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Turbulence triggers vigorous swimming
but hinders motion strategy in
planktonic copepods
François-Gaël Michalec1, Sami Souissi2 and Markus Holzner1
Research
1
Institute of Environmental Engineering, ETH Zurich, Stefano-Franscini-Platz 5, 8093 Zurich, Switzerland
Université Lille 1 Sciences et Technologies, Laboratoire d’Océanologie et de Géosciences, CNRS,
UMR 8187 LOG, 62930 Wimereux, France
2
Cite this article: Michalec F-G, Souissi S,
Holzner M. 2015 Turbulence triggers vigorous
swimming but hinders motion strategy in
planktonic copepods. J. R. Soc. Interface 12:
20150158.
http://dx.doi.org/10.1098/rsif.2015.0158
Received: 21 February 2015
Accepted: 1 April 2015
Subject Areas:
environmental science
Keywords:
calanoid copepod, turbulence, swimming
behaviour, motion strategy, three-dimensional
particle tracking
Calanoid copepods represent a major component of the plankton community.
These small animals reside in constantly flowing environments. Given the fundamental role of behaviour in their ecology, it is especially relevant to know
how copepods perform in turbulent flows. By means of three-dimensional
particle tracking velocimetry, we reconstructed the trajectories of hundreds
of adult Eurytemora affinis swimming freely under realistic intensities of
homogeneous turbulence. We demonstrate that swimming contributes substantially to the dynamics of copepods even when turbulence is significant.
We show that the contribution of behaviour to the overall dynamics gradually
reduces with turbulence intensity but regains significance at moderate intensity, allowing copepods to maintain a certain velocity relative to the flow.
These results suggest that E. affinis has evolved an adaptive behavioural mechanism to retain swimming efficiency in turbulent flows. They suggest the
ability of some copepods to respond to the hydrodynamic features of the surrounding flow. Such ability may improve survival and mating performance in
complex and dynamic environments. However, moderate levels of turbulence
cancelled gender-specific differences in the degree of space occupation and
innate movement strategies. Our results suggest that the broadly accepted
mate-searching strategies based on trajectory complexity and movement
patterns are inefficient in energetic environments.
1. Introduction
Author for correspondence:
François-Gaël Michalec
e-mail: [email protected]
Electronic supplementary material is available
at http://dx.doi.org/10.1098/rsif.2015.0158 or
via http://rsif.royalsocietypublishing.org.
Turbulence is a characteristic feature of marine and estuarine habitats and has
received considerable attention for its influence on individual planktonic organisms. Turbulence spans a wide range of scales, from large inertial structures to
small dissipative eddies. Owing to its small size and limited swimming ability,
zooplankton interacts very little with the large features of the flow, moves along
currents and follows the movements of large eddies rather passively [1]. In certain conditions, however, these small organisms can actively respond to the
flow. They can for instance swim against ambient currents to maintain their vertical position in downwelling and upwelling zones, moving at rates of up to ten
body lengths per second [2]. Calanoid copepods are ubiquitous in marine and
estuarine ecosystems where they form the largest part of the total zooplankton.
Several studies have suggested that these organisms change their behaviour in
response to turbulence in the water column, embarking into active vertical
migrations over a few tens of metres to prevent tidal flushing in macrotidal
estuaries [3] and to move below the turbulent mixed layer at the surface of
the ocean [4,5]. One explanation for this behaviour is that in open estuaries,
copepods migrate vertically to maintain their horizontal position whereas in
the open ocean, certain species that prefer low intensities of turbulence migrate
to deeper and calmer environments to maximize their fitness with respect to
foraging efficiency and predation pressure [6].
We focus here on distances of the order of a few centimetres where the individual behaviour of calanoid copepod takes on full significance [7], on weak to
moderate levels of fluid turbulence characteristic of oceanic and estuarine
& 2015 The Author(s) Published by the Royal Society. All rights reserved.
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Y
2
X
Figure 1. Sketch of the experimental set-up. The four cameras are located
around 50 cm away from the centre of the coordinate system and are
angled on an experimental volume (shown as a dashed line cube) located
in the middle of the aquarium. Turbulence is generated via eight counterrotating discs located on the side of the aquarium and illumination is
provided by an infrared diode array mounted beneath the aquarium.
To test for this hypothesis, we quantified and compared, using
millions of data points, the dynamics, motion complexity and
movement pattern of living and dead copepods. We show
that copepods are unable to maintain the sexual dimorphism
or their trajectories and motion strategy even when turbulence
is weak, but that swimming behaviour contributes substantially to the dynamics of their motion even when turbulence
levels are significant.
2. Material and methods
2.1. Copepod and algae cultures
Eurytemora affinis parent individuals were obtained from our
laboratory cultures at Wimereux Marine Station. These cultures
originate from copepods sampled in July 2012 from the oligohaline
zone of the Scheldt estuary (Belgium). New cultures were kept in
aerated 5 l buckets, at a temperature of 188C, at salinity 15 and
under a fluorescent light : dark cycle of 12 L : 12 D. Copepods
were fed every other day and in excess with a mixture of the
micro-algae Rhodomonas marina and Isochrysis galbana harvested
during the exponential growth phase and centrifuged. Algae
were cultured in autoclaved water at salinity 30 and in Conway
medium, under a 12 L : 12 D light cycle and at a temperature of
188C. Both copepods and algae were grown on artificial seawater
(Instant Ocean dissolved in deionized water).
