Synodontis nigriventris is a surface-feeding facultative air-breather that swims inverted with its zoological ventral side towards the water surface. Their near-surface drag is about double the deeply submerged drag (due to wave drag) and roughly twice the sum of frictional and pressure drags. For streamlined technical bodies, values of wave drag augmentation near the surface may be five times the deeply submerged values. However, the depth dependence of drag is similar for fish and streamlined technical bodies, with augmentation vanishing at about 3 body diameters below the surface. Draginverted' is approximately 15% less than that dorsal side up' near the surface. Consistent with this, at any given velocity, tailbeat frequency is lower and stride length higher for inverted swimming in surface proximity(P<0.05). Deeply submerged, there are no significant differences in drag and kinematics between postures (P>0.05). At the critical Froude number of 0.45, speeds in surface proximity correspond to prolonged swimming that ends in fatigue. To exceed these speeds, the fish must swim deeply submerged and this behaviour is observed. Inverted swimming facilitates efficient air breathing. Drag dorsal side up during aquatic surface respiration is 1.5 times the value for the inverted posture. Fast-starts are rectilinear, directly away from the stimulus. Average and maximum velocity and acceleration decrease in surface proximity (P<0.05) and are higher inverted (maximum acceleration: 20–30 m s–2; P<0.05) and comparable to locomotor generalists (e.g. trout). Mechanical energy losses due to wave generation are about 20% for inverted and 40% for dorsal side up, and lower than for trout fast-starting in shallow water (70% losses); bottom effects and large amplitude C-starts (c.f. relatively low amplitude rectilinear motions in S. nigriventris)enhance resistance in trout. S. nigriventris probably evolved from a diurnal or crepuscular Chiloglanis-like' benthic ancestor. Nocturnality and reverse countershading likely co-evolved with the inverted habit. Presumably, the increased energy cost of surface swimming is offset by exploiting the air–water interface for food and/or air breathing.

The position of the main trunk nerve is a fundamental anatomical difference distinguishing protostomes (nerve cord ventral) from deuterostomes (nerve cord dorsal). However, some animals swim on their backs, reversing the direction of facing of the main trunk nerve. The brine and fairy shrimps (Artemiidae,Branchiopoda), back swimmers (Corixidae, Hemiptera), and the nudibranch Glaucus atlanticus (Glaucidae, Gastropoda), swim with their true'zoological ventral side facing dorsal (upward). The upside down catfish Synodontis nigriventris (Mochokidae, Siluriformes) swims with its true zoological dorsal side facing ventral (downward). In addition to these obligate examples of inverted swimming, there are some arguable facultative cases (e.g. backstroke swimming in humans, sea otters when feeding on shellfish).

In addition to frictional and pressure drag, fish swimming close to the air–water interface experience wave drag. The surface wave pattern generated is similar to that of a ship hull (Kelvin wave system)(Lighthill, 1978). The wave pattern is generated by two moving pressure points, one downstream and one upstream of the fish. These two wave systems interfere, depending on speed relative to length. At certain speeds, transverse wave crests from the bow may combine with those from the stern producing a large wave train and, at others,the bow and stern wave systems cancel producing a small wave train. A second component of the wake consists of a diverging wave system with two wake lines forming the arms of a V' (Crawford,1984). A distinction can be made between the effects of wave drag on forms that are at or near the air–water interface in shallow versus deep water. The former case is more complex because of surface wave and bottom interactions.

Few studies address drag at the air–water interface and its biological significance. Swimming at or near the air–water interface in deep water (i.e. no bottom interactions), dispersive surface waves increase the propulsive energy required relative to deeply submerged swimming(Hertel, 1966; Hertel, 1969; Prange and Schmidt-Nielson,1970; Williams and Kooyman,1985; Stephenson et al.,1989; Webb et al.,1991). The drag of a rigid body moving at constant velocity just below the surface is about five times that when deeply submerged(Hertel, 1966). It has been suggested that porpoising in penguins, sea lions, seals and dolphins is a locomotor strategy to avoid the high energy cost of moving near the air–water interface (Au and Weihs,1980; Blake, 1983). A pioneering study showed that for rainbow trout Oncorhynchus mykissfast-starting in shallow water, distance traveled after a given time is a positive function of water depth (Webb et al., 1991). Near the surface, up to about 70% of the mechanical work generated by the fish is lost. This has critical fitness significance, as many piscivorous fish force their prey into shallow water(Schlosser, 1987).

The genus Synodontis (Mochokidae, Siluriformes) is a monophyletic group (Mo, 1991) containing 118 species, endemic to tropical African lakes and streams(Teugels, 2003). Many mochokids are benthic, nocturnal or crepuscular and feed on small invertebrates and algae (Lowe-McConnell,1975; Burgess,1989). Some Synodontis species occasionally swim inverted, e.g. S. contractus, S. multipunctatus, S. membranaceus(Burgess, 1989); S. nigriventris habitually does so for feeding (surface zooplankton, insect larvae and fine detritus) and aquatic surface respiration (ASR) in hypoxic waters (Chapman et al.,1994).

The hydrodynamics of inverted swimming in S. nigriventris has not been previously studied. However, the associated adaptation of reverse countershading is well understood. The upward facing ventral surface is darker at night and contains large numbers of melanophores at high density. Pigment migration into the ventral melanophores is mediated by a higher concentration of norepinephrine than that for the dorsal melanophores(Kasukawa et al., 1986; Nagaishi et al., 1989). Melanosome dispersion (agented by adenosine, beta-agonists and alpha-MSH) in the ventral skin is more effective than that in the dorsal skin(Nagaishi and Oshima, 1989). The mechanisms for regulating pigment migration in the melanophores maintain the relative darkness of the ventral skin, effectively concealing the fish when viewed from above at night (Nagaishi and Oshima, 1989).

Several authors have suggested that inverted swimming in S. nigriventris facilitates feeding at the surface and on the underside of leaves (Bishai and Abu Gideiri,1963; Lowe-McConnell,1975; Gosse, 1986; Burgess, 1989). ASR under hypoxic conditions was compared in S. nigriventris and S. afrofisheri (which does not swim inverted)(Chapman et al., 1994). S. afrofisheri air breathes by positioning its body nearly perpendicular to the water surface and is highly active. In contrast, S. nigriventrisswims inverted at a shallow angle and swims slowly, implying a higher respiratory efficiency (Chapman et al.,1994). Functional interpretations of inverted swimming in the context of feeding and respiration are not mutually exclusive and metabolic energy must be expended to overcome the hydrodynamic resistance of motion in both activities.

