The major part of the dataset used for this study is comprised of samples taken on the globally circumventing Galathea 3 Expedition (www.galathea3.dk) in August 2006–April 2007. These data have been supplemented with data from two cruises in the northern North Atlantic aboard the RV Dana (Technical University of Denmark) in August, 2008 and September, 2012. Sampling positions are shown in Figure 1. Identical methods and instrumentation were employed on all three cruises. Standard hydrographic profiles were made with a CTD (Seabird Instruments 911) mounted in a rosette with 5 or 30 l Niskin bottles. A profiling fluorometer (SCUFA or Dr. Hardt) and a light meter (Biospherical Instruments) were mounted on the rosette. Surface light was recorded (Biospherical Instruments) at the top of the ship. Water for inorganic nutrient determinations was tapped from the Niskin bottles and frozen until later determination at the National Environmental Research Institute, University of Aarhus, Denmark. Further detail on nutrient and all other sampling procedures is given in Hilligsøe et al. (2011).

Samples from the surface layer (5 m at latitude >50°; 10 m at latitude <50°) and the depth of the deep chlorophyll maximum (DCM) were incubated (2 h in artificial light incubators mimicking the spectral distribution of daylight and adjusted to ambient temperature for the two depths) following the addition of ¹⁴CO₂ at 12 different light intensities (~5–750 μmol photons m⁻²s⁻¹). Two samples were incubated in darkness. When no DCM was present, a second depth was arbitrarily chosen for incubation (usually 20 m). ¹⁴C incorporation in POC was determined following filtration on a GFF filter and converted to total DIC incorporation on the basis of alkalinity and pH determinations or direct determination of pCO₂ made at each station. Curves were fitted to the photosynthesis vs. light (P vs. E) relationships resulting from the incubations in order for find P_max (maxiumum hourly rate of photosynthesis) and the slope of the P vs. E relationship when P < P_max, i.e., alpha (α) (μg C (μg Chl a h)⁻¹ μmol⁻¹ photons m² s) Both P_max and α were normalized to the chlorophyll a content of the sample. Thus, PmaxB and α^B in the text refer to the chlorophyll normalized values of P_max (μg C fixed l⁻¹ h⁻¹) and α, respectively.

The complete primary production dataset (in all 209 samples taken at 121 stations) comprises results obtained in the period ± ~100 days from the summer solstice with determinations being more or less evenly distributed in this period. No seasonal signal was found in the data. Sampling was also carried out throughout the day, although most sampling took place in daylight. All of the highest values of PmaxB and α^B were recorded between 0800 and 1600 (Figure 2). However, a full range (low to high) of values was recorded in this time interval and the lowest values for these photosynthetic parameters were also recorded within this time frame. Even in the surface data, where the signal is most pronounced, only ~20 data points for PmaxB, and many fewer for α^B, are found to be higher than those found in the remainder of the dataset. Thus, while the apparent diurnal signal in photosynthetic parameters should be acknowledged, we argue that it does not drive the relationships we discern between these parameters and abiotic/biotic variables in the following analyses.

Samples from selected depths and filtered onto GFF to determine total sample chlorophyll (which could be used both in the analysis of fractionated chlorophyll and to calibrate the profiling fluorometer mounted on the rosette) and 10 μm filters, respectively. These were extracted in 96% ethanol and chlorophyll a fluorescence determined using a Turner fluorometer following the US EPA method 445.0 as suggested by Turner Designs.

At 59 stations on the Galathea 3 cruise, samples (90 in all) for phytoplankton analysis were taken from Niskin bottles closed at the surface (5 or 10 m) and/or in the DCM. These were preserved in acidified Lugol's solution (approximately 2% final concentration) and stored in darkness at ~5°C until later analysis. Identification of organisms (> ~3 μm) was made using quantitative light microscopy following the protocol used in the Danish National Water and Nature Monitoring Program (Henriksen and Kaas, 2004) according to Utermöhl (1958). Axial dimensions were measured from a subset of each taxon and used to calculate cell biovolumes using appropriate geometric volume formulas. Analyses were carried out by Orbicon A/S (Århus Denmark).

