Trends in Stroke Kinematics, Reynolds Number, and Swimming Mode in Shrimp-Like Organisms.

Metachronal propulsion is commonly seen in organisms with the caridoid facies body plan, i.e. shrimp-like organisms, as they beat their pleopods in an adlocomotory sequence. These organisms exist across length scales ranging several orders of Reynolds number magnitude, from 10 to 104, during locomotion. Further, by altering their stroke kinematics, these organisms achieve three distinct swimming modes. To better understand the relationship between Reynolds number, stroke kinematics, and resulting swimming mode, Euphausia pacifica stroke kinematics were quantified using high-speed digital recordings and compared to the results for the larger E. superba. Euphausia pacifica consistently operate with a greater beat frequency and smaller stroke amplitude than E. superba for each swimming mode, suggesting that length scale may affect the kinematics needed to achieve similar swimming modes. To expand on this observation, these euphausiid data are used in combination with previously-published stroke kinematics from mysids and stomatopods to identify broad trends across swimming mode and length scale in metachrony. Principal component analysis (PCA) reveals trends in stroke kinematics and Reynolds number as well as the variation among taxonomic order. Overall, larger beat frequencies, stroke amplitudes, between-cycle phase lags, and Reynolds numbers are more representative of the fast forward swimming mode compared to the slower hovering mode. Additionally, each species has a unique combination of kinematics that result in metachrony, indicating that there are other factors, perhaps morphological, which affect the overall metachronal characteristics of an organism. Finally, uniform phase lag, in which the timing between power strokes of all pleopods is equal, in 5-paddle systems is achieved at different Reynolds numbers for different swimming modes, highlighting the importance of taking into consideration stroke kinematics, length scale, and the resulting swimming mode.

Dual Phase-Shifted Ipsilateral Metachrony in Americamysis bahia.

Previously documented metachrony in euphausiids focused on one, five-paddle metachronal stroke, where contralateral pleopod pairs on the same abdominal segment beat in tandem with each other, propelling the animal forward. In contrast, the mysid shrimp Americamysis bahia's pleopods on the same abdominal segment beat independently of each other, resulting in two, five-paddle metachronal cycles running ipsilaterally along the length of the body, 180° out of phase. The morphology, kinematics, and nondimensional measurements of efficiency are compared primarily with the one-cycle Euphausia superba to determine how the two-cycle approach alters the design and kinematics of metachrony. Pleopodal swimming in A. bahia results in only fast-forward swimming, with speeds greater than 2 BL/s (body lengths per second), and can reach speeds up to 12 BL/s, through a combination of increasing stroke amplitude, increasing beat frequency, and changing their inter-limb phase lag. Trends with Strouhal number and advance ratio suggest that the kinematics of metachrony in A. bahia are favored to achieve large normalized swimming speeds.

The Three Dimensional Spatial Structure of Antarctic Krill Schools in the Laboratory.

Animal positions within moving groups may reflect multiple motivations including saving energy and sensing neighbors. These motivations have been proposed for schools of Antarctic krill, but little is known about their three-dimensional structure. Stereophotogrammetric images of Antarctic krill schooling in the laboratory are used to determine statistical distributions of swimming speed, nearest neighbor distance, and three-dimensional nearest neighbor positions. The krill schools swim at speeds of two body lengths per second at nearest neighbor distances of one body length and reach similarly high levels of organization as fish schools. The nearest neighbor position distribution is highly anisotropic and shows that Antarctic krill prefer to swim in the propulsion jet of their anterior neighbor. This position promotes communication and coordination among schoolmates via hydrodynamic signals within the pulsed jet created by the metachronal stroking of the neighboring krill's pleopods. The hydrodynamic communication channel therefore plays a large role in structuring the school. Further, Antarctic krill avoid having a nearest neighbor directly overhead, possibly to avoid blockage of overhead light needed for orientation. Other factors, including the elongated body shape of Antarctic krill and potential energy savings, also may help determine the three dimensional spatial structure of tightly packed krill schools.

Olfaction in a viscous environment: the "color" of sexual smells in Temora longicornis.

