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First published online September 14, 2007
Journal of Experimental Biology 210, 3328-3336 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.008292
Timing is everything: coordination of strike kinematics affects the force exerted by suction feeding fish on attached prey
1 Section of Evolution and Ecology, University of California, One Shields
Avenue, Davis, CA 95616, USA
2 Department of Mechanical Engineering, Rochester Institute of Technology,
76 Lomb Memorial Drive, Rochester, NY 14623-5604, USA
* Author for correspondence (e-mail: raholzman{at}ucdavis.edu)
Accepted 17 July 2007
| Summary |
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13 ms), the forces
recorded were brief (
12 ms from initiation to peak force), and force
magnitude declined rapidly after peak force. Statistical analysis indicated
that rate of buccal expansion, and prey size, but not strike initiation
distance, significantly affected peak force. These observed variables were
used with results from flow visualization studies to estimate the flow at the
prey's location, which allowed the calculation of drag, pressure gradient
force and acceleration reaction force. The relationship between these
calculated forces and the measured forces was strong, indicating that the
model can be used to estimate forces from strike kinematics. This model was
then used to study the effects of strike initiation distance on peak force and
on the rate of increasing force. Comparisons of model output to empirical
results indicated that bluegill time their strike so as to exert an average of
70% of the peak possible force on the prey, and that the observed strike
initiation distance corresponded to the distance that maximized modeled force
on an attached prey. Our results highlight the ability of bluegill to produce
high forces on their prey, and indicate that precision and visual acuity play
important roles in prey acquisition, beyond their recognized role in prey
detection.
Key words: Lepomis macrochirus, kinematics, prey capture, strike performance accuracy, suction feeding, force
| Introduction |
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The flow produced by suction feeding fishes is used to exert force on an
object outside their physical reach. Bluegill Lepomis macrochirus are
capable of generating flows as fast as 2.5 m s–1
(Day et al., 2005
;
Higham et al., 2006a
). Flow
speed in this species is correlated with the speed of mouth expansion,
increasing with faster times to peak gape (TTPG) and decreasing with distance
from the mouth (Day et al.,
2005
; Higham et al.,
2006a
). During the strike, high flow velocity only persists for
about 10 ms (Day et al., 2005
;
Higham et al., 2006a
).
Moreover, a trade-off exists between the magnitude of peak flow (faster flows
with shorter TTPG) (Day et al.,
2005
) and peak flow duration (longer with longer TTPG).
In order to maximize the forces exerted on the prey by the suction flow,
the predator must precisely coordinate its strikes so that the prey is
positioned near the mouth at the time of highest flow. The ephemeral nature of
the suction flow suggests that the window of time when maximum forces can be
exerted only lasts a few milliseconds. It follows, then, that there will be an
optimal timing and positioning that maximizes the force exerted on the prey.
These optima can differ between individual strikes, which differ in their peak
flow speeds and accelerations, strike initiation distances, the distance
closed between the predator and the prey during the strike, and other aspects
of strike kinematics. While bluegill are consistent in positioning their prey
in the center of the water parcel they engulf during the strike
(Higham et al., 2006a
), it is
not known whether that consistency maximizes the force that is exerted on the
prey.
The role of morphology and size in determining suction feeding performance
has received much attention (Carroll et
al., 2004
; Norton,
1991
; Van Wassenbergh et al.,
2006
). Likewise, it is recognized that predators can modify their
prey capture kinematics in response to prey type
(Coughlin and Strickler, 1990
;
Norton, 1991
;
Wainwright et al., 2001
),
inducing faster buccal expansion when feeding on evasive prey
(Coughlin and Strickler, 1990
;
Wainwright et al., 2001
).
However, previous researchers have not explored the potential synergy gained
from coordination among the kinematic events of the strike with respect to the
forces exerted on the prey.
