Role of lipids in the maintenance of neutral buoyancy by zooplankton

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1 MARINE ECOLOGY PROGRESS SERIES Vol. 263: 93 99, 2003 Published November 28 Mar Eol Prog Ser Role of lipids in the maintenane of neutral buoyany by zooplankton R. W. Campbell*, J. F. Dower Shool of Earth & Oean Sienes, University of Vitoria, PO Box 3055 Stn CSC, Vitoria, British Columbia V8W 3P6, Canada ABSTRACT: Many types of zooplankton ontain large proportions of lipids. Usually, these lipids represent energy storage ompounds, but it has also been suggested that lipids play a role in buoyany regulation. Lipids are thought to determine the overwintering depth of large alanoid opepods, and it has been widely assumed that these organisms overwinter at some depth of neutral buoyany. However, lipids are generally more ompressible, and have a larger thermal expansion than seawater. This means that any depth of neutral buoyany will be inherently unstable. Model results show that the asent rates attributable to this instability are small at depth (where temperature hanges are small), suggesting a simple way for animals to remain at depth while overwintering. However, model results also show that the buoyant properties of a opepod (or any small plankter) are extremely sensitive to its relative biohemial omposition. This presents problems to maintaining vertial position, but may also be useful for vertial migrations. KEY WORDS: Copepod Zooplankton Lipid Buoyany Model Depth distribution Vertial migration Resale or republiation not permitted without written onsent of the publisher INTRODUCTION Many planktoni organisms use lipids as an energy storage medium (Lee & Hirota 1973, Childress & Nygaard 1974, Sargent & Falk-Petersen 1988). At atmospheri pressure, lipids are less dense than seawater; they often form a layer at the top of preserved zooplankton samples and have even been found to form surfae sliks in the oean (Lee & Williams 1974). It is widely held that suh lipids play a role in buoyany ontrol (Lewis 1970, Sargent & Falk-Petersen 1988). However, a plausible mehanism by whih lipids may be used to regulate buoyany has yet to be proposed. Yayanos et al. (1978) measured the density of a lipid mixture (primarily wax esters) extrated from the alanoid opepod Neoalanus plumhrus and observed the mixture to be more ompressible, and to have a muh higher thermal expansion, than seawater. They suggested that beause of these properties, a lipid-rih plankter that is positively buoyant at the surfae will beome less so as it moves deeper in the water olumn. They onluded that lipids may initially represent a barrier to downward vertial migration, in that opepods are more buoyant at the surfae than at depth, and must therefore overome buoyany fores when moving from shallow to deeper depths. Building on this work, Visser & Jónasdóttir (1999) fit a high order polynomial to the density measurements of Yayanos et al. (1978). Using that relationship, they produed a simple model for the density of a opepod in order to demonstrate how overwintering Calanus finmarhius in the Faroe-Shetland hannel an be positively buoyant at the surfae, but neutrally buoyant at depth. Parameters for the Visser & Jónasdóttir model were alulated from field and laboratory measurements, as well as with the assumption that the opepods were neutrally buoyant at their depth of overwintering. They found that the vertial asent rate attributable to buoyany fores ould be onsiderable (10s of m d 1 ), partiularly near the surfae, where the density differene between seawater and lipids is greatest. The pressure and temperature dependene of the mass density of lipids learly has the potential to affet * rwampbe@uvi.a Inter-Researh

