A foraging ocean sunfish and the 'nearest neighbor' problem.

A predator that preys on randomly-distributed stationary energetically-equivalent small prey will probably choose its next prey to be the nearest one. But what if no prey is found within the detection range of the predator? It is hypothesized that in this case the predator will move along an arbitrary chosen direction until a prey is detected, and turn towards it. In a stochastic environment this strategy leads to a certain distribution function of distances that the predator moves between consequent prey catches. It is shown that when the detection range of the predator exceeds the average distance between prey, this distribution function becomes the nearest neighbor distribution function, whereas; wherew when the detection range is small as compared with the average distance between prey, it becomes the exponential distribution, as the distribution of distances between neighbors on a line. In the first case, the average distance between catches becomes roughly half the average distance between prey; in the second case, it becomes inversely proportional to the square of the detection range. Ocean sunfish preys on practically stationary jellyfish at depth of more than a hundred meters, in dim light. Plausibly, it can detect jellyfish only at close quarters, and hence its detection range is probably small as compared with the average distance between prey. Analysis of the tracking data from seven animals over a few days yielded many thousands of swimming segments separating consequent prey catches. Indeed, lengths of these segments were shown to have the exponential distribution. This finding not only supports the initial hypothesis of this study, but also reveals the fragility of the energetic balance of this animal. A two-fold decrease in the detection range (e.g. due to a decreased visibility) is expected to increase the average distance it moves between catches four-fold, and hence decrease its specific energy intake (the number of jellyfishes per distance moved) by the same rate.

Sharks surf the slope: Current updrafts reduce energy expenditure for aggregating marine predators.

An animal's energy landscape considers the power requirements associated with residing in or moving through habitats. Within marine environments, these landscapes can be dynamic as water currents will influence animal power requirements and can change rapidly over diel and tidal cycles. In channels and along slopes with strong currents, updraft zones may reduce energy expenditure of negatively buoyant fishes that are also obligate swimmers. Despite marine predators often residing within high-current area, no study has investigated the potential role of the energetic landscape in driving such habitat selectivity. Over 500 grey reef sharks Carcharhinus amblyrhynchos reside in the southern channel of Fakarava Atoll, French Polynesia. We used diver observations, acoustic telemetry and biologging to show that sharks use regions of predicted updrafts and switch their core area of space use based on tidal state (incoming versus outgoing). During incoming tides, sharks form tight groups and display shuttling behaviour (moving to the front of the group and letting the current move them to the back) to maintain themselves in these potential updraft zones. During outgoing tides, group dispersion increases, swimming depths decrease and shuttling behaviours cease. These changes are likely due to shifts in the nature and location of the updraft zones, as well as turbulence during outgoing tides. Using a biomechanical model, we estimate that routine metabolic rates for sharks may be reduced by 10%-15% when in updraft zones. Grey reef sharks save energy using predicted updraft zones in channels and 'surfing the slope'. Analogous to birds using wind-driven updraft zones, negatively buoyant marine animals may use current-induced updraft zones to reduce energy expenditure. Updrafts should be incorporated into dynamic energy landscapes and may partially explain the distribution, behaviour and potentially abundance of marine predators.

The energetics of 'airtime': estimating swim power from breaching behaviour in fishes and cetaceans.

Displays of maximum swimming speeds are rare in the laboratory and the wild, limiting our understanding of the top-end athletic capacities of aquatic vertebrates. However, jumps out of the water - exhibited by a diversity of fish and cetaceans - might sometimes represent a behaviour comprising maximum burst effort. We collected data on such breaching behaviour for 14 fish and cetacean species primarily from online videos, to calculate breaching speed. From newly derived formulae based on the drag coefficient and hydrodynamic efficiency, we also calculated the associated power. The fastest breaching speeds were exhibited by species 2 m in length, peaking at nearly 11 m s-1; as species size decreases below this, the fastest breaches become slower, while species larger than 2 m do not show a systematic pattern. The power associated with the fastest breaches was consistently ∼50 W kg-1 (equivalent to 200 W kg-1 muscle) in species from 20 cm to 2 m in length, suggesting that this value may represent a universal (conservative) upper boundary. And it is similar to the maximum recorded power output per muscle mass recorded in any species of similar size, suggesting that some breaches could indeed be representative of maximum capability.

Latent power of basking sharks revealed by exceptional breaching events.

