Birds invest wingbeats to keep a steady head and reap the ultimate benefits of flocking

Flapping flight is the most energetically demanding form of sustained forwards locomotion that vertebrates perform. Flock dynamics therefore have significant implications for energy expenditure. Despite this, no studies have quantified the biomechanical consequences of flying in a cluster flock relative to flying solo. Here, we compared the flight characteristics of homing pigeons (Columba livia) flying solo and in pairs, using high-precision 5 Hz GPS and 200 Hz tri-axial accelerometer biologgers. Paired flight increased route accuracy by ~7%, but, was accompanied by an increase in wingbeat frequency of ~18%. As expected, paired individuals benefitted from improved homing route accuracy, which reduced flight distance by ~7% and time by ~9%. However, realising these navigational gains involved substantial changes in flight kinematics and energetics. Both individuals in a pair increased their wingbeat frequency by c.18%, by decreasing the duration of their upstroke. This sharp increase in wingbeat frequency caused just a 3% increase in airspeed, but reduced the oscillatory displacement of the body by ~22%, which we hypothesise relates to an increased requirement for visual stability and manoeuvrability when flocking. Overall, the shorter flight distances and increased wingbeat frequency in a pair resulted in a net increase in the aerodynamic cost of returning home, which we estimate was ~14%. Our results demonstrate that flocking costs have been underestimated by an order of magnitude and force reinterpretation of their mechanistic origin. We show that, for pigeons, two heads are better than one, but keeping a steady head necessitates energetically costly kinematics.

tri-axial accelerometer biologgers. Paired flight increased route accuracy by ~7%, but, was 23 accompanied by an increase in wingbeat frequency of ~18%. As expected, paired individuals 24 benefitted from improved homing route accuracy, which reduced flight distance by ~7% and 25 time by ~9%. However, realising these navigational gains involved substantial changes in flight 26 kinematics and energetics. Both individuals in a pair increased their wingbeat frequency by 27 c.18%, by decreasing the duration of their upstroke. This sharp increase in wingbeat frequency 28 caused just a 3% increase in airspeed, but reduced the oscillatory displacement of the body by 29 ~22%, which we hypothesise relates to an increased requirement for visual stability and 30 7 paired and solo flight within the same release. The results for these six releases clearly confirm 139 that wingbeat frequency increases as a direct result of flying in a pair, because the birds' median 140 wingbeat frequency decreased by 1.01 ± 0.30 Hz (mean ± s.d.) after they separated and flew 141 solo (raw values with no covariates; Fig. 2E-H). To explore the mechanism underlying this change in wingbeat frequency, we divided each 162 wingbeat into an upstroke and a downstroke phase. We defined these phases with respect to 163 8 the peaks and troughs of the DB acceleration, which results from a combination of aerodynamic 164 and inertial forcing (see supplementary text for further detail). Whereas the dorsal aerodynamic 165 force is expected to peak mid-downstroke when the wing reaches its maximum flapping speed, 166 the dorsal inertial force is expected to peak at the start of the downstroke when the wing's 167 downwards acceleration is maximal. It follows that the maximum DB acceleration will be 168 reached somewhere between the start and middle of the kinematic downstroke, and similarly 169 for the minimum, which will be reached somewhere between the start and middle of the 170 kinematic upstroke. Hence, the downstroke phase, which we define as running from the point 171 of maximum to minimum DB acceleration, is expected to lag the kinematic downstroke slightly 172 (and similarly for the upstroke), but by less than a quarter of a cycle. With these definitions, 173 we found that birds reduced the median duration of the upstroke phase by 20.6% (-27 We hypothesise that a potential function of increasing wingbeat frequency and decreasing 182 oscillatory displacement of the body may be to enhance visual stability when attending to 183 nearby conspecifics. We therefore conducted a second experiment using head-mounted 184 accelerometers on six homing pigeons on short-range flights (950 m), flying solo and in pairs, 185 to determine if the same measured changes in wingbeat characteristics result in increased head 186 stability (see Methods). In close agreement with the first experiment, birds flying in pairs 187 increased their median wingbeat frequency by a mean of 1.10 Hz ± 0.26 relative to flying solo 188 9 (6.6 ± 0.42 Hz mean ± s.d. for pairs; 5.5 ± 0.46 Hz for solo). More importantly, however, the 189 results also show that the median peak-to-peak head displacement simultaneously decreased 190 by 5.3 ×10 -3 m ± 6.6 × 10 -4 between solo and paired flight, representing a 30% reduction in the 191 amplitude of oscillatory head displacement (Fig. 3). This substantial improvement in 192 translational head stability is expected to result in a significant reduction in the retinal slip of 193 nearby objects including flight partners. 194 195 In summary, by reducing the duration of their upstroke phase, birds flying in a pair were able 196 to accommodate one additional wingbeat per second, whilst maintaining the same peak-to-peak 197 DB acceleration and simultaneously increasing the vertical stability of the head. Intuitively, a 198 higher-frequency kinematic gait adopted in paired flight will therefore be associated with a 199 higher mechanical power input than the lower-frequency flight kinematic gait adopted in solo 200 flight. Of course, a higher mechanical power requirement in paired flight could still be 201 associated with a lower cost of transport if this increased frequency were more than 202 compensated by an increased flight speed. However, whereas birds migrating in V-formations 203 are known to increase their airspeed as flock size increases [25], the birds in our study only 204 increased their airspeed by 3.3% when flying in pairs (0.64 m s -1 increase, 95% CrI [0.08, 1.2]). 205 As we now explain, this increase in airspeed is much smaller than could have been expected to 206 be caused by the increase in wingbeat frequency alone, suggesting that there must have been 207 other compensatory changes in the kinematics. 208