Constant speed (steady) and fast-start (unsteady) swimming near the air–water interface has relevance to many fish in the context of feeding, e.g. exploiting allochthonous sources(Moyle and Cech, 1988), ASR(Chapman et al., 1994) and predator–prey interactions (Webb et al., 1991). S. nigriventris is vulnerable to piscivorous and aerial predators and acceleration (fast-starts) allows for escape from both. It was hypothesized that: (1) based on known values for technical streamlined bodies (Hertel,1966; Hertel,1969), the drag at the air–water interface would be ×5 higher than that when deeply submerged due to energy losses from wave generation; (2) Drag would be posture dependent (dorsal side up versus inverted) because the fish approximate 3-D technical bodies of triangular section where drag is posture dependent [drag coefficients of 0.7 and 1.1 for apex and base directed into the flow, respectively(McCormick, 1979)]; (3)increased drag in surface proximity relative to that when deeply submerged for both postures would require increased thrust and be reflected in increased tailbeat frequency at any given velocity; (4) fast-start swimming performance at the air–water interface would be inferior to that when deeply submerged (lower velocity and acceleration and higher propulsive energy cost due to energy losses from wave generation) and also posture dependent.

### Fish

Five dead specimens of Synodontis nigriventris David (preserved in a 10% formalin solution; Department of Zoology, University of British Columbia Fish Museum) were measured for total body length (TL), mass(Mb), maximum body depth (d) and width(w) (to ±0.05 cm; caliper, 30 cm, Helios, Mebtechnik, Germany)and weighed (to ±0.1 g; Scout-Pro, Ohaus, Pinebrook, NJ, USA). Frontally projected area (Ap) was determined by digitizing tracings (Hipad digitizer, Houston Instruments, Houston, TX, USA) of head on'photographs (Table 1).

Table 1.

Morphometric data for Synodontis nigriventris

FishMaximum width (w; cm)Maximum body depth (d; cm)Body length (TL; cm)Mass (Mb; g)Projected frontal area (Ap; cm2)
Live
1 1.5 3.0 7.0 4.6 2.0
2 1.2 2.0 5.0 2.1 1.1
3 1.3 2.5 6.5 3.3 1.5
4 1.5 2.7 6.4 4.3 1.9
5 1.2 1.4 4.9 1.9 1.0
Mean 1.3±0.1 2.3±0.6 6.0±0.8 3.2±1.0 1.5±0.4
1 2.7 2.5 13.0 23.0 5.6
2 3.4 4.1 17.0 54.0 11.0
3 2.4 3.3 12.0 20.0 6.2
4 1.9 2.5 10.0 10.0 3.7
5 3.2 3.8 15.0 50.0 9.6
Mean 2.7±0.5 3.2±0.7 13.4±2.4 31.4±0.0174 7.2±2.7
FishMaximum width (w; cm)Maximum body depth (d; cm)Body length (TL; cm)Mass (Mb; g)Projected frontal area (Ap; cm2)
Live
1 1.5 3.0 7.0 4.6 2.0
2 1.2 2.0 5.0 2.1 1.1
3 1.3 2.5 6.5 3.3 1.5
4 1.5 2.7 6.4 4.3 1.9
5 1.2 1.4 4.9 1.9 1.0
Mean 1.3±0.1 2.3±0.6 6.0±0.8 3.2±1.0 1.5±0.4
1 2.7 2.5 13.0 23.0 5.6
2 3.4 4.1 17.0 54.0 11.0
3 2.4 3.3 12.0 20.0 6.2
4 1.9 2.5 10.0 10.0 3.7
5 3.2 3.8 15.0 50.0 9.6
Mean 2.7±0.5 3.2±0.7 13.4±2.4 31.4±0.0174 7.2±2.7

Mean values are ± 2 s.e.m.

Live fish were terminated with MS 222 shortly before being weighed in air and water (to ±0.001 g; Mettler PK300 scale, Columbus, OH, USA, with manufacturer's suspension apparatus) and fish density (ρf) was calculated from:ρ f=(WaWo)–1Waρw, where Wa, Wo and ρw were weight in air, weight in water and water density, respectively. The centre of mass of each fish was determined by suspending the fish from the mouth and marking the vertical line of gravity, then repeating this procedure with suspension from the cloaca. The centre of mass was the point where the two lines crossed.

### Swimming behaviour

Five live fish were obtained from a commercial dealer and held in a 0.60 m×0.30 m×0.40 m aquarium with gravel bottom, natural plants and ironwood branches, containing fresh, aerated, dechlorinated water and 0.3%salt at 25±1°C. The natural routine swimming behaviour of the fish during the day (illumination by fluorescent lights for 12 h from above) and night (12 h illumination by infrared lamp, PAR38, Jieneng Special Lighting and Equipment Ltd., Xiaogan, Hubei, China) was recorded on video tape (Sony DCR-TRV280, IR enabled; Hi8 120 min tapes) for 2 h in daylight and under infrared light for a period of 5 days. It was unlikely that the fish could detect the infrared light (Lythgoe,1988).

### Drag

Measurements were made in a Perspex™ re-circulating flow tank (1.84 m×0.52 m×0.22 m). A 0.5 h.p. electric motor (1 h.p.=745.7 W)rotated a propeller (0.16 m diameter) to produce flow. Water velocities were measured using a current meter (12.400±0.005 m s–1; A. OTT Kempton TYP., Bayern, Germany) placed 1.25 m down from a flow-rectifying grid (0.21 m×0.20 m) made of straws (0.5 cm diameter) located just in front of the propeller. Wall interference effects were assumed to be small as the ratio of the width of the flow tank and fish was of the order of 10.

Drag (D) was measured with a force transducer (an aluminum spar of length 10 cm, width 0.7 cm and thickness 0.1 cm, respectively) attached to a strain gauge bridge, connected to a digital electronics board, calibrated with weights (1.5 g; Sto-A-Weigh, Pinebrook, NJ, USA) and mounted on a vertical adjustable stand, allowing the spar to be placed accurately at different depths below the water surface.

