© 2002 by The Society for Integrative and Comparative Biology
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Control of Posture, Depth, and Swimming Trajectories of Fishes1
1 School of Natural Resources and Environment, University of Michigan, Ann Arbor, Michigan 48109-1115
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Perturbations vary in period and amplitude, and responses to unavoidable perturbations depend on response time and scale. Disturbances due to unavoidable perturbations occur in three translational planes and three rotational axes during forwards and backwards swimming. Stability depends on hydrodynamic damping and correcting forces, which may be generated by propulsors (powered) or by control surfaces moving with the body (trimming). Hydrostatic forces affecting body orientation (posture) result in negative metacentric heights amplifying rolling disturbances. The ability to counteract perturbations and correct disturbances is greater for fishes with more slender bodies, which appears to affect habitat choices. Postural control problems are greatest at low speeds, and are avoided by some fishes by sitting on the bottom. In currents, body form and behavior affect lift, drag, weight, and friction and hence speeds to which posture can be controlled. Self-correcting and regulated damping and trimming mechanisms are most important in stabilizing swimming trajectories. Body resistance, fin trajectory, multiple propulsors, and long-based fins damp self-generated locomotor disturbances. Powered control using the tail evolved early in chordates, and is retained by most groups, although fishes, especially acanthopterygians, make greater use of appendages. As with most areas of stability, little is known of control costs. Costs and benefits of low-density inclusions and hydrodynamic mechanisms for depth control vary with habits and habitats. Control may make substantial contributions to energy budgets.
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INTRODUCTION |
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Most studies of fish swimming have focused on how fish achieve high speeds and acceleration rates (Alexander, 1983
). Such questions are enjoying renewed impetus due to new techniques (Lauder and Long, 1996). In addition, research has broadened to encompass the full locomotor repertoire. It has been found that slow swimming and maneuvers dominate time-activity and energy budgets rather than steady high-speed swimming (see Nursall, 1958; Block et al., 1992; Tang et al., 2000). Consequently, adaptations for slow swimming are being recognized that influence behavior, habitat choice and distributions of fishes (Webb, 1997, 2000; Webb and Gerstner, 2000). Among these is the deep-bodied acanthopterygian bauplan which has been postulated to be superior for maneuvering, consistent with its common occurrence in structurally complex habitats (Aleyev, 1977; Webb, 1982). However, cladistic (Rosen, 1982) and experimental studies have not supported this hypothesis (Webb et al., 1996; Schrank and Webb, 1998; Schrank et al., 1999). Instead, many mechanisms are used for maneuvering, assembled in different ways by various species, resulting in organismic convergence in performance (Webb and Gerstner, 2000; Webb, 2000; Webb and Gardiner Fairchild, 2001).
Controlling equilibrium is essential for all activities. Indeed, the low speeds and maneuvers that dominate routine swimming are only possible if fishes have good control over body orientation and swimming trajectories. However, it is well known in engineering practice that high maneuverability is the antithesis of good stability (Marchaj, 1988; Weihs, 1993). Thus maneuvers involve the creation and amplification of disturbances, while stability involves the prevention and correction of disturbances. Have fishes overcome a maneuver-stability tradeoff that constrains human designers? Questions such as this are spurring research on the role of stability in the lives of fishes, as well as a hunt for design inspirations for engineered underwater vehicles. This paper seeks to summarize stability issues for fishes and the level of our current understanding.
Perturbations
Webster's Dictionary defines a stable system as one "designed so as to resist forces tending to cause motion or change of motion" and "designed so as to develop forces that restore the original condition when disturbed from a condition of equilibrium or steady motion" (Anon, 1971). A force tending to cause a change of state is a perturbation. These forces may be produced by the fish to initiate maneuvers, or they may be unwanted when they must be stabilized.
