Swimming behavior and prey retention of the polychaete larvae Polydora ciliata (Johnston)

Spionid polychaetes are some of the most common benthic invertebrates of neritic environments. Hence, during certain periods, their planktotrophic larvae are very abundant in coastal waters. They reach concentrations >1000 l^–1 and are a major component of the zooplankton community (Anger et al., 1986; Zajac, 1991; Bochert and Brick, 1996; Pedersen et al., 2008). Spionids are one of the most common and widespread polychaete families in the Oslofjord, Norway (Schram, 1968) and in the Iseford complex, Denmark (Rasmussen, 1973) from which the present larval material was collected. Among spionids, Polydora ciliata is one of the dominant species, with a wide geographic distribution in Northwest Europe, and it is also found in Australian and Japanese waters as an introduced species (NIMPIS, 2002). P. ciliata larvae may be the single most dominant polychaete larvae in neritic waters and reach concentrations >500 l^–1 and their potential trophic role cannot be neglected (Daro and Polk, 1973, Pedersen et al., 2008; Pedersen et al., 2010).

Fig. 1 shows P. ciliata in the early, intermediate, and late larval stage. Polydora spp. larval morphology is described in detail by Wilson (Wilson, 1928), Hannertz (Hannertz, 1956), Blake (Blake, 1969) and Plate and Husemann (Plate and Husemann, 1994). Based on the detailed sketches by Wilson (Wilson, 1928), we presume that the ciliary swimming apparatus is primarily composed of a band of closely spaced cilia (the prototroch), surrounding approximately three-quarters of the head circumference, and secondarily by a band of cilia around the terminal segment (the telotroch). Many spionids lack feeding cilia (‘metatroch’) and food groove, and must therefore capture particles using alternative mechanisms (Pernet and McArthur, 2006). This is most likely the case for P. ciliata larvae.

Data on particle size retention in polychaete larvae are scarce. For example, the upper limit for ingestible particle size increased with larval size for Streblospio benedicti (Pernet and McArthur, 2006) and also for a gastropod veliger. For the gastropod veliger it was simply explained by changes in morphological dimensions of the feeding apparatus (velum structures) (Hansen, 1991). The linkage between particle retention mechanism and the morphology of the ciliary feeding apparatus are not reported for Polydora larvae. In the spionid Marenzelleria cf. viridis phytoplankton <20 μm were the principal dietary component and a maximum prey diameter of 80 μm is described for larvae with 6–10 segments (setigers) (Burckhart et al., 1997). Polydora has been reported to have been reared on microalgae (Anger et al., 1986), and Daro and Polk (Daro and Polk, 1973) reported small phytoplankters and even invertebrate larvae as prey. No comprehensive uptake efficiencies of a coherent broad regime of prey sizes are reported for any spionid larvae.

Here we address prey size selectivity and the swimming patterns of Polydora larvae following offerings of different sized prey either as single species or as mixtures of in situ prey. To facilitate the interpretation of the observed development in ontogenetic swimming behaviors we developed a simple swimming model based on low Reynolds number hydrodynamics. Using the modeling approach we further interpreted our observations of the maximum clearance rate and its dependence on larval size. Thus our aim was to explore the interaction between functional morphology and behavioral components in spionid larval suspension feeding.

Live zooplankton was collected from surface water (0–2.5 m) with a 50 μm WP-2 net equipped with a non-filtering cod-end by horizontal trawling at slow speed. The sampling station ‘Søminestationen’ (55°44′N, 11°48′E) is situated in the Isefjord, Denmark, and it is shallow with muddy bottom sediments and eutrophic waters. Once the net was retrieved, zooplankton was gently transferred to an isothermic container, diluted with surface water, and transported to the laboratory within 2 h of collection. In the laboratory, P. ciliata larvae were concentrated using a cold fiber optic light source, sorted with a pipette under the dissecting microscope and placed in a beaker with 0.2 μm filtered seawater (FSW) from the sampling area. In order to reduce contamination by other planktonic organisms, the larvae were washed repeatedly by transferring them through a series of Petri dishes with 0.2 μm FSW until ambient phytoplankton were absent.

