Measurement of phytoplankton growth by particle counting

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1 760 Notes teines. Bull Jard. Bot. Natl. Belg. 37(1 Suppl.): 23 p. MELACK, J. M Limnology and dynamics of phytoplankton in equatorial African lakes. Ph.D. thesis, Duke Univ. 453 p. -, AND P. mlham Photosynthetic rates of phytoplankton in East African alkaline, saline lakes. Limnol. Oceanogr. 19: OGAWA, T., AND G. TERUI Studies on the growth of Spirulina phtensis. (2) Growth kinetics of an autotrophic culture. J. Ferment. Technol. 50: STRICKLAND, J. D., AND T. R. PARSONS A practical handbook of seawater analysis. Bull. Fish. Res. Bd. Can TALLING, J. F Generalized and specialized features of phytoplankton as a form of photosynthetic cover, p Zn Prediction and measurement of photosynthetic productivity. PUDOC, Wageningen Primary production of freshwater microphytes, p Zn J. P. Cooper led.], Photosynthesis and productivity in different environments. IBP Synthesis Vol. 3. -, R. B. WOOD, M. V. PROSSER, AND R. M. BAXTER The upper limit of photosynthetic productivity by phytoplankton: Evidence from Ethiopian soda lakes. Freshwater Biol. 3: VARESCHI, E The ecology of Lake Nakuru (Kenya). 1. Abundance and feeding of the Lesser Flamingo. Oecologia 32: VOGLER, P Probleme der Phosphalanalytik in der Limnologie und ein neues Verfahren zur Bestimmung von gel&ten Orthophosphat neben Kondersierten Phosphaten und organischen Phosphorsaureestern. Int. Rev. Gesamten Hydrobiol. 50: ZARROUK, C Contribution a I etude d une cyanophycee influence de divers facteurs physiques et chimiques sur la croissance et la photosynthese de Spirulina maxima (Setch et Gardner) Geitler. D.S. (Appl.) thesis, Univ. Paris. 74 p. Submitted: 1 November 1977 Accepted: 14 November 1978 Limnol. Oceanogr., 24(4), 1979, 1979, by the American Society of Limnology and Oceanography, Inc. Measurement of phytoplankton growth by particle counting Abstract-Growth of phytoplankton in the presence of detritus will follow an asymptotic function. It is theoretically possible to estimate the phytoplankton and detrital standing stock and the phytoplankton growth rates from serial measurements of particle concentration, but the measurements must be very precise, and in practice this is rarely attainable. Small errors in measurement produce large errors in the plankton and detrital estimates. To measure phytoplankton growth, the phytoplankton must be identified relative to its place on the size spectrum. Within a restricted size range particle growth is exponential and represents phytoplankton growth. Particulate material in suspension in natural waters includes living material and detritus; under suitable conditions of incubation the living material will grow while the detritus remains unchanged. In the standard method of Steemann Nielsen (1952) the production of living material is estimated from the uptake of 14C. This is generally believed to give an accurate measure of production, at least in eutrophic waters, but it cannot provide information on growth rate because the initial standing stock of the phytoplankton is not determined. Cushing and Nicholson (1966) suggested that estimates of phytoplankton and detrital standing stocks and phytoplankton growth rate could be made from a series of particle counts; a variant of the method is described in the standard work of Strickland and Parsons (1968). Although the method has been used to determine standing stocks and growth rates of natural phytoplankton populations (Cushing et al. 1968; Parsons et al. 1969) it has not gained wide acceptance. This is no doubt partly due to the need for expensive equipment, for long incubations, and for a considerable degree of technical skill in the operation of the method. But it may also be because the method can produce obvious anomalies. For instance an analysis of a diatom bloom indicated more than 99% detritus (see below). The prime cause of the anomaly lies in the mathematical form of

2 the growth relationship. I will here first define the growth pattern and then give examples to show why a simple analysis of phytoplankton growth in the presence of detritus is subject to error. In the absence of constraint, growth of phytoplankton follows the relationship Pt = P,ekt (1) Notes 761 where Pt is the phytoplankton biomass at time t, PO is the initial phytoplankton biomass, and k is the instantaneous growth rate. However, if the phytoplankton is associated with detrital particles, then Pt = C, - D where C, is the total particle concentration at time t and D is the detrital concentration. The change in total particle concentration with time therefore follows the relationship Ct = D + Poekt (2) which is an asymptotic function. Given a set of values oft and C, it is not difficult to fit the data to Eq. 2. If ordinary methods of calculation are used