2.2. Experimental set-up
We conducted three-dimensional particle tracking measurements
using four synchronized Mikrotron EoSens cameras recording at
different viewing angles. A sketch of the set-up is shown in
figure 1. A four-camera system facilitates the establishment of
stereoscopic correspondences as it resolves most matching ambiguities [28]. The cameras were fitted with Nikon 60 mm lenses at
f.16 and recorded on four arrays of hard discs (IO Industries) at
100 frames per second and at a resolution of 1280 1024 pixels.
All measurements were done in a 27 cm (W) 18 cm (D) J. R. Soc. Interface 12: 20150158
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habitats [8] and on eddy sizes of the order of centimetres or
less. At these small scales, copepod swimming speed and
flow velocity fluctuations are roughly comparable. It was
suggested that certain species can move independently of the
surrounding flow in relatively calm environments [9] and
that the dominance of behaviour over flow motion may contribute to the formation of fine-scale plankton layers [10].
How turbulence affects behaviour-mediated processes and
interactions has been relatively well studied in copepods, particularly through attention to contact rates [11,12], foraging
efficiency [13], prey selectivity and capture success [14,15]
and predator avoidance [16]. What are lacking are direct, experimental results on the kinematics of these small animals in
response to background flow motion, primarily because of
the difficulties associated with tracking many zooplankters
swimming simultaneously and in three dimensions. Smallscale behaviour allows copepods to capture preys [17], find
mates [18] and escape predators [19]. Given the critical role
of motion in their ecology and the prevalence of turbulence
in their environment, it seems reasonable to assume that
these animals can control, at least to a certain extent, the
direction and magnitude of motion imposed by small-scale turbulent transport. For instance, the marine calanoids Temora
longicornis and Calanus finmarchicus are able to maintain the
geometry of their trajectories even at substantial intensities
of turbulence, presumably due to their relatively strong swimming capabilities [20]. Because three-dimensional observations
of copepods swimming freely in turbulent flows remain scarce
[20], most of what we know about their behaviour in energetic
environments derives from extrapolation of results obtained in
still water [21] or from theoretical models that have estimated copepod fitness in terms of optimal swimming strategies,
feeding efficiency and predation risk [6,22]. The interaction
between copepods and background flow remains a challenging
topic and more work is needed to better understand how
these small animals behave when turbulent advection unsettles
the innate kinematic and geometrical characteristic of their
small-scale motion.
Several methods have been developed to obtain trajectories
of moving organisms, for instance fruit flies [23], schooling
fish [24] or flocking birds [25]. Among these methods, threedimensional particle tracking velocimetry offers the advantage
that it allows fully automatic processing of long sequences
of stereoscopic images from which the position of a large
number of particles and their trajectories in the threedimensional space can be automatically recovered. The technique was originally developed to measure velocity and
velocity gradients along tracer trajectories in turbulent flows
and we have recently applied it to study the behaviour of
copepods in calm water [26].
In this study, we conducted three-dimensional Lagrangian
particle tracking experiments on the motion of adult
Eurytemora affinis swimming in still water and under environmentally realistic intensities of turbulence. We focused on the
estuarine calanoid copepod E. affinis because of its large distribution area which includes most temperate estuaries [27], its
high importance in the trophic food web and the prevalence
of turbulence in its habitat. We produced different levels of
turbulence in the laboratory using a set-up that generates
homogeneous and isotropic turbulence via counter-rotating
discs. The general hypothesis of our study is that behaviour
enables copepods to react and exert some control over the magnitude and direction of motion caused by turbulent transport.
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Table 1. Number of coordinates, number of trajectories and mean trajectory length (in frames) for the different rotation rates and for the living copepods and
the inert carcasses.
r.p.m.
0
dead
—
length + s.d.
trajectories
males
females
324 801
380 166
dead
—
males
females
253
214
dead
males
females
—
1284 + 581
1776 + 469
604 508
520 715
583 000
750 398
727 389
1 155 800
380
689
476
953
498
1216
1591 + 540
756 + 452
1225 + 600
787 + 469
1461 + 568
950 + 506
250
424 538
800 955
1 240 495
681
1404
1904
623 + 412
570 + 381
652 + 431
350
1 168 685
1 289 810
1 440 945
2256
2601
2969
518 + 357
496 + 340
485 + 339
17 cm (H) glass tank containing a forcing device creating quasihomogeneous and isotropic turbulence [29]. The device is driven
by a servomotor and is composed of two arrays of four counterrotating discs located on the lateral sides of the aquarium. The
discs are 40 mm in diameter and smooth to prevent mechanical
damage to copepods.
