Phytoplankton size is important for the pelagic food web and oceanic ecosystems. However, the size of phytoplankton is difficult to quantify because of methodological constraints. To address this limitation, we have exploited the phytoplankton package effect to develop a new method for estimating the mean cell size of individual phytoplankton populations. This method was validated using a data set that contained simultaneous measurements of phytoplankton absorption and cell size distributions from 13 phytoplankton species. Comparing with existing methods, our method is more efficient with good accuracy, and it could potentially be applied in current in situ optical instruments.
© 2014 Optical Society of America
Phytoplankton size is a major biological factor, which governs the functioning of pelagic food-webs, thereby affecting the rate of carbon flux from the upper ocean to the deep layers [1, 2]. Many biogeochemical processes are related directly to the phytoplankton size in a given environment. For example, small cells absorb nutrients with higher efficiency, while large cells sink faster than small cells [3, 4].
However, direct measurements of phytoplankton size have remained elusive due to a lack of reliable methods. The current methods used to quantify phytoplankton size rely on microscopy and flow cytometry. Microscopy is used to enumerate the larger phytoplankton cells (i.e., diameter >20 μm ,), whereas flow cytometry is used to count the smaller cells (often with an upper limit of <20 μm ,). High-performance liquid chromatography (HPLC) pigment analyses have also been performed systematically to estimate different size classes [7, 8], but this method is time-consuming and some pigment groups may not strictly reflect the true size of cells [9, 10]. In addition, the absorption characteristics of phytoplankton have been used to infer the fractions of small and large cells in a sample [11–13]. For example, Ciotti et al.  proposed a parameterized model for extracting the dominant cell size in natural phytoplankton communities based on the spectral shape of the absorption coefficient. Brewin et al.  determined the fractional contributions of three phytoplankton size classes (micro, nano, and pico) to the overall chlorophyll a concentration using a three-component model. Unfortunately, these absorption-based methods cannot provide quantitative estimates of the actual cell sizes. Recently, a method has been proposed by Roy et al.  for determining the size of phytoplankton based on the absorption at 676 nm and the chlorophyll a concentration. In practice, however, it is often difficult to ensure the matching of these measurements, which are generally determined with two different instruments, and the accuracy of this method is affected greatly by the input parameters.
Therefore, it would be beneficial to develop a new approach for quantifying the size of phytoplankton. We know that changes in phytoplankton size are linked directly to variations in phytoplankton absorption [17, 18], which can be measured directly using the quantitative filter pad technique  or in situ instruments (e.g. ACS meter) . However, quantitative evaluations of cell size based on phytoplankton absorption are always challenging. Thus, the objective of the present study was to develop a new method based on phytoplankton absorption to facilitate quantitative estimates of the mean cell size of phytoplankton.
2. Methods and data
The absorption coefficient of phytoplankton cells distributed as discrete particles is less than that of the same material dispersed in a solution . According to previous studies [22–26], a quantity (package effect index, Qa*(λ)) can be used to describe this difference. If the particles have a refractive index that is close to that of the surrounding medium (sea water) , and assuming that they are homogeneous spheres and optically soft particles, an approximation allows Qa*(λ) to be calculated by
The notations used in this study are given in Table 1. In this calculation, the quantity d is the equivalent spherical diameter, which can also be regarded as the mean cell diameter of a phytoplankton sample. The pigment package effect index decreases from 1 (no package effect) to 0 (maximal package effect), and the specific absorption of each pigment in solution is determined by summing their elementary Gaussian bands . Thus, the absorption coefficients of phytoplankton (aph(λ)) can be regarded as the combined absorption spectra of five major pigments (chla, chlb, chlc, PSC, and PPC), which is simply written as follows :
A flowchart of the method is shown in Fig. 1.We aimed to calculate the value of the product CId. To minimize the influence of absorption attributable to auxiliary pigments, we selected a red waveband (650–700 nm) where the absorption is mainly due to chla. We used a peak-fitting code (Signal Processing Tools, http://terpconnect.umd.edu/~toh/spectrum/) to determine the packaged chla absorption band with its center at ~676 nm (achla,r (λ), also regarded as a Gaussian band, see Fig. 1 Step1). The specific absorption levels of the auxiliary pigments in the red waveband are very small and Cchlb is generally much less than Cchla, which we discuss below. Thus, Eqs. (2) and (4) can be simplified as follows:25], which were the mean values obtained from cultures of phytoplankton groups. The parameter σk indicates the initial width of Gaussian band (no package effect). The width of Gaussian band is directly affected by the package effect, and it increases with an enhanced package effect.
