Comparison of measured growth rates with those calculated from rates of photosynthesis in Planktothrix spp. isolated from Blelham Tarn, English Lake District


Author for correspondence: A. E. Walsby Tel. +44 (0)117 9287490 Email:


  • • Differences in photosynthetic production and conversion to biomass of the red-coloured cyanobacterium Planktothrix rubescens and the green-coloured Planktothrix agardhii , were investigated in relation to their growth in Blelham Tarn, UK, using clonal isolates from the lake.
  • • Growth rates (µ) were measured in cultures under 12 h : 12 h light : dark cycles at 15 irradiances ( E ) in temperatures (Θ) of 10–25°C. Photosynthetic rates ( P ) were measured under the same conditions.
  • • For P. rubescens , µ reached a maximum of 0.33 d −1 at 25°C in photon irradiances > 40 µmol m −2  s −1 and exceeded µ for P. agardhii over the range of temperatures in Blelham Tarn (< 21°C), although not at temperatures > 25°C. In P. rubescens , the dif ference (Δµ) between the growth rate of cell carbon (µ C ), calculated from P , and µ was only 3% at 10°C but increased with temperature to 30% at 25°C; in P. agardhii , Δµ values were higher at low temperatures and lower at the higher temperatures.
  • • Using algorithms describing the irradiance- and temperature-dependent growth rates and measured values of E and Θ at different depths in Blelham Tarn, it was demonstrated that P. rubescens would outgrow P. agardhii , though the latter might grow better in warmer and shallower lakes. We discuss the problems of modelling phytoplankton growth from measurements of in situ photosynthesis.


This paper examines the relationship between rates of photosynthesis and growth of two strains of the planktonic cyanobacterium Planktothrix spp., which coexist in Blelham Tarn, in the English Lake District.

Measurements of photosynthesis are often used as surrogates for measurements of growth of phytoplankton populations, although the connection between the two is seldom explicitly made. The rate of carbon fixation per mass of cell carbon would be the same as the growth rate if all the carbon fixed in photosynthesis were to remain inside the cells. Inevitably, however, there are losses of carbon through respiration, photorespiration and extracellular production, which must be subtracted to reconcile the fixation rate with the growth rate.

In natural waters, limitation of nutrients rather than irradiance (E) may determine the maximum growth rate, further affecting the conversion of photosynthate into growth (Tilzer, 1984; Reynolds & Irish, 1997), while additional losses through grazing and parasitism affect the conversion of growth into population increase. Nevertheless, light limitation is a major determinant of phytoplankton growth, especially in populations residing deep in the metalimnion or mixed deeply through the water column.

Population increase has previously been related to the rates of potential photosynthesis (P) (Micheletti et al., 1998) and growth (Bright & Walsby, 2000; Walsby & Schanz, 2002) of the planktonic cyanobacterium Planktothrix rubescens in Lake Zürich, Switzerland. Micheletti et al. (1998) calculated the daily integral of photosynthesis of the population, using an algorithm for the P/E curve of the organism and data on the underwater light field; the growth rate of cell carbon calculated from the daily integral exceeded several-fold the growth rate required to explain the population increase. Bright & Walsby (2000) determined the relationship between growth rate (µ) and irradiance (in a µ/E curve) of P. rubescens and, using the same light-field data, obtained an estimate of growth in the water column that was closer to the observed population increase. The difference between the increases calculated from measurements of photosynthesis and growth rate were not, however, explicitly determined.

In this paper, we compare the rates of photosynthesis and growth by two strains of Planktothrix, under conditions that permit calculation of the efficiency of photosynthate assimilation. These measurements were performed on a green-coloured strain of Planktothrix agardhii, which possesses phycocyanin, and a red-coloured strain of P. rubescens, which, possessing both phycocyanin and phycoerythrin, might show greater efficiency in harvesting green light and in growing at lower irradiances.

Mur et al. (1978 ) demonstrated the consequences of different growth rates on competition between Oscillatoria (Planktothrix) agardhii and the green alga Scenedesmus protuberans : although the cyanobacterium grew more slowly at high irradiance, its higher growth rate at lower irradiance resulted in its outcompeting the green alga in a mixed culture as the irradiance decreased as a result of self-shading. Such a competition for light could explain the succession from small green algae to cyanobacteria during the summer in eutrophic lakes that support dense phytoplankton populations. Similarly, differences in using light may explain the dominance of green or red Planktothrix sp. observed in lakes of different depths and mixing regimes.

Materials and Methods

Clonal cultures of Planktothrix

Clonal cultures of Planktothrix spp. were made by isolating single filaments from lake-water samples with a microsyringe, using the methods of Beard et al. (1999). The cultures were maintained in test tubes containing liquid medium (Bright & Walsby, 2000) at 17°C in 12 h : 12 h light : dark cycles with a photon irradiance of approximately 15 µmol m−2 s−1 in the light phase. Larger cultures for experiments were grown in Erlenmeyer flasks bubbled with air.

Measurement of filament biomass

Estimates of Planktothrix filament concentration in a culture were made by triplicate measurements of dry mass, spectrophotometric absorbance and filament biovolume, using the same suspension. Dry mass was determined by filtering a measured volume of the culture through a preweighed cellulose nitrate membrane filter (pore size 5 µm; Whatman, Clifton, NJ, USA), drying in vacuo and reweighing with a Cahn microbalance. The absorbance at 750 nm (A750) was measured using 1-ml cuvettes with a pathlength of 1 cm in an LKB Ultraspec spectrophotometer, after collapsing gas vesicles in the suspension with a pressure of 1.4 MPa. Filament biovolume was calculated from measurements of the widths and lengths of the cylindrical filaments, determined by epifluorescence microscopy and computer image analysis (Walsby & Avery, 1996). Mean filament widths of the different isolates were determined from five measurements on each of 10 filaments in cultures grown in standard conditions.

