J. Phycol. 31, 200-208 (1995)

REVIEW

TRAJECTORIES OF AUTOTROPHIC MARINE DINOFLAGELLATES

Daniel Kamykowski Department of Marine, Earth Lk Atmospheric Sciences, North Carolina State University.

Raleigh, North Carolina 27695-8208

Flagellated cells, separated into approximately 1 0 major botanical taxonomic categories (classes or phyla), are a prominent component of the phyto- plankton (Cox 1980). The different phytoflagellate body types represented in each taxonomic category typically extend over a characteristic size range (Cox 1980) and exhibit characteristic flagellar number, external structure and insertion (Sleigh 1991), and unique flagellar beat patterns (Goldstein 1992). These attributes combine to provide a broad range of different propulsion systems with various degrees of effectiveness (Goldstein 1992). Although marine dinoflagellates, whose motility is described only qualitatively (Levandowsky and Kaneta 1987), are the focus of this review, many aspects of the discus- sion generally apply to all flagellated autotrophs.

The subsequent discussion of dinoflagellate mo- tility in an environmental context begins with a con- sideration of the group’s flagellar propulsion system. Next, the two components of cell velocity, swimming speed and swimming direction, are considered with respect to environmental sensitivity and to the cell’s biosynthetic cycle. Finally the cell’s motility is dis- cussed in the context of vertical water motions in the upper ocean.

DINOFLAGELLATE FLAGELLAR CHARACTERISTICS

Dinoflagellates (Spector 1984, Taylor 1987a) are among the most conspicuous marine phytoflagel- lates because of their abundance in accessible coastal waters (Taylor and Pollingher 1987), their unusually large cell size range extending from 10 pm to 2 mm (Steidinger and Cox 1980), and their distinctive di- nokont or desmokont morphology (Taylor 1987b). Goldstein (1 992) reviewed dinokont and desmokont flagellar morphology. In dinokonts, the two flagella, called the longitudinal (I) and the transverse (t), gen- erally have a lateral insertion (t above 1) and occur in grooves (Taylor 198713). The longitudinal flagel- lum usually is rounded but can be ribbon-like and can extend posteriorly behind the cell for over 200 pm. The transverse flagellum is ribbon-like with many inherent bends (3-4 waves per 10 pm, Taylor 1987b) and typically extends around the cell (Lev- andowsky and Kaneta 1987). The transverse flagel- lum and an adjacent strand are contained in a mem- brane. This unit assumes a complex, left-handed he- lical shape where the pitch angle is steeper within the cingulum (strand side) than at the outer edge (flagellum side). Mastigonemes, hair-like structures

that can be attached to a flagellum and that are capable of altering hydrodynamic flow, have been reported (Gaines and Taylor 1985), but their oc- currence remains controversial. Although desmo- kont flagella can be morphologically similar to those of the dinokonts, they are inserted anteriorly and do not occur in grooves. In Prorocentrales, one free flagellum extends away from the cell, while the oth- er flagellum is coiled and is attached to the cell body for most of its length.

Goldstein (1 992) also reviewed dinoflagellate fla- gellar beat characteristics that determine how the propulsive force resulting in cell motion is gener- ated. In dinokonts, the longitudinal flagellum often beats in a plane that may be either perpendicular or parallel to the dorso-ventral surface, depending on species. In Cerutium, the wave form is more rounded than a sine wave and exhibits an amplitude of 14 pm for a wavelength of 74 pm. Observed beat frequencies range from 30 to 65 Hz. The transverse flagellum beats counterclockwise as viewed from the front of the cell. Beat frequencies are not well stud- ied but are estimated at 5 Hz from line drawings in Gaines and Taylor (1985). In the best-studied des- mokont, Prorocentrum micuns, the free flagellum beats with an unusual tip-to-base motion that pulls the cell. The coiled flagellum exhibits a rotational motion that provides a whip-like result at the unattached tip.

