^{15}N

_{2}Gas

^{1}

^{2}

^{*}

^{3}

^{4}

^{5}

^{6}

^{1}

^{7}

^{1}

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{7}

Edited by: Sophie Rabouille, UMR7093 Laboratoire d'océanographie de Villefranche (LOV), France

Reviewed by: Christine Ferrier-Pagès, Scientific Centre of Monaco, Monaco; Patrick Raimbault, UMR7294 Institut Méditerranéen d'océanographie (MIO), France

This article was submitted to Aquatic Microbiology, a section of the journal Frontiers in Marine Science

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Recently, the method widely used to determine ^{15}N_{2} fixation rates in marine and freshwater environments was found to underestimate rates because the dissolution of the added ^{15}N_{2} gas bubble in seawater takes longer than theoretically calculated. As a solution to the potential underestimate of rate measurements, the usage of the enriched water method was proposed to provide constant ^{15}N_{2} enrichment. Still, the superiority of enriched water method over the previously used bubble injection remains inconclusive. To clarify this issue, we performed laboratory based experiments and implemented the results into an error analysis of ^{15}N_{2} fixation rates. Moreover, we conducted a literature search on the comparison of the two methods to calculate a mean effect size using a meta-analysis approach. Our results indicate that the error potentially introduced by an equilibrium phase of the ^{15}N_{2} gas is −72% at maximum for experiments with very short incubation times of 1 h. In contrast, the underestimation was negligible for incubations lasting 12–24 h (error is −0.2%). Our meta-analysis indicates that 84% of the measurements in the two groups will overlap and there is a 61% chance that a sample picked at random from the enriched water group will have a higher value than one picked at random from the bubble group. Overall, the underestimation of N_{2} fixation rates when using the bubble method relative to the enriched water method is highly dependent on incubation time and other experimental conditions and cannot be generalized.

^{15}N

_{2}fixation

Over the last few decades, the stable isotopic tracer ^{15}N_{2} was used to measure the production of diazotroph (N_{2}-fixer) biomass directly. This isotopic approach was first introduced by Burris and Miller (_{2} fixation rates. The protocol established by Montoya et al. (_{2} fixation data, which are particularly abundant in the North Atlantic and North Pacific Oceans (Luo et al., ^{15}N_{2} gas into a seawater sample, which is incubated for a given period (on deck or in situ), and finally terminated by filtration through glass fiber filters. The filters are later analyzed by IRMS to determine the amount of ^{15}N_{2} transferred from the aqueous phase to the particulate cell material. Montoya et al. (_{2} fixation rates using a mass-balance approach:

With V calculated as:

Where M refers to mole nitrogen fixed, L to the volume (liter) and T to the incubation time. A_{PN} is the ^{15}N atom % enrichment of the particulate nitrogen (PN) pool as measured by IRMS, at the beginning (t_{0}) and end (t_{f}) of an incubation period; A_{N2} is the ^{15}N atom % enrichment of the dissolved N_{2} gas in the incubated seawater; [PN] is the concentration of PN at the end of the incubation [if (PN) is stable over the incubation time; if (PN) varies significantly overtime, an average of initial and final (PN) values is recommended for calculations, see (Montoya et al., _{N2}. The latter term is theoretically calculated based on the volume of ^{15}N_{2} injected and the initial concentration of N_{2} dissolved in seawater based on its temperature and salinity and the N_{2} solubility equations of Weiss (^{15}N_{2} bubble with the dissolved N_{2} already present in the incubation bottle is rapid and complete relative to the incubation period. Simple mass balance tracer equations assume a constant isotope enrichment of the source pool over the duration of the incubation (Fry, ^{15}N_{2} with seawater is slow or incomplete during the experimental incubation.

Recently, Mohr et al. (^{15}N_{2} equilibration with the surrounding seawater of up to 24 h, depending on a number of factors such as incubation bottle size, volume of ^{15}N_{2} injected, bottle shaking, and incubation temperature. Amongst other things, an observed mismatch between ^{15}N_{2} fixation rates and biomass-specific growth rates motivated Mohr et al. (^{15}N_{2} bubble method introduced by Montoya et al. (^{15}N_{2}, which provides a near instantaneous enrichment of the dissolved pool of N_{2} in an incubation bottle. This “enriched water” approach resulted in a 2–6 fold increase of measured N_{2} fixation rates in comparison to the ^{15}N_{2} “bubble” method (Großkopf et al.,