We investigate chemical aspects of mating in the marine copepod Temora longicornis (Copepoda, Calanoidea). Our emphasis is the female pheromone signaling in form of well-defined trails for males to follow, observed in Doall et al. (Phil Trans R Soc Lond B 353:681-689, 1998). The viscous environment and the properties of the odorants play important roles as the spread of the pheromone trail limits the time during which it is useful for tracing. A key observation from our earlier work is the ability of a searching male to detect the direction of the female and to correct its swimming direction if necessary. We propose a simple mathematical model for the spread of a pheromone from a moving source and carry out numerical simulations of two possible detection mechanisms. We find that a searching agent that is capable to detect a ratio outperforms a searcher that depends on the gradient of a single compound. This suggests that copepod sex pheromones consist of blends of chemical compounds, and that a ratio detection mechanism similar to that in airborne insects is at work.

Intoxicated copepods: ingesting toxic phytoplankton leads to risky behaviour.

Understanding interactions between harmful algal bloom (HAB) species and their grazers is essential for determining mechanisms of bloom proliferation and termination. We exposed the common calanoid copepod, Temora longicornis to the HAB species Alexandrium fundyense and examined effects on copepod survival, ingestion, egg production and swimming behaviour. A. fundyense was readily ingested by T. longicornis and significantly altered copepod swimming behaviour without affecting copepod survival or fitness. A. fundyense caused T. longicornis to increase their swimming speed, and the straightness of their path long after the copepods had been removed from the A. fundyense treatment. Models suggest that these changes could lead to a 25-56% increase in encounter frequency between copepods and their predators. This work highlights the need to determine how ingesting HAB species alters grazer behaviour as this can have significant impacts on the fate of HAB toxins in marine systems.

Underwater flight by the planktonic sea butterfly.

In a remarkable example of convergent evolution, we show that the zooplanktonic sea butterfly Limacina helicina 'flies' underwater in the same way that very small insects fly in the air. Both sea butterflies and flying insects stroke their wings in a characteristic figure-of-eight pattern to produce lift, and both generate extra lift by peeling their wings apart at the beginning of the power stroke (the well-known Weis-Fogh 'clap-and-fling' mechanism). It is highly surprising to find a zooplankter 'mimicking' insect flight as almost all zooplankton swim in this intermediate Reynolds number range (Re=10-100) by using their appendages as paddles rather than wings. The sea butterfly is also unique in that it accomplishes its insect-like figure-of-eight wing stroke by extreme rotation of its body (what we call 'hyper-pitching'), a paradigm that has implications for micro aerial vehicle (MAV) design. No other animal, to our knowledge, pitches to this extent under normal locomotion.

Sensory-Motor Systems of Copepods involved in their Escape from Suction Feeding.

Copepods escape well by detecting minute gradients in the flow field; they react quickly, and swim away strongly. As a key link in the aquatic food web, these small planktonic organisms often encounter suction-feeding fish. Studies have identified certain hydrodynamic features that are created by the approach of this visual predator and the generation of its suction flow for capturing food. Similarly, studies have identified certain hydrodynamic features that evoke the evasive response of copepods. This is a review of the copepod sensory motor system as pertains to understanding their response to suction-feeding fish. Analyses of the reaction time, threshold sensitivity, structure of sensors, and evasive behavior by this key prey of fish can be useful for evaluating the effectiveness of feeding tactics in response to suction flow. To illustrate, we present results comparing a copepod from a fishless lake (Hesperodiaptomus shoshone) to a copepod from a rich fishing ground (Calanus finmarchicus). We designed a flow mimic that produces a realistic mushroom-cap-shaped flow field and realistic accelerations of flow; the copepods treated the mimic as a threat and performed jumps directed up and away from the siphon. Calanus finmarchicus responded at an average threshold strain rate of 18.7/s, escaped at 0.46 m/s, and traveled 5.99 mm, most frequently as a single jump. Hesperodiaptomus shoshone responded at a strain rate of 15.1/s that is not significantly different, escaped more slowly at 0.22 m/s and traveled a shorter distance of 3.01 mm using a series of hops. The high variability noted in the initial angle of the body and the maximum change in body angle suggests that unpredictability in the escape maneuver is another aspect of the tactic of copepods. The speed of the escape by small copepods 2-3 mm long is overwhelmed by the speed of the attack by the much larger, faster fish; if the copepod reacts when it is within the fish's arena of capture (<1.5 mm from mouth), it will be eaten. The copepod, however, has an acutely sensitive array of mechanosensors that perceive the flow field of the fish at distances of 3-6 mm, or outside the fish's range of capture. The copepod also has a rapid and strong locomotory response, thereby increasing the odds that the copepod will survive-but speed is unlikely to be the best tactic for staying alive. Instead, the copepod accelerates from 61.3 to 96.5 m/s(2) or more than 20 times stronger than the lunge of a fish. This collection of capabilities of copepods enables them to remain one of the most abundant multicellular organisms on our planet.

