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First published online October 17, 2008
Journal of Experimental Biology 211, 3359-3369 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.020917
Hydrodynamics of the escape response in bluegill sunfish, Lepomis macrochirus
1 Department of Biology, University of Maryland, College Park, MD 20742,
USA
2 Department of Organismic and Evolutionary Biology, Harvard University,
Cambridge, MA 02138, USA
* Author for correspondence (e-mail: tytell{at}umd.edu)
Accepted 1 September 2008
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Summary |
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Key words: fluid dynamics, escape response, C-start, turning, maneuvering, bluegill sunfish, Lepomis macrochirus, particle image velocimetry
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INTRODUCTION |
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;
Korn and Faber, 2005). These
cells trigger a strong, mostly unilateral contraction of axial muscle that
bends the body into a `C' shape, which is then typically followed by one or
more alternating tail beats. Numerous studies have described both the
characteristic pattern of muscle activity (e.g.
Ellerby and Altringham, 2001;
Jayne and Lauder, 1993;
Westneat et al., 1998) and the
kinematics (reviewed in Domenici and Blake,
1997; Wakeling,
2006). Most of these studies divide the behavior into at least two
major components; stage one – the initial `C'-bend, and stage two
– the stroke during which the body bends out of the `C' shape
(Weihs, 1973).
Because escape responses are used to flee predators, escape performance has
clear fitness consequences. Therefore, studies of fast-start responses in fish
have also served as a key component of evolutionary and ecological studies of
predator–prey interactions (e.g.
Bergstrom, 2002;
Domenici et al., 2008;
Gibb et al., 2006;
Langerhans et al., 2004).
Indeed, fish that execute slower or less effective escape responses are
preferentially eaten over individuals that have a higher escape performance
(Walker et al., 2005).
One area in which escape responses are poorly understood is the pattern of
water flow generated during the escape: how is power transferred from body
muscles into the surrounding fluid? In particular, what proportion of the
total power is transferred during the stage one C-bend relative to the
following tail beat? Stage one has often been called `preparatory'
(Weihs, 1973), suggesting that
it does not power the final escape; however, others have objected to such
terminology on the basis of theoretical calculations that show thrust during
stage one (Wakeling, 2006).
This argument is not purely semantic; the division of power among the stages
has implications for both neural control and performance. Specifically, if
substantial thrust is produced during stage one, then the Mauthner circuit
that controls stage one also has a direct effect on the overall escape
performance, and the whole body, which contributes to the C bend, is critical
for force production. However, if stage two is dominant, then the Mauthner
circuit is more like a trigger for a behavior in which other circuits may have
a greater impact on performance. In this case, because stage two involves more
caudal fin movement than body movement
(Domenici and Blake, 1997), the
caudal fin would be more important for force output than the rest of the
body.
Therefore, the goal of this study is to contribute a comprehensive,
experimental analysis of the fluid dynamics of C-start escape responses in a
teleost fish, the bluegill sunfish Lepomis macrochirus, and to
present a description of the patterns of fluid momentum that result from
escape responses. Our fluid dynamic data directly indicate the relative
importance of stage one and two for force production, along with the
contributions of the dorsal and anal fins to thrust production during the
escape response. These data are particularly valuable for understanding the
time course of locomotor power generation by escaping fish, for correlating
fluid dynamic phenomena with previously well-characterized C-start kinematics
and for characterizing the wake signature of escaping fish, which is important
for predators as they may use this signature to track fish (e.g.
Hanke and Bleckmann, 2004;
Hanke et al., 2000).
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MATERIALS AND METHODS |
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20°C) in separate 40-liter freshwater aquaria with a 12
h:12 h photoperiod, and were fed earthworms three times weekly. Juveniles were
used for flow visualization experiments. After experiments were completed,
each fish was lightly anesthetized using buffered MS222 (0.2 g
l–1) (tricaine methanosulfate; Argent Laboratories, Redmond,
WA, USA), digitally photographed, weighed, and total body length (L) was
measured. The four individual bluegill used for kinematic and flow
visualization analysis had a mean total body length L=11.0±0.4
cm (±s.e.m.) with a range from 9.7 to 13.3 cm. Mean body mass was
21±2 g (±s.e.m.). In total, 21 escape responses were analyzed,
with at least four sequences per individual.
