Integrative and Comparative Biology...understanding the influence of copepods’ behavior in...
Transcript of Integrative and Comparative Biology...understanding the influence of copepods’ behavior in...
SYMPOSIUM
Copepods’ Response to Burgers’ Vortex: DeconstructingInteractions of Copepods with TurbulenceD. R. Webster,1,* D. L. Young* and J. Yen†
*School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA; †School of
Biology, Georgia Institute of Technology, Atlanta, GA 30332, USA
From the symposium ‘‘Unsteady Aquatic Locomotion with Respect to Eco-Design and Mechanics’’ presented at the
annual meeting of the Society for Integrative and Comparative Biology, January 3–7, 2015 at West Palm Beach, Florida.
1E-mail: [email protected]
Synopsis This study examined the behavioral response of two marine copepods, Acartia tonsa and Temora longicornis, to
a Burgers’ vortex intended to mimic the characteristics of a turbulent vortex that a copepod is likely to encounter in the
coastal or near-surface zone. Behavioral assays of copepods were conducted for two vortices that correspond to turbulent
conditions with mean dissipation rates of turbulence of 0.009 and 0.096 cm2 s�3 (denoted turbulence level 2 and level 3,
respectively). In particular, the Burgers’ vortex parameters (i.e., circulation and rate of axial strain rate) were specified to
match a vortex corresponding to the median rate of dissipation due to viscosity for each target level of turbulence. Three-
dimensional trajectories were quantified for analysis of swimming kinematics and response to hydrodynamic cues. Acartia
tonsa did not significantly respond to the vortex corresponding to turbulence level 2. In contrast, A. tonsa significantly
altered their swimming behavior in the turbulence-level-3 vortex, including increased relative speed of swimming, angle
of alignment of the trajectory with the axis of the vortex, ratio of net-to-gross displacement, and acceleration during
escape, along with decreased turn frequency (relative to stagnant control conditions). Further, the location of A. tonsa
escapes was preferentially in the core of the stronger vortex, indicating that the hydrodynamic cue triggering the dis-
tinctive escape behavior was vorticity. In contrast, T. longicornis did not reveal a behavioral response to either the
turbulence level 2 or the level 3 vortex.
Introduction
The interactions between small biological organisms
and turbulence remain fascinating and mysterious to
biological oceanographers. For example, studies by
Rothschild and Osborn (1988), Saiz and Kiørboe
(1995), and Incze et al. (2001) raised puzzling
open-ended questions regarding the effect of the hy-
drodynamic forcing imposed on small organisms,
such as copepods, due to the turbulent flow field
they inhabit. It is known that copepods are of similar
size to the Kolmogorov microscale in coastal-zone
turbulence (Jimenez 1997) and that they typically
swim at speeds on the order of the fluid’s fluctuating
velocity (Yamazaki and Squires 1996). Therefore,
transport and behavior of copepods are linked by
similar scales to finescale fluctuations in velocity of
turbulence in coastal and near-surface environments.
It is likely that the effects of turbulence on copepods’
behaviors, such as feeding rate, growth rate, and
predator–prey interaction, are species-specific
(Dower et al. 1997; MacKenzie 2000; Marrase et al.
2000; Peters and Marrase 2000), which indicates that
fully understanding the interaction of zooplankters
and turbulence will prove to be an arduous task
(e.g., Jonsson and Tiselius 1990; Saiz and Alcaraz
1992; Visser et al. 2001; Saiz et al. 2003; Galbraith
et al. 2004; Lewis 2005). One observation of turbu-
lence affecting behavior was the species-specific ver-
tical distribution of copepods, seemingly in response
to the distribution of the intensity of turbulence
within the water column (Heath et al. 1988; Haury
et al. 1990; Mackas et al. 1993; Lagadeuc et al. 1997;
Incze et al. 2001; Visser et al. 2001; Manning and
Bucklin 2005). It is relatively intuitive to grasp that
the physical forcing of turbulence could mediate the
vertical distribution of copepods via advection, but,
Integrative and Comparative BiologyIntegrative and Comparative Biology, volume 55, number 4, pp. 706–718
doi:10.1093/icb/icv054 Society for Integrative and Comparative Biology
Advanced Access publication May 21, 2015
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understanding the influence of copepods’ behavior in
response to hydrodynamic cues (associated with the
fluctuation of the velocity of turbulence) on the ver-
tical distributions of copepods is less obvious and
very challenging to quantify.
To tackle this formidable topic, one must first
appreciate how copepods collect sensory information
from the surrounding environment, specifically, how
they detect the hydrodynamic cues associated with
fluctuations in velocity. To detect hydrodynamic sig-
nals, copepods possess an array of mechanosensory
hairs, called setae, on many of their appendages
(note that copepods do not possess statocysts).
These setae are most numerous and most sensitive
along the antennae (Yen and Fields 1992; Boxshall
et al. 1997; Fields et al. 2002). Setae bend in response
to differences in velocity between the animal and the
ambient fluid. The sensitivity of copepods to hydro-
dynamic cues is truly impressive. For example, Yen
et al. (1992) reported that copepods detect displace-
ments as small as 10 nm, and Woodson et al. (2005,
2007a,2007b) reported sensitivities to strain rate as
low as 0.025 s�1. Several studies have attempted to
isolate the specific hydrodynamic cues that elicit cer-
tain responses by copepods, with the majority of
them concluding that strain rate is the cue that elicits
an escape response (Haury et al. 1980; Fields and
Yen 1997; Kiørboe et al. 1999; summarized in
Woodson et al. 2014).
The nature of turbulence presents unique chal-
lenges to researchers who wish to form a mechanistic
connection between flow and behavior. Turbulent
flows are characterized by (among other things)
their random and unpredictable nature. Further,
the fluctuations in velocity are intermittent, which
appears as infrequent, but extreme, peaks and
troughs both in the time-record of velocity of flow
and in the difference in flow velocity between neigh-
boring locations (at the same time). This presents
enormous challenges to researchers wishing to per-
form behavioral assays of organisms, such as cope-
pods, in a turbulent flow. One cannot be sure when
the organism will swim through the experimental
control volume and there is no way to anticipate
the instantaneous velocity in a turbulent flow.