There are several reasons why the bubble method may underestimate true N_{2} fixation rates: (1) temperature (high temperatures inhibit dissolution of gases), (2) the volume of ^{15}N_{2} gas injected, (3) the duration of the incubation, (4) the time at which the incubation starts relative to the onset of ^{15}N_{2} fixation, and (5) possible DOM coating of the ^{15}N_{2} bubble (Mohr et al.,

Adding to these factors, Großkopf et al. (_{2} fixation rate are lower when the community is dominated by colonial cyanobacteria of the genus _{2} fixation very difficult (Großkopf et al., ^{15}N_{2} enriched water has a number of drawbacks, including the potential introduction of unwanted dissolved constituents (nutrients, dissolved organic matter or trace metals; Klawonn et al., ^{15}N_{2} enrichment of dissolved N_{2} dissolution (Klawonn et al.,

The aim of this study is twofold. Firstly, we used a laboratory experiment to determine the equilibrium time of ^{15}N_{2} in Seawater from the Baltic Sea and used these numbers for an error calculation. By doing so, we tried to generate a measure for the underestimation of ^{15}N_{2} fixation rates when using the bubble method.

Secondly, we applied a meta- analytical approach to evaluate results from published papers comparing both methods. Variability and heterogeneity of published ^{15}N_{2} fixation rates were estimated for different incubation times and a mean effect size over all studies was calculated. Finally, considerations are given for the bubble method and its use in future studies.

We tested the equilibration of ^{15}N_{2} with filtered seawater empirically using both the ^{15}N_{2} bubble method (Montoya et al., ^{15}N_{2} gas (98%, Campro Scientific lot # EB1169V) by direct injection through the septum with overpressure released via a cannula. Bottles were gently mixed for 5 min.

We followed the protocol of Mohr et al. (_{2} concentrations in the degassed water by Winkler titration until O_{2} concentration were below the detection limit. Thereupon, 1.1 liter of degassed water was transferred to a Tedlar bag (Dupont, USA), flushed with helium to ensure absence of air inside the bags to which 11 mL of ^{15}N_{2} gas (98%, Campro Scientific lot # EB1169V) was added. The bag was agitated for 5 min (in which the bubble did not disappear) at room temperature. 50 mL of the enriched water was added to each 1.1L incubation bottle filled air free with Baltic Sea water.

All bottles were incubated at 15°C on a horizontal shaker (10 rpm, IKA HS 501, USA) located in a walk- in incubator. Incubations were carried out in triplicate and lasted for 24 h. Replicate sets of bottles were sampled immediately (^{15}N_{2} for analysis of the ^{15}N atom% enrichment of dissolved N_{2}, for which duplicate sub-samples from each bottle were transferred headspace-free into 12 mL exetainers. Crimp-sealed exetainers were stored in the dark at 4°C for up to 3 days. The ^{15}N atom % enrichment of dissolved N_{2} was analyzed by measuring the abundance and concentration of masses ^{29}N_{2} and ^{30}N_{2} using a manual method similar to the automated gas chromatography-isotope ratio mass spectrometry approach described in Holtappels et al. (_{2} was introduced to a mass spectrometer through an open split interface (Conflo IV, Thermo Scientific) and analyzed on a Delta V Advantage (Thermo Scientific). After every 5th sample air a standard was introduced.

We calculated dissolved ^{15}N_{2} concentrations according to Dalsgaard and Thamdrup (

We performed an error estimation to theoretically quantify the % difference in measured ^{15}N_{2} fixation rate considering an increasing time lag (T_{i}) between ^{15}N_{2} tracer addition and the beginning of diazotrophic ^{15}N_{2} fixation and the duration of fixation (T_{f}). The error was estimated relative to instantaneous isotopic equilibration of ^{15}N_{2} gas upon bubble injection.

This estimate is relevant in case of time delay between addition of the ^{15}N_{2} tracer and the active beginning of diazotrophic ^{15}N_{2} fixation and also applies for diazotrophs fixing continuously.

Consider a seawater sample with an initial stable isotope composition of dissolved N_{2}, N_{i} = δ^{15}N_{i}. For natural systems, this initial value will be very close to the global natural abundance of 0.366 at% ^{15}N. Into this sample, ^{15}N_{2} gas is injected and after a period of time (typically a couple of hours), the system reaches its equilibrium isotopic composition, N_{e} = δ^{15}N_{eq}. The temporal development (Figure ^{15}N enrichment in the dissolved N_{2} pool is:
_{e}−N_{i} is the difference between the equilibrium and initial isotopic compositions and ^{15}N_{2} gas has the consequence that N_{e} > N_{i} and ΔN > 0.