Mass distribution
To determine both longitudinal and dorso–ventral mass distribution,
juvenile bluegill of similar size to those used in flow visualization
experiments were euthanized with an overdose of buffered MS222. Individuals
were frozen at –20°C, then weighed and photographed. Each animal was
sectioned into either transverse or frontal slices using a standard bandsaw
with a fine-toothed blade (approximately 1 mm thickness) (RIGID; Home Depot,
Atlanta, GA, USA). For transverse sections, animals were cut approximately at
the posterior margin of the eye, through the pectoral fin base, posterior to
the pelvic fins, through the base of the dorsal and anal fins, and at the end
of the hypural bones in the caudal fin
(Lauder, 1982). For frontal
sections, animals were sectioned at the base of the dorsal fin, though the
center of the peduncle and at the base of the anal fin. Sections were then
weighed individually and photographed from lateral and both cross-sectional
views (i.e. the cut surfaces on the anterior and posterior sides for
transverse sections or the dorsal and ventral sides for frontal sections). The
sum of the mass of the sections was subtracted from the total fish mass to
determine the mass lost to the bandsaw. Mass per unit length was then
estimated by interpolating 20 evenly spaced points from the snout to the tail,
assuming that mass is zero at the tips of the snout and tail, and was
normalized to the total mass of the fish and the total length. Mass per unit
height was estimated in the same way for frontal sections along the height of
the fish.
Five individuals were used to estimate the mass distribution of bluegill. The mean total body length of these fish was 10.9±0.7 cm (±s.e.m.) with a range from 10.6 to 11.3 cm. Mean body mass was 22.5±0.3 g (±s.e.m.). Three of these individuals were sectioned transversely and two individuals were sectioned frontally.
Experimental protocol
Experiments were performed in a recirculating flow tunnel (600 l) with a 28
cmx28 cmx80 cm working section used in previous experiments on
fish locomotor hydrodynamics (e.g. Tytell
and Lauder, 2004; Tytell et
al., 2008). A low flow speed was used (0.7 L
s–1) to orient the fish consistently using the rheotaxis
response and this greatly aided in positioning the fish within the laser light
sheet. This orientation swimming speed was in the range in which bluegill swim
using only their pectoral fins, and has been shown not to affect the
kinematics of the escape response (Jayne
and Lauder, 1993). Animals were gently maneuvered into the center
of the working section using a wooden dowel, which was removed prior to
filming an escape. Escape responses were elicited by dropping into the tank a
weight with a flat plate (approximately 5 cm diameter) attached to the bottom
to generate an impulsive `slap' on the water surface. The weight was secured
with a string so that it dropped just below the surface of the water and
produced a pressure wave [known to elicit escape responses
(Eaton and Emberley, 1991;
Tytell and Lauder, 2002)] but
did not substantially disturb the flow in the region of the fish. The string
also ensured that the stimulus was dropped into the tank at a consistent
location, anterior and to the right of the fish (see
Fig. 1B). This stimulus was
effective at inducing escape responses in bluegill.
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Two Coherent I310 10 W argon-ion lasers were used simultaneously to
illuminate neutrally buoyant 12 µm diameter silver-coated glass beads
(density 1.3 g cm–3; Potter Industries, Valley Forge, PA,
USA) in the region surrounding the fish. Laser light from each laser was
spread into a horizontal sheet using cylindrical lenses. Light from one laser
was reflected off a mirror in the tank to produce a light sheet oriented at 90
deg. to the other (Fig. 1A).
This configuration minimized shadows during the escape behavior
(Fig. 1B) and allowed a near
full-field analysis of water flow patterns during the escape. Where the two
light sheets overlapped, particle illumination was brighter but illumination
provided by a single laser as seen in the darker regions of the imaged area
(Fig. 1B) was sufficient for
data analysis. As a result of the orientations of the two laser light sheets,
only in very small areas near parts of the highly curved body was no
illumination present, and water flow patterns during the C-start could be
analyzed for nearly the full image. This arrangement, thus, prevented the
large shadows that would otherwise be cast by the bending fish from
prohibiting analysis in large regions of the image. Fluid flow patterns were
estimated from the ventral video using standard multiple pass particle image
velocimetry (PIV) algorithms (Hart,
2000; Willert and Gharib,
1991), performed using DaVis 7.1 software (Lavison) as in our
previous research (e.g. Lauder and Madden,
2007; Tytell,
2006). This yielded a matrix of 175x175 vectors calculated
for each image in the C-start sequence for a total of 30,625 vectors per
image. Approximately 200 images per sequence were recorded to provide full
coverage of flows throughout the entire C-start and for at least the first
full tail beat after the escape response proper.