Swimming of P. ciliata larvae (N=58) of various lengths was studied in a 15×15×15 cm³ acrylic aquarium at a temperature of 20°C and a salinity of 15 PSU. The setup allowed us to visualize swimming trajectories spatially and estimate true three-dimensional swimming velocities and behaviors. Briefly, a mirror was mounted transversely inside the aquarium allowing direct observations of larvae and their mirrored images simultaneously. Illumination was provided by an infrared light-emitting diode placed perpendicular to the camera. The diode was positioned in the focal point of a Fresnel lens (diameter 16 cm), thus creating parallel (collimated) light beams in the experimental aquarium and in turn mirrored into a monochrome analogue CCD video camera (Minitron MTV-1802CD, Minitron Enterprise Company, Taipei, Taiwan) fitted with a 105 mm lens. Size calibration was done by filming a ruler and converting pixels to millimeters. Video observations were recorded on a VHS tape recorder. After recording the video sequences of interest were digitized using a Pinnacle movie box™ (Pinnacle Systems, Mountain View, CA, USA) into QuickTime™. Movies and motion tracks were analyzed using a motion analysis software package (LabTrack, Bioras.dk, Nivå, Denmark). After the motion tracks were digitized, three-dimensional tracks were reconstructed by merging each motion track with the mirror track manually. Larval swimming was studied in three prey regimes: filtered seawater, filtered seawater with Rhodomonas salina added as small prey, and filtered seawater with Akashiwo sanguinea added as large prey (Table 1). Length and diameter of live animals (N=57) were estimated from size-calibrated video frames in the software package ImageJ (http://rsbweb.nih.gov/ij/index.html).

A sub-sample of (N=25) live larvae of a wide range of development sizes was sedated with a few drops of MgCl₂ in a small 4 mm deep micro-well and lengths of the prototroch, the telotroch and the larval body were measured. Larvae were separated in three groups according to size (Table 2). The MgCl₂ was applied until the larvae ceased moving. Apart from inducing body shrinkage, MgCl₂ seemed not to damage the larvae, as they recovered after a short period of time and resumed swimming. The larvae were photographed under a microscope at 100× magnification and the images were subsequently analyzed using the software package ImageJ.

The functional response for three different development stages of P. ciliata larvae fed the diatom Thalassiosira weissflogii was determined. The full data-sets are presented elsewhere (Almeda et al., 2009). Larvae were separated into three groups according to size (Table 2). Subsamples of larvae from each size group (N=25–30) were fixed in 5% acid lugol solution, and the average lengths and numbers of setigers were determined using an inverted microscope. Initial grazing trials with aged tank seawater turned out unsuccessfully and instead 0.2 μm filtered seawater from the sampling area was used. Thalassiosira weissflogii were provided from a stock culture growing in B1 medium (Hansen, 1989). Stock phytoplankton concentrations and the size (equivalent spherical diameter; ESD) of Thalassiosira weissflogii were determined by a Multiziser III Coulter Counter electronic particle counter (Beckman Coulter, Miami, FL, USA). The cell carbon quota used was 131 pg C cell^–1 (Dutz et al., 2008). Each grazing trial was executed in triplicate grazing bottles with parallel triplicate phytoplankton growth controls. Average concentrations of larvae ranged from 2.6 to 1.0 larva ml^–1 for early and late larval stage, respectively. The phytoplankton suspensions were amended with a nutrient mixture to compensate for nutrient enrichment due to larvae excretion. The incubations were carried out in 70 ml blue cap glass bottles mounted with plastic film before closing to prevent inclusions of air bubbles. Bottles were incubated for 24 h on a slowly rotating plankton wheel (0.5 r.p.m.) in a temperature-controlled room at 16°C and constant dim light (<5 μmol photons m^–2 s^–1).

Cell concentrations in grazing and control trials were determined by a CytoBuoy scanning flow cytometer (CSFC; CytoBuoy b.v., Woerden, The Netherlands). The CSFC is designed to process live phytoplankton particles larger than 1 μm. In this study we counted around 0.5 ml samples in triplicate. The prey cell in the experimental trials was counted by leaving the CSFC sample suction tube directly into the incubation bottles. During counting, the trial bottles were carefully stirred with a mechanical stirrer set at the lowest r.p.m. Prior to starting a series of grazing trials, we compared the counting performance of CSFC to the electronic particle counter and found no significant deviation between the instruments (Almeda et al., 2009). Clearance and ingestion rates were calculated for each food concentration according to Frost (Frost, 1972) after the verification that prey growth rates in grazing bottles were significantly lower than in the prey growth controls (one-way ANOVA, P<0.05) and the maximum rates derived from the functional response equations.