Force transducer accuracy and precision were determined by comparing the measured drag coefficient[CD=2DwApV2)–1]of a three-dimensional Perspex™ plate (0.6 cm×2.5 cm×2.5 cm)oriented normal to the flow with established technical values (1.17)(Hoerner, 1965) at Reynolds numbers 103–104(Re=LVv–1, where V andν were water velocity and kinematic viscosity of water, respectively). The drag on the spar was subtracted from that of the plate and spar together to give the drag of the plate. The measured average normal drag coefficient based on ten repeated measurements was 1.22±0.04 (mean ± 2 s.e.m.) for Re≈1.8×103, which was close to that expected.

Fish were attached to the spar in a natural position oriented with their long axis parallel to the flow with median fins (two dorsal and two pelvic)and caudal fin deployed and kept rigid by a thin steel wire to minimize body and/or fin flutter (Webb,1975). Total drag was determined by subtracting the drag of the fish and spar together from that of the spar. Drag measurements (dorsal side up and inverted) were made at four water velocities (0.38 m s–1, 0.47 m s–1, 0.55 m s–1, 0.63 m s–1) and at fifteen different depths dw [depth from the bottom of the flume to the point of maximum body depth at 0.31±0.01 l (mean ± 2 s.e.m.);0.032–0.102 m]. The drag coefficients[CD=2DwApV2)-1]for all fish and water velocities (N=20) were calculated using the drag force measurements and morphological data(Table 1). Drag at body orientation angles (angle of the long axis of the body to the horizontal) of 20°, 45° and 90° was calculated for both postures at and near the surface (0.032 m, 0.037 m and 0.042 m).

Fish were filmed using a high-speed camera (125 Hz; Troubleshooter, Model TS500MS, Fastec Imaging, San Diego, CA, USA; Berkey Coloran Halide 650 W bulb)in a tank (2.45 m×1.22 m×0.47 m; depth≈0.3 m;25±1°C) as if from above with a mirror angled at 45°. A removable rigid plastic grid (1.65 cm2 cells) was fitted tightly to the interior walls of the tank. For each of five fish, 5 measurements were made for each posture at water depths

$$d_{\mathrm{w}}^{{^\prime}}$$
[depth set by removable plastic grid (1.65 cm2 cells) fitted tightly to the interior walls of the aquarium to the point of maximum body depth at 0.30±0.01 TL; 0.025 m, 0.04 m and 0.09 m] corresponding to submersion depth indices (h/d, where h was the distance from the water surface to the centre line of the fish and d was maximum body depth)of 0.6, 1.2 and 3.4, respectively (Table 2). Feeding ceased the day before experiments to ensure a post-absorptive digestive state (Beamish,1964). Fish outlines from video segments (7–10 tailbeats with no wall interference) were analyzed by ImageJ (National Institutes of Health; http://rsb.info.nih.gov/ij). Tailbeat frequency (number of tailbeat cycles, tail movement from one side of the body to the other and back again, divided by duration), amplitude(distance between the lateral most positions of the tip of the tail during one complete tailbeat cycle), stride length (speed divided by tailbeat frequency),propulsive wave velocity (time between peaks in lateral displacement between the tip of the snout and tail divided by body length) and propulsive wavelength were determined.

Table 2.

Kinematic parameters of steady swimming for the upside down catfish in the dorsal side up and inverted posture at water depths of 0.025 m, 0.04 m and 0.09 m

Water depth (m)
0.025 (h/d=0.6)0.04 (h/d=1.2)0.09 (h/d=3.4)
Velocity (m s-1DSU 0.0781±0.0130a 0.145±0.022b 0.167±0.026b
0.0104±0.014c 0.198±0.026d 0.280±0.036e
Tailbeat frequency (Hz) DSU 4.4±0.6a 5.6±0.5b 5.7±0.7b
4.6±0.3a 6.6±0.6c 7.9±0.8d
Tail amplitude (m) DSU 0.011±0.001a 0.013±0.001b 0.014±0.001c
0.012±0.001a 0.014±0.001b 0.016±0.001d
Wavelength (m) DSU 0.063±0.001a 0.064±0.001a 0.064±0.001a
0.068±±0.001b 0.069±0.001b 0.069±±0.001b
Stride length (m) DSU 0.018±0.002a 0.025±0.002b 0.029±0.002c
0.022±0.002d 0.029±0.003e 0.035±0.002f
Water depth (m)
0.025 (h/d=0.6)0.04 (h/d=1.2)0.09 (h/d=3.4)
Velocity (m s-1DSU 0.0781±0.0130a 0.145±0.022b 0.167±0.026b
0.0104±0.014c 0.198±0.026d 0.280±0.036e
Tailbeat frequency (Hz) DSU 4.4±0.6a 5.6±0.5b 5.7±0.7b
4.6±0.3a 6.6±0.6c 7.9±0.8d
Tail amplitude (m) DSU 0.011±0.001a 0.013±0.001b 0.014±0.001c
0.012±0.001a 0.014±0.001b 0.016±0.001d
Wavelength (m) DSU 0.063±0.001a 0.064±0.001a 0.064±0.001a
0.068±±0.001b 0.069±0.001b 0.069±±0.001b
Stride length (m) DSU 0.018±0.002a 0.025±0.002b 0.029±0.002c
0.022±0.002d 0.029±0.003e 0.035±0.002f

DSU, dorsal side up; I, inverted posture; h/d, submersion depth index

Values are means ± 2 s.e.m.; N=25 in all cases

Significant effects for water depth were compared using ANOVA with post hoc Student-Newman-Keuls test and posture effects were compared using independent sample t-test. Significant differences(P<0.05) are indicated by different superscript letters

Wavelength was determined following published methods(Dewar and Graham, 1994; Donley and Dickson, 2000). The time between peaks in lateral displacement at the tip of the snout and tail was measured (lateral displacement over time for the wave of undulation to pass). This was repeated 10 times for each steady swimming bout to obtain a mean progression time. Propulsive wave velocity was obtained by dividing the body length by the mean progression time, and was divided by tailbeat frequency to give propulsive wavelength.