Assessing the in situ fertilization status of two marine copepod species, Temora longicornis and Eurytemora herdmani; how common are unfertilized eggs in nature?

We utilized an egg staining technique to measure the in situ fertilization success of two marine copepod species, Temora longicornis and Eurytemora herdmani from May to October 2008 in coastal Maine and correlated fertilization success with environmental conditions in their habitat. T. longicornis is a free spawning species that releases eggs into the ambient seawater after mating. In contrast, E. herdmani carries eggs in an egg sac until they hatch. The proportion of fertilized eggs within E. herdmani egg sacs was significantly higher than the freely spawned clutches of T. longicornis. This may be a result of the asymmetrical costs associated with carrying vs. spawning unfertilized eggs. T. longicornis frequently laid both fertilized and unfertilized eggs within their clutch. T. longicornis fertilization was negatively associated with chlorophyll concentration and positively associated with population density in their local habitat. The fertilization status of E. herdmani egg sacs was high throughout the season, but the proportion of ovigerous females was negatively associated with an interaction between predators and the proportion of females in the population. This study emphasizes that, in addition to population level processes, community and ecosystem level processes strongly influence the fertilization success and subsequent productivity of copepods.

Using computational and mechanical models to study animal locomotion.

Recent advances in computational methods have made realistic large-scale simulations of animal locomotion possible. This has resulted in numerous mathematical and computational studies of animal movement through fluids and over substrates with the purpose of better understanding organisms' performance and improving the design of vehicles moving through air and water and on land. This work has also motivated the development of improved numerical methods and modeling techniques for animal locomotion that is characterized by the interactions of fluids, substrates, and structures. Despite the large body of recent work in this area, the application of mathematical and numerical methods to improve our understanding of organisms in the context of their environment and physiology has remained relatively unexplored. Nature has evolved a wide variety of fascinating mechanisms of locomotion that exploit the properties of complex materials and fluids, but only recently are the mathematical, computational, and robotic tools available to rigorously compare the relative advantages and disadvantages of different methods of locomotion in variable environments. Similarly, advances in computational physiology have only recently allowed investigators to explore how changes at the molecular, cellular, and tissue levels might lead to changes in performance at the organismal level. In this article, we highlight recent examples of how computational, mathematical, and experimental tools can be combined to ultimately answer the questions posed in one of the grand challenges in organismal biology: "Integrating living and physical systems."

Swimming in the intermediate Reynolds range: kinematics of the pteropod Limacina helicina.

Limacina helicina (1-3 mm) lives in the environment that straddles both inertial and viscous regimes. In this intermediate Reynolds range (10(0)-10(3)), an oscillating appendage may use either drag-based or lift-based locomotion. The swimming motion of L. helicina was investigated to determine its mechanics and whether features of rowing or flying gaits were present. Mean speeds, stroke frequencies, and general paths were revealed from the trajectories of free-swimming individuals. High-speed videography of tethered animals enabled a detailed analysis of stroke parameters involved in L. helicina swimming. During swimming episodes, L. helicina ascend along a sawtooth trajectory in mostly linear and sometimes helical paths. Mean speeds varied from 13 to 44 mm/s for straight ascents and slightly more for helical paths. During swimming, the stroke cycle caused oscillations in body orientation, whereas sinking is characterized by smooth straight descents. Sinking speeds of 5-45 mm s(-1) were observed. Wing-beat frequencies decreased with body size from 4.5 to 9.4 Hz. The wing stroke is a complex, three-dimensional motion that does not perfectly correspond to theoretical concepts of drag-based or lift-based propulsion. Instead, the repertoire of movements indicates that elements of both rowing and flying are incorporated in the swimming of L. helicina with the added element of rotation. Size-dependent differences in stroke mechanics are described. Of particular note is evidence that a clap-and-fling mechanism is applied during the stroke cycle.

The hydrodynamic disturbances of two species of krill: implications for aggregation structure.

