Compensatory escape mechanism at low Reynolds number

Abstract

Despite high predation pressure, planktonic copepods remain one of the most abundant groups on the planet. Their escape response provides one of most effective mechanisms to maximize evolutionary fitness. Owing to their small size (100 µm) compared with their predators (>1 mm), increasing viscosity is believed to have detrimental effects on copepods’ fitness at lower temperature. Using high-speed digital holography we acquire 3D kinematics of the nauplius escape including both location and detailed appendage motion. By independently varying temperature and viscosity we demonstrate that at natural thermal extremes, contrary to conventional views, nauplii achieve equivalent escape distance while maintaining optimal velocity. Using experimental results and kinematic simulations from a resistive force theory propulsion model, we demonstrate that a shift in appendage timing creates an increase in power stroke duration relative to recovery stroke duration. This change allows the nauplius to limit losses in velocity and maintain distance during escapes at the lower bound of its natural thermal range. The shift in power stroke duration relative to recovery stroke duration is found to be regulated by the temperature dependence of swimming appendage muscle groups, not a dynamic response to viscosity change. These results show that copepod nauplii have natural adaptive mechanisms to compensate for viscosity variations with temperature but not in situations in which viscosity varies independent of temperature, such as in some phytoplankton blooms. Understanding the robustness of escapes in the wake of environmental changes such as temperature and viscosity has implications in assessing the future health of performance compensation.

As one of the most abundant metazoans on the planet (1, 2), copepods form a vital trophic link within marine food webs. Young copepods (nauplii) are subject to high predation rates (3) and are prey for visual (4, 5) and mechanosensitive predators (3). Thus, escapes are crucial to the survival and fitness of young copepods and they exhibit strong responses to attacks from predators (6). This behavior is present immediately after hatching (7–10) and these escapes are triggered by hydrodynamic disturbances (11), detected through mechanosensory setae on the antennae (12–14).

Copepod nauplii (Fig. 1E) can be found (15, 16) and predated upon (17) throughout the year in coastal environments. Therefore, the escape response will be subject to temperature variations from local weather (e.g., cold fronts), seasonal variations (Fig. S1), and large-scale global patterns (e.g., climate change). Because viscosity fluctuates inversely with temperature, the impact of high viscous drag on small organisms’ cruising locomotion is considered substantial in affecting swimming speeds (18–22). However, the effect on escape behavior is unknown because nonescape (cruising) locomotion occurs at Reynolds number (Re) = 0.1 (for copepod nauplii) based on body length and cruising speed, and the current study shows escaping nauplii exhibit unsteady motion and their flow environment can rapidly transit to Re = 6.

Fig. 1.

Representative velocity–time plots during escape swimming by Acartia tonsa nauplius (stage N1). (A) 30 °C filtered seawater. (B) 30 °C filtered seawater plus methylcellulose to provide a kinematic viscosity of 1.35 × 10⁻⁶ m²⋅s⁻¹, identical to that of 10 °C seawater. (C) 10 °C filtered seawater. The numbers 1–6 in A–C correspond to numbers in D. 1, the position of the appendages the moment before the power stroke commences; 2, the A2 antennae in motion during the power stroke with the A1 antennae remaining extended anterior to the body; 3, the A1 antennae in motion; 4, completion of the power stroke as all appendages have come to rest against the body; 5, all appendages being returned simultaneously to the starting position during the recovery stoke; and 6, all appendages returned to the starting position. (E) A detailed photograph of the N1 stage of A. tonsa with appendages used for swimming labeled. Scale bar = 30 μm.

Although altering viscosity will undoubtedly influence locomotion, the effect on predator and prey will not be equal. This is because larger bodies operate at a higher Reynolds number and exhibit less viscous drag than smaller bodies. Because predators (e.g., fish larvae) are often much larger (an order of magnitude or more) than the nauplii themselves, the predator will be less affected by viscosity (23) and should capture nauplii more effectively when viscosity increases. Thus, the prevailing hypothesis is that small organisms escape less effectively at colder temperatures (24). However, field studies on copepod nauplii predation have shown no evidence that nauplii are predated upon more successfully at colder temperatures (25, 26), suggesting an ability of nauplii to compensate for viscosity disadvantages at reduced temperature.