Measurement of growth rate

Measurements of growth rate under defined illumination and temperature were made using 100-ml cultures in 250-ml Erlenmeyer flasks using the apparatus described by Bright & Walsby (2000). The cultures were mixed by aeration and illuminated from below; the mean photon irradiance in the cultures was determined from measurements made at the bottom and top surfaces with a Macam SD101Q-Cos Quantum sensor (Table 1 in Appendix of Walsby, 2001).

Table 1.  Coefficients used in algorithms for calculating growth rate/irradiance (µ/ E ) curves at four different temperatures and µ/ E /Θ plots for all combinations of irradiance and temperatures, for Planktothrix rubescens and Planktothrix agardhii . Both the Q 1 (used in the calculations) and more familiar Q 10 values are given (see text)
(a) Planktothrix rubescens
Values of coefficients used in Eqn 1, for calculating µ/E at four temperatures
Θ/°CGrowth rates in a 12 h : 12 h light : dark cycleCalculated instantaneous growth rates
φm/d−1α/d−1 (µmol m−2 s−1)−1µD/d−1φLm/d−1αL/d−1 (µmol m−2 s−1)−1
Values of coefficients used in Eqn 5, for calculating µ/E/Θ
 φm′/d−1α′/d−1 (µmol m−2 s−1)−1µD/d−1φLm′/d−1αL′/d−1 (µmol m−2 s−1)−1
 < 14.71°C> 14.71°C< 14.71°C> 14.71°C
Intercept at 0°C0.073830.010060.0434 0.00000.14770.02010.0873
m /(d −1  °C −1 ) −0.0009097
(b) Planktothrix agardhii
Values of coefficients used in Eqn 1, for calculating µ/E at four temperatures
Θ/°CGrowth rates in a 12 h : 12 h light : dark cycleCalculated instantaneous growth rates
φm/d−1α/d−1 ( µmol m−2 s−1)−1µD/d−1φLm/d−1αL/d−1 (µmol m−2 s−1)−1
Values of coefficients used in Eqn 5, for calculating µ/E/Θ
 φm′/d−1α′/d−1 (µmol m−2 s−1)−1µD/d−1φLm′/d−1αL′/d−1 (µmol m−2 s−1)−1
 < 14.83°C> 14.83°C< 14.83°C> 14.83°C
Intercept at 0°C0.066380.002060.0363 0.00000.13280.004110.0726
m /(d −1  °C −1 ) −0.001168

Measurement of photosynthetic rates

Photosynthetic O2-production rates were measured with a modified apparatus of Dubinsky et al. (1987). Temperature in the 13-ml, magnetically stirred measurement chamber was controlled by a thermostatic water jacket and monitored with a thermistor probe. The chamber was illuminated with light from a 250 W tungsten-halogen bulb (Osram) in a Kodak slide projector, attenuated by neutral density filters. The irradiance at the rear window of the chamber was measured with a Macam SD101Q-Cos quantum sensor; the mean irradiance in the chamber was calculated as Em = (Ef − Eb)/[ln(Ef/Eb)], where Ef is the irradiance at the front face and Eb the irradiance at the back of the chamber (van Liere & Walsby, 1982). Estimates of Ef and Eb were made from measurements with culture and water in the chamber, respectively (Bright, 1999). Oxygen concentration was measured with a Yellow Springs oxygen electrode. Readings from the electrode and the quantum sensor were recorded at 1-s intervals by a computer, using the Handyscope program, via a Keithley picoammeter and TiePie analogue–digital interface. Measurements of O2 production were made over intervals of 200 s; the mean rate was calculated by regression analysis of the rate during the period of 30–190 s in each interval. Photosynthesis/irradiance (P/E) curves were generated from rate measurements at 7–14 different photon irradiances from 0 to 1000 µmol m−2 s−1, made sequentially from lowest to highest. Measurements were made at times between 3 h and 10 h after the start of the light period of the light : dark cycle of the cultures, to avoid the early periods where the coefficients change most rapidly (Vaughan et al., 2001).


Isolation of Planktothrix strains from Blelham Tarn

Clonal cultures of Planktothrix spp. were made by isolating single filaments from lake-water: from 144 filaments selected, 88 cultures were established. Of these, 27 were identified as P. rubescens: the filaments were reddish-brown and contained phycoerythrin. A further 61 were identified as P. agardhii: the filaments were blue-green and contained phycocyanin (Davis et al., 2002). Detailed investigations were made on two of the isolates, P. agardhii B9905 (CCAP 1460/20) and P. rubescens B9972 (CCAP 1460/19), isolated from Blelham Tarn on 3 August 1999. (CCAP is the NERC Culture Collection of Algae and Protozoa, CEH, Ambleside, Cumbria, UK).