When λ = λmax, Eq. (6) can be written as:Eq. (6) by the relationship provided by Eq. (7), such that:Eqs. (1) and (5), we find there is only one unknown parameter (the product CId in Q*a(λ)) in Eq. (8), which can be represented under the simple form: A(λ) = Q(λ)E(λ). We used a nonlinear optimization inversion technique (MATLAB, Optimization Toolbox) to calculate the value of CId. The first step is to attribute initial guess to the product CId (here we used 100 (mg m−2)). Initial values of A(λ) are then computed for waveband from 650 to 700 nm, using Eq. (8) (see Fig. 1 Step3), and these values are compared to the measured A(λ) as follows: differences = [Ameasured(λ)–Acomputed(λ)]/Ameasured(λ). An iterative solver routine is then set up, to vary CId from the initial guess, to minimize the differences between measured and computed values in all bands, by setting the sum of the differences to be equal to zero, with a 5% tolerance error, and then we obtain the optimal solution (CId) for the current function (see Fig. 1 Step4).16]. Finally, using Eq. (7), we can derive Cchla as follows:Eqs. (1) and (5) (see Fig. 1 Step6), and a*max is constant (0.02 (m2(mg chla)−1)). We provide the program code which is developed in MATLAB (see www.dropbox.com/sh/w16516ikbmakn73/tWl3kjN7pf).
It was difficult to determine the phytoplankton size distribution in natural waters, so laboratory-cultured phytoplankton species were used to validate the performance of the method. Batch cultures of 13 individual phytoplankton species were used in this study (Table 2). The spectral absorption coefficients of these phytoplankton groups were measured using an ACS meter (WET Labs Inc.). The cell size distributions and cell number densities were determined using a Multisizer III Coulter counter (Beckman Inc.). The mean cell diameter (MCD) was calculated as: d = [∑N(Di)Di3/Nt]1/3 (N(Di) is the phytoplankton abundances at the diameter Di and Nt is the total cell number). The concentration of chla was determined by HPLC. The methods used to obtain these data were described by Zhou et al. .
The method was applied to the data set of 13 phytoplankton species. The method performance was quantified in terms of the relative root mean square error (RMSE), which is expressed in percentages according to:Fig. 2 and Table 2. The estimated and measured MCDs were in relatively good agreement, i.e., determination coefficient R2 = 0.88 and RMSE = 16.35%. For the chla concentration, the performance was also satisfactory, i.e., the R2 = 0.96 and RMSE = 73.04%. The chla concentrations of three phytoplankton groups (Phaeocystis sp., Chaetoceros sp., and Thalassirosira weissflogii) were overestimated, but the other groups were estimated with relatively good accuracy. For all the measurements of the phytoplankton absorption spectra, the standard deviations of Gaussian band achla,r (λ) (σf, determined using the peak fitting code) were greater than 9.7 nm (σf > 9.7 nm). Thus, we assumed that σk varied from 8.9 to 9.5 nm and that the values of the estimated parameters would fall within specific ranges (Fig. 2, red bars). The uncertainty in σk would introduce dispersions into the results, but these parameters (MCD and chla concentration) were still obtained within reasonable ranges. In particular, the variation in σk had almost no effect on the estimated chla concentration.
There was a significant linear correlation between the MCD and the bandwidth of achla,r(λ) (BWf, where BW f = 4.7σ when calculated using the peak-fitting code) (Fig. 3(a)). The species with the lower BWf values were smaller. The linear regression determined the following relationship for BWf:
We also tested the relationship between the mean cell volume and cell-specific chla concentration, which were linked by a significant linear relationship after logarithmic transformation (Fig. 3(b)):27] is also shown in Fig. 3(b). Both the slope and the intercept with x-axis are slightly different, probably because of photo-adaptation.
The method proposed in this study uses the red waveband to calculate the values of CId and Cchla because the effect of absorption attributable to auxiliary pigments is very small in this waveband. The values of a*chlc,s(λ), a*PSC,s(λ), and a*PPC,s(λ) in the red waveband can be neglected, but a*chlb,s(λ) may still be taken into account. However, the average ratio of a*chlb,s(676) relative to a*chla,s(676) was less than 15% [25, 26, 29]. Moreover, using the HPLC data set in the NASA bio-Optical Marine Algorithm Data set (NOMAD), we also found that the mean ratio of Cchlb relative to Cchla was ~8.3%. Thus, the uncertainty related to the simplification of the Eq. (2) had almost no effect on the ultimate estimation.