In this study, we separate physical and metabolic effects of nauplius escape swimming to determine the effectiveness of escape swimming at the natural thermal extremes of Acartia tonsa nauplii. Using high-speed 3D digital holography (27, 28) (Fig. S2), we track and quantify the unsteady 3D motion of the high-speed escape of nauplii (100 µm) and beating kinematics of each appendage. From this, we demonstrate a compensatory mechanism that allows copepods to maintain escape distance and optimize velocity, which may reduce predation mortality. Details of appendage kinematics reveal a shift in appendage timing that increases power stroke (T_P) to recovery stroke (T_R) duration, counteracting elevated viscosity at low temperature. We find this behavior to be mediated by temperature and evidence for autonomous regulation by the temperature response of the swimming muscles.

Results and Discussion

When hydrodynamically stimulated to escape, the nauplius performs a series of hops. Each hop consists of a power stroke in which pairs of appendages beat sequentially anterior to posterior and a recovery stroke in which all swimming appendages return concurrently (Fig. 1D). Consequently, the nauplius swims forward in an oscillatory motion (Fig. 1 A–C). The nauplius uses mechanisms to increase the forward propulsive force during the power stroke and reduce negative forces during recovery (e.g., sequentially beating appendages then concurrently returning appendages (Movies S1 and S2 at 30 °C and 10 °C, respectively).

We assessed escapes under different environmental conditions: (i) T = 30 °C (high temperature, low viscosity), (ii) at 30 °C with addition of methylcellulose (MC) to match the viscosity at 10 °C (high temperature, high viscosity), and (iii) at 10 °C (low temperature, high viscosity). Three-dimensional kinematic analysis reveals that total escape distance by nauplii (N1 stage) at elevated viscosity (30 °C+MC) was significantly lower (P = 0.002) than total escape distance measured at 30 °C (Fig. 2A). Stroke number was consistent among treatments (Fig. 2D) and thus the distance traveled per swimming stroke at 30 °C+MC was significantly lower (P < 0.001) than at the 30 °C treatment (Fig. 2B). Both treatments at 30 °C experience comparable metabolic effects; therefore, the expected reduction in distance of the 30 °C+MC treatment can be attributable to increased drag forces experienced under the more viscous condition. Consider, however, that the 10 °C condition has viscous forces equivalent to those of the 30 °C+MC treatment yet escape distance was similar to distances observed in the warmer 30 °C seawater and significantly longer (P < 0.001) than at 30 °C+MC (Fig. 2 A and B), suggesting a mechanism other than stroke number is responsible for maintaining escape distance at lower temperatures.

Fig. 2.

Kinematic results from 3D escape swimming tracks of N1-stage Acartia tonsa nauplii in either 30 °C filtered seawater (FSW), 30 °C FSW with the addition of methylcellulose (30 °C+MC), or 10 °C FSW. (A) Total distance of the escape. (B) Escape distance traveled per stroke. (C) Time taken to complete a swimming stroke. (D) The number strokes performed during escape swimming. Error bars represent SD.