### Fast-starts

An aquarium (0.35 m×0.21 m×0.24 m) covered with black paper was filmed from above (250 Hz). Fish were acclimatized for 1 week to experimental lighting conditions (Halide 650 W bulb). Feeding ceased the day before experimentation. Fast-starts were induced by striking the side of the aquarium with a plastic bulb attached to a 1 m pole and filmed at three water depths

$$d_{\mathrm{w}}^{{^\prime}}$$
[depth set by the removable plastic grid (1.65 cm2 cells) fitted tightly to the interior walls of the aquarium to the point of maximum body depth at 0.30±0.01 TL; 0.025 m, 0.04 m and 0.09 m]. One measurement (distance/time) for each posture was made per fish (N=5) per day (total of 30 measurements) to allow for recovery. Video sequences of the escape responses(against the rigid plastic grid) were analyzed using ImageJ(http://rsb.info.nih.gov/ij/). Following Webb (Webb, 1976),we digitized the centre of mass of the stretched straight fish as a reference point (located by measuring the length of the midline from the tip of the rostrum to 0.37±0.01 TL) and the tip of the rostrum. Duration,distance, average velocity and acceleration, maximum velocity and acceleration were measured for the centre of mass. The velocity and acceleration data were derived from the raw distance-time data by using a five-point smoothing regression (Lanczos,1956).

Energy loss from wave generation near the surface was estimated following Webb et al. (Webb et al.,1991), by comparing the average work performed by a control fish'(Wc; i.e. a fish swimming deeply submerged, in this case 0.09 m): Wc=2m(1+α)s2ct–2, where α was the longitudinal added mass coefficient (representing the mass of water entrained by the accelerating fish), sc was distance traveled by the control fish and t was time. It was assumed that the fish perform the same amount of work regardless of water depth. This assumption is reasonable for a fast-start response where it can be presumed that performance is maximized (Webb et al., 1991). The longitudinal added mass coefficient is small (order of 0.2)(Webb, 1982) and was assumed to be unaffected near the surface. The proportion of energy lost(Wd) relative to the control fish was Wd=1–(s2ts–2c), where st was distance traveled by fish in shallow water (i.e. water depths of 0.025 m and 0.04 m).

### Statistics

The effect of body posture on drag, steady swimming bouts and fast-start performance was compared by employing independent two-sample t-tests. The effects of body orientation angles on drag and the effects of water depth on fast-start performance (duration, distance, average velocity, maximum velocity, average acceleration, maximum acceleration) were determined by ANOVA(SPSS 13.0 for Windows). The locations of any significant differences were obtained from the Student–Newman–Keuls test. Drag coefficients and densities for S. nigriventris and other catfishes were compared using one-sample t-tests (Zar,1999). The null hypothesis was rejected at P=0.05 in all cases.

Fish were nocturnal and characterized by six distinct swimming behaviours:(1) inverted swimming at a body orientation angle of about 20° at the air–water interface when surface feeding; (2) rapid constant speed inverted swimming in the water column from one refuge to another, initiated from a standing start with velocity rising rapidly to a constant value, ending abruptly with pectoral fin braking; (3) steady combing' of the bottom dorsal side up, associated with feeding on detritus; (4) brief transitional movements off the bottom into the water column involving bodily rotation to the inverted position; (5) localized movements employing undulatory median and paired fin propulsion when repositioning and feeding on algae on the underside of submerged wood and plant leaves; and (6) spontaneous rectilinear fast-starts when withdrawing from aggressive encounters. A representative time/frequency distribution of swimming activities (based on 2 h under infrared light per day for a 5-day period) was: 5%, 65%, 10%, 1%, 15% and 4% for behaviours (1), (2),(3), (4), (5) and (6), respectively. During daylight, the fish attached to wood and the underside of leaves (95%) with occasional localized repositioning movements.

Drag was proportional to velocity squared in all cases(D=aV2+bV+c, where a, b and c were depth-dependent constants; r2>0.95) and decreased with water depth for both body postures (Fig. 1). Inverted drag was about 15% less than that for dorsal side up in surface proximity (N=120; P<0.05) with no postural effects when deeply submerged (N=120; P>0.05). The drag augmentation factor (δ, defined as the ratio of drag in surface proximity to that deeply submerged) was a function of the submersion depth index (h/d; Fig. 2)and maximal (δ≈2.0) for both postures near the water surface(h/d≈0.5), vanishing (i.e. δ=1.0) when h/d≈2.7(depth≈9 cm).

Drag increased with increasing body orientation angle (0°, 20°,45° and 90°; N=60; P<0.05) for both postures at water velocities of 0.38–0.63 m s–1(Fig. 3). Inverted drag for body orientation angles of 20°, 45° and 90° was significantly lower than that dorsal side up (N=360; P<0.05).

Fig. 1.

Drag versus water depth for S. nigriventris (inset) for dorsal side up (A) and inverted posture (B) for water velocities of 0.38 m s–1 (open squares), 0.47 m s–1 (open diamonds), 0.55 m s–1 (open triangles) and 0.63 m s–1 (crosses). Values are means ± 2 s.e.m. For N values, see text. In all cases, r2>0.9, P<0.05.

Fig. 1.

Drag versus water depth for S. nigriventris (inset) for dorsal side up (A) and inverted posture (B) for water velocities of 0.38 m s–1 (open squares), 0.47 m s–1 (open diamonds), 0.55 m s–1 (open triangles) and 0.63 m s–1 (crosses). Values are means ± 2 s.e.m. For N values, see text. In all cases, r2>0.9, P<0.05.

Fig. 2.

Drag augmentation factor (δ) versus submersion depth index(h/d, where h is the distance from the water surface to the center line of the fish and d is maximum body depth) in the dorsal side up (A) and inverted (B) posture.

Fig. 2.

Drag augmentation factor (δ) versus submersion depth index(h/d, where h is the distance from the water surface to the center line of the fish and d is maximum body depth) in the dorsal side up (A) and inverted (B) posture.

Fig. 3.

Total near-surface drag (sum of wave, pressure and friction drags)measurements for body orientation angles of 0°, 20°, 45° and 90° for dorsal side up (A) and inverted (B) posture for water velocities of 0.38 m s–1 (open squares), 0.47 m s–1(open diamonds), 0.55 m s–1 (open triangles) and 0.63 m s–1 (crosses). Values are means ± 2 s.e.m. For N values, see text. In all cases, r2>0.9, P<0.05.

Fig. 3.

