Collective movement of schooling fish reduces locomotor cost in turbulence

(233 words): 26 The ecological and evolutionary benefits of collective behaviours are rooted in the physical 27 principles and physiological mechanisms underpinning animal locomotion. We propose a 28 turbulence sheltering hypothesis that collective movements of fish schools in turbulent flow can 29 reduce the total energetic cost of locomotion by shielding individuals from the perturbation of 30 chaotic turbulent eddies. We test this hypothesis by quantifying energetics and kinematics in 31 schools of giant danio (Devario aequipinnatus) compared to solitary individuals swimming 32 under control and turbulent conditions over a wide speed range. We discovered that, when 33 swimming at high speeds and high turbulence levels, fish schools reduced their total energy 34 expenditure (TEE, both aerobic and anaerobic energy) by 63–79% compared to solitary fish. 35 Solitary individuals spend ~25% more kinematic effort (tail beat amplitude*frequency) to swim 36 in turbulence at higher speeds than in control conditions. However, fish schools swimming in 37 turbulence reduced their three-dimensional group volume by 41–68% (at higher speeds) and did 38 not alter their kinematic effort compared to control conditions. This substantial energy saving 39 highlighted a ~261% higher TEE when fish swimming alone in turbulence are compared to 40 swimming in a school. Schooling behaviour could mitigate turbulent disturbances by sheltering 41 fish within schools from the eddies of sufficient kinetic energy that can disrupt the locomotor 42 gaits. Providing a more desirable internal hydrodynamic environment could be one of the 43 ecological drivers underlying collective behaviours in a dense fluid environment. 44 45 One-Sentence Summary: 46 47 The collective movement of fish schools substantially reduces the energetic cost of locomotion 48 in turbulence compared to that of swimming alone. 49 50 51 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576168doi: bioRxiv preprint 3

52 Nearly all animal species live with ubiquitous turbulent air or water in nature (1) (2) (3) 53 (4). Hence, turbulent flows affect many aspects of animal biology that are fundamental to 54 lifetime fitness, including dispersal and spawning, the cost of moving for both regional 55 locomotion and long-distance migration, and the dynamics of predator-prey interactions (5). In 56 particular, chaotic turbulent flows (6) (7) (8) directly subject solitary individuals to unpredictable 57 fluid fields and alter body kinematics. For animal species that routinely interact with ambient 58 flow and perceive their fluid environment, when visual input on incoming turbulent flow is 59 limited, individual animals may have limited sensory input and less anticipatory time to adjust 60 body motion on short time scales. Under such challenging conditions, individual animals may 61 have few options for mitigating the energetic costs of living and moving in turbulence. 62 This challenge is especially formidable for aquatic life in natural channels of rivers and 63 coastal seas (9) (10) (11) (12), because water is 50 times more viscous than air (13) (14) (5) (15) 64 and exerts larger perturbing forces on fish. Moving in turbulence is particularly challenging and 65 energetically expensive for solitary fish. Solitary creek chub (Semotilus atromaculatus) 66 swimming in turbulence reduced maximum sustained swimming speed (by 22%) because large 67 turbulent eddies (~76% of body length) disrupt the movement trajectories of fish (14). Also, the 68 cost of locomotion by solitary Atlantic salmon (Salmo salar) can increase by ~150% in 69 turbulence (16). Studies on animal locomotion and turbulence have profound implications for a 70 better understanding of the planetary ecosystem, e.g., turbulence generated by groups of fish can 71 contribute to vertical mixing of the ocean (17) (18) (19). Despite the widespread interest in 72 understanding how fish interact with turbulence (5) (14) (15) (18) (20) (21) (22) (23) (24) (25) 73 (26) (19) (27) (21) and the ubiquitous interactions of animals and their turbulent fluid 74 environments, no previous study has investigated the effects of turbulent flow on fish schools. 75 This can be due to the complexity of turbulent flow and the dynamic nature of collective animal 76 motion. Could the collective movement of fish schools mitigate the effects of turbulent flow by 77 alternating their locomotor characteristics? 78 Fish schools could modulate oncoming turbulent flow through the coordination of nearby 79 individuals. Nearly all fish could modify the local fluid environment through vortices shed by 80 their undulatory body motion, and by acting as nearby solid surfaces (28) (29) (30) (31) (32). A 81 school of fishes could reduce the intensity and length scale of oncoming turbulent eddies within 82 the school (Fig. 1). Hence, we propose a “turbulence sheltering hypothesis” that a fish school can 83 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576168doi: bioRxiv preprint 4 shield individuals within the group from ambient turbulence (Fig. 1). If this hypothesis holds, a 84 key prediction is that collective movement reduces the total energy expenditure per unit of 85 biomass compared to that of a solitary individual under the same flow conditions. This study 86 focuses on testing this hypothesis experimentally. 87 Vertebrates use both aerobic and non-aerobic metabolic energy to support their total 88 energy expenditure (TEE) during locomotion. Aerobic metabolism primarily supports energy use 89 at slower and steady locomotion, while glycolytic metabolism supplies faster and unsteady state 90 high-speed movement (33). Not only do the physiological mechanisms underpinning locomotion 91 shift with speed, but fluid drag also scales as the square of fluid velocity. Hence, increased 92 swimming speeds physically require substantially more metabolic energy. The characterization 93 of a locomotor performance curve (TEE as a function of speed) (34) under both turbulent and 94 control conditions will test the working hypothesis that fish schools could mitigate the expected 95 increase in the energetic cost of moving in turbulence. To test this hypothesis, we directly 96 quantified the locomotor performance curve for both solitary individuals and schools of eight 97 giant danio (Devario aequipinnatus) across a wide range of speeds from 0.3 to 8 body lengths 98 sec-1. We measured whole-animal aerobic energy expenditure (oxidative phosphorylation) 99 during swimming, as well as excess post-exercise O2 consumption (EPOC) to quantify non-100 aerobic energy expenditure after swimming (high-energy phosphates and substrate-level 101 phosphorylation) (35) (36) (37). In addition, we simultaneously quantified the kinematics of 102 individual fish and those within schools, and measured three-dimensional school volumes to 103 characterize how fish responded to both control and turbulent flow environment. 104

105 Hydrodynamics of turbulent conditions 106 Turbulent flows (generated by a passive turbulence grid) exhibit strong fluctuations and 107 chaotic patterns (Fig. 2 A,B) in contrast to controlled flows (generated by a flow straightener). 108 Quantitatively, turbulent testing conditions showed sustainably greater maximum velocity (F1,107 109 = 401.9, p < 0.001, Fig. 2C), maximum vorticity (F1,107 = 167.8, p < 0.001, Fig. 2D), and 110 maximum (Fig. 2E) and sum shear strength (F1,107 ≥ 153.7, p < 0.001, Fig. 2F). Since turbulence 111 was generated by passing the flow through a passive grid, greater turbulence was reached at 112 higher mean flows; similar rise of values of all these parameters in control flow condition was 113 also observed, but with a greatly reduced rate of increase with velocity (Fig. 2). In addition, the 114 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576168doi: bioRxiv preprint 5 probability density function (p.d.f) of flow velocity along the swimming direction (u) and 115 perpendicular direction (v) showed the broadening of p.d.f (Fig. 3A & B), a clear indication of 116 intensified turbulence as speed increases. Since turbulence fluctuation velocity increases 117 approximately linearly with the mean flow speed (Fig. 3C), the resulting turbulence intensity, 118 defined as the ratio between the two, remains nearly constant over the flow speeds studied. 119 Eddies of various sizes can differentially impact the energetics of fish locomotion. The 120 undulatory motion of fish can respond to eddies smaller than fish size, whereas eddies 121 comparable to the body size may have sufficient energy to change the fish’s movement 122 trajectory, which could result in increased energy expenditure. However, turbulence is notorious 123 for its wide spectrum of scales, which can be quantified by the largest (integral scale) and the 124 smallest (Kolmogorov scale), shown as two separate lines with the range in between showing the 125 full range (Fig. 3D). Based on the energy cascade framework of turbulence eddy scale, the large 126 eddies at the integral length scale (L) were comparable to the fish body depth (D) and are 127 capable of energetically challenging fish locomotion (Fig. 1, 3). 