Swimming speeds are known to decrease with temperature in crustaceans (29), and physiological effects of temperature on muscle function are known to reduce contraction velocity (30), slowing the movement of appendages. The measured time for A. tonsa nauplii to complete a swimming stroke at 10 °C is 16.7 ms (SD 4.4). This was significantly longer (P < 0.001) than swimming stroke durations for 30 °C and 30 °C+MC, which take 5.3 ms (SD 1.0) and 6.5 ms (SD 1.7), respectively. This result demonstrates that the metabolic effect of temperature, not viscous drag, is primarily responsible for controlling stroke duration (Fig. 2C). This increase in stroke duration at low temperature results in a reduced appendage velocity and a significant drop (P < 0.001) in mean escape swimming velocity from 29.5 mm⋅s⁻¹ (SD 7.0, n = 16) and 23.2 mm⋅s⁻¹ (SD 6.6, n = 28) at 30 °C and 30° C+MC, respectively, to 15.0 mm⋅s⁻¹ (SD 5.0, n = 14) at 10 °C. At 10 °C, both recovery stroke duration and power stroke duration increased significantly (P < 0.001) compared with the 30 °C and 30 °C+MC treatments (Fig. 3). However, this increase at low temperature was not proportional; the power stroke duration relative to recovery stroke duration (T_P:T_R) increases significantly (P < 0.001) at 10 °C, but no difference (P = 0.154) is observed between 30 °C and 30 °C+MC (Fig. 3).

Fig. 3.

Stroke duration comparisons. Duration of both power and recovery strokes of Acartia tonsa nauplii in 30 °C filtered seawater (FSW), 30 °C FSW with the addition of methylcellulose (30 °C+MC), or 10 °C FSW. Inset: Power stroke duration relative to recovery stroke duration ratio (T_P:T_R) for the three treatment conditions. Error bars represent SD.

The temperature coefficient (Q₁₀) is used to describe the metabolic rate of change as a consequence of increasing the temperature by 10 °C. Q₁₀ has been previously used to compare temperature sensitivity of various muscle groups or swimming appendages for small organisms (20, 31). These rates typically decrease twofold every 10 °C for ectotherms, leading to Q₁₀ values of 2–3 (32). Therefore, values >2 suggest a greater dependence on temperature whereas values <2 suggest lower temperature dependence. However, caution must be applied when using Q₁₀ to investigate physical movement at low Reynolds number because the influence of changing viscosity with temperature can greatly overestimate Q₁₀ and thus temperature sensitivity (18, 20). In the context of this study Q₁₀ gives a reasonable comparison of temperature sensitivity among physiological components of nauplius escape swimming as we control for viscosity changes. By comparing the 30 °C+MC treatment with the results from 10 °C, only the physiological effect of temperature is considered.

We find the escape swimming of copepod nauplii to exhibit low temperature dependence (Q₁₀ = 1.2). Therefore, whereas a 35% reduction in mean velocity is substantial, exhibiting a standard dependence rate (Q₁₀ = 2.0) would reduce swimming velocity by 75%. Thus, by exhibiting low dependence on temperature, nauplii escape more effectively. For the components involved in producing an escape, the power stroke is found to exhibit a greater Q₁₀ value (1.7) than the recovery stroke (1.5), suggesting muscles responsible for power strokes are more temperature-dependent than muscles responsible for recovery strokes. Therefore, as temperature decreases, it will take proportionally longer to complete a power stroke relative to a recovery stroke and T_P:T_R will increase.

Further investigation of appendage motion confirms a shift in appendage timing also acts to increase T_P:T_R. At 30 °C, motion of the A1 antennae commences before the completion of the previous A2 antennae stroke (Fig. 4 A and B), resulting in a temporal overlap of 0.46 ms (SD 0.36, n = 40). At 10 °C a delay, instead of overlap, of 0.45 ms (SD 0.93, n = 40) was measured, resulting in a significant difference (P < 0.001) in timing (Fig. 4C). The fact that appendages beat sequentially during the power stroke but return simultaneously during the recovery stroke (Fig. 1D and Movie S1) suggests that changing the overlap timing of the stroke between two antennae will shift the T_P:T_R. These results suggest another mechanistic explanation to account for the change in T_P:T_R at 30 °C of ∼1.5 to a T_P:T_R at 10 °C of ∼2.0 (Fig. 3).

Fig. 4.

