James A. Yode+ Graduate School of Oceanography, University of Rhode Island, Kingston 02881

Transcription

1 Limnol. Oceanogr., 24(l), 1979, by the American Society of Limnology and Oceanography, Inc. A comparison between the cell division rate of natural populations of the marine diatom Skeletonema costatum (Greville) Cleve grown in dialysis culture and that predicted from a mathematical model1 James A. Yode+ Graduate School of Oceanography, University of Rhode Island, Kingston Ahstruct At weekly intervals from January through May 1977, during the winter-spring phytoplankton bloom in Narragansett Bay, Rhode Island, a phytoplankton sample was collected from the bay, encapsulated in dialysis bags, incubated in flowing seawater for 2-5 days at two different light levels, and the cell division rate of Skeletonema costatum was determined. Light intensity, water temperature, and the ambient concentrations of dissolved inorganic nitrogen, phosphorus, and silicon were measured during each experiment. Observed cell division rates were compared with those predicted from a mathematical model incorporating terms for the effect on growth of light intensity, temperature, and silicate concentration. Regression analysis revealed that equations incorporating only the effect of temperature and light intensity were sufficient to explain the observed cell division rate in many experimcnts, but the inclusion of silicate concentration improved the relationship. The cell division rate of these natural populations of S. costatum grown in dialysis bags in flowing seawater could thus be predicted with reasonable accuracy with a simple mathematical model primarily formulated from the results of a batch culture study of a single clone of this species. Dialysis culture or similar techniques h ave been used with marine phytoplankton to assess the growth potential of seawater (Jensen et al. 1972; Jensen and Rystad 1973), to determine the effect of a pollutant on algal growth (Jensen et al. 1974, 1976), and to relate changes in cellular composition to growth rate (Sakshaug 1977). In most instances, unialgal cultures were used and the dialysis bags incubated in flowing seawater. Dialysis culture has also been used in laboratory studies to determine the effect of nutrient concentration on phytoplankton growth (Yoder 1973; Skoglund and Jensen 1976; Dodson and Thomas 1977). If the seawater medium outside the dialysis bags is replenished continuously, microalgae can be kept in logarithmic growth for extended periods at low nutrient concentrations. Durbin (unpubl.) working with unialgal cultures and Hitchcock (1977) working with natural populations both used dialysis as an alternative to batch culture to assess the simultaneous effect of light intensity, natural variability of light intensity, temperature, and other environmental influences on phytoplankton growth. Vargo (1976) used dialysis culture to determine the effect of zooplankton grazing on the population dynamics of Skeletonema costatum in Narragansett Bay. These studies have shown that many different species of marine diatoms and other forms can be cultured successfully within dialysis bags. I have studied the effect of the interaction of temperature (OO-10 C) and light intensity on the cell division rate of clone SKGC of S. costatum grown in batch culture (Yoder in prep.) and incorporated the results into a set of four equations which form a simple mathematical model. The equations can be easily expanded to include the effect of other factors on growth l This work was supported by National Science The goal of the study reported here was Foundation grant GA 31319X to T. J. Smayda. This to determine if this model could be used manuscript is a portion of a dissertation submitted to predict the cell division rate of the low in partial fulfillment of the requirement for the Ph.D. degree at the University of Rhode Island. temperature (< 1OOC) population of S. 2 Present address: Skidaway Institute of Ocean- costatum that occurs in Narragansett Bay ography, P.O. Box 13687, Savannah, Georgia during the winter-spring bloom. 97 rate.