A more definitive investigation of dinoflagellate flagellar beat patterns awaits the application of de- veloping technologies. Chen and Hallett (1982) re- viewed the use of quasi-elastic light scattering tech- niques on flagellates that may be useful for the study of the longitudinal flagellum. The properties of the transverse flagellum, however, presently are ob- scured by the proximate cell body. High-speed cin- ematography (Ruffer and Nultsch 1985) and high- speed video provide alternate approaches for the transverse flagellum but require specialized optical magnification and lighting. Until these developing technologies are refined, the information base will limit the ability to relate flagellar beat patterns, modulated by changes in environmental (e.g. tem- perature, salinity) or cellular (e.g. metabolic balance, cell cycle stage) conditions, to variations in dinofla- gellate swimming speed.

The propulsive thrust resulting from each of the dinoflagellate flagella appears to be species-specific (Goldstein 1992). For Gyrodinium dorsum, Hand and

200

DINOFLAGELLATE TRAJECTORIES 20 1

Schmidt (1 975) reported nearly equal contributions of the two flagella to forward thrust but a dominant role for the transverse flagellum in cell rotation. After a survey of over 50 species, Gaines and Taylor (1 985) reported that the longitudinal flagellum pro- vided significant thrust in a few species that exhib- ited minimal turning but acted more as a rudder in most species. Existing hydrodynamic theory (Rob- erts 1981) conceptually applies to the free part of the dinokont longitudinal flagellum that extends be- yond the groove and to the anterior desmokont fla- gella. The membrane-related dinokont transverse flagellum located in a groove and the desmokont coiled flagellum attached to the cell body await a more detailed consideration of wall effects.

DINOFLAGELLATE SWIMMING SPEED

The combined propulsive effect of the two di- noflagellate flagella, modulated by environmental and cellular dependencies, results in a characteristic swimming speed and direction that establishes the biologically determined swimming velocity for a giv- en species. Swimming speed traditionally is estimat- ed from the integrated population movement (often estimated by cell counts or fluorescence) over a die1 vertical migration (DVM) or from microscopic ob- servation of individual cells based on photography or computer analysis of video tapes (Kamykowski et al. 1988). Laser doppler spectroscopy (Bauerfeind et al. 1986) also is available. Swimming speeds de- termined by these various approaches (see Levan- dowsky and Kaneta [1987] for a recent table pro- viding swimming speed estimates for different spe- cies) generally fall in the same range (0.2-2.0 m-h-' or 56-556 pmes-'), but some speeds above 5 m-h-' (>1400 pm-s-') are reported (Lombardi and Capon 1971, Horstmann 1980). Raven and Richardson (1 984) suggested that dinoflagellates are among the fastest phytoflagellate swimmers.

Although the environmental dependence (tem- perature and salinity) of swimming speed is docu- mented (Hand et al. 1965), dinoflagellate swimming speeds often are reported without adequate refer- ence to the full range of environmental conditions under which they are determined (Kamykowski 1986, Levandowsky and Kaneta 1987). To examine potential environmental implications, Kamykowski and McCollum (1 986) surveyed the swimming speeds of 14 dinoflagellate clones representing 11 species (two clones of Gonyaulax polyedra and three clones of Prorocentrum micans). They calculated nonlinear curve fits to swimming speed data collected over a broad temperature range (5"-35" C). Mean maxi- mum swimming speeds ranged from 96 to 598 Fm- s-1 after correction for differences in species-specific temperature optima that ranged from 9.1" to 33.5" C but generally exceeded 25" C. This range of tem- perature optima suggests a differential metabolic ef- fect on different species because changes in the me- dium, like viscosity, influence all species in a similar

way. Mean maximum swimming speeds obtained for the different clones of the same species were similar; the temperature optima were similar for Gonyaulax polyedra but varied by more than 10" C for Prorocen- trum micans. This study emphasized the possible se- lective advantage for a species with a temperature optimum of swimming speed appropriate for a given environment and cautioned against merely ranking species by their room temperature (-20" C) re- sponses. For example, in one set of measurements, Gyrodinium dorsum swam at an average speed of 405 pm.s-' (1.5 m-h-I) at 20" C compared to 560 pm- s-l(2.0 meh-') at its optimum temperature of about 29" C. If these speeds are maintained over 12 h, the faster organism can access a significantly larger por- tion of the water column than the slower organism.