Total near-surface drag (sum of wave, pressure and friction drags)measurements for body orientation angles of 0°, 20°, 45° and 90° for dorsal side up (A) and inverted (B) posture for water velocities of 0.38 m s–1 (open squares), 0.47 m s–1(open diamonds), 0.55 m s–1 (open triangles) and 0.63 m s–1 (crosses). Values are means ± 2 s.e.m. For N values, see text. In all cases, r2>0.9, P<0.05.

Fig. 4.

Centrelines (tip of the snout and centre of mass indicated by arrowheads and filled red circles, respectively) for S. nigriventris during a steady swimming bout (A) and fast-start (B) in the inverted posture at intervals of 0.032 s and 0.004 s, respectively, indicated by successive numbers.

Fig. 4.

Centrelines (tip of the snout and centre of mass indicated by arrowheads and filled red circles, respectively) for S. nigriventris during a steady swimming bout (A) and fast-start (B) in the inverted posture at intervals of 0.032 s and 0.004 s, respectively, indicated by successive numbers.

During steady swimming bouts, fish swam in the carangiform mode(Fig. 4A). Tailbeat frequency,stride length and amplitude increased with velocity(Fig. 5). Fish swam at lower velocities at lower water depth (N=75; P<0.05; Table 2). The slopes of tailbeat frequency and stride length versus velocity increased and decreased significantly with decreasing water depth (N=75; P<0.05) and slopes were higher and lower dorsal side up relative to inverted near the surface, respectively (N=50; P<0.05). Wavelength was velocity and depth independent(N=75; P>0.05).

Fig. 5.

Tailbeat frequency, amplitude and stride length versus water velocity during steady swimming bouts for S. nigriventris: dorsal side up near the surface (0.025 m, h/d=0.6, green open circles; 0.04 m, h/d=1.2, red open circles) and deeply submerged (0.09 m, h/d=3.4, blue open circles); inverted near the surface (0.025 m, h/d=0.6, green open squares; 0.04 m, h/d=1.2, red open squares) and deeply submerged (0.09 m, h/d=3.4, blue open squares). Regressions for tailbeat frequency and stride length are represented by solid(dorsal side up) and dotted lines (inverted posture). Since ANCOVA shows no significant effects of water depth on amplitude (P>0.05), the data were pooled to generate an overall regression (black solid line). In all cases, r2>0.4, P<0.05.

Fig. 5.

Tailbeat frequency, amplitude and stride length versus water velocity during steady swimming bouts for S. nigriventris: dorsal side up near the surface (0.025 m, h/d=0.6, green open circles; 0.04 m, h/d=1.2, red open circles) and deeply submerged (0.09 m, h/d=3.4, blue open circles); inverted near the surface (0.025 m, h/d=0.6, green open squares; 0.04 m, h/d=1.2, red open squares) and deeply submerged (0.09 m, h/d=3.4, blue open squares). Regressions for tailbeat frequency and stride length are represented by solid(dorsal side up) and dotted lines (inverted posture). Since ANCOVA shows no significant effects of water depth on amplitude (P>0.05), the data were pooled to generate an overall regression (black solid line). In all cases, r2>0.4, P<0.05.

All fast-starts were rectilinear (Fig. 4B) and away from the stimulus. Average and maximum velocity and acceleration decreased in surface proximity (N=15; P<0.05; Table 3). Performance levels in all categories were higher for the inverted posture(N=10; P<0.05). The proportion of energy lost in wave generation increased with decreasing h/d for both postures(Fig. 6). At submersion depth indices of 0.6 and 1.2, the losses inverted were about half of that for dorsal side up.

Table 3.

Fast-start performance of S. nigriventris in the dorsal side up (DSU)and inverted posture (I) at water depths of 0.025 m, 0.04 m and 0.09 m

Water depth (m)
0.025 (h/d=0.6)0.04 (h/d=1.2)0.09 (h/d=3.4)
Duration (s) DSU 0.098±0.022a 0.089±0.005a 0.083±0.012a
0.054±0.003b 0.047±0.015b 0.046±0.008b
Distance (m) DSU 0.031±0.010a 0.036±0.010a 0.037±0.010a
0.035±0.004a 0.036±0.006a 0.036±0.006a
Velocity (m s-1
Average DSU 0.33±0.07a 0.40±0.02a,b 0.46±0.07b
0.66±0.06c 0.83±0.09d 0.87±0.13d
Maximum DSU 0.62±0.07a 0.70±0.11a,b 0.84±0.09b
1.24±0.10c 1.30±0.14c 1.47±0.07d
Acceleration (m s-2
Average DSU 3.38±0.77a 4.55±0.28b 5.47±0.85b
12.37±0.78c 17.49±2.03d 18.76±2.78d
Maximum DSU 6.50±1.34a 7.92±1.22a,b 9.54±1.61b
23.13±1.90c 27.54±3.00c,d 31.47±6.80d
Water depth (m)
0.025 (h/d=0.6)0.04 (h/d=1.2)0.09 (h/d=3.4)
Duration (s) DSU 0.098±0.022a 0.089±0.005a 0.083±0.012a
0.054±0.003b 0.047±0.015b 0.046±0.008b
Distance (m) DSU 0.031±0.010a 0.036±0.010a 0.037±0.010a
0.035±0.004a 0.036±0.006a 0.036±0.006a
Velocity (m s-1
Average DSU 0.33±0.07a 0.40±0.02a,b 0.46±0.07b
0.66±0.06c 0.83±0.09d 0.87±0.13d
Maximum DSU 0.62±0.07a 0.70±0.11a,b 0.84±0.09b
1.24±0.10c 1.30±0.14c 1.47±0.07d
Acceleration (m s-2
Average DSU 3.38±0.77a 4.55±0.28b 5.47±0.85b
12.37±0.78c 17.49±2.03d 18.76±2.78d
Maximum DSU 6.50±1.34a 7.92±1.22a,b 9.54±1.61b
23.13±1.90c 27.54±3.00c,d 31.47±6.80d

DSU, dorsal side up; I, inverted posture; h/d, submersion depth index

Values are mean ± 2 s.e.m.; N=5 for all cases

Significant effects for water depths were compared using ANOVA with post-hoc Student-Newman-Keuls test and posture effects were compared using independent sample t-test. Significant differences are indicated by different superscripts (P<0.05)