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In cruising flight, the net thrust of the wings balances the drag on the body, which scales as 210 10 wingbeat frequency, and is wingbeat amplitude [26]. Assuming all other things are equal, an 214 18% increase in wingbeat frequency would therefore be expected to produce about a 39% 215 increase in thrust. However, we also know that the time-averaged lift must balance the bird's 216 weight when cruising, and that lift scales as ~+ & in fast forward flight when the 217 contribution of the wing's own flapping speed can be ignored. This implies that the 3% increase 218 in airspeed (i.e 6% increase in & ) would have to have been countered by either a 6% decrease 219 in wing area, or an equivalent decrease in the proportionality constant of the scaling 220 relationship (i.e. the wing lift coefficient). Either kinematic change would be expected to 221 attenuate the thrust similarly, thereby reducing its expected increase to approximately 31%. 222 This is still significantly higher than the 6% increase in thrust estimated on the basis of the 3% 223 span, but is an order of magnitude smaller than the aerodynamic power requirement [27,28] so 231 is neglected here for simplicity. Assuming that the 18% increase in wingbeat frequency 232 between solo and paired flight was accompanied by a 6% decrease in wing area + and by a 233 10% decrease in wingbeat amplitude as required to meet the equilibrium conditions above, 234 then the aerodynamic power requirement (in J s -1 ) would have increased by approximately 25% 235 when flying in a pair. Given the 3% increase in airspeed, it follows that the aerodynamic cost 236 of transport (in J m -1 ) must also have increased by some 21%. However, another key benefit 237 often ascribed to flying in flocks is the ability to pool navigational knowledge. This should 238 improve homing route accuracy [7,8], which could offset the increased aerodynamic cost of 239 transport and increased aerodynamic power requirement by simultaneously decreasing the 240 distance and duration of the flight. 241