Therefore, time-resolved three-dimensional data on
velocity must be constantly acquired throughout
the behavioral assay. Furthermore, many behaviors
that are of interest (such as escape jumps of cope-
pods) are relatively infrequent events, and the events
must occur within the experimental control volume
while data on velocity are being collected (such that
the hydrodynamic cues triggering the event are
quantified). Compounding this issue is the fact that
experimental techniques for imaging flows that allow
time-resolved collection of three-dimensional data on
velocity, such as tomographic particle image veloci-
metry (Tomo-PIV), have a limited range of scales
that necessitates a relatively small measurement
volume to meet resolution requirements around the
zooplankton (Murphy et al. 2012). Continuously
taking data on flow, while waiting for an animal to
swim through the necessarily small control volume
and perform an infrequent escape jump (or other
modifications of behavior) is a recipe for countless
hours of behavioral assays to acquire even a few
quantified behavioral events. Acquiring enough
data-points in this scenario to statistically test hy-
potheses is a monumental task.
The present study took an alternate approach and
employed a laboratory apparatus to create a Burgers’
vortex (Jumars et al. 2009) in order to perform be-
havioral assays of copepods swimming in and around
a turbulent-like vortex. The Burgers’ vortex was an
ideal model because the swirling and straining mo-
tions (see Fig. 1) closely match the characteristics of
turbulent vortices in the dissipative range (Webster
and Young 2015). The goal was to test the hypothesis
that the copepods Acartia tonsa and Temora long-
icornis sense hydrodynamic cues related to vortices
in turbulent flows and actively respond via changes
in swimming kinematics.
Fig. 1 Sketch of fluid motion in the Burgers’ vortex. Fluid moves
radially-inward toward the axis while stretching outward in the
axial direction. Fluid is also rotating in a counterclockwise sense
around the axis. The combination of these motions creates
streamlines that resemble a three-dimensional spiral (not
illustrated).
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Materials and methods
Collection and maintenance of copepods
Acartia tonsa were collected off the coast of Maine,
USA, in July 2013 and subsequently shipped over-
night to Georgia Tech in Atlanta, GA, USA. Temora
longicornis were similarly collected off the coast of
Maine, USA, in September 2013 and shipped over-
night to Georgia Tech. Upon arrival, the copepods
were placed in a coldroom at 128C at low population
densities and fed a mixed diet of Tetraselmis spp. and
Rhodomonas lens. The buckets were aerated to main-
tain a reasonably high concentration of dissolved
oxygen.
Burgers’ vortex apparatus
Trials were conducted in the Burgers’ vortex appara-
tus described by Webster and Young (2015).
Following Jumars et al. (2009), the approach was
to reduce the stochastically varying nature of turbu-
lent flows to a simple vortex model. Direct numerical
simulation (DNS) experiments indicated that micro-
scale turbulence could be described as a writhing
tangle of vortex ‘‘worms’’ (Yokokawa et al. 2002).
Further, numerical simulations by Hatakeyama and
Kambe (1997) indicated that an ensemble of Burgers’
vortices under the right conditions could accurately
mimic flow characteristics of isotropic turbulence.
Combining these concepts, Jumars et al. (2009) pre-
sented a method for mimicking a single turbulence
vortex ‘‘worm’’ with a Burgers’ vortex. Such an ap-
proach had the advantage of eliminating the
temporally variable and random nature of the flow,
and the approach facilitated examination of the
mechanistic aspects of the interaction of plankton
with a turbulent-like vortex.
The apparatus consisted of a clear acrylic tank
with outer dimensions of 20.64 cm (W)� 20.64 cm
(L)� 27.31 cm (H). A mimic of a Burgers’ vortex
was created in the tank via two co-rotating discs
with a hollow driveshaft through which fluid was
drawn out of the tank (Webster and Young 2015).
Specific conditions of vortex flow were targeted
based on previous observations of behavior of
copepods. Yen et al. (2008) observed a significant
behavioral transition for Acartia hudsonica and
T. longicornis between their turbulence-level-2
(h"i¼ 0.009 cm2 s�3) and turbulence-level-3
(h"i¼ 0.096 cm2 s�3) treatments in an isotropic-
turbulence generator. In particular, the motility
number, which is the ratio of copepod transport
speed over r.m.s. of the fluctuations in velocity of
turbulent fluid, was significantly different between
the level-2 and level-3 treatments. The motility
number provided a measure of the zooplankton’s
ability to swim against, rather than be advected by,
the motion of the fluid. Gallager et al. (2004) re-
ported a critical value of 3 for the motility
number: for values more than 3 copepods were
able to aggregate, whereas for values less than 3 co-
pepods did not aggregate, which suggests that they
were unable to swim and orient effectively against
the motion of the fluid. Further, Yen et al. (2008)
observed a transition across the critical value of the
motility number of 3 for the conditions of level-2
and level-3 turbulence. As a result, we targeted
these turbulence conditions during the design of
the Burgers’ vortex apparatus. Webster and Young
(2015) described the procedure for defining the pa-
rameters associated with a typical dissipative vortex
for the target conditions and fully described the flow
fields via Tomo-PIV. The targeted conditions of tur-
bulence and the corresponding characteristics of
the vortex are summarized in Table 1. Note that
the fluctuating velocities, urms, were comparable to
the range reported by Yamazaki and Squires (1996).
Collection of data on behavioral assays
Behavioral assays were conducted with a mixed-sex
population of 250 A. tonsa (length¼ 0.9 mm) and a
separate mixed-sex population of 150 T. longicornis
(length¼ 1.6 mm). Note that the sizes of the organ-
isms were very similar to the Kolmogorov microscale
for each level of turbulence (Table 1). Each behav-
ioral assay included four stages. Stage 1 consisted of
a 30-min period to allow the animals to become ac-
climated to the tank. Stage 2 was a 55-min period of
Table 1 Summary and comparison of flow parameters
Parameter Turbulence level 2 Turbulence level 3
Target Measured Target Measured
h"i (cm2 s�3) 0.009 — 0.096 —
TKE (cm2 s�2) 0.12 — 0.82 —
� (mm) 1.0 — 0.57 —
urms (mm s�1) 2.8 — 7.5 —
rB (mm) 8.1 7.5 4.6 4.9
a (s�1) 3.2� 10�2 4.2� 10�2 9.9� 10�2 10.0� 10�2
� (cm2 s�1) 1.4 1.5 2.2 1.7
Notes: Target values for mean dissipation rate h"i, turbulent kinetic
energy TKE, Kolmogorov microscale �, and r.m.s. of the fluctuations in
velocity urms are from the isotropic turbulence generator described
by Webster et al. (2004). The characteristic vortex radius rB, axial
strain rate parameter a, and circulation parameter � compare favor-
ably between the target turbulent vortex and the flow generated in
the Burgers’ vortex apparatus. Data adopted from Webster and
Young (2015).