2.3. Recording conditions
2.3.1. Measurements with tracer particles
To characterize the flow, we used neutrally buoyant polyamide
particles with a density of 1.06 g cm23 and a mean diameter of
90 mm. The choice of an appropriate diameter for seeding particles
is a compromise between an adequate tracer response of the particles in the fluid (which requires small particles) and a high
signal-to-noise ratio of the scattered light signal (which requires
large diameters). Reasonably large tracer particles were desirable in our experiments because of the relatively large size of
the aquarium. The Stokes number of these particles is defined
as S ¼ (dp/h)2/12b, where b ¼ 3rf/(2rp þ rf ) is the modified density ratio that takes into account the added mass effect, h is the
Kolmogorov length scale and rp and rf are the particle and fluid
densities, respectively. For the different experiments, the Stokes
number ranges from 7 1024 to 4.4 1023 indicating that these
particles behave as passive tracers. In our measurements, they
were smaller than the Kolmogorov scale, the smallest length
scale in turbulence. Strong illumination was provided by two
mercury-vapour lamps. The seeding density was approximately
2000 particles per litre, and we limited our investigation volume
to a 6 6 6 cm cube at the centre of the aquarium and
mid-way between the discs, where the turbulence is quasihomogeneous and isotropic. We recorded the motion of tracer
particles at different rotation rates: 50, 150, 250 and 350 r.p.m.
Each sequence lasted 1 min and was preceded by a 1 min period
for the flow to develop fully.
2.3.2. Measurements with living copepods and inert carcasses
Measurements with copepods were carried out within a 10 10 10 cm investigation volume centred in the middle of
the aquarium. We conducted all experiments in the absence of
food and in the dark, using a high-power (300 W) infrared
diode as the light source to prevent phototaxis and a set of
fans to dissipate heat. We checked copepods for integrity
under a microscope and selected healthy and well-fed individuals only. For each measurement, we transferred 100 adult
copepods (males or both ovigerous and non-ovigerous females;
size ranging from 1 to 1.2 mm) into the experimental vessel
filled with water at salinity 15, and we allowed them to acclimate
for 5 min. We recorded their behaviour at 0, 50, 150, 250 and
350 r.p.m. Each sequence lasted 5 min and was preceded by a
1 min acclimation to the new turbulence intensity. We conducted
experiments twice for the two adult states, using new copepods
from the stock culture. Water temperature increased from 188C to
208C at the end of the recording period. All copepods were living
and actively swimming at the end of the measurements. The
mass density of calanoid copepods is generally higher than that
of water [30] and in our measurements, copepods were slightly
bigger than the Kolmogorov length scale. Their Stokes number is
thus larger than that of tracer particles and can be estimated for
our levels of turbulence between 0.06 and 0.35, assuming a body
size of 1 mm and a density of 1.03 g cm23 [30]. We conducted the
same measurements on dead copepods to account for the effect
of particle size and density [31]. We recorded the motion of dead
individuals at 50, 150, 250 and 350 r.p.m. Experiments were conducted one time only with 200 dead adults. The number of
trajectories and coordinates and the mean trajectory length are
indicated in table 1 for each experimental condition. We obtained
2 718 446 three-dimensional coordinates with the inert carcasses,
4 944 795 with the females and 3 748 964 with the males.
2.4. Particle tracking and trajectory processing
We calibrated the cameras using images of a reference object with
target points of known coordinates and performed an additional
dynamic calibration based on the images of moving particles
[32]. The reference object consisted of a machined aluminium
block on which 135 reference points were evenly distributed
along the three directions. Knowing the camera intrinsic and
extrinsic parameters from the calibration procedure, we established correspondences between particle image coordinates and
derived the three-dimensional position of the moving particles by
forward intersection, introducing their coordinates as unknowns
in the augmented projection model [33,34]. We processed the
image sequences and tracked particles and copepods using an
algorithm based on image and object space information [35]. We
glued segments belonging to the same trajectory using a spatiotemporal matching assignment [36]. Trajectories were smoothed
with a quadratic Savitzky–Golay filter to improve the measurement of velocity and acceleration [37]. In the experiments with
living and dead copepods, we filtered out trajectories shorter
than 20 frames and 1 cm in length to remove artefacts originating
from the tracking and gluing procedures.
2.5. Flow parameters
We estimated the energy dissipation rate e from the relation
kdr u dr al 2 e, where kdr u dr al is the velocity–acceleration
structure function and dr denotes the Eulerian spatial increment
of a given quantity [38]. This estimate was compared to the relation
e ≃ Ce u3RMS =L, where Ce is the dissipation rate coefficient, uRMS is
the root mean square of the velocity fluctuations and L is the integral length scale, estimated for each experimental condition via the
Eulerian velocity autocorrelation function. Accounting for the
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r.p.m.
0
e (m 2 s23)
th (s)
h (mm)
u0 (dead)
u0 (males)
u0 (females)
—
—
—
4.6
3.0
50
150
9.8 10
6.2 1026
1.0
0.4
1.0
0.7
1.6
4.1
4.9
5.2
2.8
4.2
250
350
2.4 1025
5.3 1025
0.2
0.1
0.5
0.4
6.0
7.7
6.9
8.7
6.4
8.8
coefficient Ce which depends on the Reynolds number, both
methods yielded comparable results.
2.6. Trajectory analysis
monofractal. If z(q) is nonlinear then the walk involves
non-unique exponents for different values of q and is said to be
multifractal. The behaviour of several species of copepods is multifractal and the curvature of their moment structure function
quantifies the statistical properties of their motion [21].