Filament widths were determined for 40 strains, 20 from each species. The mean filament width for the P. rubescens strains was 6.4 µm and for strain B9972 it was 7.0 µm; the mean for the P. agardhii strains was 8.1 µm and for strain B9905 it was 7.9 µm. The critical pressure distributions of gas vesicles in all of the 88 isolates of Planktothrix spp. were determined. The mean critical pressure (pc) for the 27 P. rubescens strains was 0.76 MPa and for strain B9972 it was 0.78 MPa. The mean value of pc for the 61 P. agardhii strains was 0.70 MPa and for strain B9905 it was 0.69 MPa.

Growth rates

Growth rates were determined for both organisms over a range of irradiances and temperatures. Figure 1 shows data on the growth of P. rubescens B9972 at 20°C and photon irradiances from 0 to 129 µmol m−2 s−1. Each line indicates the change in the concentration of filament dry mass, N (in mg ml−1), over time at each photon irradiance. The growth rate was calculated as µ = ln(ΔN/mg ml−1)/t by regression analysis.

Figure 1.

The relationships between filament concentration ( N ) of Planktothrix rubescens B9972 (determined by absorbance, A750nm ) and age of cultures grown at 20°C in 11 different irradiances. The plots are staggered to avoid overlap; marks on the left ordinate are at intervals of 0.5 ln ( N /mg ml −1 ) units. The numbers on the left are the intercepts of ln ( N /mg ml −1 ); numbers on the right are ( E−1 mol m −2  s −1 ), where E is the mean photon irradiance during the light period in the culture, grown on a 12 h : 12 h light : dark cycle.

From the values of µ at each photon irradiance, a growth rate/irradiance (µ/E) curve was constructed (Fig. 2a). The value at zero irradiance, µD, is the intercept obtained by linear regression analysis of the first five positive data points (van Liere & Mur, 1979). The line in Fig. 2a is a plot of the exponential equation

Figure 2.

Growth rates of Planktothrix rubescens determined from biomass changes in cultures grown in 12 h : 12 h light : dark cycles. (a) The growth rate/irradiance (µ/ E ) curve obtained from 10 data points (closed squares) derived from the measurements of exponential growth rates shown in Fig. 1 , and the value of µ D (open square) calculated by extrapolation of values at low irradiance. (b) Set of four µ/ E curves for growth at temperatures of 10, 15, 20 and 25°C obtained using the same procedures.

µ = φm[1 − exp(−αEm)] + µD(Eqn 1)

(α is the gradient of µ/E under rate-limiting irradiances; φm = (µh − µD), that is, the difference between the highest growth rate, µh (reached at saturating irradiances), and µD; Bright & Walsby, 2000). In Fig. 2a, the coefficients have the values µD =−0.0182 d−1, φm = 0.258 d−1, and α = 0.0115 d−1 (µmol m−2 s−1); the last two values were determined by the least-squares method from the 10 data points with positive values. While the states of cultures with positive growth rates remain nearly constant during exponential growth (Fogg, 1965), the states of cultures with negative growth rates must change progressively as cells deplete their reserves and eventually die. These changes must affect the ratio of absorbance/biomass used in estimating filament concentration and we therefore exclude data from cultures with negative growth rates from the analysis.

Using the same procedures, µ/E curves were obtained for P. rubescens grown at the four temperatures, 10, 15, 20 and 25°C (Fig. 2b). The initial gradient of µ/E, characterized by the light affinity coefficient α was broadly similar for the four curves, although slightly steeper at 15°C. The maximum growth rates, µh, reached at progressively higher irradiances, show an approximately linear increase with temperature. The coefficients used in the algorithms for each of the four curves are given in Table 1.

A complete description of the growth response to both irradiance (E) and temperature (Θ) can be obtained by determining the temperature-dependent change in the coefficients φm, α, and µD used in the algorithms for the µ/E curves. The effect of temperature on a rate coefficient is described by a Q1 value, the proportional increase in rate with a 1°C rise in temperature (hence, Q1 = Q100.1). For φm, if φm′ is the value at a standard reference temperature of Θ′, the value at another temperature, Θ, is

φm = φm′Q[(Θ−Θ′)/°C](Eqn 2)

In all the following analyses Θ′ was set at 0°C so that Θ – Θ′ = Θ and φm = φm′Q(Θ/°C). The values of φm′ and Q were determined as those that gave the smallest difference between the measured and calculated values of φm at each temperature, using the least-squares method. The coefficient α showed little change with temperature but the small increase in α below 15°C and small decrease in α above 15°C are described by a similar equation

α = α′Q(Θ/°C)(Eqn 3)

but with different values of Q for these two temperature ranges. A linear correction factor, m, was applied for µD:

µD = µD′ + mΘ(Eqn 4)

D′ is the value at 0°C).

The overall growth response to E and Θ was therefore described by applying the temperature corrections for φm, α and µD from Eqns 2, 3 and 4 into Eqn 1:

µ = (φm′Q(Θ/°C)){1 − exp[(−α′Q(Θ/°C)E)/ (φm′Q(Θ/°C))]} + (µD′ + mΘ)(Eqn 5)

The algorithms for the growth of P. rubescens are obtained by substituting the values of the coefficients given in Table 1.

A similar set of µ/E curves were obtained for the green strain, P. agardhii B9905. The growth rates and temperature coefficients are broadly similar. The main differences are that the increase in φm was lower between 10°C and 20°C and higher between 20°C and 25°C. The quantitative differences are summarized in Table 1 and analysed in a comparison of the instantaneous growth rates.