Dissolution kinetics observed in this study for the bubble (^{2} = 0.766,

For t → ∞, the equilibrium isotopic composition is reached and N_{e} = N_{i} + ΔN. A general assumption of the bubble method is that fixation occurs with the dissolved N_{2} pool at isotopic equilibrium. Any fixation that occurs before the system reaches equilibrium will contribute to error (underestimate) in the calculated rate, which is inversely proportional to δ^{15}N_{2}. The simplest way to estimate the error is the integration of Equation 6 over the duration of fixation. Equation (2) can be rearranged to:

which allows us to separate our experimental period into phases before and after the system reaches equilibrium. Following addition of ^{15}N_{2} to an incubation bottle, the mean δ^{15}N of the dissolved N_{2} will increase and the average enrichment of the ^{15}N_{2} pool from the start of N_{2}-fixation to any time,

where the phase lag _{i} is the difference in time between gas injection and the start of fixation, while _{f} is the duration of N_{2}-fixation. For _{i} = 0, the mixing of injected gas and the start of fixation are synchronized, as in the case of a diazotroph that fixes N_{2} continuously through the day. Integration of Equation (4) yields an expression for the mean δ^{15}N_{2} during the period of active N_{2}-fixation _{f}:

In Equation (5) the mean δ^{15}N_{2} value can be expressed as equilibrium composition and an error, ε, which represents the underestimation of the N_{2}-fixation rate:

and the relative percent error, R, is then simply:

Fitting Equation (7) to the observations (Figure ^{−1}.

We obtained data for meta-analysis from published and unpublished sources (Supplementary Table ^{15}N_{2} fixation rates were either provided personally by authors, retrieved from tables published in supplemental material or manually digitized from figures in the published studies using the software WebPlotDigitizer (version 3.10) (Ankit Rohatgi,

Before performing the meta-analysis, we determined the statistical dispersion and variability within the bubble and enriched water data sets. We calculated the mean absolute deviation (MAD) of each data set as follows:

where _{i}.

Meta-analysis and meta-regression were conducted with R 3.1.2 using the “metafor” package (Viechtbauer, _{enrichedwater}:R_{bubble}), or the effect size of individual experiments), as well as the corresponding pooled standard deviation. All lnRR values were weighted by the reciprocal of their sampling variance, followed by a random effects model to compute the overall mean effect size, which is equivalent to Cohen's ^{2}) and weights each study by the inverse sum of the individual study variance (ν_{i}) and the between- study variance. Mean effect sizes (i.e., Cohen's

Apart from calculating the mean effect sizes for all 13 studies and 368 observations, we also divided observations into two groups: short incubation time (0–12 h) and long incubation times (24 h). For short incubation times three data sets were available (Mohr et al.,

To explore heterogeneity in the meta-analysis, we calculated Cochrane Q-tests for heterogeneity (Cochran,

Random-effects meta-regression analysis using a linear mixed-effects model was used to evaluate the association between incubation time and the mean effect size of ^{15}N_{2} fixation.

For interpretation of the meta-analysis we converted Cohen's _{3} parameter (Cohen,

where Φ is the cumulative distribution function of the standard normal distribution, and δ is the population value of Cohen's

In addition, we calculated the overlapping coefficient (OVL) of data from the two methods by converting Cohen's

where Φ is the cumulative distribution function of the standard normal distribution, and δ the population Cohen's

The probability of superiority (CL) (Ruscio and Mullen,

where Φ is the cumulative distribution function of the standard normal distribution, and δ the population Cohen's

Dissolution of ^{15}N_{2} gas according to Montoya et al. (^{15}N atom% enrichment of 9.1 % (mean value for 24 h of incubation, Figure ^{15}N atom% enrichment was 1.7 h and the shift from an exponential rise in dissolved ^{15}N enrichment to a plateau with only minimal changes in ^{15}N atom% enrichment (>60% of maximum) occurred after 4 h. After 8 h, 90% of ^{15}N atom% equilibration was reached. Injection of water pre-enriched with ^{15}N_{2} gas according to Mohr et al. (^{15}N atom% enrichment over 24 h with a mean value of 7.5 ± 0. 9% (Figure

When using the bubble method, the rate of ^{15}N_{2} fixation will be systematically underestimated during the equilibration phase of ^{15}N_{2} gas with the dissolved pool of N_{2} (Figure ^{15}N_{2} fixation activity during the incubation period (Figure ^{15}N_{2} fixation is zero (T_{i} = 0 h) and the duration of ^{15}N_{2} fixation is 1 h (T_{f} = 1 h, red dot in Figure ^{15}N_{2} gas will result in an error of −0.2% (green square in Figure _{i} = 6 h and T_{f} = 12 h).