The fast swimming and associated breaching behaviour of endothermic mackerel sharks is well suited to the capture of agile prey. In contrast, the observed but rarely documented breaching capability of basking sharks is incongruous to their famously languid lifestyle as filter-feeding planktivores. Indeed, by analysing video footage and an animal-instrumented data logger, we found that basking sharks exhibit the same vertical velocity (approx. 5 m s-1) during breach events as the famously powerful predatory great white shark. We estimate that an 8-m, 2700-kg basking shark, recorded breaching at 5 m s-1 and accelerating at 0.4 m s-2, expended mechanical energy at a rate of 5.5 W kg-1; a mass-specific energetic cost comparable to that of the great white shark. The energy cost of such a breach is equivalent to around 1/17th of the daily standard metabolic cost for a basking shark, while the ratio is about half this for a great white shark. While breaches by basking sharks must serve a different function to white shark breaches, their similar breaching speeds questions our perception of the physiology of large filter-feeding fish.

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.

Energetics of the yo-yo dives of predatory sharks.

Sharks zigzag vertically through the water in a series of alternating ascending and descending segments, changing depth by a few tens of meters over a period of a few hundred seconds. This 'yo-yo' like behavior has several characteristic patterns, identifiable by the way the swimming and vertical velocities vary along the dive. We suggest that these patterns represent different optimal strategies minimizing the cost of locomotion under different constraints; moreover, these constraints can be inferred by matching the pattern of a dive with a (standard) optimal swimming strategy for which the constraints are known. We used three sets of constraints and two definitions of the 'cost of locomotion' to analytically generate four standard optimal strategies; we have used high resolution tracking data from four tiger sharks to identify two different yo-yo diving patterns. These patterns seem to match two of the standard strategies: one that maximizes range, given an alternating power supply (e.g., swimming actively on ascents and lazily on descents); and the other that maximizes range, given an alternating vertical velocity (implying an 'intentional' up-and-down motion).

Centre-of-mass and minimal speed limits of the great hammerhead.

The great hammerhead is denser than water, and hence relies on hydrodynamic lift to compensate for its lack of buoyancy, and on hydrodynamic moment to compensate for a possible misalignment between centres of mass and buoyancy. Because hydrodynamic forces scale with the swimming speed squared, whereas buoyancy and gravity are independent of it, there is a critical speed below which the shark cannot generate enough lift to counteract gravity, and there are anterior and posterior centre-of-mass limits beyond which the shark cannot generate enough pitching moment to counteract the buoyancy-gravity couple. The speed and centre-of-mass limits were found from numerous wind-tunnel experiments on a scaled model of the shark. In particular, it was shown that the margin between the anterior and posterior centre-of-mass limits is a few tenths of the product between the length of the shark and the ratio between its weight in and out of water; a diminutive 1% body length. The paper presents the wind-tunnel experiments, and discusses the roles that the cephalofoil and the pectoral and caudal fins play in longitudinal balance of a shark.

Hydrodynamics of a twisting slender swimmer.

Sea snakes propel themselves by lateral deformation waves moving backwards along their bodies faster than they swim. In contrast to typical anguilliform swimmers, however, their swimming is characterized by exaggerated torsional waves that lead the lateral ones. The effect of torsional waves on hydrodynamic forces generated by an anguilliform swimmer is the subject matter of this study. The forces, and the power needed to sustain them, are found analytically using the framework of the slender (elongated) body theory. It is shown that combinations of torsional waves and angle of attack can generate both thrust and lift, whereas combinations of torsional and lateral waves can generate lift of the same magnitude as thrust. Generation of lift comes at a price of increasing tail amplitude, but otherwise carries practically no energetic penalty.

Optimal swimming strategies and behavioral plasticity of oceanic whitetip sharks.

Animal behavior should optimize the difference between the energy they gain from prey and the energy they spend searching for prey. This is all the more critical for predators occupying the pelagic environment, as prey is sparse and patchily distributed. We theoretically derive two canonical swimming strategies for pelagic predators, that maximize their energy surplus while foraging. They predict that while searching, a pelagic predator should maintain small dive angles, swim at speeds near those that minimize the cost of transport, and maintain constant speed throughout the dive. Using biologging sensors, we show that oceanic whitetip shark (Carcharhinus longimanus) behavior matches these predictions. We estimate that daily energy requirements of an adult shark can be met by consuming approximately 1-1.5 kg of prey (1.5% body mass) per day; shark-borne video footage shows a shark encountering potential prey numbers exceeding that amount. Oceanic whitetip sharks showed incredible plasticity in their behavioral strategies, ranging from short low-energy bursts on descents, to high-speed vertical surface breaches from considerable depth. Oceanic whitetips live a life of energy speculation with minimization, very different to those of tunas and billfish.