At the same stations where micro and nano-phytoplankton were determined on the Galathea cruise, pico-phytoplankton were also quantified. Water from the CTD was stored in darkness and cool until sampling could be performed (within 30 min after collection). Samples of 4 ml were preserved in filter-sterilized glutaraldehyde to a final concentration of 2% and stored darkness at 4°C. Pico-phytoplankton abundance was determined by flow cytometry (FACS Calibur, Becton Dickinson) within 2 days of sampling. The flow rate of samples through the FACS Calibur was determined using BD Biosciences TruecountTM tubes. The gatings for Prochlorococcus and Synechococcus, and pico-phytoplankton were defined using cultures of Prochlorococcus, Synechococcus and picophytoplankton (Phaeocystis spp., Rhodomonas spp., Emiliana huxleyi, Pycnococcus spp., Pelagococcus subviridis, Pelagococcus spp.), and were verified onboard by comparison with microscopy counts. XY plots were used with data from forward scatter, side scatter and fluorescence signals. Several plots in different combination were used for Prochlorococcus, Synechococcus, and pico-phytoplankton, to ensure that there was no overlapping gating for any of the gating groups.

The sizes of the pico-phytoplankton (Prochlorococcus, Synechococcus and eukaryotic pico-phytoplankton) were estimated in all samples from forward scatter and calibrated against 8 cultures of Prochlorococcus, Synechococcus and eukaryotic picophytoplankton (Micromonas pusilla strains K-0024 and K-0023, Nannochloropsis oculata, Thalassiosira pseudonana) representing a cell diameter range from 0.6 to 3.1 μm.

The combined datasets on biovolume of nano + micro- and pico-phytoplankton were assumed to represent the majority of the phytoplankton community in each sample. Different taxa were then grouped together based on their taxonomy and size and their greatest axial linear dimension (GALD). Thus, in the nano + micro-phytoplankton data set, taxa were grouped as ciliates, diatoms <50 μm, diatoms > 50 μm, dinoflagellates <50 μm, dinoflagellates > 50 μm and green nanoflagellates. In the picophytoplankton data, set all taxa were small and we only differentiated between taxa; i.e., the cyanobacteria, Prochlorococcus and Synecococcus, and the pico-eukaryotes. Assuming that cell volume is linearly related to chlorophyll a content (see Marañón et al., 2007), we calculated the chlorophyll content of each group in each sample by multiplying the chlorophyll a concentration by the relative contribution that each group contributed to the total biovolume.

A simple model was developed on the basis of 142 samples taken at the 86 stations where fractionated chlorophyll had been determined to test for size-dependence of the photosynthetic parameters, α^B and PmaxB. The model considered two discrete size classes representing small (i.e., chlorophyll containing organisms passing through a 10 μm filter) and large cells, respectively. Their respective fractions, i.e., f_(small) and f_(large), were defined from the observed concentration of chlorophyll a associated with the two size classes: [0.7–10 μm] and [> 10 μm]. Thus, the two fractions were related as: f(small)+f(large)=1

Each size class was assumed to be characterized by a photosynthetic parameter given by φ_(small) or φ_(large) where φ represented the photosynthetic parameter, i.e., α^B or PmaxB. The bulk photosynthetic parameter of the sample was then determined from: φ=φ(small)∗f(small)+φ(large)∗f(large)

Best fit values of the two free parameters φ_(small) and φ_(large) were then found by minimizing the residual defined by: R=Σ(φ−φ(obs))2 where φ_(obs) represented the photosynthetic parameters obtained from the incubations described above and the summation included all observations. Finally, a normalized residual (R_norm) was calculated by scaling R with the residual from the best fit solution (R_min): Rnorm=R/Rmin

Best fit values for α^B and PmaxB were searched for in the intervals [0:0.15] and [0:5], respectively.

All statistical analyses were performed in the open source statistical software, R (R Core Team, 2016). In addition to the core software, we used the _R-package “vegan” (Oksanen et al., 2016).

