NOTES. General allometric equations for rates of nutrient uptake, ingestion, and respiration in plankton organisms

Transcription

1 NOTES Limnol. Oceanogr., 34(7), 1989, , by the American Society of Limnology and Oceanography, Inc. General allometric equations for rates of nutrient uptake, ingestion, and respiration in plankton organisms Abstract-General allometric equations are derived for rates of nutrient uptake, ingestion, and respiration by plan ktonic organisms. Previous studies commonly calculated parameters a and b in the allometric equation H = amb by linear regressions on log-transformed data. This practice results in variability between data sets in estimates of both a and b, making meaningful comparisons difficult. This problem is overcome by assuming the mass-specific form of b to be -0.25, based on accumulated empirical evidence. Values of a arc then recalculated from published data, with log transformations and an assumed regression slope of Resulting regressions predict values of a (in pg Co.25 d-l) at 20 C as follows: 3.6 for nutrient uptake by phytoplankton and bacteria; 63 and 13 for ingestion and respiration by particle-feeding heterotrophs. It is hypothesized that organisms that take up dissolved nutrients from solution (autotrophs and osmotrophs, e.g. phytoplankton and bacteria) have lower specific respiration rates (i.e. smaller a) when compared with organisms (either unicellular or multicellular) that ingest particulate material. Body size is an important determinant of many physiological and ecological rates (Peters 1983). Allometric equations have been derived inter alia for metabolic, respiration, ingestion, excretion, photosynthetic, and growth rates for a wide variety of organisms, ranging in size from viruses to large mammals (Fenchel 1974; Banse 1976; Blueweiss et al. 1978; Calder 1984). Allometric models are potentially useful in estimating ecolog- Acknowledgments We thank Peter Ryan, Charles Griffiths, Trevor Probyn, and Scott Turner for commenting on the manuscript, and Pierre Legendre, Rob Peters, Dave Caron, Peter Verity, and Les Underhill for helpful discussion. The comments of four anonymous referees improved the manuscript. This study forms part of the Systems Analysis Project of the Benguela Ecology Programme, funded by the South African National Committee for Oceanographic Research. ical flows in ecosystem studies, particularly because organism size is being used increasingly as a basis for characterizing marine plankton communities (Cousins 1985; Dickie et al. 1987). As a consequence of the many studies estimating allometric equations, however, there are several different allometric models, often for the same process and group of organisms (see Table I). This multiplicity can lead to distracting arguments as to which model is best (Economos 19 79; Heusner 1982; Feldman and McMahon 1983), as well as making it difficult to decide which model to use. Discrepancies among the values of allometric parameters may result in inconsistencies between estimates of ecological flows, especially if organisms over a wide range of body sizes are being considered. Rather than emphasizing differences between models, there is a need to synthesize existing information and derive general allometric equations that highlight similarities in allometry and make the models useful for predictive purposes (Platt 198 5). This note aims to remove some of the sources of these discrepancies among published allometric regressions for planktonic organisms, using literature data to calculate allometric equations for a wide range of organism sizes and a number of different processes. The equations developed here, however, may not be the best predictors of physiological rates when a study is confined to only a narrow range of body size or to a single taxonomic group of organisms. A novel approach is adopted in fitting parameters to allometric equations; it is assumed that the rate processes of organisms scale by the same, constant exponent with body masses, in keeping with theoretical and em- pirical evidence as to the power-form of the general allometric equation. Rate coeffi- 1290

2 Notes 1291 cients for each process are then calculated. This procedure avoids the problem of obtaining dissimilar estimates of the two allometric parameters for different data sets and allows comparisons to be made between rate coefficients for different allometric processes. The earliest work in quantifying allometric processes was done chiefly on body sizemetabolic rate relationships (e.g. Kleiber 1932; Brody et al. 1934; Hemmingsen 1960). These and subsequent studies found that a simple power function best described the relationship; the general allometric equation has the form R=aMb (1) where R can be one of many rates, M is body mass, a is the rate coefficient, and b is the scaling parameter. R has dimensions [time(t)]- l for mass-specific rates, A4 has dimensions [mass (A4) 1, and b is dimensionless, therefore a has dimensions (t)-1(a4-b. (See list of symbols and abbreviations.) There is