Instantaneous growth rates

The growth rate coefficients µ, φm and α, referred to above, relate to the increase that occurs over a 24-h light : dark cycle at the irradiance, E, given during the 12-h light phase (and at the temperature, Θ, throughout the cycle). Bright & Walsby (2000) showed that when the instantaneous growth rate is independent of daylength, these coefficients are related to the coefficients describing the instantaneous growth rate during the light phase of the cycle (distinguished by subscript L) in the following way: (1) µL = 2µ + µD; (2) µLh = 2µh + µD; (3) φLm = µLh + µD; (4) φLm = 2φm; (5) αL = 2α. The growth rate in the dark, µD, is the same for both the µ/E and the µL/E relationships (i.e. µD is a special case of µL at E = 0). The Q1s for the two sets of growth rates are the same. The values of the coefficients for calculating the instantaneous growth rate, µL, are also given in Table 1.

Algorithms for the E- and Θ-dependent instantaneous growth rates, µL, of P. rubescens and P. agardhii are made by substituting the values of φLm′ and αL′ given in Table 1 into a modified version of Eqn 5:

µL = (φLm′Q1Lφ(Θ/°C)){1 − exp[(−αL′Q1Lα(Θ/°C)E)/ (φLm′Q1Lφ(Θ/°C))]} + (µD′ + mΘ)(Eqn 6)

D′ is the same in Eqns 5 and 6). These algorithms are used in (1) comparing the growth of the two Planktothrix spp. (2) making comparisons with the growth rate of carbon incorporated by photosynthesis and (3) calculating the potential growth of Planktothrix in the lake (Davis et al., 2002).

Compensation point for growth

Both strains of Planktothrix grew at low irradiances. The irradiance in the light phase supporting zero growth (µ = 0) over the 12 h : 12 h light : dark cycle is referred to here as the growth compensation point (Eg). It was calculated from the same µ/E linear regression analysis used to determine µD (see above). The values of Eg at four temperatures are shown in Table 2: the Eg values are strongly temperature dependent and at each temperature are lower for P. rubescens than for P. agardhii. These Eg values are specific to the 12-h light period. For longer periods, the Eg values decrease.

Table 2.  Calculated compensation irradiances for growth of Planktothrix rubescens and Planktothrix agardhii (see text)
Θ/°CCompensation irradiances/µmol m−2 s−1
Planktothrix agardhii B9905 Planktothrix rubescens B9972
  1. Eg , the irradiance in the light phase supporting µ = 0 over a 12 h : 12 h light : dark cycle; ELg supporting an instantaneous growth rate of µ L  = 0.


We have also determined from curves of µL/E, calculated using Eqn 6, the instantaneous growth compensation points, ELg, at the different temperatures (Table 2); these are approximately half the corresponding Eg values. The ELg values would be equivalent to Eg in continuous light if the same instantaneous growth rate were maintained. Foy & Smith (1980) have shown that the efficiency of growth decreases with increasing daylength, probably owing to rate-limiting conversion of excess photosynthate into protein, which in short daylengths is made good by conversion during the dark period. At or near the compensation point, however, there should be no excess photosynthate and no such rate limitation; ELg should therefore be similar to Eg in continuous light.

The ELg values are comparable to photosynthetic compensation points (Ec) at which photosynthetic oxygen evolution just equals respiratory oxygen consumption (Kirk, 1994). The ELg values for Planktothrix in Table 2 are lower than most of the Ec values listed for phytoplankton by Kirk (1994), the notable exceptions being pennate diatoms at −1°C under sea ice, where Ec is 0.2 µmol m−2 s−1; a similar value would be expected for P. rubescens close to 0°C.

The growth compensation depth (zg) is the depth at which light-dependent growth integrated over the 24-h cycle is zero (cf. the photosynthetic compensation depth; Falkowski & Raven, 1997). It is often equated with the euphotic depth, zeu, which, arbitrarily, is taken to be the depth where the irradiance is 0.01E0. When E0 is 1000 µmol m−2 s−1, then the irradiance at zeu will be 10 µmol m−2 s−1, which is 4- to 16-fold higher than Eg for P. rubescens.

Comparison of the interrelations of growth with irradiance and temperature for the Planktothrix spp.

Graphs of µL vs E and Θ, calculated by the algorithms for P. rubescens and P. agardhii (Fig. 3), describe the growth rates under the different combinations of irradiance and temperature investigated, which cover most of the conditions encountered in Blelham Tarn. The surface plot in Fig. 3c shows the difference between the growth rates of P. rubescens and P. agardhii. The measurements-based model indicates that P. rubescens grows slightly faster under most of the conditions likely to be encountered in the lake but the difference decreases at the higher ranges. Extrapolating to higher irradiances and temperatures than those at which measurements were made, gives growth rates for P. agardhii that slightly exceed those for P. rubescens.

Figure 3.

Growth rate (µ) vs irradiance and temperature for (a) Planktothrix rubescens B9972, (b) Planktothrix agardhii B9905 and (c) the difference between growth of P. rubescens and P. agardhii . The surface plots of growth rate are calculated from the algorithms obtained by substituting the values of the coefficients in Table 1 into Eqn 6 (see text).


The photosynthesis/irradiance (P/E) curves obtained for both organisms over a range of temperatures were all of the usual form, with an initial linear response to increasing irradiance, a maximum rate reached at photon irradiances between 50 µmol m−2 s−1 and 170 µmol m−2 s−1, and a gradual decrease with higher irradiances. An example is given in Fig. 4. Algorithms for the P/E curves were calculated using the procedure of Walsby (1997), based on the exponential equation

Figure 4.