2 98 Yoder I- 50cm -I I 54cm Fig. 1. Schematic drawing of dialysis tank. Bay water is continuously pumped into tank at bottom and exits through standpipe shown on right. Dialysis bags are labeled A and B (from Vargo 1976). I thank T. J. Smayda for help in preparing this manuscript. The idea to perform the experiments originated from discussions with E. G. Durbin. I. R. Lawrence and M. Furnas carried out the nutrient measurements. B. Coyne typed the manuscript and drafted the figures. Methods The experiments were conducted from January to May Natural populations of phytoplankton used were obtained each week from a pooled sample collected from a station in the West Passage of Narragansett Bay (41 34 N, W), about 15 km from the mouth of the bay. This station has been monitored weekly since 1959, initially by D. Pratt and since 1963 by T. J. Smayda, and has been called station 2 (Pratt 1959, 1965; Smayda 1973; Furnas et al. 1976). The pooled sample consists of a mixture of equal volumes of water collected from 0, 4, and 8 m. Dialysis bags were formed by tying off the two ends of regenerated cellulose dialyzer tubing (2.9-cm inflated diameter) (Arthur H. Thomas Co.), which is permeable to water and solutes of molecular weight <12,000; the average pore diameter is 4.8 nm. Before use, the tubing was rinsed in hot water and then autoclaved to remove glycerin and to kill any bacterial contamination. Exposing dialysis bags to unfiltered water can result in extensive colonization of the bag exterior by bacteria, protozoans, and benthic microalgae (Vargo et al. 1975). There was no appreciable colonization during the experiments described here, due to the relatively low water temperature (< 1OOC) and the short duration of the experiments (2-5 days). The pooled sample was passed through a fractionator consisting of an acrylic plastic cylinder with a 64-pm-mesh net attached to one end. This removed all large predators including adult and juvenile stages of copepods, but also removed some of the longer chains of S. costatum, Thalassiosira spp., Asterionella japonica, and other chain-forming diatoms. The initial concentration of phytoplankton cells was always determined after the sample was fractionated. The fractionated sample was poured directly into the bag (containing about 150 ml). After filling, the bags were sealed and placed in specially constructed acrylic plastic tanks (Fig. 1) designed after those of Jensen et al. (1972). Narragansett Bay water was continuously pumped through the tanks at a flow rate of about 1 tank volume every 10 min. The source of this water is about 9 km closer to the mouth of the bay than the station from which the sample was collected; at both locations, the salinity ranges from about 27-30%0. An electric motor rotated the assembly to which the bags were attached at 15 rpm. A small air bubble was left within each bag. As the two ends of the bag were offset in the vertical plane, this air bubble moved along the length of the bag. The rotation of the bag facilitates diffusion of solutes into the bag, and the motion of the air bubble keeps phytoplankton in the bag suspended and well mixed. A scries of these tanks on a platform near the aquarium building of the Graduate School of Oceanography (U.R.I.) is exposed to full sunlight during the entire

3 Growth rate predictions 99 day, Neutral density plastic screens were placed outside the tanks to reduce intensities to 30 and 5% of incident irradiance ( nm) as determined with a Lambda quantum sensor. Two replicate bags were placed at each light intensity. Water temperature was continuously monitored; the average daily temperature was calculated by intergrating hourly readings. A water sample collected from the tank each day was analyzed with a Technicon AutoAnalyzer for dissolved inorganic phosphate (Grasshof 1966), ammonia (Solorzano 1969), nitrate + nitrite (Wood et al. 1967), and silicate (Armstrong 1951), Samples that were not immediately analyzed were filtered and frozen. Readings of incident irradiance from a pyranometer at the Eppley Laboratories about 7 km away from the tank platform were multiplied by to obtain an estimate of photosynthetically active radiation (Jitts et al. 1976). Initial and final concentrations of Chl a in the bags were determined fluorometrically by the method of Yentsch and Menzel (1963) as described by Strickland and Parsons (1968). Diatoms were counted at the beginning and end of each experiment in a Palmer-Maloney or Sedgwick-Rafter counting chamber. Since the reason for counting was to obtain statistically valid growth rates