considerable debate as to the true value of b. Several theoretical explanations have been proposed to explain allometry (Peters 1983), and attempts have been made to derive b theoretically, initially from the now discredited surface law (see Schmidt-Nielsen 1970) but more recently from the results of dimensional analysis and the theory of biological similitude (Gunther 1975; Economos 1979; Platt and Silvert 198 1; Heusner 1982). The latter studies are based on the theorem that all natural laws can be expressed as relationships between dimensionless quantities (Stahl 1962). Using this theorem, Heusner (1982) calculated a value of for b as a mathematical consequence of homomorphism, but Platt and Silver-t ( 198 1) calculated values of for aquatic organisms and for terrestrial organisms. Empirical evidence, however, is divided (Table 1). Some studies indicate a value of for both aquatic and terrestrial organisms (e.g. Fenchel 1974; Blueweiss et al. 1978), whereas other studies indicate a value of (e.g. Baldock et al. 1980; Banse and Mosher 1980). In the absence of consensus as to the true value of b or its underlying theoretical basis, the value supported best by real data should be a a, b GGE I I Inax M MNGE N n Symbols and abbreviations Rate coefficient in allometric equation, pg CO25 d-1 Allometric coefficients for rates of ingestion (a,), production (a,), and respiration (a,), pg Co 25 d-l Exponent in allometric equation, dimensionless Gross growth efficiency Ingestion rate, d-l Maximal ingestion rate, d-l Organism mass, pg C Maximum net growth efficiency Total number of data points for each rate process Number of data points from single data source Net growth efficiency Rate variable, d-l NGE R R, Respiration rate of particle-feeding heterotrophs, d-l RF Respiration rate of phytoplankton and bacteria, d-l u Assimilation efficiency, d-l V Nutrient uptake rate, d-l V max Maximal nutrient uptake rate, d-l P Growth rate, d-l used (Lavigne 1982). Estimated values of b range between about -0.1 and -0.4 (see Peters 1983). Most values of b are close to (Lavigne 1982; Calder 1984) however, and we decided to use a value of for b in all calculations described below. Most studies have been primarily concerned with estimating b, with little attention being paid to a (Platt 1985). Literature estimates of a are influenced by the corresponding estimates of b, because of the practice of estimating these two parameters simultaneously (by using linear regressions on log/log-transformed data). To avoid this problem, we extracted appropriate data from the literature, body masses and rate processes were log-transformed, and regression estimates of a were calculated assuming a value of b of Data were obtained from a number of sources, in some cases secondhand, having been converted from different units and temperatures by others. Some data were obtained from figures, which may have resulted in some error in estimation, especially because axes are usually logarithmic. Calculations were done to two significant figures throughout. Units were not always

3 1292 Notes Table 1. Allometric equations for rates of growth, ingestion, and respiration of different groups of organisms. Parameters a and b were converted to values compatible with carbon masses (pg C) and mass-specific rates (d-l) at 20 C. Organisms a b Growth Virus-mammals Virus-mammals Ciliates and amoebae Ciliates Copepod Ingestion Marine amphipod Detritivores Invertebrates Respiration Rat-steer Mouse-elephant Bacteria-mammals Marine plankton Unicellular algae Marine amphipod Daphnia Zooplankton Crustacea Copepod Fenchel Blueweiss et al Baldock et al Taylor and Shuter Ross 1982a Dagg Cammen Capriulo Kleiber Brody et al Hemmingsen Ikeda Banse Dagg Lampert Ikeda and Motoda Ivleva Ross 1982a comparable among studies. Where necessary, data were converted to standard units of mass (pg C) and specific rates (d- ) with the conversions presented in Table 2. The respiratory quotient (RQ) (Table 2) was assumed to equal one (Parsons et al. 1977) because most of the respiration data were for unstarved animals (Ikeda 1970; Ross 1982a; Fenchel and Finlay 1983). Hourly rates were converted to daily rates by multiplying by 24, and all data were standardized to 20 C with Q10 values from the appropriate sources (see below). Where practical, data were combined into a single set. Often the raw data were not readily available (not presented or difficult to extract from graphical representations). When this problem occurred and the published ex- ponent was close to -0.25, the published rate coefficients were compared to the ones calculated below. Data sources are described in detail below and summarized in Table 3. Bacteria and phytoplankton are grouped together here because both take up dissolved nutrients from solution (Azam et al. 1983); they are distinguished from particlefeeding heterotrophs. Growth rates (p) of phytoplankton and bacteria are often limited by nutrient availability (McCarthy 198 1; Laake et al. 1983a). Uptake rates (v) of the limiting nutrient therefore may be equated approximately to growth rates on an ecological time scale. Data for calculated maximum values of V and p with corresponding cell sizes were used to estimate the Table 2. Conversions used to standardize all body mass data to units of pg C. Respiratory quotient--q (see text). Conversion Reference 1 pm3 = 1 pg wet Fenchel and Finlay pg dry = 0.4 pg C Peters pg wet = 0.07 pg C 1pgC=1p102x xRQ Peters 1983 Parsons et al nj = 0.05 pl 0, Peters 1983