Period and amplitude
Unwanted perturbations vary in period and amplitude over a continuum of values. Small period (high frequency), small amplitude perturbations cancel out over the body and are probably ignored (Pavlov et al., 1988; Shtaf et al., 1983). Indeed this assumption is made when inducing microturbulent flow to create a rectilinear flow profile in flumes (Bell and Terhune, 1970). Above some (unknown) threshold, larger period and amplitude perturbations require correction. At yet longer periods, perturbations are rare enough that they are probably unpredictable. Such long-period perturbations are often associated with large amplitudes that can have high impacts on fitness. For example, freshets can displace individuals, wash out nests, and locally eliminate populations (Poff and Ward, 1989). However the importance of a given perturbation depends on the physiological status of a fish, especially factors affecting response latency, and scale.
First, some control systems are self-correcting, when stability needs only "unconscious attention" (Weihs, 1993). However, biological materials are typically deformable (Wainwright et al., 1976), a feature more likely to amplify than correct destabilizations. As a result, most stabilization involves some active intervention. Numerous systems are involved, including sensory, neural, and musculo-skeletal components, which eventually determine the attitude, shape, and motions of the body and appendages. As a result, responses have latencies, which also are affected by factors such as temperature, physiological stress, and previous experience (Wright, 2000). If the response latency between sensing a perturbation and the motor response approaches half that of the perturbation period, attempted corrective actions may amplify the disturbing force in a phenomenon called "pilot-induced error." The response latencies of control systems are not known, but probably fall between giant-fiber mediated fast starts with latencies of 10 to 15 msec to predator responses to maneuvers by prey averaging about 100 msec (Eaton and Hackett, 1984; Webb, 1984a). Then, induced error might add to perturbations with frequencies from 5 to 50 Hz.
Second, scale is important in terms of perturbation amplitude. For example, a shark in a surge flow over a reef could experience a destabilizing torque from sheer forces along its length. Smaller fishes tend to move with surges. For these fishes, a surge is dynamically similar to still water.
Self-generated and external perturbations
Two other characteristics of perturbations are important from a biological perspective. They may be self-generated or arise externally to a fish (Webb, 2000). Self-generated perturbations arise from hydrostatic forces on the body, gill ventilation, and locomotor movements. Self-generated perturbations may be used for maneuvering, but others will be unwanted. For example, the head and fins ahead of the center of mass, like canards, can create large torques, when small errors in their attitudes can rapidly destabilize swimming trajectories (Weihs 1989, 1993).
External perturbations are usually associated with turbulence, which may be biotic or abiotic in origin. Biotic perturbations undoubtedly occur in schools. For example, fishes in a polarized school swim and maneuver as a unit (Nursall, 1973) so that each member will experience predictable perturbations from the wakes shed by neighbors (Weihs, 1973a). During flash expansion and in non-polarized shoals, wakes will vary unexpectedly as neighbors change direction. Biotic external perturbations are probably common occurrences in agnostic interactions, and might even be used for signaling.
Abiotic perturbations arise from flow at interfaces and over topographic features. The major factors affecting period and amplitude of perturbations at the air/water interface are wind strength, fetch, water depth, and bottom topography, which together determine wave height and current. Flow rates over the substratum and around submerged objects depend on wind strength and fetch, and in streams, on stream gradients and hydraulic input (Gordon et al., 1994). The sizes and shapes of in-stream structures (substratum, ripples, rocks, boulders, macrophytes, rootwads etc.) and flow rates (wind, tide, and gradient) determine if and when flow separates. Many in-water structures built by humans are sources of turbulent perturbations that can have negative effects on fish populations, for example water intakes, propeller wash, and ships in narrow channels.
Disturbances
An intentional self-generated change of state is a maneuver. An unwanted change of state caused by a perturbation is a disturbance. Disturbances may occur in three translational planes and three rotational axes. Translations occur as heave (a vertical displacement), slip (lateral), and surge (antero-posterior). Rotations are pitch (head up/down rotation about the lateral axis), yaw (left/right rotation about dorso-ventral axis), and roll (rotation about longitudinal axis).