Acartia tonsa nauplii appendage motion of the A1 and A2 antennae. (A) Representative plot of appendage tip velocity over time showing a temporal overlap in A2 and A1 appendage motion in the 30 °C FSW treatment. (B) Overlap duration between A2 and A1 antennae during power strokes of escape swimming. Positive overlap values represent both appendages being in motion during the power stroke and negative values represent a temporal lag between the completion of the A2 antennae and the commencement of the A1 antennae. Error bars represent SD. (C) Representative plot of appendage tip velocity over time showing no temporal overlap in A2 and A1 appendage motion in the 10 °C FSW treatment.

How can changing the T_P:T_R lead to changes in swimming performance? The answer relies on a subtle balance between propulsive force generated by the appendages and the drag force acting on the body. If the power stroke is fast, this lowers the T_P:T_R and increases the propulsive force, but at the same time the impulse (time that propulsive force can act on the body) is also reduced. In addition, the body will experience higher drag force. The overall result of greater drag and a shorter impulse can create a lower mean escape velocity over the beat cycle. Likewise, a power stroke that is too long (large T_P:T_R) creates small propulsive force and consequently the mean velocity decreases. Therefore, an optimal T_P:T_R should exist for each environmental condition based on temperature (metabolic constraints of appendage motion) and viscosity (alters drag).

To qualitatively test the assertion that changing the stroke ratio (T_P:T_R) of appendage motion can influence swimming performance, we use a simple swimming model (Materials and Methods) based on resistive force theory (RFT) (Fig. 5 and Fig. S3). The results of the model clearly demonstrate that by increasing T_P:T_R at 10 °C, accomplished by the differential temperature dependence of power and recovery strokes and by altering the temporal overlap between A1 and A2 antennae during the power stroke (Fig. 4B), nauplii can optimize escape performance with regard to both distance and velocity. Here, the observed shift of T_P:T_R from ∼1.5 at 30 °C to ∼2.0 at 10 °C matches the overall trend of the model prediction, in which a lower T_P:T_R is best suited for high temperature and a larger T_P:T_R works best at low temperature (Fig. 5). Velocity optimization shows a clear shift to a lower T_P:T_R when temperature is elevated (Fig. 5), and although velocity is greatly reduced due to metabolic effects at low temperature, it can still be optimized within this reduced range at a greater T_P:T_R. Whereas the observed T_P:T_R (1.5) at 30 °C is lower than that predicted by the model, a T_P:T_R of 1.5 operates near peak effectiveness with respect to velocity at high temperature (97% of the maximum possible).

Fig. 5.

Results of an RFT-based model of an Acartia tonsa nauplius escape swimming at two natural kinematic viscosities [0.85 × 10⁻⁶ m²⋅s⁻¹ (30 °C) and 1.35 × 10⁻⁶ m²⋅s⁻¹ (10 °C)] in relation to T_P:T_R. The solid green line represents escape performance at 30 °C viscosity and appendage kinematics (experimentally determined). The dashed red line represents escape performance at 10 °C viscosity and appendage kinematics, and the dotted blue line represents escape performance under the condition of 10 °C viscosity and 30 °C appendage motion. Mean experimentally determined values are also shown for comparison. (A) Estimated escape distance per beat cycle showing improved distance with increased T_P:T_R for all treatment conditions. At elevated viscosity (blue line), escape distance is reduced when using 30 °C power stroke durations (∼2 ms per appendage). (B) Mean escape velocity per beat cycle showing reduced velocity with elevated viscosity. Metabolic slowing of appendage motion further decreases velocity but the observed T_P:T_R at 10 °C (∼2.0) allows nearly maximal performance under this condition.