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recording under conditions of stagnant flow to ob-
serve the copepods’ behavior in the absence of hy-
drodynamic stimuli—hereinafter referred to as the
‘‘control’’. Stage 3 was a 30-min period for the es-
tablishment of Burgers’ vortex flow to allow the
Burgers’ vortex to reach the prescribed steady-state
conditions. The fourth stage consisted of a 55-min
period of recording the behavior of the copepods in
the presence of the Burgers’ vortex—hereinafter re-
ferred to as the ‘‘treatment’’. This procedure was
repeated twice for each strength of Burgers’ vortex,
for a total of four runs for each species (since each
run consists of collecting data for one control and
one treatment).
Pulnix cameras (JIA Inc.), with a resolution of
720� 480 pixels, recorded the copepods’ positions
from the front and bottom perspectives (Fig. 2).
The front camera was equipped with a 60-mm
Nikon lens and the bottom camera was equipped
with a 24-mm Nikon lens. Each camera recorded
images at 30 Hz via a Digital Video Cassette
Recorder (Sony model GV-D900 NTSC) that re-
corded the footage on 60-min miniature digital
video cassettes (Mini-DVs). The cameras were fo-
cused on the region surrounding the rotating discs
within the Burgers’ vortex apparatus, with roughly
equivalent viewing windows of 9 cm� 7 cm.
Illumination of the tank was provided by two near-
infrared fiber-coupled diodes (CVI Melles Griot
model 57PNL054/P4/S, 660 nm, 22 mW) (Fig. 2).
Processing of data on behavioral assays
All recordings were converted to digital files (down-
sampled to 15 Hz). As a first step, the copepods in
the recording from the front camera were tracked
manually in DLTdv5, a Matlab particle tracking soft-
ware developed by Hedrick (2008). Second, using the
common spatial coordinate and time-stamp, trajec-
tories in the bottom camera were matched to those
from the front camera. Matches were considered
‘‘high-quality’’ if the trajectories exceed 70 frames
in length and the match was quite certain. The tra-
jectories from the front and bottom perspectives
were combined to form a fully three-dimensional
time-resolved track (examples shown in Fig. 3). To
obtain the velocity and acceleration of the copepod
at each instant in time, calculations of finite differ-
ence (i.e., central-difference method) were performed
on the data on copepods’ positions.
For the treatments, the copepods’ trajectories and
experimental data on velocity (Webster and Young
2015) were aligned in a common frame of reference.
At each time-step, the flow velocity at the copepod’s
position was calculated via a trilinear interpolation
function by weighting the contributions from the
eight neighboring data-points on velocity.
Seven parameters are reported here to define co-
pepods’ swimming behavior in and around the
Burgers’ vortex flow. First, relative swimming speed
quantified how fast the copepod was moving relative
to the local flow velocity. Second, turn frequency
quantified the number of times per second the co-
pepod changed its directional heading by more than
208. Third, net-to-gross displacement ratio (NGDR)
quantified the straightness of the path. For reference,
a NGDR of 1 corresponded to a perfectly straight
line, and a NGDR of 0 referred to a trajectory that
ended at the exact position as it began. When com-
paring values of NGDR, it was critical to compare
trajectories of the same length of time (or same dis-
placement) since NGDR was dependent on scale
(Tiselius 1992). Thus, to ensure unbiased results,
each copepod’s trajectory was divided into 3-s sub-
trajectories before computing the NGDR. The results
were insensitive to the selection of the period of the
sub-trajectories in the range of 1–4 s. The fourth pa-
rameter was the alignment of the trajectory with the
axis of the vortex, which corresponded to the angle
between the copepod’s heading and the axis of rota-
tion of the Burgers’ vortex. An angle of 08 indicated
the trajectory was parallel to the axis of the vortex,
whereas an angle of 908 was orthogonal. The fifth
parameter was the number of escapes per copepod
per 5 s, which provided a normalized measure of
the copepod frequency of escape. In this study, a
‘‘copepod escape’’ was systematically defined as any
instance of the copepod’s acceleration equaling or ex-
ceeding twice the mean acceleration of the copepod.
Fig. 2 Schematic of the camera and lighting arrangement (from
side perspective), as well as the region of interest (ROI) sur-
rounding the Burgers’ vortex.
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The sixth behavioral parameter was the ‘‘escape-
jump location’’, i.e., the radial distance from the
axis of the vortex to the location of an escape
jump. The seventh behavioral parameter was the
magnitude of the escape acceleration.
Statistical analysis
The copepods’ behavioral data for control-versus-
treatment cases were statistically compared using
one-way single-factor (two-level) repeat-measures
ANOVA (Zar 1999). The factor of interest was the
presence of the Burgers’ vortex or not, and the two
levels within that factor were the two replicates. The
null hypothesis, H0, was that the means of the two
datasets were equal. The replicates were nested inside
of the turbulence-level effect and tested for signifi-
cance. If there was no effect of the replicate on the
data, then the data of the two replicates were pooled.
This statistical analysis was performed on each of the
behavioral parameters introduced above. A post hoc
correction for false discovery rate was employed to
remove the potential for false significance (Type 1
error) that could result from a high number of sta-
tistical tests (Benjamini and Hochberg 1995). A two-
sample Kolmogorov–Smirnov test was performed on
each of the pairs of distributions of escape locations
(control versus treatment). To perform this analysis,
the bins of these distributions were uniformly scaled
such that they summed to one (i.e., they represented
an empirical PDF) and then converted to CDFs.
Results
Recall that the flow conditions, which were
denoted turbulence level 2 and level 3, were selected
because the behavioral data on copepods published
by Yen et al. (2008) indicated a significant change
in copepods’ motility number between their isoto-
pic turbulence-level-2 and level-3 trials. We hypoth-
esized that the change was due to a behavioral
response to the finescale structure of the turbulent
vortices.
Acartia tonsa
Turbulence-level-2 behavioral assays
Table 2 shows the behavioral parameters for A. tonsa
for the turbulence-level-2 cases: control A and B and
treatment A and B, where A and B signify the rep-
licate. Overall, the data for turbulence level 2 ap-
peared inconclusive. The relative swimming speed
and NGDR both significantly changed between con-
trol and treatment. Although the effect of the treat-
ment on these two parameters was significant, this
result was not definitive, as the replicate effect was
also significant. Neither the treatment nor the repli-
cate were significant for the escapes per copepod per
5-s period, the alignment of the trajectory with the
axis of the vortex, or the mean turn frequency. The
mean acceleration of escapes appeared to signifi-
cantly change, but only the effect of the replicate
was significant. Therefore, this statistical result was
due to the drastic difference between replicates A and
B, rather than an effect of the treatment.
