The notochord of hagfishMyxine glutinosa: visco-elastic properties and mechanical functions during steady swimming

Form and function of anguilliform swimming

Anguilliform swimmers are long and narrow animals that propel themselves by undulating their bodies. Observations in nature and recent investigations suggest that anguilliform swimming is highly efficient. However, understanding the underlying reasons for the efficiency of this type of locomotion requires interdisciplinary studies spanning from biology to hydrodynamics. Regrettably, these different fields are rarely discussed together, which hinders our ability to understand the repeated evolution of this swimming mode in vertebrates. This review compiles the current knowledge of the anatomical features that drive anguilliform swimming, compares the resulting kinematics across a wide range of anguilliform swimmers, and describes the resulting hydrodynamic interactions using data from both in vivo experiments and computational studies.

Biphasic burrowing in Atlantic hagfish (Myxine limosa)

Myxine limosa is a burrowing species of hagfish that occurs in the western North Atlantic in areas with muddy substrate and at depths generally greater than 100 meters. Burrowing of M. limosa has been observed from submersibles, but little is known about the behavior of these animals within the substrate or the biomechanical mechanisms involved. Here, we investigated burrowing in M. limosa by observing individuals as they burrowed through transparent gelatin. A photoelastic setup using crossed polarizers allowed us to visualize stress development in the gelatin as the hagfish moved through it. We found that M. limosa created U-shaped burrows in gelatin using a stereotyped, two-phase burrowing behavior. In the first ('thrash') phase, hagfish drove their head and their anterior body into the substrate using vigorous sinusoidal swimming movements, with their head moving side-to-side. In the second ('wriggle') phase, swimming movements ceased, with propulsion coming exclusively from the anterior, submerged portion of body. The wriggle phase involved side-to-side head movements and movements of the submerged part of the body that resembled the internal concertina strategy used by caecilians and uropeltid snakes. The entire burrowing process took on average 7.6 min to complete and ended with the hagfish's head protruding from the substrate and the rest of its body generally concealed. Understanding the burrowing activities of hagfishes could lead to improved understanding of sediment turnover in marine benthic habitats, new insights into the reproductive behavior of hagfishes, or even inspiration for the design of burrowing robots.

Computational Study of Stiffness-Tuning Strategies in Anguilliform Fish

Biological evidence demonstrates that fish can tune their body stiffness to improve thrust and efficiency during swimming locomotion. However, the stiffness-tuning strategies that maximize swimming speed or efficiency are still unclear. In the present study, a musculo-skeletal model of anguilliform fish is developed to study the properties of variable stiffness, in which the planar serial-parallel mechanism is used to model the body structure. The calcium ion model is adopted to simulate muscular activities and generate muscle force. Further, the relations among the forward speed, the swimming efficiency, and Young's modulus of the fish body are investigated. The results show that for certain body stiffness, the swimming speed and efficiency are increased with the tail-beat frequency until reaching the maximum value and then decreased. The peak speed and efficiency are also increased with the amplitude of muscle actuation. Anguilliform fish tend to vary their body stiffness to improve the swimming speed and efficiency at a high tail-beat frequency or small amplitude of muscle actuation. Furthermore, the midline motions of anguilliform fish are analyzed by the complex orthogonal decomposition (COD) method, and the discussions of fish motions associated with the variable body stiffness and the tail-beat frequency are also presented. Overall, the optimal swimming performance of anguilliform fish benefits from the matching relationships among the muscle actuation, the body stiffness, and the tail-beat frequency.

Tunable stiffness in fish robotics: mechanisms and advantages

One of the emerging themes of fish-inspired robotics is flexibility. Adding flexibility to the body, joints, or fins of fish-inspired robots can significantly improve thrust and/or efficiency during locomotion. However, the optimal stiffness depends on variables such as swimming speed, so there is no one 'best' stiffness that maximizes efficiency in all conditions. Fish are thought to solve this problem by using muscular activity to tune their body and fin stiffness in real-time. Inspired by fish, some recent robots sport polymer actuators, adjustable leaf springs, or artificial tendons that tune stiffness mechanically. Models and water channel tests are providing a theoretical framework for stiffness-tuning strategies that devices can implement. The strategies can be thought of as analogous to car transmissions, which allow users to improve efficiency by tuning gear ratio with driving speed. We provide an overview of the latest discoveries about (1) the propulsive benefits of flexibility, particularlytunableflexibility, and (2) the mechanisms and strategies that fish and fish-inspired robots use to tune stiffness while swimming.

Foretelling the Flex-Vertebral Shape Predicts Behavior and Ecology of Fishes

We modeled swimming kinematics and body mechanics of several fish species of varying habitat and body shape based on measurements of internal vertebral morphology.

SYNOPSIS

One key evolutionary innovation that separates vertebrates from invertebrates is the notochord, a central element that provides the stiffness needed for powerful movements. Later, the notochord was further stiffened by the vertebrae, cartilaginous, and bony elements, surrounding the notochord. The ancestral notochord is retained in modern vertebrates as intervertebral material, but we know little about its mechanical interactions with surrounding vertebrae. In this study, the internal shape of the vertebrae-where this material is found-was quantified in 16 species of fishes with various body shapes, swimming modes, and habitats. We used micro-computed tomography to measure the internal shape. We then created and mechanically tested physical models of intervertebral joints. We also mechanically tested actual vertebrae of five species. Material testing shows that internal morphology of the centrum significantly affects bending and torsional stiffness. Finally, we performed swimming trials to gather kinematic data. Combining these data, we created a model that uses internal vertebral morphology to make predictions about swimming kinematics and mechanics. We used linear discriminant analysis (LDA) to assess the relationship between vertebral shape and our categorical traits. The analysis revealed that internal vertebral morphology is sufficient to predict habitat, body shape, and swimming mode in our fishes. This model can also be used to make predictions about swimming in fishes not easily studied in the laboratory, such as deep sea and extinct species, allowing the development of hypotheses about their natural behavior.