4 uptake coefficient in the allometric equation. Cell dimensions (pm) and maximal specific growth rates (d-l) for four strains of bacteria (n = 4) at 2 C were taken from tables 1 and 3 of Laake et al. (1983b). Cell volumes were estimated with the formula for a cylinder and converted to carbon masses with the relationship 1 pm3 = pg C (Laake et al. 1983b). Growth rates were standardized to 20 C with a Q10 of In pure cultures, bacterial isolates of these strains followed the Arrhenius curve from 5 C to > 15 C (Laake et al. 1983b), so the extrapolation to 20 C is justified. Cell carbon (pg C) and specific growth rates (h-l) for unicellular algae (n = 14) were read from figure 1 of Banse (1976), who used data from a number of sources and standardized them to 20 C. Cell carbon (pg C) and maximal specific growth rates (h-l) for freshwater green algae (n = 26) were similarly read from figure 1 of Schlesinger et al. (198 1). All these data span a size range from 0.3 to loo-pm esd (equivalent spherical diameter) and were combined into a single data set (N = 44) for parameter estimation (Table 3). Data from Taguchi (1976) for specific phytosynthetic rates of marine diatoms, converted to 20 C with a Qlo of 2.0, were an order of magnitude faster than those for similar-sized phytoplankton cells in the data sets described above and therefore were omitted from the regression. Maximal specific ingestion rates have been shown to decrease with increasing body size both within species (Dagg 1976) and between species (Fenchel 1980; Paffenhiifer 197 1; Ikeda 1977; Ross 1982~; Capriulo 1982). Maximal ingestion rates (h-l) and cell volumes (pm ) for 17 species of ciliates at C (n = 18) were read from figure 2 of Fenchel(l980). Daily rations and body masses (pg C) for the copepod Calanus helgolandicus at 15 C (n = 5) were taken from table 5 of Paffenhijfer (197 l), and rates were standardized to 20 C with a Qlo of 3.0 (Ross 1982a). Maximal daily rations (d-l) and dry masses (pg) for five species of marine copepod at 20 C (n = 24) were obtained from table 2 of Ikeda (1977). Ingestion rates (pg C d-l) and body masses (pg C) for the euphausiid Euphausia pac$ca at 12 C (n = Notes 1293

5 1294 Notes 27) were read from figure 2 of Ross (1982a) and standardized to 20 C with a Qlo of 3.0 (Ross 1982a). All these data were combined into a single data set (N = 74) with ingestion rates for body sizes ranging from 8- to 4,450- pm esd (Table 3). Banse (1982) presented allometric equations for respiration rates of unicellular organisms from data of Hemmingsen (1960) (for procaryotes and eucaryotes combined) and Dewey (1976) (for eucaryotes). These equations yielded estimates for b of and respectively-very close to the value of assumed here. The mean (1.7) of the two estimated values of a (1.54 and 1.89) was therefore used as the respiration rate (RV) coefficient for phytoplankton and bacteria. Data for respiration rates (R,) and body masses of particle-feeding heterotrophs over a wide range of body sizes were taken from the literature and combined into one data set (see Table 3). Respiration rates (nl 0, cell-l h- ) and cell volumes (pm ) for growing free-living protozoa at 20 C (n = 48) were extracted from table 1 of Fenchel and Finlay (1983) and converted to standard units of mass and specific rates. An additional 14 data points were obtained from table 1 of Caron et al. (1989), who also presented the data of Fenchel and Finlay ( 1983). Respiration rates (pg C d- l) and body masses (pg C) for the euphausiid E. pacz$ca at 12 C (n = 92) were read from figure 2 of Ross (1982a), and a Qlo of 2.0 (Ross 1982a) was used to convert the rates to 20 C. Respiration rates (~10, d- ) and dry masses (mg) for marine plankton (n = 103) were obtained from table 3 of Ikeda (1970). The measurements were made at temperatures ranging from 5.1 to 30.3 C; they were standardized to 20 C with a Qlo of 2.0 (Ross 1982a). Specific respiration rates &l O2 mg- 1 h- l) and body masses (mg wet) for 27 species of marine copepods were taken from table 1 of Gaudy and Boucher (1983) and converted to 20 C with their Qlo of These five data sets (N = 284) cover a range of body sizes from 5- to 4,600-pm esd (Table 3). Body masses and rate variables were logtransformed. Thus the form of the allometric Eq. 1 becomes log[rate] = log a + b log M. (2) An a priori assumption was made that b was equal to , and a was calculated by substituting b = and the mean values of log(rate) and log M into Eq. 2, assuming that the regression passes through the means of both variables as for ordinary least-squares