Figure 4 shows the normalized histograms of
escape jump location as a function of radius. The
histograms were normalized by the effective area of
each bin: each bin represented an annulus in physical
space (hence the area was a function of radius). As
such, the histograms graphically represented the
escape jump density as a function of radial position.
Figure 4a did not show a clear preferred escape
jump location for either turbulence-level-2 control-
replicate A or B (disregarding the spike at a radius of
approximately 17.5 mm for control replicate B). This
result was to be expected; no flow was present in the
tank during the control cases; therefore there were
no hydrodynamic cues to trigger an escape jump.
Figure 4b revealed no obvious trend in the distribu-
tion of escape densities for turbulence level 2. The
results of the Kolmogorov–Smirnov tests were incon-
sistent; replicate A indicated a significant difference
(P50.05) between control and treatment and repli-
cate B showed no significant difference. Therefore,
the density of escape jumps for A. tonsa in the pres-
ence of a turbulence-level-2 vortex varied very little,
if at all, from the escape-jump density for copepods
in stationary fluid.
Fig. 3 Three examples of trajectories of Acartia tonsa swimming
in and around the turbulence-level-3 vortex. The vortex is rep-
resented by the cylinder with radius equal to the characteristic
radius of the Burgers’ vortex rB. Symbols indicate locations sep-
arated by 10 time points. Although shown on the same plot,
these trajectories were not simultaneously recorded during the
experiment. (This figure is available in black and white in print
and in color at Integrative and Comparative Biology online.)
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Turbulence-level-3 behavioral assays
The statistical analysis of A. tonsa for the behavioral
data at turbulence level 3 revealed much clearer
trends. There was a significant effect of treatment
on the relative swimming speed, turn frequency,
alignment of the trajectory with the axis of the
vortex, NGDR, and escape-acceleration parameters.
In each case, there was no significant replicate
effect (Young 2014). Neither the treatment nor the
replicate was significant for the number of escapes
Fig. 4 Normalized histograms of escape jump locations for Acartia tonsa as a function of radius for the turbulence-level-2 (a) control,
and (b) treatment, and turbulence-level-3 (c) control, and (d) treatment. The dashed line indicates the characteristic radius of the
Burgers’ vortex rB.
Table 2 Variables of swimming kinematics for Acartia tonsa for the turbulence-level-2 treatment
Parameter Control A Treatment A Control B Treatment B Treatment effect Replicate effect
F-ratio P-value F-ratio P-value
n 60 65 58 55
Relative speed [mm s�1] (SE) 4.3 (0.32) 4.7 (0.24) 2.6 (0.30) 4.1 (0.27) 11.9 0.0021* 8.8 0.0008*
Turn frequency [turn ind�1 s�1] (SE) 0.89 (0.020) 0.86 (0.015) 0.87 (0.019) 0.88 (0.017) 0.20 0.66 0.84 0.47
Alignment of the trajectory to
the axis of the vortex [8] (SE)
63.7 (1.5) 66.2 (1.1) 61.1 (1.4) 63.4 (1.2) 3.5 0.13 2.3 0.15
NGDR (SE) 0.41 (0.031) 0.65 (0.023) 0.52 (0.029) 0.62 (0.026) 38.3 0.0012* 4.2 0.039*
Number of escapes per copepod
per 5-s period (SE)
0.017 (0.00089) 0.014 (0.00086) 0.014 (0.00091) 0.014 (0.00093) 2.1 0.20 2.4 0.15
Escape acceleration [mm s�2] (SE) 206 (9.7) 180 (9.4) 149 (9.8) 191 (10.1) 0.66 0.49 8.9 0.0012*
Notes: ANOVA results are reported for the effect of treatment (i.e., treatment versus control) and replicate (i.e., A versus B). *P50.05.
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per copepod per 5-s period (Young 2014). These
findings indicated that the replicate did not signifi-
cantly affect the turbulence-level-3 dataset and there-
fore allowed pooling of the data (i.e., combining
replicates A and B).
The ANOVA results for the combined dataset are
shown in Table 3. Turbulence level 3 resulted in
clearly defined changes in copepods’ swimming kine-
matics from control to treatment. Acartia tonsa swam
substantially faster relative to the velocity of ambient
flow in the presence of the turbulence-level-3 vor-
tex (significantly greater mean relative speed of
swimming in the treatment than in the control).
They swam in a straighter path in the presence of
turbulence-level-3 vortex (significantly higher
NGDR) and turned significantly less frequently.
Further, copepods swam more orthogonally to the
axis of the vortex in the presence of the
turbulence-level-3 vortex, as seen in the increase in
mean angle of alignment of the trajectory with the
axis of the vortex. While A. tonsa did not escape
more frequently (no significant change in the
number of escapes per copepod per 5-s period),
when they did escape, they did so more powerfully,
with significantly greater escape accelerations in the
presence of the turbulence-level-3 vortex than in the
control case.
The turbulence-level-3 control case (Fig. 4c) did
not show a clear preferred escape jump location for
either replicate A or B. Again, this result was ex-
pected since no flow was present in the tank
during the control cases. Both replicates (A and B)
of the turbulence-level-3 treatment (Fig. 4d) ex-
hibited large spikes in escape jump density for
radial locations less than the vortex’s characteristic
radius, rB (i.e., closer to the core of the vortex).
The results of the Kolmogorov–Smirnov tests
revealed significant differences (P50.05) between
treatment and control for both replicates.
Temora longicornis
Behavioral assays at turbulence level 2 and level 3
Tables 4 and 5 show the behavioral parameters for
T. longicornis for turbulence level 2 and level 3, re-
spectively. The majority of the data revealed a signif-
icant replicate effect, which indicated that differences
in behavior, if any, were not repeatedly observed.
The one exception was relative swimming speed for
turbulence level 2. In that case, relative swimming
speed increased significantly from control to treat-
ment, and there was no significant replicate effect.