Form and function of the caudal fin throughout the phylogeny of fishes

Fishes are the longest persisting living vertebrates and as such, display an incredible array of diversity. Variation in the tail, or caudal fin, is often a reflection of a fish's environment, and affects movement, predation, defense, and reproduction. Previous literature has discussed many aspects of caudal fin form and function in particular taxonomic groups; however, no previous work has synthesized these studies in order to detail how the caudal fin is structured, and what purpose this structure serves, throughout the phylogeny of fishes. This review examines the caudal fin throughout the main lineages of fish evolution, and highlights where changes in shape and usage have occurred. Such novelties in form and function tend to have far-reaching evolutionary consequences. Through integration of past and present work, this review creates a coherent picture of caudal fin evolution. Patterns and outliers that demonstrate how form and function of this appendage are intertwined can further inform hypotheses that fill critical gaps in knowledge concerning the caudal fin.

Evolution: Spinal Innovation Enabled by Genome Duplication

Solid vertebrae evolved multiple times across vertebrates, but the origins and relationships of different spine forms remain unclear. A new study reveals teleost fishes evolved their solid vertebrae following genome duplication, when a novel gene repressed ancestral spine programming.

A Tail of Four Fishes: An Analysis of Kinematics and Material Properties of Elongate Fishes

The elongate body plan is present in many groups of fishes, and this morphology dictates functional consequences seen in swimming behavior. Previous work has shown that increasing the number of vertebrae, or decreasing the intervertebral joint length, in a fixed length artificial system increases stiffness. Tails with increased stiffness can generate more power from tail beats, resulting in an increased mean swimming speed. This demonstrates the impacts of morphology on both material properties and kinematics, establishing mechanisms for form contributing to function. Here, we wanted to investigate relationships between form and ecological function, such as differences in dietary strategies and habitat preferences among fish species. This study aims to characterize and compare the kinematics, material properties, and vertebral morphology of four species of elongate fishes: Anoplarchus insignis, Anoplarchus purpurescens, Xiphister atropurpureus, and Xiphister mucosus. We hypothesized that these properties would differ among the four species due to their differential ecological niches. To calculate kinematic variables, we filmed these fishes swimming volitionally. We also measured body stiffness by bending the abdominal and tail regions of sacrificed individuals in different stages of dissection (whole body, removed skin, and removed muscle). Finally, we counted the number of vertebrae from CT scans of each species to quantify vertebral morphology. Principal component and linear discriminant analyses suggested that the elongate fish species can be distinguished from one another by their material properties, morphology, and swimming kinematics. With this information combined, we can draw connections between the physical properties of the fishes and their ecological niches.

Fish without Tail Fins-Exploring the Function of Tail Morphology of the First Vertebrates

We use a series of hydrodynamic experiments on abstracted models to explore whether primitive vertebrates may have swum under various conditions without a clearly-differentiated tail fin. Cambrian vertebrates had post-anal stubby tails, some had single dorsal and ventral fins, but none had yet evolved a clearly differentiated caudal fin typical of post-Cambrian fishes, and must have relied on their long and flexible laterally-compressed bodies for locomotion, i.e., by bending their bodies side-to-side in order to propagate waves from head to tail. We approach this problem experimentally based on an abstracted model of Metaspriggina walcotti from the 506-million-year old Burgess Shale by using oscillating thin flexible plates while varying the tail fin geometry from rectangular to uniform, and finally to a no tail-fin condition. Despite a missing tail fin, this study supports the observation that the abstracted Metaspriggina model can generate a strong propulsive force in cruise conditions, both away from, and near the sea bed (in ground effect). However, when the abstracted Metaspriggina model moves in ground effect, a weaker performance is observed, indicating that Metaspriggina may not necessarily have been optimized for swimming near the sea bed. When considering acceleration from rest, we find that the Metaspriggina model's performance is not significantly different from other morphological models (abstracted truncate tail and abstracted heterocercal tail). Statistical analysis shows that morphological parameters, swimming modes, and ground effect all play significant roles in thrust performance. While the exact relationships of Cambrian vertebrates are still debated, as agnathans, they share some general characteristics with modern cyclostomes, in particular an elongate body akin to lampreys. Lampreys, as anguilliform swimmers, are considered to be some of the most efficient swimmers using a particular type of suction thrust induced by the traveling body wave as it travels from head to tail. Our current experiments suggest that Metaspriggina's ability in acceleration from rest, through possibly a similar type of suction thrust, which is defined as the ability to generate low pressure on upstream facing sections of the body, might have evolved early in response to increasing predator pressure during the Cambrian Explosion.