Measurements of the biomass-specific photosynthetic rate at 20°C made with a culture of Planktothrix rubescens B9972 grown at the same temperature (closed squares) and the photosynthesis/irradiance curve (line) obtained using Eqn 7 (see text).

P  =  Pm [1 − exp(−α E / Pm )] +  R  + β E(Eqn 7)

(Pm is the maximum biomass-specific photosynthetic rate (µmol mg−1 h−1) at saturating irradiances; R is the rate (negative, due to respiration) at zero irradiance; α is the gradient of P/E in rate-limiting irradiances (µmol mg−1 h−1 (µmol m−2 s−1) −1); β is the gradient (also negative) due to photoinhibition at high irradiances; Fig. 4). The values of the coefficients Pm, R, α, β at each temperature, given in Table 3 are the means of the values obtained from four or more such curves.

Table 3.  Coefficients used in algorithms for calculating P / E curves at four different temperatures and P / E /Θ plots for all combinations of irradiance and temperatures, for Planktothrix rubescens and Planktothrix agardhii (see text)
(a) P. rubescens
Coefficients used in Eqn 7, for calculating P/E at four temperatures
Θ/°CPm /µmol mg −1  h −1R /µmol mg −1  h −1α/µmol mg−1 h−1 (µmol m−2 s−1)−1β/µmol mg−1 h−1 (µmol m−2 s−1)−1
100.87−0.03660.05921.18 × 10−4
151.48−0.1290.05761.82 × 10−4
201.50−0.1090.05302.76 × 10−4
252.99−1.8500.05947.70 × 10−4
Coefficients used in Eqn 8, for calculating P/E
 Pm ′ /µmol mg −1  h −1R ′ /µmol mg −1  h −1α′/µmol mg−1 h−1 (µmol m−2 s−1)−1β′/µmol mg−1 h−1 (µmol m−2 s−1)−1
Intercept at 0°C0.382−0.0890.05902.77 × 10−5
Q11.086 1.03711
Q102.275 1.43911
(b) P. agardhii
Coefficients used in Eqn 7, for calculating P/E at four temperatures
Θ/°CPm /µmol mg −1  h −1R /µmol mg −1  h −1α/µmol mg−1 h−1 (µmol m−2 s−1)−1β/µmol mg−1 h−1 (µmol m−2 s−1)−1
101.21−0.0660.05802.24 × 10−4
151.36−0.0720.05108.77 × 10−6
201.48−0.1050.04601.54 × 10−4
252.14−1.7300.04615.62 × 10−4
Coefficients used in Eqn 8, for calculating P/E/Θ
Coefficients used in Eqn 8, for calculating P/E/Θ
 Pm ′ /µmol mg −1  h −1R ′ /µmol mg −1  h −1α′/µmol mg−1 h−1 (µmol m−2 s−1)−1β′/µmol mg−1 h−1 (µmol m−2 s−1)−1
Intercept at 0°C0.743−0.02910.0702.37 × 10−4
Q11.041 1.0730.9791
Q101.498 2.0130.8121

The effect of temperature on photosynthetic rate was investigated using cultures acclimated to the experimental temperature for at least 3 d previously. Algorithms for the P/E curve at each temperature were calculated for at least four independent data sets at each of the temperatures, 10, 15, 20 and 25°C. The resultant sets of P/E curves for each organism are shown in Fig. 5. The main trend is a substantial increase in Pm with temperature in both organisms; the rate of increase was more in P. rubescens, which showed substantially greater rates at the highest temperature investigated. Extrapolation of these trends below 10°C suggested that P. agardhii would photosynthesize faster at lower temperatures (Fig. 6), although there were no direct measurements in this range. Another difference was the relatively greater respiration rate of P. rubescens at the lower temperatures (Fig. 6).

Figure 5.

Photosynthesis/irradiance curves for Planktothrix rubescens (thinner line) and Planktothrix agardhii (bold line) and the difference between the P/E curves (dashed line), at four different temperatures, 10, 15, 20 and 25°C, for cultures acclimated to these temperatures. The coefficients Pm , R, α and β used in constructing the curves are those shown in Table 3 .

Figure 6.

Changes in the photosynthetic coefficients Pm , R, α and β with temperature for Planktothrix rubescens (left) and P. agardhii (right). The filled symbols are values calculated from measurements made at the temperature to which the culture had been acclimated; the solid lines are for the acclimated values, calculated from the 0°C intercept and Q 1 values in Table 3 . The open symbols are calculated from measurements made at 5°C lower or 5°C higher than the corresponding acclimated values, and are connected to the latter with broken lines.

It is commented here that while the cultures were acclimated to the temperature at which the photosynthesis was measured, they were not irradiance-acclimated. The sudden transfer of a culture to darkness that occurs during the P/E measurement must therefore affect the respiration rate, R, which will have been stimulated by the previous exposure to light (Gibson, 1975). The cultures were grown at the relatively low irradiance of about 15 µmol m−2 s−1, which is within the range encountered by the organism where it stratifies in the metalimnion of Blelham Tarn.