Figure 5 shows the normalized histograms of
escape jump locations. More variability (both spa-
tially and between replicates) was observed in the
escape density for the control cases for T. longicornis
(compared with A. tonsa). However, again no trend
was observed, as was expected, since the control case
had no flow present (Fig. 5a, c). For the turbulence-
level-2 treatment (Fig. 5b), the histogram again did
not have an obvious peak in escape density, and the
replicates showed substantial variability. The results
of the Kolmogorov–Smirnov tests revealed no signif-
icant differences between treatment and control for
both replicates for turbulence level 2. For the turbu-
lence-level-3 treatment (Fig. 5d), the largest escape
densities were observed for radial locations less than
rB, although there was substantial variability between
replicates and the peaks were not as substantial as
observed for A. tonsa (Fig. 4d). The results of the
Kolmogorov–Smirnov tests for turbulence level 3
were inconsistent; replicate B indicated a significant
difference (P50.05) between control and treatment
and replicate A showed no significant difference.
Table 3 Swimming kinematics variables for Acartia tonsa for the pooled turbulence level-3-treatment (i.e., combining replicates A
and B)
Parameter Control Treatment Treatment effect
F-ratio P-value
n 114 126
Relative speed [mm s�1] (SE) 3.4 (0.51) 6.7 (0.50) 7.8 0.0006*
Turn frequency [turn ind�1 s�1] (SE) 0.90 (0.011) 0.87 (0.011) 3.0 0.04*
Alignment of the trajectory to the axis of the vortex [8] (SE) 62.1 (0.71) 65.8 (0.69) 6.1 0.0012*
NGDR (SE) 0.42 (0.018) 0.59 (0.017) 16.0 0.0003*
Number of escapes per copepod per 5-s period (SE) 0.015 (0.0006) 0.015 (0.0006) 1.4 0.23
Escape acceleration [mm s�2] (SE) 199 (10.0) 247 (9.6) 4.8 0.005*
Notes: P-values are reported for the effect of treatment (i.e., treatment versus control). *P50.05.
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Discussion
Acartia tonsa
Acartia tonsa exhibited strong changes in swimming
kinematics and escape behavior in the presence of
the turbulence-level-3 vortex (Table 3). As summa-
rized in Table 6, A. tonsa increased relative speed of
swimming, angle of alignment with the axis of the
vortex, NGDR, and escape acceleration, as well as
decreased turn frequency, when in the presence of
a turbulence-level-3 vortex (relative to control).
These specific changes in swimming kinematics effec-
tively moved the copepod away from the core of the
vortex (i.e., faster, straighter trajectories aligned more
perpendicular to the axis of the vortex). Further, the
normalized histograms of escape density revealed an
increase in escape density near the region of the core
of the vortex when copepods were exposed to a tur-
bulence-level-3 vortex (Fig. 4d).
This contrasted with the observation in the pres-
ence of the turbulence-level-2 vortex. The data
showed that the replicate effect was responsible for
the variability in the turbulence-level-2 dataset, and
that the effect of the treatment itself (i.e., the presence
of the vortex) was inconclusive at best (Table 2). Also,
the normalized histograms of escape density for the
turbulence-level-2 vortex did not exhibit preferred lo-
cations of escape (Fig. 4b). Therefore, it was reason-
able to conclude that the presence of a turbulence-
level-2 Burgers’ vortex did not significantly affect the
swimming kinematics of A. tonsa.
The transition between turbulence level 2 and level
3 was consistent with our hypothesis that A. tonsa
sense hydrodynamic cues associated with turbulent
vortices and actively respond via changes in swim-
ming kinematics. As discussed further below, it also
suggested that there was a threshold hydrodynamic
cue that induced the behavioral response. It was also
consistent with the observations by Yen et al. (2008)
of a transition in swimming kinematics between tur-
bulence level 2 and level 3 (Acartia hudsonica in their
study).
Table 5 Variables of swimming kinematics for Temora longicornis for the turbulence-level-3 treatment
Parameter Control A Treatment A Control B Treatment B Treatment effect Replicate effect
F-ratio P-value F-ratio P-value
n 25 35 41 24
Relative speed [mm s�1] (SE) 3.0 (0.32) 5.5 (0.28) 5.0 (0.34) 5.2 (0.33) 18.0 0.0002* 10.3 0.0003*
Turn frequency [turn ind�1 s�1] (SE) 0.76 (0.024) 0.92 (0.020) 0.90 (0.025) 0.77 (0.024) 0.26 0.61 19.7 0.0002*
Alignment of the trajectory to
the axis of the vortex [8] (SE)
68.8 (1.9) 60.9 (1.6) 56.4 (2.0) 72.0 (1.9) 4.4 0.066 20.4 0.0004*
NGDR (SE) 0.48 (0.035) 0.48 (0.030) 0.49 (0.036) 0.56 (0.036) 1.5 0.27 1.6 0.28
Number of escapes per
copepod per 5-s period (SE)
0.016 (0.0011) 0.009 (0.00089) 0.013 (0.00082) 0.018 (0.0011) 1.1 0.32 26.0 0.0006*
Escape acceleration [mm s�2] (SE) 165 (14.9) 244 (13.0) 224 (12.0) 182 (15.2) 1.8 0.25 9.5 0.0012*
Notes: ANOVA results are reported for the effect of treatment (i.e., treatment versus control) and replicate (i.e., A versus B). *P50.05.
Table 4 Variables of swimming kinematics for Temora longicornis for the turbulence-level-2 treatment
Parameter Control A Treatment A Control B Treatment B Treatment Effect Replicate Effect
F-ratio P-value F-ratio P-value
n 30 20 46 49
Relative speed [mm s�1] (SE) 3.3 (0.25) 4.7 (0.31) 3.6 (0.29) 4.5 (0.25) 17.7 0.0012* 0.49 0.67
Turn frequency [turn ind�1 s�1] (SE) 0.84 (0.026) 0.93 (0.032) 0.84 (0.030) 0.79 (0.025) 0.38 0.65 6.3 0.016*
Alignment of the trajectory to the
axis of the vortex [8] (SE)
57.4 (2.2) 64.9 (2.7) 65.8 (2.5) 65.6 (2.1) 2.3 0.23 3.3 0.13
NGDR (SE) 0.48 (0.036) 0.57 (0.044) 0.61 (0.041) 0.63 (0.035) 2.0 0.24 3.1 0.12
Number of escapes per copepod
per 5-s period (SE)
0.012 (0.00097) 0.012 (0.0012) 0.013 (0.00079) 0.015 (0.00076) 0.58 0.60 4.1 0.07
Escape acceleration [mm s�2] (SE) 166 (11.2) 191 (13.7) 172 (9.0) 183 (8.8) 2.8 0.19 0.22 0.80
Notes: ANOVA results are reported for the effect of treatment (i.e., treatment versus control) and replicate (i.e., A versus B). *P50.05.