Comparative biomechanics of hagfish skins: diversity in material, morphology, and movement

The baggy skins of hagfishes confer whole-body flexibility that enables these animals to tie themselves into knots without injury. The skin's looseness is produced by a subcutaneous blood sinus that decouples the skin and body core and permits the core to contort dramatically without loading the skin in tension or shear. Hagfish skin represents a biological composite material comparable in strength and stiffness to the conventionally taut skins of other fishes. However, our understanding of hagfish skin is restricted to only one of 78 species: The Pacific hagfish Eptatretus stoutii. To determine if other hagfish share similar characteristics with E. stoutii, we measured material properties and compared histological data sets from the skins of four hagfish species: E. springeri, E. stoutii, Myxine glutinosa, and M. hubbsi. We also compared these material properties data with skins from the American eel, Anguilla rostrata. We subjected skin samples from all species to uniaxial tensile tests in order to measure strength, stiffness, extensibility, and toughness of skins stretched along longitudinal and circumferential axes. We also used a series of equibiaxial tensile tests on skin samples from E. stoutii, M. glutinosa, and A. rostrata to measure stiffness of skins simultaneously strained along both axes. Significant results of uniaxial and biaxial tests show that the skins from Eptatretus are anisotropic, being stiffer in the longitudinal axis, and more extensible than the isotropic skins of Myxine. Skins of A. rostrata were stiffer in the circumferential axis and they were stronger, tougher, and stiffer than all hagfish skins examined. The skins of Eptatretus are histologically distinct from Myxine skins and possess arrays of fibers that stain like muscle. These interspecific differences across hagfish skins show a phylogenetic pattern with knotting kinematics and flexibility; both genera belong to distinct but major subfamilies within the Myxinidae, and Eptatretus is known for creating and manipulating a greater diversity of knotting styles than Myxine.

The Spine: A Strong, Stable, and Flexible Structure with Biomimetics Potential

From its first appearance in early vertebrates, the spine evolved the function of protecting the spinal cord, avoiding excessive straining during body motion. Its stiffness and strength provided the basis for the development of the axial skeleton as the mechanical support of later animals, especially those which moved to the terrestrial environment where gravity loads are not alleviated by the buoyant force of water. In tetrapods, the functions of the spine can be summarized as follows: protecting the spinal cord; supporting the weight of the body, transmitting it to the ground through the limbs; allowing the motion of the trunk, through to its flexibility; providing robust origins and insertions to the muscles of trunk and limbs. This narrative review provides a brief perspective on the development of the spine in vertebrates, first from an evolutionary, and then from an embryological point of view. The paper describes functions and the shape of the spine throughout the whole evolution of vertebrates and vertebrate embryos, from primordial jawless fish to extant animals such as birds and humans, highlighting its fundamental features such as strength, stability, and flexibility, which gives it huge potential as a basis for bio-inspired technologies.

Body stiffness and damping depend sensitively on the timing of muscle activation in lampreys

Unlike most manmade machines, animals move through their world using flexible bodies and appendages, which bend due to internal muscle and body forces, and also due to forces from the environment. Fishes in particular must cope with fluid dynamic forces that not only resist their overall swimming movements but also may have unsteady flow patterns, vortices, and turbulence, many of which occur more rapidly than what the nervous system can process. Has natural selection led to mechanical properties of fish bodies and their component tissues that can respond very quickly to environmental perturbations? Here, we focus on the mechanical properties of isolated muscle tissue and of the entire intact body in the silver lamprey, Ichthyomyzon unicuspis. We developed two modified work loop protocols to determine the effect of small perturbations on the whole body and on isolated segments of muscle as a function of muscle activation and phase within the swimming cycle. First, we examined how the mechanical properties of the whole lamprey body change depending on the timing of muscle activity. Relative to passive muscle, muscle activation can modulate the effective stiffness by about two-fold and modulate the effective damping by >10-fold depending on the activation phase. Next, we performed a standard work loop test on small sections of axial musculature while adding low-amplitude sinusoidal perturbations at specific frequencies. We modeled the data using a new system identification technique based on time-periodic system analysis and harmonic transfer functions (HTFs) and used the resulting models to predict muscle function under novel conditions. We found that the effective stiffness and damping of muscle varies during the swimming cycle, and that the timing of activation can alter both the magnitude and timing of peak stiffness and damping. Moreover, the response of the isolated muscle was highly nonlinear and length dependent, but the body's response was much more linear. We applied the resulting HTFs from our experiments to explore the effect of pairs of antagonistic muscles. The results suggest that when muscles work against each other as antagonists, the combined system has weaker nonlinearities than either muscle segment alone. Together, these results begin to provide an integrative understanding of how activation timing can tune the mechanical response properties of muscles, enabling fish to swim effectively in their complex and unpredictable environment.

Scaling of swimming performance in baleen whales

The scale-dependence of locomotor factors have long been studied in comparative biomechanics, but remain poorly understood for animals at the upper extremes of body size. Rorqual baleen whales include the largest animals, but we lack basic kinematic data about their movements and behavior below the ocean surface. Here we combined morphometrics from aerial drone photogrammetry, whale-borne inertial sensing tag data, and hydrodynamic modeling to study the locomotion of five rorqual species. We quantified changes in tail oscillatory frequency and cruising speed for individual whales spanning a threefold variation in body length, corresponding to an order of magnitude variation in estimated body mass. Our results showed that oscillatory frequency decreases with body length (∝ length−0.53) while cruising speed remains roughly invariant (∝ length0.08) at 2 m s−1. We compared these measured results for oscillatory frequency against simplified models of an oscillating cantilever beam (∝ length−1) and an optimized oscillating Strouhal vortex generator (∝ length−1). The difference between our length-scaling exponent and the simplified models suggests that animals are often swimming non-optimally in order to feed or perform other routine behaviors. Cruising speed aligned more closely with an estimate of the optimal speed required to minimize the energetic cost of swimming (∝ length0.07). Our results are among the first to elucidate the relationships between both oscillatory frequency and cruising speed and body size for free-swimming animals at the largest scale.