2 94 Mar Eol Prog Ser 263: 93 99, 2003 the way that lipid-rih planktoni organisms relate to and pereive the pelagi environment. Here, we propose that these properties may have a different relationship than that whih has generally been assumed in the literature, and argue that the presene of large proportions of lipids requires some other buoyany regulation mehanism(s) in the zooplankton. NEUTRAL BUOYANCY BY LIPIDS IS NOT STABLE Whether an animal floats or sinks depends on the density differene between it and the surrounding seawater. Thus, a neutrally buoyant animal must have the same aggregate density as the surrounding seawater. However, the greater ompressibility of lipids ompared to seawater means that any depth of neutral buoyany will not be stable. In other words, below the depth of neutral buoyany, lipid will beome denser (as pressure inreases), and thus the aggregate density of the animal will beome greater as well. The onverse is also true. Therefore, any displaement of the animal away from its depth of neutral buoyany should result in it aelerating away from that depth. Hene, the presene of lipids is more than a barrier to downward migration (as suggested by Yayanos et al. 1978), or a means to promote upward migration (as suggested by Visser & Jónasdóttir 1999); it atually represents an impediment to maintaining position in the water olumn. Moreover, as we will illustrate, the buoyany properties of an animal are extremely sensitive to the relative omposition of its biohemial onstituents. ROLE OF LIPIDS IN BUOYANCY REGULATION: A COPEPOD EXAMPLE A simple model for mass density Visser & Jónasdóttir (1999; VJ99 hereafter) divided their model opepod into 3 omponents. At its simplest, the mass of the model opepod an be expressed as the sum of the masses of the omponents: m opepod m water + m lipid + m other (1) If rearranged in terms of density (ρ) and volume (V; i.e. m ρv), this is equivalent to Eq. (3) of VJ99 (subsripts will be abbreviated hereafter). VJ99 further generalized their model with volume proportions (e.g. V l /V ). However, volume is not onservative with pressure (eah omponent is ompressible to some degree), whereas mass is, and so it is preferable to express the model in terms of mass proportions. The density of the model opepod an also be expressed as: This is oneptually idential to the VJ99 model, in that the opepod is divided into 3 omponents (i.e. V V w + V l + V o ). Volume may be expressed in terms of mass and density (e.g. V l m l /ρ l ), and mass proportions (e.g. l m l /m ) may then be substituted into Eq. (2) to yield: ρ ρ m V V V w + l + o w l + + ρ ρ ρ w ρ l an be modeled as a funtion of temperature and pressure (using the polynomial of VJ99, their Eq. 2). ρ w an be determined as a funtion of pressure, temperature and salinity (assuming osmoti equilibrium between the animal and the seawater around it) using the UNESCO seawater equation of state (Millero et al. 1980). ρ o represents the strutural mass of the opepod (e.g. protein, exoskeleton) and here will be held onstant. VJ99 reported values for ρ o of 1080 to 1240 kg m 3. Although the strutural omponents are not ompletely inompressible, they are onsiderably less so than lipids. Kharakoz (2000) ites a oeffiient of ompressibility (β) for protein on the order of 10 to bar 1. By omparison, β for opepod wax esters is of the order bar 1 (alulated from Table 2 of Yayanos et al. [1978], using an exponential fit to volume data at 5.1 C). The hange in seawater and lipid density with hanges in pressure is generally quite small (of the order 1% over 100 bar). However, sine it is the differene between these densities that drives buoyany fores, even very small hanges in density an result in large hanges in asent or deent rates. Furthermore, only small hanges in the relative proportion of the 3 model onstituents (i.e. lipid, water and other ) are neessary to produe dramati hanges in the buoyany properties of the model opepod. To demonstrate the sensitivity of the model to hanges in the parameters, we have altered water and lipid ontents while keeping ρ o ( other ) fixed, and alulated asent rates given the density alulated for the model opepod (Fig. 1). To make the reformulated model omparable to that of VJ99, their volume proportions (α o ) were onverted to mass proportions ( l ; see Appendix 1). VJ99 hose their parameters given lipid:dry weight ratios from 0.29 (opepods used in laboratory measurements of density and lipid ontent) to 0.59 (representative of overwintering Calanus finmarhius in the Faroe-Shetland Channel). To assess a likely parameter spae for the model, the range of alulated asent rates given those upper and lower limits is indiated within the shaded areas of Fig. 1. l o o (2) (3)

3 Campbell & Dower: Lipids and buoyany of zooplankton 95 In the examples presented here, a ~2% hange in water (and lipid) ontent is suffiient to ahieve neutral buoyany over the entire 850 m water olumn (dashed zero ontours of Fig. 1). However, most parameter ombinations result in a model opepod that is always positively or negatively buoyant, regardless of pressure. The first senario of VJ99 ( Case 1 ), overlaps the neutral buoyany ontour, while the seond senario ( Case 2 ) does not. Neither senario is onsistent with neutral buoyany over the range of the only published observations of water ontent for Calanus finmarhius (~79 to 85%: Tande 1982). Obviously, there are ountless parameter ombinations to hoose from. However, the points we wish to make are that (1) the model is very sensitive to the hoie of parameters; and (2) the buoyany properties of the model opepod are extremely sensitive to its relative biohemial ontent. Maintenane of overwintering depth In our example of Calanus finmarhius in the Faroe-Shetland Channel, overwintering individuals are found primarily at depths below 600 m, and appear to maintain their position at depth for periods of about 6 mo (Heath 1999). At those depths, even extremely small hanges in the relative omposition (parts per 1000) will result in very large hanges in the buoyany properties (100s of m). However, C. finmarhius overwintering at depth are generally quiesent, and have not been observed to swim (Hirhe 1996). How then are they able to maintain position during the overwintering period? If we take an average water ontent of 82% (Tande 1982), and ρ o 1260 kg m 3, neutral buoyany ours in the Faroe-Shetland Channel at approximately 690 m A B Depth ( m) W W Fig. 1. Contours of veloity attributable to buoyany (m d 1, positive upwards) of a model opepod as a funtion of relative hemial omposition (based on data for overwintering Calanus finmarhius from the Faroe-Shetland Channel, Marh 1995). Rates were alulated with model results for ρ and ρ seawater and Stokes law (w g ρd 2 /18µ, where w is asent rate in m s 1, g is aeleration due to gravity in m s 2, ρ is density differene in kg m 3, d is effetive diameter in m and µ is absolute visosity in kg m 1 s 1 ). Effetive diameter (d) was m (Visser & Jónasdóttir 1999) and µ was alulated as a funtion of pressure, temperature and salinity with the equation of Matthäus (1972; values ranged from to kg m 3 ). For these examples, o has been held fixed, and w and l have been varied suh that w + l + o 1 (i.e. lipid inreases in diret proportion to a derease in water and vie versa). Neutral buoyany (w 0) is denoted by the dashed line. Parameter sets have been hosen to math those of Visser & Jónasdóttir (1999): (A) Case 1 ( o 0.12, ρ o 1080 kg m 3 ), (B) Case 2 ( o 0.21, ρ o 1240 kg m 3 ). See Appendix 1 for details on onversion alulations. Grey boxes indiate likely parameter spae for C. finmarhius given lipid to dry weight ratios between 0.29 and 0.59

4 96 Mar Eol Prog Ser 263: 93 99, 2003 Depth (m) A Positive buoyany Negative buoyany Density (kg m -3 ) B Asent time (days to surfae or bottom) Veloity (m d -1 ) with l 0.11 and o 0.07 (Fig. 2). This orresponds to a lipid:dry weight ratio of 0.61, only slightly greater than the value of 0.59 given by VJ99 for lipid-rih Calanus finmarhius from the Faroe-Shetland Channel. At depths near the point of neutral buoyany, asent rates are very low. The asent time, the time it takes a passive partile to reah 10 or 860 m (i.e. the surfae or the bottom), an be onsiderable. Positioning at or near the point of neutral buoyany (e.g. between 635 and 777 m; Fig. 2) does however allow the animal to remain at depth for an extended period (~6 mo). In other words, if an animal is able to find its depth of neutral buoyany during the summer/fall desent, one an expet it to maintain that position during the overwintering period, if hanges in the biohemial onstituents are ignored. Metaboli rates in overwintering Calanus finmarhius are quite low (Hirhe 1996), but some expenditure of biohemial ontents is to be expeted. Lipid reserves are onsumed over the overwintering period, partiularly during the latter portions when gonadogenesis begins (Hopkins et al. 1984). Protein ontents also deline (Orr 1934). In the ase of our model opepod, we have assumed that its water omponent has the same density as seawater (as did VJ99). Consequently, the balane between the other omponent (whih is denser than seawater) and the lipid omponent (whih is less dense than seawater) determines its overall buoyany. Therefore, a derease in lipid omposition will redue the upward buoyany fore, tending to make a neutrally buoyant animal beome negatively buoyant. Similarly, a derease in the other omponent (e.g. protein) will tend to make a neutrally buoyant animal beome positively buoyant. This balane between lipid and protein loss during the overwintering period may therefore partially balane eah other in their effet on buoyany. Currently, however, there is insuffiient information about loss rates of either omponent to realistially model this effet. Fig. 2. (A) In situ seawater density (dashed line), Faroe-Shetland Channel, Marh 1995 (same data as Visser & Jónasdóttir 1999, their Fig. 2) and alulated density for the model opepod (ρ : solid line), given w 0.82, l 0.11, o 0.07 and ρ o 1240 kg m 3. See text for details. (B) Asent veloity (solid line, positive upwards) given the alulated density differene and alulated with Stokes equation (see Fig. 1), and time to 10 m (i.e. surfae) or 860 m (i.e. bottom; dashed line). The dark gray area enompasses the depth range within whih a passive partile will take 90 d to reah the surfae or bottom, the light gray area enompasses the depth range within whih a passive partile will take 180 d to reah the surfae or bottom Termination of overwintering Termination of the overwintering state and moulting to adulthood by Calanus finmarhius ours at depth. Males appear first and move up slightly in the water olumn, to about 500 m. Females appear shortly afterwards and migrate to the surfae, where spawning ours (Heath 1999). The maturation proess is fueled by the lipid reserves, and will presumably alter the buoyany properties of an animal (a redution in the proportion of lipids tending to make the animal more negatively buoyant). The model shows us that asent rates are extremely sensitive to relative biohemial ontent (Fig. 1). The asent rates presented here, and by VJ99, should therefore be viewed with aution. Moreover, if the assumption of osmoti equilibrium between the opepods and seawater is violated (see below), asent rates will also be affeted. However, the asent rates alulated may be reasonable if one is willing to aept ertain assumptions. If we assume that the opepod begins from a state of quasi neutral buoyany, then as it moves atively towards the surfae, its lipids will expand and upward buoyany fores will inrease, eventually resulting in positive asent rates attributable to lipid expansion alone (Fig. 2). Above 500 m, temperature begins to inrease and asent rates also rise, driven by the large thermal expansivity of the lipids. The asent rates alulated here are omparable to those of VJ99 (their Figs. 4 & 5).

5 Campbell & Dower: Lipids and buoyany of zooplankton 97 IMPLICATIONS Case for a buoyany ontrol mehanism in opepods For lipid-rih organisms like opepods and other zooplankton, any depth of neutral buoyany is not a stable position. This will be true for any animal that ontains a large proportion of any substane that is more ompressible (and/or has a larger thermal expansivity) than seawater. Although the model shows that the depth of neutral buoyany is not stable, it also shows that asent rates around some position of neutral buoyany an be very small, permitting an animal to remain in the water olumn for long periods without adjustment (partiularly in the ase where temperature does not vary greatly with depth). However, the buoyany properties of an individual are extremely sensitive to the relative biohemial omposition (see above), and biohemial omposition does hange. In the example presented here, a hange of only a few perent makes a tremendous differene on the buoyany properties of the animal (Fig. 1). It is therefore not unreasonable to expet large hanges in the buoyany properties of individuals as they grow, mature and reprodue. It is also not unreasonable to expet them to possess a buoyany ontrol mehanism of some sort to deal with those hanges. Buoyany regulation has not been observed in the Copepoda beyond the supralittoral harpatioid opepods of the genus Tigriopus, whih maintain negative buoyany by altering their osmoti balane (MAllen et al. 1998). Ioni replaement, i.e. the seletive transport of heavier ions (e.g. SO 4 and Mg 2+ ) and 2 replaement with either lighter ions (e.g. Na +, Cl and NH + 4 ) or ions with a higher partial molal volume (e.g. trimethylamine, Me 3 NH + 4 ), has been observed in other rustaeans (Sanders & Childress 1988, Newton & Potts 1993). In this way, an organism an remain isoosmoti with the surrounding seawater, while seletively reduing or inreasing its aggregate density. Ion replaement has not yet been investigated in the pelagi Copepoda, but if it does our, then the assumption that ρ w ρ seawater used in our model is violated. Although it is urrently unknown whether oeani opepods are apable of buoyany regulation, there is evidene that ertain estuarine opepods (e.g. Aartia, Temora, Eurytemora and Centropages spp.) are apable of osmoregulation (Gaudy et al. 2000, Lane 1963, Roddie et al. 1984, Bayley 1969, respetively). If oeani alanoids are able to exploit this pathway in order to alter water or ioni ontent, they should also be able to regulate their apparent buoyany. Effets in surfae waters Although the present example deals with overwintering alanoid opepods, it is important to note that both the steepest gradient of in situ seawater density and the greatest density ontrast between the model opepod and seawater our near the surfae. This is driven by temperature, whih has a larger effet on lipid mass density (although in terms of our example of overwintering opepods this is not relevant). Many opepods (as well as other zooplankton) undergo ative diel vertial migrations of 10s to 100s of m (reviewed by Forward 1988, Pearre 2003). Presumably, they expend a signifiant deal of energy to do so, swimming being energetially quite ostly to most zooplankton (Klyashtorin 1978, Torres et al. 1982, Mauhline 1998 and referenes therein). The strongest temperature and density gradients are almost always found in surfae waters (Pikard & Emery 1990), and so it is possible that even slight alterations to buoyany (to aid asend or desent) ould represent onsiderable energeti savings to a vertially migrating animal. For instane, the drag fore (F D in N) on a partile moving at intermediate Reynolds numbers an be alulated with Rayleigh s formula: F D C D ( 1 / 2 ρ w U 2 A) (4) where C D is the drag oeffiient (C D 24[ Re ]/Re for 100 > Re > 1; Clift et al. 1978), U is veloity (m s 1 ) and A is the ross-setional area (m 2 ). The buoyany fore (F B ) is: FB m g ρw 1 (5) ρ where m is mass (kg) and g is aeleration due to gravity (m s 2 ; Glikman 2000). With the parameters in the example given here for Calanus finmarhius (Fig. 2), assuming a wet weight of 1000 µg (Tande 1982) and a swimming speed of 1 m s 1, F D (10 0 )(10 3 )(10 4 )(10 6 ) 10 7 N and F B (10 3 )(10 1 )(10 3 ) 10 5 N at the surfae. At the depth of neutral buoyany, F D is essentially unhanged, while F B 0. Clearly, buoyany fores an be muh greater than drag fores, although the latter will be size- and veloity-dependent. However, sine the buoyany fore inreases as depth dereases (i.e. the animal aelerates), any organism exploiting this mehanism to move upwards must possess a way to rapidly hange mass density in order to stop its asent when nearing the surfae. Similarly, any animal moving downwards from quasi-neutral buoyany at the surfae will experiene progressively less buoyany fore as it desends, and will need to hange its mass density in order to stop sinking one the desired depth has been reahed.

6 98 Mar Eol Prog Ser 263: 93 99, 2003 Given the large thermal expansion of lipids, it is possible for true neutral buoyany to our in areas where temperature inreases with depth. An inrease in temperature dereases lipid density, so that an animal moving deeper will experiene an inrease in the upward buoyany fores of its lipids. Conversely, a move upwards would ause an inrease in lipid density and a derease in upward buoyany fores. Inreases in temperature with depth do our in neriti zones (e.g. Gulf of Maine) and large estuaries (e.g. Gulf of St. Lawrene) and ould be exploited in those areas by plankton to ahieve neutral buoyany. Again, whether an individual an passively ahieve neutral buoyany, or be positively or negatively buoyant over the entire water olumn, will depend on its relative hemial omposition. Measurements of mass density and aousti baksatter The fat that lipids are more ompressible than seawater also suggests that measurements of mass density made at atmospheri pressure (Knutsen et al and referenes therein) are underestimates of in situ values. Beause lipid onstituents will expand following olletion at depth, mass density measured at the surfae will be greater than mass density under pressure. Similarly, mass density measurements will be affeted by the temperature at whih they are made. However, the greater thermal expansivity of lipids means that it is muh more important that measurements be made at the in situ temperature from whih the animals were olleted. Measurements of mass density at in situ temperature and pressure ertainly add to the already onsiderable methodologial hallenges of measuring mass density (reviewed by Knutsen et al. 2001), but they are not insurmountable. The differential ompressibility of lipids also has pratial impliations. Measurements of aousti baksatter are ommonly used to estimate zooplankton biomass. Aousti baksatter, however, is extremely sensitive to the density ontrast between the ensonified partiles and the fluid they are suspended in (Greenlaw 1979, Køgeler et al. 1987). The effet is strongly size- and frequeny-dependent, but Knutsen et al. (2001) report a 1% hange in density ausing a 2 db hange in baksatter. There have been measurements of the density ontrast of several types of zooplankton, partiularly euphausiids and opepods (see Knutsen et al. 2001), but all have been made at atmospheri pressure. That density ontrast hanges with depth and temperature (and perhaps even hange sign) is a potentially onfounding fator for in situ measurements of aousti baksatter. CONCLUSIONS The high ompressibility of lipids makes any position of neutral buoyany unstable. Although we use a opepod example, this priniple holds true for any organism ontaining a large proportion of any substane more ompressible than seawater. It follows, then, that a lipid-rih organism attempting to maintain neutral buoyany will have to atively maintain that position in some way. The model also shows that the density differene (and resulting buoyany fore) is highly sensitive to hanges in the relative hemial omposition of the organism (with some assumptions, outlined above). Again, this will apply to any organism (opepod or otherwise) that does not atively maintain its buoyany in some way. In fat, sine asent or desent rates at low Reynolds numbers sale with the square of size, larger organisms (e.g. deapods, nidarians and fish) should asend or desend at muh greater rates than those presented here. This mehanism for moving up and down in the water olumn ould result in signifiant energeti savings for animals undergoing large vertial migrations on a regular basis (e.g. Euphausiids, Myhtophids). Aknowledgements. We thank M. R. Heath for providing TS data for the Faroe-Shetland Channel, and S. E. Allen, T. J. Miller and 3 anonymous reviewers for their omments on earlier versions of the manusript. This work was supported by a University of Vitoria Graduate Fellowship to R.W.C. and an NSERC (Natural Sienes and Engineering Researh Counil of Canada) Disovery grant to J.F.D. LITERATURE CITED Bayley IAE (1969) The body fluids of some Centropagid opepods: total onentration and amounts of sodium and magnesium. Comp Biohem Physiol 28: Childress JJ, Nygaard M (1974) Chemial omposition and buoyany of midwater rustaeans as funtion of depth of ourrene off southern California. Mar Biol 27: Clift R, Grae JR, Weber M (1978) Bubbles, drops, and partiles. Aademi Press, New York Forward RB (1988) Diel vertial migration: zooplankton photobiology and behaviour. Oeangr Mar Biol Annu Rev 26: Gaudy R, Cervetto G, Pagano M (2000) Comparison of the metabolism of Aartia lausi and A. tonsa: influene of temperature and salinity. J Exp Mar Biol Eol 247:51 65 Glikman TS (2000) Glossary of meteorology, 2nd edn. Amerian Meteorologial Soiety, Boston Greenlaw CF (1979) Aoustial estimation of zooplankton populations. Limnol Oeanogr 24: Heath MR (1999) The asent migration of Calanus finmarhius from overwintering depths in the Fareo-Shetland Channel. Fish Oeanogr 8(Suppl 1):84 99 Hirhe HJ (1996) Diapause in the marine opepod, Calanus finmarhius a review. Ophelia 44: Hopkins CCE, Tande KS, Gronvik S, Sargent JR (1984) Eologial investigations of the zooplankton ommunity of

7 Campbell & Dower: Lipids and buoyany of zooplankton 99 Balsfjorden, northern Norway: an analysis of growth and overwintering tatis in relation to nihe and environment in Metridia longa (Lubbok), Calanus finmarhius (Gunnerus), Thysanoessa inermis (Kroyer) and T. rasshi (M. Sars). J Exp Mar Biol Eol 82:77 99 Kharakoz DP (2000) Protein ompressibility, dynamis, and pressure. Biophys J 79: Klyashtorin LB (1978) Estimation of energy expenditures for ative swimming and vertial migrations in planktoni rustaeans. Oeanology 18:91 94 Knutsen T, Melle W, Calise L (2001) Determining the mass density of marine opepods and their eggs with a ritial fous on some of the previously used methods. J Plankton Res 23: Køgeler JW, Falk-Petersen S, Kristensen Å, Pettersen F, Dalen J (1987) Density- and sound speed ontrasts in sub-arti zooplankton. Polar Biol 7: Lane J (1963) The salinity toleranes of some estuarine planktoni rustaeans. Biol Bull 127: Lee RF, Hirota J (1973) Wax esters in tropial zooplankton and nekton and the geographial distribution of wax esters in marine opepods. Limnol Oeanogr 18: Lee RF, Williams PM (1974) Copepod slik in the northwest Paifi Oean. Naturwissenshaften 61: Lewis RW (1970) The densities of three lasses of marine lipids in relation to their possible role as hydrostati agents. Lipids 5: Matthäus DJ (1972) Die Viskosität des Meerwassers. Beitr Meereskd 29: Mauhline J (1998) The biology of alanoid opepods. Adv Mar Biol 33:1 710 MAllen RJ, Taylor AC, Davenport J (1998) Osmoti and body density response in the harpatioid opepod Tigriopus breviornis in supralittoral rok pools. J Mar Biol Asso UK 78: Millero FJ, Chen CT, Bradshaw A, Shleiher K (1980) A new high pressure equation of state for seawater. Deep-Sea Res I 27: Newton C, Potts WTW (1993) Ioni regulation and buoyany in some planktoni organisms. J Mar Biol Asso UK 73:15 23 Orr AP (1934) On the biology of Calanus finmarhius. IV. Seasonal hange in the weight and hemial omposition in Loh Fyne. J Mar Biol Asso UK 19: Pearre S (2003) Eat and run? The hunger/satiation hypothesis in vertial migration: history, evidene and onsequenes. Biol Rev 78:1 79 Pikard GL, Emery WJ (1990) Desriptive physial oeanography. Butterworth Heinemann, Oxford Roddie BD, Leakey RJG, Berry AJ (1984) Salinity-temperature tolerane and osmoregulation in Eurytemora affinis (Poppe) (Copepoda: Calanoida) in relation to its distribution in the zooplankton of the upper reahes of the Forth estuary. J Exp Mar Biol Eol 79: Sanders NK, Childress JJ (1988) Ion replaement as a buoyany mehanism in a pelagi deep-sea rustaean. J Exp Biol 138: Sargent JR, Falk-Petersen S (1988) The lipid biohemistry of alanoid opepods. Hydrobiologia 167/168: Tande KS (1982) Eologial investigations on the zooplankton ommunity of Balsfjorden, northern Norway: generation yles, and variations in body weight and body ontent of arbon and nitrogen related to overwintering and reprodution in the opepod Calanus finmarhius (Gunnerus). J Exp Mar Biol Eol 62: Torres JJ, Childress JJ, Quetin LB (1982) A pressure vessel for the simultaneous determination of oxygen onsumption and swimming speed in zooplankton. Deep-Sea Res 29: Visser AW, Jónasdóttir SH (1999) Lipids, buoyany and the seasonal vertial migration of Calanus finmarhius. Fish Oeanogr 8(Suppl 1): Yayanos AA, Benson AA, Nevenzel JC (1978) The pressurevolume-temperature (PVT) properties of a lipid mixture from a marine opepod, Calanus plumhrus: impliations for buoyany and sound sattering. Deep-Sea Res 25: Appendix 1. Conversion of volume proportions to mass proportions To onvert volume proportions (α) to mass proportions (), the volume proportion α o V o /V may be rearranged (sine V m/ρ) to: m moρ αρ o o (A1) and substituted into the expression for mass proportion ( o m o /m ): αρ o ρ o (A2) In this ase, ρ is the density of the model opepod as given by the model of Visser & Jónasdóttir (1999), whih varies with depth. The alulated value of o thus dereases with depth, a onsequene of the volume proportion being fixed in their model. Visser & Jónasdóttir (1999) measured parameters at atmospheri pressure, so the value of o at the minimum depth (10 m) was used. For their Case 1 situation (α o 0.2, ρ o 1080 kg m 3 ), o varied from (surfae) to (maximum depth). For Case 2 (α o 0.1, ρ o 1260 kg m 3 ), o varied from (surfae) to (maximum depth). Editorial responsibility: Thomas Kiørboe (Contributing Editor), Charlottenlund, Denmark Submitted: Otober 21, 2002; Aepted: August 18, 2003 Proofs reeived from author(s): Otober 16, 2003

11/ This paper not to be cited without prior reference to the author. I'

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