The model shows that owing to metabolic changes in stroke time (Fig. 3) escapes at 10 °C can achieve a distance equivalent to escapes at 30 °C. Using the same metabolically driven stroke timing at elevated viscosity leads to overall reduced performance (Fig. 5B). Whereas distance seems fully optimized at a T_P:T_R >2 for all cases (Fig. 5A), velocity begins to decrease after a T_P:T_R of 1.8 (Fig. 5C) and acceleration (important for avoiding predatory strikes) decreases after a T_P:T_R of 1.4 to a minimum at 1.8 (Fig. S4). So, the observed T_P:T_R at 30 °C may represent the most effective with respect to overall propulsive performance (distance, mean velocity, and acceleration), which is important when metabolic rates (thus predatory strikes) are faster and viscous effects are lessened. Therefore, at each end of the thermal range experienced by A. tonsa nauplii, escapes seem to occur with nearly optimal effectiveness owing to a variation in stroke mechanics.

To determine whether assumptions made by using a simplistic RFT model of nauplius swimming were appropriate for determining the effect of T_P:T_R on swimming performance, we also used a nonlinear propulsive model (SI Materials and Methods, Fig. S5, and Table S1) and found that the trend predicted by the simple RFT model was correct. In addition, the use of nonlinear terms improved the predictability of optimal T_P:T_R at the highest Re condition (30 °C) by 20% whereas the lower Re conditions showed little change relative to the RFT predicted values (Fig. S5 and Tables S2 and S3). Both models found good agreement with empirically measured velocities (Fig. S6 and SI Materials and Methods, Nauplius Swimming Model). For example, at 30 °C experimentally measured mean velocities were 29.5 ± 7.0 mm⋅s⁻¹ compared with the RFT and nonlinear model predictions of 28.6 and 27.1 mm⋅s⁻¹, respectively.

Experimentally, no difference was found in stroke mechanics or T_P:T_R when viscosity was elevated (equivalent to a 20 °C drop) independently of temperature, yet significant differences in escape distance and velocity were observed. Model results confirm that escape performance is reduced when viscosity increases independent of temperature. This has important implications considering viscosity of seawater can naturally change independently of temperature through release of compounds during phytoplankton blooms (33–35). The change in viscosity can be substantial, with increases of 259% observed during blooms of Phaeocystis globosa (34). Our results suggest copepods will be most susceptible to predators under conditions such as this because the controlling mechanism in altering stroke kinematics seems to be temperature. Therefore, without alterations in temperature, elevated viscosity should favor larger raptorial predators (e.g., larval fish, chaetognaths, and adult copepods) because small swimmers at lower Reynolds number are more negatively affected by viscosity (23). These results show that copepod nauplii have natural adaptive mechanisms to compensate for viscosity variations with temperature but not in situations in which viscosity varies independent of temperature, such as in some phytoplankton blooms.

Understanding the robustness of escapes in the wake of environmental changes such as temperature and viscosity has implications in assessing the future health of coastal ecosystems. These results represent evidence of metazoans exhibiting changes in swimming kinematics to optimize locomotory performance during temperature-induced viscosity change. Although studies have observed kinematic changes during routine swimming of small metazoans at various temperatures and viscosities (20, 36), these did not act to offset lost propulsive performance at low temperature/high viscosity. Instead, Fumian and Batty (20) concluded that kinematic changes were a result of elevated viscosity impeding normal kinematic motion. Seurant and Vincent (35) observed changes in swimming behavior of copepods when located in natural Phaeocystis blooms (elevated viscosity) but suggested this as a mechanism to optimize foraging, not propulsion. Other organisms exhibit energetic compensation for temperature-induced viscosity change through morphological changes. In the case of jellyfish, phenotypic plasticity among juveniles is adapted to altered fluid regimes imposed by changes in ambient temperature (37). Other studies have suggested morphological variation in exoskeleton and muscles can improve performance at elevated viscosity (38), and the presence of spines has been suggested to aid in reducing sinking rates of plankton at low viscosity (39, 40).