Three sets of separate experiments were conducted on all individuals with the laser light sheet oriented first at mid-body, then intersecting the fish at the dorsal fin and tail, and finally intersecting the fish at the anal fin and tail. The location of the light sheet on the body was determined from the lateral view camera (Fig. 1C). This allowed separate analysis of whole body flows as well as the fluid flow patterns generated by the dorsal fin and the anal fin. Due to slight variations in fish position in the light sheet when the C-start was elicited, data from the body were divided into upper body and lower body analyses. Fig. 2 shows the number of hydrodynamic sequences collected with the laser light sheets at four approximate positions along the dorso–ventral body axis: through the dorsal fin, the upper body, the lower body and the anal fin. The largest number of sequences (N=11) was for the lower body, which included most of the caudal peduncle and the fork of the caudal fin.
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) and 20 evenly spaced points were interpolated.
Stages of the escape response were defined according to the angular
velocity of the head, using standard definitions
(Domenici and Blake, 1997).
Angular velocity of the head was determined by calculating the angle of the
segment from the tip of the snout to the fourth point (near the posterior
margin of the operculum) and taking a numerical derivative with respect to
time using a second-order central difference algorithm
(Press et al., 1992). Stage
one, in which the fish bends into a `C' shape, was defined to be the period
from the first visible motion of the tip of the snout until the angular
velocity of the head changed sign. As all turns were to the fish's left due to
the consistent location of the stimulus relative to the fish body, stage one
was, thus, the time period in which the head was moving to the fish's left.
Stage two was the period from the end of stage one until the head's angular
velocity went to zero or changed sign again (i.e. the period when the head was
moving to the fish's right). Stage one duration is represented by
t1, stage two duration is
t2 and the total duration of the escape is
T (=t1+t2).
The true center of mass (COM) position was determined by integrating the x and y coordinates of the midline multiplied by the mass per unit length (estimated above) as a function of position along the arc of the midline. The final angle of the COM trajectory was determined by fitting a line to the COM position in at least 10 frames at the end of stage two. COM velocity was estimated by fitting a smoothing spline (MSE=0.125 pixels2) and taking the time derivative of the spline. Total fish momentum, Mbody, was estimated by multiplying the fish's mass by the COM velocity. At each instant in time, fish momentum was divided into components parallel and perpendicular to the final trajectory angle. At the end of stage two, all of the fish's momentum is, by definition, parallel to the final trajectory and is therefore represented by the scalar M.
Lateral images (Fig. 1C) were used to estimate the position and angle of the light sheet on the fish's body by noting anatomical landmarks that were illuminated by the laser (such as the tip of the snout and the upper margin of the caudal peduncle) and measuring the position of these landmarks on a still, lateral image of a bluegill sunfish. Escape responses were divided into four classes according to where the light sheet intersected the fish's body: dorsal fin, upper body, lower body and anal fin (Fig. 2).
Fluid flow analysis
Background fluid velocity 
was determined by manually
identifying a small region far from the fish prior to the C-start and
determining the mean of both streamwise and cross-stream flow velocity in that
region. Mean velocities were then subtracted from the flow fields.
Inspection of the high-speed videos revealed three distinct jets of water produced by each C-start. These three fluid jets were easily identified manually in each sequence. Using custom software in Matlab, ellipsoidal regions Ji were drawn around the fluid flow in each jet i. Jet one was defined to be the first jet formed, produced by the tail during stage one. Jet two was generated approximately in the opposite direction as jet one and was initially produced along the body in stage one and the tail in stage two. Jet three was approximately 90 deg. to jet two and was formed during stage two.
For each jet i, the fluid momentum per unit height
µjet,i was determined by integrating fluid velocity
over the ellipsoidal region:
 | (1) |
is fluid density, u is the velocity vector,
is the mean velocity, dA is a unit of area and Ji
is the ellipse that surrounds the jet. Effectively, this integral takes the
mean flow vector in the ellipsoid and multiplies it by the area of the elipse
and the density of water.