the curve fitting can be time consuming (Stevens 1951; Patterson 1956), but there are computer programs available for this, such as the BMD program BMD P3R and the 1MSL subroutine RSMITZ. In the method of Cushing and Nicholson (1966) data are not fitted to Eq. 2. This is rewritten as where the initial concentration C, = P, + D. On the right-hand side of Eq. 3 only D is not known. Therefore, estimates of D are made and the relationship of k against l/t is worked out for each. If the estimate of D is incorrect k will vary with t, but if the estimate of D is correct k will not vary with t. For this value of D, k and PO (= Co - D) can be calculated. Equations 2 and 3 are equivalent and results for phytoplankton growth should be similar, but there are disadvantages to the Cushing and Nicholson method compared to nonlinear curve fitting. For example, it is clear from the form of Eq. 3 PARTICLE DIAMETER (jm) Fig. 1. Particle size spectrum of a diatom bloom (see Fig. 2). Growth measurements made only in size range indicated by shading. that any error in the measurement of Co will affect all the results, and in practice it is found that the slope of the regression line of k against l/t often does not become zero for any value of D in the range 0 to co. The examples given below were selected to illustrate problems associated with measuring phytoplankton growth by particle counting. They formed part of a series of experiments performed during a year s study of phytoplankton growth in Bedford Basin, Nova Scotia. Samples were taken at a depth of 5 m and incubated in a running seawater incubator with fluorescent illumination (about 8,000 lux). The lights were switched off at night to give a very rough approximation to a natural cycle. Sampling errors were minimized by taking all sampl es for one experiment from one large (4.7 liter) bottle.-the water was not treated in any way and no attempt was made to remove zooplankton. However, the method of collection (5-liter Niskin) tended not to catch copepods-the most abundant zooplankters--and the samples were checked visually to en sure that they were not abundant. Particles were counted with a model T Coulter Counter, and all sizes quoted refer to equivalent spherical diameters. The particulate material was also iden- L 64

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5 764 Notes 3.0 t A 4 0 IO Fig. 7. Growth of dinoflagellates in the size range pm (Figs. 4 and 5). A. Solid lineexponential function C, = 1.63e.085t; dashed lineasymptotic function C, = e0.167f. B. Diurnal growth pattern. Shaded areas represent periods of darkness; arrows indicate noon. nential function with a high level of significance (P = 0.01). The asymptotic function gives an even better fit, but it gives an interpretation of the dinoflagellate growth that is very hard to accept. It is just not reasonable to believe that a dinoflagellate bloom consists of 99.99% detritus. An alternative explanation of the growth pattern is shown in Fig. 7B. If considered in isolation there would be little justification for placing the curve as shown, but by comparison with Fig. 6B such a growth pattern is not improbable. According to this interpretation there were two periods of growth for 6 h after midday on two successive days. The growth rates during these times (k = and h-l indicating TD of 12 and 10 h) are comparable to those of Fig. 6. In the examples given above it is fairly clear from the microscopic evidence that we are dealing with growth of phytoplankton in the absence of detritus, yet an uncritical application of curve fitting to the form of Eq. 2 would produce very misleading results. An analysis by the method of Cushing and Nicholson would produce similar anomalies. As a comparison it would be desirable to examine growth of phytoplankton in the presence of obvious detritus, but this was difficult to do because at those times when detritus was abundant the phytoplankton tended not to grow. However, we can make artificial samples with detritus simply by adding a constant amount to the data of Figs. 3 and 6A. If this is done we obtain the following equations. For diatoms (data of Fig. 3 plus 50% of C, added to each data point): C, = 9.91e0*024t for exponential growth; C, = O.le 0.431t for asymptotic growth. For dinoflagellates (data of Fig. 6A plus 50% of Co added to each data point): Cc = II.78e0+044t for exponential growth; Cc = e0.072t for asymptotic growth. In both cases the addition of detritus had no effect on the estimate of k for the exponential approximation. For the asymptotic approximation the diatom data were consistent though still biologically meaningless. This is hardly surprising, for if there was 99% detritus to begin with, then adding more was hardly likely to change the situation very much. However, for the dinoflagellate data, addition of detritus caused the value of PO to increase by a factor of 2 even though the value of k did not change. It is clear that, in practical terms, estimating phytoplankton growth by particle counting is not possible either by curve fitting or by the method of Cushing and Nicholson. The reason for this is mainly the form of the growth pattern (Eq. 2). If data could be obtained without error then the relationship of Cc to t could be cal- culated, but small errors of measurement produce great effects on the estimates of D, PO, and k. A simple example of this is shown in Fig. 8. The curve was derived from dinoflagellate growth but the data points are artificial. They were calculated