Patterns in the distribution of the dominant phytoplankton groups in relation to PmaxB, α^B and the environmental variables (temperature, depth, nitrate, phosphate and silicate) were investigated by performing a non-metric multidimensional scaling analysis (Legendre and Legendre, 2012) on the distribution of the group specific chlorophyll a content. The underlying dissimilarity matrix was calculated using the Bray-Curtis dissimilarity index and the analysis was run multiple times to avoid getting trapped in a local optimum. When the global optimum had been estimated, we projected the distribution of PmaxB and α^B into the ordination space using thin plate regression splines (Wood, 2003). In addition, the environmental variables were fitted as linear vectors indicating the direction of the association between the community composition and changes in the environment.

As our data suggested an effect of both temperature and depth of sampling, we split the data set into four groups: Group 1: depth > 10 m and temperatures ≥ 15°C; Group 2: depth <10 m and temperatures ≥ 15°C; Group 3: depth > 10 m and temperatures ≤ 15°C and; Group 3: depth ≤ 10 m and temperatures ≤ 15°C. We then calculated the median values of all the variables measured and assessed if the values in each group could be considered to come from the same distribution using a Kruskal-Wallis rank sum test.

Both PmaxB and α^B are seen in the dataset to vary in relation to temperature, the depth of sample collection (possibly a proxy for light availability), ambient inorganic nutrient (nitrate and phosphate) concentrations, and the size distribution of the phytoplankton community (fractionated chlorophyll) (Figures 3, 4A). Not all of the relationships appear to be linear and all of these variables correlate to some degree with one another. Thus, it is not possible to ascertain cause and effect in these relationships or to rank these variables in order of their potential importance in terms of controlling photosynthetic performance. Nevertheless, some generalizations can be made about the global distribution of PmaxB when these relationships are considered together. From Figure 4B, the generalization can be made that the highest values of PmaxB will be found in warm (>~15°C) surface waters. Although communities dominated by both large and small organisms can exhibit high PmaxB, communities dominated by small organisms appear particularly likely in this data set to be associated with high PmaxB. Relatively high PmaxB can be recorded down to ~100 m. Furthermore, PmaxB exhibits a negative relationship with the inorganic nutrient concentrations (Figure 3C), where all of the highest values of PmaxB were recorded in waters where the ambient concentration of nitrate was <5 μmol kg⁻¹.

Patterns associated with the distribution of α^B (Figures 5, 6) are less clear. Also this photosynthetic parameter can be related to temperature (bell-shaped curve), the depth of sample collection and nutrient availability. Although the highest values of α^B were recorded in surface waters, the relationship between depth of sampling and value of α^B is not as strong as is the case for PmaxB. Alpha was most clearly related to the size structure of the community with the highest values recorded being associated with communities dominated by small phytoplankton. Thus, the overall patterns in the distribution of α^B are less clear (Figure 6B) than those found for Pmax.B

That the association with α^B and the variables examined is weaker than for PmaxB is confirmed when the median values for the two photosynthetic parameters and the variables shown to be associated with them are compared (Table 2). The median values of each of the parameters and variables at the depths of the DCM and in surface samples in warm (≥15°C) and cold (<15°C) waters are examined individually. In all cases, there is a significant difference between the values when the four environment types, i.e., warm and cold waters in surface and DCM, respectively, are compared. However, the level of significance when α^B is compared in the four different environments is less (p = 0.016) than is the case for PmaxB (p = 0.006).

When the entire dataset was considered, best fit solutions were found for [α^B(small) = 0.040, α^B(large) = 0.025] and [PmaxB(small) = 2.56, PmaxB(large) = 1.53]. The resulting best fit solutions of the bulk photosynthetic parameters were then calculated to α^B = 0.038 μg C (μg Chl a h)⁻¹ (μmol photons)⁻¹ m² s and PmaxB= 2.38 μg C (μg Chl a h)⁻¹, respectively (Figure 7). When data collected from surface and DCM samples were considered separately, the differences between photosynthetic performance of the large and small cells were even more pronounced (Table 3). In the depth separated analysis, PmaxB(small) was calculated to be nearly twice as high in surface (≤ 10 m) waters than in deeper waters while PmaxB(large) was lower in surface than in deeper waters. For both size groups, α^B increased with depth, as would be expected in response to adaptation of the photosynthetic apparatus to low light (Richardson et al., 1983).