regressions (Zar 1984). This procedure probably does not give the best statistical regression line through the data points, but it is believed that it provides the best estimates of the rate coefficients a in the allometric models that have been proposed, where b is set at The variation that is explained by the forced regression lines was investigated by estimating coefficients of determination (r2) between the lines of slope and the data points (Zar 1984). Estimated allometric equations of slope are presented in Table 4. The esti- mated rate coefficient for uptake rates of phytoplankton and bacteria Vmax is an order of magnitude smaller than that for ingestion rates I,,, of particle feeders (Table 4). Similarly, the rate coefficient for phytoplankton and bacterial respiration rates (R,) is much smaller than the coefficient for respiration rates of particle-feeding heterotrophs (RI). There is much scatter about the regressions for rates of uptake (Fig. l), ingestion (Fig. 2) and respiration of particle-feeding heterotrophs (Fig. 3). The scatter is partially due to natural variability; not all organisms are exactly alike, and cells in different physiological states will have different reaction times for physiological processes (see Fenchel and Finlay 1983). Some of the variability is also probably due to measurement error and errors in estimating body carbon with general conversions (Table 2). For example, in Fig. 3 most of the protozoan data appear to lie below the regression line. This offset can be attributed to underestimating body carbon when converting from volumes because a simple linear conversion was used (Table 2), whereas a nonlinear conversion would probably be more appropriate, as has been found for phytoplankton cells (e.g. Strathmann 1967). Fenchel and Finlay (1983), using different units for organism size, have shown that there are no

6 Notes 1295 Table 4. Allometric models for maximal nutrient uptake rates (V,,,,,) of phytoplankton and bacteria, and maximal ingestion rates (I,,,) and respiration rates (R,) of particle-feeding heterotrophs. The equation for respiration rates of phytoplankton and bacteria (R,,), modified from Banse 1982, is also presented. Units of a are pg Co 25 d-l. Values of r2 were calculated for the variation of data points about the line of slope Equation V,,,,, (d-l) = 3.6 A4 (pg C)-O Z,,,,, (d-l) = 63 M (pg C))O R, (d-l) = 14 M (pg C)-Oz5 R, (d-l) = 1.7 M(pgC)) significant differences between the allometric relationships for respiration rates of particle-feeding protozoan and metazoan invertebrates. Similar conversions are used by most workers (e.g. Finlay 1977; Banse 1982; Fenchel and Finlay 1983; Peters 1983) because it is not always possible to take measurements in units that are useful for ecological interpretation and the same limitations and potential sources of error probably apply to many physiological studies. Despite this problem, the forms of the allometric relationships remain remarkably consistent, giving some confidence in the average rate constants calculated here. When allometric equations calculated by previous studies are compared (Table l), it is evident that there is not always agreement between parameter estimates. This disparity is expected, taking into account potential sources of error in measurements and conversion factors used by most workers as well as statistical problems related to small sam- N ; 0 al H 10' 6.- iii %.G 10 3 E 'R r" 10 ;+; I I , a. 1. rm( 10' IO2 lo3 lo4 lo5 lo6 lo7 lo8 log 1o'O Body mass(pg C) Fig. 2. As Fig. 1, but for maximal specific ingestion rates (ImaX) of particular-feeding heterotrophs. ple sizes and small mass ranges (Calder 1984). These factors confound the problem of deciding which allometric model is appropriate for use in mass budgets and energy balance equations in ecological studies of plankton communities. Complications in applying allometric models arise from the fact that allometric equations for different rate processes for the same group(s) of or- ganisms often have different values for the exponent b (Table 1). For example, the model of Capriulo ( 1982) for ingestion rates of invertebrates has an exponent of , and the model of Ivleva (1980) for respiration rates of crustaceans has an exponent of For two animals with body masses of 10 and lo6 pg C, these models predict maximal specific ingestion rates of 27 and 0.39 d- * and specific respiration rates of 8.6 and d- *. Percentage respiration relative to ingestion for the smaller species is thus 32% and for the larger one 54%, with this difference becoming larger as the size difference increases. This disparity implies that growth and respiration do not change lo* Body mass(pg C) Fig. 1. Allometric model describing the size dependence of maximal specific uptake rates (I,,,) of phytoplankton and bacteria. The line passes through the centroid of the data (geometric means) and has a fixed slope of Details given in text and Table 4. Bodymass(pgC) Fig. 3. As Fig. 1, but for specific respiration rates (R,) of particle-feeding heterotrophs.

7 1296 Notes among species in the same fashion with body size, which is unrealistic because growth efficiencies are generally size invariant from species to species (Humphreys 1979). It should be noted that these arguments do not apply to ingestion, respiration, and growth efficiencies within species, because changes in physiological relationships during growth result in characteristic growth curves within individual species. By standardizing the value of b to in this study, this unrealistic source of interspecific variation has been removed. A similar procedure was advocated by Smith (1984) to analyze allometric data. He discussed a number of problems associated with allometric techniques and suggested some alternative methods, including a priori models (e.g. setting the exponent to a constant value) instead of a posteriori ones derived solely from the data. Values of rate coefficients for particle feeders calculated in regressions in Table 4 can be compared with literature values (estimated from data not used in the regressions) after they have been converted to standard units and a temperature of 20 C. These values are all associated with exponents of (or very close to) The rate coefficient for ingestion rates was estimated to be 66 (pg Co.25 d- ) by Dagg (1976) for a marine copepod, 54 (pg Co.25 d-l) by Capriulo (1982) for a range of invertebrates, and 82 (pg Co.25 d- ) by Cammen (1980) for benthic deposit feeders and detritivores. The second value was associated with an exponent of , and the value of a would increase above 54 if the value of b is Our estimate of 63 (pg Co.25 d- l) is comparable to these estimates. The rate coefficient for respiration rates of particle feeders was estimated to be 14 (pg Co.25 d- *) (Table 4). Values of 13.7 (pg Co.25 d-l) for poikilotherms (Banse 1982) and 16 (pg Co.25 d-l) for crustaceans (n = 247) (Ivleva 1980) are similar to this estimate. Values of rate coefficients (a) are important in ecological models and mass budgets. Relative magnitudes of a for different processes affect growth efficiencies.. Comparisons of relative values of a (calculated in this study) with theoretical and measured growth efficiencies make it possible to assess how realistic the calculated values are. For the discussion below, only organisms growing at maximal rates are considered because intraspecific growth efficiencies change as individuals age, usually peaking and then decreasing as organisms reach maturity (Parsons et al. 1977). Therefore, all relationships described are for maximal rates and are intended for use in interspecific comparisons among a large size range of organisms. In growing organisms, a substantial proportion of the daily carbon mass balance is composed of ingestion and respiration: production = ingestion - respiration. (3) All three processes are body-size-dependent. Equation 3 can be rewritten in allometric terms: apmb = a,mb - a,mb. (4) If it is assumed that the scaling parameter b is the same for all rates for organisms growing maximally, it follows that the rate coefficient for production (a,) depends on the difference between the rate coefficients for ingestion (a,) and respiration (a,): ap = a, - ar. (5) Values of a for rates of uptake and respiration (Table 4) can be substituted into Eq. 5. Therefore, for a phytoplankton or bacterial cell growing under optimal conditions at 20 C in the absence of grazing, maximal net carbon production will be ( ) f 3.6 = 53% of gross carbon production, i.e. maximum net growth efficiency (MNGE) for carbon will be 53%. This estimate is slightly lower than values based on theoretical arguments; Fenchel and Finlay ( 1983) propose that MNGE should be 67% for procaryotic microorganisms, and Penning de Vries et al. (1974) theoretically derive general MNGE values between 60 and 70% for autotrophs. These relationships are appropriate for cells growing optimally, and net growth efficiency (NGE) will decrease as conditions become suboptimal. Measured NGE values for bacteria growing on various substrates range from 26 to 70% (Lucas 1986), and phytoplankton respiration is generally accepted as constituting