Because PIV only produces flow velocities in a plane,
µjet,i has units of momentum per unit height. To
estimate the total jet momentum in three dimensions, we must account for two
points: (1) given the same movement, larger fins will produce larger jets and
(2) because the light sheet intersects a two-dimensional slice, not all of the
jet will be visible. To account for point 1, note that each jet is produced by
a different section of the fish's body: jet one by the caudal fin and jets two
and three by the body. The dorsal or anal fins could also contribute to jet
two in trials with the light sheet at the level of each fin. In this case, the
contribution is referred to as the `dorsal fin jet' or `anal fin jet'. As a
general term, we will refer to the fins or body, when used to generate a jet,
as an actuator surface and we will denote their lateral area by
Ai, for the surface that produces jet i. To
account for point 2, note that µjet,i will depend on
the level of the PIV light sheet. For instance, if the sheet is closer to the
midline, it will intersect a longer section of the caudal fin actuator surface
than if the sheet is more dorsal, and µjet,i will be
correspondingly larger. We will use li(z) to
denote the length of the actuator surface at the level z of the light
sheet on the fish's body. Note that li(z) does not depend
on the jet flow direction or the position of the jet ellipsoid but only on the
level of the light sheet on the fish's body (as determined from the lateral
camera; Fig. 1C). Thus, as a
first approximation of the 3-D structure, the total momentum
Mjet,i in jet i should be proportional to
the momentum per unit height, scaled by the total area of the actuator surface
(point 1) and the length of the surface intersected by the PIV plane (point
2), as follows:
 | (2) |
For simplicity, the scaling factor li(z) was determined for the light sheet level z at the end of stage one, rather than the time-varying height. Note that both Mjet,i and µjet,i are vectors and can be decomposed into components parallel and perpendicular to the final trajectory. Force was estimated from the time derivative of Mjet,i. Fluid momentum is normalized throughout by dividing by the final fish momentum M, and force is normalized by dividing by the mean force required to produce the final momentum, M/T.
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=0.016;
2=47.4; d.f.=33; P=0.051), although the P
value was close to significance indicating that there was a trend toward
systematic differences in C-start kinematics among individuals. Stage one
durations were nearly twice that of stage two, and peak COM velocity during
the escape response was nearly 3x that at the end of stage one
(Table 1).
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Flow structure
Three fluid jets were identified in each escape response, and Figs
5 and
6 show the development of fluid
momentum in the jets. These jets represent momentum added to the water as a
result of body and fin movements during the escape response. Jet one was
formed by the tail during the initial C-bend in stage one
(Fig. 5A,B; Movie 1) and was
fully developed during stage two (Fig.
5C). Jet two was initiated during stage one and was formed by the
body at the center of the C-bend (Fig.
5B). As the body began to turn after stage one, the tail continued
to add momentum until the end of stage two. At the end of stage two, momentum
in jet two was fully developed (Fig.
5C,D). Jet three developed near the mid-body region during stage
two and afterwards, on the opposite side as jet two
(Fig. 5C,D). This jet was often
more diffuse than jets one or two. Thus, by the conclusion of the escape
response, three well-developed fluid jets had formed and these jets are nearly
orthogonal to each other (Fig.
5).
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Fig. 7 shows the development of vorticity in the flow field, as well as the identified boundaries of the jets. Two well-defined, counter-rotating vortices were shed with jet one (Fig. 7C) suggesting that it is a vortex ring. Jet two had less clear vortices. Instead, as the tail swept around through stage two, it produced shear layers of opposite sign on either side of the jet (Fig. 7D,E). These shear layers were unstable and tended to break up into multiple vortices (Fig. 7F). Finally, because jet three was fairly diffuse, it was rarely accompanied by clearly defined vortical structures.
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). Mean total fluid momentum was not significantly different
from the fish's momentum M (t=0.464; d.f.=3;
P=0.67), as predicted by conservation of momentum. However, the fluid
momentum perpendicular to the final trajectory, summarized in
Fig. 8B, was significantly
different from zero (t=9.599; d.f.=3; P=0.002). This result,
which is contrary to the predicted conservation of momentum, was most likely
due to the fact that the momentum estimates were made at the end of stage two
but jet three generally continued growing after stage two. The relatively
narrow field of view needed to visualize escape response flow patterns
precluded a detailed analysis of the momentum in jet three but its growth
would tend to push the perpendicular fluid momentum closer to zero.