The objectives of this study were twofold: to measure the force exerted by
a suction-feeding fish on an attached prey and to determine how effective the
fish was at timing the initiation of the strike to maximize the force exerted
on the prey. Forces were measured by allowing the fish to strike on shrimp
attached to a small force transducer. Analyses of strike kinematics were used
to estimate temporal and spatial patterns of water flow, which were used in
calculations of the peak forces that bluegill exert on prey [based on a model
by Wainwright and Day (Wainwright and Day,
2007
)]. That model was subsequently used to calculate the peak
force that would be produced with varying strike initiation distances, in
order to compare the force exerted at the observed distance to that exerted at
the optimal initiation distance. This approach allows us to evaluate the
ability of bluegill to coordinate the timing of the onset of the strike with
the profile of kinematics in each strike in a way that maximizes the force
exerted on the prey item. In this study we focus on a scenario where the prey
does not try to escape from the feeding fish, but instead resists the force
exerted by the suction feeder by gripping the substratum. While encounter
scenarios with free moving prey may result in different strategies by the
predator, the fixed prey situation occurs frequently in nature.
| Materials and methods |
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The prey, live ghost shrimp, were stretched out and their ventral surface was glued with a cyanoacrylate adhesive to a metal wire (0.3 mm in diameter) protruding from a load cell (Futek S-Beam Jr load cell 1 lb, Irvine, CA, USA). The output of the load cell (voltage) was recorded at 5000 Hz on a PC running a custom LabView script through a DAQpad 6070E data acquisition system (National Instruments, Austin, TX, USA). The camera and the load cell were synchronized using an external trigger. Conversion of voltage data to force was based on factory calibration of the load cell, which was verified independently using a series of measured weights before each experimental day. The sensitivity of the load cell, combined with the data acquisition system was 0.001 N in the range of 0–4.44 N.
Video sequences taken during feeding events were downloaded to a PC and
analyzed using ImageJ version 1.33 (NIH, Bethesda, MD, USA). For each
sequence, we analyzed each frame starting
10 frames before the onset of
gape expansion and ending
10 frames after the fish started closing its
mouth (Fig. 2A). For each
frame, the x and y coordinates of the position of the fish's
upper and lower jaw (at their most anterior end) and the prey's eye were
determined. These three landmarks were used to calculate the following
variables: gape distance, the distance between the predator and prey (defined
as the distance between the center of the bluegill's mouth and the eye of the
prey), as well as mouth displacement, defined as the displacement of the
center of the mouth on the predator–prey axis (the imaginary line
connecting the prey and the fish at the initiation of the strike). For each
sequence we also determined the time to peak gape (TTPG), defined as the time
it took the fish to open its mouth from 20% to 95% of the maximal gape
observed during the strike (see Day et al.,
2005
; Sanford and Wainwright,
2002
), the distance between the center of the fish's mouth and the
prey at the time of strike initiation (the onset of gape increase), the size
of peak gape, prey length and maximal prey diameter (maximal height in lateral
view). Peak flow speed at the mouth was estimated for each strike based on the
relationship between TTPG and peak flow speed (see
Day et al., 2005
). The force
measured at each frame was averaged for the three consecutive force readings
at –0.2, 0 and +0.2 ms relative to the timing of the frame (to
temporally coordinate the samples taken by the camera and the force
transducer). Twelve strikes were analyzed for each of the four fish. Strikes
were included in the analyses only if there was no contact between the prey
and the bluegill's jaws prior to mouth closing, and only if the prey remained
attached to the transducer through the strike.
|
Calculations of the forces exerted on a prey item
If the temporal and spatial pattern of water flow is known, along with some
features of the prey item, then the forces exerted by the flow on the prey
item can be calculated (Wainwright and
Day, 2007
). In general, the flow of water around an immersed
object exerts three forces: drag, pressure gradient force and acceleration
reaction (Batchelor, 1967
;
Denny, 1988
;
Wainwright and Day, 2007
).