128 129 Energetics of collective movement 130 We discovered that aerobic metabolic rate – speed curves of fish schools and solitary 131 individuals both are concave upward in turbulence across the entire 0.3–7 BL s-1 speed range 132 (Fig. 4). We demonstrate that turbulent flow has resulted in upshifted aerobic metabolic rate – 133 speed curves of solitary individuals across the entire speed range (F1, 69=4.45, p=0.0003) 134 compared to locomotion by fish schools. In particular, the energetic cost of swimming was 32% 135 lower at 6 BL s-1 in schools compared to individuals swimming alone in turbulence (719.3 vs 136 1055 mg O2 kg-1 h-1, F1,69 = 4.1, p = 0.0015, Fig. 4A). Aerobic energy conservation enabled by 137 schooling dynamics is more pronounced at the higher speeds when the energy demands are at a 138 premium. 139 Because fish body musculature operating at high frequencies during locomotion at high 140 speed mostly uses white muscle fibres powered in part through glycolysis (38) (39), we predict 141 that the schooling dynamics should also conserve non-aerobic energy (estimated by EPOC) and 142 reduce the recovery time when compared with solitary individuals. Indeed, the non-aerobic cost 143 for fish schools to swim through the entire speed range in turbulence was nearly 8-fold lower 144 than that of solitary individuals (EPOC: 0.68 vs 5.4 mg O2, t=7.0, p=0.0005, Fig. 4C). Fish that 145 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576168doi: bioRxiv preprint 6 swam in schools recovered 1.8-fold faster than solitary individuals (EPOC duration: 11.8 vs 21.5 146 h, t=2.3, p=0.035). 147 As a result, both total energetic expenditure (TEE) and total cost of transport (TCOT) of 148 fish schools was 62–79% lower than that of solitary individuals swimming in turbulence over the 149 3–7 BL s-1 range Fig. 4G). Non-aerobic costs contribute 72–83 % of total energy consumption in 150 solitary fish, whereas the non-aerobic contribution was only 20–40% in fish schools (Table S1). 151 If non-aerobic locomotor costs are not accounted for, 75–177% of locomotor energy expenditure 152 in solitary individuals (Fig. 4D), and 251–800% of the energy expenditure in fish schools (Fig. 153 4E) would not have been accounted for. 154 Despite the substantial energy saving enabled by fish schooling in turbulence compared 155 to swimming in the same turbulent environment alone, fish schools do not completely eliminate 156 the effects of turbulence on locomotor cost. After accounting for both aerobic and non-aerobic 157 energy costs, we discovered that the TEE of fish schools swimming in turbulence was 51–76% 158 higher (F1, 7=54.3, p ≤ 0.0072, Fig. 4F) than the cost for fish schools swimming under control 159 (low turbulence) hydrodynamic conditions over the speed range of 5–7 BL s-1, and TCOT of fish 160 schools was 68 and 76% higher in turbulence than in control low-turbulence flow (F1, 91=36.2, p 161 ≤ 0.007) at 6 and 7 BL s-1 respectively (Fig. 4G). The proportional increase in the total energetic 162 cost of swimming in turbulence is again mostly from non-aerobic energy production. 163 Nevertheless, the magnitude of the increased total costs of swimming in turbulence is only a 164 fraction (9–24%) of the costs for solitary individuals. Solitary individuals spent 190–342% 165 higher total energy swimming in turbulence across the speed range of 2.5–7 BL s-1 compared to 166 locomotion in control fluid conditions (Fig. 4F, G). 167 Kinematics 168 Using high-speed videography, we discovered that, as speed increases to speeds >1.7 BL 169 s-1, school volume becomes smaller, and the 3-D convex hull representing school volume is 170 reduced by 74% as individuals within the school swim in closer proximity (F12,143 = 11.74, p < 171 0.0001). Over the speed range of 1.7–7 BL s-1, fish schools become denser and form a prolate 172 spheroid shape compared to the streamlined school structure when fish schools swim in 173 controlled flows of the same speed. The 3-D convex hull volume of fish schools swimming in 174 turbulent conditions is 40–68% lower than that for schools swimming in control conditions at 175 similar speeds (t1,8 ≥ 2.147, p ≤ 0.032, Fig. 5). 176 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576168doi: bioRxiv preprint 7 Also, kinematics of individual fish (Tail beat frequency, ftail; tail beat amplitude, Amptail; 177 ftail•Amptail) within schools swimming in turbulence were not different from when fish schools 178 swam in control flow conditions (Fig. 6F, MANOVA: F1,25 ≤ 0.028, p ≥ 0.868). However, 179 solitary fish spend up to 22% more effort (estimated as tail beat frequency times amplitude, 180 f•Amptail) swimming in turbulence than for control flow locomotion (Fig. 6E, MANOVA: F1,28 ≥ 181 1.167, p ≤ 0.006). Solitary fish increase ftail at lower speeds (ANOVA: F1,575 ≥ 4.67, p ≤ 0.031, 182 Fig. 6A) and also reducing Amptail (ANOVA: F1,639 ≥ 26.35, p < 0.001, Fig. 6C). As a result, 183 swimming effort remains the same at lower speeds when compared to solitary individuals 184 swimming in controlled flows, as indicated by both kinematics (f•Amp) (MANOVA: F1,28 = 185 1.167, p = 0.281) and energetics (Fig. 6F, ANOVA: F1,71 ≤ 1.23, p ≥ 0.96). As speed increases in 186 turbulence, solitary fish increase Amptail by 26% (Fig. 6C) (ANOVA: F14,639 = 3.69, p < 0.001), 187 and there is no further increase in ftail (Fig. 6A). Locomotor effort (Ftail•Amptail) increased with 188 speed at a greater rate for individuals in turbulence compared to individuals swimming under 189 control conditions over the range of speeds tested (ANOVA: F7,536 = 173.14 p ≤ 0.006, Fig. 6E). 190 191

192 Despite the ubiquity of vertebrates moving in environments with turbulent flows, we 193 know remarkably little about the energetic costs of moving in turbulence as a collective group 194 compared to moving in the same conditions as a solitary individual. Hence, we integrate three 195 lines of evidence (energetics, individual kinematics, and schooling dynamics) and compare them 196 between fish schools and solitary individuals over the same speed range in turbulence. 197 Our results support the turbulence sheltering hypothesis. We first discovered that the 198 collective movement of fish schools substantially dampens the effects of turbulence by 199 downshifting the locomotor performance curve at higher speeds, compared to when solitary 200 individuals swim in turbulence. Fish schools in turbulence expend up to 79% less energy than 201 fish under control conditions (Fig. 4F). One of the essential mechanisms by which fish schools 202 dampen turbulent disturbances is by collectively swimming in up to a 68% tighter schooling 203 formation compared to control conditions. As a result, fish swimming within schools showed no 204 difference in their swimming kinematics regardless of whether the fish schools swim in 205 turbulence or control conditions. We also discovered that one of the key reasons for higher 206 locomotor costs when solitary individuals swim in turbulence is the increase in tail beat 207 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576168doi: bioRxiv preprint 8 amplitude (Amptail) at higher speeds (Fig. 6C), which increases the kinematic effort of swimming 208 as estimated by tail beat frequency times amplitude (f•Amptail) (Fig. 6E, F). As a result, the total 209 energy expenditure (TEE) and total cost of transport for solitary individuals, including both the 210 aerobic and non-aerobic energy contributions, are ~261% higher compared to when solitary 211 individuals swim in control conditions (Fig. 4F, G). 212 Therefore, collective behaviour provides effective turbulence sheltering, not only 213 mitigating the kinematic responses needed in turbulent flow, but also providing a large energetic 214 advantage by downshifting most of the locomotor performance curve. We highlight three key 215 considerations regarding collective movement in turbulent flows: 1) How does collective 216 movement dampen the turbulent disturbance on locomotor energetics? 2) How do body 217 kinematic patterns act as a linchpin between fluid dynamic and energetic effects? 3) How does 218 the hydrodynamic scale of turbulence relative to fish size matter for broader considerations of 219 fish locomotor ecology? 220 221 1) Schooling dynamics dampens the effects of turbulence 222 Fish schools (i.e. giant danio) are effective at reducing the energetic costs of swimming in 223 turbulence. The TEE and TCOT of solitary individuals are 188–378% higher than that of fish 224 schools at higher speeds, per kilogram of biomass. By studying both aerobic and non-aerobic 225 locomotor costs, we discovered that most of the energy saving stems from the reduced use of 226 non-aerobic energy (Table S1 & S2). Specifically, fish schools swimming in turbulence 227 generated an 8-fold lower excess post-exercise oxygen consumption (EPOC, including the use of 228 high-energy phosphate stores and glycolytic energy contributions) than that of a solitary 229 individual. The aerobic cost of swimming at higher speeds was also 47% higher in solitary 230 individuals compared to that of fish schools. Collectively, over the entire range of swimming up 231 to maximum and sustained speeds, schooling dynamics effectively dampens the additional 232 metabolic costs of moving in the turbulent flow by 3.8 folds (the integral area under the TEE 233 curve of schools versus individuals in turbulence: 165.5 vs. 633.3 kj kg-1). 