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To examine the timing of force production in more detail, Fig. 9 shows the time derivative of jet two momentum, which is an approximation of the force producing the jet. Such force traces typically had two peaks, one in each stage. Fig. 9A shows an example trace. So that different sequences can be compared, force was non-dimensionalized by dividing by the mean force required to produce the final fish momentum (M/T; an example is shown with the broken line in Fig. 9A). Fig. 9B shows the mean normalized force peaks from each stage. The first peak occurred 27.9±0.8% of the way through stage one or 9.3±3 ms after the first movement, whereas the second was 56±1% through stage two or 46.0±0.4 ms after the first movement. In non-dimensional force, the mean height of the two peaks were 0.45±0.01 and 2.23±0.07. On average, peak forces in stage two were 6.2±0.5x peak forces in stage one (range 2.2 to 17.7).
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Jet one was perpendicular to the initial fish orientation (Fig. 10A,B). Thus, it might appear that jet one indicated a reaction force that starts the initial rotation of the turn. However, the data did not support this hypothesis. Linear regression revealed that there was no significant relationship between peak angular velocity and total jet one momentum (P=0.134; data not shown).
The fluid momentum data indicated a performance gradient associated with perpendicular momentum. Turns with more fluid momentum perpendicular to the final trajectory had significantly lower final velocities. Fig. 11 shows the final fish momentum plotted against the perpendicular fluid velocity component as a fraction of the total fluid momentum. Linear regression indicated a significant negative relationship (P=0.029).
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DISCUSSION |
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;
Tytell, 2006;
Tytell et al., 2008). Fish momentum along the escape trajectory quantitatively matches the summed momentum of the three identified hydrodynamic jet flows plus the dorsal and anal fin flows (Fig. 8A), suggesting that our analysis has captured the major hydrodynamic events contributing to the escape. Jet one is generated by the caudal fin area of the fish, and the bulk of the jet one momentum opposes the escape trajectory. Production of this jet, which would act to reduce the efficiency of the escape response, may be an unavoidable consequence of having a flexible body bending into a C-shape. Fluid will naturally separate from the sharp trailing edge of the fish tail as the body bends and the tail moves toward the head, resulting in a distinct jet as the tail decelerates at the end of stage one.
Jet two, which is first formed in stage one and continues developing through stage two, contributes the bulk of escape trajectory momentum (Fig. 8A). Bending of the body into the `C' shape produces a large suction region on the inside curve of the body, which, in turn, produces a large bulk flow in a direction generally opposite to that of the final escape trajectory and hence opposite to the direction of jet one. The importance of the suction region is clearly seen in the vector fields calculated for stage one (Fig. 5B; Movie 1 in supplementary material), where the side motion of the mid-body region has induced a large diameter high-velocity jet. Much lower flows are visible on the pressure side of the bending body.
Finally, jet three contains much less momentum along the final escape trajectory than either jet one or jet two, and has a mean direction that is largely perpendicular to the escape (Fig. 8B; Fig. 10). Examination of the flow velocity field (Fig. 5C,D) in the region of jet three shows that this jet is oriented in a largely perpendicular direction to jets one and two and is generated by bending along the posterior half of the body during stage two. The momentum in this jet may contribute to steering the fish out of stage one and into stage two by countering angular momentum generated during the C-bend phase of the escape. Alterations of body bending during stage two may allow adjustment of the final escape heading but our data show that momentum allocated to directions orthogonal to the final trajectory decreases escape performance overall. The escapes with the highest stage two momentum have the lowest fraction of momentum perpendicular to the final trajectory (Fig. 11).
Our experimental setup deliberately controlled, as much as possible, for initial body orientation and stimulus location and so variation in the direction taken by escaping fishes was low. Future studies could induce a diversity of escape directions and profitably compare the directions of each jet, particularly jet three, with the final escape direction. We hypothesize that the angle of jet three will be strongly correlated with the final turn angle.
One key finding of the present study is that a substantial portion of jet
two is generated during stage one (Fig.
8A). Even though the COM moves relatively little during stage one,
the forces and accelerations are high and contribute to the final escape
performance. This result indicates that stage one is not well described as a
`preparatory' phase, followed by the `propulsive' phase two
(Weihs, 1973). These terms
have been persistent in the fast-start literature (e.g.
Frith and Blake, 1995;
Harper and Blake, 1990;
Muller et al., 2008;
Tytell and Lauder, 2002), even
though various researchers have argued against them (reviewed in
Wakeling, 2006). In
particular, the term `preparatory' produces a misconception that the strong
muscle activity generated by the Mauthner response does not contribute to
forward propulsion (e.g. Eaton et al.,
2001). Our results demonstrate that the opposite is true: both
stage one and two are propulsive.