Disturbances can occur while a fish is at rest, when swimming forwards and backwards, and during maneuvers while moving in either direction. In addition, disturbances may occur simultaneously in one or more translocational planes and rotational axes. Rotational disturbances appear to present larger control problems than displacements. Motions following a rotational perturbation are more likely to amplify (Kermack, 1943; Hoerner, 1975; Cruickshank and Skews, 1980; Bunker and Machin, 1991) and can quickly lead to "tumbling." In contrast, a translation in the swimming path is rarely amplified, and correction is rarely pressing.
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Avoiding perturbations
Energy is expended in responding to any change in a regulated system (Weihs, 1993
) and some disturbances may exceed stabilization capabilities. Therefore, one option is to avoid perturbations. This may the basis for many species of coral fishes refuging in reef structures at the height of the ebb and flood, and swimming and feeding around slack tides (Hobson, 1974; Keenleyside, 1979; Sale, 1991). Flow variations are often associated with diurnal, lunar, seasonal, and decadal cycles, and avoidance of habitats with a high probability of large amplitude perturbations is often integral to life history patterns. For example, fall migrations to flow refuges are common to avoid effects of winter storms (Diana, 1995).
Damping and correction
Many perturbations are unavoidable. The first step towards stability is damping perturbations. More effective control systems minimize the rate of growth of a disturbance (Weihs, 1993). The second step in control is correction of a disturbance, an active intervention to restore initial conditions.
Damping and correcting forces may be hydrostatic or hydrodynamic. Hydrostatic forces alone may stabilize a fish on the substratum but are destabilizing for fishes in the water column. Hydrodynamic forces improve stability on current-swept substrata and are often the sole means for counteracting perturbations and correcting disturbances for fishes in the water column.
All hydrodynamic correction forces arise from flow over the body and appendages (Hoerner, 1965, 1975). These are created in two different ways. First, propulsors are actively moved independent of the motion of the body to generate powered correction forces (Webb, 2000), either directly, like bow thrusters, or by orienting the normal force, like outboard motors, to provide both thrust and powered correction components. Second, flow is induced over control surfaces which, like boat keels, move with the body. Varying the attitude of the body and appendages can modulate the resultant force vectors. I will define these as trimming forces, synonymous with, but more descriptive, than the term "passive forces" (Webb, 2000).
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STABILIZATION OF POSTURE, DEPTH, AND TRAJECTORY |
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There are three categories of locomotor-related control problems: control of body orientation (posture), depth in the water column ("negative altitude"), and trajectory. Stabilizing posture provides a stable base for sensory systems and minimizes energy costs by orientating the body to minimize drag (Weihs, 1993
). Control of depth is important for many activities, such as exploiting productive surface waters, vertical migrations for feeding and predator avoidance, and in benthic living (Diana, 1995; Allan, 1995; Matthews, 1998). Stable sensory bases and energy minimization also require stabilization of swimming trajectories during translocation and hovering at zero speed, in addition to controlling posture and depth.
Posture
Posture is usually considered to be horizontal with the dorsal side upper most. In practice, posture varies greatly during routine activity, for example with feeding, breeding, gill irrigation at the air/water surface, and camouflage (Matthews, 1998).
There has been considerable discussion on postural stability for fishes in the water column, when hydrostatic forces are usually destabilizing. Animal tissues and inclusions vary in density and distribution through the body. The centers of mass and buoyancy typically occur at different locations, with the center of buoyancy below the center of mass (Aleyev, 1977; Alexander, 1990; Webb and Weihs, 1994). As a result, torques typical amplify rotational disturbances for which effects on rolling are most important (Weihs, 1993; Webb and Weihs, 1994; Ullén et al., 1995). Reduction of rolling torques is believed to have played a role in the evolution of gas inclusions in fishes (Lagler et al., 1977). Osteichthyan gas inclusions were originally ventral to the gut, as found in some modern lungfishes and in tetrapods. In bony fishes, the lung migrated early to a more dorsal position to become the swimbladder of modern representatives (Lauder and Liem, 1983). These evolutionary changes undoubtedly reduced rolling instability, but there are no data on the magnitude of rolling torques or the magnitude of necessary correction forces.
