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First published online September 14, 2007
Journal of Experimental Biology 210, 3374-3386 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.007484

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The ontogeny of fin function during routine turns in zebrafish Danio rerio

Nicole Danos^* and George V. Lauder

Department of Organismic and Evolutionary Biology, Harvard University, 26 Oxford Street, Cambridge, MA 02138, USA

View larger version (41K): [in this window] [in a new window]   Fig. 1. Body regions tracked using Digital Particle Image Velocimetry (DPIV) cross-correlation (see text for details). Dorsal view of an adult fish (FL=3.24 cm). Yellow arrows are velocity vectors (in m s–1) describing the change in position of local pixel intensity patterns between two consecutive frames (time between frames=1 ms). Arrowheads are constant size but arrow shafts are proportional to vector magnitude. Boxes: 1, tip of upper caudal fin lobe; 2, base of caudal fin; 3, left pectoral fin; 4, right pectoral fin; 5, base of pectoral fins; 6, head. Body velocities nearest to fins (boxes 2 and 5) were subtracted from fin velocities (boxes 1, 3 and 4) to obtain the velocity of the fins relative to the body.

View larger version (11K): [in this window] [in a new window]   Fig. 2. A model predicting turn angle based only on midbody curvature and body length. If body bending was the only factor controlling turn angle, turn angle should equal the product of body curvature and body length (see text for more details). Curvature, K=1/R; L=fish length; =turn angle.

View larger version (64K): [in this window] [in a new window]   Fig. 3. Representative turning sequences across zebrafish ontogeny showing movie frames near the start, midpoint and end (top, middle and bottom rows, respectively) of each turning sequence. The first frame shown from each sequence was selected as the one where the dominant point of rotation along the body was clearly visible. The last frame selected was the frame where the head had reached its final angular displacement and the body is nearly straight. Maximum body curvature, which was usually reached near the midpoint of the turn, is largest in larvae and smallest in adults. Linear velocity of fins is greatest in adult fish even though angular velocity of the head is smallest in adults. The most prominent center of rotation for routine turns remains over the pectoral girdles in all stages examined (top row); other areas of the body may also exhibit rotational motion.

View larger version (145K): [in this window] [in a new window]   Fig. 4. Comparison of pectoral fin and tail function and their contribution to angular velocity at three sizes representative of the larval, juvenile and adult stages. Fin velocities in all three graphs are relative to body velocity (Fig. 1). Thus negative velocities indicate that the fin is moving slower than the body. (A) In the larval individual (FL=0.38 cm) the pectoral fins are moving more slowly than the body. The caudal fin, in contrast, is moving faster than the body and reaches its maximum linear velocity at the same time that maximum angular head velocity is reached. (B) In juvenile fish (FL=0.99 cm) the pectoral and caudal fins are all moving faster than the body around the time of maximum angular head velocity, suggesting that the generation of turning momentum is created by the interaction of both fin types. The caudal fin remains active longer than the pectoral fins that attain a speed close to body speed after 0.05 s, suggesting that the caudal fin is engaged in angular control later in the turn cycle as well. (C) In the adult (FL=1.65 cm) the fin opposite to the direction of turning is moving faster before maximum head angular velocity although the kinematic profile of adults showed very high variation.

View larger version (14K): [in this window] [in a new window]   Fig. 5. Kinematic variables plotted against fork length. (A) Turn angle; (B) angular velocity; (C) duration; (D) curvature. Turn angle (A) and angular velocity (B) show a biphasic pattern of change. The transition points as identified by piecewise linear regression occur at FL=1.18±0.28 cm for turn angle and FL=1.16±0.23 cm for angular velocity. The piecewise regression for turn duration (C) against FL, although significant overall, did not have a significant transition point. Body curvature (D) did not have a significant piecewise regression and so we interpret the rate of change as constant across ontogeny with a slope of –16±6; a quadratic model did not fit the data significantly better than a single linear regression model. For further explanation of the regressions, see Statistics in Materials and methods. In all graphs each point represents the mean value per individual, from 2 or 3 turning sequences.

View larger version (12K): [in this window] [in a new window]   Fig. 6. Kinematic variables against fork length. (A) Head velocity; (B) tail velocity; (C) pectoral fin velocity, as the average of left and right fin velocities; (D) Reynolds number. (A) Head velocity had a slope not significantly different from zero. Tail velocity (B) increased with a slope of 3.32±1.03 and pectoral fin velocity (C) increased with a slope of 3.24±0.74. Since Re (D) was not measured directly but was calculated from other measured variables we did not include it in this analysis. We report the slope of its linear regression for general interest (slope=730±301). For further explanation of the regressions, see Statistics in Materials and methods. All graphs show mean value per individual, from 2 or 3 turning sequences.

View larger version (5K): [in this window] [in a new window]   Fig. 7. Turn angles predicted by a simple model of body curvature during turning plotted against measured turning angles. The model predicts maximum turn angle to be the product of maximum body curvature (K) and fish fork length (FL), which is dimensionless. Points are coded according to FL (see key) and are the mean values of all turning sequences from each individual. If actual turn angles matched predicted turn angles, there should be a 1:1 relationship between the two variables. All the turn angles measured are substantially smaller than the angles predicted by the model.

View larger version (7K): [in this window] [in a new window]   Fig. 8. Pectoral fin contribution to turn direction. The difference between right and left pectoral fin velocities, after subtraction of the body velocity, is plotted against turn angle for each sequence measured. Points are coded according to fish fork length (see key). Left turn angles are coded as negative while right turn angles are coded as positive. During a turn in either direction there is no pattern of the same fin (left or right) consistently moving faster than the other. The lack of pattern persists throughout ontogeny.