A second key finding is that both the dorsal and anal fins contribute
significant momentum to the escape by adding to jet two
(Fig. 6). We have termed these
contributions the dorsal and anal fin jets but one should recognize that these
jets are probably continuations of jet two, generated along the body. The fins
are erected during the C-start (Eaton et
al., 1977; Tytell et al.,
2008) and are controlled actively throughout the behavior
(Jayne et al., 1996). This
active control serves a propulsive role during the C-start, and does not
solely stabilize the fin against the flow as previously hypothesized
(Jayne et al., 1996). By
contrast, our data suggest that the dorsal and anal fins contribute 37% of
total momentum (Fig. 6). This
value is similar to the estimate made by Frith and Blake that these two fins
together contribute 28% of total thrust in the pike Esox lucius
(Frith and Blake, 1991). Our
results suggest that dorsal and anal fin dynamics may be an important
mechanism for increasing escape performance.
Webb addressed median fin function experimentally in escaping fishes by
comparing the escape performance of an unmodified body shape in trout with the
performance of fishes on which he had amputated the dorsal and anal fins
(Webb, 1977). He indicated
that his data were too variable to formulate conclusions on the effects of
median fin amputation and he could not detect a significant effect of dorsal
and anal fins, despite theory suggesting that increasing body depth during the
C-start should enhance thrust generation
(Weihs, 1973). Our data
support both Weihs's model and Webb's argument that median fins function to
increase dorso–ventral height and are important to C-start performance
(Webb, 1977;
Weihs, 1973). Additionally, we
demonstrated that these fins contribute substantially to thrust generation
along the escape trajectory.
Comparison to previous studies
There are relatively few experimental studies of fluid flow with which to
compare the results of the present study. Recently, Epps and Techet studied
giant danio (Danio aequipinnatus) using PIV and quantified flow
patterns generated during rapid maneuvering
(Epps and Techet, 2007). This
maneuver is presented as a C-start escape response but three lines of evidence
suggest that it is instead a rapid maneuver. First, the time to the end of the
initial body bending is quite long, in the order of 100–150 ms, which is
a long time for stage one of a C-start
(Domenici and Blake, 1997).
Second, the plot of head angular velocity vs time shows that the head
angular velocity never changes sign, as is typical during stage two of a
C-start (Fig. 4)
(Domenici and Blake, 1997).
Third, the value of head angular velocity (approximately 1500 deg.
s–1) is low for C-starts (which is typically 3000 deg.
s–1 or higher) (Fig.
4) but is within the range for rapid turning [reported to be
approximately 1000 deg. s–1
(Danos and Lauder, 2007)].
Nonetheless, the data from Epps and Techet
(Epps and Techet, 2007) for
this one maneuvering event show some similarities to the vortical patterns to
those we report here for C-starts. The initial body bend does show evidence of
a vortex ring shed by the caudal fin in direction opposing the final
trajectory of the fish, a similar result to our jet one. A jet two is also
visible as the main propulsive jet, although vector fields are not presented
to allow comparison with this large stage one momentum jet illustrated here
(Fig. 5). No jet three is
evident in their figures but one would not be expected as the final trajectory
of the fish was not different from the head orientation at the end of stage
one.
Müller et al. (Müller et al.,
2008) also presented flow visualization data on one larval
zebrafish executing a rapid maneuver and they also identified the two vortex
rings, which appear to be comparable with jet one and jet two from the
bluegill sunfish escape behaviors reported in the present study. Their
equivalent of jet one does not persist for long into stage one, while jet one
from bluegill is distinct and well-formed even at the end of the entire escape
sequence (Fig. 5D). They did
not observe formation of a jet three. Differences between their data and those
reported here are probably due to the substantial differences in Reynolds
number between the 4 mm larval zebrafish and the approximately 10 cm long
bluegill studied here.