234 Solitary individuals increased tail beat frequency (ftail) but reduced tail beat amplitude 235 (Amptail) to compensate for turbulent disturbances at the lower speeds (≤ 43% critical swimming 236 speed, Ucrit), which yielded the same kinematic effort (estimated as ftail•Amptail) as swimming 237 under control flow conditions. As water velocity increases to ≥ 86% of Ucrit, solitary individuals 238 can no longer increase ftail to compensate for the effects of turbulence. Instead, solitary 239 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576168doi: bioRxiv preprint 9 individuals increased Amptail to compensate for the turbulent disturbances which increased 240 kinematic effort and reflected in substantially higher energetic cost. In contrast, schooling is 241 highly effective at reducing the effects of turbulent eddies on fish kinematics within the school, 242 and fish within a school in turbulence move similarly to fish swimming in controlled flow. 243 Bioenergetics is critical to understanding the cost of behaviours (40) (41) (42), and allows 244 direct quantification of the amount of energy used to answer fundamental questions including 245 “How much does a behaviour cost?” and “How do altering environmental conditions affect this 246 cost?”. Energetic measurements are particularly useful in evaluating hypotheses involving 247 locomotion occurring over a range of movement speeds and in comparison to control conditions. 248 The kinematic effort of fish swimming (estimated as f•Amptail) suggested that energy saving by 249 schooling danio in turbulence is ~25%, whereas direct measurement of energy expenditure 250 shows a total energy saving of ~79%. Kinematic analyses typically use snapshots of body motion 251 of individuals to quantify biomechanical effort, but do not necessarily reflect total energy use, 252 particularly when sampled intermittently during an incremental speed test. Our energetic 253 measurements detected that turbulent flow increased the total cost of locomotion of fish schools 254 by 51–76% at higher speeds compared to when fish schools swim in controlled flow conditions, 255 whereas fish schools swimming in turbulent and control conditions showed no difference in tail 256 kinematics. Although understanding the biomechanics of locomotion and movement are essential 257 adjuncts to studying locomotion energetics, the cost of movement for any animal is also 258 governed by the underlying physiological mechanisms relating to the cardiorespiratory system, 259 circulatory system, musculature and metabolic pathways that generate the ATP needed for 260 movement. We thus advocate here for integrated studies of kinematics and energetics, and 261 caution that kinematic studies alone may not reflect actual levels of energy use. 262 263 2) Kinematics and schooling dynamics in turbulence 264 To better understand the interactions between fish kinematics and fluid dynamics, we 265 characterized Strouhal number (St, dimensionless undulatory propulsive effort at a movement 266 speed) (43) (44) and Reynolds number (Re, dimensionless fluid speed showing the ratio between 267 inertial and viscous forces) (13). Regardless of whether solitary individuals or fish schools swim 268 in controlled or turbulent conditions, the St ranged 0.25–0.35 (Fig. 7A). The general relationship 269 of St and Re is independent of added turbulence and whether or not fish swim within a school. 270 The general relationship of Re and St (the log-log linear relationship, Fig. 7A) falls in the 271 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576168doi: bioRxiv preprint 10 vicinity of a general scaling hypothesis for aquatic undulatory locomotion (45). However, these 272 data show that even in the turbulent flows giant danios maintain the linear relationship between 273 St and Re instead of transitioning to a different relationship as proposed by the previous scaling 274 hypothesis (45). It is possible that, if the Re of locomotion is increased beyond Re > 105 (e.g. 275 larger species moving at faster speeds), the relationship of Re and St could change, but our data 276 do not support the previously suggested scaling of locomotor St and Re in turbulence. Future 277 laboratory studies are needed to better inform the relationship of Re and St across a wide range 278 of swimming velocities in turbulent conditions that are ubiquitous in nature. 279 Since our data collapse onto a single scaling relationship (Fig. 7A), how can we explain 280 the difference in metabolic rates between turbulent and control conditions? As a completed swim 281 oscillatory body wave typically starts from the head of the fish, hence we tracked the oscillation 282 at the nostril region of the fish head (oscillatory amplitude as a function of time) to examine the 283 fluid conditions surrounding the fish. We reason that locations within a school can reduce the 284 turbulent disturbances that would otherwise increase locomotor costs for solitary fish. 285 Individuals swimming alone under controlled conditions show a regular pattern of head 286 oscillation frequency and near-constant oscillation amplitude (Fig. 7B, blue wave). However, the 287 head oscillations of solitary individuals in turbulent flows are irregular and of varying frequency 288 (Fig. 7B, purple wave). Individuals within a school swimming in turbulence have rhythmical 289 head oscillations and more distinct peaks than those under turbulent conditions (Fig. 7B, orange 290 wave), and the pattern of head oscillation is more like that of solitary individuals swimming in 291 control flow conditions. The benefit of swimming within a school is most likely the result of the 292 tighter schooling formation as fish schooling volumes are reduced in turbulent flows. Smaller 293 inter-individual distances allow the myriad of hydrodynamic mechanisms that are associated 294 with reduced cost of locomotion to become effective, including fish swimming side-by-side, in 295 front and behind other fish, and in the reduced velocity zone behind two fish (34) (46) (32) (47) 296 (48). These results suggest that fish schools act as effective “shelters” that enhance 297 hydrodynamic mechanisms that reduce locomotor cost, a strategy that is not available to 298 individual fish swimming alone in turbulence. 299 As a topic for future investigation, we suggest that the fish schools could alter the size 300 scale of turbulent eddies within the school and thus reduce the impact that environmental 301 perturbations have on the cost of individuals swimming. Fish schools could function as band-302 pass filters as a result of their undulatory body motion and the proximity of individuals within 303 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576168doi: bioRxiv preprint 11 the school to each other. This collective undulatory movement could create a more predictable 304 flow field within the group that reduces kinematic efforts and swimming costs compared to 305 individuals swimming alone in turbulence. 306 Measuring flow conditions within a school would provide a more direct and detailed 307 understanding of how turbulent eddies within fish schools are modified in comparison to the 308 free-stream turbulent flow field. However, this is currently a considerable experimental and 309 technical challenge. Even when using multiple laser light sheets or volumetric approaches to 310 illuminate flow within a school, the bodies of fish in a dense school inevitably cast shadows and 311 hinder the resolution of imaging turbulent flow within the school. In the absence of direct 312 measurements for within-school flow fields, kinematic and energetic data provide the best 313 available evidence for the turbulence sheltering hypothesis. 314 315 3) Turbulence length scale and fish ecology 316 Turbulent disturbances on animal movement are multifaceted and context-specific. 317 Turbulent flows are chaotic and unpredictable by fish, and contain energy over a wide spectral 318 range (Figs. 2, 3), which differs from a Kármán vortex wake where a solitary fish can interact 319 with a regular and predictable pattern of oncoming vortices (49). Fish swimming in a Kármán 320 vortex street can save energy by tuning their body dynamics to interact with oncoming vortices, 321 and greatly reduce their muscle activity and energetic cost (3) (50). When fish are exposed to the 322 true chaotic turbulent flow with a length scale on the same order of magnitude of body size, as in 323 the experiments presented here, the energetic cost of locomotion greatly increases. 324 Demonstrating the reduction in the total cost of locomotion in turbulence by group 325 dynamics in aquatic vertebrates has direct implications for the movement ecology of migratory 326 species. For example, a “feast-or-famine” life history is common to many migratory species. 