We conducted experiments to examine larval feeding efficiency as a function of particle size for early and late larval stages. The two stages were separated from collected larvae according to their size. Larvae were offered potential prey of different size (ESD) ranging from 4 to 53 μm (Table 3). Otherwise the experimental procedure was as described above. The experiments were performed with one phytoplankton species per experimental treatment and with an equal initial phytoplankton biomass (0.2 μg C ml^–1 and 1 μg C ml^–1 for early and late larval stages, respectively). The prey retention efficiencies are given as the clearance rates on the different sized prey, according to Frost (Frost, 1972).

The experiments consisted of incubations of natural microplanktonic communities with the addition of P. ciliata larvae for the experimental treatments. Natural seawater (NSW) for grazing incubations was collected at 1 m depth with a Niskin bottle and screened through a 200 μm mesh by reverse filtration in order to exclude mesozooplankton. The water was amended with a nutrient mixture to compensate for nutrient enrichment due to larval excretion. Twelve 70 ml blue cap bottles were filled with NSW. Then 75 late-stage larvae approximately 900 μm long, were added to six of the NSW-containing bottles. Two bottles with larvae and two without larvae were fixed with 1% acidic Lugol's solution to determine the initial microplankton abundance. The remaining eight bottles consisting of four grazing bottles and four control bottles were incubated for 24 h on a plankton wheel (0.5 r.p.m.) in a temperature-controlled room at 16°C and constant dim light.

Ciliate, dinoflagellate and diatom abundance was estimated by settling 10 ml aliquots in Utermöhl chambers for 24 h in two replicates per treatment and counted under an inverted microscope. Digital images of each cell type were taken and sized with the open source software package ImageJ. Cell volumes were converted into carbon content using a factor of 0.19 pg C μm^–3 (Putt and Stoecker, 1989) whereas the carbon of dinoflagellates and diatoms were estimated accordingly to the recommendations of Menden-Deuer and Lessard (Menden-Deuer and Lessard, 2000). Grazing was calculated if prey types in grazing trails were significantly different from controls (one-way ANOVA, P<0.05). Clearance and ingestion rates were calculated for each prey type according to Frost (Frost, 1972).

The body length (l) of the larvae that we used for motion analysis ranged from 0.3 mm to 1.0 mm (Fig. 2). The diameter of the larval head and hence the circumference of the prototroch cilia band increased as the larval body length increased. The number of setigers increased from typically three to 13 during growth (Fig. 1 and Table 2). The diameter of the larvae (d) ranged from 0.16 mm to 0.26 mm and l/d increased by a factor of two during growth from l/d=1.9 on average for the early larval stage to l/d=3.8 on average for the late larval stage and hence the larvae did not grow isometrically (Fig. 2). The prototroch cilia were of comparable length in the intermediate and late larval stages and in these stages the cilia were significantly longer than the cilia in the early stage (one-way ANOVA, P<0.001; Table 2). The telotroch cilia, however, seemed not to increase in length significantly during larval ontogeny and remained statistically invariable during the larval development (one-way ANOVA, P=0.356).

The larvae were swimming in helical paths and showed large individual variations (Fig. 3). A typical swimming path is a sequence of downwards, upwards, and horizontal trajectories. We tested swimming speed of the general swimming groups, i.e. horizontal, downwards and upwards swimming against prey and filtered seawater and found no significant differences in the swimming speed when different prey was offered (one-way ANOVA, P>0.05; Table 1). Furthermore we did not see any differences in swimming pattern and the data sets were pooled into one data set consisting of swimming paths divided into three groups based on the overall swimming direction: horizontal, downwards and upwards swimming. The average of all our measured horizontal swimming speeds (V) is 0.50±0.21 mm s^–1 and we observed that the average horizontal swimming speed decreases slightly with increasing body length (Fig. 4). The larvae swam downwards significantly faster than they swam upwards: V_down=0.93±0.40 mm s^–1versus V_up=0.42±0.19 mm s^–1 (t-test, t=5.6, d.f.=58, P<0.001) and the difference between the average upward and downward swimming speed increased with increasing body length. In the following we show that our observations on the swimming behavior can be explained using a simple swimming model based on low Reynolds number hydrodynamics and taking the effect of gravity on the slightly negatively buoyant larvae into account.