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Temora longicornis
Temora longicornis did not show a strong behavioral
response to either vortex treatment (relative to con-
trol). Among the cases in which significant differ-
ences were observed, the replicate effect was
significant for almost every case, which meant the
effect of the treatment was inconclusive at best
(Tables 4 and 5). The plots of escape density
showed a slight increase in the core of the vortex
(Fig. 5a, d), but again there was significant variability
between replicates and the response was not nearly as
clear as for A. tonsa. Thus, we concluded that T.
longicornis did not strongly respond to the presence
of either treatment, in contrast to the clear transition
described above for A. tonsa.
Yen et al. (2008) observed a significant change in
motility number between turbulence level 2 and level
3 for T. longicornis, whereas the current data did not
reveal a significant change in response to a typical
vortex for these levels. Possible explanations were
that T. longicornis was not responding to the struc-
ture of the vortex, but rather was affected by the
advection of turbulence or perhaps was responding
to another characteristic, such as unsteadiness of
flow, that the Burgers’ vortex apparatus was not rep-
licating. Further, since a turbulent flow consisted of a
broad range of vortices, it was possible that T. long-
icornis was responding to stronger vortices present in
the turbulent conditions compared with the typical
vortex that was mimicked in the Burgers’ vortex
apparatus. It would be very interesting to evaluate
behavior (particularly for T. longicornis) in a stronger
vortex in order to assess potential behavioral re-
sponses and the ability to swim relative to the stron-
ger velocities of flow.
Further, there were a number of differences be-
tween A. tonsa and T. longicornis that could help to
explain the present data. First, the setal array on the
antennae has quite different morphology. The setae
of A. tonsa extend in all directions from the antennae
Fig. 5 Normalized histograms of escape jump locations for Temora longicornis as a function of radius for the turbulence-level-2 (a)
control, and (b) treatment, and turbulence-level-3 (c) control, and (d) treatment. The dashed line indicates the characteristic radius of
the Burgers’ vortex rB .
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to form a complex three-dimensional array. The setal
array for T. longicornis is much more confined to
a single plane. Therefore, it is possible that the
three-dimensional setal array for A. tonsa was more
tuned to sense the disturbance to flow associated
with a turbulent-like vortex. Second, the style of
swimming was quite distinct between these species,
with A. tonsa swimming in a hop-sink manner and
T. longicornis swimming in a cruise fashion. Thus, it
is possible that the behavioral changes in T. longicor-
nis were more subtle and therefore more difficult to
quantify. In fact, Yen et al. (2008) observed that the
transport speed of A. hudsonica in isotropic turbu-
lence was significantly different between turbulence
level 2 and level 3, whereas there was no significant
difference in transport speed for T. longicornis.
Furthermore, although not for these specific species,
Incze et al. (2001) and Manning and Bucklin (2005)
showed considerable variability in the vertical distri-
butions among species of copepods; hence, it was not
too surprising to observe a difference between species
in the present data.
Hydrodynamic cue inducing escapes
It was desirable to quantify the hydrodynamic cue
that triggered the dramatic increase in escape density
in the core of the vortex for A. tonsa at turbulence
level 3 (Fig. 4b). The most likely hydrodynamic cues
that could trigger an escape response were: circum-
ferential velocity u�, shear strain rate er�, maximum
principal strain rate (MPSR), and vorticity !x , since
these were the primary parameters of flow that vary
with radial position for a Burgers’ vortex (Fig. 6). It
was interesting to note that relative swimming speed
is in the range of 3–6 mms�1 (Tables 2–5) and the
maximum velocity of flow (3.9 mms�1) was a very
similar value in Fig. 6a. The similarity in swimming
speed and flow velocity suggested that for these
conditions copepods were likely able to propel them-
selves relative to the motion of the fluid.
Circumferential velocity u� was unlikely to be the
trigger for an escape response for two reasons. First,
the magnitude of u� was already quite high as the
copepod approached the center of the vortex; u�gradually increased to its peak value as the copepod
moved from peripheral radial positions inward
(Fig. 6a). In fact as a copepod moved radially
inward, u� was already decreasing after passing the
location of maximum u�. Therefore, if one assumed
that the copepod had a threshold sensitivity to the
magnitude of u�, the threshold would be met for a
radial distance greater than rB (unless the threshold
magnitude of u� was exactly ðu�Þmax for the turbu-
lence-level-3 vortex—a very unlikely event). Second,
prior results by Haury et al. (1980), Fields and Yen
(1997), Kiørboe and Visser (1999), and Kiørboe et al.
(1999) all indicated that quantities related to veloc-
ity-gradient, such as strain rate, were the least vari-
able in eliciting an escape response from copepods.
Neither MPSR nor er� were good candidates for
triggering the escape behavior of A. tonsa seen in the
Burgers’ vortex treatment. MPSR was constant in the
near-the-vortex-core region (due to the constant rate
of axial strain), increased to a maximum value at a
radial position slightly greater than rB, and decreased
back to the same constant value (as the near-the-
vortex-core region) at peripheral radial positions
(Fig. 6b). The shear-strain rate, er�, was zero at the
axis of the vortex, increased to a maximum value at
a radial position greater than rB, and decreased back
to zero at peripheral radial positions (Fig. 6b).
Similar to the reasoning for u�, if one assumed
that copepods had a threshold sensitivity to MPSR
or to magnitude of er�, the threshold would be met
for radial locations greater than rB.
The most likely hydrodynamic cue for triggering
the escape behavior seen in these Burgers’ vortex
treatments was vorticity. Vorticity was zero far
from the core of the vortex, and began to rise at a
distance of approximately 2rB away from the axis of
the vortex (Fig. 6b). As a copepod approached a
distance rB away from the core, the vorticity in-
creased rapidly, until the vorticity peaked at the
axis of the vortex (Fig. 6b). Therefore, the locations
of the peak in vorticity and strain rate (both er� and
MPSR) were spatially segregated in the Burgers’
vortex flow, and the peak in vorticity was co-located
with the location of increased escape density by
A. tonsa (Fig. 4d). Further, the magnitude of vortic-
ity was substantially larger than the magnitude of
either strain-rate parameter (Fig. 6b). To our knowl-
edge this was the first direct observation of vorticity
Table 6 Behavior of Acartia tonsa in presence of a turbulence-
level-3 vortex during treatment in comparison to behavior under
control conditions
Relative speed "*
Turn frequency #*
Alignment of trajectory
to the axis of the vortex
"*
NGDR "*
Number of escapes
per copepod per 5-s period
No change
Escape acceleration "*
Notes: Indicators marked with an asterisk (*) are considered signifi-
cant (P50.05).