Long-axis twisting during locomotion of elongate fishes

Fish live in a complex world and must actively adapt their swimming behavior to a range of environments. Most studies of swimming kinematics focus on two-dimensional properties related to the bending wave that passes from head to tail. However, fish also twist their bodies three dimensionally around their longitudinal axis as the bending wave passes down the body. We measured and characterized this movement, which we call 'wobble', in six species of elongate fishes (Anoplarchus insignis, Xiphister mucosus, Lumpenus sagitta, Pholis laeta, Apodichthys flavidus and Ronquilus jordani) from three different habitats (intertidal, nearshore and subtidal) using custom video analysis software. Wobble and bending are synchronized, with a phase shift between the wobble wave and bending wave. We found that species from the same habitats swim in similar ways, even if they are more closely related to species from different habitats. In nearshore species, the tail wobbles the most but, in subtidal and intertidal species, the head wobbles more than or the same as the tail. We also wanted to understand the relationship between wobble and the passive mechanics of the fish bodies. Therefore, we measured torsional stiffness and modulus along the body and found that modulus increases from head to tail in all six species. As wobble does not correlate with the passive properties of the body, it may play a different role in swimming behavior of fishes from different habitats.

Regional variation in undulatory kinematics of two hammerhead species: the bonnethead (Sphyrna tiburo) and the scalloped hammerhead (Sphyrna lewini)

Hammerhead sharks (Sphyrnidae) exhibit a large amount of morphological variation within the family, making them the focus of many studies. The size of the laterally expanded head, or cephalofoil, is inversely correlated with pectoral fin area. The inverse relationship between cephalofoil and pectoral fin size in this family suggests that they might serve a complementary role in lift generation. The cephalofoil is also hypothesized to increase olfaction, electroreception and vision; however, little is known about how morphological variation impacts post-cranial swimming kinematics. Previous studies demonstrate that the bonnethead and scalloped hammerhead have significantly different yaw amplitude, and we hypothesized that these species utilize varied frequency and amplitude of undulation along the body. We analyzed video of free-swimming sharks to examine kinematics and 2D morphological variables of the bonnethead and scalloped hammerhead. We also examined the second moment of area along the length of the body and over a size range of animals to determine whether there were shape differences along the body of these species and whether those changed over ontogeny. We found that both species swim with the same standardized velocity and Strouhal number, but there was no correlation between two-dimensional morphology and swimming kinematics. However, the bonnethead has a dorso-ventrally compressed anterior trunk and undulates with greater amplitude, whereas the scalloped hammerhead has a laterally compressed anterior trunk and undulates with lower amplitude. We propose that differences in cross-sectional trunk morphology account for interspecific differences in undulatory amplitude. We also found that for both species, undulatory frequency is significantly greater in the anterior body compared with all other body regions. We hypothesize that the bonnethead and scalloped hammerhead swim with a double oscillation system.

The notochord in Atlantic salmon (Salmo salar L.) undergoes profound morphological and mechanical changes during development

We present the development of the notochord of the Atlantic salmon (Salmo salar L.), from early embryo to sexually mature fish. Over the salmon's lifespan, profound morphological changes occur. Cells and gross structures of the notochord reorganize twice. In the embryo, the volume of the notochord is dominated by large, vacuolated chordocytes; each cell can be modeled as a hydrostat organized into a larger cellular-hydrostat network, structurally bound together with desmosomes. After the embryo hatches and grows into a fry, vacuolated chordocytes disappear, replaced by extracellular lacunae. The formation of mineralized, segmental chordacentra stiffens the notochord and creates intervertebral joints, where tissue strain during lateral bending is now focused. As development proceeds towards the parr stage, a process of devacuolization and intracellular filament accumulation occur, forming highly dense, non-vacuolated chordocytes. As extracellular lacunae enlarge, they are enclosed by dense filamentous chordocytes that form transverse intervertebral septa, which are connected to the intervertebral ligaments, and a longitudinal notochordal strand. In the vertebral column of pelagic adults, large vacuolated chordocytes reappear; cells of this secondary population have a volume up to 19 000 times larger than the primary vacuolated chordocytes of the early notochord. In adults the lacunae have diminished in relative size. Hydrostatic pressure within the notochord increases significantly during growth, from 525 Pa in the alevins to 11 500 Pa in adults, at a rate of increase with total body length greater than that expected by static stress similarity. Pressure and morphometric measurements were combined to estimate the stress in the extracellular material of the notochordal sheath and intervertebral ligaments and the flexural stiffness of the axial skeleton. The functional significance of the morphological changes in the axial skeleton is discussed in relation to the different developmental stages and locomotor behavior changes over the lifespan of the fish.

Automatic control: the vertebral column of dogfish sharks behaves as a continuously variable transmission with smoothly shifting functions

During swimming in dogfish sharks, Squalus acanthias, both the intervertebral joints and the vertebral centra undergo significant strain. To investigate this system, unique among vertebrates, we cyclically bent isolated segments of 10 vertebrae and nine joints. For the first time in the biomechanics of fish vertebral columns, we simultaneously characterized non-linear elasticity and viscosity throughout the bending oscillation, extending recently proposed techniques for large-amplitude oscillatory shear (LAOS) characterization to large-amplitude oscillatory bending (LAOB). The vertebral column segments behave as non-linear viscoelastic springs. Elastic properties dominate for all frequencies and curvatures tested, increasing as either variable increases. Non-linearities within a bending cycle are most in evidence at the highest frequency, 2.0 Hz, and curvature, 5 m−1. Viscous bending properties are greatest at low frequencies and high curvatures, with non-linear effects occurring at all frequencies and curvatures. The range of mechanical behaviors includes that of springs and brakes, with smooth transitions between them that allow for continuously variable power transmission by the vertebral column to assist in the mechanics of undulatory propulsion.