327 Food availability can be scarce and fluctuate during the migration journey (51). Migratory (fish) 328 species typically accumulate energy and nutrients during the feeding season prior to undertaking 329 a long migration. As a result, migratory species often rely on a finite number of onboard stores of 330 metabolic substrates to fuel migration. We demonstrated here that the total cost of transport 331 when fish schools move through turbulence is substantially decreased. Thus, fish schools should 332 migrate a longer distance for the same amount of energy. By migrating in a collective group, as 333 many fish species do, fish should be able to sustain migration against unexpected costs 334 associated with changing environmental stressors such as heat, hypoxic episodes, and storms. 335 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576168doi: bioRxiv preprint 12 Fish encounter turbulence not only in natural environments as a result of rapid stream 336 flows, bottom topography, or obstacles in the water, but also under conditions where human-337 designed structures such as dams or fish passage structures create turbulence (52) (53) (54). A 338 key issue in considering how fish must contend with these structures is understanding the length 339 scale of turbulence encountered by fishes and whether or not fish prefer and could even benefit 340 from a turbulent environment (55). Our experiments utilized a passive turbulence grid to 341 generate turbulent eddies with a length scale approximating the body depth of the giant danio 342 studied. In nature, however, turbulent flows can differ in the turbulence length scale, and in the 343 energy present at each eddy size, and variations in turbulence scale can be important for 344 understanding the effects of turbulence on animals of different sizes. It remains unknown if fish 345 (either individuals or schools) select particular turbulent length scales when swimming that could 346 also allow locomotor energy savings in contrast to the increased costs demonstrated at other 347 length scales. Perhaps the design of fish passage devices for habitat restoration should consider 348 the ratio of turbulence eddy scale relative to the animal size to improve locomotor ability and 349 reduce the cost of movement for fish (52). Alternatively, energetically costly turbulence flow 350 generators could serve as aquatic barriers to perturb invasive species. 351 352 Given the ubiquity of turbulent flows in natural aquatic ecosystems, we suggest that one 353 of the important roles of collective behaviour in fish species is to shelter individuals within a 354 collective group from challenging hydrodynamic conditions. More broadly, our study proposes 355 that vertebrate collectives can also function as a larger size biological entity than the solitary 356 individual, which could reduce the effect of turbulence perturbation on animal movement. Using 357 aquatic vertebrates moving in the dense water fluid as a model system to directly demonstrate 358 energy saving can be the foundation for future studies of the ‘turbulence sheltering’ hypothesis in 359 flying and terrestrial vertebrates. Locomotor performance curves, where metabolic or kinematic 360 variables are evaluated against swimming speed, are a useful comparative framework to broadly 361 understand the energetic cost of collective movement (34). 362 363

364 Experimental animals 365 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576168doi: bioRxiv preprint 13 Experiments were performed on giant danio (Devario aequipinnatus) that were acquired 366 from a local commercial supplier near Boston, Massachusetts USA. Five schooling groups are 367 randomly distributed and housed separately in five 37.9 l aquaria (n=8 per tank). The five 368 solitary individuals are housed separately in five 9.5 l aquaria (n=1 per tank). All aquaria have 369 self-contained thermal control (28 °C), an aeration system (>95 % air saturation, % sat.) and a 370 filtration system. Water changes (up to 50% exchange ratio) were carried out weekly. Fish were 371 fed ad libitum daily (TetraMin, Germany). Animal holding and experimental procedures were 372 approved by the Harvard Animal Care IACUC Committee (protocol number 20-03-3). 373 374 Experimental system – Integrated Biomechanics & Bioenergetic Assessment System (IBAS) 375 The experimental system and similar experimental protocols are available in (56). To 376 promote reproducibility, we reiterate the methodologies in detail and the additional experimental 377 detail specific to the study of collective movement in turbulent conditions. 378 The core of our experimental system is a 9.35-l (respirometry volume plus tubing) 379 customized Loligo® swim-tunnel respirometer (Tjele, Denmark). The respirometer has an 380 electric motor, and a sealed shaft attached to a propeller located inside the respirometer. By 381 regulating the revolutions per minute (RPM) of the motor, the water velocity of the motor can be 382 controlled. 383 The swim-tunnel respirometer is oval-shaped. The central hollow space of the respirometry 384 increases the turning radius of the water current. As a result, the water velocity passing the cross-385 section of the swimming section (80 × 80 × 225 mm) is more homogenous (validated by PIV). 386 Moreover, a honeycomb flow straightener (80 × 80 × 145 mm) is installed in upstream of the 387 swimming section to create laminar flow (validated by PIV). The linear regression equation 388 between RPM and water velocity (V) of control flow is established (V = 0.06169•RPM – 5.128, 389 R2 = 0.9988, p < 0.0001) by velocity field measured by particle image velocimetry (PIV). 390 To increase the signal-to-noise ratio for the measurement of water dissolved O2, a water 391 homogenous loop is installed 95 cm downstream of the propeller and the water is returned to the 392 respirometer 240 cm before the swimming section. The flow in the water homogenous loop 393 moves (designated in-line circulation pump, Universal 600, EHEIM GmbH & Co KG, Deizisau, 394 Germany) in the same direction as the water flow in the swimming tunnel. A high-resolution 395 fibre optic O2 probe (Robust oxygen probe OXROB2, PyroScience GmbH, Aachen, Germany) is 396 sealed in the homogenous loop at downstream of the circulation pump (better mixing) to 397 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576168doi: bioRxiv preprint 14 continuously measure the dissolved O2 level in the water (recording frequency ~1 Hz, response 398 time < 15s). The oxygen probe was calibrated to anoxic (0 % sat., a solution created by super-399 saturated sodium sulphite and bubbling nitrogen gas) and fully aerated water (100 % sat.). The 400

ṀO2 in the swim-tunnel respirometer was measured for 20 min before and after each 401 trial. The average background ṀO2 (< 6% of fish ṀO2) was used to correct for the ṀO2 of fish. 402 The pre-filtered water (laboratory grade filtration system) is constantly disinfected by UV light 403 (JUP-01, SunSun, China) located in an external water reservoir to suppress the growth of 404 microbial. Water changes of 60% total volume occurred every other day and a complete 405 disinfection by sodium hypochlorite is conducted weekly (Performance bleach, Clorox & 1000 406 ppm). 407 To simultaneously measure schooling dynamics and swimming kinematics, the customized 408 oval-shaped swim-tunnel respirometer is located on a platform with an open window beneath the 409 swimming section. The platform is elevated 243 mm above the base to allow a front surface 410 mirror to be installed at a 45° angle. This mirror allows a high-speed camera (FASTCAM Mini 411 AX50 type 170K-M-16GB, Phontron Inc., United States, lens: Nikon 50mm F1.2, Japan) to 412 record the ventral view. The second camera (FASTCAM Mini AX50 type 170K-M-16GB, 413 Phontron Inc., United States, lens: Nikon 50mm F1.2, Japan) is positioned 515 mm to the side of 414 the swimming section to record a lateral view. Synchronized lateral and ventral video recordings 415 were made at 125 fps, and each frame was 1024 by 1024 pixels. To avoid light refraction passing 416 through the water and distorting the video recordings, the swim-tunnel respirometry is not 417 submerged in the water bath. Temperature regulation of the respirometer is achieved by 418 regulating room temperature, installing thermal insulation layers on the respirometry and 419 replenishing the water inside the respirometer from a thermally regulated (28 °C, heater: ETH 420 300, Hydor, United States & chiller: AL-160, Baoshishan, China) water reservoir (insulated 421 37.9-l aquarium) located externally. 