### Drag

Hypothesis 1, that drag near the surface would be ×5 greater than that deeply submerged, is rejected (Fig. 1). For S. nigriventris of 40 000<Re>91 000, δ≈2.0 for h/d=0.5 and h/d≈2.7 for δ=1 (Fig. 2). The drag of streamlined technical bodies in surface proximity(Hoerner, 1965; Hertel, 1966; Hertel, 1969) has been employed to assess the swimming energetics of marine mammals(Au and Weihs, 1980; Blake, 1983; Blake, 2000) and penguins(Blake and Smith, 1988). At Reynolds numbers >106, drag augmentation due to gravitational waves on a streamlined body close to the surface (h/d≈0.5) may be×5 that when deeply submerged and vanishes for h/d>3 (i.e.δ=1) (Hertel, 1966; Hertel, 1969). Whilst the general trend of depth dependence of δ on h/d of S. nigriventris is similar to that for streamlined technical bodies, the magnitude of drag augmentation is about a half(Fig. 2).

Fig. 6.

Proportion of fast-start mechanical energy lost versus submersion depth index (h/d) for S. nigriventris, dorsal side up (blue)and inverted posture (red), and rainbow trout (black)(Webb et al., 1991) after 20 ms (open circles), 40 ms (filled circles), 60 ms (filled triangles), 80 ms(open squares) and 100 ms (filled squares).

Fig. 6.

Proportion of fast-start mechanical energy lost versus submersion depth index (h/d) for S. nigriventris, dorsal side up (blue)and inverted posture (red), and rainbow trout (black)(Webb et al., 1991) after 20 ms (open circles), 40 ms (filled circles), 60 ms (filled triangles), 80 ms(open squares) and 100 ms (filled squares).

This reflects differences in Reynolds number (i.e. size and speed), Froude number[Fl=V2(gTL)–1,where g is gravitational acceleration] and body form (a streamlined circular axisymmetric section versus a broadly triangular one). From a practical standpoint (e.g. scale model ship testing), it is impossible to simultaneously scale both the Reynolds number and the Froude number because their ratio(g1/2TL3/2v–1)must remain constant [see Newman, chapter 1, for details(Newman, 1977)]. If length is decreased, either the gravitational acceleration must be increased or the kinematic viscosity decreased. However, a rough approximation allows for the relative magnitude of the sum of frictional and pressure drag relative to that of wave drag to be assessed (Newman,1977; Lighthill,1978): D(0.5ρwApV2)–1=CD(Re,Fl)and CD(Re,Fl)≃ CF,P(Re)+CW(Fl),where CF,P is the sum of the frictional and pressure drag coefficient and CW is the wave drag coefficient. Therefore: CW(Re,Fl)=CD(Re,Fl)–CF,P(Re)and the contribution of frictional and pressure drag and wave drag are about equal (i.e. CF,P+CW=0.41, CF,P=0.21; Table 4). Larger, faster bodies also generate drag components [e.g. ventilation drag (arising from pressure differences between the anterior and posterior of the form) and spray] not produced by S. nigriventris.

Table 4.

Mean drag coefficients, Reynolds number ranges and density for Synodontis nigriventris and other catfishes*

NDReNρf
Synodontis nigriventris
Near surface (h/d=0.5) 20 0.41±0.05 40000-91000 1.011±0.003
Submerged (h/d>2.5) 20 0.21±0.03 40000-91000
Otocinclus 25 0.46±0.02 4500-8800 21 1.062
Gyrinocheilus 25 0.42±0.03 3600-16700 20 1.069
Hypostomus 25 0.29±0.02 12700-43100 29 1.086
Pterygoplichthys 25 0.47±0.02 9800-31500 12 1.035
Chaetostoma 10 0.87±0.04 9300-17000 20 1.097
Farlowella 25 0.23±0.02 13400-31600 20 1.129
NDReNρf
Synodontis nigriventris
Near surface (h/d=0.5) 20 0.41±0.05 40000-91000 1.011±0.003
Submerged (h/d>2.5) 20 0.21±0.03 40000-91000
Otocinclus 25 0.46±0.02 4500-8800 21 1.062
Gyrinocheilus 25 0.42±0.03 3600-16700 20 1.069
Hypostomus 25 0.29±0.02 12700-43100 29 1.086
Pterygoplichthys 25 0.47±0.02 9800-31500 12 1.035
Chaetostoma 10 0.87±0.04 9300-17000 20 1.097
Farlowella 25 0.23±0.02 13400-31600 20 1.129

D, Mean drag coefficient (given for S. nigriventris in and out of surface proximity); Re, Reynolds number; ρf, density

*

Values taken from (Blake,2006)

By convention, a plot of the square root of the Froude number

$$[F_{1}=V(\sqrt{gTL})^{-1}]$$
against resistance is employed to assess the magnitude of wave drag generated by bodies at or close to the water surface. Small wave drag peaks occur at Fl≈0.2 and 0.3 and a large broad peak at the critical Froude number (Fcrit) of 0.45 (e.g. Lighthill, 1978). For
$$\overline{TL}=0.14$$
m (mean body length of the drag tested' fish) over a velocity range of 0.38–0.63 m s–1,0.32<Fl>0.54. At Fcrit=0.45, V=0.53 m s–1 (about 4 TLs–1) in still water or holding position against a current of the same speed. For the live fish (
$$\overline{TL}=0.06$$
m), Fcrit=0.45 corresponds to V=0.35 m s–1 (5.8 TL s–1). Specific swimming speeds of this order are prolonged swimming (20 s to 200 min)(Beamish, 1978), which ends in fatigue. Limits to prolonged swimming duration near the surface may be set by Fcrit. To exceed these speeds, the fish must swim out of surface proximity. Night video recordings in a large aquarium showed that rapid swimming to/from refuge is common (65% of time/activity frequency distribution) and occurs deeply submerged. Upper values of velocity for inverted, rapid constant speed swimming in the water column are 0.32 m s–1 (Table 2: h/d=3.4, velocity based on mean ± 2 s.e.m.), close to the velocity corresponding to Fcrit (0.35 m s–1). For S. nigriventris deeply submerged(h/d>2.5), CD(Re,Fl)=CF,P(Re)=0.21,where 40 000<Re>91 000(Table 4). In surface proximity(h/d=0.5), CD(Re,Fl)=CF,P(Re)+CW(Fl)=0.41 over the same Re range.

