Energetic advantages of burst swimming of fish

Intermittent swimming and muscle power output in brook trout, Salvelinus fontinalis

Slow and sustainable intermittent swimming has recently been described in several Centrarchid fishes, such as bluegill and largemouth bass. This swimming behavior involves short periods of body-caudal fin undulation alternating with variable periods of coasting. This aerobic muscle powered swimming appears to reduce energetic costs for slow, sustainable swimming, with fish employing a "fixed-gear" or constant tailbeat frequency and modulating swimming speed by altering the length of the coasting period. We asked if this swimming behavior was found in other fish species by examining volitional swimming by brook trout in a static swimming tank. Further, we employed muscle mechanics experiments to explore how intermittent swimming affects muscle power output in comparison to steady swimming behavior. Brook trout regularly employ an intermittent swimming form when allowed to swim volitionally, and consistently showed a tailbeat frequency of ~2 Hz. Coasting duration had a significant, inverse relationship to swimming speed. Across a range of slow, sustainable swimming speeds, tailbeat frequency increased modestly with speed. The duration of periods of coasting decreased significantly with increasing speed. Workloop experiments suggest that intermittent swimming reduces fatigue, allowing fish to maintain high power output for longer compared to continuous activity. This study expands the list of species that employ intermittent swimming, suggesting this behavior is a general feature of fishes.

Pectoral Fin Propulsion Performance Analysis of Robotic Fish with Multiple Degrees of Freedom Based on Burst-and-Coast Swimming Behavior Stroke Ratio

The pectoral fin propulsion of a bionic robotic fish always consists of two phases: propulsion and recovery. The robotic fish moves in a burst-and-coast swimming manner. This study aims to analyze a pair of bionic robotic fish with rigid pectoral fin propulsion with three degrees of freedom and optimize the elliptical propulsion curve with the minimum recovery stroke resistance using computational fluid dynamics methods. Then, the time allocated to the propulsion and recovery phases is investigated to maximize the propulsion performance of the bionic robotic fish. The numerical simulation results show that when the time ratio of the propulsion and recovery phases is 0.5:1, the resistance during the movement of the robotic fish is effectively reduced, and the drag-reducing effect is pronounced. According to a further analysis of pressure clouds and vortex structures, the pressure difference between the upstream and downstream fins of the pectoral fin varies with different stroke ratios. The increase in recovery phase time helps to prevent premature damage to the vortex ring structure generated during the propulsion process and improves propulsion efficiency.

Selective social interactions and speed-induced leadership in schooling fish

Animals moving together in groups are believed to interact among each other with effective social forces, such as attraction, repulsion, and alignment. Such forces can be inferred using "force maps," i.e., by analyzing the dependency of the acceleration of a focal individual on relevant variables. Here, we introduce a force map technique suitable for the analysis of the alignment forces experienced by individuals. After validating it using an agent-based model, we apply the force map to experimental data of schooling fish. We observe signatures of an effective alignment force with faster neighbors and an unexpected antialignment with slower neighbors. Instead of an explicit antialignment behavior, we suggest that the observed pattern is the result of a selective attention mechanism, where fish pay less attention to slower neighbors. This mechanism implies the existence of temporal leadership interactions based on relative speeds between neighbors. We present support for this hypothesis both from agent-based modeling as well as from exploring leader-follower relationships in the experimental data.

A design of a nature-like fishway to solve the fractured river connectivity caused by small hydropower based on hydrodynamics and fish behaviors

Achieving a harmonious alignment between the biological characteristics of fish and hydrodynamics patterns is crucial for ensuring the efficacy of fish passage facilities. In this study, based on the hydrodynamic characteristics of the river and the biological characteristics of fish, we evaluated the internal flow field in the nature-like fishway of Congen II hydropower station located along the Chabao river and explored methods to improve the operation efficiency. Based on comprehensive considerations of the flow field, turbulent kinetic energy, and the migration pathways of fish, it is found that the implementation of a continuous oblique bottom slope represents a more cost-effective and operationally convenient solution. The influence of different permutation of bulkheads in the nature-like fishway on operational efficiency was further examined. Our investigation revealed that the nature-like fishway with the continuous slope of 2% and the arrangement of three bulkheads in each row (model 3) exhibited a relatively simple velocity distribution and linear flow line, which poses challenges for fish in locating resting areas. In addition, the distribution of low turbulence kinetic energy area in the mainstream made it less favorable for fish to transition from the mainstream to the rest area within the fishway. The nature-like fishway with the continuous slope of 2% and the arrangement of two or three bulkheads in staggered rows (model 4) demonstrated better performance. Several potential fish migration routes for both model 3 and model 4 were proposed based on the numerical simulation results. In model 3, fish exhibited a continuous sprint through the concentrated high-speed area, which was less favorable for fish to rest and forage. In contrast, model 4 exhibited a diversified flow velocity distribution, enabling fish to make timely changes in their direction during migration. This feather proved to be advantageous in enhancing fish migration within the passage. The design of nature-like fishway in this study provides an important reference and technical support for the construction and optimization of the nature-like fishway for low dams, and is of great significance for restoring river connectivity destroyed by small hydropower construction and improving fish migration.

Muscle power production during intermittent swimming in bluegill sunfish

Locomotion is essential for the survival and fitness of animals. Fishes have evolved a variety of mechanisms to minimize the cost of transport. For instance, bluegill sunfish have recently been shown to employ intermittent swimming in nature and in laboratory conditions. We focused on the functional properties of the power-producing muscles that generate propulsive forces in bluegill to understand the implications of intermittent activity. We used in vivo aerobic or red muscle activity parameters (e.g., oscillation frequency and onset time and duration of activation) in muscle physiology experiments to examine muscle power output during intermittent versus steady swimming in these fish. Intermittent propulsion involves swimming at relatively slow speeds with short propulsive bursts alternating with gliding episodes. The propulsive bursts are at higher oscillation frequencies than would be predicted for a given average swimming speed with constant propulsion. The work-loop muscle physiology experiments with red muscle demonstrated that intermittent activity allows muscle to produce sufficient power for swimming compared with imposed steady swimming conditions. Further, the intermittent muscle activity in vitro reduces fatigue relative to steady or continuous activity. This work supports the fixed-gear hypothesis that suggests that there are preferred oscillation frequencies that optimize efficiency in muscle use and minimize cost of transport.