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We calculated the birds' route accuracy flying solo and in pairs using a weighted mean cosine 243 of the angle between the birds' heading and destination. Flying in a pair resulted in a 6.9% 244 increase in route accuracy relative to both the Phase 1 and Phase 4 solo releases (0.06, 95% CrI 245 [0.01, 0.10]; Fig. 1), and a 6.5% decrease in route length (Table S2). This is consistent both 246 with theory[7,8] and with previous empirical studies [5,6]. Offsetting the 21% higher cost of 247 transport when flying in a pair against the 6.5% reduction in route length, we would expect a 248 net increase of approximately 14% in the total mechanical energy expended when flying home 249 to the loft in a pair. The increase in the total metabolic energy expended could be higher or 250 lower than this, depending upon whether and how the efficiency of the flight muscles varies 251 with flapping frequency, but it is reasonable to assume that an increase in mechanical energy 252 would also be associated with an increase in metabolic energy. in pairs were simultaneously able to offset some of the energetic cost by flying more accurate 283 routes home, the increases in route accuracy and airspeed were insufficient to compensate for 284 the increased aerodynamic power requirements, which resulted in a net energetic loss on the 285 order of 14% when flying moderate distances (~7 km) together in a cluster formation. 286 Moreover, the fact that pigeons flying in pairs display a 18% increase in wingbeat frequency 287 over solo flight suggests that the majority of the additional cost comes merely from the act of 288 13 flying with another individual, rather than from the density of the flock, the relative spatial 289 position of the bird, or the size of its partner. Indeed, the size of a bird's partner, and whether 290 that bird was a leader or follower, had almost no effect on its measured wingbeat pattern. Even 291 so, differences in inter-individual horizontal spacing did result in a 0.54 Hz difference in 292 wingbeat frequency between birds travelling 0 to 50 m apart, with this increase ranging from 293 11.9 to 21.6 %, respectively. Thus, the act of flying with a conspecific resulted in a substantial 294 alteration of the wingbeat -even the adoption of a different kinematic gait. As we now explain, 295 not only does this earlier omission mean that the costs of flocking have been massively 296 underestimated -it also means that their mechanistic origin must be re-evaluated. Birds make kinematic control inputs on a wingbeat-to-wingbeat basis, so increasing wingbeat 315 frequency will increase the rate at which control inputs can be made, enhancing the bird's 316 ability to respond to the movements of others and increasing the precision of its response. dorsal accelerometer measurements were filtered by taking a running mean over three data 454 points (0.015 s). Static acceleration (or gravity) was removed by subtracting a running mean 455 over 15 wingbeat cycles (> 2 s; Fig S5). The wingbeat frequency (number of wingbeats per 456 second; Hz) and peak-to-peak dorsal body (DB) acceleration (g) using the dorsal acceleration 457 signal (Z-axis) were calculated for each individual wingbeat. The amplitude of the DB 458 displacement (mm) was then calculated by the double integration of dorsal accelerometer 459 measurements [14,20]. In addition, we calculated the duration of the "downstroke" from the 460 peak downstroke force (maximum g-force) to the lower reversal point (minimum g-force). The 461 "upstroke phase" duration, which included the start of the downstroke, was measured from 462 minimum g-force to the maximum. We used the maximum and minimum g-force peaks to airspeed (m s -1 ) was also added as a covariate on all models except for models of airspeed. We 528 used airspeed rather than ground speed as a covariate because ground speed and wind support 529 were correlated (Fig. S5). In terms of the response variable, there was almost no difference 530 between the models of airspeed and ground speed as the model accounts for the effect of wind 531 In addition to modelling the median values, we also took a random sample of 100 individual 537 wingbeats to analyse the effect of horizontal distance between birds in pairs. We analysed 538 horizontal distance rather than three-dimensional distance because GPS precision is generally 539 poorer in the vertical than the horizontal [42]. Horizontal distance (m) was added as a covariate 540 to the paired data, along with a categorical covariate identifying the specific bird and flight to 541 account for the repeated measures of 50 wingbeats from one flight. In total, 44,500 wingbeats 542 from 454 unique bird and flight combinations were analysed. 543

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To investigate whether the birds were flying in phase, we used the following model to identify 545 whether the median wingbeat frequency of the follower ( _ t ) is related to the leader ( _ u ) in 546 pair ( ): 547 We also investigated whether the difference between the leader and follower's tarsus length, 550 body mass or solo airspeed ( ) predicted why the bird was a leader ( ) in the pair using a 551 Bernoulli regression: 552 The model priors were centred on the null hypothesis using the mean, standard deviation and 555 square root standard deviation of the solo data (Table S4)  We used a custom-built 'p-Sensor' to simultaneously record head movement and position. The 594 p-Sensor included an IMU with a combination of a tri-axial gyroscope, tri-axial accelerometer 595 and tri-axial magnetometer recording at 60 Hz, and a GPS logger recording at 10 Hz. The IMU 596 was mounted using double-sided tape onto a custom-made and custom-fitted wire mask 597 designed to fit each bird's head. The GPS logger, SD card, battery and microcomputer were 598 placed in an elasticated backpack on the birds back. The instrumentation, mask, and backpack 599 weighed 28.1 g and constituted 4.9 % of the body mass of the smallest bird, of which the IMU 600 unit on the bird's head only weighed 1 g. For more details, see Kano et al. [36]. 601 602 All birds were habituated to wearing the custom-made mask for at least seven days prior to the 603 flight. For each day of habituation, the bird was fitted with a mask and carefully monitored for 604 two hours within its home loft for signs of discomfort and abnormal patterns of locomotion. Releases were only conducted when the wind was low (<5 m s -1 ) and the sun's disc was visible. 613 For the day of testing, the birds were fitted with a mask and allowed to habituate to wearing 614 the mask in the home loft before being transported to the release site by car. The birds were 615 released once solo and once in a pair on the same day. The release order was randomised. 616 617 iv) Data processing and analysis 618 619 620 The data processing was conducted as outlined in Taylor et al. [20]. Vertical (Z-axis) 621 accelerometer measurements were smoothed by taking a running mean over five datapoints 622 (0.083 s) and then filtered using a 4 th order high-pass Butterworth filter with a cut-off frequency 623 of 1 Hz. The peak-to-peak vertical head displacement was calculated by the double integration 624 of the vertical accelerometer measurements. We compared the median peak-to-peak vertical 625 head displacement between solo and paired releases for each bird. 626

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The raw data will be available on data dryad after acceptance. 628