of S. costatum, the chamber used was chosen on the basis of the expected cell concentration. From 200 to 500 cells were counted for each replicate at each sampling, Cell division rates were calculated by a linear regression of the log base 2 of the ccl1 concentration of each replicate vs. time (Guillard 1973). The regression coefficient (slope) is the mean cell division rate, and the standard error of the regression coefficient is a measure of the statistical variability of the mean. Experiments lasted from 2 to 5 days and were ended after this relatively short period to ensure that the nutrient demand of the phytoplankton in the bags did not exceed the diffusion rate of nutrients into them. For selected expcriments, the concentration of dissolved plant nutrients in the bags was compared Table 1. Equations l-3 are from Yoder (in prep.); Eq. 4 is hyperbolic tangent function (Jassby and Platt 1976); Eq. 5 is Monod equation; Eq. 6 is rearrangement of Eq. 5, pmax = 0.48eO.12~ a = T T2 I,= 1.0 lyd F = p.,,,tanh[4z - LVCL~~J P = LLln,,S~(K8 + 9 KS = bhaxs~p) - s where p is cell division rate, divmd-1; T is temperature, C; Z is irradiance ( nm), lye d-l; S is silicate concentration, Z-kg-atoms Si * liter- ; CL max is maximal cell division rate, div. d-r; (Y is initial slope for light-limited growth, div. ly-1; I, is compensation intensity, ly* d-l; K, is concentration at which p = pmax/2, pg-atoms Sieliter-l. to that of the seawater in the tanks; in no instance was the former significantly less than the latter. These results suggest that diffusion rate of plant nutrients into the bags was of a sufficient magnitude to compensate for nutrient uptake by the encapsulated phytoplankton. The equations of the mathematical model used to predict growth rates for comparison with observed growth rates are given in Table 1. Results The results of 26 experiments are summarized in Table 2. During this period, S. costatum was the dominant species numerically of the diatoms in the <64- pm fraction of the sample collected from station 2. Its concentration in the initial sample ranged from about 1.0 x lo5 to about 3.0 x 10 cells * liter-l. Small flagellates were not counted. The concentrations of plant nutrients in Narragansett Bay shown were generally much lower than in previous years (Pratt 1959, 1965; Smayda 1973, unpubl.). The initial as- sumption had been that, as in previous years, the concentration of inorganic nitrogen, phosphorus, and silicon would be at relatively high levels until the peak of the winter-spring bloom in February or

4 100 Yoder Table 2. Summary of data and analysis of dialysis bag experiments. PhAR = photosynthetically active radiation (if two values are given, they represent 5 and 30% of incident); N = NO, + NO, + NH,; P = orthophosphate, Si = silicate; p0 = observed cell division rate (SE in parentheses); p1 = cell division rate predicted from Eq. l-4; pz = cell division rate predicted from Eq. 1 and 5; 2 Chl a = mean concentration within bags at end of each experiment. 4 Jan 5 11 Jan 4 25 Jan 4 2 Feb 3 8 Feb 4 15 Feb 3 22 Feb 4 1 Mar 3 8 Mar 3 16 Mar 5 22 lmar 3 29 Mar 3 5 Apr 3 12 Apr 3 26 Apr 2 3 May 3 f Nutrient concn Growth rates (pg-atoms. liter- ) (dive d- ) Duration.X Temp.f PhAR f Chl a (days) PC) (1~. d -1) N P Si I4 PI CL2 (bg. liter- ) (0.03) 0.24( - ) 0.41(0.09) 0.32(0.08) 0.22(0.10) 0.14(0.05) 0.10(0.02) 0.09(0.07) 0.35(0.08) oyoy4; 0:65( - ) 0.53( - ) 0.67( - ) 0.48(0.09) 0.65(0.08) 0.64(0.02) 0.96(0.04) O-73(0.04) 0.77(0.02) 0.90(0.06) l.og(o.06) 0.78(0.01) 1.36(0.05) 0.53(0.07) 1.45(0.04) March and that the cell division rate of phytoplankton within the dialysis bags would be largely controlled by temperature and light intensity until the postbloom period (see Smayda 1973). During this particular year, however, nutrient concentrations were quite low from December through spring ( ). Accordingly, the potential limitation of phytoplankton growth imposed by low nutrient concentrations had to be considered. Equations l-4 (Table 1) were used as the basis for the analysis of the observed cell division rates of S. costatum. These equations were found to provide a reasonable representation of the interaction of temperature and light intensity on the cell division rate of S. costatum clone SKGC for temperatures between 0 and 10 C and daylengths between 9 and 12 h of light during a 24-h light-dark cycle (Yoder in prep.). May daylengths reach 14 h, but the difference between the effect of 12 and 14 h of daylight is probably not significant. It should be noted that although Eq. 1 was derived from experiments in which light intensity was limiting growth, the equation can be used in any formulation requiring a temperaturedependent term for pmax of S. costatum clone SK6C. The cell division rates of natural populations of S. costatum grown in dialysis bags are shown as a function of the average temperature of each experiment in Fig. 2, as is a plot of Eq. 1 which defines the relationship between temperature an d pmax for clone SKGC. All of the observed cell division rates are enveloped by this curve. If temperature alone controlled cell division rate in these experiments, all observed rates would fall on the curve. In a majority of these experi-