Krill aggregations vary in size, krill density and uniformity depending on the species of krill. These aggregations may be structured to allow individuals to sense the hydrodynamic cues of neighboring krill or to avoid the flow fields of neighboring krill, which may increase drag forces on an individual krill. To determine the strength and location of the flow disturbance generated by krill, we used infrared particle image velocimetry measurements to analyze the flow field of free-swimming solitary specimens (Euphausia superba and Euphausia pacifica) and small, coordinated groups of three to six E. superba. Euphausia pacifica individuals possessed shorter body lengths, steeper body orientations relative to horizontal, slower swimming speeds and faster pleopod beat frequencies compared with E. superba. The downward-directed flow produced by E. pacifica has a smaller maximum velocity and smaller horizontal extent of the flow pattern compared with the flow produced by E. superba, which suggests that the flow disturbance is less persistent as a potential hydrodynamic cue for E. pacifica. Time record analysis reveals that the hydrodynamic disturbance is very weak beyond two body lengths for E. pacifica, whereas the hydrodynamic disturbance is observable above background level at four body lengths for E. superba. Because the nearest neighbor separation distance of E. superba within a school is less than two body lengths, hydrodynamic disturbances are a viable cue for intraspecies communication. The orientation of the position of the nearest neighbor is not coincident with the orientation of the flow disturbance, however, which indicates that E. superba are avoiding the region of strongest flow.

Coordination of multiple appendages in drag-based swimming.

Krill are aquatic crustaceans that engage in long distance migrations, either vertically in the water column or horizontally for 10 km (over 200,000 body lengths) per day. Hence efficient locomotory performance is crucial for their survival. We study the swimming kinematics of krill using a combination of experiment and analysis. We quantify the propulsor kinematics for tethered and freely swimming krill in experiments, and find kinematics that are very nearly metachronal. We then formulate a drag coefficient model which compares metachronal, synchronous and intermediate motions for a freely swimming body with two legs. With fixed leg velocity amplitude, metachronal kinematics give the highest average body speed for both linear and quadratic drag laws. The same result holds for five legs with the quadratic drag law. When metachronal kinematics is perturbed towards synchronous kinematics, an analysis shows that the velocity increase on the power stroke is outweighed by the velocity decrease on the recovery stroke. With fixed time-averaged work done by the legs, metachronal kinematics again gives the highest average body speed, although the advantage over synchronous kinematics is reduced.

Quantitative analysis of tethered and free-swimming copepodid flow fields.

We quantified the flow field generated by tethered and free-swimming Euchaeta antarctica using the particle image velocimetry (PIV) technique. The streamlines around the free-swimming specimens were generally parallel to the body axis, whereas the streamlines around all of the tethered copepodids demonstrated increased curvature. Differences noted in the streamline pattern, and hence the vorticity, dissipation rate and strain rate fields, are explained by considering the forces on the free-swimming specimen compared to the tethered specimen. Viscous flow theory demonstrates that the force on the fluid due to the presence of the tether irrevocably modifies the flow field in a manner that is consistent with the measurements. Hence, analysis of the flow field and all associated calculations differ for tethered versus free-swimming conditions. Consideration of the flow field of the free-swimming predatory copepodid shows the intensity of the biologically generated flow and the extent of the mechanoreceptive signal quantified in terms of shear strain rate. The area in the dorso-ventral view surrounded by the 0.5 s(-1) contour of e(xy), which is a likely threshold to induce an escape response, is 11 times the area of the exoskeletal form for the free-swimming case. Thus, mechanoreceptive predators will perceive a more spatially extended signal than the body size.

The prevalence and implications of copepod behavioral responses to oceanographic gradients and biological patchiness.

Several species and developmental stages of calanoid copepods were tested for responses to environmental cues in a laboratory apparatus that mimicked conditions commonly associated with patches of food in the ocean. All species responded to the presence of phytoplankton by feeding. All species responded by increasing proportional residence time in one, but not both, of the treatments defined by gradients of velocity or density. Most species increased swimming speed and frequency of turning in response to the presence of chemical exudates or gradients of velocity. Only one species, Eurytemora affinis, increased proportional time of residence in response to gradients in density of the water. Responses of E. affinis to combined cues did not definitively demonstrate a hierarchical use of different cues as previously observed for Temora longicornis and Acartia tonsa. A simple foraging simulation was developed to assess the applicability in the field of the behavioral results observed in the laboratory. These simulations suggest that observed fine-scale behaviors could lead to copepod aggregations observed in situ. The present study demonstrates that behavioral response to cues associated with fine-scale oceanographic gradients and biological patchiness is functionally important and prevalent among copepods and likely has significant impacts on larger-scale distributional patterns.