2.6.1. Box-counting dimension
We estimated the degree of convolutedness of the trajectories
through their box-counting dimension, which is a scale-independent
metric commonly used to assess the complexity of zooplankton
swimming paths [26]. We created a three-dimensional bounding
box around each trajectory. The origin of this bounding box lay at
the intersection of the planes defined by the minimal coordinates
of the trajectories and its height, length and depth were equal to
the maximal displacement of the copepod along each dimension.
We superimposed a regular three-dimensional grid of varying
mesh size on the trajectory and we counted the number of occupied
boxes versus the mesh size. This number increases with decreasing
mesh size, leading to the power-law relationship N(l) lD ,
where l is the mesh size, N(l ) is the number of occupied boxes and
D is the box-counting dimension. The mesh size followed a geometric sequence with maximal and minimal cut-off values set to
half the embedding volume and 0.5 mm, respectively. To prevent
lacunarity during the box-counting procedure, we characterized
each swimming track using a cubic spline interpolation and built a
new trajectory by extrapolating new positions at equal separation
distance along the original curve. This separation distance was
always shorter than the minimal mesh size. The box-counting
dimension was given by the slope of the power fit of the log–log
plot of the number of occupied boxes versus mesh size.
2.6.2. Moment structure function of the displacement
We quantified changes in the statistical properties of the motion
using the moment structure function of the displacement [39].
The norm of a displacement is a non-stationary process with
stationary increment, meaning that its statistical properties vary
only with the time increment. We note Xt the position of a copepod at time t and we consider the moments of order q . 0 of
the norm of its displacement jjdXtjj for all time increments t.
When a scaling behaviour is present over some range of t and
for every q, the moments of order q of the norm of the displacement depend only on the time increment t following the relation
kjjdXt jjq l t z(q) 8 s t S, where z(q) is the exponent which
governs the local power-law scaling of the absolute moments
of the fluctuations dXt at any scale s up to a scale S. The exponents z(q) were estimated from the slope of the power fit of the
log – log plot of kjjdXtjjql versus t for each value of q and for
time increments up to 5 s [40]. The scaling of z(q) for different
q values quantifies how the statistics of the motion grow with
time and represents a scale-invariant indicator of the strategy
used by an organism to explore its environment. When the exponents z(q) are linear in q then a single scaling exponent is
involved in all fractal subsets and the function is said to be
3. Results
3.1. Flow parameters
Relevant parameters for the flow in the measurement domain
for the different forcings applied are given in table 2. We varied
the forcing such that the energy dissipation rate e increased
from 9.8 1027 to 5.3 1025 m2 s23 and the Kolmogorov
time scale th decreased from 1 to 1021 s as the rotation speed
of the discs increased. The intensities of turbulence produced with our set-up are comparable to characteristic values
observed in coastal zones, tidal fronts and megatidal estuaries,
three relatively energetic environments where e ranges from
1027 to 1024 m2 s23 [41]. Although our device does not recreate
every aspect of fluid movement in nature, it generates a turbulent environment most relevant to the behavioural ecology of
zooplanktonic organisms [42].
3.2. Motion kinematics
Eurytemora affinis males and females swimming in calm water
show a continuous slow swimming pattern interrupted by frequent relocation jumps (electronic supplementary material,
movie S1). The slow forward motion derives from the creation
of feeding currents accomplished by the high-frequency
vibration of the cephalic appendages [43]. Relocation jumps
have been commonly observed in calanoid copepods and
result in a sequence of small velocity bursts leading to an
unsteady motion [44]. Copepods are also reputed for their
powerful escape jumps that occur in response to a nearby
deformation of the fluid and that have a higher amplitude
and a shorter duration [45]. When exposed to a turbulent
flow, copepods do not behave passively even at substantial
turbulence intensities; jumps and swift movements are clearly
visible from the recorded movies. These jumps are limited in
amplitude and similar to the relocation events observed in
calm water. They clearly differ from the much stronger
escape reactions that occur outside the investigation volume,
near the rotating discs (electronic supplementary material,
movie S2). During escape reactions, we observed accelerations
over 2000 mm s22 and velocities above 150 mm s21, in agreement with previously published values for E. affinis [46].
Relocation jumps also differ from escape reactions in that
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Table 2. Turbulence parameters for the different rotation rates and velocity fluctuations for the living copepods and the inert carcasses. u0 is the root mean square
of the velocity fluctuations (in mm s21) for the living and dead copepods. e is the turbulent energy dissipation rate. th ¼ (n 3/e )1/4 and h ¼ (n/e )1/2 are the
Kolmogorov length and time scales, respectively. For living animals, the velocity includes both the advection due to background flow and the behavioural
component of motion, whereas for inert carcasses it only reflects turbulent transport.
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(a) 10–1
5
0 r.p.m.
50 r.p.m.
150 r.p.m.
250 r.p.m.
350 r.p.m.
P(u)
10–2
10–3
10–4
10
20
u (mm s–1)
30
40
0
10
20
u (mm s–1)
30
40
0
50
100
a (mm s–2)
150
200
250
50
150
rotational speed (r.p.m.)
