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Overview of the FluxNet methodThe FluxNet approach is based on a mechanistic model, which includes multiple species/types of phytoplankton, bacteria, dissolved and particulate organic matter (DOM, POM), inorganic nutrients, micronutrients and inhibitors (see Table 1). For phytoplankton—bacteria carbon flux, which is the focus here, phytoplankton produce organic carbon by exudation and death. For exudation, living phytoplankton produce total DOM at constant and photosynthesis-proportional rates (ke, ef), with a composition defined by an exudation fraction (Fe) for each DOM species. These parameters vary by phytoplankton type. For example, for green algae (gre), the constant exudation rate is kegre and the fraction of glucose-containing HMW DOM (gl2) is Fegre,gl2. For one phytoplankton type the total DOM production varies in time with the photosynthesis rate, but the composition is constant. Phytoplankton die by a general death function and inhibition. The death function is time-variable (a bell-shaped function with a maximum at a specific time of year) and does not differentiate between various death mechanisms like zooplankton grazing or viral lysis, but presumably it represents mostly grazing in this case. Upon death, the phytoplankton biomass is converted to POM and DOM, where e.g., the content of chrysolaminarin (chr) for the diatom Rhizosolenia styliformis (rst) is defined by a composition fraction (Fxrst,chr). POM dissolves to DOM at a first-order rate. Bacteria consume DOM using Monod-level kinetics, where e.g. the affinity for Polaribacter (pol) for chrysolaminarin is defined by a half-saturation constant (Kshpol,chr).Table 1 Model components.Full size tableThe novel aspect is the upscaling to hundreds of state variables and thousands of parameters, which is accompanied by several conceptual and practical modeling challenges. To balance mass and account for the action of unobserved components, cryptic or hypothetical species are included [17], like DOM types d01-d15, which may represent e.g., threonine [18]. To simulate a diverse community with a smaller number of drivers (“paradox of the plankton”) and control chaos, interaction via micronutrients and inhibitors, as well as dormancy is included [19,20,21,22]. Parameters are optimized/calibrated to minimize the discrepancy between the model and observations. Which parameters are optimized and the corresponding ranges is based on available information (complete model equations and parameters are in Table S1–S25). For example, the constant DOM production rate (ke) is optimized for all phytoplankton, with a range adopted from a previous modeling study [23]. For rst (Rhizosolenia styliformis), the exudation fractions for most DOM components, like the cryptic species d01 (Ferst,d01), are optimized. Others, like glucose-containing HMW DOM (Ferst,gl2), are fixed based on literature (Table S14). The optimization is challenging because of the many components, nonlinear interactions, and resulting local optima in the objective function. We developed an optimization routine customized for microbial ecosystems with a number of key features.First, the method mimics natural speciation, where a coarse-grained model is gradually de-lumped to a finer resolution, a strategy also used in manual model development [13, 24, 25]. This is illustrated in Fig. 1, which shows how the model starts with just one component in each ecological compartment (Fig. 1E). This model is optimized until a threshold is reached, and then all species are de-lumped/split into two, followed by another round of optimization and so on. During the course of the optimization, with time or model runs, the number of components and parameters increase, and the total error generally decreases, although there can be a transient increase when new species are introduced (Fig. 1A, B). This way the optimization routine works with a smaller model on average and computational effort can be directed to a smaller set of parameters corresponding to newly introduced species, and the performance increases (Fig. 1C).Fig. 1: FluxNet inference method illustration.A Number components and optimized parameters. B Error for entire model (Total) and selected individual observations (rst = R. styliformis, pol = Polaribacter, lam = particulate chrysolaminarin). Best of 128 replicate runs. C Diversification of chrysolaminarin uptake affinity (max. heterotrophy rate/half-saturation constant). D Method performance with and without de-lumping. E Network corresponding to different de-lump levels. See Table 1 for component names and abbreviations.Full size imageAt each