Algorithm for variation of photosynthesis with E and Θ

Algorithms describing the variation of photosynthesis with both photon irradiance and temperature were constructed by the same methods used for the analysis of growth rate: the changes in each of the four photosynthetic coefficients with temperature were described with a 0°C intercept value (Pm′, R′, α′ and β′) and corresponding Q1 values (Q1P, Q1R, Q and Q), given in Table 3. The photosynthetic rate at specified values of E and Θ was then calculated with the values of these coefficients substituted in Eqn 7:

P  = ( Pm ′Q 1p(Θ/°C) ){1 − exp[(−α′Q (Θ/°C)E )/ ( Pm ′Q 1p(Θ/°C) )]} + ( RQ1R(Θ/°C)) + (βQ(Θ/°C))E)(Eqn 8)

These algorithms are used in (1) comparing photosynthesis by the two Planktothrix spp., (2) making comparisons with the growth rate, and (3) calculating the potential photosynthesis of Planktothrix in Blelham Tarn (Davis, 2002).

Temperature acclimation and temperature change

In the studies described above, the Planktothrix cultures were acclimated to the temperature at which the photosynthetic rates were measured. Measurements of photosynthesis were also made at temperatures 5°C higher and 5°C lower than the acclimation temperature. The results are shown in Fig. 6. In summary, short-term changes in temperature tend to produce changes in the coefficients that are in the same direction as, but rather less than, the changes that occur during full acclimation.

For an organism circulating within a mixed water layer, the temperature will tend to change rather slowly and it will be acclimated; organisms moving across the thermocline, however, may be subject to more rapid changes.

Comparison of measured growth rates with those calculated from rates of photosynthesis

In order to compare rates of photosynthesis and growth, it is necessary to express the photosynthetic rate as a carbon-specific rate of CO2 fixation. We followed the procedure of Bright & Walsby (2000): the biomass-specific rate of O2 evolution (in µmol mg−1 h−1) was converted to a CO2 fixation rate by adopting a photosynthetic quotient of 1 µmol C fixed per 1.34 µmol O2 evolved (for growth on nitrate); cell carbon content was calculated with a ratio of 0.49 mg C/mg dry biomass and 12 × 10−3 mg µmol−1. Hence the relationship between photosynthetic oxygen production rate (PO) and the equivalent (instantaneous) carbon growth rate (µC) for Planktothrix can be represented by the equation

PO /(1 µmol mg −1  h −1 ) ≡ µ C /(0.01828 h −1 ) ≡ µ C /(0.000761 d −1 ) (Eqn 9)

These conversions yield a maximum growth rate of cell carbon, µC, net of losses by respiration and excretion, which should equal or exceed the instantaneous growth rate, µL, measured under the same conditions. In Fig. 7 we compare the two rates at different irradiances and temperatures for both organisms: µC is calculated using Eqn 8 (with the coefficients in Table 3) and Eqn 9; µL is calculated from Eqn 6 (with the coefficients in Table 1). For the most part, the expected condition µC > µL holds. For P. rubescens, there was a slight excess growth rate at low irradiances; the probable cause is the possible overestimate of respiratory losses (R in the P/E algorithm) discussed above.

Figure 7.

Comparisons of growth-rate/irradiance curves in Planktothrix rubescens (left side) and P. agardhii (right side) at four different temperatures: the cell carbon growth rate, µ C (thinner lines), calculated from photosynthetic rate using Eqns 8 and 9 (see text); the cell growth rate, µ L (bold line), calculated from Eqn 6 (see text); and the difference between the two rates (dashed line).

Comparisons of µ and µC in Blelham Tarn

The growth rate model (Bright & Walsby, 2000) and photosynthetic model (Micheletti et al., 1998) have been used to calculate the potential daily increase in a Planktothrix population for comparison with the observed changes in the population, but the two models have not been explicitly compared with one another. We made such a comparison for the populations of the two species in Blelham Tarn on contrasting days in summer and winter. Data were collected on the photon irradiance (Eij) and temperature (Θij) at each depth (zi, at intervals of Δz = 0.5 m), and each time (tj, at intervals of Δt = 1.0 h). The value of µL at each depth and time was then calculated by substituting these values for E and Θ in Eqn 6, together with the coefficients in Table 1. The overall growth rate, µi, over the whole 24-h period at each depth, zi, was calculated by the methods of Bright & Walsby (2000) and Walsby & Schanz (2002). From the biomass concentration at the start of the day (Ni0), the concentration at the end of the first 1-h interval was calculated as Ni1 = Ni0 exp(µLΔt); this calculation was repeated for each of the 24 1-h intervals so that the last gave the concentration at the end of the day, Ni24. The overall growth rate was then calculated as µi = ln(Ni24/Ni0)/td, where td = 24 h. This whole procedure was repeated for µC, calculated by Eqns 8 and 9 using the coefficients in Table 3. The values of µi calculated from µL and µC at each depth are shown in Fig. 8.

Figure 8.

Comparison of vertical distributions of growth rates calculated for Planktothrix rubescens and Planktothrix agardhii on 3 August 1999 and 5 February 2000, from information on the vertical distributions of light and temperature in Blelham Tarn: the biovolume concentration (dashed line); the relative increase in cell carbon over 24 h, calculated from the photosynthetic rate ( P ) converted to µ C (thinner line); the relative increase in biovolume over 24 h, calculated from growth rate, µ L (bold line).