Drag inverted is about 15% less than that dorsal side up in surface proximity (N=120; P<0.05; Fig. 1). The power (P)required to overcome total drag is: P=DV, and this implies that swimming inverted at the air–water interface is energy efficient relative to swimming dorsal side up and that there is no relative hydrodynamic disadvantage to swimming inverted at depth.

Drag coefficients for S. nigriventris when deeply submerged are less than those of rheotactic catfish (N=30–45; P<0.05; Table 4). S. nigriventris is neutrally buoyant [specific gravity≈1.01,cf. S. afrofisheri (Chapman et al., 1994)] similar to many nektonic fishes (e.g. Aleyev, 1977)(Table 2). Rheotactic catfishes are characterized by high drag, density, morphological frictional adaptations(e.g. frictional pads, odontodes) and armour (e.g. large opercular spines)(Blake, 2006). S. nigriventris is smooth skinned with small opercular spines and few frictional adaptations.

### Body orientation angle, drag and aquatic surface respiration(ASR)

Hypothesis 2 is supported; drag increases with body orientation angle(N=60; P<0.05) and is lower for the inverted posture(N=360; P<0.05; Fig. 3). When inverted at a low body orientation angle (⩽20°), S. nigriventris presents a low drag streamlined profile to the flow. With increasing body orientation angle, the form becomes less streamlined until at 90° when the fish approximates a triangular form with apex directed into the flow. If the zoological ventral side faced forward(corresponding to the dorsal side up posture), the base of the triangular section would face the flow. The drag coefficients of 3-D technical triangular sections are higher when the base is directed into the flow(CD=0.7 and 1.1 for apex and base directed into the flow,respectively, Re>103)(McCormick, 1979). The ratio of the drag coefficients for the two directions of facing is 0.65, close to that measured for Synodontis (0.68; Fig. 3).

S. nigriventris and S. afrofisheri (dorsal side up swimmer) are similar in form and respire at the surface when PO2<15 mmHg, orienting their body at about 20° and nearly perpendicular to the surface, respectively(Chapman et al., 1994). The drag at 90° is 2.1–3.0 times that at 20° for a velocity range of 0.38–0.63 m s–1 for S. nigriventris(Fig. 3). This suggests that the resistance of S. afrofisheri is more than double that of S. nigriventris during ASR. The inverted posture facilitates efficient skimming of the well-oxygenated microlayer at the surface of hypoxic waters. The mormyrid Petrocephalus catostoma swims inverted during ASR at a body orientation angle of about 45° to the air–water interface(Chapman and Chapman, 1998). It is likely that drag will be independent of posture in P. catostomabecause of its symmetrical laterally compressed body form.

### Steady swimming bouts and fast-starts

Speed increases with water depth for both postures (N=75; P<0.05; Table 2),supporting hypothesis 3. Increased drag at any given swimming speed at the surface must be compensated for by an increase in thrust production. This is reflected kinematically; at any given speed, tailbeat frequency and stride length are higher and lower, respectively, in surface proximity for both postures than that at depth (N=75; P<0.05; Fig. 5). In addition, tailbeat frequency is higher near the surface for dorsal side up relative to that inverted (N=50; P<0.05). There is no significant difference for slopes between the two postures deeply submerged(N=50; P>0.05) where drag is posture independent.

Hypothesis 4 is supported; fast-start performance decreases in surface proximity and is higher in the inverted posture(Table 3). The decrement in performance near the air–water interface can be attributed to energy lost in wave generation. In surface proximity (h/d=0.6; Fig. 6), about 40% of the mechanical work was lost in wave generation in the dorsal side up posture and 20% when inverted. Maximum inverted' accelerations (20–30 m s–2; Table 3)are comparable to those of trout (Domenici and Blake, 1997) (see Table 1) and other locomotor generalists (sensuWebb, 1984; Blake, 2004). Energy losses due to wave generation at a similar submersion depth index are less than for rainbow trout (70%) in shallow water (Webb et al., 1991). The reason for this is attributable to the hydrodynamics of fast-start resistance in surface proximity for shallow versus deep water.

Dispersive wave systems in shallow water are slowed down, changing the relationship between wavelength and speed relative to deep water. Waves have to become longer to maintain a given speed. There is a critical wave speed(Vcrit) that cannot be exceeded:

$$V_{\mathrm{crit}}=\sqrt{gd_{\mathrm{w}}^{{^\prime}}}$$
[fig. 7 in Wellicome (Wellicome,1967)]. For boats, when the non-dimensional parameter
$$(V=\sqrt{gd_{\mathrm{w}}^{{^\prime}}})$$
is<0.5, the resistance in shallow water relative to that in deep water is about the same. However, resistance in shallow water rises sharply between
$$0.5{<}V\sqrt{gd_{\mathrm{w}}^{{^\prime}}}{>}0.9$$
to three times that in deep water and falls rapidly for values of
$$0.9{<}V\sqrt{gd_{\mathrm{w}}^{{^\prime}}}{>}1.25$$
. For
$$V\sqrt{gd_{\mathrm{w}}^{{^\prime}}}{>}1.25$$
,the resistance in deep water is greater than that in shallow water [Fig. 7 in Wellicome (Wellicome, 1967)]. The initial rise in resistance occurs because the transverse waves become longer and steeper and require more energy to maintain at any given speed. The resistance due to diverging waves remains as they travel much more slowly than the transverse waves and are unaffected. Beyond Vcrit, the transverse waves cannot keep up and cease to exist, hence resistance falls. This analysis is based on steady motions. For unsteady motions, wave pattern changes are time dependent and we assume that such effects are small given the accelerations involved and a reasonable first approximation, justifying a quasi-steady approach.

Webb et al. give a mean velocity of 0.5 m s–1 for the mean distance traveled by the centre of mass over 100 ms with dw=0.05 m corresponding to

$$V\sqrt{gd_{\mathrm{w}}^{{^\prime}}}=0.71$$
[fig. 1 in Webb et al.(Webb et al., 1991)]. For this value, wave drag enhancement for shallow water relative to deep water is about 25% (Wellicome, 1967) (Fig. 7). Referencing velocity to the maximum distance traveled by the centre of mass over the same period (mean ±2 s.e.m. of V=0.58 m s–1) gives
$$V\sqrt{gd_{\mathrm{w}}^{{^\prime}}}=0.83$$
,corresponding to a 100% increase in resistance relative to deep water(Wellicome, 1967) (Fig. 7). Given this and the large amplitude C-start motions of trout relative to the low amplitude fast-start pattern of S. nigriventris(Fig. 4B), it is not surprising that values of energy loss for trout fast-starting in shallow water(Webb et al., 1991) are higher than those for S. nigriventris in deep water.