A major factor determining the magnitude of rolling moments following a disturbance is the vertical distance between the centers of mass and buoyancy. This distance is called the metacentric height (Marchaj, 1988), which takes negative values when the center of mass is above the center of buoyancy, as is common among fishes. The larger the negative metacentric height, the greater is the amplification of a rolling disturbance. I explored the effect of swimbladder location on metacentric height for homogenous fishes (density 1.05 g·cm–3) of constant volume and constant thickness, but differing in fineness ratio (total length/body depth). Locations of the centers of mass and of buoyancy were determined from the weight and buoyancy torques of longitudinal strips (see Srygley and Dudley, 1993) with the swimbladder at various locations from fully dorsal to fully ventral. The latter might have been approached in early bony fishes. Thus a theoretical range of metacentric heights was obtained (Fig. 1). To make comparisons with data in other situations, I chose to determine a non-dimensional (normalized) metacentric height by dividing values by volume1/3.
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The theoretical range of metacentric heights for actual tissue distributions was also determined using measurements of the dorso-ventral mass and density distribution for bluegill, Lepomis macrochirus. Mass and weight in freshwater were measured for longitudinal 1 cm thick slices, from which volume was calculated (Fig. 2). The metacentric height range was virtually identical with that of the homogenous model of the same fineness ratio (Fig. 1).
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In addition, the ability of fishes to correct rolling disturbances was measured using neutrally buoyant combinations of dorsal weights and ventral floats to increase torques on three teleost species (L. Eidietis, T. L. Forrester, and P. W. Webb, unpublished data). Decreases in the metacentric height (which is negative),
MH, were determined for rolls exceeding 90° for 80 sec in a 90 sec period (i.e., fishes were no longer able to correct for roll disturbances). For fusiform creek chub (Semotilus atromaculatus), MH exceeded the theoretical range for the homogenous models indicating a surplus capability for stabilizing rolling perturbations (Fig. 1). In contrast, MH for the deeper-bodied bluegill was smaller than the theoretical range, suggesting stabilizing posture for rolling is a larger problem for more gibbose fishes. In terms of the evolution of gas inclusions, these data show that the range of metacentric heights (Fig. 1), and hence the destabilizing potential for ventral gas inclusion locations is smaller in fish with large fineness ratio, typical of early fishes. In addition, the point at which fish can no longer correct for disturbances is similar to minimum metacentric heights that appear possible in early fishes. Thus the advantages of reducing metacentric height by a more dorsal location of gas inclusions are supported, and it is not surprising to find modern fish have very small metacentric heights (Webb and Weihs, 1994).
In addition, differences among species in their ability to stabilize posture in rolling appear to have ecological implications. Chub are stream fish, and like other soft-rayed species, are common in more turbulent riffles and races to which they are displaced by predation risk (Schlosser, 1982; Gordon et al., 1989; Webb and Gardiner Fairchild, 2001). In lakes, similar cyprinids are abundant in the shallow littoral zone, even during storm conditions (P. W. Webb, unpublished observations). In contrast, bluegill are common in ponds (Scott and Crossman, 1973), and like many other percomorphs, tend to move offshore and avoid storm-induced turbulent situations (Helfman, 1981). Bass are found in both lotic and lentic habitats, but in slow-moving water in streams (Probst et al., 1984).
Because hydrostatic forces are usually destabilizing, and are, at best neutrally stable (Webb and Weihs, 1994), dynamic forces are essential to stabilize posture. However, the importance of trimming versus powered control depends on speed. Trimming systems are lift-based. Therefore forces are proportional to speed2 and hence trimming becomes less effective at low speeds. Some fishes seek to compensate at low swimming speeds by extending their fins to increase area (Bone et al., 1995) and hence the trimming force. However, trimming becomes costly at low speeds because lift generation incurs induced drag, proportional to speed–2.