The first comparison was made for 3 August 1999, when the lake was thermally stratified. Both organisms formed maxima (6.1 cm3 m−3 for P. rubescens and 34 cm3 m−3 for P. agardhii) at a depth of 4 m in the upper metalimnion (where the temperature was 18.8°C), although a small part of each population was mixed into the surface layer (Fig. 8). Calculations with µL indicated that the relative daily increase for P. rubescens was slightly greater than for P. agardhii at all depths down to the daily integrated compensation depth for growth (zg), which was 4.0 m for P. rubescens and 3.9 m for P. agardhii. Below zg, the relative daily loss was slightly less for P. rubescens than for P. agardhii. Calculations based on µC from the photosynthetic measurements gave relative daily increases that were higher at depths down to 2.3 m but lower below this depth. They also indicated smaller compensation depths, of 3.6 m for both species.

The overall daily changes in the population can be calculated by multiplying the biovolume concentration by the relative change at each depth. By integrating the increase at all depths through the water column, the overall change in the population was calculated to be 0.33 cm3 m−2 (an increase of 3.5%) for P. rubescens and 1.0 cm3 m−2 (an increase of 2.2%) for P. agardhii. The conditions allowed photoautotrophic growth by both organisms but at a higher rate for P. rubescens. Integrating the daily increases calculated from µC down the water column indicated that the production in the surface layers was totally (for P. rubescens) or almost (for P. agardhii) compensated by respiratory losses.

On 5 February 2000, when the water temperature was a uniform 5.3°C, both organisms were distributed down the mixed water column and the average biovolume concentrations were much lower (0.35 cm3 m−3 for P. rubescens and 0.033 cm3 m−3 for P. agardhii). The lower daily insolation (1.1 mol m−2 on 6 February compared with 11.5 mol m−2 on 3 August) was offset by a lower Kd (0.73 m−1, cf. 1.7 m−1 in August), and the compensation depth (zg) calculated from µL for P. rubescens was deeper, 5.1 m, than in the summer; the value of zg for P. agardhii, however, occurred at only 3.2 m. For P. rubescens, integration of the daily increases, calculated from µL down the water column, indicated a small net daily increase of 0.8% by the circulating population; for P. agardhii the increase was only 0.3%. Calculations based on µC, however, indicated a substantial decrease in P. rubescens, owing to the relatively greater contribution of respiratory losses during the longer dark periods. The same analyses made for P. agardhii produced a closer agreement between the growth integrals based on µC and µL.

It is notable that the two models produce a different outcome in the two periods (e.g. with P. rubescens the µC-based model gives a higher growth rate near the surface in August whereas the µL-based model gives a higher growth rate at all depths in February). This is explained by the lower irradiance and lower temperature in February, conditions in which the µL algorithm for this species gives higher growth rates (Fig. 7).


Effects on growth rate of filament width, pigmentation and gas vesicles

The growth rate of an organism is affected by processes that influence the rate at which new cell material is produced. For a phototroph, such as Planktothrix, the growth rate at low irradiances may be determined by the specific rate of photon absorption, on which the synthesis of all the cell components depends. The actual growth rate achieved under a given irradiance, however, will depend on the proportion of the radiation absorbed and the burden placed on growth by production of components that do not directly contribute to the growth process. These generalities are illustrated by the three characteristics of Planktothrix investigated.

First, cell size. Owing to the package effect, a suspension of narrow filaments absorbs more of the incident irradiance than a suspension of wider filaments at the same biomass concentration (Kirk, 1976). Other things being equal, narrower filaments should therefore grow faster than wide ones at limiting irradiances. The filaments of P. agardhii B9905 are 13% wider than those of P. rubescens B9972. Small size also has other effects on growth rate (see below) and other consequences in natural situations: small organisms may be more readily grazed (Reynolds, 1984) and they will sink or float more slowly (Stokes's Law).

Second, pigmentation. The filaments that possess the pigment phycoerythrin will absorb green light more strongly and will therefore absorb a greater proportion of the visible radiation. At limiting irradiances, these filaments will have a higher specific rate of photosynthesis. It does not necessarily follow, however, that they will have a higher growth rate. The production of the additional pigment itself consumes part of the photosynthate; the overall growth rate will increase only if the increase in photosynthate exceeds the protein burden of phycoerythrin production (Raven, 1984). We lack the quantitative information required to assess whether the net benefits of phycoerythrin production would give P. rubescens B9972 a higher growth rate. In lakes, however, the proportion of green light increases with depth and this would provide additional benefits to cyanobacteria that produce phycoerythrin.

Third, the gas vesicle. This is one of many other components whose production costs constitute a burden that will affect growth rate. From the inverse relationship between the cylinder radius (r) and pc of a gas vesicle, described by the equation (r/nm) = (pc/275 MPa)−3/5 (Walsby, 1994), it is calculated that the gas vesicles of P. rubescens B9972, which have a pc of 0.78 MPa, would have a cylinder radius of 33.8 nm compared with 36.3 nm for the gas vesicles of P. agardhii B9905, which have the lower pc of 0.69 MPa. From the equations of Walsby & Armstrong (1979) and calculations of Walsby & Bleything (1988) based on the Anabaena gas vesicle, it is calculated that the ratio of protein wall volume to gas volume in the narrower gas vesicles is 0.15 g cm−3 compared with 0.14 g cm−3 for the wider gas vesicles. The costs of providing buoyancy are therefore 7% higher in P. rubescens. The amount of gas vesicle protein required to provide buoyancy represents 5.4% of the total cell protein in P. rubescens compared with 5.1% in P. agardhii. Applying the logic in Walsby (1994) it is calculated that these extra costs might decrease the growth rate of P. rubescens by about 0.23%.