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inducing an escape response, although in many pre-
vious treatments the location of peaks (or variation)
in vorticity and strain rate was co-located. It is im-
portant to appreciate that vorticity (through the ro-
tation tensor) and strain rate both are components
of the velocity-gradient tensor; hence, they both
relate to spatial gradients of velocity. Therefore, if
copepods could sense the differential velocity associ-
ated with strain rate using their setal array, then they
similarly should be able to sense the differential ve-
locity associated with vorticity.
There was a substantial difference in the magnitude
of the vorticity for turbulence level 2 and level 3. For
the turbulence level 2, the peak vorticity equaled
1.0 s�1 in comparison to the peak value of 2.7 s�1
for turbulence level 3 (Fig. 6d). This suggested that
the threshold for inducing an escape response by A.
tonsa was in this range due to the change in escape
density between treatments (Fig. 4). As discussed
above, the lack of significant response for T. longicor-
nis in these treatments may indicate that a larger
threshold was required to induce a response, possibly
because the more planar morphology of their setal
array had poorer sensitivity to vorticity. In their
thin-layer mimic, Woodson et al. (2005) reported a
threshold for shear strain rate that was nearly identical
for these species: 0.035–0.06 s�1 for A. tonsa and 0.03–
0.06 s�1 for T. longicornis. Hence, the setal array of
both species may be effective at sensing a simple
two-dimensional shear flow, but the magnitude of
vorticity was much larger in Fig. 6 for the turbu-
lence-level-3 vortex, which suggested reduced sensitiv-
ity of A. tonsa to fluid rotation (i.e., vorticity)
compared with a simple two-dimensional shear flow
(i.e., shear strain rate). Further, sensing vorticity
required quantifying two orthogonal gradients in ve-
locity (i.e., vorticity in Cartesian coordinates is given
by !z ¼@v@x �
@u@y). Shear strain rate is given by the ex-
pression exy ¼12
@v@x þ
@u@y
� �(again in Cartesian coordi-
nates). While this expression includes the same spatial
derivatives of velocity (as the vorticity expression), in
the case of the thin-layer mimic of Woodson et al.
(2005), the term @v@x was extremely small. Hence, sens-
ing shear strain rate in the thin-layer mimic required
only sensing @u@y. Returning to the Burgers’ vortex, in
order to respond to vorticity the copepod must sense
both @v@x and @u
@y (or another pair of orthogonal velocity
gradients) accurately enough to perform the difference
and hence sense the local rate of fluid rotation. The
results here suggested that the three-dimensional setal
array of A. tonsa may be much more suited to the
task of sensing vorticity compared with the more
planar array of T. longicornis. This conclusion was
logically consistent with the morphology of the
arrays, since the three-dimensional setal array would
presumably be geometrically arranged in ways that
sensed orthogonal gradients in velocity (i.e., setae sep-
arated in two orthogonal directions), whereas the
planar array would not (i.e., setae separated in only
one direction).
Acknowledgments
The authors gratefully acknowledge the financial sup-
port of the National Science Foundation [OCE-
0928491 and DUE-1022778]. Thanks to Nerida H.
De Jesus Villanueva, Jennifer Young, John Jung,
Yichao Qian, Briana Corcoran, Julia Wang, and
Dorsa Elmi for help with the copepod-tracking analysis.
Fig. 6 Radial profiles of (a) velocity u�, (b) shear strain rate jer�j, MPSR, and vorticity !x. Values of parameters are equal to those for
the turbulence-level-3 treatment (shown in Table 1). The dashed-double-dotted line indicates the characteristic radius of the vortex rB.
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Thanks to Rachel Lasley-Rasher for collecting copepods
in the field.
References
Benjamini Y, Hochberg Y. 1995. Controlling the false discov-
ery rate: A practical and powerful approach to multiple
testing. J R Stat Soc B 57:289–300.
Boxshall GA, Yen J, Strickler JR. 1997. Functional significance
of the sexual dimorphism in the cephalic appendages of
Euchaeta rimana Bradford. Bull Mar Sci 61:387–98.
Dower JF, Miller TJ, Leggett WC. 1997. The role of micro-
scale turbulence in the feeding ecology of larval fish. Adv
Mar Biol 31:169–220.
Fields DM, Yen J. 1997. The escape behavior of marine co-
pepods in response to a quantifiable fluid mechanical dis-
turbance. J Plankton Res 19:1289–304.
Fields DM, Shaeffer DS, Weissburg MJ. 2002. Mechanical and
neural responses from the mechanosensory hairs on the an-
tennule of Gaussia princeps. Mar Ecol Prog Ser 227:173–86.
Galbraith PS, Browman HI, Racca RG, Skiftesvik AB, Saint-
Pierre J-F. 2004. Effect of turbulence on the energetics of
foraging in Atlantic cod Gadus morhua larvae. Mar Ecol
Prog Ser 281:241–57.
Gallager SM, Yamazaki H, Davis CS. 2004. Contribution of
fine-scale vertical structure and swimming behavior to for-
mation of plankton layers on Georges Bank. Mar Ecol Prog
Ser 267:27–43.
Hatakeyama N, Kambe T. 1997. Statistical laws of random
strained vortices in turbulence. Phys Rev Lett 79:1257–60.
Haury LR, Kenyon DE, Brooks JR. 1980. Experimental eval-
uation of the avoidance reaction of Calanus finmarchicus.
J Plankton Res 2:187–202.
Haury LR, Yamazaki H, Itsweire EC. 1990. Effects of turbu-
lent shear flow on zooplankton distribution. Deep Sea Res
37:447–61.
Heath MR, Henderson EW, Baird DL. 1988. Vertical distri-
bution of herring larvae in relation to physical mixing and
illumination. Mar Ecol Prog Ser 47:211–28.
Hedrick TL. 2008. Software techniques for two- and three-
dimensional kinematic measurements of biological and bio-
mimetic systems. Bioinspir Biomim 3:034001(6 pp).
