Matthew J. McHenry

The linear relationship between tail-beat frequency and swimming speed in fish, first described by Bainbridge in 1958, has since been confirmed in species as disparate as eels and tuna. Dimensional scaling has explained why linearity should emerge at high Reynolds numbers, but the frequency–speed relationship itself has remained empirical, with no physical framework describing its behavior across swimming regimes, and no account of what sets the two quantities that define it: the distance covered per tail beat and the frequency below which forward motion supposedly ceases. Here, we derive a relationship from a balance of fin thrust, generated by a leading-edge vortex, and drag due to the boundary layer on the body. This framework yields an explicit expression for speed in terms of midline kinematics and body morphology. This formulation shows that the maximum stride length is set by the undulatory wavelength and the tail-beat phase offset, rather than by the conventional scaling metric of body length, and that no minimum frequency is required for forward motion. The model reproduces kinematic measurements from freely swimming glass catfish, published simulations, and Bainbridge’s original data. Without recalibration, it predicts the results of independent simulations spanning wide variations in wavelength, phase offset, and morphology to within ten percent. Linear scaling is thus one asymptotic limit of a more general propulsive relationship linking morphology and body-wave kinematics to swimming speed in fishes and bioinspired vehicles, where the body waveform, rather than the actuation frequency, emerges as the variable that sets performance.

The control and mechanics of locomotion determine the outcome of a variety of predator–prey interactions. The strategies that optimize prey survival have primarily been considered for cases where the prey initiates an escape in response to a predator's approach. However, a diversity of prey survive by avoiding encounters with predators without the aid of evasive maneuvers. To understand locomotor strategies for these conditions, we developed an agent-based numerical model for individual prey damselfish (Chromis viridis) when targeted by a lionfish predator (Pterois volitans). Based on previous experiments, we modeled the predator to track prey with a pure-pursuit strategy and the prey avoided the predator with intermittent bouts of swimming that were biased away from the threat. We found that simulations were statistically similar to experimental measurements in the duration of the interactions. In contrast to distance-optimal evasion models, a sensitivity analysis revealed that prey survived encounters with faster predators most successfully by swimming towards the predator and capitalizing on the relatively slow capacity of the predator to change direction. These findings demonstrate the power of agent-based mathematical modeling to determine the salient features that determine the outcome of coupled predator–prey interactions.

Fish schooling depends on social interactions between animals. Studies on schooling overwhelmingly focus on a single species, which challenges our ability to resolve what features of this collective behavior are universal and how schooling has diversified over the course of evolution. Here, we studied interspecific variation in schooling behavior among five species of neotropical tetras to examine how social networks relate to schooling kinematics among species. We quantified differences in speed, polarization, spacing, mutual information and network properties within, and between, species. Our results demonstrate substantial interspecific variation in schooling behavior, with polarized species exhibiting higher speeds and more cohesive social networks. In contrast, shoaling species showed greater variability in their spatial arrangement and a less cohesive social structure. This comparison demonstrates how closely related species are capable of exhibiting distinct forms of schooling that reflect divergent traits in sensing, motivation and locomotor control.

Fish swim with flexible fins that stand in stark contrast to the rigid propulsors of engineered vehicles. Using numerical simulations of the dynamic of flow-structure interaction (FSI), we have found that dorso-ventral flexibility in caudal fins results in a 70% increase in efficiency of caudal fin swimmers compared to a rigid fin generating the same amount of thrust. By comparing the dynamics of fin deformation and the fluid physics, we find that the greater power requirements of rigid fins can be largely attributed to their propensity to generate high-magnitude lateral forces. In contrast, flexible fins achieve high efficiency local-redirection of force where deformations orient pressure forces on the fin in fore-aft and dorso-ventral directions to reduce the power demand of generating thrust forces. These deformations occur at phases in the tail-beat cycle when large velocities and pressure differentials due to the mechanics of the fin and surrounding flow accentuate these advantages. In this way, the flexibility of a caudal fin offers a simple and elegant solution for efficient locomotion which does not require sensing and computational control that might otherwise be provided by the nervous system of a fish or a computer within a underwater vehicle. Caudal fin deformation driven by flow-structure interactions are therefore important to swimming of caudal fin swimmers and they also offer solutions for efficient propulsion in robotics and other engineering applications.