Thus as speed decreases, trimming forces must be supplemented and eventually replaced with powered forces. In hovering at zero speed in the water column, fishes use powered forces alone for stability (Blake, 1979). It is becoming apparent that as speed decreases, fishes swim at increasing angles to the flow (tilt) (He and Wardle, 1986; Webb, 1993; Ferry and Lauder, 1996; Wilga and Lauder, 1999, 2000). This will increase resistance and hence tail-beat frequencies at low swimming speed, and is considered to provide additional force to correct disturbances. Thus tilting is seen as a behavioral response to improve stability at low speeds at which stability is most difficult (Webb, 1993, 1997; Wilga and Lauder, 2000). Nevertheless, tilting will presumably increase resistance and energy costs at low speeds.
Because of the difficulties and costs of stabilizing swimming trajectories at low speeds, some fishes may avoid swimming at low speeds (Arnold et al., 1991; Webb et al., 1996) by sitting on the substratum, providing they have some negative buoyancy. Posture control then involves static forces due to fish weight in water and friction with the substratum. The body is stable, typically supported with the center of mass within a triangle of one posterior ground contact at the ventral surface or anal fin, and two anterior contacts usually provided by the pectoral fins spread as props.
Holding position is more difficult in a flow when the primary stability problem becomes avoiding displacement downstream. A lift force due to flow over the body opposes weight and decreases the normal force. This in turn reduces the friction force, which opposes drag (Arnold and Weihs, 1978). The interaction of these forces determines the speed at which a fish is displaced. Drag and lift are reduced by appropriate postures (Arnold and Weihs, 1978; Gerstner, 1998; Gerstner and Webb, 1998) while powered forces may be generated to offset the remaining lift or drag, and increase friction (Webb, 1989; Webb et al., 1996).
Depth
The density of tissues exceeds that of seawater and freshwater. Therefore, fish tissues tend to sink, a heaving disturbance. Numerous reviews have documented the use of low-density inclusions (gas, lipids, and in seawater only, ion replacement) to attain neutral buoyancy to damp sinking disturbances (Alexander, 1990). Inclusions are not self-correcting following a depth change. Each also has advantages and disadvantages. Gas gives the highest hydrostatic lift per unit volume, but depth disturbances are amplified because volume is proportional to pressure, and hence depth. Amplification is avoided by lipid inclusions, but for a given hydrostatic lift, lipids require more volume, resulting in higher form drag.
Because inclusions are not self-correcting, depth control ultimately depends on dynamic forces. Body shape and posture, paired fin attitude, and caudal peduncle shape all generate trimming forces (Harris, 1937a, b; Fierstine and Walters, 1968; Lauder, 1989; Bunker and Machin, 1991; Ferry and Lauder, 1996; Fish and Shannahan, 2000). Those produced by the hypochordal lobe of the caudal fin of selachians and early bony fishes have been studied in detail (Alexander, 1965, 1990). These trimming forces probably supplemented and eventually replaced those created by modulating tail orientation and/or the stiffness of the fin lobes (Ferry and Lauder, 1996). The role of powered forces for depth control has not been studied, with the exception of body and tail undulations with tilt to swim "up-hill" by negatively buoyant fishes (Weihs, 1980; He and Wardle, 1986; Wilga and Lauder, 1999, 2000).
Swimming trajectories
Swimming trajectories may be perturbed by self-generated and external, predictable and unpredictable, perturbations. Thrust production is the largest source of self-generated perturbations. Propulsion is based on oscillations ranging from propulsive elements within a fin to whole fin motions. Momentum transfer is not perfectly matched with resistance and a component of the normal force causes recoil (Lighthill, 1977). These forces from propulsors reverse every half-beat, reducing the growth and correcting recoil disturbances, but damping is still desirable if only to minimize energy losses.