350
(b) 10–1
P(u)
10–2
10–3
10–4
(c) 10–1
P(a)
10–2
10–3
10–4
RMS (u.a) (W kg–1)
(d) 800
males
females
dead
600
400
200
0
0
Figure 2. Probability density functions of the magnitude of the velocity for
males (a) and females (b) and probability density functions of the magnitude
of the Lagrangian acceleration for males (c) for the five conditions of turbulence tested (living animals: solid lines;pdead
animals: dashed
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi lines). The
2 þ u 2 þ u 2 ) and the accelvelocity magnitude is computed
as
u
¼
(u
x ffi
y
z
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
eration magnitude as a ¼ (ax 2 þ ay 2 þ az 2 ), where the indices x, y and
z refer to the three orthogonal axes of the reference frame. Females show
similar differences in P(a) between turbulence conditions. The velocity of
living copepods exceeds that of inert particles at all turbulence intensities.
However, differences narrow as turbulence increases. They reach a minimum
at 250 r.p.m. and increase again at 350 r.p.m., suggesting a higher
swimming effort once flow velocity passes a moderate intensity.
3.3. Trajectory convolutedness
In species of copepods that produce pheromones for mating,
such as E. affinis, males and females generally have distinct
motility patterns. Females display convoluted and complex
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they do not begin with an initial reorientation of the animal
[46]; copepods most often jump in the direction of their
motion both in calm water and in turbulent flows (electronic
supplementary material, movie S1).
As a first metric, we computed the probability density
functions of the velocity and acceleration of living and dead
copepods (figure 2 and table 2). The velocity magnitude u of
living animals exceeds that of inert carcasses at all turbulence
intensities but varies between genders. Since the velocity consists of an active swimming component and an advective
component that is due to transport by turbulent flow, differences in the probability density P(u) between males and
females indicate gender-specific differences in behaviour. As
expected, males swam faster than females, in line with their
more active motility pattern [47]. During steady propulsion,
swimming velocities are low and do not contribute significantly to motion in turbulent flows. Copepods approximately
drift with the flow unless executing a relocation jump, and consequently we observed little differences in the frequency of low
velocity values between dead and living copepods. We also
observed similar shapes of P(u) and comparable root mean
square velocities between copepods swimming in still water
and at weak turbulence levels. This suggests that a very low
intensity of turbulence, with velocity fluctuations lower than
the typical swimming speed of a copepod, does not trigger
significant behavioural response (figure 2a,b).
In both genders, the difference in P(u) between dead and
living animals narrows considerably and reaches a minimum
at moderate turbulence levels (250 r.p.m.) (figure 2a,b). The
spread between the two curves increases again at 350 r.p.m.;
at this intensity of turbulence, behaviour contributes more to
the velocity than it does at 250 r.p.m. The behavioural response
to turbulence is hence dependent on the turbulent intensity.
This can also be seen in the distribution of the Lagrangian acceleration, as shown in figure 2c, where P(a) is plotted for the
males and the inert carcasses. In both males and females, we
observed similar shapes of P(a) in calm water, at 50 r.p.m.
and at 150 r.p.m. despite a steady increase in flow acceleration
(table 2). At 250 r.p.m., the probability of moderate acceleration
values increased in proportion, whereas at 350 r.p.m. both
moderate and strong accelerations became more significant.
We further quantified the effort associated with active swimming by considering the instantaneous power per unit mass
p(t) ¼ a(t) u(t), where a(t) and u(t) are the acceleration and
velocity vectors at time t, respectively (figure 2d). For inert carcasses, the magnitude of p(t) increased steadily with the
turbulence intensity. For living organisms, the magnitude
of p(t) remained approximately constant up to 150 r.p.m.,
increased substantially at 250 r.p.m. and sharply at 350 r.p.m.
Consequently, the difference in p(t) between active and passive
organisms is minimal at 150 r.p.m.; swimming contributes less
to the instantaneous power than it does at higher turbulence
intensities. Above 150 r.p.m. and for both males and females,
the magnitude of p(t) deviates strongly from the trend
observed with the inert carcasses. The minimum in the magnitude of p(t) and the sharp increase observed in living copepods
at 250 r.p.m. and especially at 350 r.p.m. agree well with the
trend observed in P(u) and P(a) and confirm that copepods
adjust their swimming effort depending on the background
flow, i.e. copepods swim more actively at substantial turbulence intensities. Differences in the Lagrangian acceleration
between living animals and inert carcasses are also illustrated
qualitatively in figure 3.
(a)
100
75
50
25
6
1.35
**
**
75
50
50
25
25
0 0
(b)
*
**
1.25
1.20
males
females
dead
1.15
50
150
250
rotational speed (r.p.m.)
350
Figure 4. Box-counting dimension (+s.e.) for the trajectories of males (red)
and females (blue) and for the inert carcasses (black) for the five levels of
turbulence tested. Asterisks indicate significant differences between consecutive r.p.m. conditions (Wilcoxon –Mann – Whitney test, p , 0.01 and p ,
0.05). The box-counting dimension of dead copepods remained statistically
similar between all turbulence intensities ( p . 0.1).