de-lumping level, the new species generally inherits the parameter values (i.e., the genome [26]) from the old species. Subsequent optimization then diversifies the population. This is illustrated in Fig. 1C, which shows the uptake affinity of all bacteria species for chr. However, different parameter values can also be specified for the new species, and then they are adopted and overwrite those inherited from the old species. This is used, for example, to assign species-specific cell sizes or prevent species from taking up a substrate. In Fig. 1C, those species that are not capable of assimilating chr, like rei (Reinekea), have an affinity equal to 0. The method thus allows for natural and automated expansion of the model to very large scale, yet provides a way to constrain/curate it based on available information.Second, the routine includes multi-parameter optimization (Nelder-Mead simplex method) on selected subsets of dependent parameters, like those involved in the production and consumption of chrysolaminarin (chr) or directly affecting the photosynthesis of the diatom R. styliformis (rst). Dependence between parameters, like max. photosynthesis rate and nutrient half-saturation constant, are explicitly considered. Also, Monte Carlo scans are performed on selected parameter sets at various points in the process.Application to Helgoland time seriesThe FluxNet method is applied to a four-year time series at Helgoland [27], including near-daily observations of 15 phytoplankton and 38 heterotrophic bacteria types (e.g., species, strains) and various bulk and auxiliary parameters (e.g., Chlorophyll a, DAPI, temperature, nitrate+nitrite, ammonium, phosphate, light extinction) (Tables S19 and S20). Data from more focused studies characterizing DOM and POM are also included [28, 29] (Table S21).In addition to the time-series data, the model is informed by literature information. Model parameters, incl. general properties like phytoplankton exudation fraction or bacteria growth efficiency, are constrained based on past models and data. Also, constraints are implemented for parameters controlling composition, exudation and utilization for the specific components included in the model. Those were based on a literature meta-analysis, where we searched primarily for studies with strains from Helgoland, but included strains from other locations if necessary. These constraints include, for example, for the phytoplankton storage polysaccharide chrysolaminarin, the typical content (~30% for diatoms, none for dinoflagellates) and ability of bacteria to assimilate it (yes for Polaribacter, no for Roseobacters and Reinekea) (Tables S4 and S11). Imposing constraints from the literature generally results in a worse agreement with the observations, but also increased realism of the model. Removing the constraints of phytoplankton composition (Table S4) significantly improves the agreement with observations, but also predicts substantial glycogen content of diatoms (e.g., Fxmhe,gly+ply = 0.19). Removing uptake constraints by bacteria (Table S11) reduces the error, but not significantly, suggesting that there is enough flexibility of the model to reproduce the observations even with this constraint. However, that model also includes features that disagree with literature, like substantial uptake of chr by s11 (Kshs11,chr = 25 L/mmolC/d).Carbon fluxes through and within in the ecosystemThe final model includes 210 components and their behavior and interaction are described by a total of 8200 calibrated parameters of 50 different parameter types (e.g., the composition of each of the 53 microbes is described by 76 fractions Fx, or 4000 total parameters) (Fig. 1), and it constitutes a mass-balancing, mechanistically-constrained, quantitative representation of the ecosystem. It reproduces many of the observed patterns of summary parameters like Chlorophyll a (chl), total bacteria (dap), particulate chrysolaminarin (lam), various high-molecular weight (HMW) DOM compounds, as well as absolute concentrations of individual phytoplankton and bacteria species (Fig. 2A–C). Only subset of the hundreds of model components is shown in Fig. 2B, C, which were selected based on (a) importance (e.g., rst is the dominant OM producer in 2009), (b) availability of data (e.g., chrysolaminarin, [29]) and (c) illustration of co-blooming (panel B) and succession (panel C). All model-data comparisons are presented in the SI (Fig. S1). The model under-predicts total DOM (doc), probably because a large fraction of observed DOM is more refractory allochthonous material, which is not considered in the model.Fig. 2: FluxNet model results and comparison