The escape fast-starts of S. nigriventris are rectilinear,directly away from the stimulus direction(Fig. 4B), in contrast to the common pattern of C' or S' starts (defined by body shape at the end of the first contraction of the lateral musculature) employed by escaping prey and attacking predators, respectively. However, some fish execute one type of fast start for both behaviours [e.g. S-starts and C-starts for both prey capture and escape responses in pike (Schriefer and Hale, 2004) and archer fish(Wohl and Schuster, 2007)respectively]. In addition, whilst many piscivorous predator–prey interactions occur on an essentially x,y-plane, some fish execute escape responses that involve the acceleration of the centre of mass in three dimensions [e.g. marbled hachet fish Carnegiella strigata(Eaton et al., 1977),knifefish Xenomystus nigri(Kasapi et al., 1993) and limnetic sticklebacks Gasterosteus spp.(Law and Blake, 1996)]. Variability in fast-start behaviour for fish with different modes of life and predator–prey relationships is to be expected. O'Steen et al.(O'Steen et al., 2002) have shown that fast-start behaviour is closely linked to survival and evolves quickly with changes in predation pressure.

S. nigriventris in surface proximity is vulnerable to attack from below and above. If the attack paths of both piscivorous and aerial predators occur on planes at a high angle relative to the surface, the evasive rectilinear response of S. nigriventris would quickly maximize the distance away from an attack. Unfortunately, nothing is known about the dynamics of natural predator–prey interactions in S. nigriventris. Arguably, the classic, evasive C-start (two-dimensional response) could also place the fish off a predator's attack path. However,good C-start and turning performance are associated with lateral compression and flexibility (Domenici and Blake,1997; Blake, 2004)and S. nigriventris is not characterized by these features.

### Evolution of the inverted habit

Based on the Baldwin effect (selection of general learning ability with selected offspring tending to have an increased capacity for learning new skills), Dawkins suggests that inverted swimming in S. nigriventrisevolved by natural selection favoring individuals that learned to exploit food from the water surface and underside of floating leaves [p. 401 in Dawkins(Dawkins, 2005)]. Selection has favoured this propensity to learn to the point where the behaviour has become instinctive. Nocturnality (low competition for resources and low predation pressure relative to the diurnal situation), reverse countershading and ASR likely co-evolved with the inverted habit.

Koblmüller et al. analyzed the mitochondrial control region of the NADH dehydrogenase subunit 6 gene to establish a phylogeny in West and Central and East African synodontids(Koblmüller et al.,2006). A composite consensus phylogenetic tree suggests that a Central and/or West African common ancestor gave rise to Chiloglanissp., Microsynodontis batesii and the genus Synodontis. Major cladogenetic events for Synodontis [estimated employing the r8s computer model for inferring absolute rates of molecular evolution and divergence times in the absence of a molecular clock(Sanderson, 2003)] give the age of the genus at about 35 million years. The oldest fossil records of Synodontis are earlier than 20 million years old(Stewart, 2001). At about 20 million years ago, six major lineages of Synodontis diverged from a Central and/or West African ancestor in East Africa(Koblmüller et al.,2006).

There are examples of Central and West African [e.g. S. nigriventris,S. nigrita (Sanyanga,1998)] and East African [e.g. S. zambezensis(Sanyanga, 1998), S. njassae (Thompson et al.,1996), S. multipunctatus(Burgess, 1989)] synodontids that sometimes swim inverted. It would be interesting to map the phylogeny of S. nigreventris and other synodontids capable of inverted swimming onto the extent of the habit. However, whilst S. nigriventris is substantially older than the East African species, the internal branches of the phylogenetic tree interrelating the major Central and West African lineages are short and unresolved(Koblmüller et al.,2006). The route and rate of evolution of inverted swimming in S. nigriventris from its oldest living ancestor [Chiloglanissp., which feeds on benthic invertebrates and employs an oral suction disc to maintain position in fast-flowing water(Ntakimazi, 2005; Kleynhans, 1997)] awaits further phylogenetic studies.

List of symbols and abbreviations

• Ap

frontally projected area

•
• ASR

aquatic surface respiration

•
• CD

drag coefficient

•
• CF,P

sum of the frictional and pressure drag coefficient

•
• CW

wave drag coefficient

•
• D

drag

•
• d

maximum body depth

•
• dw

depth from the bottom of the flume to the point of maximum body depth

•
• $$d_{\mathrm{w}}^{{^\prime}}$$

depth from removable plastic grid (1.65 cm2 cells) to the point of maximum body depth

•
• Fcrit

critical Froude number

•
• Fl

Froude number (indicates the ratio of dynamic forces to static forces in the fluid)

•
• g

gravitational acceleration

•
• h

distance from water surface to fish centre line

•
• Mb

fish mass

•
• P

total drag power

•
• Re

Reynolds number (ratio of inertial to viscous forces in the fluid)

•
• sc

distance traveled in a fast-start for a fish unaffected by wave generation (control fish)

•
• st

distance traveled in a fast-start by a fish subject towave drag

•
• t

time

•
• TL

total body length

•
• V

water velocity

•
• Vcrit

critical wave speed

•
• w

body width

•
• Wa

weight in air

•
• Wc

average work performed in a fast-start unaffected by wave generation(control fish)

•
• Wd

proportion of energy lost due to wave generation in a fast-start

•
• Wo

weight in water

•
• α

longitudinal added mass coefficient representing the mass of water entrained by an accelerating fish

•
• δ

drag augmentation factor (ratio of drag in surface proximity relative to that deeply submerged)

•
• ν

kinematic viscosity of water

•
• ρf

fish density

•
• ρw

water density

We thank P. Y. L. Kwok for technical assistance. R.W.B. is funded by a grant and K.H.S.C. by an Undergraduate Summer Research Award from the Natural Sciences and Engineering Research Council of Canada.

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