100
3.4. Motion strategy
75
50
25
0
100
100
75
75
50
50
25
25
0 0
0
50
acceleration (mm s–2)
100
150
200
250
300
Figure 3. Subset of trajectories displayed by living male copepods (a) and
inert carcasses (b) at 350 r.p.m. Coordinates are in millimetres. Living animals
show strong behavioural accelerations, whereas inert particles move passively
and display weaker accelerations.
trajectories, whereas males swim faster and turn substantially
less [47]. These behavioural features are believed to reflect a
strategy aiming at increasing encounter rate; by swimming
faster and in straight trajectories, males explore a larger
volume. Here we ask whether this strategy remains valid in
realistic environments with turbulent flow. We compared
the degree of convolutedness of trajectories and hence the
degree of space occupation through the three-dimensional
box-counting dimension, and we show that the strategy
observed in calm conditions is no longer relevant in turbulent
environments. As the intensity of turbulence increases, the
box-counting dimension of both male and female trajectories quickly relaxes towards the nearly flat curve observed
using dead animals (figure 4). Although copepods could
maintain some degree of trajectory sinuosity even at
high turbulence intensities (Wilcoxon–Mann–Whitney test,
p , 0.01), flow motion at 150 r.p.m. cancelled gender-specific
differences in swimming complexity (p . 0.5). At 350 r.p.m.,
the path geometry of both males and females is close to that
of inert particles.
In planktonic organisms, motion strategy and movement pattern assume an important role, because they determine both
the probability of interaction with other organisms and how
individuals explore and exploit their dilute and unsteady
environment [48]. In copepods, they reflect an optimized
trade-off between beneficial encounters with resources and
mates and dangerous meetings with predators [49]. Therefore,
we investigated the extent to which copepods can maintain
the optimal diffusive properties of their behaviour in the presence of unpredictable, turbulence-imposed constraints on
their movement. We analysed long-range correlations in the
q-order structure function of copepod displacements. The function of the scaling exponents z(q) is species-specific and
characterizes the scale-free statistics of the motion and the strategy used by an organism to explore its environment. We show
that E. affinis males and females swimming in still water and
under weak to moderate turbulence follow a multifractal
random walk characterized by a convex moment structure function z(q) (figure 5). In calm conditions, multifractality is very
pronounced in males. In females, the function is only slightly
convex and close to the ballistic limit. Increasing background
flow motion gradually reduced and at high forcing cancelled
multifractality in male behaviour. In females, the function z(q)
progressively relaxed towards the linear trend observed with
the inert carcasses as turbulence increased. At 350 r.p.m., the
movement pattern of both genders is indistinguishable from
the monofractal superdiffusive motion of passive particles in
turbulence. The superdiffusive motion observed here for
passive particles may be due to limited trajectory length
(which was comparable to a few turnover times) and moderate
Reynolds number, which has been shown to result in deviation
from self-similarity diffusion [50].
4. Discussion
Our findings have two important implications. First, they
experimentally reveal an unrecognized ability of certain planktonic copepods to adjust their swimming effort according to
the background flow. Second, they suggest that swimming
dynamics, rather than movement patterns, determine the
behavioural efficiency of copepods in turbulent flows.
J. R. Soc. Interface 12: 20150158
100
75
**
**
1.30
0
0
100
**
**
rsif.royalsocietypublishing.org
box-counting dimension ± s.e.
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(a) 4
(q)
3
2
1
0
(q)
3
2
1
0
0
1
2
3
q
4
5
6
Figure 5. Effect of turbulence on the motion strategy of males (a) and
females (b). The values z(q) correspond to the scaling exponents for the
qth moment of the norm of the displacement versus the time increment.
The linear functions expected for Brownian motion (z(q) ¼ q/2; black
dotted line) and for ballistic motion (z(q) ¼ q; black dashed-dotted line)
and the structure function of inert particles at 350 r.p.m. (black dashed
line) are shown for comparison. When z(q) = q/2 with exponents z(q)
that are linear in q, the walk belongs to the class of monofractal anomalous
diffusion. If z(q) . q/2 the process is referred to as superdiffusive, whereas
sub-diffusion corresponds to z(q) , q/2. If z(q) is nonlinear in q then the
walk involves non-unique exponents for different values of q and is said to
be multifractal.
By considering the kinematic properties of the motion of
living animals and inert carcasses, we show that self-induced
motion contributes substantially to the dynamics of copepods
under background flow motion, even when turbulence is
significant, that is, comparable to or stronger than their
typical swimming velocity. However, the contribution of behaviour reduces as flow motion increases and it requires a
moderate level of turbulence for copepods to swim much
more actively and accelerate strongly. This intensity-dependent
response is reminiscent of classic energy budget models that
predict, in calanoid copepods, an optimized motility strategy
balancing foraging efficiency and mating encounters with predation risk and energy expenditure [51], except it relates to
their swimming behaviour in a dynamic environment. Our
results show that copepods adjust their behaviour and swimming effort according to the background flow. When
turbulence intensity falls below a certain level, copepods maintain a sufficient velocity relative to the flow. Energy
expenditure during movements can cost copepods a substantial portion of their energy intake [52]. We suggest that these
animals do not adjust their swimming effort in weak turbulence because swimming and jumping faster than required
would add unnecessary energy expense and increase the risk
of meeting predators [53]. Above this threshold, we show
that copepods increase their activity; behaviour regains significance and the relative velocity to the background flow and the
acceleration increase. We suggest that the increase in the
7
J. R. Soc. Interface 12: 20150158
(b) 4
contribution of behaviour represents an adaptation to optimize
the trade-off between gains and costs. Gains would arise from
retaining the ability to carry out behavioural processes and
interactions while at the same time being advected by the
flow. Costs would result from unnecessary energy expenditure
and increased hydrodynamic conspicuousness.