Drag is exerted due to the movement of the fluid relative to the object
(Batchelor, 1967
;
Denny, 1988
;
Wainwright and Day, 2007
). The
magnitude of drag depends on the prey's drag coefficient and size, and on
relative flow speed squared. Pressure gradient force is the consequence of
spatial and temporal gradients in flow velocity
(Batchelor, 1967
;
Denny, 1988
;
Wainwright and Day, 2007
). In
a suction feeding fish, the flow speed in front of the mouth decreases
non-linearly with the distance from the mouth
(Day et al., 2005
). Therefore,
the upstream end of the prey is located in a region of relatively high flow
velocity, and thus, lower pressure. The pressure gradient force scales with
prey volume and with the magnitude of pressure gradient. The acceleration of
flow around the prey generates an acceleration reaction
(Batchelor, 1967
;
Vogel, 1994
;
Wainwright and Day, 2007
),
which is a function of prey volume and shape (the latter denoted by the
object-specific added mass coefficient), the density of the water, and of the
magnitude of relative fluid acceleration.
A function describing the change in gape as a function of time was fitted
to empirical gape measurements for each individual sequence (see
Muller et al., 1982
). That
function describes gape kinematics using six discrete variables: initial and
peak gape, time of gape initiation and time of peak gape,
(a form
coefficient for the rate of gape increase) and the amount of time spent at
peak gape (Muller et al.,
1982
) (see Table
1). Similar functions were fitted to describe the position of the
mouth as a function of time (mouth displacement) and to describe speed at the
mouth as a function of time (Table
1). Time of flow initiation and peak flow speed were set to equal
the time of 20% and 95% of peak gape (see
Day et al., 2005
). Initial flow
speed was 0, and peak flow speed was estimated based on TTPG using the
relationships found in Day et al. [(Day et
al., 2005
), see their fig. 9] for similar-sized bluegill. The form
coefficient
for flow speed was equated to that of the gape, with no
plateau in flow speed (i.e. flow decreasing after peak flow speed). Forces
were calculated at time increments of 0.03 ms based on the resulting
continuous function fit to the observed kinematics of gape and mouth
displacement (see Table 1 for a
complete list of variables used in the model).
|
The flow in front of the mouth of a suction-feeding fish decreases rapidly
with the distance from the mouth (Day et
al., 2005
; Ferry-Graham et
al., 2003
; Higham et al.,
2006a
; Nauwelaerts et al.,
2007
). Therefore, for an elongate prey positioned with its long
axis normal to the mouth opening (such as our 20 mm shrimp), the flow speed
and acceleration will change as a function of the position along the
anterior–posterior axis. To account for the change in flow pattern along
that axis, we integrated the force along the anterior–posterior axis of
the prey in 2 mm bins, summing the forces that act on the bins at each time
step. The flow speed at each bin was calculated for each time step based on
the distance between the center of the bin and the mouth. The volume and
wetted area for each bin were calculated, assuming a cylindrical shape for
each bin, with a diameter that was a function of the bin's position along the
anterior–posterior axis. For each bin, the wetted area was defined based
on its position; it included the cylindrical envelope in all the bins
(calculated as the product of the bin's circumference and height) and, only
for the proximal and distal bins, the frontal area of the cylinder. For each
shrimp in the experiment, we measured the maximal diameter (maximal height in
a lateral view, Fig. 1) and
estimated the diameter at each bin based on the average proportional height at
that bin. A consensus profile of height vs length of a stretched
shrimp was obtained by measuring the cross-sectional height of five individual
shrimp at multiple locations along the anterior posterior axis.
Drag force, Fd (N), acting on each bin was calculated
as:
![]() |
is the density of the
medium (kg m–3) and FS is the speed of the fluid at
the location of the object (m s–1). For the range of Reynolds
numbers Re=300–10 000 we used the drag coefficient measured for
Euphausia superba (Kils,
1982
0.25–3.6 m s–1) we used empirically determined
drag coefficients that we measured for live tethered shrimp,
Palaemonetes, in a flume under conditions of steady, uniform flow
over a range of flow speeds (see Denny et
al., 1985
Pressure gradient force (Fpg) was calculated as:
![]() |
Acceleration reaction force (Far) was calculated as:
![]() |
is the
density of the medium (kg m–3) and a is the
acceleration of the water surrounding the prey (m s–2). The
coefficient of added mass, Cam, was estimated based on our
measured forces, by calculating expected force with added mass coefficients
ranging from 0.3 to 1.0 [the range of Cam often measured
for marine invertebrates (Daniel,
1984
The contribution of the transducer's rod to the observed forces was
estimated by calculating the force exerted on a bare rod located in front of
the fish, using the observed fish kinematics. The rod was treated as a 100 mm
long cylinder, 0.3 mm in diameter, with its proximal end 4 mm posterior to the
original location of the prey's eye. Drag and added mass coefficients were
taken from Vogel (Vogel,
1994
). The total calculated force was 2.6% (± s.d.=1.6%) of
the total force exerted on the prey. Our force measurements (observed values)
were corrected accordingly.