_{i} (time lag between gas injection and start of ^{15}N_{2} fixation by diazotrophs) and to T_{f} (length of active fixation period). The contour interval is 5%. In addition the −0.5% (dashed) and the −0.1% (dotted) line are added. Red dot = error of −72% (T_{i} = 0 h, T_{f} = 1 h), Green square = error of −0.2% (T_{i} = 6 h, T_{f} = 12 h), blue diamond = error of −12% (T_{i} = 0 h, T_{f} = 12 h). ^{15}N_{2} fixation (solid green line) occurs over a 12 h period (T_{f}). The time lag (T_{i}) between ^{15}N_{2} gas injection and beginning of diazotrophic ^{15}N_{2} fixation is 6 h. Fitted data from experimental dissolution of ^{15}N_{2} is also shown (black line, see also Figure

When organisms are able to fix N_{2} continuously, the error would be −12% (blue diamond in Figure _{i} = 0 h and T_{f} = 12 h) over a 12 h incubation and −6% over a 24 h incubation (_{i} = 0 h and _{f} = 24 h).

Variability among the replicates of individual studies was quite large as indicated by the standard deviation for the single studies and MAD of the two methods applied (Figure

Mean value and standard deviation for N_{2} fixation (different units)

To determine a mean effect size (i.e., Cohen's _{2} fixation for each study (Figure _{3}, for subgroup analysis 73%) and that 84% of the measurements in the two groups will overlap (subgroup analysis 76%). In addition, there is a 61% chance that a sample picked at random from the enriched water group will have a higher value than one picked at random from the bubble group (subgroup analysis 66%).

^{15}N_{2} fixation and corresponding standard error for the different studies and incubation time intervals. _{M}(df = 20) = 28.99,

A subgroup analysis excluding the unpublished data sets revealed a significant mean effect size of 0.631 ± 0.125 (

We also performed a meta-regression to evaluate the influence of time on the overall mean effect size. No significant impact was detected (data not shown). Moreover, we checked for publication bias, which is expected when scatter of data in the funnel plot is asymmetric. In our analysis, assessment of the contour-enhanced funnel plot indicates an asymmetrical scatter of data and potential publication bias introduced by a lack of non-significant studies (Supplementary Figure

We furthermore, did separate meta- analysis for observations with short incubation times (0–12 h) and long incubation times (24 h only, Supplementary Figures

We found no significant correlations with ocean province or temperature in exploring which factors might influence the mean effect size (data not shown).

We combined a theoretical examination of the error associated with the equilibration time of the bubble of ^{15}N_{2} gas and a meta-analysis of published and unpublished sets of N_{2}-fixation measurements comparing both methods. Our findings allows us to detect mean differences in rate estimates and provide critical insight into the strengths and weaknesses of the two experimental approaches.

Our error estimation of the bubble method during a 24 h experiment reveals a negligible error of −0.2% assuming a diazotroph community that fixes only during 12 h daytime and starting of nitrogen fixation 6 h after the injection of ^{15}N_{2} gas i.e., the addition was done 6 h before sunrise. Considering that the error introduced by using a gas-tight syringe to inject ^{15}N_{2} gas of ±1% (according to the manufacturer, Hamilton USA), the error introduced by using bubble injection is insignificant. The error introduced by using the bubble method will increase to −6% when diazotrophs fix continuously over 24 h (assuming there is no time lag between bubble injection and start of active fixation). Overall, it is important to adjust incubation times relative to the onset of active N_{2} fixation (which is in turn is depended on the dominating diazotrophs present), as has been indicated before (Mohr et al.,

Statistical dispersion, as represented by the MAD from the mean value, appears to be higher in the data set based on the enriched water method (mean MAD of all studies 7) than in the data set of studies that used the bubble method (mean MAD of all studies 5). That is, measured N_{2} fixation rates appear to be more consistent when determined using the bubble method. A larger dispersion of data in experiments using the enriched water method might be introduced in by the process of preparing the enriched water for later usage, i.e., degassing water of different volumes and varying accuracy of degassing. In addition, Wilson et al. (_{2}-fixation estimates that were 30% greater when samples were incubated aboard ship in deck incubators than when incubated on an

Our meta- analysis revealed a large congruence in the estimates of ^{15}N_{2} fixation rate produced using the two experimental methods. The 84% overlap of rate estimates make it very difficult at this stage to estimate any sort of a global factor to quantify the degree of underestimation of ^{15}N_{2} fixation rates when using the bubble method. Our literature review moreover revealed that a thorough comparison over a 24-h cycle is needed with only three studies on sort incubation times of 0–12 h. A larger comparative analysis is clearly necessary especially in view of the elevated dispersion (i.e., larger MAD) of ^{15}N_{2} fixation rates measured using the enriched water method.