The uncertainty in the parameter σk accounted for a relatively large part of the uncertainty in the estimated cell size. Using the peak-fitting code (see Material and Methods), we fitted the specific absorption spectra of chla measured in solvent by Bidigare et al.  to obtain the Gaussian band in the red waveband, and we then obtained an approximate value of σk (σk = 9.27 nm). However, the value of σk should not be a constant in natural waters, so a future research should aim to reduce the uncertainty when estimating the cell size by adjusting the parameter σk. Despite this, the validation conducted in the present study demonstrated that the deviation due to the variation in σk (which ranged from 8.9 to 9.5 nm) was still reasonable and acceptable. For the parameter a*max, it had a negligible effect on the cell size estimation (Eq. (8)), but the accuracy of the estimated chla concentration was affected greatly by this parameter. For example, if 0.03 m2(mg chla)−1 is used as the value of a*max, the chla concentrations would be underestimated by 66.7% according to Eq. (10).
Some errors in the estimated diameter were related to uncertainties when assigning the parameters c0 and m. A sensitivity analysis was performed in a previous study by Roy et al. , which suggested that a small uncertainty in these parameters need not lead to magnified errors during size estimation. However, the relationship between CId and d is likely to change with the light environment, so future research is required to achieve improvements in this area.
The method proposed in the present is based on the anomalous diffraction approximation of the Mie theory, which provides a solution to the bulk inherent optical properties of a known particle suspension. We assumed that the phytoplankton cells were homogeneous spheres and optically soft particles, but these assumptions rarely hold in natural phytoplankton species. The phytoplankton species used in the present study were characterized by their different cell shapes. For example, the cells of Prymnesium patelliferum are oval in shape, whereas Biddulphiales sp. has a relatively short box shape. These differences would also introduce some errors into the estimated results. Nevertheless, some studies have shown that these assumptions are acceptable [30–34]. In our study, a Coulter counter was used to determine the cell size distribution based on the equivalent spherical diameter and our proposed method produced similar estimation. This consistency probably reduced the dispersion between the estimated and measured mean cell size in the validation. In addition, it indicated that the cell shape of phytoplankton species should not be a major source of uncertainty when estimating the mean cell size.
In this study, all of the cultures were grown in enriched medium, which was filtered through 0.45-μm filter membranes. The algal cell density was counted during the exponential growth stage for all species, so the degraded detritus attributable to dead algae was not significant. Light microscopy was also used to confirm the negligible effect of detritus. Thus, the effect of detritus on the phytoplankton absorption and cell size density measurements was shown to be negligible. In addition, bacteria only accounted for ~2–5% of the algal cell density in most cultures and the majority of the bacteria measured ~0.2 μm in size . Therefore, bacteria also had a negligible effect on the algal cell size density.
A peak-fitting code was used to obtain the Gaussian band of the absorption spectra. The code decomposed a complex and overlapping peak signal into its component parts, regardless of noise effects. This peak-fitting method may be applied directly to non-water total absorption spectra when they are measured using an ACS meter, because the absorption contributions of detritus and colored dissolved organic matter to the red waveband are always small, and they can also be regarded as noise.
In the present study, the method was validated using individual samples of each phytoplankton group, which were cultured separately, rather than a mixture of cultured phytoplankton groups. Thus, it is still not clear whether this method could be applied to mixed populations of phytoplankton, which are always found in natural waters. However, the validation showed that the proposed method performed with good accuracy, regardless of the cell shape and phytoplankton species, so this method could probably also be applied to natural waters. In addition, compared with existing methods (e.g., Flow Cytometer and Microscopy), this method is more efficient regardless of size distribution and it can be applied directly using current optical instruments (e.g., ACS meter and hyper-spectral sensors).
In this study, we developed a new method for quantifying the size of phytoplankton cells. Although some uncertainties may affect the estimation accuracy, the analysis indicated that the estimated errors attributable to these uncertainties are acceptable. This method facilitates the determination of the cell size and chla concentration in phytoplankton, and it has great potential for application to current in situ optical instruments.
We thank the Marine Biology Group of the South China Sea institute of Oceanography (SCSIO) for providing the algal species and algae cultivation. We appreciate the thoughtful comments from all reviewers, which helped to greatly improve an earlier version of this manuscript. This study was supported by the National Natural Science Foundation of China (Grant Nos. 41376042, 41076014, U0933005, and 41176035), the Natural Science for Youth Foundation (Grant No. 41206029), the Open Project Program of the State Key Laboratory of Tropical Oceanography (No. LT0ZZ1201), and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDA11040302).
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