6 Notes 765 A TIME z3t I,,, 0 TIME Fig. 9. Diagrammatic representation of asymptotic functions. A. A cooling curve can be derived accurately. B. A plankton growth curve cannot be defined in the same way because there are no data near asymptote. It is not possible to separate asymptotic (-) and exponential (-----) approximations. I I, I I Tltl: (h) Fig. 8. Hypothetical growth situation based on actual growth data. Observations are artificial and follow exponential function C = 3.20e In all cases data were analyzed by asymptotic regression. A. Observations with no error. D = 0, PO = 3.2, TD = 38 h. B. With 2% error. D = 0.72, PO = 2.53, TD = 31 h. C. With 5% error. D = 1.43, PO = 1.87, TD = 27 h. from an exponential but were then analyzed by asymptotic regression (i.e. on the assumption that they followed the form Ct = D + Poekt). In Fig. 8A the analysis correctly indicated an exponential function (i.e. D = 0 and TD = 39 h). When the points were displaced from the curve by 2% (Fig. 8B) an asymptotic regression indicated 22% detritus and TD of 31 h. Displacing the points by 5% (Fig. 8C) gave 43% detritus and TD of 26 h. These examples represent but one possible arrangement of data points dispersed around a curve. Silvert (1979) has recommended a procedure for randomly dispersing data to a predetermined limit and then calculating the parameters for the best fit. In several replicate runs with actual experimental data dispersed to a maximum of 5%, the Cushing and Nicholson method failed to 1 orovide a solu-

7 766 Notes tion for over half the cases. With asymptotic regression the values of k varied by a factor of five and in two cases negative detritus was indicated. For a rigorous treatment of the errors associated with curve fitting, Silvert s paper should be consulted. It is sufficient to state here that much seems to depend on the estimation of the asymptotic value D. It is possible to extrapolate to an asymptote with, say, a cooling curve, because the data points can be spaced along the curve and some can be near to the asymptote (Fig. 9A); but this cannot be done with a plankton growth curve because the data points are not well spaced and none are close to the asymptote (Fig. 9B). In spite of the foregoing, it is possible to measure phytoplankton growth rates in natural waters, but the experimental procedures are not routine. Each experiment has to be carefully planned. For instance, in the example shown in Fig. 7 it would be essential to recognize the diurnal growth variation, as failure to do this would have a profound effect on the interpretation of the growth pattern. It seems that asymptotic approximations cannot be used, but if we consider the exponential approximation in Fig. 7A and the diurnal pattern in Fig. 7B, we get very different results. In Fig. 7A the generation time is 82 h. If we assume continuous growth this represents a population increase of 23% per day. In Fig. 7B the generation time is lo-12 h. For a 6-h growth period this would give a population increase of 50% per day. I would suggest that in designing experiments to measure phytoplankton growth, attention should be given to the following points. 1. The growing material must be identified either with a microscope or by some other method such as a chemical determination (Sheldon 1978). 2. The size range over which growth occurs must be identified on the size spectrum. One can often assume that over a restricted size range phytoplankton will grow essentially free of detritus. The growth pattern is then exponential. 3. Experimental error must be reduced to a minimum. Sample variation can be reduced if all samples are taken from one large bottle, as variation from bottle to bottle can be considerable (Venrick et al. 1977). To minimize counting error the counts must be large (many thousands) and large samples may have to be taken. In the experiments described, counts were made on 50-loo-ml aliquots. 