Results of the NMDS ordinations relating the dominant (by biovolume) phytoplankton group in the community to the measured photosynthetic parameters of the total community are shown in Figure 8 (PmaxB) and 9 (α^B). The highest PmaxB determinations were associated with communities dominated by dinoflagellates, small (<10 μm) unidentified flagellates, Synecococcus and pico-eucaryotes. Of the large phytoplankton, only dinoflagellate dominated communities in warm water are associated with high PmaxB. The large dinoflagellate dominated communities also are associated with the highest values of α^B recorded (Figure 9).

Large and small diatom dominated communities occupy similar positions (intermediate both with respect to PmaxB and α^B) in the NMDS ordinations of both photosynthetic parameters. Diatom dominated communities are associated with colder waters and high inorganic nutrient concentrations. The “ciliates” recorded in the NMDS ordinations are primarily comprised by Mesodinium rubrum. These are associated in this dataset with relatively warm waters and again, exhibit intermediate values for both of the photosynthetic parameters examined. Prochlorococcus is associated with deep waters and with low values for both photosynthetic parameters. This genus dominated in samples taken in the Sargasso Sea where the DCM is found at depths >100 m and this likely explains the placement of this genus in the ordinations.

Sea surface temperature (SST) is readily estimated from remotely sensed surface ocean characteristics. Therefore, photosynthetic performance is often parameterized in relation to SST. The analysis presented here indeed demonstrates a relationship between temperature and both PmaxB and α^B (Figures 3, 5). In the case of both parameters, vs. temperature, the relationships appear to be non-linear.

As noted earlier, the fact that photosynthetic parameters appear to relate to temperature does not necessarily imply a direct temperature effect on these parameters. PmaxB and α^B are also shown here to vary as a function of ambient nutrient concentration and depth of sampling. Both of these environmental variables can be predicted to vary as a function of temperature. Thus, all of these environmental variables are correlated, making cause, and effect in the relationships identified difficult to identify. It is interesting, however, to note that both photosynthetic parameters are, in our dataset negatively correlated with ambient nutrient concentration (Figures 3C, 5C), i.e., all of the highest values were recorded when nitrate concentrations were <5 μmol kg⁻¹. This result contrasts with the findings of Palmer et al. (2013) who found the highest values of PmaxB in environments with nitrate concentrations over 10 μmol kg⁻¹ in a study of Arctic waters, thus raising the interesting question of a possible influence of an interaction between temperature and nutrient availability on photosynthetic parameters.

Size structure of the phytoplankton community also correlates with both temperature and ambient nutrient concentrations (Hilligsøe et al., 2011; Mousing et al., 2014) and both PmaxB and α^B are here shown to be clearly correlated with phytoplankton size structure, i.e., the relative proportion of total chlorophyll retained on a 10 μm filter (Figures 4, 6). Model fits describing median values of best fit values for photosynthetic parameters (Figure 7, Table 3) indicate that smaller organisms exhibit higher values of both PmaxB and α^B. Recent field studies (Strom et al., 2010; Morán and Scharek, 2015) have also reported higher PmaxB for small than for large cells.

When the surface and DCM data are considered separately, the best fit model suggests a lower PmaxB for large cells in the surface layer than at the DCM. While this result was not expected, earlier studies (From et al., 2014) suggest that photoinhibition may be more common in the surface layer than normally assumed. For both the large and small components of the phytoplankton community, α^B increases with depth (Table 3). This result would be expected as a universal adaptation to low light is believed to be an increase in alpha (Richardson et al., 1983).