8 Notes 1297 some 10-45% of photosynthesis (Raymont 1980) which includes values estimated with Eq. 5. For grazers and predators similar calculations can be made, although efficiencies of heterotrophs should be larger than those of autotrophs because autotrophs incur extra metabolic costs in assembling organic monomers from their inorganic constituents (Calow 1977). Particle-feeding heterotrophs grazing optimally with abundant food supply have MNGE values for carbon calculated as MNGE=l-R =I----- U I a,mb U a,mb (6) where u is assimilation efficiency. Because body mass terms in allometric equations for R, and Z cancel, the equation reduces to MNGE=l -% U al (7) Substituting values of a, and ar (Table 4) and Eq. 7 and assuming U = 90% (Barthel 1983; Miller and Landry 1984) we assume MNGE is size-independent and has a value of 75% for particle-feeding heterotrophs growing optimally at 20 C. This value is larger than that calculated for autotrophs and bacteria in keeping with the prediction of Calow (1977). He estimated that the best possible efficiency that can be expected from any growing heterotroph is between 70 and 80%, which theoretical range includes the value estimated here. These theoretical estimates are also supported by measured values. Ross ( 19823) measured NGE values of up to 74% for larval stages of E. pacijica. The copepod Eurytemora affinis was predicted to have a gross growth efficiency (GGE) of 60% when growing at 15 C (Ikeda and Motoda 1978) and maximum GGE for Daphnia pulex was estimated to be 60% at 20 C (Sushchenya 1970). If we assume 90% assimilation efficiency, these GGE values are equivalent to NGE values of 67%. It has frequently been stated that respiration rates for similarly sized unicells and multicellular poikilotherms differ by a fac- tor of eight or nine (Hemmingsen 1960; Banse 1982) with unicells believed to have slower rates. In this study, two different allometric equations for respiration rates have been presented. One was obtained from the literature and can be applied to unicellular phytoplankton and bacteria (Table 4). The other was calculated from combined data of unicellular ciliates and marine invertebrates (Table 4; Fig. 3). These equations thus do not conform to the usual unicell-multicell division. The grouping of ciliate respiration rates with those of other unicellular organisms has been questioned by Fenchel and Finlay (1983) because most of the ciliate rates were faster than predicted for unicells. After selecting only those data for actively growing ciliates, Fenchel and Finlay showed that the ciliate line is similar to that calculated by Hemmingsen (1960) for multicellular organisms. Ciliate assimilation rates can be calculated from ingestion rates Z,,, (Table 4) with the calculated rate coefficient (a = 63) and an assumed assimilation efficiency of 80% (Stoecker 1984). If we adopt the unicell respiration equation with a coefficient of 1.7 (Table 4) NGE is calculated from Eq. 7 to be 97%-an impossibly large value; Calow ( 1977) predicted theoretical maximum efficiencies of 90-95%. Fenchel (1980) questioned the application of a unicell respiration rate to ciliates by Laybourn and Finlay (1976) because their estimates were an order of magnitude too small. Therefore, when the mass balance of organisms is taken into account, it is clearly unrealistic to describe all unicell respiration rates by a single unicell respiration model. Based on the analyses described above, we propose that respiration rates for planktonic organisms be distinguished on the basis of method of food uptake. On the one hand, organisms that rely chiefly on dissolved nutrients from solution (e.g. phytoplankton and bacterioplankton) conform to the traditional unicell model and have slower respiration rates than similar-sized organisms that feed mainly on particulate material. On the other hand, unicellular predators such as microflagellates and ciliates have fast respiration rates, similar to the size-specific rates observed for multi-