to data.A All model types lumped. Phytoplankton (chl, μgChla/L), POM (poc, incl. microbes, μmolC/L ×0.1*), DOM (doc, μmolC/L ×0.1*), bacteria (dap, 1e6/mL ×3*). Gray shading are spring blooms, defined as the first time of the year the phytoplankton exceeds 3 µgChla/L plus 28 days. B Selected types for 2009 spring bloom. Rhizosolenia styliformis (rst, centric diatom, 1e6/L ×1.2*), Thalassiosira nordenskioeldii (tno, centric diatom, 1e6/L ×0.05*), particulate chrysolaminarin (lam = phr + phytoplankton content, μmolC/L ×0.002*), dissolved chrysolaminarin (chr, μmolC/L ×0.002*, no data available), Polaribacter (pol, DAPI × CARD-FISH, 1e6/mL ×0.1*), NS3a marine group (ns3, 1e6/mL ×0.2*). C Selected types for 2010 spring bloom. Mediopyxis helysia (mhe, centric diatom, 1e6/L), Thalassiosira nordenskioeldii (tno, centric diatom, 1e6/L), glucose-containing HMW DOM (glc, μmolC/L ×0.01*), arabinose-containing HMW DOM (ara, μmolC/L ×3*), Reinekea (rei, 1e6/mL ×5*), Alteromonas (alt, 1e6/mL ×1.5*). Lines are model and symbols are data [27,28,29]. *Individual concentration series scaled to illustrate dynamics. See Fig. S1 for all model-data comparisons. Upside-down triangles mark various bloom stages for networks in (D) and Fig. 4A. D Inferred carbon flux network. Nodes are components. Size indicates in/outflux (μmolC/L/d), color varied randomly within each ecological compartment. Lines are fluxes. Thickness is proportional to log flux (μmolC/L/d), colored based on the source node, lines below a threshold distance are colored gray to highlight most important fluxes. Italic numbers are total fluxes (μmolC/L/d). Flux cut off is 0.01%. See Table 1 for component names and abbreviations. See Movie S1.Full size imageIt is important to understand that the model was calibrated to these observations, so this is not a prediction per se. The main information produced by this analysis (emergent property) are the mass fluxes. Predicted ecosystem-level fluxes can be compared to independent estimates, which were not used as input here. For the period 2009–2012, the gross primary production rate in the model is 28 (±1.2 standard deviation) mmolC/m2/d. Uncertainty of fluxes and parameters are based on top 5% of 128 replicate runs, as in [23]. This flux compares well to a regional estimate of 29 (26–33) mmolC/m2/d for the Transitional East Region of the North Sea for the same period [30]. At the end of March, the bacterial production rate in the model is 0.32 (±0.041), 0.14 (±0.017), 0.20 (±0.025) and 0.45 (±0.057) μmolC/L/d for the 4 years, respectively. This is consistent with measurements of 0.20 μmolC/L/d in 1992 ~30 km from Helgoland [31].These comparisons provide confidence in other aggregate fluxes predicted by the model. The C, N and P fluxes to the sediment bed, via settling of phytoplankton and POM, are 5.8 (±0.91) mmolC/m2/d, 0.87 (±0.14) mmolN/m2/d and 0.054 (±0.0085) mmolP/m2/d, which constitute 20%, 16% and 18% of the input via photosynthesis (C) or external input (N, P) (see Fig. S2). External “new” input of N is 0.66 μmolN/L/d, which is 6.0 time higher than the 0.11 (±0.023) μmolN/L/d released or “recycled” by bacteria.The resulting flux network includes quantitative carbon fluxes between all components at each time point, like 28 days into the 2009 spring bloom (Fig. 2D, Dataset S1 list all fluxes). The dominant source of organic matter is rst at 0.36 (±0.19) μmolC/L/d, 30% of which is dissolved and particulate chrysolaminarin (chr + phr). These instantaneous fluxes exhibit a higher uncertainty than the integrated fluxes discussed in the previous paragraph, which can be explained by small timing differences (Table S26). The DOM is consumed by a diverse consortium of bacteria, mostly Polaribacter (pol) at 0.46 (±0.22) μmolC/L/d, 35% of which is chr. chr has a through-flux of 0.25 (±0.049) μmolC/L/d and a turnover time of 8.8 (±2.0) days. In the model, phytoplankton and bacteria interact via DOM, but the carbon flux can be traced and used to quantify phytoplankton – bacteria associations. Here, the carbon flux via all DOM types from rst to pol is 0.27 (±0.20) μmolC/L/d, 58% of carbon to pol, making this the second-strongest (after ns3) microbial linkage in the system at this time. This who produces/consumes how much of what when information is the main output of the FluxNet method, and it is critical for moving our understanding of microbial ecosystem functioning beyond bulk parameters like respiration and photosynthesis rates towards a higher resolution.Whereas the 2009 spring bloom illustrates co-blooming of phytoplankton and bacteria, the 2010 bloom shows succession of phytoplankton, DOM and bacteria. Several