Using neuronal models to capture burst-and-glide motion and leadership in fish

While mathematical models, in particular self-propelled particle models, capture many properties of large fish schools, they do not always capture the interactions of smaller shoals. Nor do these models tend to account for the use of intermittent locomotion, often referred to as burst-and-glide, by many species. In this paper, we propose a model of social burst-and-glide motion by combining a well-studied model of neuronal dynamics, the FitzHugh-Nagumo model, with a model of fish motion. We first show that our model can capture the motion of a single fish swimming down a channel. Extending to a two-fish model, where visual stimulus of a neighbour affects the internal burst or glide state of the fish, we observe a rich set of dynamics found in many species. These include: leader-follower behaviour; periodic changes in leadership; apparently random (i.e. chaotic) leadership change; and tit-for-tat turn taking. Moreover, unlike previous studies where a randomness is required for leadership switching to occur, we show that this can instead be the result of deterministic interactions. We give several empirically testable predictions for how bursting fish interact and discuss our results in light of recently established correlations between fish locomotion and brain activity.

The lost art of mathematical modelling

We provide a critique of mathematical biology in light of rapid developments in modern machine learning. We argue that out of the three modelling activities - (1) formulating models; (2) analysing models; and (3) fitting or comparing models to data - inherent to mathematical biology, researchers currently focus too much on activity (2) at the cost of (1). This trend, we propose, can be reversed by realising that any given biological phenomenon can be modelled in an infinite number of different ways, through the adoption of an pluralistic approach, where we view a system from multiple, different points of view. We explain this pluralistic approach using fish locomotion as a case study and illustrate some of the pitfalls - universalism, creating models of models, etc. - that hinder mathematical biology. We then ask how we might rediscover a lost art: that of creative mathematical modelling.

Tough places and safe spaces: Can refuges save salmon from a warming climate?

The importance of thermal refuges in a rapidly warming world is particularly evident for migratory species, where individuals encounter a wide range of conditions throughout their lives. In this study, we used a spatially explicit, individual-based simulation model to evaluate the buffering potential of cold-water thermal refuges for anadromous salmon and trout (Oncorhynchus spp.) migrating upstream through a warm river corridor that can expose individuals to physiologically stressful temperatures. We considered upstream migration in relation to migratory phenotypes that were defined in terms of migration timing, spawn timing, swim speed, and use of cold-water thermal refuges. Individuals with different migratory phenotypes migrated upstream through riverine corridors with variable availability of cold-water thermal refuges and mainstem temperatures. Use of cold-water refuges (CWRs) decreased accumulated sublethal exposures to physiologically stressful temperatures when measured in degree-days above 20, 21, and 22°C. The availability of CWRs was an order of magnitude more effective in lowering accumulated sublethal exposures under current and future mainstem temperatures for summer steelhead than fall Chinook Salmon. We considered two emergent model outcomes, survival and percent of available energy used, in relation to thermal heterogeneity and migratory phenotype. Mean percent energy loss attributed to future warmer mainstem temperatures was at least two times larger than the difference in energy used in simulations without CWRs for steelhead and salmon. We also found that loss of CWRs reduced the diversity of energy-conserving migratory phenotypes when we examined the variability in entry timing and travel time outside of CWRs in relation to energy loss. Energy-conserving phenotypic space contracted by 7%-23% when CWRs were unavailable under the current thermal regime. Our simulations suggest that, while CWRs do not entirely mitigate for stressful thermal exposures in mainstem rivers, these features are important for maintaining a diversity of migration phenotypes. Our study suggests that the maintenance of diverse portfolios of migratory phenotypes and cool- and cold-water refuges might be added to the suite of policies and management actions presently being deployed to improve the likelihood of Pacific salmonid persistence into a future characterized by climate change.

The Kinematics and Dynamics of Schizopygopsis malacanthus Swimming during Ucrit Testing

The swimming kinematics (how fish move) and dynamics (how forces effect movement) of Schizopygopsis malacanthus were investigated during the determination of Ucrit by stepped velocity testing. A video tracking program was used to record and analyze the motion of five test fish in a Brett-type flume during each velocity step. The findings fell into three groups: (1) Even when flow was uniform, fish did not swim steadily, with speeds fluctuating by 2.2% to 8.4% during steady swimming. The proportion of unsteady swimming time increased with water velocity, and defining steady and unsteady swimming statistically, in terms of the definition of standard deviation of instantaneous displacements, may have higher accuracy. (2) In steady swimming, the forward velocity and acceleration of fish were correlated with body length (p < 0.05), but in unsteady swimming the correlations were not significant. The maximum swimming speed (1.504 m/s) and acceleration (16.54 m/s2) occurred during unsteady swimming, but these measurements may not be definitive because of tank space constraints on fish movement and the passive behavior of the test fish with respect to acceleration. (3) Burst-coast swimming in still water, investigated by previous scholars as an energy conserving behavior, is not the same as the gait transition from steady to unsteady swimming in flowing water. In this study, the axial force of fish swimming in the unsteady mode was significantly higher (×1.2~1.6) than in the steady mode, as was the energy consumed (×1.27~3.33). Thus, gait transition increases, rather than decreases, energy consumption. Our characterization of the kinematics and dynamics of fish swimming provides important new information to consider when indices of swimming ability from controlled tank testing are applied to fish passage design.

Large size in aquatic tetrapods compensates for high drag caused by extreme body proportions

Various Mesozoic marine reptile lineages evolved streamlined bodies and efficient lift-based swimming, as seen in modern aquatic mammals. Ichthyosaurs had low-drag bodies, akin to modern dolphins, but plesiosaurs were strikingly different, with long hydrofoil-like limbs and greatly variable neck and trunk proportions. Using computational fluid dynamics, we explore the effect of this extreme morphological variation. We find that, independently of their body fineness ratio, plesiosaurs produced more drag than ichthyosaurs and modern cetaceans of equal mass due to their large limbs, but these differences were not significant when body size was accounted for. Additionally, necks longer than twice the trunk length can substantially increase the cost of forward swimming, but this effect was cancelled out by the evolution of big trunks. Moreover, fast rates in the evolution of neck proportions in the long-necked elasmosaurs suggest that large trunks might have released the hydrodynamic constraints on necks thus allowing their extreme enlargement.

