Data from three separate case studies were used, data from Lamberts Bay were taken from a fixed station (32°05.020′S, 18°16.010′E) at 0 m, 3.5 km off Lamberts Bay, as daily samples during the periods 25 February–11 March 2004 and 15 March–6 April 2005. In Saldanha Bay, sampling took place at a fixed station (33°01.748′ S, 18°00.888′ E) from 0, 3, 6, and 9 m, every 2 months for a period of 3 days from January 2012 to January 2013. Water samples were collected using a 5 L Niskin water sampler and stored in 20 L black buckets, which were then transported to the laboratory within 1–2 h of collection for the determinations of particle size distributions, nutrient concentrations, ¹⁵N uptake and particulate nitrogen calculations. Methods employed in all three case studies were consistent, unless stipulated otherwise. Data from the different systems within the Benguela ecosystem were chosen to try obtain a good spread in biomass and uptake rate values.

Theoretical uptake rates were calculated from measured in situ PSDs and ambient nitrogen concentrations. Details of each step are discussed further below. In brief,

The range of values for measured particulate nitrogen, ambient nitrogen concentrations and uptake rates vary among the three case studies (Figure 2). This variability reflects distinct assemblages observed in each case study. Highest values of particulate nitrogen (PN) were observed in Lamberts Bay (LB04 and LB05) relative to Saldanha Bay. LB05 was dominated by a dinoflagellate Prorocentrum triestinum with maximum particulate nitrogen reaching 146 μmol N L⁻¹, in association with lowest ambient nitrogen concentrations. SB samples had relatively low biomass (average 10.3 μmol N L⁻¹), almost completely dominated by diatoms. Highest field-measured uptake rates of total nitrogen (Figure 3A) and nitrates (Figure 3B) were seen in LB04, corresponding to an assemblage dominated by a ciliate (Myrionecta rubra) and a diatom (Skeletonema spp.) with a maximum of 0.67 μmol N L⁻¹h⁻¹. Rates of NH₄ uptake were lower on average than NO₃ uptake in all case studies (Figure 3C). The size spectra measured were highly variable per sample. Figures 4A,C,E show typical size distributions of a low biomass range, and Figures 4B,D,F show samples of high biomass, illustrating distributions of bimodality.

The two methods of conversion from cell volume to mass gave estimates of particulate nitrogen that were significantly correlated with measured in situ values (Figure 5). For the combined data set (SB and LB), the correlation for the non-linear conversion was r = 0.78, p < 0.005 and for the linear conversion r = 0.76, p < 0.005. The two regressions comparing measured in situ and estimated particulate nitrogen using the linear and non-linear conversion methods were assessed by testing H₀: slope = 1 (Table 2). The regression slopes for the linear and non-linear conversions were greater than one, but were not significantly different; linear (t_{0.05, 72} = 3.65, p = 0.99) and non-linear (t_{0.05, 72} = 3.33, p = 0.99). Both slopes provided good predictions of biomass from particle size distributions and both conversion methods. The non-linear conversion of Menden-Deuer and Lessard (2000) was used in further estimates of uptake rates.

The ranges of estimated N uptake rates were similar to those measured in situ (Figure 6). Predictions of nitrogen uptake rates were significantly correlated with respective measured uptake rates: NO₃ (r = 0.60, p < 0.005); NH₄ (r = 0.61, p < 0.005) and total N (r = 0.67, p < 0.005). The slopes of the relationship between measured and estimated uptake rate values were also assessed testing H₀:slope = 1 (Table 2). The regression slopes were not statistically different from 1 for NH₄ (t_{0.05, 67} = −0.26 =, p = 0.30) and total N (t_{0.05, 72} = −0.26, p = 0.40); this was not the case for NO₃(t_{0.05, 72} = −3.06, p = 0.00). An inhibition term (ψ) of 1.99 μmol N⁻¹ was estimated for NO₃ uptake. The resulting predictions for ρNO₃ were similar to those of ρNO₃ with no inhibition, with a increase in bias when inhibition is included (bias ρNO₃ = 0.03, bias ρNO₃^ψ = −0.72). Predictions of total N uptake do not differ greatly when an inhibition term is applied; ρN (slope = 0.97), ρN^ψ(slope = 1.05) (Table 2) but more bias is introduce with an inhibition term (ρN^ψ = −0.89, bias ρN = −1.10). Estimations for ρNO₃ (both with and without an inhibition term) did not match those measured in situ (Table 2). The comparisons between measured and calculated mass-specific rates showed poor agreement, and no statistical similarity was observed between the two data sets (Table 2). The relationships between estimated and measured ρNH₄, ρN and ρN^ψ are not statistically different (Table 2) and are thus considered good predictions of the uptake of NH₄ and total N. The non-allometric rates were also compared with each other and a hypothetical 1:1 slope (Figure 7). Of the 9 different combinations of uptake parameters tested (H₀ slope = 1), one set was close to 1 but not statistically significant (slope = 0.96, p < 0.00) for NO₃, and 2 sets for NH₄, the closest being significantly similar to 1 (slope = 1.2, p = 0.78) (Table 3).