9 1298 Notes cellular animals. They are therefore grouped with other particle feeders. This grouping resolves the problem of apparently unrealistically large net growth efficiencies of ciliates and is consistent with the hypothesis that maximal net growth efficiencies for organisms grazing under optimal food conditions, whether ciliates or copepods, remain constant (Humphreys 1979). The allometric models developed here are not intended to replace earlier models in predicting rates of nutrient uptake, ingestion, and respiration for planktonic organisms. When allometric models are used to estimate a number of material (or energy) flows for a wide size range of planktonic organisms, however, consistency is required between estimates of the scaling parameter b for the different processes. In such cases, it is believed that the models in Table 4 are preferable to others in which the allometric scaling parameter b differs, and these stan- dardized models should be used together in community and ecosystem studies. Marine Biology Research Institute University of Cape Town Rondebosch 7700, South Africa References Coleen L. Maloney John G. Field AZAM, F., AND OTHERS The ecological role of water-column microbes in the sea. Mar. Ecol. Prog. Ser. 10: BALDOCK, B. M., J. H. BAKER, AND M. A. SLEIGH Laboratory growth rates of six species of freshwater Gymnamoebia. Oecologia 47: BANSE, K Rates of growth, respiration and photosynthesis of unicellular algae as related to cell size-a review. J. Phycol. 12: Mass-scaled rates of respiration and intrinsic growth in very small invertebrates. Mar. Ecol. Prog. Ser. 9: AND S. MOSHER Adult body mass and annual production/biomass relationships of field populations. Ecol. Monogr. 50: BARTHEL, K.-G Food uptake and growth efficiency of Eurytemora afinis (Copepoda: Calanoida). Mar. Biol. 74: BLUEWEISS, L., AND OTHERS Relationships between body size and some life history parameters. Oecologia 37: BRODY,~., R.C. PROCTER,AND U.S. ASHWORTH Basal metabolism, endogenous nitrogen, creatinine and neutral sulphur excretions as functions of body weight. MO. Agric. Exp. Sta. Res. Bull p. CALDER, W. A., III Size, function, and life history. Harvard. CALOW, P Conversion efficiencies in heterotrophic organisms. Biol. Rev. 52: CAMMEN, L. M Ingestion rate: An empirical model for aquatic deposit feeders and detritivores. Oecologia 44: CAPRIULO, G. M Feeding of field collected tintinnid micro-zooplankton on natural food. Mar. Biol. 71: CARON, D.A.,J.C. GOLDMAN,AND T. FENCHEL Protozoan respiration and metabolism, in press. Zn G. M. Capriulo [ed.], The ecology of marine protozoa. Academic. COUSINS, S. H The trophic continuum in marine ecosystems: Structure and equations for a predictive model, p In Ecosystem theory for biological oceanography. Can. Bull. Fish. Aquat. Sci DAGG, M. J Complete carbon and nitrogen budgets for the carnivorous amphipod, Cdiopius laeviusculus (Kroyer). Int. Rev. Gesamten Hydrobiol. 61: DEWEY, J. M Rates of feeding, respiration, and growth for the rotifer Brachionus plicatilis and the dinoflagellate Noctiluca miliaris in the laboratory. Ph.D. thesis, Univ. Washington. 149 p. DICKIE, L.M.,S.R. KERR,AND P.R. BOUDREAU Size-dependent processes underlying regularities in ecosystem structure. Ecol. Monogr. 57: ECONOMOS, A. C On structural theories of basal metabolic rate. J. Theor. Biol. 80: FELDMAN, M-A., AND T. A. MCMAHON The 3/4 mass exponent for energy metabolism is not a statistical artefact. Respir. Physiol. 52: 149-l 63. FENCHEL, T Intrinsic rate of natural increase: The relationship with body size. Oecologia 14: Suspension feeding in ciliated protozoa: Feeding rates and their ecological significance. Microb. Ecol. 6: l-l 1. AND B. J. FINLAY Respiration rates in heierotrophic, free-living protozoa. Microb. Ecol. 9: FINLAY, B. J The dependence of reproductive rate on cell size and temperature in freshwater ciliated protozoa. Oecologia 30: GAUDY, R., AND J. BOUCHER Relation between respiration, excretion (ammonia and inorganic phosphorous) and activity of amylase and trypsin in different species of pelagic copepods from an Indian Ocean equatorial area. Mar. Biol. 75: GUNTHER, B Dimensional analysis and theory ofbiological similarity. Physiol. Rev. 55: HEMMINGSEN, A. M Energy metabolism as related to body size and respiratory surfaces and its evolution. Rep. Steno Mem. Hosp. Nord. Insulin Lab. 9(2): l-l 10. HEUSNER, A. A Energy metabolism and body size. 2. Dimensional analysis and energetic non- similarity. Respir. Physiol. 48: HUMPHREYS, W. F Production and respiration