factors control this pattern in the model. Reinekea (rei) is negative for chrysolaminarin (chr) based on literature (Table S11), but is predicted to have a relatively high affinity for other glucose-containing DOM (gl2) (khrei / Kshrei,gl2 = 63 (±22) L/mmolC/d). A substantial fraction of gl2 is produced relatively early by phytoplankton exudation, and it is the primary substrate for rei at bloom stage 14 days. Alteromonas (alt) is predicted to have a low affinity for gl2 (khalt / Kshalt,gl2 = 0.015 (±0.0097) L/mmolC/d), but it is positive for chr based on literature and predicted to have a high affinity (khalt / Kshalt,chr = 52 (±4.7) L/mmolC/d). Chr is a death (i.e. grazing) product of phytoplankton and produced relatively later in the bloom, and it is the primary substrate for alt at this time. The substrate spectra of bacteria emerge in the analysis, within literature constraints, and can be considered a prediction testable with modern experimental techniques [6].Oligotrophic and copiotrophic carbon processingThe network includes concentrations and fluxes for each bacteria type, and a natural question is to what extend they are correlated. There is increasing awareness that high abundance may not necessarily mean high importance and vice versa, including the over-proportional role of rare species in biogeochemical cycles [32]. In the model, there is a strong correlation between concentration and carbon flux of bacteria, but for the same concentration there is also about an order of magnitude variation in flux (Fig. 3). The spread reflects differences in growth rates during the bloom periods. Some species, like the oligotroph SAR11 (s11), have consistently lower flux and others, like the copiotroph Polaribacter (pol), have consistently higher flux. There are also some, like the cryptic alphaproteobacteria (alx), that go in different directions in different years.Fig. 3: Correlation between spring bloom abundance and importance.Concentration and carbon flux for all model bacteria types during spring bloom periods (see Fig. 2 caption for definition). Lines: All(dashed)/Olig.(thick)/Copi.(thin), log Flux = –0.93/–1.03/–0.81 + 0.93/1.00/0.94 × log Conc., R2 = 0.88/0.92/0.92.Full size imageIt is important to realize that, in dynamic systems, microbial interactions and the corresponding networks are not static [3, 33]. The dynamics of the entire Helgoland flux network over the four-year period is illustrated in an animation, which shows the production of DOM and POM during and after phytoplankton blooms and later blooming of bacteria (Movie S1). These features are also evident in the phytoplankton – DOM – bacteria interactions at two selected time points during the 2009 spring bloom (Fig. 4A, B). At the onset of the bloom, the oligotroph SAR11 (s11) consumes the most DOM, primarily the cryptic species d08, which comes mostly from grazing death of green algae (gre) and exudation by rst. After 28 days the copiotroph pol dominates, which consumes primarily chr, a death product of mostly rst. SAR11 continues to be a major carbon processor in the early parts of the bloom, which was unexpected, because it is an inferior competitor at this time (growth rate s11 = 0.051 vs. pol = 0.15 1/d, bloom average), but can be explained by the higher biomass concentration (s11 = 0.68 vs. pol = 0.13 μmolC/L, bloom start). The flux is proportional to concentration and growth rate, and neither measure alone is a good proxy for the importance of a species [4]. Across all four years, oligotrophic bacteria, defined based on below-average growth rates (literature classifications are often ambiguous), dominate carbon processing for the first 18 days, generally past the phytoplankton peak (Fig. 4C).Fig. 4: Carbon processing during the course of blooms.A Phytoplankton—DOM—bacteria carbon flux network for the start and +28 days of 2009 spring bloom. See Fig. 2 legend. Flux cut off is 0.3%. B Cell concentrations, growth rate and relative carbon processing for s11 and pol for 2009 spring bloom. C Fraction of DOM processed by oligotrophic bacteria and exudate fraction in DOM pool for all blooms. Oligotrophs are defined based on literature as shown in Table S23 or based on below-average growth rates (kg). For the later, the oligotrophic fraction or weight given for type i, is based on fOLIi = kgAVEn / (kgAVEn + kgin), n = 5. kg is the net growth rate calculated from biomass change, plus dilution rate.Full size imageThe use of d08 by s11 and chr by pol in 2009 suggests are more general pattern, i.e., use of exudation products earlier by oligotrophs and death (i.e., grazing) products later by copiotrophs. Across all years, the fraction of DOM