Kamykowski et al. (1988) added a consideration of qualitative gravitational influences, where de- scent is greater than ascent due to sinking rate add- ing to the descent, and quantitative photokinetic influences, where swimming speed increases as a function of light intensity, to those of temperature. T h e goal of this study was to simulate instantaneous environmental influences on the progress of a prob- able DVM. Swimming speed at photosynthetically active radiation intensities above 200 pmol.m-*.s-' exceeded that in the dark by 20%. Ascents aided by phototaxis in the light may compensate for descents aided by cell sinking in the dark. Kamykowski et al. (1 992) considered quantitative gravitational effects and examined the species-specific differences in cell rotation as related to translational velocity. In the former case, the swim : sink ratios decreased from a maximum of about 25 for the smallest cell to a con- stant value of 7.6 for cells with equivalent spherical diameters above 25 pm. In the latter case, cell paths ranged from rotation around the cell's longitudinal axis to helical rotation around an axis with a helix radius equal to several body widths. A large helical radius requires a more complicated view of trans- lational velocity defined as the cell's progress along the axis of the helix.

Studies that examine how different species adjust their swimming speed in response to other environ- mental variables are required. For example, the spectral characteristics of light or various nutrient concentrations may contribute selectively to the sur- vival and growth of different dinoflagellate species through motility modulation and consequent envi- ronmental exposure. Also, the swimming speeds re- ported above as measured in Kamykowski's labo- ratory are exclusively for cells maintained under strict auxotrophic growth conditions with vitamins as the only organic supplement. Because many pho- tosynthetic dinoflagellates are mixotrophic (Gaines and Elbrachter 1987), studies of swimming speed in the presence of organic supplements that support heterotrophy (phagotrophy and organotrophy) are required to better represent these dinoflagellate species under natural conditions.

202 DANIEL KAMYKOWSKI

DINOFLAGELLATE SWIMMING DIRECTION

Natural dinoflagellate populations often aggre- gate in discrete layers in the water column (Levan- dowsky and Kaneta 1987). This phenomenon often requires that the individual cells direct their swim- ming ability to maintain a chosen position in the water column. DVM will be discussed in detail as a well-developed, readily observed expression of di- rected mobility that cycles over a convenient obser- vation period.

“Normal” DVM of autotrophic dinoflagellates classically is modeled as ascent during daylight and descent at night (Kamykowski 1974). Studies of di- noflagellate DVM, however, often report that the organisms descend prior to sunset (e.g. Eppley et al. 1968, Kamykowski 198 lb). This pattern deviates from that expected based on simple positive pho- totaxis. Even more unexpectedly, dinoflagellates frequently exhibit variable phase relationships with daylight (Sournia 1974). These observations range from dusk ascents (Hasle 1950,1954, Forward 19’76) to a field population of Gymnodinium sanguineum that ascended between 2300 and 0400 (Kiefer and Las- ker 1975).

Several studies have examined the effects of dif- ferent external environmental and internal cellular factors on dinoflagellate DVM. External factors in- clude irradiance (Eppley et al. 1968, Blasco 1978, Heaney and Eppley 198 1, Passow 199 l), tempera- ture (Kamykowski 198 lb), salinity (Kamykowski 1981b), oxygen (Harris et al. 1979), and nutrients (Cullen and Horrigan 1981, Heaney and Eppley 1981, Tyler and Seliger 1981). Some of these ex- ternal influences may affect photosynthetic re- sponses (Kamykowski 198 la) or the internal balance among different biochemical pools (Cullen 1985, Cullen et al. 1985), but these physiological and bio- chemical relationships are not established very strongly for dinoflagellates.

Recent research on circadian rhythms (Edmunds 1988) and on passive (Hader 1979, Kessler 1986) and active (Kessler 1986) orientation mechanisms provides additional insight into how dinoflagellates may direct their swimming capability. These topics will be considered next.

Circadian rhythms are reported in the stop re- sponse of Gyrodinium dorsum and Gymnodinium san- guineum (Forward and Davenport 1970) and in the DVM of Ceratiumfurca (Weiler and Karl 1979). In fact, dinoflagellates exhibit circadian rhythms in sev- eral aspects of their physiology and biochemistry (Sournia 1974, Edmunds 1988). The “normal” DVM pattern apparently results from tight coupling to the photocycle such as under the conditions considered by Chisholm et al. (1984). The “deviant” phase re- lationships of DVM with daylight discussed earlier may be interpreted as a reset of the circadian rhythm by non-standard regulating factors, possibly some of the DVM-sensitive environmental factors listed pre- viously. Irrespective of the phase relationship to the

daylight cycle, however, the DVM appears to be circadian. Prezelin (1992), Berdalet et al. (1992), and Latasa et al. (1992) each provided a partial chronotype scheme, a table that outlines biosyn- thetic sequences through the cell division cycle, for dinoflagellates; Edmunds (1 988) provided a more complete listing as an acrophase chart for Euglena. These biosynthetic sequences may dictate a chang- ing optimal orientation in the ambient environment through the cell cycle. Frempong’s (1982) obser- vation that phased cell division in freshwater species of Ceratium hirundinella occurred predominantly in cells that did not descend at night, possibly as an energy conservation measure, provides an example of this tendency.

Passive orientation mechanisms have received re- cent attention as related to gyrotaxis, defined as the orientation of a swimming cell in a velocity gradient resulting from compensating torques due to gravity and shear (Kessler 1986, Pedley and Kessler 1992). The gravitational torque results from an unbalanced mass distribution caused by eccentric position of an organelle (chloroplast or nucleus) or a storage prod- uct pool (carbohydrates or lipids) relative to the cell’s geometric center (Mitchell et al. 1990). The result- ing lever arm interacts with the propulsion system of the taxon under consideration to determine pos- itive or negative geotaxis. For example, a posteriorly weighted cell with anterior flagella pulling the cell contributes to negative geotaxis. At the population level, Mitchell et al. (1 990) suggested that gyrotaxis may contribute to the formation of shear-mediated cell clusters in natural water columns that promote increased passive descent velocities due to 1 0-fold enhanced sinking rates.

Some intriguing observations exist on the possible role of dinoflagellate organelles (chloroplasts and nucleus) and storage product pools (carbohydrate and lipid), as they may contribute to changes be- tween positive and negative geotaxis. First, dinofla- gellate chloroplasts may remain stationary relative to the geometric center since chloroplast motility has been observed, to date, only in non-motile algae (Wagner and Grolig 1991). However, Herman and Sweeney (1975) observed a circadian rhythm in chloroplast ultrastructure characterized by changes in thylakoid spacing and by the presence/absence of ribosomes that may alter the gravitational influ- ence of this organelle over the diurnal cycle. Second, the dinoflagellate nucleus, which contains an enor- mous amount of DNA and, thus, may represent a larger portion of cell mass compared to other uni- cellular algae (Rizzo 1987), can appear as a small compact body in the epitheca after cell division. As the cell matures, the nucleus gains volume and moves under the cingulum, and DNA is synthesized in an- ticipation of cell division. Third, Crawford and Dodge (1974) reported that dinoflagellates can store both polysaccharides and fat as food reserves that lie free in the cytoplasm. Dodge and Greuet (1 987)

DINOFLAGELLATE TRAJECTORIES 203

TABLE 1 . Hypothetical relationships suggesting how changes in organelles or starage pools may injuence geotuxis in an organism with a propulsion system that pushes the cell. Positive geotaxis corresponds to ascent, and negative geotaxis corresponds to ascent.

Structure Descent Ascent

Chloroplasts Postphotosynthesis Prephotosynthesis Nucleus

Position Anterior (newly divided) Central (mature) DNA Post DNA synthesis Pre-DNA synthesis

Lipid Small anterior pool Large anterior pool Carbohydrate Large posterior pool Small posterior pool

Storage

suggested that when both storage products are pro- duced together there is a tendency for anterior lipid droplets and posterior starch grains in the cell body. Cullen’s (1 985) observation that starch tends to in- crease in daylight and to convert to protein at night, especially when nitrate depletion occurs near the sea surface, supports the possibility of a DVM switch related to carbohydrate pool size. Any of these or- ganelle or storage pool transitions may influence individual passive orientation over the diurnal cycle or in interaction with the cell cycle. Although Table 1 suggests some hypothetical relationships between isolated organelle or storage pool changes and as- cent/descent, the actual relationships may be dif- ferent. Because several of these changes may occur simultaneously in natural cells, the end result prob- ably depends on a complex weighting of cooperating and competing processes and not on any individual property.

The consideration of active orientation to light, gravity, and chemicals depends on the existence of sense organelles, most of which are not well known in dinoflagellates. Levandowsky and Kaneta (1987) reviewed the available information on several prob- able dinoflagellate senses. For light responsiveness, no single type of dinoflagellate sensory structure is found. In general, the location of the light-sensitive area for phototaxis is on the ventral side just under the sulcus and often occurs near the junction of the sulcus and cingulum below the base of the longitu- dinal flagellum. Different species appear to respond to different light wavelengths, but blue (450-475 nm) sensitivity is most frequently observed; Proro- centrum micans responds at 570 nm. For gravitational responsiveness, Levandowsky and Kaneta (1 987) speculated that the crystalline inclusions found in some dinoflagellate species may provide a true grav- ity sensing apparatus analogous to statoliths in me- tazoa. This conjecture is strengthened by Fenchel and Finlay (1984, 1986), who implicated a well-de- veloped, mineral-bearing organelle, the Muller ves- icle, in the geotaxis of loxodid ciliate protozoans. Chemical responsiveness is probably universal in di- noflagellates, since phagotrophy and parasitism are common, but is not well known in autotrophs. If these different sensory mechanisms are important for orientation, then changes in orientation may be

correlated with the optimization of cell growth or cell division as related to net photosynthesis or spe- cific biosynthetic requirements (Kamykowski 198 1 a). In this case, the determination of a positive or a negative taxis may be related to how the biochemical balance in the cell affects the interpretation of a sensory signal.

Irrespective of how circadian rhythms are phased with daylight, or whether the orientation is set pas- sively or actively, Eggersdorfer and Hader (1 99 1 a, b) and Kessler et al. (1992) have described motion analysis techniques that monitor the sign (positive or negative) of phototaxis or geotaxis that a dino- flagellate population expresses at a given time. This monitoring tool can support a detailed inquiry into the mechanisms of dinoflagellate swimming direc- tion. Organism characteristics, like the organelle and storage pool distribution or the bulk biochemical state of synchronous cultures, can be related to changes in swimming direction during DVM. These relationships, in turn, can suggest changes in cell state that should be monitored in Lagrangian bio- physical models of DVM (Yamazaki and Kamy- kowski 1991) in the upper mixed layer to control cell orientation. Individual organisms follow inde- pendent trajectories and are capable of cell-specific biosynthetic progress based on unique light expo- sure acting on a realistic photosynthesis submodel (Janowitz and Kamykowski 199 1). Each organism’s photosynthetic history influences the size and/or distribution of its organelles or storage product pools or of its biochemical quota in response to its unique environmental exposure (Yamazaki and Kamykow- ski 1991) and to the progress of its cell cycle (Chis- holm et al. 1984, Olson et al. 1991).

Active orientation models may be conceptualized on optimization arguments (Shuter 1979) and even- tually may be applied in the context of an adaptive behavioral network approach (Beer 1990) that in- corporates feedback loops and response thresholds, as discussed by Keiyu et al. (1993) for zooplankton. In a simple example (Fig. l), the physical dynamics are supplied by a version of the Yamazaki and Ka- mykowski (1 99 1) model. The respiration (night)/ photosynthesis (day) response model, which serves as a proxy for the passive or active orientation mech- anisms already discussed, is adapted from Janowitz

204 DANIEL KAMYKOWSKI

Rim)

0 2 4 6 8 10 12 14 18 18 20 22 24

FIG. 1 . The depths (m) attained by 10 pairs of dinoflagellates swimming around 350 Wm.s-' and undergoing DVMs starting at sunset (0 h) in a turbulent upper Ocean forced by a variable wind speed averaging 3 rnss-' and illuminated with a 12-h sinusoidal daylight cycle that maximizes at 1500 pmol.rn-'.s-'. The 10 organisms represented by open squares follow metabolically trig- gered ascents and descents; the 10 organisms represented by filled squares follow taxis-triggered ascents and descents.

and Kamykowski (199 1). Ten organisms (open squares) begin their ascents on surpassing a thresh- old of cumulative respiration and their descents on surpassing a threshold of cumulative photosynthesis; the other 10 organisms (filled squares) are positively phototactic during the day and positively geotactic during the night. The individuals in the two sets of 10 are paired in the sense that the sequence of wind forcing is identical for both individuals in a pair, but turbulence exposure can vary because of the differ- ent depths occupied at the same time. All of the organisms descend similarly over the first 10 h. The metabolically triggered organisms simultaneously begin their ascent before sunrise because the cu- mulative respiratory threshold is surpassed at the same time in this model run. Due to different light exposures based on the turbulence model, these or- ganisms begin their descents at different times be- fore sunset determined by when the cumulative pho- tosynthetic threshold is surpassed by each individ- ual. In contrast, the taxis-triggered organisms as- cend at sunrise and descend at sunset without regard to their physiological experiences. Under the mod- eled conditions, the metabolically triggered DVM yields greater cumulative production than the taxis- triggered DVM in 9 out of 10 individuals (Fig. 2). This example demonstrates that alternate orienta- tion mechanisms that are tied to cell physiology can support a dynamic interaction, at least in the context of Lagrangian models, in which cumulative light exposure alters behavior to optimize cell growth.

WATER MOTION

Although the biologically determined swimming velocity determines a cell's vertical progress in sta- tionary water columns, vertical water motion can combine with the biological vector to determine the

" 1

-10 1 l l o u

FIG. 2. The difference (metabolically triggered minus taxis- triggered) in cumulative production @g-at O1 (cell)-' (elapsed time)-') attained by the paired cells in Figure 1 throughout the light period beginning at hour .12.

cell's actual trajectory in natural water columns. Denman and Powell (1 984) discussed several differ- ent physical processes related to phytoplankton pat- terns and activity. The subsequent discussion, how- ever, is based on the more restricted discussion in Denman and Gargett (1 983). They specifically con- sidered vertical water motion, due to turbulence, Langmuir circulation, and internal waves, that oc- curs over time/space scales which can influence phy- toplankton photosynthesis. These physical processes affect photos nthesis by influencing the movement

gradients in the upper ocean. Denman and Gargett (1 983) specifically discounted individual cell sinking as a significant biological vector, but they did not consider swimming, which Kamykowski et al. (1992) found to exceed sinking by 7.6 X in cells with equiv- alent spherical diameters >25 pm. The subsequent discussion will review studies that provide infor- mation concerning this interaction between the physical and biological vectors primarily as related to light exposure.

Small-scale turbulence is an emerging topic per- tinent to dinoflagellate motility primarily due to a greater inhibitory effect compared to other algal classes. Berdalet (1 992) provided a recent summary with an emphasis on cell division and growth. Chis- holm et al. (1984) hypothesized that dinoflagellates descend in the water column to undergo phased cell division under the less turbulent conditions that ex- ist deeper in the water column. The benefits based on this hypothesis suggest a possible role for DVM in response to variations in upper ocean mixing based on wind or convective forcing. Small-scale turbu- lence can influence cell trajectories directly due to cell dispersion and disorientation (White 1976) and possible breakage or loss of the longitudinal flagel- lum (Thomas and Gibson 1990a, b). Although lab- oratory-based studies in Couette chambers presently are difficult to transfer to field situations, partly due

of phytoplan E ton cells through light and nutrient

205 DINOFLAGELLATE TRAJECTORIES

to the spatial patchiness and temporal intermittency of natural turbulence, a possible role in dinoflagel- late ecology is suggested. Yamazaki (1993) reviewed the developing ability to examine physical/biolog- ical interactions related to small-scale turbulence through direct numerical simulation that solves the full set of the Navier-Stokes equations. Numerical studies to simulate elusive field effects by combining realistic turbulence and laboratory observations of dinoflagellate responses to turbulence will become possible with the increased availability of high-per- formance computing and communication capabili- ties (Orszag and Zabusky 1993).

Yamazaki (1 993) also reviewed the application of Lagrangian methods to detailed studies of plank- tonic trajectories in predominantly wind-driven up- per ocean layers. This approach typically follows the progress of individual cells with an imposed biolog- ical speed (sinking or swimming) and a preferred direction of progress. The representative vertical water motion depends on how the modeler perceives the turbulent process under consideration. Turbu- lence often is modeled as constant throughout the water column and is represented simplistically as a random walk. The different cell trajectories can be combined to represent the end result of the inter- action on the ensemble. Although dinoflagellates are not necessarily considered, studies by Falkowski and Wirick (1981), Woods and Onken (1982), and Lande and Wood (1987) present versions of this perspective. Yamazaki and Kamykowski (1 99 1) ex- amined the case of depth-dependent turbulence un- der unstratified conditions as suggested by turbu- lence measurements in natural water columns. They explored how well individual dinoflagellate cells with different motility capabilities succeed at DVMs un- der different intensities of vertical water motion. In their model, wind speeds approaching 5 mes-’ gen- erated enough turbulence within the upper 10 m of the water column to overwhelm the persistent swim- ming efforts of the represented dinoflagellates (Gym- nodinium splendens and Gyrodinium dorsum averaged 100 and 350 pmas-’, respectively). Figure 3 provides a detailed example of the effects of turbulence on the DVM of a metabolically triggered dinoflagellate (direction determined by cumulative respiration [night] or photosynthesis [day] thresholds) under a specific set of modeled turbulence conditions. The physical dynamics are supplied by a version of the Yamazaki and Kamykowski (1991) model. The res- piration/photosynthesis response model is based on Janowitz and Kamykowski (1991). The upper part of the figure represents the ratio (zd/z,) given by the turbulent displacement (zd in pm), where zd = (K,t)”, with K, as the eddy diffusivity coefficient (prn*.s-l) and t as 1 s, divided by the distance (z, = v,t in pm) that the organism swims (v,) in 1 s. If the ratio is between 1 and - 1, the swimming speed equals or exceeds the turbulent displacement; increasing ab- solute values of the ratio outside this range signify

15

10 .

0

- 5

s -10 6 -15

-20

-2s

s 5 0

- 5

-10

0 24 48 72 911 120 1U I@ 102 218 240 cuuunnlyo

FIG. 3. The upper part of the figure shows the ratio (D/S) derived by dividing the turbulent displacement distance at the organism’s depth by the organism’s instantaneous swimming dis- tance over the same time increment throughout a IO-day period (240 h). Both turbulent displacement and swimming speed can be positive (moving up) or negative (moving down). The lower part of the figure shows the depths attained by the dinoflagellate during DVMs over a lO-day period (240 h) while exposed to the turbulence regime in the upper part forced by an average wind speed of about 3 m.s-l. Illumination follows a 12-h sinusoidal cycle that maximizes at 1500 ~mol.m-*.s- l ; the time axis begins at sunset.

the increasing influence of turbulence. The lower part of this figure provides the path followed by the dinoflagellate over a 10-day sequence of DVMs. Note that the turbulence causes significant distortion of the swimming path above 10-m depth under the modeled conditions. The shift in the migration phase with daylight over the 10-day sequence is due to light history-related changes in the respiration (as- cent trigger) and photosynthesis (descent trigger) thresholds that were incorporated into the model. Although the modeling approach of Yamazaki and Kamykowski (1994) is controversial (Holloway 1994), the results still can provide useful representations of natural particle dynamics in unstratified water columns. MacIntyre (1 993) recently suggested that future models of upper mixed layer dynamics in stratified water columns need to incorporate esti- mates of time and length scales from microstructure data to provide even more realistic phytoplankton trajectories than have been offered to date.

Langmuir circulation as an organized flow rep- resents a special case of wind-driven vertical water motion. Since Weller and Price (1 988) observed Langmuir-type flows in current meter records, pre- vious deterministic conceptual models of flow effects on biological particles have taken on new immedi- acy. Stavn (1971), Titman and Kilham (1976), and Ledbetter (1979) improved the realism of circula- tion and increased the variety of planktonic organ- isms considered in Stommel’s (1 949) early model. Evans and Taylor (1980) provided a direct analysis of the effect of Langmuir circulation on dinoflag- ellates. They emphasized that the trajectories and

206 DANIEL KAMYKOWSKI

population distribution of the entrained cells strong- ly depended on the time course of dinoflagellate swimming speed and direction rather than on the details of the water motion. As field measurements of Langmuir circulation improve, more realistic bio- physical models incorporating this process soon will follow. For example, Lande and Wood (1987) point- ed out the large amount of turbulence superimposed on Langmuir circulation in the measurements by Weller et al. (1985). In this case, the model by Ka- mykowski (1990) in which Langmuir circulation is treated as a quasi-stochastic process may be more applicable. Different motility capabilities including sinking, neutral, and buoyant cells and cells with different swimming speeds were compared under identical hydrodynamic conditions after 24 h. The observation that each motility type exhibited a unique hyperbolic relationship between depth pen- etration and mixing strength suggested that differ- ences in particle motility can have a measurable ef- fect on the statistics of particle distributions.

The upper ocean internal wave spectrum at a giv- en latitude (A) (Phillips 1969) extends from the sea- sonally variable Brunt-Vaisala frequency deter- mined by water column stratification to the inertial frequency ((2r/l2) sin A). The component internal waves can be multidirectional depending on the geo- graphic location, but, in coastal areas, the waves often are progressive and pro agate toward shore.

eled how motile organisms including dinoflagellates may interact with deterministic water motion asso- ciated with internal waves, especially of tidal periods and with wave heights of 20 m. In general, the ver- tical currents associated with internal tides appear capable of differentially influencing the vertical progress of dinoflagellates along the wave form. A resonance may develop between the DVM period and the semidiurnal or diurnal internal tidal periods; this interaction yields dramatic patch formation if the vertical water motion due to internal tides dom- inates the water columns.

The final qualifying statement in the previous sen- tence identifies a major limitation of the various modeling studies previously discussed. They all ex- amine isolated physical processes instead of the in- tegrated effect of all, simultaneously occurring phys- ical processes as they may interact to determine ver- tical water motion in a natural water column (Haury et al. 1978, Denman and Powell 1984). More real- istic representations of vertical particle trajectories must await more precise field measurements of ver- tical water motion (Kirkpatrick et al. 1990) or pos- sibly a future generation of trackable Lagrangian drifters that are scaled for the Reynolds number regimes appropriate for phytoflagellates. The better definition of dinoflagellate and other phytoflagellate trajectories due to the combined influence of bio- logically and physically induced vectors is an exciting challenge for the future. Realistic trajectories are a

Kamykowski (1974, 1976, 19 ! 9, 1981c) has mod-

prerequisite for accurate interpretations of phyto- flagellate physiology and ecology in the dynamic up- per ocean.

The author acknowledges the research assistance of G. S. Jan- owitz, A. Y. Keiyu, G. J. Kirkpatrick, S. A. McCollum, R. E. Reed, and H. Yamazaki. Support was received from NSF/ONR grant OCE-9115393 and NASA grant NOOO1492-J-1428. The manu- script benefitted from the suggestions of the anonymous review- ers and of the review editor, J. A. Raven.

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