422 The aerated (100% sat., air pump: whisper AP 300, Tetra, China) reservoir water is flushed 423 (pump: Universal 2400, EHEIM GmbH & Co KG, Deizisau, Germany) to the respirometer 424 through an in-line computer-controlled motorized ball valve (U.S. Solid) installed at the in-flow 425 tube. The other in-line one-way valve is installed at the out-flow tube. The out-flow tube is also 426 equipped with a valve. The value is shut during the measurement period, a precautionary practice 427 to eliminate the exchange of water between the respirometer and the external reservoir when the 428 water moves at a high velocity inside the respirometer. This flushing was manually controlled to 429 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576168doi: bioRxiv preprint 15 maintain DO above 80 % sat. Every time the respirometer was closed to measure ṀO2, the water 430 temperature fluctuates no more than 0.2 °C. The water temperature inside the respirometer is 431 measured by a needle temperature probe (Shielded dipping probe, PyroScience GmbH, Aachen, 432 Germany) sealed through a tight rubber port of the respirometer. 433 To allow fish to reach the undisturbed quiescent state during the trial, the entire Integrated 434 Biomechanics & Bioenergetic Assessment Platform (IBAP) is covered by laser blackout sheet 435 (Nylon Fabric with Polyurethane Coating; Thorlabs Inc, New Jersey, United States). The room 436 lights are shut off and foot traffic around the experimental rig is restrained to the absolute 437 minimum. Fish are orientated by dual small anterior spots of white light (lowest light intensity, 438 Model 1177, Cambridge Instruments Inc, New York, United States) for orientation (one to the 439 top and the other to the side) of the swimming section. The test section is illuminated by infrared 440 light arrays. 441 442 Creating turbulent flows in swim-tunnel respirometer 443 We used a passive turbulence grid (height × width: 7.5 × 8.6 cm) to generate the turbulence 444 flow for the swimming section in the swim-tunnel respirometer (Fig. S1). The turbulence grid 445 has a configuration of 3 × 3 square openings (each opening is in 1.5 × 1.5 cm). The openings 446 produce 9 streams of jets which mix and form turbulent flow. The turbulent grid is upstream of 447 the swimming section (Fig. S1). The opening of the grid is guarded by thin metal wires to 448 prevent fish from going through. The turbulence grid is effective in generating turbulence, as 449 illustrated by the fluid dynamic features of the turbulences measured by PIV (see Fig. S2 and 450 Figs. 2 and 3). As a result, the linear regression equation between RPM and average water 451 velocity (V) of turbulent flow is changed (V = 0.03515•RPM – 1.597, R2 = 0.9985, p < 0.0001) 452 and quantified by velocity field measured by particle image velocimetry (PIV) (see Fig. S3). 453 Quantifying average water velocity allowed us to match the swimming kinematics and metabolic 454 energy consumption of tested fish at the same mean speed between control and turbulent flows. 455 456 Experimental Protocol 457 The same individuals or schools are repeatedly measured in laminar or turbulent flow to 458 control for biological variations. Giant danio (Devario aequipinnatus) is a model species, 459 capable of actively and directionally swimming from a minimum to maximum sustained speeds 460 (0.3–8.0 body lengths s-1; BL s-1 & Reynolds number range of 6.4•103 to 1.8•105 in controlled 461 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576168doi: bioRxiv preprint 16 flow). We studied five replicate schools and five replicate individuals drawn from within each 462 school. Swimming performance test trials were conducted with Devario aequipinnatus fasted for 463 24 hours, a sufficient period for a small-sized species at 28 °C (i.e. high resting ṀO2) to reach an 464 absorptive state. In fact, we observed no specific dynamic action, in the amount of oxygen 465 consumed for digestion during the first diurnal cycle (Fig. S3). Prior to the swimming 466 performance test, testing fish were gently weighted and placed in the swim-tunnel respirometer. 467 The fish swam at 35% Ucrit for 30 mins to help oxidize the inevitable but minor lactate 468 accumulation during the prior handling and help fish become accustomed to the flow conditions 469 in the swim-tunnel respirometer (57). After this time, the fish to be tested were habituated (>20 470 hours) to the respirometer environment under quiescent and undisturbed conditions. During this 471 time, we used an automatic system to measure the resting ṀO2 for at least 19 hours. Relays 472 (Cleware GmbH, Schleswig, Germany) and software (AquaResp v.3, Denmark) were used to 473 control the intermittent flushing of the respirometer with fresh water throughout the trial to 474 ensure O2 saturation of the respirometer water. ṀO2 was calculated from the continuously 475 recorded dissolved O2 level (at 1 Hz) inside the respirometer chamber. The intermittent flow of 476 water into the respirometer occurred over 930 s cycles with 30 s where water was flushed into 477 the respirometer and 900 s where the pumps were off and the respirometer was a closed system. 478 The first 240 s after each time the flushing pump was turned off were not used to measure ṀO2 479 to allow O2 levels inside the respirometer to stabilize. The remaining 660 s when the pumps were 480 off during the cycle were used to measure ṀO2. The in-line circulation pump for water in the O2 481 measurement loop stayed on throughout the trial. 482 We characterize the locomotor performance curve of fish using an established 483 incremental step-wise critical swimming speed (Ucrit) test (35). The first preliminary trial 484 determined the Ucrit of this population of Devario aequipinnatus as 8 BL s-1. Characterizing the 485 swimming performance curve required a second preliminary trial to strategically select 10 water 486 velocities (0.3, 0.5, 0.8, 1.0, 1.3, 1.5, 1.8, 2.3, 2.8 BL s-1) to bracket the hypothesized concave 487 upward metabolism-speed curve at the lower speed (< 40% Ucrit). Additional five water 488 velocities (3.8, 4.9, 5.9, 6.9, 8.0 BL s-1) are used to characterize the exponentially increasing 489 curve to the maximum and sustained swimming speed, Ucrit (see Fig. S5). Altogether, 14 points 490 provide a reliable resolution to characterize the locomotor performance curve. At each water 491 velocity, fish swam for 10 mins (58) to reach a steady state in ṀO2 at low speeds (see Fig. S6). 492 Above 40% Ucrit , ṀO2 can become more variable (59). Hence, in this protocol, we focus on 493 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576168doi: bioRxiv preprint 17 measuring the sustained aerobic energy expenditure by calculating the average ṀO2 for each 10-494 min velocity step using Eqn 1. The respirometry system reaches a stable signal-to-noise ratio 495 once the sampling window is longer than 1.67 mins (see Fig. S7), well within the duration of the 496 velocity step to obtain a stable signal-to-noise ratio for calculating ṀO2 (59). At the 5th min of 497 each velocity step, both ventral and lateral-view cameras are triggered simultaneously to record 498 10-sec footage at 125 frames per second, at 1/1000 shutter speed and 1024 ×1024 pixel 499 resolution. Thus, both data streams of ṀO2 and high-speed videos are recorded simultaneously. 500 The Ucrit test is terminated when 12.5% of fish in the school or a solitary individual touches the 501 back grid of the swimming section for more than 20 secs (57). The Ucrit test lasted ~140 mins and 502 estimates the aerobic portion of energy expenditure over the entire range of swimming 503 performance. 504 To measure the contribution of non-aerobic O2 cost, where most of the cost is related to 505 substrate-level phosphorylation, and to calculate the total energy expenditure for swimming over 506 the entire speed range, we measured excess post-exercise oxygen consumption (EPOC) after the 507 Ucrit test for the ensuing 19 hours, recorded by an automatic system. Most previous 508 measurements of EPOC after Ucrit test have used a duration of ~5 hours, but our extended 509 measurement period ensured that longer duration recovery O2 consumption (EPOC) was 510 measured completely as fish were exercised to Ucrit (see summary table in 16). The intermittent 511 flow of water into the respirometer occurred over 30 s to replenish the dissolved O2 level to 512 ~95% sat. For the following 900 s the flushing pump remained closed, and the respirometer 513 became a closed system, with the first 240 s to allow O2 saturation inside the respirometer to 514 stabilize. The remaining 660 s when the flushing pump was off during the cycle were used to 515 measure ṀO2 (see Eqn 1). The cycle is automated by computer software (AquaResp v.3) and 516 provided 74 measurements of ṀO2 to compute EPOC. Upon the completion of the three-day 517 protocol, the school or individual fish are returned to the home aquarium for recovery. The fish 518 condition was closely monitored during the first 48 hours after the experiment, during which no 519 mortality was observed. 520 521 Bioenergetic measurement and modeling 522 To estimate the steady-rate whole-animal aerobic metabolic rate, ṀO2 values were 523 calculated from the sequential interval regression algorithm (Eqn. 1) using the dissolved O2 (DO) 524 points continuously sampled (~1 Hz) from the respirometer. 525 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576168doi: bioRxiv preprint 18 ṀO! = $ "!"