Simulations
To test whether bluegill optimally positioned the prey relative to their
mouth in each strike, we calculated the force that would have been exerted on
the prey had the strike been initiated (and ended) at a range of different
distances. For each strike, we used the observed kinematics (gape and mouth
displacement, as well as prey size and peak flow velocity), but varied the
strike initiation distance from 0.5 to 20 mm in 0.5 mm increments
(corresponding to the observed range of strike initiation distances; see
results). We then compared the observed strike starting distance with the
distance that yielded the maximal simulated force, and calculated the ratio
between the observed peak force and the maximal potential force (hereafter
defined as `force efficiency').
It could be that the fish were expecting the prey to dismount from the rod
to which they were glued. Thus, the fish may have been coordinating their
strikes to optimize the forces exerted on free (rather than an attached) prey.
To test this alternative hypothesis, we modeled the force exerted on a free
shrimp, for strikes starting at the same range of strike initiation distance
(0.5–20 mm), using the observed kinematics of the fish. The path of the
prey, however, was simulated as that of an unattached prey by calculating the
expected movement of the prey according to the prey's mass and the force
exerted on the prey at each time step (see
Wainwright and Day, 2007
). The
distance yielding the highest force on the simulated `free' prey was compared
to the observed distance, and the force efficiency was also calculated.
Statistical analysis
Since we repeatedly measured the force exerted by four fish, these
observations cannot be considered independent. The correspondence between
observed values of peak force and those calculated based on the model was
assessed using repeated-measures (RM) ANOVA
(Rao, 1998
) with fish as
subjects, the difference between observed and calculated force for each strike
as the dependent variable and strike sequential number as repeated-measure
factor. A significant deviation between the model's results and observed
forces was interpreted if the least square mean of the difference was
significantly different than 0. A similar analysis was performed to test the
relationship between observed and calculated time of peak forces. As an
indicator for the model's precision in predicting the force on the prey, we
also report the average slope and R2 of regression between
the magnitude and timing of the observed and calculated force (as well as
other variables), made separately for each of the four fish used in the
experiment. Note that these statistics should be viewed as descriptive
statistics, since repeated force measurements for each fish are not
independent. The deviation of each observed strike initiation distance from
the distance associated with maximum potential force (calculated from our
simulations) was used as a metric of `strike precision'. Variation in strike
precision for fixed and free prey was tested using RM-ANOVA with fish as
subjects, strike precision as the dependent variable and strike sequential
number as the repeated-measured factor. If no difference in precision between
the four fish was observed, the overall least square mean was taken as the
measure of strike precision. The sphericity assumption was verified prior to
running RM-ANOVA. Linear regression is reported after verifying normal
distribution of the residuals. All the parametric and non-parametric tests
were performed using JMP IN version 5.0 (SAS institute, NC, USA).
| Results |
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Comparisons with calculated forces
While TTPG and prey length affected the magnitude of peak force in a
multiple linear regression (see above), this linear model ignores possible
non-linear effects of the independent variables on the force, which can be
derived from theory. Therefore, we studied the effect of the kinematic
variables using a mechanistic model
(Wainwright and Day, 2007
).