The model results show that the residuals are narrower in the direction of smaller cells than in the direction of large cells (Figures 7A,B) and this implies that both PmaxB and α^B are better constrained for small cell sizes. We can suggest two reasons for why this might be the case. Firstly, the size range of the “small” phytoplankton in this study is well defined as being those organisms not retained on a 10 μm filter. This, presumably, would mean organisms with an axial length of <10 μm. Within this size range, the morphological shape of organisms is usually relatively simple (round or oblong). The “large” organisms in this study would be all those retained on a 10 μm filter, i.e., no maximum size. The variety of morphological forms found in these larger organisms is, everything being equal, greater than for the smaller organisms. One possibility is that that this greater variety of cell forms in the larger phytoplankton might result in a greater variability in light absorption capability and thereby, photosynthetic parameters in the larger phytoplankton than in the smaller.

Phytoplankton size is also, at least to some degree, related to taxonomy. For the stations where we had taxonomic data, we, therefore, attempted to relate the dominant (by biovolume) taxonomic group to photosynthetic characteristics. Here, it should be noted that we have a relatively limited number of samples (90) with taxonomic data. Furthermore, the preservation method we used for phytoplankton samples (acidified Lugol fixation) would not preserve all phytoplankton groups (coccolithophorids are, for example, missing). Therefore, we cannot use the relationships we find here as being universal and diagnostic for the global ocean. Nevertheless, the NMDS ordinations (Figures 8, 9) relating dominant phytoplankton group and the two photosynthetic parameters reveal some interesting patterns that can be used to develop a more nuanced understanding of the general pattern of higher PmaxB and α^B being associated with the smaller phytoplankton.

With respect to PmaxB (Figure 8), the ordination identifies high values to be associated with dinoflagellates of all sizes, flagellates, and in warmer waters, pico-eukaryotes and Synecococcus. We were surprised to find the dinoflagellates here, i.e., associated with a higher PmaxB than diatoms, as earlier studies (e.g., Chan, 1980) have suggested that the two groups may perform similarly when their photosynthesis is compared on a per chlorophyll basis. A possible explanation for this finding is that dinoflagellates in our dataset often occur in communities with a relatively large proportion of pico-plankton. In such cases, the biovolume of a small number of large dinoflagellates could provide the dominate biovolume in the community, while the photosynthetic profile of the community is determined by the smaller organisms. Another possibility, of course, is that dinoflagellates under natural conditions may be more efficient photosynthesizers than usually assumed.

Prochlorococcus dominated communities show a relatively low PmaxB in our dataset and are associated here with deep, warm waters. This fits well with the fact that we found them primarily in the DCM samples in the Sargasso Sea, where the DCM is located at >100 m. Diatom dominated communities were associated with cold waters and high nutrient concentrations and exhibited an intermediate PmaxB.

The patterns emerging from the NMDS ordination for α^B, are less clear than for PmaxB (Figure 9). This, however, is not surprising given that the relationships between α^B and environmental variables are shown here to be less clear than for PmaxB. Also here, the highest values for α^B were found to be associated with communities where large dinoflagellates dominated the biovolume. In the case of α^B, diatom dominated communities appear to be characterized by relatively high values. Thus, a picture emerges of diatom dominated communities being well adapted to utilize low light levels but not among the most efficient in terms of PmaxB. Such a photosynthetic strategy would make diatoms well adapted to the kinds of conditions where they are known to dominate (i.e., spring bloom in temperate waters).

As noted above, we do not mean to imply that the taxonomic patterns we find in relation to the data on photosynthetic parameters that we present here are diagnostic for the global ocean under all conditions. However, we do believe that the strong relationship we find in this study between phytoplankton community size structure and photosynthetic performance of the community, as well as the fact that nuances in this relationship can be discerned from study of the taxonomic composition of the community, to be of great potential interest in terms of improving the parameterization of photosynthetic potential when collection of physiological data is not possible, i.e., when estimating ocean primary production from remotely sensed surface data.

Estimation of both the size distribution of phytoplankton and to some extent, the taxonomic groupings represented in surface waters is possible using remote sensing techniques to quantify surface optical characteristics (e.g., Le Quere et al., 2005; Chust et al., 2013; Boyce et al., 2015; Cetinić et al., 2015). Thus, a prospective avenue to follow in the pursuit of a better parameterization of the photosynthetic potential of natural phytoplankton population could be to further explore the relationship between community size (and taxonomic) structure and photosynthetic performance.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.