C-starts have more commonly been analyzed using the slender body theory
developed by Weihs (Weihs,
1972). Wakeling provided a review of this theory and its
application, and noted that current mathematical models include several
assumptions that can best be evaluated by direct measurement of flows produced
during escape responses (Wakeling,
2006). Weihs estimated the forces and moments acting on the body
of slender-bodied fishes and considered the effect of adding fins to the body
on escape performance. Weihs concluded that `the caudal fin is shown to play a
dominant role in the production of the thrust force required...' [p. 343 in
Weihs (Weihs, 1973)] and that
early in stage one the caudal fin produces `...rather large side forces
approximately in the direction of movement...' [p. 348 in Weihs
(Weihs, 1973)]. However, our
data show that the caudal fin plays a relatively small role in stage one and,
in fact, generates momentum as jet one that opposes acceleration of the fish
away from the stimulus. Furthermore, jet one momentum showed no correlation
with escape angular velocity during stage one and, thus, we conclude that
movement of the caudal region of the body does not enhance stage one
performance. However, in other aspects, the measurements of the present study
correspond well with theory. For instance, Frith and Blake recorded C-start
kinematics in pike and, using Weihs's model, estimated that peak forces in
stage two range from 2.8 to 8.7x greater than those in stage one
(Frith and Blake, 1995). Since
they had relatively few C-starts compared with the number analyzed in this
study, it is not surprising that our maximal performance is also greater
(Adolph and Pickering, 2008).
Additionally, their estimates of the force produced by the dorsal and anal
fins, again based on Weihs's model (Frith
and Blake, 1991), support our argument for the importance of these
fins.
Future comparative analyses
The existing literature on fish C-start escape responses contains kinematic
data from a wide diversity of species and ontogenetic stages, and includes
data on elongate fishes such as pike and bichirs
(Hale et al., 2002;
Tytell and Lauder, 2002;
Westneat et al., 1998), larval
fishes (Eaton and Nissanov,
1985; Gibb et al.,
2006; Hale, 1996),
classically shaped perciform fishes
(Brainerd and Patek, 1998;
Eaton et al., 1988;
Goldbogen et al., 2005;
Jayne and Lauder, 1993;
Wakeling and Johnston, 1999),
sharks (Domenici et al., 2004)
and even species that appear to lack Mauthner neurons
(Hale, 2000). Although a
diversity of fish body shapes have been studied, there is much less
information on the role of the dorsal and anal fins during escape responses
(however, see Eaton et al.,
1977; Frith and Blake,
1991; Webb, 1977).
Fish vary greatly not only in body shape but also in the location and shape of
the dorsal and anal fins along the body
(Drucker and Lauder, 2005;
Standen and Lauder, 2007;
Tytell et al., 2008), and the
location of these fins can have important functional consequences.
Fish dorsal and anal fins are under active muscular control
(Jayne et al., 1996;
Lauder and Madden, 2007) and
generate distinct wake flow patterns that make significant contributions to
locomotor thrust during steady swimming
(Arreola and Westneat, 1997;
Lauder and Madden, 2007;
Standen and Lauder, 2005;
Tytell, 2006;
Tytell et al., 2008). During
escape responses, the dorsal and anal fins are rapidly erected
(Eaton et al., 1977;
Tytell et al., 2008)
increasing their surface area. In addition, active curvature control by fin
ray muscles (Alben et al.,
2007; Geerlink and Videler,
1974; Jayne et al.,
1996; Lauder and Madden,
2007; Lauder et al.,
2006) allows dorsal and anal fins to both actively resist
hydrodynamic loading, and to actively contribute to force generation.
Perciform fishes (like bluegill sunfish) also possess anterior fin spines in
the dorsal and anal fins, and the hydrodynamic consequences of spiny supports
in fins are unknown. Are median fins with spines stiffer during the escape
than the fins of species (such as trout) without spines and, thus, better able
to transmit muscular power to the fluid?
Comparative analysis of hydrodynamics of escape responses will clarify
these questions. The studies of Webb provide a direction for these future
studies. In particular, he compared fast-start performance in seven species of
teleost fishes (Webb, 1978).
Among the fishes he studied, he observed the best fast-start performance in
bluegill sunfish and the worst fast-start performance in yellow perch
(Perca flavescens). He hypothesized that the body form of the
bluegill sunfish, in which the body is dorso–ventrally deep and the
median fins are large, represented the best compromise morphology
(Webb, 1978). The current
study provides a framework for quantitatively evaluating his hypotheses and
determining mechanisms underlying escape performance across multiple species.
Because fishes are under strong selective pressure for effective escape
responses to escape predators (Walker et
al., 2005) or capture prey, such comparative studies will help to
understand the evolution of body and fin morphology across all vertebrate
species.
LIST OF ABBREVIATIONS
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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