Hopscotching jellyfish: combining different duty cycle kinematics can lead to enhanced swimming performance

Jellyfish (Medusozoa) have been deemed the most energy-efficient animals in the world. Their bell morphology and relatively simple nervous systems make them attractive to robotocists. Although, the science community has devoted much attention to understanding their swimming performance, there is still much to be learned about the jet propulsive locomotive gait displayed by prolate jellyfish. Traditionally, computational scientists have assumed uniform duty cycle kinematics when computationally modeling jellyfish locomotion. In this study we used fluid-structure interaction modeling to determine possible enhancements in performance from shuffling different duty cycles together across multiple Reynolds numbers and contraction frequencies. Increases in speed and reductions in cost of transport were observed as high as 80% and 50%, respectively. Generally, the net effects were greater for cases involving lower contraction frequencies. Overall, robust duty cycle combinations were determined that led to enhanced or impeded performance.

Cool your jets: biological jet propulsion in marine invertebrates

Pulsatile jet propulsion is a common swimming mode used by a diverse array of aquatic taxa from chordates to cnidarians. This mode of locomotion has interested both biologists and engineers for over a century. A central issue to understanding the important features of jet-propelling animals is to determine how the animal interacts with the surrounding fluid. Much of our knowledge of aquatic jet propulsion has come from simple theoretical approximations of both propulsive and resistive forces. Although these models and basic kinematic measurements have contributed greatly, they alone cannot provide the detailed information needed for a comprehensive, mechanistic overview of how jet propulsion functions across multiple taxa, size scales and through development. However, more recently, novel experimental tools such as high-speed 2D and 3D particle image velocimetry have permitted detailed quantification of the fluid dynamics of aquatic jet propulsion. Here, we provide a comparative analysis of a variety of parameters such as efficiency, kinematics and jet parameters, and review how they can aid our understanding of the principles of aquatic jet propulsion. Research on disparate taxa allows comparison of the similarities and differences between them and contributes to a more robust understanding of aquatic jet propulsion.

Analysis of why sea turtles swim slowly: a metabolic and mechanical approach

Animals with high resting metabolic rates and low drag coefficients typically have fast optimal swim speeds in order to minimise energy costs per unit travel distance. The cruising swim speeds of sea turtles (0.5-0.6 m s^-1) are slower than those of seabirds and marine mammals (1-2 m s^-1). This study measured the resting metabolic rates and drag coefficients of sea turtles to answer two questions: (1) do turtles swim at the optimal swim speed?; and (2) what factors control the optimal swim speed of turtles? The resting metabolic rates of 13 loggerhead and 12 green turtles were measured; then, the cruising swim speeds of 15 loggerhead and 9 green turtles were measured and their drag coefficients were estimated under natural conditions. The measured cruising swim speeds (0.27-0.50 m s^-1) agreed with predicted optimal swim speeds (0.19-0.32 m s^-1). The resting metabolic rates of turtles were approximately one-twentieth those of penguins, and the products of the drag coefficient and frontal area of turtles were 8.6 times higher than those of penguins. Therefore, our results suggest that both low resting metabolic rate and high drag coefficient of turtles determine their slow cruising speed.

Burst-and-coast swimmers optimize gait by adapting unique intrinsic cycle

This paper addresses the physical mechanism of intermittent swimming by considering the burst-and-coast regime of fish swimming at different speeds. The burst-and-coast regime consists of a cycle with two successive phases, i.e., a phase of active undulation powered by the fish muscles followed by a passive gliding phase. Observations of real fish whose swimming gait is forced in a water flume from low to high speed regimes are performed, using a full description of the fish kinematics and mechanics. We first show that fish modulate a unique intrinsic cycle to sustain the demanded speed by modifying the bursting to coasting ratio while maintaining the duration of the cycle nearly constant. Secondly, we show using numerical simulations that the chosen kinematics by correspond to optimized gaits for swimming speeds larger than 1 body length per second.

Li et al. use experimental observations of red-nose tetrafish and mathematical simulations to model the burst-and-coast swimming regime. This study shows that in order to sustain the necessary speed, fish adopt a unique intrinsic cycle by modifying the burst to coast ratio and can implement this pattern at a range of swimming speeds.

Hydrodynamic benefits of intermittent locomotion of a self-propelled flapping plate

Intermittent locomotion is a widely used behavioral strategy for fish and birds to reduce the cost of movement. The intermittent locomotion performance of a self-propelled flapping plate is investigated numerically. Two intermittent swimming modes, namely, the multiple-tail-beat mode (MT mode) and the half-tail-beat mode (HT mode), as well as the continuous swimming mode (CT mode), are considered. Performance is evaluated from propulsive speed, efficiency, and cost of transport. The hydrodynamic performances of the intermittent modes are found to be better than the hydrodynamic performance of the CT mode when the bending stiffness K is moderate [i.e., K≈O(1)] and the duty cycle is not too small. For the two intermittent modes, the performance of the HT mode is better than that of the MT mode when K is small or moderate, while the situation is opposite when K is large. It is found that compared to the asymmetric wake of the MT mode, the symmetric wake of the HT mode is favorable to generate more thrust force and therefore achieve better performance. Besides, at moderate K, the largest bending deformation of the plate in the HT mode, as well as the large normal force, produces the largest thrust during the flapping. The present results can help us to better understand the intermittent locomotion of animals and may be helpful for bionic design.

Pursuit predation with intermittent locomotion in zebrafish

The control of a predator's locomotion is critical to its ability to capture prey. Flying animals adjust their heading continuously with control similar to guided missiles. However, many animals do not move with rapid continuous motion, but rather interrupt their progress with frequent pauses. To understand how such intermittent locomotion may be controlled during predation, we examined the kinematics of zebrafish (Danio rerio) as they pursued larval prey of the same species. Like many fishes, zebrafish move with discrete burst-and-coast swimming. We found that the change in heading and tail excursion during the burst phase was linearly related to the prey's bearing. These results suggest a strategy, which we call intermittent pure pursuit, that offers advantages in sensing and control. This control strategy is similar to perception and path-planning algorithms required in the design of some autonomous robots and may be common to a diversity of animals.