The magnitude and timing of the observed forces exerted on the tethered
shrimps were in good agreement with those expected based on the model
(Fig. 5A,B). The average
deviation between the timing of the observed and calculated peak forces was
not significantly different from 0 (average 2.2±0.83 ms; indicated by
the overall least square mean in RM-ANOVA; F1,3=3.76,
P>0.15). There was no effect of strike order (sequential number)
on the difference in timing of observed and expected peak force (RM-ANOVA;
F11,33=1.03, P>0.45). Similarly, the average
deviation between the magnitude of the peak observed and calculated forces was
not significantly different from 0 (average –0.012±0.135 N;
indicated by the overall least square mean in RM-ANOVA;
F1,3=0.45, P>0.54) with no effect of strike
order (sequential number) on the difference in magnitude between observed and
expected force (RM-ANOVA; F11,33=0.9, P>0.54).
Calculated peak forces exerted on prey were strongly correlated with observed
forces (average R2=0.59±0.07; N=4 fish;
Fig. 5B) and the average slope
was 0.78±0.1 (N=4 fish). Similarly, the timings of the
observed and calculated peak forces were linearly correlated (average
R2=0.78±0.06; N=4 fish;
Fig. 5A) and the average slope
was 0.89±0.09 (N=4 fish).
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The strongest force exerted on the shrimp was the pressure gradient force (65.7±1.6% of the force at the time of peak force; Fig. 6), followed by acceleration reaction force (32.9±3.3%) and drag force (1.4±3.3%). Thus, fast acceleration of the water in front of the mouth has a much stronger effect on force than the fluid speed. Peak drag occurred 4.1 ms (±3.5 ms) after peak force, while pressure gradient force and acceleration reaction peaked simultaneously at 0.3±1.4 ms before peak force (Fig. 6).
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In addition to peak force, fish could potentially maximize the rate of increasing force, defined as the slope of increasing force from force onset to peak force. Although the strike initiation distance that resulted in maximum slope was correlated with the distance of maximal force, the latter was closer to the mouth, and the fit between the observed distance and that corresponding to the highest slope was weak (average R2=0.33±0.1; N=4 fish).
To test the hypothesis that the fish were optimizing their kinematics for a
free-swimming prey, rather than attached prey, we calculated the distance
associated with the highest force for such prey. As in the case of attached
prey, altering strike initiation distance resulted in a concave response of
peak force (data not shown). Maximal peak force exerted on the prey in this
scenario was much lower than that on attached prey, because the prey was
modeled to move with the water [hence the relative acceleration and speed are
small (Wainwright and Day,
2007
)]. The distance associated with maximal force exerted on a
free prey was (on average) 85±20% longer than that observed, with a
higher deviation (5.5±3.0 mm, intercept in RM-ANOVA significantly
different than 0; F1,3=120, P<0.001) and a
poorer fit with the observed distance (average
R2=0.26±0.1; N=4 fish). Strike efficiency,
however, was similar to that of attached prey (0.71±0.09).
| Discussion |
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The observed strike starting distance was correlated with the distance
associated with highest force exerted on an attached prey, but not on a free
prey. This comparison indicates that the fish, being trained to feed from the
transducer, adapted their kinematics according to this feeding mode. Moreover,
different prey behaviors (attached and free prey) result in different
solutions that optimize the force on the prey, because the trajectory of the
prey during a strike is different. Bluegill are also known to encounter prey
that display escape responses [such as copepods and shrimps
(VanderKooy et al., 2000
)]
that are triggered by the hydromechanical disturbances created by the suction
feeding fish (Arnott et al.,
1999
; Fields and Yen,
1997
). Both the bow wave in front of the approaching fish and the
slower flow produced during the early stages of the strike can stimulate an
escape response from the prey. In this situation, the relative velocity,
escape trajectory and timing of the response can be critical in determining
the outcome of the interaction (Howland,
1974
). For example, the optimal strike starting distance can be
expected to vary according to the prey's sensitivity and the timing of its
escape response. However, investigation of interactions between fish and their
prey often ignore the effect of suction forces on the prey's trajectory (e.g.
Arnott et al., 1999
;
Fields and Yen, 1997
;
Howland, 1974
;
Weihs and Webb, 1984
).