5 Growth rate predictions 101 / TEMPERATURE / C) 0.0 Fig. 2. Observed cell division rate of Skeletonema cost&urn shown as a function of mean temperature of each dialysis bag experiment. Curve shows relationship between ~~~~ and temperature of S. costatum clone SKGC (Eq. 1). Fig. 3. Observed cell division rate of Skeletonema costatum shown as a function of a prediction from equations incorporating effect of temperature ments, S. costatum was unable to attain the maximum cell division rate allowed by the ambient temperature; this suggests that other factors were limiting growth rates. Equations l-4 were used to calculate a daily growth rate from the observed daily temperature and light intensity of each experiment. These daily calculations were averaged for each experiment and compared to the average observed cell division rate over the same period. The average of the calculated rates is given as,x~ in Table 2, and observed cell division rates (po) are also given. Figure 3 shows the observed average daily division rate for each experiment as a function of the average predicted growth rate. If agreement were perfect between predicted and observed, all of the points would fall on a straight line (y = mx + b) where b = 0.0 and m = 1.0. A least-squares linear regression analysis was used to fit a straight line to the data presented in Fig. 3. The equation giving the best fit (r = 0.91, n = 26) has m = 1.05 (SE = 0.10) and b = The slope of this line is close to that which would indicate perfect agreement between predicted and observed cell division rates, but the in- tercept is significantly lower. These results suggest that the cell division rate of and light intensity (pl of Table 2). Straight line (m = 1.05, h = -0.17) fit by least-squares linear regression. S. costatum predicted from Eq. l-4 (pl in Table 2) was consistently higher than the observed for these experiments. This result is not surprising given the relatively low average concentration of plant nutrients to which the encapsulated phytoplankton were exposed (Table 2). The simplest model that relates the concentration of a plant nutrient to phytoplankton growth rate that could also be applied in the analysis of the dialysis bag experiments is the Monod equation. Models requiring knowledge of the cell quota of the limiting nutrient (i.e. Droop 1974; Davis et al. 1978) could not be used for the assemblages of phytoplankton, since th e cell quota of a chemical constituent for any-single species cannot be determined if that species cannot be separated from other components of the plankton and from detritus. The Monod equation is given as Eq. 5. No experimental results are yet available that describe the relationship between the concentration of the plant nutrients measured in these experiments (silicate, nitrate, ammonia, or phosphate) and the cell division rate of S. costatum at temperatures

6 102 Yoder 0 Table 3. Results of linear regression of S vs. S/h, where S is one of the three nutrients and l-b = h-hax (see text). Slope (m) is asymptote of hyperbola and intercept (b) has magnitude and opposite sign of K,. Nutrient Si 0.96 N 0.30 P 0.36 r m b IL T-- - I I St Concentmt/on f//g-atoms,ifier- j Fig. 4. Normalized cell division rate (p ) shown as a function of average silicon concentration of each experiment. Curve is Monod equation fit to data. below 10 C; thus, an analysis directly analagous to that just described for the effect of light intensity on growth could not be made. An alternate procedure was used, however, to incorporate into the model an expression relating growth rate to the concentration of a single limiting nutrient. The assumptions inherent in the procedure used to accomplish this are that only a single nutrient (or light intensity) was limiting growth for the entire period during which the experiments were conducted, that the K, value for the limiting nutrient is temperature-independent between 0 and lo C, that