Burst-and-coast swimming is not always energetically beneficial in fish (Hemigrammus bleheri)

Burst-and-coast swimming is an intermittent mode of locomotion used by various fish species. The intermittent gait has been associated with certain advantages such as stabilizing the visual field, improved sensing ability, and reduced energy expenditure. We investigate burst-coast swimming in rummy nose tetra fish (Hemigrammus bleheri) using a combination of experimental data and numerical simulations. The experiments were performed in a shallow water channel where the tetra fish swam against an imposed inflow. High speed video recordings of the fish were digitized to extract the undulatory kinematics at various swimming speeds. The kinematics data were then used in Navier-Stokes simulations to prescribe the undulatory motion for three-dimensional geometrical models of the fish. The resulting steady-state speeds of the simulated self-propelled swimmers agree well with the speeds observed experimentally. We examine the power requirements for various realistic swimming modes, which indicate that it is possible to use continuous swimming gaits that require considerably less mechanical energy than intermittent burst-coast modes at comparable speeds. The higher energetic cost of burst-coast swimming suggests that the primary purpose of intermittent swimming may not be to conserve energy, but it may instead be related to a combination of other functional aspects such as improved sensing and the likely existence of a minimum tail-beat frequency. Importantly, using sinusoidal traveling waves to generate intermittent and continuous kinematics, instead of using experiment-based kinematics, results in comparable power requirements for the two swimming modes.

Intermittent sliding locomotion of a two-link body

We study the possibility of efficient intermittent locomotion for two-link bodies that slide by changing their interlink angle periodically in time. We find that the anisotropy ratio of the sliding friction coefficients is a key parameter, while solutions have a simple scaling dependence on the friction coefficients' magnitudes. With very anisotropic friction, efficient motions involve coasting in low-drag states, with rapid and asymmetric power and recovery strokes. As the anisotropy decreases, burst-and-coast motions change to motions with long power strokes and short recovery strokes, and roughly constant interlink angle velocity on each. These motions are seen in the spaces of sinusoidal and power-law motions described by two and five parameters, respectively. Allowing the duty cycle to vary greatly increases the motions' efficiency compared to the case of symmetric power and recovery strokes. Allowing further variations in the concavity of the power and recovery strokes improves the efficiency further only when friction is very anisotropic. Near isotropic friction, a variety of optimally efficient motions are found with more complex waveforms. Many of the optimal sinusoidal and power-law motions are similar to those that we find with an optimization search in the space of more general periodic functions (truncated Fourier series). When we increase the resistive force's power-law dependence on velocity, the optimal motions become smoother, slower, and less efficient, particularly near isotropic friction.

Why whales are big but not bigger: Physiological drivers and ecological limits in the age of ocean giants

The largest animals are marine filter feeders, but the underlying mechanism of their large size remains unexplained. We measured feeding performance and prey quality to demonstrate how whale gigantism is driven by the interplay of prey abundance and harvesting mechanisms that increase prey capture rates and energy intake. The foraging efficiency of toothed whales that feed on single prey is constrained by the abundance of large prey, whereas filter-feeding baleen whales seasonally exploit vast swarms of small prey at high efficiencies. Given temporally and spatially aggregated prey, filter feeding provides an evolutionary pathway to extremes in body size that are not available to lineages that must feed on one prey at a time. Maximum size in filter feeders is likely constrained by prey availability across space and time.

Active hydrodynamic imaging of a rigid spherical particle

A body with mechanical sensors may remotely detect particles suspended in the surrounding fluid via controlled agitation. Here we propose a sensory mode that relies on generating unsteady flow and sensing particle-induced distortions in the flow field. We demonstrate the basic physical principle in a simple analytical model, which consists of a small spherical particle at some distance from a plate undergoing impulsive or oscillatory motion. The model shows that changes in pressure or shear on the plate can be used to infer the location and size of the sphere. The key ingredient is to produce strong shear or strain around the sphere, which requires careful tuning of the viscous boundary layer on the moving plate. This elucidates how some organisms and devices may control their unsteady dynamics to enhance their range of perception.

In the corner of the eye: camouflaging motion in the peripheral visual field

Most animals need to move, and motion will generally break camouflage. In many instances, most of the visual field of a predator does not fall within a high-resolution area of the retina and so, when an undetected prey moves, that motion will often be in peripheral vision. We investigate how this can be exploited by prey, through different patterns of movement, to reduce the accuracy with which the predator can locate a cryptic prey item when it subsequently orients towards a target. The same logic applies for a prey species trying to localize a predatory threat. Using human participants as surrogate predators, tasked with localizing a target on peripherally viewed computer screens, we quantify the effects of movement (duration and speed) and target pattern. We show that, while motion is certainly detrimental to camouflage, should movement be necessary, some behaviours and surface patterns reduce that cost. Our data indicate that the phenotype that minimizes localization accuracy is unpatterned, having the mean luminance of the background, does not use a startle display prior to movement, and has short (below saccadic latency), fast movements.

Energetics of optimal undulatory swimming organisms

Energy consumption is one of the primary considerations in animal locomotion. In swimming locomotion, a number of questions related to swimming energetics of an organism and how the energetic quantities scale with body size remain open, largely due to the difficulties with modeling and measuring the power production and consumption. Based on a comprehensive theoretical framework that incorporates cyclic muscle behavior, structural dynamics and swimming hydrodynamics, we perform extensive computational simulations and show that many of the outstanding problems in swimming energetics can be explained by considering the coupling between hydrodynamics and muscle contraction characteristics, as well as the trade-offs between the conflicting performance goals of sustained swimming speed U and cost of transport COT. Our results lead to three main conclusions: (1) in contrast to previous hypotheses, achieving optimal values of U and COT is independent of producing maximal power or efficiency; (2) muscle efficiency in swimming, in contrast to that in flying or running, decreases with increasing body size, consistent with muscle contraction characteristics; (3) the long-standing problem of two disparate patterns of longitudinal power output distributions in swimming fish can be reconciled by relating the two patterns to U-optimal or COT-optimal swimmers, respectively. We also provide further evidence that the use of tendons in caudal regions is beneficial from an energetic perspective. Our conclusions explain and unify many existing observations and are supported by computational data covering nine orders of magnitude in body size.