The undulatory swimming gait of elongated swimmers revisited.

An undulatory swimming gait is characterized by short lateral displacement waves that propagate backwards along the body of the swimmer faster than it swims. Hydrodynamic theory of elongated bodies predicts that if the amplitude of the displacement waves does not increase toward the caudal end, the part of the swimmer posteriad of the dorso-ventrally widest point takes no part in propulsion. It also predicts that if the amplitude does increase, then the hydrodynamic propulsion efficiency suffers. Cusk eels have their widest point located in the anterior half of the body with the bulk of their locomotive muscles located posteriad of it; indeed, they swim so that the amplitude of the propulsion wave increases toward the caudal end. Anguillid eels have their widest point posteriad of the mid-body, and their locomotive muscles are distributed along their entire length-but they swim as cusk eels, using the posterior half only. Apparently, both use hydrodynamically inefficient gaits. The paper questions the definition of propulsion efficiency and shows that biomechanical considerations are more important than hydrodynamic, and that most probably fish adjust their gait to maximize the ratio between the energy made good (the product of thrust and distance) and the chemical energy consumed by the muscles. The role of body shape is discussed.

Hydrodynamics of a Flexible Soft-Rayed Caudal Fin.

The paper addresses hydrodynamic performance of a slender swimmer furnished with a flexible small-aspect-ratio soft-rayed caudal fin. The recoil of the fin is found by solving the coupled hydro-elastic problem, in which the structure of the fin is modeled by a cantilever of variable cross section and the hydrodynamic forces acting on it are modeled using the elongated body theory. It is shown that the recoil has practically no effect on the propulsion efficiency of anguilliform swimmers, but has a profound effect on the efficiency of carangiform swimmers, which can increase almost four-fold between low-speed (low-thrust) cruise and high-speed (high-thrust) burst. Whilst the magnitude of this effect furnishes a plausible argument in favor of burst-and-coast locomotion strategies, it also infers that carangiform swimmers cannot rely on elastic recoil of the caudal fin to be efficient throughout the usable speed range, and must actively flex it at low speeds.

Relations between morphology, buoyancy and energetics of requiem sharks.

Sharks have a distinctive shape that remained practically unchanged through hundreds of millions of years of evolution. Nonetheless, there are variations of this shape that vary between and within species. We attempt to explain these variations by examining the partial derivatives of the cost of transport of a generic shark with respect to buoyancy, span and chord of its pectoral fins, length, girth and body temperature. Our analysis predicts an intricate relation between these parameters, suggesting that ectothermic species residing in cooler temperatures must either have longer pectoral fins and/or be more buoyant in order to maintain swimming performance. It also suggests that, in general, the buoyancy must increase with size, and therefore, there must be ontogenetic changes within a species, with individuals getting more buoyant as they grow. Pelagic species seem to have near optimally sized fins (which minimize the cost of transport), but the majority of reef sharks could have reduced the cost of transport by increasing the size of their fins. The fact that they do not implies negative selection, probably owing to decreased manoeuvrability in confined spaces (e.g. foraging on a reef).

Great hammerhead sharks swim on their side to reduce transport costs.

Animals exhibit various physiological and behavioural strategies for minimizing travel costs. Fins of aquatic animals play key roles in efficient travel and, for sharks, the functions of dorsal and pectoral fins are considered well divided: the former assists propulsion and generates lateral hydrodynamic forces during turns and the latter generates vertical forces that offset sharks' negative buoyancy. Here we show that great hammerhead sharks drastically reconfigure the function of these structures, using an exaggerated dorsal fin to generate lift by swimming rolled on their side. Tagged wild sharks spend up to 90% of time swimming at roll angles between 50° and 75°, and hydrodynamic modelling shows that doing so reduces drag-and in turn, the cost of transport-by around 10% compared with traditional upright swimming. Employment of such a strongly selected feature for such a unique purpose raises interesting questions about evolutionary pathways to hydrodynamic adaptations, and our perception of form and function.