produced by exudation decreases during the course of the bloom (Fig. 4C), a common feature of phytoplankton blooms [33]. This is reflected in the diet of these bacterial groups, i.e., for oligotrophs (vs. copiotrophs), exudates make up a higher portion of the diet (27 vs. 18%), and they have a higher affinity for exudates (39 vs. 35 L/mmolC/d), which is also consistent with experimental evidence from another system [7].After the model was developed, while this paper was in peer review, metaproteomic data for the Helgoland Island spring bloom in 2016 were published that suggest that algal storage compounds (e.g., chrysolaminarin) are used throughout the bloom, whereas cell wall-related compounds (e.g., fucose-containing) are used at later bloom stages [34]. Our model also predicts an increase in the consumption of cell-wall vs. storage compounds at later bloom stages (Fig. 5), which validates our outcomes, although a direct comparison is not possible because of the different time.Fig. 5: Consumption of cell wall vs. storage compounds during the course of blooms.Total consumption (all bacteria) in µmolC/L/d of cell wall compounds divided by storage compounds. Cell wall compounds = man (mannan) + glo (glucoromannan) + fcs (FCSP). Storage compounds = chr (chrysolaminarin) + gly (glycogen) + sta (starch). Averages for all four years.Full size imagePhytoplankton functional similarity decouples them from bacteriaAn important question is to what extent the patterns recur from year to year [27]. We compare networks of phytoplankton producers, DOM exchanged and bacteria consumers, as well as phytoplankton – bacteria interactions quantified in absolute (μmolC/L/d moving between phytoplankton X to bacteria Y) and relative (% of carbon for bacteria Y supplied by phytoplankton X) terms (Fig. 6A). All networks show significant similarity so there is recurrence from year to year. The recurrence is higher for DOM than phytoplankton, suggesting that different phytoplankton produce similar DOM, which is expected considering similar composition (e.g., chr in diatoms). There are no phytoplankton producers that recur in the top quartile every year, but chr and others are in the top quartile of DOM exchanged (produced and consumed) every year. The recurrence is lower for bacteria consumers suggesting factors beyond DOM shape the bacteria community.Fig. 6: Recurring patterns and comparison of FluxNet and LSA methods.A Similarity of networks for spring blooms. Error bars are 95% confidence limits. Bray-Curtis similarity was calculated as 1 – Bray-Curtis dissimilarity. Text on top of symbols lists components that recur in the top quartile every year, listed in order of average rank. B Carbon flux networks for top recurring bacterial consumer, top four DOM sources and top coupled phytoplankton. (C&D) LSA network (showing top 15% of significant local similarity scores) and sample time series.Full size imageAn important question is how specific interactions are and how tightly networks are interconnected [35, 36], which depends on the mechanisms of interaction and will affect the recurrence. Consistent with the relatively low recurrence of phytoplankton producers, phytoplankton—bacteria coupling shows relatively low recurrence, i.e. low specificity. The primary substrate for the consumer pol is mostly chr and gl2, although it does change from year to year with varying DOM, consistent with the known assimilation capabilities of pol (Polaribacter) [37] (Fig. 6B). However, the primary associated phytoplankton for pol is different each year, although it is always a diatom. The de-coupling of phytoplankton production and bacteria consumption was also concluded from the lower recurrence of phytoplankton and higher recurrence of bacteria abundance in the same dataset [27]. It suggests that carbon processing is resilient to changes in phytoplankton, which may arise from factors like species invasion or climate change.The above discussion focused on one-way/commensal (phytoplankton  > DOM  > bacteria) interactions, but the network also includes specific two-way/mutualistic phytoplankton-bacteria interactions. Phaeocystis (pha) has the highest exudation fraction and Bacteroidetes nvi the highest affinity for DOM d04, whereas nvi has the highest exudation fraction and pha the highest requirement for micronutrient m15. Such mutualism is observed in other systems and the interactions predicted here can be tested experimentally [20]. Alternatively, experimentally-observed interactions could be used as input to the method, as constraints.Robustness of the analysisTo understand the effect of some of the choices made in the model structure we