Direct measurement of swimming and diving kinematics of giant Atlantic bluefin tuna (Thunnus thynnus)

Tunas possess a range of physiological and mechanical adaptations geared towards high-performance swimming that are of considerable interest to physiologists, ecologists and engineers. Advances in biologging have provided significant improvements in understanding tuna migrations and vertical movement patterns, yet our understanding of the locomotion and swimming mechanics of these fish under natural conditions is limited. We equipped Atlantic bluefin tuna (Thunnus thynnus) with motion-sensitive tags and video cameras to quantify the gaits and kinematics used by wild fish. Our data reveal significant variety in the locomotory kinematics of Atlantic bluefin tuna, ranging from continuous locomotion to two types of intermittent locomotion. The tuna sustained swimming speeds in excess of 1.5 m s-1 (0.6 body lengths s-1), while beating their tail at a frequency of approximately 1 Hz. While diving, some descents were entirely composed of passive glides, with slower descent rates featuring more gliding, while ascents were primarily composed of active swimming. The observed swimming behaviour of Atlantic bluefin tuna is consistent with theoretical models predicting such intermittent locomotion to result in mechanical and physiological advantages. Our results confirm that Atlantic bluefin tuna possess behavioural specializations to increase their locomotory performance, which together with their unique physiology improve their capacity to use pelagic and mesopelagic habitats.

Effects of body plan evolution on the hydrodynamic drag and energy requirements of swimming in ichthyosaurs

Ichthyosaurs are an extinct group of fully marine tetrapods that were well adapted to aquatic locomotion. During their approximately 160 Myr existence, they evolved from elongate and serpentine forms into stockier, fish-like animals, convergent with sharks and dolphins. Here, we use computational fluid dynamics (CFD) to quantify the impact of this transition on the energy demands of ichthyosaur swimming for the first time. We run computational simulations of water flow using three-dimensional digital models of nine ichthyosaurs and an extant functional analogue, a bottlenose dolphin, providing the first quantitative evaluation of ichthyosaur hydrodynamics across phylogeny. Our results show that morphology did not have a major effect on the drag coefficient or the energy cost of steady swimming through geological time. We show that even the early ichthyosaurs produced low levels of drag for a given volume, comparable to those of a modern dolphin, and that deep 'torpedo-shaped' bodies did not reduce the cost of locomotion. Our analysis also provides important insight into the choice of scaling parameters for CFD applied to swimming mechanics, and underlines the great influence of body size evolution on ichthyosaur locomotion. A combination of large bodies and efficient swimming modes lowered the cost of steady swimming as ichthyosaurs became increasingly adapted to a pelagic existence.

Intermittent locomotion of a fish-like swimmer driven by passive elastic mechanism

The intermittent locomotion performance of a fish-like elastic swimmer is studied numerically in this paper. The actuation is imposed only at the head and the locomotion is indirectly driven by passive elastic mechanism. For intermittent swimming, certain time durations of passive coasting are interspersed between two half-periods of active bursting. To facilitate the comparison of energy efficiencies in continuous and intermittent swimming at the same cruising speed, we consider both intermittent swimming at various duty cycles and also continuous swimming at reduced actuation frequencies. The result indicates that the intermittent style is more economical than the continuous style only when the cruising Reynolds number is sufficiently large and the duty cycle is moderate. We also explore the passive tail-beating pattern and wake structure for intermittent swimming. It is found that the kinematics of the tail contains a preparatory burst phase which lies in between the active bursting and the passive coasting phases. Three vortex streets are found in the wake structures behind the intermittent swimmers. The two oblique streets consist of strong vortex dipoles and the horizontal street is made up of weak vortices. The results of this study can provide some insight into the burst-and-coast swimming of fish and also inform the design of efficient bio-mimetic under-water vehicles.

The locomotor system of the ocean sunfish Mola mola (L.): role of gelatinous exoskeleton, horizontal septum, muscles and tendons

Adult ocean sunfish are the heaviest living teleosts. They have no axial musculature or caudal fin. Propulsion is by unpaired dorsal and anal fins; a pseudocaudal fin ('clavus') acts as a rudder. Despite common perception, young sunfish are active predators that swim quickly, beating their vertical fins in unison to generate lift-based propulsion and attain cruising speeds similar to salmon and marlin. Here we show that the thick subcutaneous layer (or 'capsule'), already known to provide positive buoyancy, is also crucial to locomotion. It provides two compartments, one for dorsal fin musculature and one for anal fin muscles, separated by a thick, fibrous, elastic horizontal septum that is bound to the capsule itself, the roof of the skull and the dorsal surface of the short vertebral column. The compartments are braced sagittally by bony haemal and neural spines. Both fins are powered by white muscles distributed laterally and red muscles located medially. The anal fin muscles are mostly aligned dorso-ventrally and have origins on the septum and haemal spines. Dorsal fin muscles vary in orientation; many have origins on the capsule above the skull and run near-horizontally and some bipennate muscles have origins on both capsule and septum. Such bipennate muscle arrangements have not been described previously in fishes. Fin muscles have hinged tendons that pass through capsular channels and radial cartilages to insertions on fin rays. The capsule is gelatinous (89.8% water) with a collagen and elastin meshwork. Greasy in texture, calculations indicate capsular buoyancy is partly provided by lipid. Capsule, septum and tendons provide elastic structures likely to enhance muscle action and support fast cruising.

Hydrodynamic advantages of swimming by salp chains

Salps are marine invertebrates comprising multiple jet-propelled swimming units during a colonial life-cycle stage. Using theory, we show that asynchronous swimming with multiple pulsed jets yields substantial hydrodynamic benefit due to the production of steady swimming velocities, which limit drag. Laboratory comparisons of swimming kinematics of aggregate salps (Salpa fusiformis and Weelia cylindrica) using high-speed video supported that asynchronous swimming by aggregates results in a smoother velocity profile and showed that this smoother velocity profile is the result of uncoordinated, asynchronous swimming by individual zooids. In situ flow visualizations of W. cylindrica swimming wakes revealed that another consequence of asynchronous swimming is that fluid interactions between jet wakes are minimized. Although the advantages of multi-jet propulsion have been mentioned elsewhere, this is the first time that the theory has been quantified and the role of asynchronous swimming verified using experimental data from the laboratory and the field.