In our hydrodynamic model we assumed that each individual larva swims lengthwise with constant velocity due to the propulsion force generated by the ciliary swimming apparatus, and that the propulsion force is balanced by the drag on the larval body. We will not attempt to describe the helical swimming paths of the larvae, but only the observed average swimming speed. For simplicity we model the cigar shaped body of the larva as a prolate spheroid with polar radius a=body length/2 and equatorial radius b=body diameter/2.

The maximum clearance rate increased approximately proportionally to the larval body length, and the body volume specific clearance rate therefore showed a dramatic 10-fold decrease from 10⁵ body volume h^–1 in the early larval stage to 10⁴ body volume h^–1 found in the late larval stage (Fig. 6). The same characteristics are exhibited by the maximum ingestion rate that increased from approximately 2×10³Thalassiosira weissflogii cells per larva per day to approximately 10⁴T. weissflogii cells per larva per day. A dramatic decrease in the body volume specific ingestion rate, similar to the decrease in the body volume specific clearance rate was likewise observed (Fig. 7).

The larvae of P. ciliata are able to feed on prey ranging in size from 4 μm to 53 μm (Fig. 8). Clearance rates varied with prey size and larval length. The early larval stage displayed a maximum retention (optimal prey size) for particles of 12.9 μm and showed a reduced retention for smaller and larger particles. The late larval stage retention increased with particle size until a maximum somewhere between 19 μm and 53 μm was reached.

The protist plankton community was initially dominated by the dinoflagellate Heterocapsa triquetra with more than 400 cells ml^–1, and its abundance exceeded the abundance of ciliates of approximately 4 cells ml^–1 with a factor of 100. The ciliate community consisted mainly of Strombidium spp. Diatoms were scarce with only 0.1 cells ml^–1 and they consisted mainly of Ditylum cf. brightwellii and Coscinodiscus spp. Feeding rates on dinoflagellates and ciliates are shown in Table 4. The dominance of H. triquetra made dinoflagellates the most important source of food for P. ciliata in this situation. However, ciliates that made a much less abundant food source were in fact cleared at a rate that was 2.5-fold higher than the clearance rate on H. triquetra.

No systematic differences in the patterns of the swimming paths related to larval size or food particle regime were observed, and we found similar swimming paths even when the larvae were exposed to 0.2 μm filtered seawater. Earlier observations, which were interpreted as raptorial feeding behavior, are most likely reactions to physical obstruction by a large particle as shown for gastropod veligers and calanoid copepodites (Hansen et al., 1991). Moreover, at any given larval development stage, the larval swimming paths of individuals were very variable (Fig. 3). This is also described by Wilson (Wilson, 1928) where the larvae frequently swims slowly rotating on their longitudinal axes, sometimes in circles about one place, and sometimes they curl up and erect their body spines when disturbed. We have speculated that the adaptive significance of an apparently non-predictable swimming path besides the spine erection could be a means of predator avoidance, but this remains to be verified.

The horizontal swimming speed decreases slowly with body length, which indicates that the propulsion force due to the ciliary swimming apparatus increases slower with body length than the drag on the body. Wilson (Wilson, 1928) suggested that body spines contribute negligibly to the drag, and that the notochord moderately or not at all contributes to the swimming force. Hence, we modeled the propulsion force as generated by the prototroch and the telotroch solely. The decrease of the measured average horizontal speed is well described by the simple swimming model (Eqn 10 and Fig. 4) which takes into account that the larvae become relatively more slender (Figs 1 and 2) during their ontogenetic development. However, we speculate that our fit C_FηU=2.0×10^–6 N m^–1 may be an underestimate of the cilia force per unit length of the cilia band, and also that the cilia force per unit length is not constant but increases slowly throughout larval development as each cilium gets longer. There are two main reasons for the possible underestimate of the propulsion force. First, in the simple model we balance the propulsion force due to the cilia swimming apparatus by the drag on a passively sinking prolate spheroid. In general the flow around a freely swimming larva is different from the flow around a passively sinking larva, and we note that our modeling approach does not take this into account. Langlois et al. (Langlois et al., 2009) considered a simple model of a self-propelled flagellate consisting of a spherical body with a cylindrical flagellum, and showed that the drag on the body is larger for a self-propelled flagellate relative to the drag on a passively sinking sphere. We presume that our estimate of the propulsion force for the swimming larvae similarly underestimates the true propulsion force, since we do not take into account the increase of the flow speed near the larval body due to the beating cilia. Second, the drag on the larval body may be larger than the prediction obtained from the prolate spheroid expression in Eqn 3, since this expression is derived for an object with a smooth surface and ignores the rough surface and setae structures on the larval body. This could lead to an underestimate of the propulsion force. Presumably this effect is more pronounced in the late larval stage, since the larvae at this stage begin to develop large palps (Fig. 1). Both a detailed morphological description of the cilia band structures and close observations of the metachronal wave of the beating cilia in swimming larvae in combination with direct numerical simulations of the flow past the larva would be needed to fully address these issues.