Both conversion models used to derive particulate nitrogen from particle size distributions (via non-linear or linear functions) yield similar results with a good correlation between estimated and measured values. The regression equations used to estimate biomass were applied to all assemblages, which were most often mixed assemblages, i.e., containing dinoflagellates (LB05), ciliates (LB04), and diatoms (SB). LB05 had a high percentage of the dinoflagellate Prorocentrum triestinum at very high biomass (max. 146 μmol N L⁻¹), and the correlation coefficients for this particular data set are strongest. Even so, when applied to assemblages containing different taxa (ciliates or diatoms), overall the conversion factors performed well and the regression fit is close to a 1:1 relationship between measured and estimated nitrogen biomass. An even better fit may have resulted if group-specific conversion factors were used, but such empirical relationships for volume:nitrogen of the groups measured in this study were not found in the literature. It is noted that diatoms, for example, contain less carbon per unit volume than other groups, attributed to their significantly higher vacuole volume (Strathmann, 1967; Sicko-Goad et al., 1984). Cellular nitrogen content or nitrogen stores have also been observed to vary considerably between different species of phytoplankton (Parsons et al., 1961; Dortch et al., 1984).

Further errors could have been introduced by the assumptions made in deriving particle size distributions via a Coulter Counter, which assumes sphericity of cells. This could lead to underlying bias because of non-spherical groups (e.g., dinoflagellates) or particles of elongate shape, e.g., chain-forming diatoms, which are known to introduce error and can lead to an under/overestimation of total volume (Boyd and Johnson, 1995). Furthermore, the Coulter Counter measures down to 2 μm diameter (with confidence from 5 μm) and thus omits the submicron range due to limitations in technical capabilities. Nevertheless, the Coulter Counter has been used in several studies to successfully derive volume to carbon ratios (Mullin et al., 1966; Strathmann, 1967; Montagnes et al., 1994) and the presented results provide confidence that such data can adequately represent the particulate biomass of the nitrogen inventory in natural, diverse assemblages in eutrophic systems, characterized by large cells and high biomass.

The data presented here show that particle size distributions convert well to a measure of biomass, despite the broad scale application of a dinoflagellate volume:nitrogen conversion to mixed assemblages, the exclusion of submicron size ranges, and the assumptions of sphericity when using the Coulter counter. It has been noted that quantitative measurements of particulate carbon/nitrogen are in general lacking (Behrenfeld and Boss, 2006), and we suggest tha Coulter Counter derived PSDs can provide adequate measures of nitrogen biomass, most notably, when examining communities in eutrophic systems. Such conversions may not be as successful in oligotrophic areas, where cell size distributions are characteristically dominated by pico/nano plankton (<2 μm), but would need further investigation.

A significant correlation exists between the estimated and measured uptake rates of NO₃, NH₄ and total N, for natural assemblages. The slopes of the regressions for the estimated vs. measured values of NH₄ and total N uptake were close to 1, indicating statistical similarity to what was measured in situ. The size-dependence of the Michaelis-Menten uptake parameters, V_max and K_s, used by Ward et al. (2012) proved to be adequate values and yielded comparable results of nitrogen uptake to what had been measured in situ. Several studies have called into question the adequacy of the Michaelis-Menten kinetics equation to describe nutrient uptake in phytoplankton (Droop, 1974; Pasciak and Gavis, 1974; Aksnes and Egge, 1991). These criticisms are based on the premise that the equation does not account for differences in uptake rates in limiting or non-limiting conditions (Rhee, 1974; Grover, 1991), or that internal stores of nutrients can dictate uptake based on simple diffusion limitation (Droop, 1974). Both Michaelis-Menten uptake parameters are subject to variability, not only in different species but due to differences in nutrient availability and varying environmental conditions (Lomas and Glibert, 1999; Collos et al., 2005 and references therein). Smith et al. (2009) suggest that optimal uptake kinetics, which accounts for physiological acclimation to fluctuating environmental conditions, is a superior alternative to standard Michaelis-Menten descriptions of V_max and K_s. A flexible phytoplankton functional type (FlexPFT) model (Smith et al., 2015), which resolves the dynamic response of phytoplankton communities, which was able to reproduce productivity and chlorophyll values of two contrasting time series better than when no flexible response was included. Thus, the limitations of Michaelis-Menten are recognized, more particularly in its assumption that parameter values are constant during environmental fluctuations. However, its use will most likely remain popular due its simplicity and the availability of parameter values in the literature. The variability of in situ measured uptake rates of NH₄ and total N is statistically matched by the variability in what was estimated using size-scaled parameters, which implies that much of the variability in Michaelis-Menten parameters, when applied at an assemblage scale, can be accounted for by simple size scaling of V_max and K_s. The results also imply that net community rates of NH₄ and total nitrogen uptake are driven by ambient concentrations and cell size.