4. Enough samples must be taken to define the form of the growth pattern, and more than one experiment may have to be made. For instance, a preliminary run could determine what was growing and at what size. In a second experiment, by sampling at 30-min intervals, diurnal variation of growth could be established. Finally, a third experiment could check the long term growth pattern. These procedures are offered only as suggestions, as each experimental situation may call for a different strategy. However, it is possible, by adopting the optimum experimental procedure, to gain considerable insight into the intricacies of phytoplankton growth dynamics. R. W. Sheldon Marine Ecology Laboratory Bedford Institute of Oceanography P.O. Box 1006 Dartmouth, Nova Scotia B2Y 4A2 References COLE, H. A., AND E. W. KNIGHT-JONES Quantitative estimation of marine nanoplankton. Nature 164: CUSHING, D. H., AND H. F. NICHOLSON Method of estimating algal production rates at sea. Nature 212: , AND G. P. Fox The use of the CoultLr Counter for the determination of marine primary productivity. J. Cons., Cons. Int. Explor. Mer 32: EPPLEY, R. W Temperature and phytoplankton growth in the sea. Fish. Bull. 70: FENCHEL, T Intrinsic rate of natural increase: The relationship with body size. Oecologia 14: PARSONS, T. R., K. STEPHENS, AND R. J. LE- BRASSEUR Production studies in the Strait of Georgia. Part 1. Primary production

8 Notes 767 under the Fraser River plume, February to May J. Exp. Mar. Biol. Ecol. 3: PATTERSON, H. D A simple method for fitting an asymptotic regression curve. Biometrics 12: SHELDON, R. W Sensing zone counters in the laboratory. Zn A. Sournia Led.], A phytoplankton manual. Monogr. Ocean Methodol. 3. UNESCO. - W. H. SUTCLIFFE, JR., AND A. PRAKASH The production of particles in the surface waters of the ocean with particular reference to the Sargasso Sea. Limnol. Oceanogr. 18: SILVERT, W Practical curve fitting. Limnol. Oceanogr. 24: STEEMANN NIELSEN, E The use of radio- active carbon (C-14) f or measuring organic production in the sea. J. Cons., Cons. Int. Explor. Mer 18: STEVENS, W. L Asymptotic regression. Biometrics 7: STRICKLAND, J. D., AND T. R. PARSONS A practical handbook of seawater analysis. Bull. Fish. Res. Bd. Can VENRICK, E. L., J. R. BEERS, AND J. F. HEINBOK- EL Possible consequences of containing microplankton for physiological rate measurements. J. Exp. Mar. Biol. Ecol. 26: Submitted: 16 March 1978 Accepted: 19 January 1979 Limnol. Oceanogr., 24(4), 1979, , by the American Society of Limnology and Oceanography, Inc Practical curve fitting Abstruct-Several techniques for estimating parameter values and confidence ranges for nonlinear fitted curves are evaluated and compared. Simple methods for using computers for curve fitting and parameter estimation are described. Alternate methods can be tested with randomized replicate data sets. Many of the theoretical models encountered in the aquatic sciences are nonlinear, and the fitting of such models to data is a frequent problem. As Sheldon (1979) shows, a strictly mathematical approach may lead to erroneous results even when a standard fitting package is used. It is essential to use a fairly sophisticated methodology for curve fitting to get not only the best possible estimates for the fitting parameters, but also reliable confidence limits on these parameters. Fortunately, recent advances in the technology of computation make it possible for scientists without extensive statistical background to do an excellent job of curve fitting and parameter estimation without spending a great deal of time on computation. I describe here in general terms the methodology that was used in initially evaluating Sheldon s data. There are two basic computer applications involved in this approach. The first is an interactive way to estimate fitting parameters and their confidence ranges, the second is a test of the reliability of fits obtained by this or any other method that can be used to evaluate packaged programs and other fitting techniques. I deal primarily with fitting of asymptotic curves such as arise in Sheldon s model, although the procedures can be used for any nonlinear model. Techniques for fitting nonlinear functions often seem difficult and unreliable, and confidence limits on the fitted values of the parameters are seldom provided. Crude techniques that were originally developed to simplify computation in the field before the days of pocket calculators and personal computers are still being used in many modern laboratories. With recent developments in computational technology it is possible for a scientist without a sophisticated statistical background to do an excellent job of curve fitting and parameter estimation by methods that are neither simplistic nor arcane. I will discuss two ways in which computers can be used for curve fitting. The first enables the user to estimate fitting parameters and confidence ranges for them, while the second can be used to evaluate the reliability of fits obtained by any method and to evaluate packaged programs and other aids to fitting. For