Conclusion

An unavoidable consequence of reduced temperature is slowing of neural transmission (41) and muscle contraction (30), which results in reduced appendage velocity. We show this reduces swimming velocity in copepod nauplii but is partially offset through a modulation of swimming kinematics. By exhibiting differential temperature sensitivity (Q₁₀ values) and altering appendage timing during the power stroke during escape swimming, the copepod nauplius varies T_P:T_R, which acts to maintain escape effectiveness as temperature changes. We hypothesize that because temperature (not viscosity) controls these rate-dependent processes, modulation is autonomous and continuously variable, thus providing optimal escape kinematics across short-term or seasonal cycles. However, the results suggest that conditions in which viscosity changes independently of temperature can place small copepods, relying on rapid escape swimming, at a distinct disadvantage.

Materials and Methods

Experimental Setup.

Viscosity was adjusted by dissolving methylcellulose polymer (25 cP) in filtered seawater. A Cannon-Fenske routine viscometer was used to determine the concentration of methylcellulose solution that matches the viscosity of 30 °C seawater (ν = 0.85 × 10⁻⁶ m²⋅s⁻¹) to that of 10 °C seawater (ν = 1.35 × 10⁻⁶ m²⋅s⁻¹). Methylcellulose has no effects on the metabolic rates of organisms (20, 42). Experiments were conducted in a temperature-controlled walk-in incubator accurate to ±1 °C. For each trial, twenty Acartia nauplii were transferred from the hatching beakers to an observation cuvette of 10 × 10 × 45 mm. The nauplii were allowed to acclimate for 30 min before testing, and no more than 10 escape responses are recorded per trial to reduce the probability of multiple recordings of the same animal. The hydrodynamic stimulus that emulates an approaching predator was provided by a submerged sphere (4-mm diameter) attached to a piezoelectric pusher. The stimulus controlling both the high-speed camera and piezoelectric pusher was manually activated when one or more copepod nauplii were positioned near the plastic sphere. Thirty escapes were recorded for each experimental condition.

Escape Characterization Using High-Speed Digital Holographic Cinematography.

Holograms were created by illuminating the cuvette with a coherent, collimated near- IR laser beam (808-nm wavelength) from a 40-mW continuous-wave laser diode. Near-IR light was chosen to illuminate the field of view because A. tonsa exhibits low sensitivity to this wavelength (43). Magnification was provided by a 4× objective. The resulting interference pattern was recorded at 3,000 Hz by a complimentary metal-oxide semiconductor video camera (Y4; IDT) with 1,024 × 1,024 pixel resolution. The 3D optical field is numerically reconstructed (44) at depth intervals of 15 µm over the 10-mm sample volume. Once a stack of images is reconstructed, the position of the copepod is extracted using a hybrid two-step autofocusing routine (44). The first procedure determines the 3D coordinates of each particle using an automated segmentation procedure (27, 45), which extracts the characteristics of each object, including particle size, 3D centroid, and intensity distribution. These characteristics are used to track the movement of the nauplius over time. To improve accuracy in locating the in-focus z plane, a second procedure relying on the sharpness of the nauplius image edge (46) is applied to planes located within ±200 µm around the estimated centroid. The sharpness is defined based on the edge of nauplius body (47). To ensure accuracy of automatic analysis based on measured dimensions and to gain confidence in the results, all in-focus files were manually examined and any frames out of focus were manually corrected based on the measurement of object sharpness over the depth.

Data Analysis.

We compared the difference in escape performance parameters of the A. tonsa nauplii among the 30 °C, 10 °C, and 30 °C+MC treatments using a one-way ANOVA or Student’s t test (when only two groups were compared). All data were log-transformed and checked for normality using a Shapiro–Wilk test. In a few cases when normality was not achieved through transformation, the nonparametric Mann–Whitney test was used to compare means between two treatment groups. No smoothing functions were applied to raw data, but figures with line graphs were plotted using a simple spline curve.

A simple model was created to determine the relative contribution of stroke timing to swimming performance, based on resistive force theory (SI Materials and Methods). Temperature dependence of swimming kinematics was determined from the Q₁₀ formula (SI Materials and Methods).