[$,($'()] "+[$,($'()] ∗ &𝑉# − 𝑉$) ∗ 𝑆%+ (𝑡 ∗ 𝑀$)0 (Eqn. 1) 526 527 Where 𝑑&% 𝑑' 0 is the change in O2 saturation with time, Vr is the respirometer volume, Vf is 528 the fish volume (1 g body mass = 1 ml water), So is the water solubility of O2 (calculated by 529 AquaResp v.3 software) at the experimental temperature, salinity and atmospheric pressure, t is a 530 time constant of 3600 s h-1, Mf is fish mass, and a is the sampling window duration, i is the next 531 PO2 sample after the preceding sampling window. 532 To account for allometric scaling, the ṀO2 values of solitary fish were transformed to match 533 the size of the individual fish in the school using an allometric scaling exponent (b = 0.7546). 534 The calculation of the scaling relationship [Log10(ṀO2) = b•Log10(M) + Log10(a), where M is 535 the body mass & a is a constant] was performed by least squares linear regression analysis (y = 536 0.7546•x + 0.2046; R2 = 0.6727, p < 0.0001) on the 180 data points of metabolic rate and body 537 mass from a closely related species (the best available dataset to our knowledge) (61). The 538 allometrically scaled ṀO2 values were used to derive other energetic metrics (listed below) for 539 the solitary fish. The energetic metrics of fish schools are calculated from the mass-specific ṀO2. 540 The resting oxygen uptake (ṀO2rest), the minimum resting metabolic demands of a group of 541 fish or a solitary individual, is calculated from a quantile 20% algorithm (62) using the ṀO2 542 estimated between the 10th–18th hour and beyond the 32nd hour of the trial. These are the periods 543 of quiescent state when fish completed the EPOC from handling and swimming test. 544 The excess post-exercise oxygen consumption (EPOC) is an integral area of ṀO2 measured 545 during post-exercise recovery, from the end of Ucrit until reached ṀO2rest plus 10% (60). This 546 approach reduces the likelihood of overestimating EPOC due to spontaneous activities (60). To 547 account for the allometric scaling effect, we used the total amount of O2 consumed (mg O2) by 548 the standardized body mass of fish (1.66 g) for fish schools and solitary fish. 549 We model EPOC (i.e. non-aerobic O2 cost) to estimate a total O2 cost over the duration of 550 the swimming performance test. Our conceptual approach was pioneered by Brett (35) in fish 551 and is also used in sports science (33). Mathematical modeling was applied to study the effects 552 of temperature on the cost of swimming for migratory salmon (57). We improved the 553 mathematical modeling by applying the following physiological and physics criteria. The first 554 criterion is that significant accumulation of glycolytic end-product occurred when fish swimming 555 above 50% Ucrit (63) which corresponds to > ~40% ṀO2max (or ~ 50% aerobic scope) (33). This 556 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576168doi: bioRxiv preprint 19 is also when fish start unsteady-state burst-&-glide swimming gait (63). The second criterion is 557 that the integral area for the non-aerobic O2 cost during swimming can only differ by ≤ 0.2% 558 when compared to EPOC. The non-aerobic O2 cost during swimming is the area bounded by 559 modeled ṀO2 and measured ṀO2 as a function of time when fish swim > 50% Ucrit (see Fig. 2A 560 & Table S2). The third criterion is that total energy expenditure is expected to increase 561 exponentially with swimming speed (Fig. S7). Specifically, these curves were fitted by power 562 series or polynomial models, the same models that describe the relationship between water 563 velocity and total power and energy cost of transport (Fig. S7). Following these criteria, the non-564 aerobic O2 cost at each swimming speed is computed by a percentage (%) modifier based on the 565 aerobic O2 cost (Table S1 & S2). The exponential curve of total O2 cost as swimming speed of 566 each fish school or solitary individual was derived by an iterative process until the difference 567 between non-aerobic O2 cost and EPOC met the 2nd criterion. The sum of non-aerobic O2 cost 568 and aerobic cost gives the total O2 cost. 569 The best model fitting following the relationships between water velocity and energetic 570 costs of locomotion suggests that the glycolysis starts at 2–3 BL s-1 for fish swimming in the 571 turbulence flow, whereas the same model suggests that the glycolysis starts at 4–5 BL s-1 for fish 572 swimming in the controlled flow. We are confident in this model, because the engaging 573 glycolysis at the lower swimming speed for the fish swimming in turbulent flow corresponded 574 with their lower Ucrit (controlled flow: 8 BL s-1 vs. turbulent flow: 7 BL s-1). The model of 575 aerobic and non-aerobic energy costs of locomotion enabled the estimation of total energy 576 expenditure and total cost of transport as detailed below: 577 Total energy expenditure (TEE) is calculated by converting total O2 cost to kJ × kg-1 using 578 an oxy-calorific equivalent of 3.25 cal per 1 mg O2 (64). 579 Total cost of transport (COT), in kJ × km-1 × kg-1 is calculated by dividing TEE by speed (in 580 km × h-1) (58). 581 582 Hydrodynamic flow visualization & analysis 583 We used a horizontal plane of laser sheet (LD pumped all-solid-state 532nm green laser, 584 5w, MGL-N-532A, Opto Engine LLC) to visualize and quantify the hydrodynamic conditions of 585 laminar and turbulent flows (i.e. particle image velocimetry, PIV). The horizontal planes of the 586 water fluid field in laminar and turbulent conditions were calculated from consecutive video 587 frames (1024 × 1024 pixels) using DaVis v8.3.1 (LaVision Inc., Göttingen, Germany). A vector 588 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576168doi: bioRxiv preprint 20 field (covering a horizontal plane of 34.3 cm2 with 2193 vectors) is characterized by a sequential 589 cross-correlation algorithm applied with an initial interrogation window size of 64 × 64 pixels 590 that ended at 12 × 12 pixels (3 passes, overlap 50%). To optimize the signal-to-noise ratio on the 591 sequential cross-correlation algorithm, we used an increment of 10 frames at the lowest speed of 592 laminar and turbulent flow conditions. The rest of the speeds in both flow conditions were 593 analyzed using an increment of 1 frame. Five sets of consecutive video frames (1st, 250th, 500th, 594 750th and 990th frame out of 1000 frames) in laminar (n=5) and turbulent flows (n=5) were used 595 for calculating the metrics. 596 To optimize the sampling resolution of consecutive PIV frames, the six lowest testing 597 speeds (106, 131, 156, 181, 256, 356 RPM) of both flow conditions were captured by 1000 598 frame rate per sec (shutter speed: 1/1000), whereas the six highest testing speed (456, 556, 656, 599 756, 856 RPM) of both flow conditions were captured by 2000 frame rate per sec (shutter speed: 600 1/1000) using a high-speed camera (FASTCAM Mini AX50 type 170K-M-16GB, Phontron Inc., 601 United States, lens: Nikon 50mm F1.2, Japan). 602 From the fluid field, we used DaVis (v8.3.1) to calculate the following fluid parameters: 603 Vmax (m s-1): Extract the maximum value of the velocity at the vector that is perpendicular 604 to the free-stream flow. 605 Maximum vorticity (sec-1): calculated according to the central difference scheme with four 606 closest neighbours at the horizontal plane. This method achieves a high spatial resolution. 607 Maximum shear strength (1/S2): maximum value of the shear strength. Shear strength is the 608 positive Eigenvalue of the Matrix for two-dimensional vorticity on the horizontal plane. 609 Sum of shear strength (1/S2): sum of the shear strength. The calculation of shear strength is 610 stated above. 611 To compute the fluctuation velocity, turbulence intensity, and eddy size distribution in the 612 turbulent flow, a subsection of the full velocity field was extracted. This subsection spans an area 613 of 22.4 cm2 and was located approximately 4 cm from the passive grid (Fig. S1) and 0.5 cm from 614 the walls of the tunnel. For this analysis, velocity fields were computed on all 2000 frames. For 615 further information about the quantification of turbulence and the distribution of eddy sizes, 616 readers can refer to the supplementary material (see computing fluctuation velocity and 617 turbulence intensity). 618 619 Three-dimensional kinematic data extraction from high-speed videography 620 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576168doi: bioRxiv preprint 21 We used two synchronized 10-sec high-speed videos (lateral and ventral views, at each 621 speed) for kinematic analyses. We calibrated the field of view of the high-speed cameras using a 622 direct linear transformation for three-dimensional kinematic reconstruction (DLTdv8) (65) by 623 applying a stereo calibration to the swimming section of the respirometer (see Fig. S8). We 624 digitized the anatomical landmarks of fish (see Fig. S10) to obtain the X, Y, Z coordinates for 625 each marker at the 1st sec, 5th sec and 10th sec for videos recorded at each speed. These 626 coordinates are used to calculate the following kinematic parameters. All the calculations are 627 validated on the known length and angle of test objects inserted into the tank working section. 