Accelerating fishes increase propulsive efficiency by modulating vortex ring geometry

Swimming animals need to generate propulsive force to overcome drag, regardless of whether they swim steadily or accelerate forward. While locomotion strategies for steady swimming are well characterized, far less is known about acceleration. Animals exhibit many different ways to swim steadily, but we show here that this behavioral diversity collapses into a single swimming pattern during acceleration regardless of the body size, morphology, and ecology of the animal. We draw on the fields of biomechanics, fluid dynamics, and robotics to demonstrate that there is a fundamental difference between steady swimming and forward acceleration. We provide empirical evidence that the tail of accelerating fishes can increase propulsive efficiency by enhancing thrust through the alteration of vortex ring geometry. Our study provides insight into how propulsion can be altered without increasing vortex ring size and represents a fundamental departure from our current understanding of the hydrodynamic mechanisms of acceleration. Our findings reveal a unifying hydrodynamic principle that is likely conserved in all aquatic, undulatory vertebrates.

Brain size does not impact shoaling dynamics in unfamiliar groups of guppies (Poecilia reticulata)

Collective movement is achieved when individuals adopt local rules to interact with their neighbours. How the brain processes information about neighbours' positions and movements may affect how individuals interact in groups. As brain size can determine such information processing it should impact collective animal movement. Here we investigate whether brain size affects the structure and organisation of newly forming fish shoals by quantifying the collective movement of guppies (Poecilia reticulata) from large- and small-brained selection lines, with known differences in learning and memory. We used automated tracking software to determine shoaling behaviour of single-sex groups of eight or two fish and found no evidence that brain size affected the speed, group size, or spatial and directional organisation of fish shoals. Our results suggest that brain size does not play an important role in how fish interact with each other in these types of moving groups of unfamiliar individuals. Based on these results, we propose that shoal dynamics are likely to be governed by relatively basic cognitive processes that do not differ in these brain size selected lines of guppies.

The influence of body size on the intermittent locomotion of a pelagic schooling fish

There is a potential trade-off between grouping and the optimizing of the energetic efficiency of individual locomotion. Although intermittent locomotion, e.g. glide and upward swimming (GAU), can reduce the cost of locomotion at the individual level, the link between the optimization of individual intermittent locomotion and the behavioural synchronization in a group, especially among members with different sizes, is unknown. Here, we continuously monitored the schooling behaviour of a negatively buoyant fish, Pacific bluefin tuna (N = 10; 21.0 ∼ 24.5 cm), for 24 h in an open-sea net cage using accelerometry. All the fish repeated GAU during the recording periods. Although the GAU synchrony was maintained at high levels (overall mean = 0.62 for the cross-correlation coefficient of the GAU timings), larger fish glided for a longer duration per glide and more frequently than smaller fish. Similar-sized pairs showed significantly higher GAU synchrony than differently sized pairs. Our accelerometry results and the simulation based on hydrodynamic theory indicated that the advantage of intermittent locomotion in energy savings may not be fully optimized for smaller animals in a group when faced with the maintenance of group cohesion, suggesting that size assortative shoaling would be advantageous.

Field swimming performance of bluegill sunfish, Lepomis macrochirus: implications for field activity cost estimates and laboratory measures of swimming performance

Mobility is essential to the fitness of many animals, and the costs of locomotion can dominate daily energy budgets. Locomotor costs are determined by the physiological demands of sustaining mechanical performance, yet performance is poorly understood for most animals in the field, particularly aquatic organisms. We have used 3‐D underwater videography to quantify the swimming trajectories and propulsive modes of bluegills sunfish (Lepomis macrochirus, Rafinesque) in the field with high spatial (1–3 mm per pixel) and temporal (60 Hz frame rate) resolution. Although field swimming trajectories were variable and nonlinear in comparison to quasi steady‐state swimming in recirculating flumes, they were much less unsteady than the volitional swimming behaviors that underlie existing predictive models of field swimming cost. Performance analyses suggested that speed and path curvature data could be used to derive reasonable estimates of locomotor cost that fit within measured capacities for sustainable activity. The distinct differences between field swimming behavior and performance measures obtained under steady‐state laboratory conditions suggest that field observations are essential for informing approaches to quantifying locomotor performance in the laboratory.

How predation shapes the social interaction rules of shoaling fish

Predation is thought to shape the macroscopic properties of animal groups, making moving groups more cohesive and coordinated. Precisely how predation has shaped individuals' fine-scale social interactions in natural populations, however, is unknown. Using high-resolution tracking data of shoaling fish (Poecilia reticulata) from populations differing in natural predation pressure, we show how predation adapts individuals' social interaction rules. Fish originating from high predation environments formed larger, more cohesive, but not more polarized groups than fish from low predation environments. Using a new approach to detect the discrete points in time when individuals decide to update their movements based on the available social cues, we determine how these collective properties emerge from individuals' microscopic social interactions. We first confirm predictions that predation shapes the attraction-repulsion dynamic of these fish, reducing the critical distance at which neighbours move apart, or come back together. While we find strong evidence that fish align with their near neighbours, we do not find that predation shapes the strength or likelihood of these alignment tendencies. We also find that predation sharpens individuals' acceleration and deceleration responses, implying key perceptual and energetic differences associated with how individuals move in different predation regimes. Our results reveal how predation can shape the social interactions of individuals in groups, ultimately driving differences in groups' collective behaviour.

A simple game-theoretic model for upstream fish migration

A simple game-theoretic model for upstream fish migration, which is a key element in life history of diadromous fishes, is proposed. Foundation of the model is a minimization problem on the cost of migration with the swimming speed and school size as the variables to be simultaneously optimized. Finding the optimizer ultimately reduces to solving a self-consistency equation without explicit solutions. Mathematical analytical results lead to the sufficient condition that the self-consistency equation has a unique solution, which turns out to be identified with the condition where the unique optimizer exists. Behavior of the optimizer is analyzed both mathematically and numerically to show its biophysical and ecological consequences. The analytical results demonstrate reasonable agreement between the present mathematical model and the theoretical and experimental results of upstream migration of fish schools reported in the past research.

Signatures of optimal control in pairs of schooling zebrafish

Animals moving in groups coordinate their motion to remain cohesive. A large amount of data and analysis of movement coordination has been obtained in several species, but we are lacking theoretical frameworks that can derive the form of coordination rules. Here, we examine whether optimal control theory can predict the rules underlying social interactions from first principles. We find that a control rule which is designed to minimize the time it would take a pair of schooling fish to form a cohesively moving unit correctly predicts the characteristics of social interactions in fish. Our methodology explains why social attraction is negatively modulated by self-motion velocity and positively modulated by partner motion velocity, and how the biomechanics of fish swimming can shape the form of social forces. Crucially, the values of all parameters in our model can be estimated from independent experiments that need not relate to measurement of social interactions. We test our theory by showing a good match with experimentally observed social interaction rules in zebrafish. In addition to providing a theoretical rationale for observed decision rules, we suggest that this framework opens new questions about tuning problems and learnability of collective behaviours.

Kinematics of ram filter feeding and beat-glide swimming in the northern anchovy Engraulis mordax

In the dense aquatic environment, the most adept swimmers are streamlined to reduce drag and increase the efficiency of locomotion. However, because they open their mouth to wide gape angles to deploy their filtering apparatus, ram filter feeders apparently switch between diametrically opposite swimming modes; highly efficient, streamlined 'beat-glide' swimming, and ram filter feeding, which has been hypothesized to be a high-cost feeding mode because of presumed increased drag. Ram filter feeding forage fish are thought to play an important role in the flux of nutrients and energy in upwelling ecosystems, however the biomechanics and energetics of this feeding mechanism remain poorly understood. We quantified the kinematics of an iconic forage fish, the northern anchovy, Engraulis mordax, during ram filter feeding and non-feeding, mouth-closed beat-glide swimming. Although many kinematic parameters between the two swimming modes were similar, we found that swimming speeds and tailbeat frequencies were significantly lower during ram feeding. Rather than maintain speed with the school, a speed which closely matches theoretical optimum filter feeding speeds was consistently observed. Beat-glide swimming was characterized by high variability in all kinematic parameters, but variance in kinematic parameters was much lower during ram filter feeding. Under this mode, body kinematics are substantially modified, and E. mordax swims more slowly, and with decreased lateral movement along the entire body, but most noticeably in the anterior. Our results suggest that hydrodynamic effects that come with deployment of the filtering anatomy may limit behavioral options during foraging and result in slower swimming speeds during ram filtration.

Empirical observations of the spawning migration of European eels: The long and dangerous road to the Sargasso Sea

The spawning migration of the European eel (Anguilla anguilla L.) to the Sargasso Sea is one of the greatest animal migrations. However, the duration and route of the migration remain uncertain. Using fishery data from 20 rivers across Europe, we show that most eels begin their oceanic migration between August and December. We used electronic tagging techniques to map the oceanic migration from eels released from four regions in Europe. Of 707 eels tagged, we received 206 data sets. Many migrations ended soon after release because of predation events, but we were able to reconstruct in detail the migration routes of >80 eels. The route extended from western mainland Europe to the Azores region, more than 5000 km toward the Sargasso Sea. All eels exhibited diel vertical migrations, moving from deeper water during the day into shallower water at night. The range of migration speeds was 3 to 47 km day-1. Using data from larval surveys in the Sargasso Sea, we show that spawning likely begins in December and peaks in February. Synthesizing these results, we show that the timing of autumn escapement and the rate of migration are inconsistent with the century-long held assumption that eels spawn as a single reproductive cohort in the springtime following their escapement. Instead, we suggest that European eels adopt a mixed migratory strategy, with some individuals able to achieve a rapid migration, whereas others arrive only in time for the following spawning season. Our results have consequences for eel management.

Assessing hydrodynamic space use of brown trout, Salmo trutta, in a complex flow environment: a return to first principles

It is commonly assumed that stream-dwelling fish should select positions where they can reduce energetic costs relative to benefits gained and enhance fitness. However, the selection of appropriate hydrodynamic metrics that predict space use is the subject of recent debate and a cause of controversy. This is for three reasons: (1) flow characteristics are often oversimplified, (2) confounding variables are not always controlled and (3) there is limited understanding of the explanatory mechanisms that underpin the biophysical interactions between fish and their hydrodynamic environment. This study investigated the space use of brown trout, Salmo trutta, in a complex hydrodynamic flow field created using an array of different sized vertically oriented cylinders in a large open-channel flume in which confounding variables were controlled. A hydrodynamic drag function (D) based on single-point time-averaged velocity statistics that incorporates the influence of turbulent fluctuations was used to infer the energetic cost of steady swimming. Novel hydrodynamic preference curves were developed and used to assess the appropriateness of D as a descriptor of space use compared with other commonly used metrics. Zones in which performance-enhancing swimming behaviours (e.g. Kármán gaiting, entraining and bow riding) that enable fish to hold position while reducing energetic costs (termed 'specialised behaviours') were identified and occupancy was recorded. We demonstrate that energy conservation strategies play a key role in space use in an energetically taxing environment with the majority of trout groups choosing to frequently occupy areas in which specialised behaviours may be adopted or by selecting low-drag regions.

Locomotion of neutrally buoyant fish with flexible caudal fin

Historically, burst-and-coast locomotion strategies have been given two very different explanations. The first one was based on the assumption that the drag of an actively swimming fish is greater than the drag of the same fish in motionless glide. Fish reduce the cost of locomotion by swimming actively during a part of the swimming interval, and gliding through the remaining part. The second one was based on the assumption that muscles perform efficiently only if their contraction rate exceeds a certain threshold. Fish reduce the cost of locomotion by using an efficient contraction rate during a part of the swimming interval, and gliding through the remaining part. In this paper, we suggest yet a third explanation. It is based on the assumption that propulsion efficiency of a swimmer can increase with thrust. Fish reduce the cost of locomotion by alternating high thrust, and hence more efficient, bursts with passive glides. The paper presents a formal analysis of the respective burst-and-coast strategy, shows that the locomotion efficiency can be practically as high as the propulsion efficiency during burst, and shows that the other two explanations can be considered particular cases of the present one.

Recent advances in telemetry for estimating the energy metabolism of wild fishes

Metabolic rate is a critical factor in animal biology and ecology, providing an objective measure that can be used in attributing a cost to different activities and to assessing what animals do against some optimal behaviour. Ideally, metabolic rate would be estimated directly by measuring heat output but, until recently, this has not been easily tractable with fishes so instead metabolic rate is usually estimated using indirect methods. In the laboratory, oxygen consumption rate is the indirect method most frequently used for estimating metabolic rate, but technical requirements preclude the measurement of either heat output or oxygen consumption rate in free-ranging fishes. There are other field methods for estimating metabolic rate that can be used with mammals and birds but, again, these cannot be used with fishes. Here, the use of electronic devices that record body acceleration in three dimensions (accelerometry) is considered. Accelerometry is a comparatively new telemetric method for assessing energy metabolism in animals. Correlations between dynamic body acceleration (DBA) and oxygen consumption rate demonstrate that this will be a useful proxy for estimating activity-specific energy expenditure from fishes in mesocosm or field studies over extended periods where other methods (e.g. oxygen consumption rate) are not feasible. DBA therefore has potential as a valuable tool for attributing cost to different activities. This could help in gaining a full picture of how fishes make energy-based trade-offs between different levels of activity when faced with conflicting or competing demands arising from increased and combined environmental stressors.

Accelerometer-derived activity correlates with volitional swimming speed in lake sturgeon (Acipenser fulvescens)

Quantifying fine-scale locomotor behaviours associated with different activities is challenging for free-swimming fish. Biologging and biotelemetry tools can help address this problem. An open channel flume was used to generate volitional swimming speed (Us) estimates of cultured lake sturgeon (Acipenser fulvescens Rafinesque, 1817) and these were paired with simultaneously recorded accelerometer-derived metrics of activity obtained from three types of data-storage tags. This study examined whether a predictive relationship could be established between four different activity metrics (tail-beat frequency (TBF), tail-beat acceleration amplitude (TBAA), overall dynamic body acceleration (ODBA), and vectorial dynamic body acceleration (VeDBA)) and the swimming speed of A. fulvescens. Volitional Us of sturgeon ranged from 0.48 to 2.70 m·s−1 (0.51–3.18 body lengths (BL)·s−1). Swimming speed increased linearly with all accelerometer-derived metrics, and when all tag types were combined, Us increased 0.46 BL·s−1 for every 1 Hz increase in TBF, and 0.94, 0.61, and 0.94 BL·s−1 for every 1g increase in TBAA, ODBA, and VeDBA, respectively. Predictive relationships varied among tag types and tag-specific parameter estimates of Us are presented for all metrics. This use of acceleration data-storage tags demonstrated their applicability for the field quantification of sturgeon swimming speed.

The foraging benefits of being fat in a highly migratory marine mammal

Foraging theory predicts that breath-hold divers adjust the time spent foraging at depth relative to the energetic cost of swimming, which varies with buoyancy (body density). However, the buoyancy of diving animals varies as a function of their body condition, and the effects of these changes on swimming costs and foraging behaviour have been poorly examined. A novel animal-borne accelerometer was developed that recorded the number of flipper strokes, which allowed us to monitor the number of strokes per metre swam (hereafter, referred to as strokes-per-metre) by female northern elephant seals over their months-long, oceanic foraging migrations. As negatively buoyant seals increased their fat stores and buoyancy, the strokes-per-metre increased slightly in the buoyancy-aided direction (descending), but decreased significantly in the buoyancy-hindered direction (ascending), with associated changes in swim speed and gliding duration. Overall, the round-trip strokes-per-metre decreased and reached a minimum value when seals achieved neutral buoyancy. Consistent with foraging theory, seals stayed longer at foraging depths when their round-trip strokes-per-metre was less. Therefore, neutrally buoyant divers gained an energetic advantage via reduced swimming costs, which resulted in an increase in time spent foraging at depth, suggesting a foraging benefit of being fat.

Introduction to the Symposium-Unsteady Aquatic Locomotion with Respect to Eco-Design and Mechanics

The importance of unsteadiness in the aquatic environment has come to the forefront in understanding locomotor mechanics in nature. The impact of unsteadiness, starting with control of posture and trajectories during aquatic locomotion, is ultimately expressed in energy costs, morphology, and fitness. Unsteadiness from both internal and external perturbations for aquatic animals is important at scales ranging from micro to macro to global.

Gait switches in deep-diving beaked whales: biomechanical strategies for long-duration dives

Diving animals modulate their swimming gaits to promote locomotor efficiency and so enable longer, more productive dives. Beaked whales perform extremely long and deep foraging dives that probably exceed aerobic capacities for some species. Here, we use biomechanical data from suction-cup tags attached to three species of beaked whales (Mesoplodon densirostris, N=10; Ziphius cavirostris, N=9; and Hyperoodon ampullatus, N=2) to characterize their swimming gaits. In addition to continuous stroking and stroke-and-glide gaits described for other diving mammals, all whales produced occasional fluke-strokes with distinctly larger dorso-ventral acceleration, which we termed ‘type-B’ strokes. These high-power strokes occurred almost exclusively during deep dive ascents as part of a novel mixed gait. To quantify body rotations and specific acceleration generated during strokes we adapted a kinematic method combining data from two sensors in the tag. Body rotations estimated with high-rate magnetometer data were subtracted from accelerometer data to estimate the resulting surge and heave accelerations. Using this method, we show that stroke duration, rotation angle and acceleration were bi-modal for these species, with B-strokes having 76% of the duration, 52% larger body rotation and four times more surge than normal strokes. The additional acceleration of B-strokes did not lead to faster ascents, but rather enabled brief glides, which may improve the overall efficiency of this gait. Their occurrence towards the end of long dives leads us to propose that B-strokes may recruit fast-twitch fibres that comprise ∼80% of swimming muscles in Blainville's beaked whales, thus prolonging foraging time at depth.