Morphological adaptations that are used to increase intra-oral pressure
(and thereby fluid speed) in centrarchids include an increase in the cross
section area of epaxial muscles, changes in the lever system that controls the
rotation of the neurocranium (Carroll et
al., 2004
), and reduced mouth size
(Carroll et al., 2004
;
Wainwright and Day, 2007
).
Behavioral modifications recognized to enhance the forces exerted by suction
feeders have previously been limited to increased flow by increasing the rate
of buccal expansion (Day et al.,
2005
; Wainwright and Day,
2007
). Under the same rate of buccal expansion (i.e. same flow
speed at the mouth) the effects of head kinematics on either intra-oral
pressure (Nemeth, 1997
) or
modeled flow speed outside the mouth (Van
Wassenbergh et al., 2006
) have been considered insignificant,
except for the timing of opening the opercular slits
(Van Leeuwen and Muller,
1984
). However, the fact that there is a fivefold range in force
exerted on the prey in strikes with a similar strike effort and flow speed may
indicate the ability to generate high flow speed is insufficient to exert high
force on the prey. Proper positioning of the prey in the narrow region of high
flow speed in front of the mouth, during the short time period in which high
flow persists, may also be required to optimize the effects of the flow on the
prey. Modulation of strike kinematics, through strike starting distance or the
extent of mouth displacement, are possible ways by which suction feeding fish
can optimize their performance. Throughout our experiments, strikes performed
by the same fish on the same prey frequently showed very different kinematics.
Even though experimental conditions were fixed, convergence for a single
solution was not observed. This observation may indicate that there is more
than one solution for an optimized strike at any given strike effort. However,
the chosen kinematics appears to be a non-random subset, coordinated with
initiation distance and prey behavior.
The concave response of maximal peak force with increasing strike
initiation distance (Fig. 7 for
attached prey; similar results for free prey not shown), supports the
hypothesis of a strike-specific position of maximal efficiency, spanning only
a few mm. Gauging the initiation distance of the strike is likely to involve
visual feedback and may be an underappreciated function of vision in suction
feeders. The keen visual acuity of bluegill relative to other centrarchids has
previously only been linked to prey detection (e.g.
Hairston et al., 1982
;
Hawryshyn et al., 1988
).
In this study we were able to accurately predict the forces exerted on the
prey, based on a suite of kinematic measurements (jaw kinematics and the
distance from the prey). This was possible due to the tight link between
kinematics and flow speed in front of the bluegill's mouth
(Day et al., 2005
) and our
understanding of the nature of the forces exerted on an object in a suction
feeding flow (Wainwright and Day,
2007
). It is a major goal in organismal biomechanics to measure
the forces that are exerted on animals during locomotion and feeding (e.g.
Peng et al., 2007
;
Van Wassenbergh et al., 2006
;
Vogel, 1994
). For animals in a
fluid environment, however, it is usually difficult to measure these forces
directly. Here we took advantage of the presence of a prey in the flow field
to combine fluid mechanical calculations with empirical measurements, and to
further use the mechanics to test the fish's performance in an ecologically
relevant scenario. The current understanding of the effect of water flow on
the prey can be used to calculate the forces exerted on prey in other
scenarios, such as escaping prey, neutrally buoyant detached prey or heavy
attached prey. These are all ecologically relevant scenarios, which may
represent a fish striking on an escaping shrimp, a fish egg, and a snail,
respectively. This model can also be used to examine the effects of
inter-specific morphological and behavioral variability on suction feeding
performance, a highly time consuming and demanding task if approached by
empirical methods.
The force exerted by an aquatic suction feeding fish on its prey was measured here for the first time. As a suction feeding specialist, bluegill carefully time their strike and exert high, abrupt forces on their prey. Future research can now begin to make comparisons of the ability of different species to exert force on their prey, and because these forces depend intimately on the details of prey capture kinematics, suction feeding is emerging as a model behavior in which the ability of organisms to coordinate aspects of their movement can be directly and mechanistically tied to performance.
| Acknowledgments |
|---|
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|---|
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|---|
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