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
Constraints on starting and stopping: behavior compensates for reduced pectoral fin area during braking of the bluegill sunfish Lepomis macrochirus
Timothy E. Higham1,*,
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
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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© The Company of Biologists Ltd 2005
