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First published online December 2, 2005
Journal of Experimental Biology 208, 4735-4746 (2005)
Published by The Company of Biologists 2005
doi: 10.1242/jeb.01966

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Constraints on starting and stopping: behavior compensates for reduced pectoral fin area during braking of the bluegill sunfish Lepomis macrochirus

Timothy E. Higham^1,*, Brett Malas², Bruce C. Jayne³ and George V. Lauder⁴

¹ Section of Evolution and Ecology, University of California, One Shields Avenue, Davis, CA 95616, USA
² Department of Ecology and Evolutionary Biology, University of California, Irvine, CA 92717, USA
³ Department of Biological Sciences, University of Cincinnati, PO Box 210006, Cincinnati, OH 45221-0006, USA
⁴ Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA

View larger version (14K): [in a new window]   Fig. 1. A model of how stopping ability and total travel distance could constrain modulation of velocity during a start and stop. The hypothetical movements in A and B have identical starting accelerations (astart=slope=1) and total displacements (Stotal=areas under the triangles or trapezoids with a vertex indicated by a circle=3 units), but the stopping acceleration (astop) varies among the cases indicated by the different colors within each panel. (A) Starting acceleration continues up to the instant when stopping begins (indicated by circles). Compared to astop=1, increased stopping ability (green) allows more distance to accelerate to a greater maximal velocity (Vmax), which decreases total travel time. Decreased stopping ability (red) has detrimental effects on Vmax and total travel time. Consequently, the average velocities (Stotal divided by total time) for astop=2 and 0.5 are 115% and 81% of the value when astop=1, respectively. (B) When the total distance provides sufficient time so that a physiologically maximum speed is attained and momentarily sustained, stopping ability will not affect Vmax. However, increased stopping ability decreases total time and hence the average velocities for astop=2 and 0.5 are 107% and 89% of the value when astop=1, respectively. Maintaining a constant velocity in between the starting and stopping accelerations (B) increases total travel time and hence decreases average velocity compared to beginning a stop immediately after the cessation of a starting acceleration (compare A vs B for equal values of astart and astop). If the only objective of starting and stopping is to minimize total travel time (and maximize average speed) for a given distance, then maximal accelerating and decelerating capacities should be used. (C) For a linear increase in velocity followed immediately by a linear decrease in velocity as in A, Vmax=astart[(2Stotal)/(astart+1/astop)]0.5 and hence the upper limit of Vmax is astart0.5(2Stotal)0.5. Axes show arbitrary units.

View larger version (25K): [in a new window]   Fig. 2. Schematic diagram of our test arena and equipment. A mirror below the tank provided ventral views of the fish for two cameras. The right portion of the tank is the starting chamber, and the stopping chamber at the left contains a worm attached to a weighted line. Note the two openings in the vertical partitions, which required the sunfish to travel in a straight line to reach the worm and execute the braking action.

View larger version (11K): [in a new window]   Fig. 3. Landmarks digitized in each mirror ventral view of fish. Kinematic variables calculated included jaw protrusion (1), angles of the pectoral (2) and pelvic fins (3) relative to the body, and angles of the median (4) and caudal fins (5) relative to the overall trajectory of the fish (x axis). Although only illustrated for one side, the angles of the paired fins were determined for both sides of the fish.

View larger version (19K): [in a new window]   Fig. 4. Representative kinematics for sequences before (A–D) and after (E–H) pectoral fin reduction from the same individual, including displacement (A,E), forward velocity (B,F), acceleration (C,G) and angles of the median and paired fins during the final rapid deceleration (D,H). The broken vertical line indicates the time of maximal jaw protrusion, which is nearly coincident with prey capture. P (green) and B (red) indicate the behaviors of propulsion only and braking only, respectively.

View larger version (23K): [in a new window]   Fig. 5. Outline figures drawn directly from bitmaps of the mirror ventral view videotapes of representative start–stop episodes before (A) and after (B) pectoral fin reduction of the same individual. Elapsed times (ms) from the initiation of movement are indicated at the lower left of each figure. From top to bottom, the images within each sequence represent the following events: start, maximum velocity, moderate deceleration, maximum jaw protrusion (during rapid deceleration), and stop.

View larger version (14K): [in a new window]   Fig. 6. Variation in modulation of velocity and locomotor behaviours, including (A) a sequence with a glide (G) and (B) one with propulsion plus braking (PB). Note that Vmax is attained substantially before the cessation of propulsion.

View larger version (14K): [in a new window]   Fig. 7. Forward velocity vs time (percentage of total) for both intact (N=19, red circles) and reduced (N=18, blue triangles) pectoral fin treatments. Values are mean ± S.E.M.

View larger version (13K): [in a new window]   Fig. 8. Pectoral fin angles for the final 50 ms of each trial before (N=19, circles) and after (N=18, triangles) pectoral fin reduction. Values are mean ± S.E.M.

View larger version (15K): [in a new window]   Fig. 9. The magnitudes of maximum acceleration vs maximum deceleration within each of 37 trials of fish with intact (N=19, red circles) or partially ablated (N=18, blue triangles) pectoral fins. The broken reference line indicates a 1:1 ratio of these two quantities.