Copepods dominate the zooplankton community and
motility strategies contributed much to their impressive
evolutionary success [54]. The widespread perception is that
copepods rely on movement patterns and gender-specific
differences in trajectory geometry to enhance mating encounters and foraging efficiency and to minimize dangerous
encounters with planktonic predators [49]. The strong multifractality observed in males swimming in a still environment
devoid of chemical or biological cues confirms the existence of
an innate movement strategy. Movement strategies have been
observed in a variety of marine organisms including zooplankton [48]. They confer advantages over random search motion
and simple, spatially intensive behaviours because they lead
to higher efficiency in encounter statistics and ultimately to an
optimized fitness [55]. A fundamental question in this context
is: to what extent can copepods maintain trajectory geometry
and movement patterns in the presence of small-scale turbulent
transport? We demonstrate that even a weak flow motion
reduces the geometry complexity and the sexual dimorphism
of copepod trajectories and the dispersive properties of their
motion with respect to those of inert particles. We therefore
suggest that motion strategies are inefficient in realistic environments with turbulent flow. Our results do not support the
recent assumption that movement patterns increase mate
encounter rates in the turbulent waters of the surface ocean
[21]. If turbulence deprives copepods from motion strategies,
how can these small animals remain so competitive?
Calanoid copepods rely on remote detection, through either
chemical or hydromechanical signals [56]. Their success
in feeding, reproducing and escaping predation depends on
their relative velocity with respect to their prey, their mate
and their predator from the time of the detection to the end of
the interaction [57]. Copepods race up pheromone trails left
by cruising females [18], flee from predators via powerful
escape jumps [45] and perform spectacular attacks on their
preys [58]. We suggest that copepods may not need to respond
to advective transport due to eddies that are much larger than
their size because at very large scale, turbulence redistributes preys, mates and small planktonic predators both in time
and space, regardless of their swimming strategy. What may
matter most is their ability to perform rapid movements
towards or away from a fellow zooplankter while at the same
time being transported by the flow. This ability depends on
the perception distance of the two animals [16] and on their relative velocity [57]. Our results show that copepods maintain a
certain velocity and accelerate strongly relative to the flow, providing additional effort when turbulence becomes significant.
We suggest that this increase in swimming effort represents
a compensatory response to the increase in flow velocity
and underlines a behavioural adaptation to retain swimming
efficiency in energetic environments. The importance of smallscale turbulence in enhancing contact rates between planktonic
organisms is now well established [59]. Flow will occasionally
bring two organisms in close contact and below a certain perception distance; we suggest that only then does behaviour become
significant. Swimming faster than the flow increases the probability of outpacing an approaching suction-feeding predator
rsif.royalsocietypublishing.org
ballistic motion
Brownian motion
inert 350 r.p.m.
0 r.p.m.
50 r.p.m.
150 r.p.m.
250 r.p.m.
350 r.p.m.
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8
J. R. Soc. Interface 12: 20150158
Turbulence is highly variable in both intensity and duration, varies spatially and temporally with weather and
seasons and decreases substantially with depth [74]. Dissipation rates are in the range of 1027 to 1024 m2 s23 in the
coastal zone but much lower in the open ocean where they
range from 1029 to 1026 m2 s23 [75]. The temporal and spatial
variability of turbulence offers important windows where the
motion of an organism can be independent of the local flow
field. In these environments, the motility strategies that have
been observed in calm water may remain significant. Such situations may for instance occur above the pycnocline in stratified
coastal water where turbulence is minimal and velocity fluctuations below 1 mm s21 [9] or during the tidal current reversal
associated with the absence of flow in megatidal estuaries
[76]. Irrespective of their feeding behaviour and size, copepods
converge on optimal, size-independent specific clearance rates
that maximize the net energy gain over the predation risk [51].
Depression of clearance rates at high turbulence intensities due
to lower mechanosensor perception capability and lower capture success [13,77] or variations in the optimal configuration
of their trajectories [78] are some of the negative outcomes
that can strongly affect the fitness of copepods. Consequently,
these small animals may also actively seek a calmer environment. Idealized models have determined where copepods
should reside in a turbulent water column in terms of fitness
gains, i.e. with respect to predation pressure, foraging ability
and energy expenditure. It was suggested that organisms
with sufficient swimming ability should migrate down with
increasing surface turbulence to optimize the trade-off between
energy gain from clearance rates and risk of feeding from
swimming velocity and hydrodynamic signals [6].
Eurytemora affinis resides in highly energetic environments; in tidal channels, dissipation rates can reach up to
1023 m2 s23 [79]. This species often dominates the zooplankton community in the low salinity zone; population densities
can exceed 600 individuals per litre despite current velocities
beyond 2 m s21 [76]. Field studies conducted in several European and North American estuaries have evidenced the role
of active movement in the maintenance of populations of
E. affinis along the estuarine salinity gradient [80]. Active
downward swimming of late developmental stages of
E. affinis was for instance observed in the Seine estuary, the
largest megatidal estuary of the English Channel, and
linked to variations in water velocity [3]. This behaviour
depends on swimming capabilities. Adults and late-stage
copepodites migrate to the bottom layer in response to
higher water velocities, whereas nauplii are transported as
passive particles in the turbidity maximum zone [3]. Whether
the increase in swimming activity observed in our measurements pertains to vertical tidal migrations remains to be
tested. The range of turbulence intensities over which these
small animals remain able to perform some of the striking
behavioural features that they display in still water, for
instance trail-following behaviour, is also worth exploring.
In a turbulent flow, particles with small to moderate inertia
and size below or equal to the Kolmogorov length scale
tend to move preferentially to regions of low vorticity and
high strain [81]. Because in these regions peak density of particles can be much higher than the mean value [82], it was
suggested that preferential concentrations can increase copepod encounter rates in the ocean [62]. This aspect deserves
further study. Measurements on the interaction between
motility and turbulence will certainly be very useful in
rsif.royalsocietypublishing.org
such as a fish larvae [60,61]. This strategy may be particularly
important for calanoid copepods, considering that turbulence
impairs their ability to detect velocity gradients associated
with a predator [16]. It may also increase the probability of
capturing passive preys transported nearby or racing up a
short-lived pheromone trail and make contact with a female.
Other physical processes or behavioural traits may exist
to increase encounter rates in highly turbulent ecosystems;
potential mechanisms may include flow-driven preferential concentrations in the ocean [62] or behaviour-mediated aggregation
and retention mechanisms in tide-dominated estuaries [63].
Copepods remotely detect an approaching predator by the
hydrodynamic signals it generates. These fluid disturbances
trigger escape reactions [64] and strain rate is the responsible
cue [65]. The threshold needed to elicit an escape reaction in
laminar flows varies between studies and species, ranging for
instance from 0.4 s21 in Acartia tonsa to 6 s21 in Paracalanus
parvus [66,67]. In our experimental set-up and for a disc rotation
speed of 300 r.p.m., the distribution of the magnitude of the
strain rate tensor peaks at 2.25 s21 with events larger than
4 s21 having an occurrence probability of 15% [68]. These
values are higher than the threshold, previously estimated at
2.1 and 3 s21, needed to trigger escape reactions in E. affinis
[46,69]. However, in the studies cited above, copepods were
exposed to localized fluid disturbances in the absence of flow,
whereas in our measurements, they were exposed to realistic
levels of isotropic turbulence. Small-scale turbulence triggers
swift movements in copepods [70,71] that have often been
linked to escape reactions, based on the assumption that copepods react to shear regions of the flow as they react to localized
disturbances in a still environment, i.e. that they incorrectly
interpret the fluid deformations associated with turbulence as
generated by other planktonic organisms. That is however not
always the case. For instance, A. tonsa jumped more often
when perceiving flow acceleration but this reaction was not
attributed to an escape behaviour [65]. Acartia tonsa also stayed
within turbulent regions of very high strain rate (values
distributed around 8 s21 and extending beyond 20 s21) without
displaying escape reactions, rather than moving towards
lower strain regions [72]. Similar results were obtained with
other species of pelagic copepods for dissipation rates up to
2.5 1025 m2 s23 [16,20,73], suggesting that escape reactions
are not always evoked even at substantial turbulence intensities.
Because in our measurements strong escape reactions happened
close to the discs only, whereas relocation jumps of limited
amplitude occurred everywhere, both in calm water and under
background flow motion, we have proposed an alternative
explanation for the higher swimming activity of copepods in turbulent flows. How copepods locally react to the intense vorticity
and shear regions of the flow remains relatively unknown and is
an important topic for future investigation. Characterizing a flow
field that constantly varies in space and time around many
organisms swimming freely in a large volume requires fully
time-resolved three-dimensional flow velocity data over the
entire measurement domain. For our measurements, this was
not feasible because the seeding density would prevent particle
detection, stereo-matching and tracking. This approach is however possible in smaller volumes and valuable insights are
emerging from simultaneous measurements of copepod and
flow motion [60,72]. Simultaneous measurements may also
help in identifying possible particle–flow coupling mechanisms,
such as inertial effects due to a smaller sampling time scale that
arise from the higher relative velocity of the living copepods.
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Acknowledgements. We thank F. G. Schmitt for his comments on the manuscript and the anonymous referees for their constructive criticism. We are
grateful to A. Souissi and Y.-J. Pan for providing copepods and algae.
Funding statement. This work was supported by Swiss National Science
Foundation (SNSF) grant no. 144645 and by ETH grant no. 29 14-1
and is a contribution to the bilateral agreement between ETH
Zurich and Lille 1 University. We acknowledge support from COST
MP 1305 Flowing Matter and GIP Seine-Aval.
9
Authors’ contributions. F.-G.M. and M.H. designed the experiments. S.S.
rsif.royalsocietypublishing.org
understanding how flow motion affects the life of those that
are neither passive nor strong swimmers.
provided the test organisms. F.-G.M. carried out the measurements,
performed data analysis and drafted the manuscript. S.S. and
M.H. participated in data analysis and helped draft the manuscript.
All authors gave final approval for publication.
Conflict of interests. We have no competing interests.
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