628 Strouhal number (St) represents the dimensionless flapping frequency and amplitude at a 629 given movement speed. St = $( ) Where f, 𝐴 and U are the tailbeat frequency, amplitude, and 630 swimming speed (13). The measurement is conducted on the calibrated high-speed video in 631 video analysis software (Phontron FASTCAM Viewer 4, Photron USA, Inc.). 632 Reynolds number (Re) represents the dimensionless fluid inertial to viscous forces at a 633 given speed. Re = *)+ , , where 𝜌 and 𝜇 are the density and dynamic viscosity of the water, and 634 𝑈 and 𝐿 are the swimming speed and length of the fish (13). Water density and dynamic viscosity 635 are given at 28 °C. 636 In addition to the manual digitization, we also developed a contrast-based segmentation 637 algorithm for automatic tracking of 2D kinematics in the ventral view. The video analysis was 638 performed in MATLAB (R2022b). We processed each frame in the video independently. We 639 first converted the frame into grayscale and then used a brightness threshold to obtain masks of 640 the fish (Fig S9A). We removed masks with an area larger than that expected for a single fish, 641 excluding masks with multiple overlapping fish. For every streamwise location on the mask (x-642 location), we calculated the midpoint across the span to obtain the midline of the animal at each 643 instant. The midlines were pieced together across frames according to their locations. We 644 centered and rotated a series of midlines to account for the rigid-body component of the fish 645 body. At this stage of the image analysis, we obtained midline envelopes of the fish (Fig. S9B). 646 We extracted a time series of head and nose spanwise oscillation, identified peaks and troughs of 647 the signal and calculated the amplitude and frequency of the fish (Fig. S9C, D). We excluded 648 time series that are shorter than a tail beat cycle and those associated with unsteady swimming, 649 either with a high relative velocity with flow or fast rotation. 650 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576168doi: bioRxiv preprint 22 To further characterize the head oscillation of fish in different flow environments, we 651 processed trajectories that are several dozen cycles long at 6 BL s-1, extracted through manual 652 digitization (DLTdv8a) (8.2.10) (65). To distinguish the nose oscillation from the background 653 movement of the fish during the period, we performed Fast Fourier Transform (FFT) in 654 MATLAB (R2022b). The FFT analyses enabled us to separate the original time series of the 655 nose trajectories into background motion (low-frequency component) and oscillation due to fish 656 swimming (high-frequency component). The latter is plotted in Fig 7B. 657 658 Statistical analyses 659 Measurement points are presented as mean ± s.e.m. For the metrics that failed normality 660 tests, logarithm transformations were applied to meet the assumptions of normality of residuals, 661 homoscedasticity of the residuals, and no trend in the explanatory variables. We conducted 662 supervised statistical tests to specifically evaluate our hypotheses about the effects of turbulence 663 on the biomechanics and bioenergetics of fish swimming, either in school or alone. The 664 statistical comparisons for the different responses of fish schools (or solitary fish) between 665 swimming in laminar flows and in turbulent flow used a mixed effects model (laminar flow vs. 666 turbulent flow & swimming speed) with Holm–Šídák post-hoc tests. The statistical comparisons 667 for the difference between fish schools and solitary fish swimming in the turbulence used a 668 general linear model (solitary fish vs. fish schools & swimming speed) with Holm–Šídák post-669 hoc tests. The statistical comparison for the characteristics of fluid dynamics between laminar 670 and turbulent flow conditions used a general linear model that used speed as a covariance. The 671 statistical comparison of EPOC between fish schools and solitary fish after performing the Ucrit 672 test in turbulent conditions used an unpaired t-test. The statistical analyses were conducted in 673 SPSS v.28 (SPSS Inc. Chicago, IL, USA). The best-fitting regression analyses were conducted 674 using Prism v.9.4.1 (GraphPad Software, San Diego, CA, USA). 95% C.I. values were presented 675 for all regression models as shaded areas around the regression or data points. Statistical 676 significance is denoted by *, **, ***, **** for p-values of ≤ 0.05, ≤ 0.01, ≤ 0.001, ≤ 0.0001 677 respectively. 678 679 Acknowledgments: Many thanks to members of Lauder Laboratory for numerous discussions 680 about fish schooling behaviour, for comments on the manuscript, to Dr. Robin Thandickal for 681 assistance with the convex hull calculations, and to Cory Hahn for fish care. 682 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576168doi: bioRxiv preprint 23 Funding: Funding provided by the National Science Foundation grant 1830881 (GVL), the 683 Office of Naval Research grants N00014-21-1-2661 (GVL), N00014-16-1-2515 (GVL), 00014-684 22-1-2616 (GVL), and a Postdoctoral Fellowship of Natural Sciences and Engineering Research 685 Council of Canada PDF - 557785 – 2021 (YZ). 686 Author contributions: 687 Conceptualization: YZ, GL. RN 688 Methodology: YZ, GL, HK, MC, HK, RN 689 Investigation: YZ, HK, MC 690 Visualization: YZ, GL, MC, HK, RN 691 Funding acquisition: GL, YZ, RN 692 Project administration: GL, RN 693 Supervision: GL, RN 694 Writing – original draft: YZ 695 Writing – review & editing: YZ, GL, HK, MC, RN 696 Competing interests: Authors declare that they have no competing interests. 697 Data and materials availability: All data are available in the main text or the supplementary 698

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It is made The copyright holder for this preprintthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576168doi: bioRxiv preprint 28 850 851 FIGURES CAPTIONS 852 853 854 855 Fig. 1. Illustration of the environmental turbulence sheltering hypothesis. Schematic 856 diagram of a school of giant danio (Devario aequipinnatus) swimming in oncoming turbulence 857 where the largest eddies have an integral length scale (𝐿) on the same order of magnitude as the 858 body depth (D) of the fish. Fish within the school could benefit from a region of reduced 859 turbulence created within the school as a result of nearby neighbours and undulatory body 860 motion modifying flow within the school compared to free stream oncoming flow. As a result, 861 we propose a “turbulence sheltering” hypothesis that fish schools can protect individuals within 862 the group from free-stream turbulence. As a result, we predict fish swimming in turbulence could 863 reduce their locomotor costs by schooling in contrast to swimming alone.864 ! ! / # ~ 1 "Region of modulated turbulence Surrounding turbulent environment 29 865 Fig. 2. Characterization of hydrodynamic features in controlled and turbulent flows across 866 a range of speeds used for danio schooling energetic and kinematic measurements. 867 Representative flow patterns of (A) turbulent and (B) control conditions in the swim-tunnel 868 respirometer as quantified by particle image velocimetry. Velocity vectors are yellow arrows, 869 and the vorticity field is shown by blue (-40 sec-1) to red (40 sec-1) gradient heat maps in the 870 background. The hydrodynamic features of turbulent (orange colour) and controlled (green 871 colour) flows are characterized by (C) maximum vertical velocity, (D) maximum vorticity, (E) 872 maximum and (F) the sum of shear strength as a function of absolute speed (meter sec-1). More 873 detailed flow characteristics are illustrated in the Supplemental materials for characteristics of 874 the turbulent flow generated in the respirometer (Fig. S2. The statistics in each panel denote the 875 0.0 0.2 0.4 0.60.00 0.05 0.10 0.15 0.20 U (m s-1) Vmax (m s-1) Laminar Turbulence F = 401.9 p < 0.001 0.0 0.2 0.4 0.60 1000 2000 3000 4000 U (m s-1) Max shear strength (1/S2) Laminar Turbulence F = 153.7 p < 0.001 0.0 0.2 0.4 0.60 50 100 150 U (m s-1) Vorticitymax (sec -1) Turbulence Laminar F = 167.8 p < 0.001 0.0 0.2 0.4 0.60 2×107 4×107 6×107 8×107 1×108 U (m s-1) Sum shear strength (1/S2) Laminar Turbulence F = 189.4 p < 0.001 C D E F A B 0.5 m s-1 5 mm 40 -400---Vorticity (sec-1) 0.5 m s-1 5 mm 40 -400---Vorticity (sec-1) 30 main effect of the flow condition. Shading indicates the 95% confidence interval. Statistical 876 details are available in the statistical analyses section. The controlled fluid condition is a 877 laminarized flow environment. 878 31 879 Fig. 3. Analysis of turbulent flow in the respirometer used for testing schooling energetics. 