Mechanisms of anguilliform locomotion in fishes studied using simple three-dimensional physical models

Physical models enable researchers to systematically examine complex and dynamic mechanisms of underwater locomotion in ways that would be challenging with freely swimming animals. Previous research on undulatory locomotion, for example, has used rectangular flexible panels that are effectively two-dimensional as proxies for the propulsive surfaces of swimming fishes, but these bear little resemblance to the bodies of elongate eel-like swimming animals. In this paper we use a polyurethane rod (round cross-section) and bar (square cross-section) to represent the body of a swimming Pacific hagfish (Eptatretus stoutii). We actuated the rod and bar in both heave and pitch using a mechanical controller to generate a propulsive wave at frequencies between 0.5 and 2.5 Hz. We present data on (1) how kinematic swimming patterns change with driving frequency in these elongate fish-like models, (2) the thrust-generating capability of these simple models, (3) how forces and work done during propulsion compare between cross-sectional shapes, (4) the wake flow patterns in these swimming models using particle image velocimetry. We also contrast kinematic and hydrodynamic patterns produced by bar and rod models to comparable new experimental data on kinematics and wake flow patterns from freely swimming hagfish. Increasing the driving frequency of bar and rod models reduced trailing edge amplitude and wavelength, and above 2 Hz a nodal point appeared in the kinematic wave. Above 1 Hz, both the rod and bar generated net thrust, with the work per cycle reaching a minimum at 1.5 Hz, and the bar always requiring more work per cycle than the rod. Wake flow patterns generated by the swimming rod and bar included clearly visible lateral jets, but not the caudolaterally directed flows seen in the wakes from freely swimming hagfish.

Material Properties of Hagfish Skin, with Insights into Knotting Behaviors

Hagfishes (Myxinidae) often integrate whole-body knotting movements with jawless biting motions when reducing large marine carcasses to ingestible items. Adaptations for these behaviors include complex arrangements of axial muscles and flexible, elongate bodies without vertebrae. Between the axial muscles and the hagfish skin is a large, blood-filled subcutaneous sinus devoid of the intricate, myoseptal tendon networks characteristic of the taut skins of other fishes. We propose that the loose-fitting skin of the hagfish facilitates the formation and manipulation of body knots, even if it is of little functional significance to steady swimming. Hagfish skin is a relatively thick, anisotropic, multilayered composite material comprising a superficial, thin, and slimy epidermis, a middle dermal layer densely packed with fibrous tissues, and a deep subdermal layer comprised of adipose tissue. Hagfish skin is stiffer when pulled longitudinally than circumferentially. Stress-strain data from uniaxial tensile tests show that hagfish skins are comparable in tensile strength and stiffness to the taut skins of elongate fishes that do not engage in knotting behaviors (e.g., sea lamprey and penpoint gunnel). Sheath-core-constructed ropes, which serve as more accurate models for hagfish bodies, demonstrate that loose skin (extra sheathing) enhances flexibility of the body (rope). Along with a loose-fitting skin, the morphologies of hagfish skin parallel those of moray eels, which are also known for generating and manipulating figure-eight-style body knots when struggling with prey.

Effects of non-uniform stiffness on the swimming performance of a passively-flexing, fish-like foil model

Simple mechanical models emulating fish have been used recently to enable targeted study of individual factors contributing to swimming locomotion without the confounding complexity of the whole fish body. Yet, unlike these uniform models, the fish body is notable for its non-uniform material properties. In particular, flexural stiffness decreases along the fish's anterior-posterior axis. To identify the role of non-uniform bending stiffness during fish-like propulsion, we studied four foil model configurations made by adhering layers of plastic sheets to produce discrete regions of high (5.5 × 10(-5) Nm(2)) and low (1.9 × 10(-5) Nm(2)) flexural stiffness of biologically-relevant magnitudes. This resulted in two uniform control foils and two foils with anterior regions of high stiffness and posterior regions of low stiffness. With a mechanical flapping foil controller, we measured forces and torques in three directions and quantified swimming performance under both heaving (no pitch) and constant 0° angle of attack programs. Foils self-propelled at Reynolds number 21 000-115 000 and Strouhal number ∼0.20-0.25, values characteristic of fish locomotion. Although previous models have emphasized uniform distributions and heaving motions, the combination of non-uniform stiffness distributions and 0° angle of attack pitching program was better able to reproduce the kinematics of freely-swimming fish. This combination was likewise crucial in maximizing swimming performance and resulted in high self-propelled speeds at low costs of transport and large thrust coefficients at relatively high efficiency. Because these metrics were not all maximized together, selection of the 'best' stiffness distribution will depend on actuation constraints and performance goals. These improved models enable more detailed, accurate analyses of fish-like swimming.