The body/caudal fin used to swim at the highest speeds generates the largest recoil. Damping may be especially important because tail-beat frequencies create perturbations (equal to twice the tail beat frequency) with frequencies of the order of 20 to 30 Hz, in the range where pilot-induced error seems possible. The resistance of the anterior body serves as a trimming force to damp recoil (Lighthill, 1977; Webb, 1992). The effectiveness of damping for carangiform swimmers can be evaluated in terms of the ratio, 
, between the tail side force, F, and the lateral resistance (Lighthill, 1977), resulting in:
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where k = constant, 
= radian tail-beat frequency, 
= density of water, Bmax = maximum depth of the body and median fins, and L = length. Bmax is especially important in maximizing lateral resistance of the anterior body, and can be increased by the dorsal fin when cruising or sprinting.
Appendage-based propulsion may also self-generate perturbations that must be damped and corrected. Oscillatory pectoral fins are commonly used for propulsion at lower speeds. When used alone, these fins often cause surge in the same way as other single oscillatory propulsors (DuBois and Ogilvy, 1978; Drucker and Jensen, 1996), plus vertical forces causing heaving disturbance. Such heaving recoil disturbance may be minimized by the figure-8 trajectory of propulsive elements (Gibb et al., 1994). Thus acceleration reaction, a resistance force parallel to the direction of motion, is high at the start of the stroke (in forward swimming) when an element moves caudally in line with the drag of the body. Similarly, lift components, which are normal to the direction of motion, tend to be maximized at mid-stroke when an element moves across the incident flow.
Other recoil components cancel each other out when fins work in pairs, for example, the lateral (slip) component of the normal force on each pectoral fin (Drucker, 2000). Some more derived teleosts go further and use multiple short-based median and paired fins phased to negate recoil in all directions, resulting in remarkably smooth swimming trajectories (Gordon et al., 1989, 2001). A different approach to minimize recoil is found among fishes with long-based pectoral, dorsal, and anal fins, as in rays and many actinopterygians. Stabilization is presumably the result of canceling positive and negative side forces from numerous propulsive elements along the fin. Stabilizing kinematics and fin morphological features have not been studied.
In addition to these self-generated locomotor perturbations, swimming fishes experience external perturbations. Therefore, overall trajectories must be stabilized. The median and paired fins of fishes are typically arranged in the longitudinal and transverse planes, where they may permit both self-correction and controlled trimming. In concert with compressed or depressed body shapes, the fins damp and self-correct yawing, pitching, heaving, and slip disturbances. In addition, the paired fins damp roll and can be self-correcting for rolling disturbances at a positive dihedral angle (von Mises, 1945; Aleyev, 1977; Weihs, 1993). Paired fins can reduce slip when used in banked turns (Weihs, 1981). Paired fins are furled whenever possible to minimize drag, but can be deployed into the transverse plane for controlled braking (Aleyev, 1977; Webb, 1984b; Webb and Gardiner Fairchild, 2001).
In addition to trimming systems, the ability to generate powered stabilizing forces, initially with the tail, arose among chordates. The ability to orient the thrust from the tail both for maneuvers and stability remains important in all groups of aquatic vertebrates. The evolution of bony skeletons made it possible to supporting relatively large forces on thin fins, capable of changing their area and shape. This greatly expands the capabilities for producing hydrodynamic stabilizing forces (Lauder and Liem, 1983; Webb, 1982; Fricke and Hissman, 1992). The median and paired fins became the dominant stabilizers in bony fishes. Indeed, there is an evolutionary trend to restrict the caudal part of the body to lateral movements. The degrees of freedom of the caudal peduncle and the tail are reduced by the extension of the neural and hemal spines to span much of the body depth, and the fusion and/or expansion of these elements in the caudal fin skeleton (Lauder and Leim, 1983). Unlike many morphological innovations, these changes do not appear to be irreversible. Elongate burrowing forms recur in major actinopterygian radiations (Lauder and Liem, 1983; Webb, 1982). Such fishes must stabilize trajectories when swimming using only caudal propulsors with many degrees of freedom (Ullén et al., 1995).