Planktotrophic larvae display actively phototactic behavior after hatching and this is also described for P. ciliata (Wilson, 1928). This is an adaptation to swim towards the photic zone of the water column where phytoplankton availability is highest. Later when approaching competence for metamorphosis they become negatively phototactic, which is interpreted as an adaptation to seeking settlement on the sea floor (Thorson 1950; Thorson, 1964). The relationship between propulsion force and gravity suggests that the hydrodynamic constraints could play a direct role in the settlement process (Fig. 5). The buoyancy-corrected weight of the slightly negatively buoyant larva becomes more and more important in comparison with the propulsion force as the larval size increases, and gravity therefore puts a final constraint on how large the larva can be without sinking. Eqn 12 suggests that the maximum body length l_max increases with increasing propulsion force per unit length of the cilia band C_FηU and decreases with increasing density difference ρ_s–ρ. In our estimate we used the value C_FηU=2.0×10^–6 N m^–1 obtained from our fit of the swimming model prediction to the measured horizontal swimming speed. We assumed that the larvae on average are 0.5% denser than water and found good agreement with the observation that the largest free swimming larvae have a body length of approximately 1.0 mm, which is supported by the findings by Hansen (Hansen, 1999). The larvae in the present study had up to 13 setigers where they at maximum can obtain 18 setigers and still be pelagic (Thorson, 1946). However, the largest possible value of the average larval density would be larger if the actual value of the cilia force per unit length is larger than our present estimate as discussed above. It is very challenging to measure the excess density, since the larvae contract upon fixation, and we have not been able to find values for the excess density of polychaete larvae in the literature.

The propulsion force generated by the cilia apparatus of the larva balances the drag on the body of the larva when the larva is swimming freely with constant velocity. The net force exerted on the water by the larva is therefore zero and the flow relative to the larva is well approximated by a velocity field with parallel streamlines and constant flow speed equal to the swimming speed (Visser, 2001). The flow generated by a freely swimming larva differs from the flow generated by a larva that is tethered either by gravity as discussed by Strickler (Strickler, 1982) and Emlet and Strathman (Emlet and Strathman, 1985) or by mucous threads as explored by Fenchel and Ockelmann (Fenchel and Ockelmann, 2002). However, in general, the effect of tethering on the maximum clearance rate depends on the prey capture mechanism and the interaction between prey and cilia as discussed by Emlet (Emlet, 1990). We have not found evidence that P. ciliata larvae have mucous threads or that gravity, despite the observed effect on the upward and downward swimming speeds of P. ciliata larvae, should have a qualitative influence on the flow structure and result in an increase of the maximum clearance rate in the late larval stage.

The maximum specific clearance and ingestion rates should be measured using prey with size as close as possible to the optimal prey size, especially when comparing different developmental stages of given larvae. Here it was recorded on Thallassiosira weisflogii, which were close to the optimal prey size for both early and late larvae (Fig. 8). It was recorded to be higher than reported for Mediomastus fragile and Marenzelleria cf. viridis (Hansen, 1993; Burckardt et al., 1997), but similar to other ciliated larvae (Jespersen and Olsen, 1982; Hansen and Ockelmann, 1991). We assume that the particle capture is by the prototroch and maybe more ciliary structures in combination as described by Strathmann (Strathmann, 1971) and Hart (Hart, 1996). The measured maximum clearance rates are described reasonably well by Eqn 14, using 27 μm as the prototroch cilia length (l_c) for the early larval stage, 45 μm for the intermediate larval stage, and 48 μm for the late larval stage (Table 2; Fig. 6). The maximum clearance rate increased approximately proportionally to the larval body length, and the body volume specific clearance rate therefore showed a dramatic 10-fold decrease. Increasing clearance and ingestion rates as well as increasing optimal prey size has been demonstrated for crustaceans, e.g. the shrimp Sergestes similis and the copepod Acartia tonsa (Omori, 1979; Berggreen et al., 1988). However, specific food uptake rates declined with body weight (Omori, 1979) and optimal prey size remained constant for a ciliated gastropod veliger (Hansen and Ockelmann, 1991). Moreover, a thorough compilation of 13 echinoderm larval species reveals a substantial variation in feeding capabilities among larvae of similar size and shows that some are better suspension feeders than the others. Hence, no clear pattern in size-related clearance rate was detected (Hart, 1996).