repeated the analysis with added or removed components or processes. Models without micronutrients or inhibitors produce significantly worse fit to the data (Fig. 7A), highlighting the need for a two-way interaction between phytoplankton and bacteria to maintain diversity. Models with more micronutrients or inhibitors are similar to the basecase. Together, these results provide some justification for the complexity (i.e., number of parameters) in the basecase model. The analysis including osmotrophy (aka absorbotrophy, i.e., phytoplankton can perform heterotrophy) produces a better fit to the observations, but that model was not adopted as basecase, because the osmotrophy process is poorly constrained and includes some probably unrealistic features/fluxes, like significant exudation and uptake of the same substance by one phytoplankton species. Importantly, excluding the runs with worse fit to the observations, the main conclusions (as shown in Figs. 4C and 5A) are the same, confirming that the results are reproducible and robust to some of the choices made in model structure.Fig. 7: Reproducibility of main results.A Total error for runs with different models. “w” or “b” indicates performance is significantly worse (open bars, think lines) or better than basecase, p  ns9 interaction ranks in the top 1% for LSA and FluxNet (relative interaction). However, the lack of mechanistic constraints is evident. One of the strongest links for the 2009 spring bloom (rank 13%) is between the diatom Chaetoceros debilis (cde) and Roseobacters (ros) (Fig. 6C, D). The shifted peaks line up nicely, but the bacteria biomass is higher than that of the phytoplankton and genome analysis suggests ros do not assimilate chrysolaminarin [37], which is a major death product of diatoms. Considering this, growth yield and other competing consumers, it is unlikely that cde is a major source of carbon to ros.Summary and outlookModern observational tools are generating high-resolution descriptions of the components of microbial ecosystems, and an ongoing grand challenge is to use these data to understand how systems function. Our method predicts dynamic mass fluxes between marine phytoplankton and bacteria, which provides insights into the functioning of the ecosystem. Specifically, it showed that there is a strong correlation between concentration and flux of bacteria during blooms, but oligotrophs are relatively less important than copiotrophs. However, due to their higher biomass, they are major carbon processors during early phases of blooms, well past the peak. Oligotrophs grow preferentially on exudation products, which are more abundant earlier in the bloom. Also, our results suggest that phytoplankton are functionally similar in terms of what organic carbon species they produce, and that this decouples them from bacteria.FluxNet is an inference method for microbial time series data that serves the same general purpose as existing empirical inference methods, like LSA [38]. In general, both approaches have strengths and weaknesses (see Introduction) and may complement each other. A main advantage of FluxNet is that it produces quantitative concentrations and fluxes, and associated conclusions (e.g., preferential use of exudates by oligotrophs). Also, it is constrained by mass balance and additional information from the literature (i.e., beyond the time series data), which make the results more realistic.The existing FluxNet code can readily be applied at a higher resolution (microdiversity), explicit representation of other ecosystem components, like viruses and zooplankton, and more processes, like photoheterotrophy and mixotrophy. It may also be applied to understand other microbial ecosystems, like the human gut or wastewater treatment plants. For an inference method it is important to be applicable to various types of observations, including modern environmental -omics observations, like transcript, protein and metabolite levels, and the present model will have to evolve in this direction [39]. The present model includes a relatively simple representation of the various processes, and the current biological understanding supports increasing the mechanistic realism (and complexity). For example, the present version assumes constant composition of DOM produced by phytoplankton, but observations show that it changes with physiology and interaction with bacteria [18, 40]. Also, the model assumes simple first-order dissolution of POM to DOM and direct utilization by bacteria, whereas break-down of especially polysaccharides is often mediated by extracellular enzymes [41]. More

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