Among more derived actinopterygians, there may be increased reliance on powered forces for stabilizing swimming activities, including hovering and station holding. The deep body of many acanthopterygian teleosts places the lateral pectoral fins, antero-ventral pelvic fins, and the relatively large dorsal and anal fins close to orthogonal planes through the center of mass, and relatively close to the center of mass. This appears to be associated with a larger role of hovering, slow swimming, and braking in the voluntary behavior of such fishes (Keenleyside, 1979). Furthermore, largemouth bass attempt to stabilize the body while holding station in the wake of cylinders using powered correction movements of the median and paired fins, while the soft-rayed cyprinid, chub, appear to rely more on trimming forces (Webb, 1998). Additional study is essential, because it is far from clear why powered control should be more prevalent in spiny-rayed fishes. Are thin fins too deformable to hold the shape necessary to be effective trimming surfaces? Or does harnessing powered control increase behavioral options and expand habitat options? Does hovering promote saltatory searches? Does hovering provide a more stable sensory base to detect small but abundant prey items? Does hovering provide more control for suction feeding? Is a better aiming platform provided to augment suction feeding in a strike?
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Stabilizing posture, depth, and swimming trajectories carries costs. Most studies have focussed on the relative costs of different mechanisms for depth control (Alexander, 1990
). Gas inclusions are least stable in shallow water, but require substantial energy to remain inflated at the high pressures of deep water. They also increase overall volume, and hence form drag when swimming. Lipids are not depth sensitive, but larger volumes are needed to achieve neutral buoyancy, and hence carry a larger form drag penalty than that associated with gas inclusions. All fishes also use dynamic stabilizing mechanisms, which incur high induced drag at low speeds. At high swimming speeds, the energy lost in overcoming induced drag is lower than for form drag. A broad-brush approach (Alexander, 1990) shows that fishes tend to rely more on gas inclusions at low speeds in constant-depth shallow-water habitats. Hydrodynamic forces are prevalent among fishes that tend to swim at higher speeds. Lipids are common in slow, deep-water fishes and those making long daily vertical migrations.
Negatively buoyant fishes rely on dynamic forces for depth control. Such fishes can offset costs of transport using burst-and-glide behavior when swimming in the water column (Weihs, 1973b; Blake, 2000) and ground effect near the substratum (Blake, 1979; Lighthill, 1979).
The greatest challenges for stability occur at low speeds (Marchaj, 1988; Webb, 1993, 1997), and stabilization costs may play a large role in energy expenditures. Fin extension and tilting increase beating rates, probably better matching forces produced to perturbations, but must increase swimming costs. Thus stability problems may explain the common, but otherwise anomalous observation that the relationship between tail-beat frequency and swimming speed does not pass through the origin, but intersect the zero-speed axis at a finite tail-beat frequency (e.g., Bainbridge, 1958). Similarly, stabilizing the body at low speeds may explain the variable and often elevated metabolic rates and contribute to high costs of transport at lower speeds (Webb, 1997). In addition, some studies suggest resistance of a swimming fish is of the same order as that for an equivalent rigid body (Drucker and Lauder, 1999). Costs of transport suggest very much more mechanical energy is dissipated than expected on this basis (see Videler, 1993), again especially at low speeds. Perhaps stability costs contribute to the difference.
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ACKNOWLEDGMENTS |
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Some of the ideas described above are supported by observations made in projects largely involving undergraduates. I thank Erin Babich, Jenny Birnbaum, Amy Boetcher, Laura Eidietis, Tommy Feisel, Tracy Forrester, Toni Gardiner Fairchild, Ryan Jonna, Julia Lippert, and Jennifer Metz. Laura Eidietis and Tracy Forrester made valuable comments on a manuscript draft. Support was proved by NSF grants No. IBN 9507197 and IBN 9973942, the University of Michigan Undergraduate Research Opportunities Program, and the University of Michigan Biological Station Research Experience for Undergraduates.
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FOOTNOTES |
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1 From the Symposium Stability and Maneuverability presented at the Annual Meeting of the Society for Integrative and Comparative Biology, 3–7 January 2001, at Chicago, Illinois.
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References |
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