Energetics of collective movement in vertebrates

Mapping spatial patterns to energetic benefits in groups of flow-coupled swimmers

The coordinated motion of animal groups through fluids is thought to reduce the cost of locomotion to individuals in the group. However, the connection between the spatial patterns observed in collectively moving animals and the energetic benefits at each position within the group remains unclear. To address this knowledge gap, we study the spontaneous emergence of cohesive formations in groups of fish, modeled as flapping foils, all heading in the same direction. We show in pairwise formations and with increasing group size that (1) in side-by-side arrangements, the reciprocal nature of flow coupling results in an equal distribution of energy requirements among all members, with reduction in cost of locomotion for swimmers flapping inphase but an increase in cost for swimmers flapping antiphase, and (2) in inline arrangements, flow coupling is non-reciprocal for all flapping phase, with energetic savings in favor of trailing swimmers, but only up to a finite number of swimmers, beyond which school cohesion and energetic benefits are lost at once. We explain these findings mechanistically and we provide efficient diagnostic tools for identifying locations in the wake of single and multiple swimmers that offer opportunities for hydrodynamic benefits to aspiring followers. Our results imply a connection between the resources generated by flow physics and social traits that influence greedy and cooperative group behavior.

Inferring the metabolic rate of zebrafish from ventilation frequency

Fish schooling has attracted the interest of the scientific community for centuries. Energy savings have been long posited to be a key determinant for the emergence of schooling patterns. Yet, current methodologies do not allow the precise quantification of the metabolic rate of specific individuals within the school, typically leaving researchers with only a single, global measurement of metabolic rate for the collective. In this paper, we demonstrate the feasibility of inferring metabolic rate of swimming fish using the mouth-opening frequency, a simple proxy that can be scored utilizing video recordings in the laboratory or in the field, even for small fish. The mouth-opening frequency is independent of hydrodynamic interactions within the school, thereby mitigating potential confounding factors that arise when using locomotory measures associated with tail-beat motion. We assessed the reliability of mouth-opening frequency as a proxy for metabolic rate by conducting experiments on zebrafish (Danio rerio) using swimming respirometry. We varied the flow speed from 0.8 to 3.2 body lengths per second and extracted tail-beat motion and mouth opening from video recordings. Our results revealed a strong correlation between oxygen uptake and mouth-opening frequency for nonzero flow speeds but not in quiescent water. Contrary to our expectations, we did not find evidence in favor of the use of tail-beat frequency as a proxy for metabolic rate. Overall, our results open the door to the study of individual metabolic rates in fish schools without confounding factors related to hydrodynamic interactions.

It pays to follow the leader: Metabolic cost of flight is lower for trailing birds in small groups

Many bird species commonly aggregate in flocks for reasons ranging from predator defense to navigation. Available evidence suggests that certain types of flocks-the V and echelon formations of large birds-may provide a benefit that reduces the aerodynamic cost of flight, whereas cluster flocks typical of smaller birds may increase flight costs. However, metabolic flight costs have not been directly measured in any of these group flight contexts [Zhang and Lauder, J. Exp. Biol. 226, jeb245617 (2023)]. Here, we measured the energetic benefits of flight in small groups of two or three birds and the requirements for realizing those benefits, using metabolic energy expenditure and flight position measurements from European Starlings flying in a wind tunnel. The starlings continuously varied their relative position during flights but adopted a V formation motif on average, with a modal spanwise and streamwise spacing of [0.81, 0.91] wingspans. As measured via CO2 production, flight costs for follower birds were significantly reduced compared to their individual solo flight benchmarks. However, followers with more positional variability with respect to leaders did less well, even increasing their costs above solo flight. Thus, we directly demonstrate energetic costs and benefits for group flight followers in an experimental context amenable to further investigation of the underlying aerodynamics, wake interactions, and bird characteristics that produce these metabolic effects.

Collective movement of schooling fish reduces the costs of locomotion in turbulent conditions

The ecological and evolutionary benefits of energy-saving in collective behaviors are rooted in the physical principles and physiological mechanisms underpinning animal locomotion. We propose a turbulence sheltering hypothesis that collective movements of fish schools in turbulent flow can reduce the total energetic cost of locomotion by shielding individuals from the perturbation of chaotic turbulent eddies. We test this hypothesis by quantifying energetics and kinematics in schools of giant danio (Devario aequipinnatus) and compared that to solitary individuals swimming under laminar and turbulent conditions over a wide speed range. We discovered that, when swimming at high speeds and high turbulence levels, fish schools reduced their total energy expenditure (TEE, both aerobic and anaerobic energy) by 63% to 79% compared to solitary fish (e.g., 228 versus 48 kj kg-1). Solitary individuals spend approximately 22% more kinematic effort (tail beat amplitude•frequency: 1.7 versus 1.4 BL s-1) to swim in turbulence at higher speeds than in laminar conditions. Fish schools swimming in turbulence reduced their three-dimensional group volume by 41% to 68% (at higher speeds, approximately 103 versus 33 cm3) and did not alter their kinematic effort compared to laminar conditions. This substantial energy saving highlights that schooling behaviors can mitigate turbulent disturbances by sheltering fish (within schools) from the eddies of sufficient kinetic energy that can disrupt locomotor gaits. Therefore, providing a more desirable internal hydrodynamic environment could be one of the ecological drivers underlying collective behaviors in a dense fluid environment.

Energy conservation by collective movement in schooling fish

Many animals moving through fluids exhibit highly coordinated group movement that is thought to reduce the cost of locomotion. However, direct energetic measurements demonstrating the energy-saving benefits of fluid-mediated collective movements remain elusive. By characterizing both aerobic and anaerobic metabolic energy contributions in schools of giant danio (Devario aequipinnatus), we discovered that fish schools have a concave upward shaped metabolism-speed curve, with a minimum metabolic cost at ~1 body length s-1. We demonstrate that fish schools reduce total energy expenditure (TEE) per tail beat by up to 56% compared to solitary fish. When reaching their maximum sustained swimming speed, fish swimming in schools had a 44% higher maximum aerobic performance and used 65% less non-aerobic energy compared to solitary individuals, which lowered the TEE and total cost of transport by up to 53%, near the lowest recorded for any aquatic organism. Fish in schools also recovered from exercise 43% faster than solitary fish. The non-aerobic energetic savings that occur when fish in schools actively swim at high speed can considerably improve both peak and repeated performance which is likely to be beneficial for evading predators. These energetic savings may underlie the prevalence of coordinated group locomotion in fishes.