As expected, the case for NO₃ was more complex. Although the slope of the estimated ρNO₃ was positive and close to 1, statistically it was not significant and reveals the potential importance of other influencing factors, in addition to cell size and ambient concentration. The suppression of NO₃ uptake by NH₄ may explain some of the variability observed in in situ measured values that is not accounted for in the model estimates. Numerous studies have shown an interaction between NH₄ and NO₃ uptake (e.g., McCarthy et al., 1975; Muggli and Smith, 1993; Harrison et al., 1996). NH₄ is generally considered to suppress the uptake of NO₃ (Dortch, 1990) but this is observed to be a highly variable process, where NH₄ can have little to no effect on NO₃ uptake (Kokkinakis and Wheeler, 1987) or can enhance rather than inhibit NO₃ uptake (Dortch, 1990). The extent to which NH₄ will affect NO₃ uptake is not just species-dependent, but is also affected by physiological state and the preconditioning nutrient concentrations (Varela and Harrison, 1999; L'Helguen et al., 2008). Equally, the concentration of NH₄ at which suppression of NO₃ uptake occurs varies between systems (Dortch, 1990; Dugdale et al., 2006, 2007; Probyn et al., 2015). The effect of incorporating an inhibition term, in this case, made little difference to the estimates of ρNO₃ and ρN. A range of inhibition parameter values used in other studies were also investigated, ranging from 1.5 (Kishi et al., 2007) to 4.6 (Dutkiewicz et al., 2009), with little significant change in statistical comparisons. The value of 1.99, the outcome of a best fit model to the NO₃ uptake values for this study, was deemed optimal for the range of values measured. Another suggestion to explain the deviations from Michaelis-Menten kinetics for NO₃ uptake, is the potential for “shift-up” kinetics described in Dugdale et al. (1990, 2006). It was observed that NO₃ uptake may not follow Michaelis-Menten kinetics consistently along the upwelling timeframe, where initial (highest) concentrations of NO₃ will not equate to highest uptake rates, as communities take time to respond to new injections of NO₃.

The predictions did not work when measured and calculated biomass-specific rates (h⁻¹) were compared (Table 2). This is not surprising. The measured uptake rates result from an interplay between ambient nitrogen concentrations, total particulate nitrogen and the structure (size and taxa) of the phytoplankton assemblage, which will affect mass-specific rates as well as affinity for nitrogen. Mass-specific values influence physiological efficiency, with small cells having faster mass-specific rates and greater affinity for nitrogen at low concentrations than large cells. These influences of assemblage structure cannot be accounted for when dividing uptake rates by measured particulate nitrogen. Much of the uptake signal is dominated by the small fractions (<15 um) of the size spectra (Figure 6) and highest uptake rates are observed when the small size fractions dominate and thus biomass is low, illustrating that the successful predictions of uptake rates is not driven by high biomass. Absolute uptake rates can be considered an ecosystem metric of nitrogen dynamics, and this study shows that, in a eutrophic environment, size-scaled MM parameters can be used to predict NH₄ and total N uptake, keeping the numbers of parameters to a minimum and thus minimizing uncertainty associated with each parameter. Data to constrain added parameters are not available from the in situ experiments. The non-allometric predictions, which use constant V_max and K_s values across the entire spectrum resulted in a variety of regression slopes, with few matching a 1:1 relationship. The kinetic parameter values used all fall within a realistic range observed in the region, and of the nine combinations tested (Figure 7), no significant prediction was made for NO₃ (although the slope was close to 1) and one successful prediction was made for NH₄. However, it would be difficult to know in advance which parameter values to use, whereas the allometric calculations produced good matches to the observations.

To conclude, a large proportion of the variability observed in uptake rates of nitrogen measured in situ, in various assemblages, was explained by ambient nutrient concentrations and cell size, in spite of several simplifications and sources of error. The case for NO₃ uptake was not as strong as NH₄ and is suggested to be due to the complex suppressive behavior of NH₄ on NO₃ uptake as well potential “shift-up” effects observed in upwelling systems. In addition, accounting for the internal storage of NO₃ may have improved estimations of ρNO₃, but are beyond the scope of these data. Nevertheless, realistic approximations of nitrogen uptake, and thus new production (Dugdale and Goering, 1967) are achieved when using size-scaled Michaelis-Menten uptake parameters and particle size distributions. The strength of this study lies in its application to in situ measurements of cell size distributions and ambient nutrient concentration, to derive approximations of nitrogen uptake. Further research is recommended to include Dissolved Organic Nitrogen uptake rates into approximations of total N uptake, given its significant contribution to total production (Harrison et al., 1985; Probyn, 1988). This is no menial task however, given its complex kinetic behavior (Eppley et al., 1971; Bronk et al., 2004; Solomon et al., 2010) and current lack of size-scaling relationships in the literature. New production, considered to be the portion of primary production with the highest implications for carbon export or the flow of energy to higher trophic levels (Hutchings, 1992; Probyn, 1992; Dugdale et al., 2006), is a useful measurement in studies of ecosystem dynamics. In the absence of laborious and expensive ¹⁵N data, the use of particle size distributions to estimate nitrogen uptake can be a useful tool in assemblage scale studies of nitrogen dynamics in productive coastal upwelling systems.

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.