The ontogenetic retention spectrum exhibits a constant sized minimum prey, an increased optimal prey size and also an increased maximum prey size with larval body size. This is most probably related to the morphological constraints and the ontogenetic changes in the ciliary apparatus (Hansen, 1991; Riisgaard et al., 2000). However, in contrast to the opposed band veliger the maximum prey size for late P. ciliata larvae seems to be larger, which is supported by late stage larvae when capturing motile oligotrich ciliates in the natural prey regime. This could be due to the increasing length of the prototroch cilia, dimensions of the mouth structure, or a contribution from the tentacles. Oral diameter is, for instance, described as being the upper limit for the size of prey for single band echinoplutei larvae (e.g. Rassoulzadegan et al., 1984). Since the principle behind food particle capture is not thoroughly understood we suggest that there should be further investigation of the morphology and functional capability of P. ciliata larvae. However, no matter how prey capture takes place the resulting principal ontogenetic changes in particle retention add to a reduction in intraspecific food competition among the various larval stages as suggested for a calanoid copepod (Berggreen et al., 1988).

When larvae were exposed to a natural prey field, ciliates were cleared significantly more than dinoflagellates, even though the dinoflagellate concentration was two orders of magnitude higher than the ciliate concentration (Table 4). Since dinoflagellates swim slower than ciliates (Hansen et al., 1997) and diatoms are non-motile in the water column, the higher clearance rates observed on ciliates, may be the results of a swimming-velocity-driven increased encounter probability of ciliates over the alternative prey particles (Jakobsen, 2005).

The larva did not display any specialized behavior as a response to the ambient prey regime. Not only do larval morphology and behavior govern larval feeding, prey behavior such as swimming speed also influence the feeding efficiency of P. ciliata. The larvae ontogeny seems to favor high prey uptake rates in the early stage with a remarkable 10-fold decrease of the specific clearance rate from 10⁵ to 10⁴ body volumes h^–1 during ontogeny (Fig. 6). The same phenomenon is reported for larvae of Philine aperta with a factor of five decrease in maximum clearance during ontogeny (Hansen and Ockelmann, 1991). Additionally, a decrease in maximum specific clearance rate with size of zooplankton within the 2–2000 μm body size range reveals a common scaling factor of –0.23 (Hansen et al., 1997).

We would like to thank an anonymous reviewer and Dr R. R. Strathmann for constructive criticism and suggestions for changes of an earlier version of this manuscript. This work is based on research performed at Roskilde University's field station “Søminestationen”.

 
• a

  larva model, polar radius (mm)

 
• b

  larva model, equatorial radius (mm)

 
• c

  larva model, geometric parameter (mm)

 
• C_D

  drag coefficient (dimensionless)

 
• C_F

  propulsion force coefficient (dimensionless)

 
• d

  larva diameter (mm)

 
• d_max

  maximum larva diameter (mm)

 
• D

  drag (nN)

 
• F

  propulsion force (nN)

 
• g

  acceleration due to gravity (m s^–2)

 
• 

  maximum ingestion rate (cell larva^–1 day^–1)

 
• l

  larva length (mm)

 
• l_c

  prototrochal cilia length (mm)

 
• l_max

  maximum larva length (mm)

 
• m′

  buoyancy-corrected mass of larva (kg)

 
• 

  maximum clearance rate (ml larva^–1 day^–1

 
• U

  effective speed of the beating cilia (m s^–1)

 
• V

  swimming speed, horizontal (mm s^–1)

 
• V_down

  swimming speed, downward (mm s^–1)

 
• V_up

  swimming speed, upward (mm s^–1)

 
• α

  prototroch, geometric parameter (dimensionless)

 
• η

  dynamic viscosity (Pa s)

 
• ρ

  density of water (kg m^–3)

 
• ρ_s

  average density of larva (kg m^–3)

 
• τ₀

  larva model, geometric parameter (dimensionless)