These three cases address factors that affect growth at light-limiting irradiances. Similar considerations may be made of factors that affect growth rate at light-saturating irradiances. For example, narrower filaments, which have a larger ratio of surface area to volume, will show higher rates of nutrient uptake (Raven, 1988). Foy (1980) has demonstrated the inverse relationship between filament diameter and growth rate in a survey of 22 strains of filamentous planktonic cyanobacteria.

We have considered just three characters that may vary between the two organisms and affect their growth. Of these, the smaller filament width should contribute to the higher growth rate demonstrated in P. rubescens, whereas the narrower gas vesicles should partly counteract the increase; phycoerythrin production will contribute to an increased growth rate in the lake metalimnion and may also do so under the experimental conditions. There are many other characters that may contribute to the different growth rates. Some of these should explain the observed differences in the responses of the two organisms to temperature change.

Comparison with rates in other organisms

Comparisons between different phytoplankton species indicate that cyanobacteria grow more slowly than many eukaryotic algae (Reynolds, 1984) and among cyanobacteria, Planktothrix spp. have the lowest growth rates (Foy, 1980). Bright & Walsby (2000) compared and discussed the growth rates of different Planktothrix isolates. The values of µh at 20°C for the isolates investigated here (0.240 d−1 for P. rubescens and 0.194 d−1 for P. agardhii) are substantially higher than µh-values for strains of P. rubescens isolated from Lake Zürich, 0.111 d−1 for Pla 9303, 0.123 d−1 for Pla 9316 (Bright & Walsby, 2000) and 0.170 d−1 for Pla 97112 (C. Johnson & Y. Nakamura, unpubl.).

Comparisons of growth rate with carbon growth rate

The relative difference between µC and µL, expressed as Δµ = (µC – µL)/µL, indicates the relative loss of carbon fixed in photosynthesis. The lower Δµ of P. rubescens, especially at lower temperatures and irradiances, is correlated with its higher growth rate. At the higher temperatures the trend is reversed and P. agardhii has the lower Δµ. The green P. agardhii strains are found more commonly in shallower lakes, such as the fen lakes in The Netherlands, where they more frequently become entrained in the warmer epilimnion.

The contributions of respiration, excretion and cell death to Δµ could be investigated. They may explain the different responses of photosynthesis and growth in the two Planktothrix species to temperature, which is a factor in their competition in Blelham Tarn.

Modelling growth and photosynthesis in lakes

The algorithms for growth rate described here have provided the basis for models of growth by Planktothrix populations in Blelham Tarn, which can be compared with the observed changes in the lake. At certain times of year the modelled and observed changes are similar, indicating that photoautotrophic growth is the major cause of change; at other periods the modelled increase exceeds the observed increase, indicating that there are losses through other processes, such as grazing or water flow (Davis et al., 2002).

Such models can be based on measurements of either µL, the growth rate (Bright & Walsby, 2000) or µC, based on photosynthesis (Micheletti et al., 1998); models based on µL are clearly preferable because growth rate is both the subject and object of the model. Models based on µC depend on the relationship between rates of carbon assimilation and growth, which, it is illustrated, changes as a function of both irradiance and temperature and differs even in related species.

The difficulty with models based on µL is that the measurements of growth require cultures of the organism and take a very long time to perform. There is an understandable preference for techniques that can be performed more rapidly and in situ, such as the determination of the quantum yield of photosynthetic CO2 fixation (ΦCO2), which takes a few hours, or of O2 production (ΦO2), measured in minutes (Dubinsky et al., 1987). Even these are said to be ‘so laborious and time-consuming’ (Flameling & Kromkamp, 1998) that attention has turned to variable chlorophyll fluorescence for the instantaneous measurement of ΦP, the quantum yield of photosystem II (PSII) charge separation (Kolber & Falkowski, 1993). Nevertheless, the problem remains, how to relate the measurement to growth rate: the ratios of ΦP : ΦO2 vary widely with irradiance and light history (Flameling & Kromkamp, 1998) and the photosynthetic quotient (ΦO2 : ΦCO2) varies with the type of nitrogen source (Williams & Robertson, 1991). These difficulties are hardly likely to result in the replacement of such techniques by measurements of growth rate; is it possible, then, to relate the in situ measurements to growth by making comparisons of the sort described here?

Such measurements would generate a different type of model where, rather than calculating the potential value of µL from measurements of E and Θ, at each depth and time, the in situ photosynthetic rate of the population forms the basis of the growth rate calculations. This would not, however, obviate the need to collect the information required in the µL-based model: Ν is needed to calculate the biomass-specific photosynthetic rate, P, which is converted to µC (Eqn 9); E and Θ are needed to calculate the conversion of µC to µL (Eqns 6 and 8). The result will be identical if the in situ value of P is the same as in the culture at the same E and Θ (modelled by the algorithm of Eqn 8 and Table 3) but the result may be also affected by other factors not included in the growth rate model (such as light history and nutrient availability).

This investigation shows that the relationship between photosynthesis and growth rate varies with the physical conditions and varies differently between closely related species. Even larger differences can be expected with other phytoplankton organisms and it would be necessary to investigate the relationship in other species if estimates were needed of their growth rates from in situ measurements of photosynthesis.


We thank Dr S. J. Beard and Professor C. S. Reynolds for helpful discussion. This work was supported by a grant from the UK Natural Environment Research Council to AEW. PAD was supported by a NERC CASE award by the Centre for Ecology and Hydrology.