Eq. 1 accurately describes the relationship between pmax and temperature, and that nitrate, nitrite, and ammonia can be treated as a single nutrient (i.e. a source of nitrogen). Organic sources of nitrogen and phosphorus are ignored in the analysis, as they were not measured. The average concentrations of SiO,-Si, PO,-P, and (NO3 + NO2 + NH&-N for each experiment are given in Table 2. The first step in the procedure to determine which of the three elements (N, P, or Si) was most likely to be limiting growth was to normalize the observed growth rates from the experiments conducted at 30% incident light to pmax calculated for each experiment. This step is necessary because pmax is not constant for the experiments, but changes by a factor of about 3.5 as temperature increases from 0 to 10 C (Eq. 1). If K, is independent of temperature and Eq. 1 describes the correct relationship between temperature and pmax, a plot of this normalized growth rate (p,j versus the concentration of the limiting nutrient will yield a single Monod hyperbola having an asymptote of 1.0. Only those growth rates obtained at 30% of incident light were used (n = 16) to reduce the probability that light intensity was limiting growth rate. Any difference between the observed growth rate and pmax (i.e. p,, < 1.0) could therefore be attributed to nutrient limitation. The values calculated for pn were plotted against the concentrations of N, P, and Si. Leastsquares linear regression analysis was used to fit straight lines to a linear transformation of the Monod equation, S vs. S/P~, for each nutrient. For this particular transformation, the slope of the line is the asymptote of the hyperbola and the y-axis intercept has the magnitude and the opposite sign of K,. The results of the regression for each nutrient are presented in Table 3. Of the three, Si is the only nutrient yielding meaningful results as the asymptote is close to 1.0, the K, value is positive, and the regression yields a high correlation coefficient (r = 0.96). A plot of pn vs. silicate concentration and the hyperbola resulting from the statistical analysis are shown in Fig. 4. The analysis just described suggests that Si is the nutrient most likely to have been limiting the growth of S. costn turn in the dialysis bags during the experiments. Two constants, pmax and K,, are required if one is to use the Monod equation to relate cell division rate to silicate concentration. Equation 1 can be used to

7 liter-l, liter-l Growth rate predictions 103 l l obtain a value for pmax. Equation 5 can be rearranged (Eq. 6) so that a KS value for silicate can be obtained from the results of each experiment. For each of the experiments conducted at 30% of incident light, a value for K, for silicate-limited growth was calculated by solving Eq. 6 using the average water temperature of each experiment and Eq. 1 to obtain a value for t-c,,,, the observed cell division rate as the value for p (Table 2), and the average silicate concentration of each experiment as the value for S (Table 2). This procedure yielded a mean K, for growth of pg-atom SiO,-Si (SD = 0.17, n = 16). The results of the regression technique previously described yielded a value for KS of 0.26 pgatom SiO,-Si * liter-l (Table 3). The difference between these K, values is small. The K, value obtained by the regression technique was not used as the regression yielded an asymptote for the hyperbola of 0.94, slightly less than the value that should have been obtained (1.0) if the Monod equation perfectly described the data from all the experiments. The other technique yields a KS value for each experiment, using in each case the pm,, value obtained from Eq. 1. The observed cell division rate for S. costatum from each experiment is compared with that predicted from equations that incorporate the combined effect of temperature, light intensity, and silicate concentration (Fig. 5). The effect of light intensity and temperature were calculated as before from Eq. 14 to yield a predicted growth rate based on light limitation of growth (pl of Table 2). An additional cell division rate (pz of Table 2) was calculated using Eq. 5 where K, = 0.31 Fg-atom SiO,-Si pmax from Eq. 1, and S = the average silicate concentration of each experiment. The lower of these two calculated division rates (i.e. the factor most limiting growth) was used as the final predicted division rate. In Fig. 5, two different symbols are used to indicate whether silicate concentration or light intensity was more limiting to the growth of S. costatum in each experiment. Least-squares