10 Notes 1299 in animal populations. J. Anim. Ecol. 48: IKEDA, T Relationship between respiration rate and body size in marine plankton animals as a function of the temperature of habitat. Bull. Fat. Fish. Hokkaido Univ. 21: Feeding rates of planktonic copepods from a tropical sea. J. Exp. Mar. Biol. Ecol. 29: , AND S. MOTODA Zooplankton production in the Bering Sea calculated from Oshoro Muru data. Mar. Sci. Comm. 4: IVLEVA, I. V The dependence of crustacean respiration rate on body mass and habitat temperature. Int. Rev. Gesamten Hydrobiol. 65: l- 47. KLEIBER, M Body size and metabolism. Hilgardia 6: LAAKE, M., A. B. DAHLE, K. EBERLEIN, AND K. REIN. 1983a. A modelling approach to the interplay of carbohydrates, bacteria and non-pigmented flagellates in a controlled ecosystem experiment with Skeletonema costatum. Mar. Ecol. Prog. Ser. 14: 7 l AND G. HENTZSCHEL Productivity and population diversity of marine organotrophic bacteria in enclosed planktonic ecosystems. Mar. Ecol. Prog. Ser. 14: LAMPERT, W Studies on the carbon balance of Daphnia pulex de Geer as related to environmental conditions 2. The dependence of carbon assimilation on animal size, temperature, food concentration and diet species. Arch. Hydrobiol. Suppl. 48, p LAVIGNE, D. M Similarity in energy budgets of animal populations. J. Anim. Ecol. 51: LAYBOURN, J., AND B. J. FINLAY Respiratory energy losses related to cell weight and temperature in ciliated protozoa. Oecologia 24: LUCAS, M. I Decomposition on pelagic marine ecosystems. J. Limnol. Sot. So. Africa 12: MCCARTHY, J. J The kinetics of nutrient utilisation, p. 2 1 l-233. In Physiological bases of phytoplankton ecology. Can. Bull. Fish. Aquat. Sci MILLER, C. A., AND M. R. LANDRY Ingestionindependent rates of ammonium excretion by the copepod Calanus pacificus. Mar. Biol. 78: PAFFENH~FER, G. A Grazing and ingestion rates of nauplii, copepodids and adults of the marine planktonic copepod Calanus helgolandicus. Mar. Biol. 11: PARSONS, T. R., M. TAKAHASHI, AND B. HARGRAVE Biological oceanographic processes, 2nd ed. Pergamon. PENNING DE VRIES, F. W. T., A. H. M. BR~~STING, AND H. H. VAN LAAR Products, requirements and efficiency of biosynthesis: A quantitative approach. J. Theor. Biol. 45: PETERS, R. H The ecological implications of body size. Cambridge. PLATT, T Structure of the marine ecosystem: Its allometric basis, p Zn Ecosystem theory for biological oceanography. Can. Bull. Fish. Aquat. Sci ~ AND W. SILVERT Ecology, physiology, allbmetry and dimensionality. J. Theor. Biol. 93: RAYMONT, J. E. G Plankton and productivity in the oceans (2nd ed.) V. 1 -Phytoplankton. Pergamon. Ross, R. M. 1982a,b. Energetics of Euphausia pacificu. 1. Effects of body carbon and nitrogen and temperature on measured and predicted production. 2. Complete carbon and nitrogen budgets at 8 C and 12 C throughout the life span. Mar. Biol. 68: 1-13, SCHLESINGER, D. A., L. A. MOLOT, AND B. J. SHUTER Specific growth rates of freshwater algae in relation to cell size and light intensity. Can. J. Fish. Aquat. Sci. 38: SCHMIDT-NIELSEN, K Energy metabolism, body size, and problems of scaling. Proc. Fed. Am. Sot. Exp. Biol. 29: SMITH, R. J Allometric scaling in comparative biology: Problems of concept and method. Am. J. Physiol. 246: R 152-R160. STAHL, W. R Similarity and dimensional methods in biology. Science 137: STOECKER, D. K Particle production by planktonic ciliates. Limnol. Oceanogr. 29: STRATHMANN, R. R Estimating the organic carbon content of phytoplankton from cell volume or plasma volume. Limnol. Oceanogr. 12: 41 l SUSHCHENYA, L. M Food rations, metabolism and growth of crustaceans, p Zn J. H. Steele [ed.], Marine food chains. Oliver and Boyd. TAGUCHI, S Relationship between photosynthesis and cell size of marine diatoms. J. Phycol. 12: TAYLOR, W. D., AND B. J. SHUTER Body size, genome size, and intrinsic rate of increase in ciliated protozoa. Am. Nat. 118: ZAR, J. H Biostatistical analysis, 2nd ed. Prentice-Hall. Submitted: 17 June 1988 Accepted: 28 June 1989 Revised: 7 August 1989