using dotstimuli, the training stimulus consisted of stationary dot fields with 20 min ateach of the three dot densities (0.47, 0.95, and 1.89 dots/cm2).

Data Collection and Analyses. Experimental treatments were applied in blocks,such that the stimulus changed after a bird was observed to have fed fivetimes. We define a feeding event as the bird traversing the tunnel to dock atthe feeder before returning to the perch. The order of treatment blocks wasrandomized for each bird. Eight cameras (Prosilica GE680, Allied VisionTechnologies; Computar H2Z0414C-MP lenses) filmed from above at 100frames per second (Fig. 1A). Flydra image-based tracking software was usedto automatically track the birds’ flight trajectories and compute the birds’ 3Dposition (x, y, and z coordinates) in each frame (43). We limited our analysesto times when the birds were within positions 1–5 m along the axial (x)length of the tunnel to omit take-off, landing, and feeder docking. Weidentified trajectories during feeding events that had a consistent axialflight direction (i.e., toward or away from the feeder), and if more than onetrajectory occurred as a bird traversed the chamber, we selected the tra-jectory with the longest axial (x) distance for analysis. If a bird was trackedfor fewer than 2.5 m, that flight was discarded as having insufficient data. Intotal, 75 of 3,270 flights were discarded (2%) and these were not biasedtoward any particular treatment.

Because the hummingbirds varied their flight speeds, the times when theyflew slowly are representedwithmore data points in the output of the trackingsystem. We therefore grouped position and velocity data into 1-cm bins alongthe axial (x) axis, taking the mean for each bin, and then taking the mean ofthe bins for each flight to represent the average value while traversing thetunnel. Movie S1 illustrates how average lateral position was calculated fromsample flight trajectories. All statistical analyses were performed on theseflight averages using R 3.2.1 (44). We analyzed average position using mixed-effects regression models in the nlme package 3.1-120 (45), with a randomeffect of treatment block nested within individual to account for noninde-pendence of repeated measures. Hypotheses were evaluated using the glhtfunction in the multcomp package 1.4-0 (46), and P values < 0.05 were con-sidered statistically significant. Data and analyses are provided at https://figshare.com/articles/statistical_supplement_flight_course_control_R/3382759and in SI Appendix.

ACKNOWLEDGMENTS. We thank P. S. Segre, B. Goller, M. V. Srinivasan,D. Lentink, K. Meier, D. Giaschi, D. Schluter, and two anonymous reviewers.The work was supported by a Human Frontier Science Program GrantRGP0003/2013 (to D.L.A.); a Natural Sciences and Engineering Research Council(NSERC) Grant 402677 (to D.L.A.); an NSERC postdoctoral fellowship (to R.D.);and an NSERC graduate fellowship (to T.K.F.).

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