linear regression I PREDICTED,U (DIV. DAY-/l Fig. 5. Observed cell division rate of Skeletonema costatum shown as a function of a prediction from equations incorporating effect of temperature, light intensity, and silicon concentration. O-S% con limitation of growth (pz of Table 2); O-light limitation (pl of Table 2). Straight line (m = 0.99, b = 0.04) fit by least-squares linear regression. analysis was used to fit a straight line to the data. The results of this regression (n = 26, r = 0.95) yield m = 0.99 (SE = 0.06) and b = If the data point having the largest residual is removed from the regression analysis (n = 25, r = 0.98), m = 1.03 and b = In either case, the values for m and b are very close to those indicating perfect agreement between predicted and observed cell division rates. Equations incorporating the effect of silicate concentration, light intensity, and temperature, therefore, can account for about 90% of the observed variation (i.e. r2) in cell division rate of S. costatum in the 26 dialysis bag experiments, or 96% if the data point having the largest residual is removed from the analysis. Discussion The dialysis culture technique used in this study does not yield in situ growth rates but does allow the culture of natural populations of phytoplankton under natural conditions of irradiance, at ambient temperature, with an approximation of the in situ chemical environment that is

8 104 Yoder maintained throughout the experiment. The cell division rates of S. costatum growing in situ in Narragansett Bay and that of the same population growing in dialysis bags may differ because of three characteristics of the technique used. First, seawater was continuously pumped through the tanks in which the bags were suspended; the encapsulated cells therefore could not deplete the plant nutrients available outside. Since neither the concentration nor the total amount of nutrients outside the bags is significantly affected by the nutrient demand of the encapsulated population, the carrying capacity of the environment of the encapsulated population is much greater than that of the same population growing in situ and exponential growth can be sustained for a much longer period in the bags than would be expected in situ. Second, the phytoplankton in the bags is well mixed by the movement of the air bubble. At low concentrations of plant nutrients, Pasciak and Gavis (1974) have shown that the rate of diffusion of nutrients to the immediate environment of a phytoplankton cell may limit the uptake rate. Such limitation may be overcome to some extent by water turbulence, and the turbulence induced in the bags is probably greater than would normally be encountered in the natural environment. Finally, a subtle, but potentially signifi- cant, modification of the in situ chemical environment results from the presence of mussels (Myths eduh) and other fouling organisms in the pipes through which seawater is pumped from the bay into the dialysis tanks. These organisms excrete considerable amounts of ammonia and other nitrogenous compounds which can increase the ratio of dissolved nitrogen to dissolved silicon. The magnitude of this effect will depend on the flow rate of seawater through the pipes relative to the biomass and metabolic activity of the fouling organisms. If we assume that the cell division rates in dialysis bags are representative of in situ rates, these three characteristics of the dialysis culture apparatus must be taken into account. These characteristics, however, are not directly relevant to the purpose of the experiments discussed here. These experiments were not designed to deter- mine the in situ cell division rate of natural populations of S. costatum, but rather to ascertain cell division rates of natural populations under natural conditions of irradiance, at nutrient concentrations close to ambient levels, and in the presence of other chemical characteristics of bay water. The mathematical expressions used in mechanistic models that describe phytoplankton growth in marine waters are formulated primarily from the results of laboratory experiments or closely controlled field experiments. One must isolate the individual effects of temperature, light intensity, and nutrient concentration if values for constants such as pmax, KS, etc. are to be established through experimentation The variability of the natural environment and the complex interactions between important environmental factors tend to obscure the effect of any single factor unless the experiments are closely controlled. Although valuable for other