880 Probability density function (p.d.f) of velocity components (A) parallel (𝑢) and (B) 881 perpendicular (𝑣) to the swimming direction for different swimming speeds with the passive 882 turbulence grid. As speed increases, the width of the distribution increases, signifying increasing 883 turbulence. (C) The turbulence intensity (𝐼) and fluctuation velocity (𝑢-.) as a function of 884 swimming speed. Fluctuation velocity increases with increasing speed. However, the increase in 885 the fluctuation velocity is proportional to the increase in the speed resulting in a near constant 886 turbulence intensity. (D) Distribution of eddy sizes present for a given swimming speed, from 887 largest (integral length scale) to smallest (Kolmogorov length scale). The eddy size distribution 888 was determined by approximating the energy dissipation rate via computation of the two-889 dimensional structure functions (See Supplemental Material for further information). The largest 890 eddies were roughly the same size as the fish’s body depth, or 30% of their body length. The 891 control fluid test condition is a laminarized flow environment.892 0.00.20.40.6 u (m s-1)10-4 10-2 100 102p.d.f 1BL s-12BL s-1 -0.20.00.2 v (m s-1)10-4 10-2 100 102p.d.f 3BL s-14BL s-15BL s-16BL s-17BL s-18BL s-1 02468Speed (BL s-1)10-3 10-2 10-1 100 uo (m s-1), I uo I02468Speed (BL s-1)10-210-1100101102Length Scale (mm) A B C Integral Length Scale (L) Scale Separation Kolmogorov Length Scale () D 32 893 Fig. 4. Measurements of aerobic and non-aerobic locomotor costs for fish schools and 894 solitary fish in control and turbulent flow conditions. (A) Comparison of concave upward 895 metabolic rate (ṀO2)-speed curve over 0.3–8 body length s-1 (BL s-1) range for fish schools and 896 solitary fish swimming in control and turbulent flow conditions. (B) recovery time of excess 897 post-exercise O2 consumption (EPOC) and (C) EPOC of fish schools and solitary fish after 898 swimming in control and turbulent conditions. Concave upward total ṀO2-speed curve of (D) 899 fish schools and (E) solitary fish when swimming in control and turbulent conditions. The total 900 ṀO2-speed curve (dashed line) is calculated from a model that integrates the measurements 901 (solid line) of aerobic and non-aerobic locomotion costs (see Supplemental Material). (F) Total 902 0 2 4 6 8 0 300 600 900 1200 1500 Speed (BL s-1) R2 = 0.9791, AIC = 101.8R2 = 0.9936, School laminar AIC = 112.4 Individual laminar ṀO2 (mg O2 kg-1 h-1) School turbulence Individual turbulence AIC = 96.09R2 = 0.9933, AIC = 114.8R2 = 0.9876, ✱✱ ✱✱✱✱ ✱✱✱ 32% ▴ 012345678 0 500 1000 1500 2000 2500 3000 Speed (BL s-1) ṀO2 (mg O2 kg-1 h-1) R2 = 0.9975, AIC = 98.56R2 = 0.9949, Laminar: school measureAIC = 115.9 Laminar: school model +177%✱✱✱✱ ✱✱✱✱ +126% Turbulence: school measure Turbulence: school modelR2 = 0.9983, R2 = 0.9933, AIC = 109.8 AIC = 96.09 ▴ ▴ ▴ +75%✱✱✱✱ 0123456780 50 100 150 200 250 300 Speed (BL s-1) Total energy expenditure (kJ kg-1) R2 = 0.956, AIC = 188.1 AIC = 276.5R2 = 0.9218, ✱✱✱✱ ✱✱✱✱✱✱ -79% -79%-62% School laminar Individual laminar ✱✱✱✱-63% School Turbulence Individual TurbulenceR2 = 0.8415,AIC = 297.7 R2 = 0.9421,AIC = 187.3 ✱-65% ✱✱✱✱✱✱✱✱ ✱✱✱✱ ✱ ✱✱✱✱ ✱✱✱✱ ✱✱▴ ▴ ▴ ▴ School laminarSchool turbulenceIndividual laminarIndividual turbulence 0 2 4 6 8EPOC (mg O2 ) ✱✱✱ ✱✱✱✱ 2.8 fold8.0 fold 012345678 0 2000 4000 6000 8000 10000 12000 14000 Speed (BL s-1) ṀO2 (mg O2 kg-1 h-1) AIC = 130.4R2 = 0.9920, AIC = 106.8R2 = 0.9866, +799% +800% +363% ✱✱✱✱ ✱✱✱✱ ✱✱✱✱ ✱✱ +251% Turbulenace: individual measure Turbulence: individual model +751%✱✱✱✱ Laminar: individual model laminar: individual measure R2 = 0.9876,AIC = 114.8 R2 = 0.99,AIC = 180.3 ▴ ▴ ▴ ▴ ▴ ✱ +528% 0123456780 6 12 18 24 30 Speed (BL s-1) Total cost of transport (kJ km-1 kg-1) R2 = 0.9615, AIC = -45.55R2 = 0.9974, AIC = -10.87 School Turbulence Individual Turbulence Individual laminar School laminar R2 = 0.9987,AIC = -37 R2 = 0.9454,AIC = 26.99 ✱✱✱✱ ✱✱✱✱✱✱ -79% -79%-68% ✱✱✱✱-76% ✱✱✱✱✱✱✱✱ ✱✱✱✱ ✱✱ ✱-65% ✱ ✱✱✱✱✱✱▴ ▴ ▴ ▴ ▴ A C D E F G School laminarSchool turbulenceIndividual laminarIndividual turbulence 0 5 10 15 20 25EPOC duration (h) ✱ 1.8 fold B 33 energy expenditure (TEE) and (G) concave upward total cost of the transport (TCOT)-speed 903 curves for fish schools and solitary fish when swimming in control and turbulent conditions. 904 Total Energy Expenditure (TEE) and the Total Cost of transport (TCOT) are calculated using the 905 sum of aerobic and non-aerobic costs. Green colour = fish schools in control conditions (n=5); 906 blue colour = solitary fish in control conditions (n=5); orange colour = fish schools in turbulence 907 (n=4); purple colour = solitary fish in turbulence (n=3). Statistical significance is denoted by 908 asterisk(s). Shading indicates the 95% confidence interval. Statistical details are available in the 909 statistical analyses section. The control fluid condition is a laminarized flow environment. 910 911 912 34 913 Fig. 5. Characterization of fish school three-dimensional volume in turbulent and control 914 flow conditions. Representative three-dimensional (3-D) convex hull volume of fish schools in 915 (A) control and (B) turbulent flow conditions. (C) 3-D convex hull volume as a function of speed 916 for fish schools swimming in control (n=9 snapshots per speed increment) and turbulent (n=12 917 snapshots per speed increment) flow conditions. Statistical significance is denoted by asterisk(s). 918 Shading indicates the 95% confidence interval. Statistical details are available in the statistical 919 analyses section. The control fluid condition is a laminarized flow environment.920 0 1 2 3 4 5 6 7 8 0 50 100 150 200 Speed (BL s-1) Convex hull volume (cm3) School laminar School control ✱ ✱✱ ✱✱ ✱ ✱ ✱ ✱ AIC = 1085R2 = 0.4719, R2 =0.1946,p = 0.1143 -41% -61% -53% -68% -53% -50% Laminar A B C Turbulence Distance (mm) Distance (mm) Distance (mm) Distance (mm) Distance (mm) Distance (mm) 35 921 Fig. 6. Kinematic data on individual fish within the school during locomotion in control 922 and turbulent flow conditions. Tail beat frequency (ftail) of (A) solitary fish and (B) fish schools 923 across 0.3–8 body length s-1 (BL s-1) in control and turbulent flow conditions. Tail beat 924 amplitude (Amptail) of (C) solitary fish and (D) fish schools across 0.3–8 body length s-1 (BL s-1) 925 in control and turbulent flow conditions. An estimate of swimming effort, Ftail • Amptail, of (E) 926 solitary fish and (F) fish schools across 0.3–8 body length s-1 (BL s-1) in control and turbulent 927 flow conditions. Green colour = fish schools in control conditions (n=295–379 sequences); blue 928 colour = solitary fish in control conditions (n=351–416 sequences); orange colour = fish schools 929 in turbulence (n=104–146 sequences); purple colour = solitary fish in turbulence (n=220–258 930 sequences). Statistical significance is denoted by asterisk(s). Shading indicates the 95% 931 confidence interval. Statistical details are available in the statistical analyses section. The control 932 fluid condition is a laminarized flow environment. 933 0123456780.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 Speed (BL s-1) Tail beat frequency • Amplitude (BL•sec-1) School control School turbulence R2 = 0.9846,p < 0.0001 R2 = 0.9535,p < 0.0001y = 0.215x + 0.468 y = 0.199x + 0.487 0123456780.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 Speed (BL s-1) Tail beat frequency • Amplitude (BL•sec-1) Individual control Individual turbulence ✱✱✱ ✱✱ ✱✱ ✱ p < 0.0001R2 = 0.9726, p < 0.0001R2 = 0.9535, y = 0.157x + 0.407 y = 0.202x + 0.314 +13% +15% +22% 0123456780.12 0.14 0.16 0.18 0.20 0.22 0.24 Speed (BL s-1) Tail amplitude (BL) Individual controlIndividual turbulence ✱✱✱✱✱✱ ✱✱✱ ✱✱✱ ✱✱ ✱✱ 20% 26% ▲ ▲ 0123456780.12 0.14 0.16 0.18 0.20 0.22 Speed (BL s-1) Tail amplitude (BL) School controlSchool turbulence✱ 0123456780 2 4 6 8 10 12 14 Speed (BL s-1) Tail beat frequency (Hz) School control School turbulenceR2 = 0.983,p < 0.0001 R2 = 0.989,p < 0.0001 ✱ 0123456780 2 4 6 8 10 12 Speed (BL s-1) Tail beat frequency (Hz) Individual control Individual turbulencep < 0.0001 p < 0.0001 R2 = 0.965, R2 = 0.994, ✱✱✱ ✱✱✱ ✱✱✱ ✱ A C B D E F 36 934 103 104 105 10-1 100 Re St Individual laminar School laminar Individual turbulence School turbulence Log(y) = 0.0321 – 0.0495 • Log(x), R 2 = 0.84, p < 0.0001 A B Individual laminar Individual turbulence School turbulence Head oscillation ( amplitude in body length) Time (s) -0.05 0 0.05 -0.05 0 0.05 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.05 0 0.05 37 Fig. 7. Responses of schooling fish to the fluid dynamic environment within fish schools 935 under control and turbulent conditions. (A) Relationship between two key dimensionless 936 parameters (Strouhal number and Reynolds number) for fish swimming in schools and alone 937 under both control and turbulent conditions. Locomotion follows a generally linear relationship 938 (R2=0.84, p<0.0001). The horizontal dashed line provides the hypothesized relationship of St and 939 Re in the turbulent flow following (45). The St number at the lowest speed, when fish exhibited 940 unsteady turning behaviour, is excluded from the analysis to prevent bias in the scaling 941 relationship of directional oscillatory propulsion. (B) Plots of fish head lateral oscillation through 942 time (blue: individual laminar, purple: individual turbulence, orange: school turbulence) in water 943 velocity of 6 body length sec-1. Shading indicates the 95% confidence interval. Statistical details 944 are available in the statistical analyses section. The control fluid condition is a laminarized flow 945 environment. 946 947 948