Schooling fish rely on a social network created through signaling between its members to interact with their environment. Previous studies have established that vision is necessary for schooling and that flow sensing by the lateral line system may aid in a school's cohesion. However, it remains unclear to what extent flow provides a channel of communication between schooling fish. Based on kinematic measurements of the speed and heading of schooling tetras (Petitella rhodostoma), we found that compromising the lateral line by chemical treatment reduced the mutual information between individuals by ∼13%. This relatively small reduction in pairwise communication propagated through schools of varying size to reduce the degree and connectivity of the social network by more than half. Treated schools additionally showed more than twice the spatial heterogeneity of fish with unaltered flow sensing. These effects were much more substantial than the changes that we measured in the nearest-neighbor distance, speed and intermittency of individual fish by compromising flow sensing. Therefore, flow serves as a valuable supplement to visual communication in a manner that is revealed through a school's network properties.

Hydrostatic skeletons, such as an elephant trunk or a squid tentacle, permit the transmission of mechanical work through a soft body. Despite the ubiquity of these structures among animals, we generally do not understand how differences in their morphology affect their ability to transmit muscular work. Therefore, the present study used mathematical modeling, morphometrics, and kinematics to understand the transmission of force and displacement in the tube feet of the juvenile six-rayed star (Leptasterias sp.). An inverse-dynamic analysis revealed that the forces generated by the feet during crawling primarily serve to overcome the submerged weight of the body. These forces were disproportionately generated by the feet at more proximal positions along each ray, which were used more frequently for crawling. Owing to a combination of mechanical advantage and muscle mass, these proximal feet exhibited a greater capacity for force generation than the distal feet. However, the higher displacement advantage of the more elongated distal feet offer a superior ability to extend the feet into the environment. Therefore, the morphology of tube feet demonstrates a gradient in gearing along each ray that compliments their role in behavior.

A hydrostatic skeleton allows a soft body to transmit muscular force via internal pressure. A human's tongue, an octopus' arm and a nematode's body illustrate the pervasive presence of hydrostatic skeletons among animals, which has inspired the design of soft engineered actuators. However, there is a need for a theoretical basis for understanding how hydrostatic skeletons apply mechanical work. We therefore modeled the shape change and mechanics of natural and engineered hydrostatic skeletons to determine their mechanical advantage (MA) and displacement advantage (DA). These models apply to a variety of biological structures, but we explicitly consider the tube feet of a sea star and the body segments of an earthworm, and contrast them with a hydraulic press and a McKibben actuator. A helical winding of stiff, elastic fibers around these soft actuators plays a critical role in their mechanics by maintaining a cylindrical shape, distributing forces throughout the structure and storing elastic energy. In contrast to a single-joint lever system, soft hydrostats exhibit variable gearing with changes in MA generated by deformation in the skeleton. We found that this gearing is affected by the transmission efficiency of mechanical work (MA×DA) or, equivalently, the ratio of output to input work. The transmission efficiency changes with the capacity to store elastic energy within helically wrapped fibers or associated musculature. This modeling offers a conceptual basis for understanding the relationship between the morphology of hydrostatic skeletons and their mechanical performance.

A hydrostatic skeleton allows a soft body to transmit muscular force via internal pressure. A human’s tongue, an octopus’ arm, and a nematode’s body illustrate the pervasive presence of hydrostatic skeletons among animals, which has inspired the design of soft engineered actuators. However, there is a need for a theoretical basis for understanding how hydrostatic skeletons apply mechanical work. We therefore model the shape change and mechanics of natural and engineered hydrostatic skeletons to determine their mechanical advantage (MA) and displacement advantage (DA). These models apply to a variety of biological structures, but we explicitly consider the tube feet of a sea star and the body segments of an earthworm, and contrast them with a hydraulic press and a McKibben actuator. A helical winding of stiff, elastic fibers around these soft actuators plays a critical role in their mechanics by maintaining a cylindrical shape, distributing forces throughout the structure, and storing elastic energy. In contrast to a single-joint lever system, soft hydrostats exhibit variable gearing with changes in MA generated by deformation in the skeleton. We found that this gearing is affected by the transmission efficiency of mechanical work (MA × DA) or, equivalently, the ratio of output to input work), which changes with the capacity to store elastic energy within helically wrapped fibers or associated musculature. This modeling offers a conceptual basis for understanding the relationship between the morphology of hydrostatic skeletons and their mechanical performance.