reasons, most field experiments or observations cannot, therefore, be used to determine the kinetic constants used in mathematical expressions that describe phytoplankton processes. The steps taken to ensure adequate control over experiments conducted in the laboratory or in the field, however, may severely limit the applicability of the results to events in the natural environment. Laboratory studies of phytoplankton physiology will often be done with enriched or artificial seawater medium, a single clone of the species under study, irradiance of constant intensity, long periods of acclimation to the experimental conditions, and other techniques designed to control and define the experimental conditions. All of these techniques tend to create an artificial environment, and the results must be viewed with some skepticism when used to form hypotheses concerning plankton dynamics in natural waters. Dialysis culture can be used to obtain cell division rates of natural populations of marine phytoplankton that are exposed

9 Growth rate predictions 105 to a chemical environment and irradiance close to in situ conditions. The cell division rates of individual species, size categories, or other classification can be determined and compared to predictions from laborabory studies. When laboratory results are quantified with mathematical expressions, the observed conditions of dialysis bag experiments can be used to predict a cell division rate which can be statistically compared to an observed rate. I believe that dialysis culture can best be used to test the validity of laboratory-derived expressions relating phytoplankton growth rate to environmental factors. The results presented here demon- strate that during the 1977 winter-spring bloom in Narragansett Bay, the cell division rate of natural populations of S. costatum encapsulated in dialysis bags and exposed to bay water could be predicted with reasonable accuracy from equations primarily formulated from the results of a batch culture study of a single clone of this species. Equations incorporating only the effect of temperature and light intensity were adequate to explain the cell division rate observed in many of the experiments. As a whole, however, predictions based on the ob- served levels of temperature and light intensity tended to overestimate the observed division rates of this species. When an expression incorporating the combined effect of silicate concentration, light intensity, and temperature on cell division rate was used, the relationship was improved. The K, value for silicate-limited growth that was used in the model was not obtained in the same manner as the constants that defined light-limited growth. A statistical technique was used that yielded the best single value for K, given several simplifying assumptions. This K, value should, therefore, not be considered in the same way as one derived from a laboratory study in which the conditions are more carefully controlled. However, the value used in the analysis given here (0.31) is close to previously reported K, values for silicate- limited growth of marine diatoms. Guillard et al. (1973) obtained a KS value of 0.98 pg-atom SiO,-Sisliter-l for growth of an estuarine clone of Thalassiosira pseudonana. Paasche (1975) found that tem- perature affected the KS value for silicatelimited growth of Thalassiosira nordenskioeldii. At 3, the constant was 0.09 pgatom SiOs-Si. liter-l; at lo C, it was Davis et al. (1978) d cveloped a biochemically based simulation model for siliconlimited growth of S. costatum. Within the context of their model, growth was not a direct function of the concentration of silicate in the surrounding medium; however, they used a KS value of 1.1 pgatoms SiOs-Si * liter-l for silicate uptake. The excellent agreement between the predicted and observed cell division rates of the dialysis bag experiments is surprising, given the simplicity of the model and the number of factors known to affect phytoplankton growth rate that were ignored. For example, no terms were incorporated into the model for light acclimation, temperature-dependence of KS, or the effect of short period changes in nutrient concentration of the bay water. It is of particular significance that the experimental results from batch culture studies of a single clone of S. costatum could be used to explain quantitatively about 90-95% of the observed variation in the cell division rate of natural populations of the same species selected essentially at random from Narragansett Bay on 16 different occasions over a period of about 4 months. These results are particularly encouraging given the widespread use of laboratory clones for experimental work and the use of such results to form general conclusions concerning the ecology of natural populations. The results presented here tend to support the validity of an autecological approach in the study of the dynamics of marine phytoplankton. References ARMSTRONG, F. A The determination of silicate in seawater. J. Mar. Biol. Assoc. U.K. 30: DAVIS, C. O., N. F. BREITNER, AND P. J. HARFU-