Evolution of the notochord

A notochord is characteristic of developing chordates (which comprise amphioxus, tunicates and vertebrates), and, more arguably, is also found in some other animals. Although notochords have been well reviewed from a developmental genetic point of view, there has heretofore been no adequate survey of the dozen or so scenarios accounting for their evolutionary origin. Advances in molecular phylogenetics and developmental genetics have, on the one hand, failed to support many of these ideas (although, it is not impossible that some of these rejects may yet, at least in part, return to favor). On the other hand, current molecular approaches have actually stimulated the revival of two of the old proposals: first that the notochord is a novelty that arose in the chordates, and second that it is derived from a homologous structure, the axochord, that was present in annelid-like ancestors. In the long term, choosing whether the notochord is a chordate novelty or a legacy from an ancient annelid (or perhaps an evolutionary derivative from precursors yet to be proposed) will probably require descriptions of gene regulatory networks involved in the development of notochords and notochord-like structures in a wide spectrum of animals. For now, one-way forward will be studies of all aspects of the biology of enteropneust hemichordates, a group widely thought to be the key to understanding the evolutionary origin of the chordates.

Passive mechanical models of fish caudal fins: effects of shape and stiffness on self-propulsion

Fishes are found in a great variety of body forms with tail shapes that vary from forked tuna-like tails to the square-shaped tails found in some deep-bodied species. Hydrodynamic theory suggests that a fish's body and tail shape affects undulatory swimming performance. For example, a narrow caudal peduncle is believed to reduce drag, and a tuna-like tail to increase thrust. Despite the prevalence of these assertions, there is no experimental verification of the hydrodynamic mechanisms that may confer advantages on specific forms. Here, we use a mechanically-actuated flapping foil model to study how two aspects of shape, caudal peduncle depth and presence or absence of a forked caudal fin, may affect different aspects of swimming performance. Four different foil shapes were each made of plastics of three different flexural stiffnesses, permitting us to study how shape might interact with stiffness to produce swimming performance. For each foil, we measured the self-propelling swimming speed. In addition, we measured the forces, torques, cost of transport and power coefficient of each foil swimming at its self-propelling speed. There was no single 'optimal' foil exhibiting the highest performance in all metrics, and for almost all measures of swimming performance, foil shape and flexural stiffness interacted in complicated ways. Particle image velocimetry of several foils suggested that stiffness might affect the relative phasing of the body trailing edge and the caudal fin leading edge, changing the flow incident to the tail, and affecting hydrodynamics of the entire foil. The results of this study of a simplified model of fish body and tail morphology suggest that considerable caution should be used when inferring a swimming performance advantage from body and tail shape alone.

Diverse anguilliform swimming kinematics in Pacific hagfish (Eptatretus stoutii) and Atlantic hagfish (Myxine glutinosa)

Anguilliform mode swimmers pass waves of lateral bending down their elongate bodies to propel forward. Hagfishes (Myxinidae) are classified as anguilliform swimmers, but their unique habits and reduced morphology—including a flexible body lacking a vertebral column—have the potential to translate into unique swimming behaviour within this broad classification. Their roles as active scavengers and hunters can require considerable bouts of swimming, yet quantitative data on hagfish locomotion are limited. Here, we aim to provide a more complete mechanistic understanding of hagfish swimming by quantifying whole-body kinematics of steady swimming in Pacific hagfish (Eptatretus stoutii (Lockington, 1878)) and Atlantic hagfish (Myxine glutinosa L., 1758), species from the two main lineages of Myxinidae. We analyzed high-speed video of hagfishes swimming at voluntary swim speeds and found that both species swim using high-amplitude undulatory waves. Swim speed is generally frequency-modulated, but patterns in wave speed, wavelength, and amplitude along the body and across swim speeds are variable, implying versatile mechanisms for the control of swim speed in these highly flexible fishes. We propose mechanistic explanations for this kinematic variability and compare hagfish with other elongate swimmers, demonstrating that the hagfish’s rich locomotory repertoire adds variety to the already diverse set of locomotory kinematics found in anguilliform swimmers.

Strategies for swimming: explorations of the behaviour of a neuro-musculo-mechanical model of the lamprey

Experiments were performed on a neuro-musculo-mechanical model of a lamprey, to explore the strategies for controlling swimming speed. The muscle component of the model was based on previous experiments on isolated lamprey muscle. The patterns of muscle activation were those found in EMG studies on swimming lampreys. The fluid mechanics were modelled with G.I. Taylor's simplification. Tail beat frequencies of 2-6 sec(-1) were combined with muscle activation strengths of 0.1% to 20% of maximum tetanic isometric strength. The resulting forward swimming speed and changing body shape were recorded. From the changing body shape the speed of the backward-travelling wave of curvature was calculated, as well as the ratio between the speeds of the waves of activation and curvature. For any given activation strength there was a tail beat frequency that gave maximal forward speed. Furthermore, for all the combinations of activation strength and tail beat frequency that gave such maximum swimming speeds, the ratio of the speed of the wave of curvature to the wave of muscle activation was approximately 0.75. This is similar to the ratio found in swimming lampreys.

Undulatory locomotion of flexible foils as biomimetic models for understanding fish propulsion

An undulatory pattern of body bending in which waves pass along the body from head to tail is a major means of creating thrust in many fish species during steady locomotion. Analyses of live fish swimming have provided the foundation of our current understanding of undulatory locomotion, but our inability to experimentally manipulate key variables such as body length, flexural stiffness, and tailbeat frequency in freely-swimming fish has limited our ability to investigate a number of important features of undulatory propulsion. In this paper we use a robotic apparatus to create an undulatory wave in swimming passive flexible foils by creating a heave motion at their leading edge, and compare this motion to body bending patterns of bluegill sunfish (Lepomis macrochirus) and clown knifefish (Notopterus chitala). We found similar swimming speeds, Reynolds and Strouhal numbers, and patterns of curvature and shape between these fish and foils suggesting that passive flexible foils provide a useful model for understanding fish undulatory locomotion. We swam foils with different lengths, stiffnesses, and heave frequencies while measuring forces, torques, and hydrodynamics. From measured forces and torques we calculated thrust and power coefficients, work, and cost of transport for each foil. We found that increasing frequency and stiffness produced faster swimming speeds and more thrust. Increasing length had minimal impact on swimming speed, but had a large impact on Strouhal number, cost of transport, and thrust coefficient. Foils that were both stiff and long had the lowest cost of transport (in mJ m-1 g-1) at low cycle frequencies, and the ability to reach the highest speed at high cycle frequencies.

The role of mechanical resonance in the neural control of swimming in fishes

The bodies of many fishes are flexible, elastic structures; if you bend them, they spring back. Therefore, they should have a resonant frequency: a bending frequency at which the output amplitude is maximized for a particular input. Previous groups have hypothesized that swimming at this resonant frequency could maximize efficiency, and that a neural circuit called the central pattern generator might be able to entrain to a mechanical resonance. However, fishes swim in water, which may potentially damp out many resonant effects. Additionally, their bodies are elongated, which means that bending can occur in complicated ways along the length of the body. We review previous studies of the mechanical properties of fish bodies, and then present new data that demonstrate complex bending properties of elongated fish bodies. Resonant peaks in amplitude exist, but there may be many of them depending on the body wavelength. Additionally, they may not correspond to the maximum swimming speed. Next, we describe experiments using a closed-loop preparation of the lamprey, in which a preparation of the spinal cord is linked to a real-time simulation of the muscle and body properties, allowing us to examine resonance entrainment as we vary the simulated resonant frequency. We find that resonance entrainment does occur, but is rare. Gain had a significant, though weak, effect, and a nonlinear muscle model produced resonance entrainment more often than a linear filter. We speculate that resonance may not be a critical effect for efficient swimming in elongate, anguilliform swimmers, though it may be more important for stiffer carangiform and thunniform fishes.

Understanding undulatory locomotion in fishes using an inertia-compensated flapping foil robotic device

Recent advances in understanding fish locomotion with robotic devices have included the use of flapping foil robots that swim at a constant swimming speed. However, the speed of even steadily swimming live fishes is not constant because the fish center of mass oscillates axially throughout a tail beat cycle. In this paper, we couple a linear motor that produces controlled oscillations in the axial direction to a robotic flapping foil apparatus to model both axial and side to side oscillatory motions used by freely-swimming fishes. This experimental arrangement allows us to compensate for the substantial inertia of the carriage and motors that drive the oscillating foils. We identify a 'critically-oscillated' amplitude of axial motion at which the cyclic oscillations in axial locomotor force are greatly reduced throughout the flapping cycle. We studied the midline kinematics, power consumption and wake flow patterns of non-rigid foils with different lengths and flexural stiffnesses at a variety of axial oscillation amplitudes. We found that 'critically-oscillated' peak-to-peak axial amplitudes on the order of 1.0 mm and at the correct phase are sufficient to mimic center of mass motion, and that such amplitudes are similar to center of mass oscillations recorded for freely-swimming live fishes. Flow visualization revealed differences in wake flows of flexible foils between the 'non-oscillated' and 'critically-oscillated' states. Inertia-compensating methods provide a novel experimental approach for studying aquatic animal swimming, and allow instrumented robotic swimmers to display center of mass oscillations similar to those exhibited by freely-swimming fishes.

Whole-organ cell shape analysis reveals the developmental basis of ascidian notochord taper

Here we use in toto imaging together with computational segmentation and analysis methods to quantify the shape of every cell at multiple stages in the development of a simple organ: the notochord of the ascidian Ciona savignyi. We find that cell shape in the intercalated notochord depends strongly on anterior-posterior (AP) position, with cells in the middle of the notochord consistently wider than cells at the anterior or posterior. This morphological feature of having a tapered notochord is present in many chordates. We find that ascidian notochord taper involves three main mechanisms: Planar Cell Polarity (PCP) pathway-independent sibling cell volume asymmetries that precede notochord cell intercalation; the developmental timing of intercalation, which proceeds from the anterior and posterior towards the middle; and the differential rates of notochord cell narrowing after intercalation. A quantitative model shows how the morphology of an entire developing organ can be controlled by this small set of cellular mechanisms.

Histology and histochemistry of the gekkotan notochord and their bearing on the development of notochordal cartilage

The persistence of the notochord into the skeletally mature life stage is characteristic of gekkotans, but is otherwise of rare occurrence among amniotes. The taxonomic diversity of Gekkota affords the opportunity to investigate the structure and development of this phylogenetically ancestral component of the skeleton, and to determine its basic characteristics. The gekkotan notochord spans almost the entire postcranial long axis and is characterized by a moniliform morphology with regularly alternating zones of chordoid and chondroid tissue. Chordoid tissue persists in the region of intervertebral articulations and occupies the cavitations that lie between the centra of the amphicoelous vertebrae. Chondroid tissue is restricted to zones in which the diameter of the notochord is reduced, corresponding to mid-vertebral locations. In the tail, these zones of chondroid tissue are associated with the autotomic fracture planes. Chondroid tissue first manifests during late embryogenesis, appears to differentiate from pre-existing chordoid tissue, and has the histological and histochemical characteristics of cartilage. Our observations lend support to the hypothesis that cartilage can be derived directly from notochordal tissue, and suggest that the latter may be an evolutionary and developmental precursor to chordate cartilage. The persistence of chordoid tissue in the intervertebral regions of amphicoelous vertebrae is consistent with a suite of paedomorphic traits exhibited by gekkotans and suggests that the typical hydrostatic nature of notochordal tissue may play a role in mechanically governing patterns of displacement between adjacent amphicoelous vertebrae that lack extensive centrum-to-centrum contact.

Go reconfigure: how fish change shape as they swim and evolve

The bodies of fish change shape over propulsive, behavioral, developmental, and evolutionary time scales, a general phenomenon that we call "reconfiguration". Undulatory, postural, and form-reconfiguration can be distinguished, studied independently, and examined in terms of mechanical interactions and evolutionary importance. Using a combination of live, swimming fishes and digital robotic fish that are autonomous and self-propelled, we examined the functional relation between undulatory and postural reconfiguration in forward swimming, backward swimming, and yaw turning. To probe how postural and form reconfiguration interact, the yaw turning of leopard sharks was examined using morphometric and kinematic analyses. To test how undulatory reconfiguration might evolve, the digital robotic fish were subjected to selection for enhanced performance in a simulated ecology in which each individual had to detect and move towards a food source. In addition to the general issue of reconfiguration, these investigations are united by the fact that the dynamics of undulatory and postural reconfigurations are predicted to be determined, in part, by the structural stiffness of the fish's body. Our method defines undulatory reconfiguration as the combined, point-by-point periodic motion of the body, leaving postural reconfiguration as the combined deviations from undulatory reconfiguration. While undulatory reconfiguration appears to be the sole or primary propulsive driver, postural reconfiguration may contribute to propulsion in hagfish and it is correlated with differences in forward, and backward, swimming in lamprey. Form reconfigures over developmental time in leopard sharks in a manner that is consistent with an allometric scaling theory in which structural stiffness of the body is held constant. However, correlation of a form proxy for structural stiffness of the body suggests that body stiffness may scale in order to limit maximum postural reconfiguration during routine yaw turns. When structural stiffness and undulatory frequency are modeled as determining the tail's undulatory wave speed, both factors evolve under selection for enhanced foraging behavior in the digital fish-like robots. The methods used in making these distinctions between kinds of reconfiguration have broad applicability in fish biology, especially for quantifying complex motor behaviors in the wild and for simulating selection on behavior that leads to directional evolution of functional phenotypes.

Biomimetic evolutionary analysis: testing the adaptive value of vertebrate tail stiffness in autonomous swimming robots

For early vertebrates, a long-standing hypothesis is that vertebrae evolved as a locomotor adaptation, stiffening the body axis and enhancing swimming performance. While supported by biomechanical data, this hypothesis has not been tested using an evolutionary approach. We did so by extending biomimetic evolutionary analysis (BEA), which builds physical simulations of extinct systems, to include use of autonomous robots as proxies of early vertebrates competing in a forage navigation task. Modeled after free-swimming larvae of sea squirts (Chordata, Urochordata), three robotic tadpoles (`Tadros'), each with a propulsive tail bearing a biomimetic notochord of variable spring stiffness, k (N m-1), searched for, oriented to, and orbited in two dimensions around a light source. Within each of ten generations, we selected for increased swimming speed, U (m s-1) and decreased time to the light source, t (s),average distance from the source, R (m) and wobble maneuvering, W (rad s-2). In software simulation, we coded two quantitative trait loci (QTL) that determine k: bending modulus, E (Nm-2) and length, L (m). Both QTL were mutated during replication, independently assorted during meiosis and, as haploid gametes, entered into the gene pool in proportion to parental fitness. After random mating created three new diploid genotypes, we fabricated three new offspring tails. In the presence of both selection and chance events(mutation, genetic drift), the phenotypic means of this small population evolved. The classic hypothesis was supported in that k was positively correlated (r2=0.40) with navigational prowess, NP, the dimensionless ratio of U to the product of R, t and W. However, the plausible adaptive scenario, even in this simplified system, is more complex, since the remaining variance in NP was correlated with the residuals of R and U taken with respect to k, suggesting that changes in k alone are insufficient to explain the evolution of NP.

Development of the Escape Response in Teleost Fishes: Do Ontogenetic Changes Enable Improved Performance?

Teleost fishes typically first encounter the environment as free-swimming embryos or larvae. Larvae are morphologically distinct from adults, and major anatomical structures are unformed. Thus, larvae undergo a series of dramatic morphological changes until they reach adult morphology (but are reproductively immature) and are considered juveniles. Free-swimming embryos and larvae are able to perform a C-start, an effective escape response that is used evade predators. However, escape response performance improves during early development: as young fish grow, they swim faster (length-specific maximum velocity increases) and perform the escape more rapidly (time to complete the behavior decreases). These improvements cease when fish become juveniles, although absolute swimming velocity (m s(-1)) continues to increase. We use studies of escape behavior and ontogeny in California halibut (Paralichthys californicus), rainbow trout (Oncorhynchus mykiss), and razorback suckers (Xyrauchen texanus) to test the hypothesis that specific morphological changes improve escape performance. We suggest that formation of the caudal fin improves energy transfer to the water and therefore increases thrust production and swimming velocity. In addition, changes to the axial skeleton during the larval period produce increased axial stiffness, which in turn allows the production of a more rapid and effective escape response. Because escape performance improves as adult morphology develops, fish that enter the environment in an advanced stage of development (i.e., those with direct development) should have a greater ability to evade predators than do fish that enter the environment at an early stage of development (i.e., those with indirect development).