As Großkopf et al. (_{2} fixation rates using the bubble method, especially when buoyant diazotrophs are presented. Thus, in habitats dominated by filamentous species like ^{15}N_{2} when using the bubble method. Alternatively, as proposed in the sub-chapter below (see “Experimental Recommendations”) the determination of the final ^{15}N_{2} (i.e., substrate) enrichment in the incubation bottle enables a concerted calculation of N_{2} fixation rates.

In our analysis, we have included two data sets that are currently unpublished (Benavides and Wannicke et al., Fabian et al., Supplementary Table

A number of experimental factors have a strong influence on the precision and accuracy of the determination of N_{2}-fixation rates. Firstly, the sensitivity of any experiment using ^{15}N_{2} depends on the amount of tracer added to the dissolved pool of N_{2}. For example, addition of 1 mL of ^{15}N_{2} per liter of sample will produce an equilibrium enrichment of ~5–10 atom% ^{15}N, depending on the size of the ambient pool of N_{2}. In contrast, the procedure proposed by Großkopf et al. (_{2} availability does not limit N_{2}-fixation activity, greater additions may easily be realized to increase the substrate labeling, thereby increasing the sensitivity of the rate measurement. This is especially important in systems where rates are expected to be low, for example in aphotic deep waters. In general, we recommend adding sufficient ^{15}N_{2} to raise the ^{15}N content of the dissolved N_{2} pool to 9–10 at% as noted by Montoya et al. (

Secondly, the natural variability of δ^{15}N of the particulate nitrogen (PN) pool sets a lower limit to rate measurements. If the variability in δ^{15}N of PN is high at the start of the incubation (t_{0}) and the final increase in δ^{15}N values of the PN in the incubation bottles is low due to low N_{2} fixation rates, then N_{2}-fixation activity may not be detectable. For example, Wasmund et al. (^{15}N_{2} fixation rate measurements in the Benguela upwelling region where they compared initial (t_{0}) and final δ^{15}N measurements of samples incubated with ^{15}N_{2}. The mean values of the two batches of filters differed only by 0.9‰, leading Wasmund et al. (^{15}N_{2} fixation rates were too low to resolve with the tracer method. Nowadays, mass spectrometers clearly perform analytical precisions of 0.2‰ and better. Therefore, the detection limit of enriched PN is well below 4‰, as original proposed in the paper by Montoya et al. (

Finally, the two experimental approaches differ fundamentally in the degree and nature of experimental manipulation of the sample. The bubble method involves minimal handling (a thourough mixing of water and gas bubble after injection has to be guaranteed, by using e.g., a continuously rotating) and perturbation of the system, but can lead to a systematic underestimate of N_{2}-fixation rate if a significant fraction of the overall activity during the experiment occurs during the isotopic equilibration phase. In contrast, the enriched water method requires extensive processing in advance to prepare the ^{15}N_{2}-labeled water used to inject tracer into the experimental bottle as described by Klawonn et al. (_{2} fixation rates are very difficult to constrain but can clearly compromise the reliability of the final rate estimates. Another approach using the bubble addition followed by the removal of the bubble after only few hours and retrieval of a subsample for determination of ^{15}N_{2} atom% enrichment requires the tedious determination of the ^{15}N_{2} atom% enrichment for each incubation bottle (Jayakumar et al.,

Our dissolution experiments investigating the isotopic equilibration in seawater along with the theoretical error calculation both suggest that incubation times longer than about 6 h are minimally affected by the equilibration of the added ^{15}N_{2} gas and the dissolved pool of N_{2} in the experimental bottle (Figures

A final recommendation to improve the accuracy of N_{2} fixation measurements and potentially help resolve the source of variability among replicates is collection and preservation of a water sample from each experimental bottle for determination of the final ^{15}N_{2} (i.e., substrate) enrichment. This would improve the accuracy of the enriched water, as well as the bubble method, both of which typically rely on solubility calculations to estimate the size of the ambient pool of N_{2}, which in turn determines the actual ^{15}N_{2} enrichment of the dissolved pool.

All authors contributed to the design of the study. Laboratory and analytical work was conducted by NW, MB, JM, and TD. Data search and meta- analysis was performed by NW and MB. Error analysis was contrived by MV and JD and calculated by JD. NW wrote the initial draft of the manuscript and all authors contributed to its revision.

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.

We thank Dr. Sophie Rabouille for handling the editorial process and the two referees whose comments improved this manuscript.

The Supplementary Material for this article can be found online at: