Turbulence triggers vigorous swimming but hinders motion strategy in planktonic copepods

Abstract

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

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 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. Small-scale 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, three-dimensional 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 three-dimensional 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. 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 18°C, 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 18°C. 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) × 17 cm (H) glass tank containing a forcing device creating quasi-homogeneous and isotropic turbulence [29]. The device is driven by a servomotor and is composed of two arrays of four counter-rotating discs located on the lateral sides of the aquarium. The discs are 40 mm in diameter and smooth to prevent mechanical damage to copepods.

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 counter-rotating discs located on the side of the aquarium and illumination is provided by an infrared diode array mounted beneath the aquarium.

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 cm⁻³ and a mean diameter of 90 µm. 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 = (d_p/η)²/12β, where β = 3ρ_f/(2ρ_p + ρ_f) is the modified density ratio that takes into account the added mass effect, η is the Kolmogorov length scale and ρ_p and ρ_f are the particle and fluid densities, respectively. For the different experiments, the Stokes number ranges from 7 × 10⁻⁴ to 4.4 × 10⁻³ 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 quasi-homogeneous 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 18°C to 20°C 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 cm⁻³ [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.

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.

	coordinates			trajectories			length ± s.d.
r.p.m.	dead	males	females	dead	males	females	dead	males	females
0	—	324 801	380 166	—	253	214	—	1284 ± 581	1776 ± 469
50	604 508	583 000	727 389	380	476	498	1591 ± 540	1225 ± 600	1461 ± 568
150	520 715	750 398	1 155 800	689	953	1216	756 ± 452	787 ± 469	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

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 spatio-temporal 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 ε from the relation , where is the velocity–acceleration structure function and δ_r denotes the Eulerian spatial increment of a given quantity [38]. This estimate was compared to the relation , where C_ε is the dissipation rate coefficient, u_RMS 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 coefficient C_ε which depends on the Reynolds number, both methods yielded comparable results.

2.6. Trajectory analysis

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 , 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 X_t the position of a copepod at time t and we consider the moments of order q > 0 of the norm of its displacement ||δX_τ|| for all time increments τ. When a scaling behaviour is present over some range of τ and for every q, the moments of order q of the norm of the displacement depend only on the time increment τ following the relation , where ζ(q) is the exponent which governs the local power-law scaling of the absolute moments of the fluctuations δX_τ at any scale s up to a scale S. The exponents ζ(q) were estimated from the slope of the power fit of the log–log plot of 〈||δX_τ||^q〉 versus τ for each value of q and for time increments up to 5 s [40]. The scaling of ζ(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 ζ(q) are linear in q then a single scaling exponent is involved in all fractal subsets and the function is said to be monofractal. If ζ(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].

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 ε increased from 9.8 × 10⁻⁷ to 5.3 × 10⁻⁵ m² s⁻³ and the Kolmogorov time scale τ_η decreased from 1 to 10⁻¹ 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 ε ranges from 10⁻⁷ to 10⁻⁴ m² s⁻³ [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].

Table 2.

Turbulence parameters for the different rotation rates and velocity fluctuations for the living copepods and the inert carcasses. u′ is the root mean square of the velocity fluctuations (in mm s⁻¹) for the living and dead copepods. ε is the turbulent energy dissipation rate. τ_η = (ν³/ε)^1/4 and η = (ν/ε)^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.

r.p.m.	ε (m 2 s−3)	τη (s)	η (mm)	u′ (dead)	u′ (males)	u′ (females)
0	—	—	—	—	4.6	3.0
50	9.8 × 10−7	1.0	1.0	1.6	4.9	2.8
150	6.2 × 10−6	0.4	0.7	4.1	5.2	4.2
250	2.4 × 10−5	0.2	0.5	6.0	6.9	6.4
350	5.3 × 10−5	0.1	0.4	7.7	8.7	8.8

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 s⁻² and velocities above 150 mm s⁻¹, in agreement with previously published values for E. affinis [46]. Relocation jumps also differ from escape reactions in that 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).

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; dead animals: dashed lines). The velocity magnitude is computed as and the acceleration magnitude as , 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.

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 , where and 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.

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.

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 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.

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).

3.4. Motion strategy

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 ζ(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 ζ(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 ζ(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].

Figure 5.

Effect of turbulence on the motion strategy of males (a) and females (b). The values ζ(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 (ζ(q) = q/2; black dotted line) and for ballistic motion (ζ(q) = 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 ζ(q) ≠ q/2 with exponents ζ(q) that are linear in q, the walk belongs to the class of monofractal anomalous diffusion. If ζ(q) > q/2 the process is referred to as superdiffusive, whereas sub-diffusion corresponds to ζ(q) < q/2. If ζ(q) is nonlinear in q then the walk involves non-unique exponents for different values of q and is said to be multifractal.

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.

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 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 small-scale 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 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 s⁻¹ in Acartia tonsa to 6 s⁻¹ 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 s⁻¹ with events larger than 4 s⁻¹ having an occurrence probability of 15% [68]. These values are higher than the threshold, previously estimated at 2.1 and 3 s⁻¹, 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 s⁻¹ and extending beyond 20 s⁻¹) 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 × 10⁻⁵ m² s⁻³ [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.

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 10⁻⁷ to 10⁻⁴ m² s⁻³ in the coastal zone but much lower in the open ocean where they range from 10⁻⁹ to 10⁻⁶ m² s⁻³ [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 s⁻¹ [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 10⁻³ m² s⁻³ [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 s⁻¹ [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 understanding how flow motion affects the life of those that are neither passive nor strong swimmers.

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.

Authors' contributions

F.-G.M. and M.H. designed the experiments. S.S. 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.