10 106 Yoder SON Continuous culture of marine diatoms under silicon limitation. 3. A model of Silimited diatom growth. Limnol. Oceanogr. 23: 4 l-52. DODSON, A.N., AND W. H. THOMAS Marine phytoplankton growth and survival under simulated upwelling and oligotrophic conditions. J. Exp. Mar. Biol. Ecol. 26: DROOP, M. Ft The nutrient status of algal cells in continuous culture. J. Mar. Biol. Assoc. U.K. 54: FURNAS, M.J., G. L. HITCHCOCK, AND T. J. SMAY- DA Nutrient-phytoplankton relationships in Narragansett Bay during the 1974 summer bloom, p Zn M. Wiley [ed.], Estuarine processes, v. 1. Academic. GUILLARD, R. R Division rates, p Zn J. R. Stein [ed.], Handbook of phycological methods. Cambridge Univ. -, P. KILHAM, AND T. A. JACKSON Kinetics of silicon-limited growth in the marine diatom Thalassiosira pseudonana Haslc and Heimdal (= Cyclotella nana Hustedt). J. Phycol. 9: GRASSHOF, K Automatic determination of fluoride, phosphate and silicate in seawater, p Zn L. T. Skiggs [ed.], Automation in analytical chemistry Technicon Symp., New York. HITCHCOCK, G. L The time course of photosynthetic adaptation, the growth rate response, the variations in the pigment, carbohydrate and protein content of Skeletonema costatum and Detonula confervacea to changes in light intensity. Ph.D. thesis, Univ. Rhode Island. 198 p. JASSBY, A. D., AND T. PLATT Mathematical formulation of the relationship between photosynthesis and light for phytoplankton. Limnol. Oceanogr. 2 1: JENSEN, A. AND B. RYSTAD Semi-continuous monitoring of the capacity of seawater for supporting growth of phytoplankton. J. Exp. Mar. Biol. Ecol. 1 I: AND S. MEISOM Heavy metal tolerance of marine phytoplankton. 1. The tolerance of three algal species to zinc in coastal seawater. J. Exp. Mar. Biol. Ecol. 15: ,AND Heavy metal tolerance of marine phytoplankton. 2. Copper tolerance of three species in dialysis and batch cultures. J. Exp. Mar. Biol. Ecol. 22: ,-, AND L. SKOGLUND The use of dialysis culture in phytoplankton studies. J. Exp. Mar. Biol. Ecol. 8: JITTS, H. R., A. MOREL, AND Y. SAIJO The relation of oceanic primary production to avail- able photosynthetic irradiance. Aust. J. Mar. Freshwater Res. 27: PAASCHE, E Growth of the plankton diatom Thalassiosira nordenskioeldii Cleve at low silicate concentrations. J. Exp. Mar. Biol. Ecol. 18: PASCIAK, W. J., AND J. GAVIS Transport limitation of nutrient uptake in phytoplankton. Limnol. Oceanogr. 19: PRATT, D. M The phytoplankton of Narragansett Bay. Limnol. Oceanogr. 4: The winter-spring diatom flowering in Narragansett Bay. Limnol. Oceanogr. 10: SAKSHAUG, E Limiting nutrients and maximum growth rates for diatoms in Narragansett Bay. J. Exp. Mar. Biol. Ecol. 28: SKOGLUND, L., AND A. JENSEN Studies on N-limited growth of diatoms in dialysis culture. J. Exp. Mar. Biol. Ecol. 21: SMAYDA, T. J The growth of Skeletonema costatum during a winter-spring bloom in Narragansett Bay. Norw. J. Bot. 20: SOL~RZANO, L Determination of ammonia in natural waters by the phenylhypochlorite method. Limnol. Oceanogr. 14: STRICKLAND, J. D., AND T. R. PARSONS A practical handbook of seawater analysis. Bull. Fish. Res. Bd. Can VARGO, G The influence of grazing and nutrient excretion by zooplankton on the growth and production of the marine diatom, Skeletonema costatum (Greville) Cleve, in Narragansett Bay. Ph.D. thesis, Univ. Rhode Island. 216 p. -, P. HARGRAVES, AND P. JOHNSON Scanning electron microscopy of dialysis tubes incubated in flowing seawater. Mar. Biol, 31: WOOD, E. D., F. A. ARMSTRONG, AND F. A. RICH- ARDS Determination of nitrate in sea water by cadmium-copper reduction to nitrite. J. Mar. Biol. Assoc. U.K. 47: YENTSCH, C. S., AND D. W. MENZEL A method for the determination of phytoplankton chlorophyll and phaeophytin by fluorescence. Deep-Sea Res. 10: YODER, J, A The interaction of temperature and nutrient concentration on the growth of Detonula confervacea (Cleve) Gran, Skeletonema costatum (Greville) Cleve, and Thalassiosira nordenskioeldii Cleve. M.S. thesis, Univ. Rhode Island. 78 p. Submitted: 27 April 1978 Accepted: 5 July 1978