Incze LS, Hebert D, Wolff N, Oakey N, Dye D. 2001.
Changes in copepod distributions associated with increased
turbulence from wind stress. Mar Ecol Prog Ser
213:229–40.
Jimenez J. 1997. Oceanic turbulence at millimeter scales. Sci
Mar 61:47–56.
Jonsson PR, Tiselius P. 1990. Feeding behaviour, prey detec-
tion and capture efficiency of the copepod Acartia tonsa
feeding on plankton ciliates. Mar Ecol Prog Ser 66:35–44.
Jumars PA, Trowbridge JH, Boss E, Karp-Boss L. 2009.
Turbulence-plankton interactions: A new cartoon. Mar
Ecol 30:133–50.
Kiørboe T, Saiz E, Visser A. 1999. Hydrodynamic signal per-
ception in the copepod Acartia tonsa. Mar Ecol Prog Ser
179:97–111.
Kiørboe T, Visser AW. 1999. Predator and prey perception in
copepods due to hydromechanical signals. Mar Ecol Prog
Ser 179:81–95.
Lagadeuc Y, Boule M, Dodson JJ. 1997. Effect of vertical
mixing on the vertical distribution of copepods in coastal
waters. J Plankton Res 19:1183–204.
Lewis DM. 2005. A simple model of plankton population
dynamics coupled with a LES of the surface mixed layer.
J Theor Biol 234:565–91.
Mackas DL, Sefton H, Miller CB, Raich A. 1993. Vertical
habitat partitioning by large calanoid copepods in the oce-
anic sub-Arctic Pacific during spring. Prog Oceanogr
32:259–94.
MacKenzie BR. 2000. Turbulence, larval fish ecology and fish-
eries recruitment: A review of field studies. Oceanol Acta
23:357–75.
Manning CA, Bucklin A. 2005. Multivariate analysis of the
copepod community of near-shore waters in the western
Gulf of Maine. Mar Ecol Prog Ser 292:233–49.
Marrase C, Saiz E, Redondo JM. 2000. Lectures on plankton
and turbulence. Sci Mar 61:1–238.
Murphy DW, Webster DR, Yen J. 2012. A high speed tomo-
graphic PIV system for measuring zooplanktonic flow.
Limnol Oceanogr Methods 10:1096–112.
Peters F, Marrase C. 2000. Effects of turbulence on
plankton: An overview of experimental evidence and
some theoretical considerations. Mar Ecol Prog Ser 205:
291–306.
Rothschild BJ, Osborn TR. 1988. Small-scale turbulence and
plankton contact rates. J Plankton Res 10:465–74.
Saiz E, Alcaraz M. 1992. Enhanced excretion rates induced by
small-scale turbulence in Acartia (Copepoda: Calanoida).
J Plankton Res 14:681–9.
Saiz E, Kiørboe T. 1995. Predatory and suspension feeding of
the copepod Acartia tonsa in turbulent environments. Mar
Ecol Prog Ser 122:147–58.
Saiz E, Calbet A, Broglio E. 2003. Effects of small-scale tur-
bulence on copepods: The case of Oithona davisae. Limnol
Oceanogr 48:1304–11.
Tiselius P. 1992. Behavior of Acartia tonsa in patchy food
environments. Limnol Oceanogr 37:1640–51.
Visser AW, Saito H, Saiz E, Kiørboe T. 2001. Observations of
copepod feeding and vertical distribution under natural
turbulent conditions in the North Sea. Mar Biol
138:1011–9.
Webster DR, Brathwaite A, Yen J. 2004. A novel laboratory
apparatus for simulating isotropic oceanic turbulence
at low Reynolds number. Limnol Oceanogr Methods
2:1–12.
Webster DR, Young DL. 2015. A laboratory realization of the
Burgers’ vortex cartoon of turbulence-plankton interac-
tions. Limnol Oceanogr Methods 13:92–102.
Woodson CB, Webster DR, Weissburg MJ, Yen J. 2005.
Response of copepods to physical gradients associ-
ated with structure in the ocean. Limnol Oceanogr
50:1552–64.
Woodson CB, Webster DR, Weissburg MJ, Yen J. 2007a. Cue
hierarchy and foraging of calanoid copepods: Ecological
implications of oceanographic structure. Mar Ecol Prog
Ser 330:163–77.
Woodson CB, Webster DR, Weissburg MJ, Yen J. 2007b. The
prevalence and implications of copepod behavioral re-
sponses to oceanographic gradients and biological patchi-
ness. Integr Comp Biol 47:831–46.
Copepods’ response to Burgers’ vortex 717
at Georgia Institute of T
echnology on September 22, 2015
http://icb.oxfordjournals.org/D
ownloaded from
Woodson CB, Webster DR, True AC. 2014. Copepod behavior:
Oceanographic cues, distributions, and trophic interactions.
In: Seuront L, editor. Copepods: Diversity, habitat, and be-
havior. New York: Nova Publishers. p. 215–53.
Yamazaki H, Squires KD. 1996. Comparison of oceanic tur-
bulence and copepod swimming. Mar Ecol Prog Ser
144:299–301.
Yen J, Fields DM. 1992. Escape responses of Acartia hudsonica
(Copepoda) nauplii from the flow field of Temora long-
icornis (Copepoda). Arch Hydrobiol Beih 36:123–34.
Yen J, Lenz PH, Gassie DV, Hartline DK. 1992.
Mechanoreception in marine copepods: Electrophysical
studies on the first antennae. J Plankton Res 14:495–512.
Yen J, Rasberry KD, Webster DR. 2008. Quantifying copepod
kinematics in a laboratory turbulence apparatus. J Mar Syst
69:283–94.
Yokokawa M, Itakura K, Uno A, Ishihara T, Kaneda Y. 2002.
16.4-Tflops direct numerical simulation of turbulence by a
Fourier spectral method on the Earth Simulator.
Supercomputing 2002 Proceedings of the 2002 ACM/IEEE
Conference on Supercomputing, Baltimore, Maryland.
Young DL. 2014. Turbulence–copepod interaction: Acartia
tonsa behavioral response to Burgers’ vortex [MS Thesis].
[Atlanta (GA)]: Georgia Institute of Technology.
Zar JH. 1999. Biostatistical analysis. Upper Saddle River (NJ):
Prentice Hall.
718 D. R. Webster et al.
at Georgia Institute of T
echnology on September 22, 2015
http://icb.oxfordjournals.org/D
ownloaded from