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Swimming in needlefish (Belonidae): anguilliform locomotion with fins

James C. Liao

Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138 USA

View larger version (38K): [in a new window]   Fig. 1. (A) Ventral view of a needlefish swimming at 1.0 L s-1 (where L is the total body length), with subsequent digitized outlines (below) based on 40 digitized points and midline reconstructions from a customized splinefitting program. Scale bar, 2 cm. (B) Lateral tracing of a needlefish. Point 1 corresponds to the tip of the jaw, point 2 corresponds to the edge of the operculum, and point 7 corresponds to the tip of the ventral lobe of the tail. Note that a point 80% down the body corresponds to the tip of the dorsal and anal fins.

View larger version (14K): [in a new window]   Fig. 3. (A) Tail-beat frequency (f) increases linearly with length-specific swimming speed (U1). The equation for the line is f=1.5 U1+2.4 (r2=0.98, P<0.0001). The regression is fitted to the mean tail-beat frequency values. (B) Stride length (distance moved for each tail beat) increases as swimming speed increases. Stride values are reported as a proportion of the total body length (L) as well as in absolute distance (cm). Values at each speed represent the mean of four tail beats (± S.E.M.) for each of the four individuals.

View larger version (24K): [in a new window]   Fig. 5. Plot of lateral excursion of the apices of the median fins relative to the body for approximately one tail beat at 1.0 L s-1. Values are means ± S.E.M. from four tail-beat cycles for all fish and are unfiltered. Note that sometimes the standard error is small enough to be contained by the data symbol. Black circles represent a point at 80% L, gray circles represent the apex of the dorsal fin, white circles represent the apex of the anal fin, and triangles and squares represent the tips of the dorsal and ventral lobes of the caudal fin, respectively (inset). The lateral excursions of dorsal and anal fin tips are slightly less than 180° out-of-phase with the body, but are similar to each other in magnitude and phase. The phasing of the caudal fin is shifted ahead of the body, resulting from approximately one wavelength being contained between the point at 80% L and the caudal fin. The amplitudes of the anterior median fins are similar to the amplitude of the point 80% down the body.

View larger version (18K): [in a new window]   Fig. 2. Mean wave amplitudes (± S.E.M.) for seven points along the body for four fish at three swimming speeds. The y axes show amplitude as a percentage of the total body length (L) and in cm. Black bars, 2.0 L s-1 (absolute speed 46.5 cm s-1), gray bars, 1.0 L s-1 (absolute speed 23.3 cm s-1) and white bars, 0.25 L s-1 (absolute speed 5.8 cm s-1). At the lowest speed, only the posterior 44% of the body undulates. As the swimming speed increases, a larger proportion of the body undulates and the body wave amplitude increases non-linearly. Note that over the speeds tested the tail-beat amplitude (determined by tracking point 7) does not plateau.

View larger version (18K): [in a new window]   Fig. 4. (A) Mean propulsive wave speed for the lowest (white), middle (hatched), and highest (black) swimming speeds (mean ± S.E.M., N=16 cycles). Wave speed was determined by calculating the time required for a wave to travel past two points of a known distance. Note that the proportion of the body that undulates depends on the swimming speed. In each case, the body wave traveled posteriorly faster than the forward speed of the fish. (B) Changes in propulsive wave speed down the body were investigated for the two extreme swimming speeds. At 0.25 L s-1, only a small region of the body undulates. When that region is divided in half, both the anterior (light gray column) and posterior (dark gray column) section contain part of the dorsal and anal fins. Wave speeds for the two segments are not significantly different (=0.05). (C) At 2.0 L s-1, the entire body undulates except for the rigid neurocranium. Due to the presence of the median fins, the posterior section of the propulsive wave is significantly slower (P<0.001) than the anterior section, reflecting an overall deceleration of the body wave.

View larger version (12K): [in a new window]   Fig. 6. Posterior view of the digitized edge of the caudal fin as it beats from right to left (arrow) for one representative fish across three swimming speeds. The lateral displacement and configuration of the tail change dramatically as swimming speed increases. At the lowest speed, the dorsal lobe of the tail leads the ventral lobe. At higher speeds, the procurrent and middle rays of the caudal fin lead the tail as it sweeps to one side, causing the tail blade to adopt a `W' conformation.

View larger version (29K): [in a new window]   Fig. 7. Digitized outline traces of simultaneous posterior and ventral images of the pectoral fins during swimming at 0.25 L s-1: thrust cycle and the beginning of the recovery cycle (from left to right). The body is drawn for reference and is not to scale. Hollow arrows indicate the direction of fin motion. (A) During the beginning of adduction, the dorsal edge of the fin is anterior to its ventral edge such that the plane of the fin is oriented obliquely relative to the transverse (z,y) plane. Rotation of the fin chord about its base causes the dorsal-most ray to move posteriorly relative to the ventral edge of the fin, which exposes a large surface area along the transverse plane. (B) At the end of adduction, the dorsal-most fin ray has completed rotation and has been retracted back towards the body wall, revealing its resting position above the dorsal surface of the body. (C) At the beginning of abduction, the dorsal-most ray leads the ventral-most ray in protraction, rotating the fin into the z,x plane so that it exposes the least surface area in the transverse plane to minimize drag. The time from the beginning of adduction to the end of adduction is 160 ms, while the time from the end of adduction to the beginning of abduction is 80 ms.

View larger version (59K): [in a new window]   Fig. 8. Posterior view of one needlefish swimming steadily at three speeds, showing the position of the various fins. When the fins are not obstructed from view, arrows are used to denote their location. Solid arrows point to the pectoral fins, hollow arrows point to the tips of the dorsal and anal fins, and double-headed arrows point to the trailing edge of caudal fin. Scale bar, 1 cm. (A) At the lowest speed, the pectoral fins are clearly seen in the horizontal plane during mid-abduction. The dorsal fin is angled to the left of the body while the anal fin is obscured by the caudal fin, which is vertical and held in line with the body axis. (B) At intermediate speeds, the pectoral fins are held away from the body. The dorsal and anal fins are offset from the body midline, and the caudal fin adopts a W shape as it completes a beat to the left. (C) At the highest sustainable speed, the pectoral fins are held flush against the body and the W shape of the caudal fin becomes more exaggerated (see text for a description). From this view, the lateral excursion of the dorsal and anal fin is not clear, but as the tail beats to the left the flexible median fins lag towards the right of the fish. Note that the height of the median fins is not as great as in B.