Stoichiometry on the edge—humans induce strong imbalances of reactive C:N:P ratios in streams

Anthropogenic nutrient inputs led to severe degradation of surface water resources, affecting aquatic ecosystem health and functioning. Ecosystem functions such as nutrient cycling and ecosystem metabolism are not only affected by the over-abundance of a single macronutrient but also by the stoichiometry of the reactive molecular forms of dissolved organic carbon (rOC), nitrogen (rN), and phosphorus (rP). So far, studies mainly considered only single macronutrients or used stoichiometric ratios such as N:P or C:N independent from each other. We argue that a mutual assessment of reactive nutrient ratios rOC:rN:rP relative to organismic demands enables us to refine the definition of nutrient depletion versus excess and to understand their linkages to catchment-internal biogeochemical and hydrological processes. Here we show that the majority (94%) of the studied 574 German catchments show a depletion or co-depletion in rOC and rP, illustrating the ubiquity of excess N in anthropogenically influenced landscapes. We found an emerging spatial pattern of depletion classes linked to the interplay of agricultural sources and subsurface denitrification for rN and topographic controls of rOC. We classified catchments into stoichio-static and stochio-dynamic catchments based on their degree of intra-annual variability of rOC:rN:rP ratios. Stoichio-static catchments (36% of all catchments) tend to have higher rN median concentrations, lower temporal rN variability and generally low rOC medians. Our results demonstrate the severe extent of imbalances in rOC:rN:rP ratios in German rivers due to human activities. This likely affects the inland-water nutrient retention efficiency, their level of eutrophication, and their role in the global carbon cycle. Thus, it calls for a more holistic catchment and aquatic ecosystem management integrating rOC:rN:rP stoichiometry as a fundamental principle.


Introduction
Organic carbon (OC), nitrogen (N), and phosphorus (P) sources and cycling in terrestrial and aquatic environments have been strongly altered by anthropogenic activities in the last decades (Schlesinger and Bernhardt 1997, Peñuelas et Beusen et al 2022), leading to eutrophication, while the intensive drainage and hydrological disconnection of carbon-rich wetlands have heavily disturbed OC delivery to streams (Stutter et al 2018, Xenopoulos et al 2021. These resulted in severe degradation of surface water resources with implications for human usability (van Vliet et al 2017, Ma et al 2020, instream ecosystem health (Young et al 2008, Woodward et al 2012, and the ecological state of receiving estuaries and marine environments (Diaz andRosenberg 2008, Berthelsen et al 2020). Responses of aquatic organisms to nutrient inputs are not only a function of single macronutrient concentrations but also of the stoichiometry of the reactive molecular forms of organic carbon (rOC), nitrogen (rN), and phosphorus (rP) that can be expressed as molar ratios rOC:rN, rOC:P, rN:rP. These macronutrient ratios, together with energetic constraints, shape the reaction rates of microbiological processes within and across aquatic ecosystems (Helton et al 2015, Casquin et al 2020, Stutter et al 2020. At a catchment scale, separately investigated nutrient concentrations, as well as C:N, C:P, and N:P ratios of different nutrient species, have been shown to deliver important insights into the catchmentinternal source contributions and linkages of OC, N, and P cycles; and helped to disentangle the stoichiometric limitations of heterotrophic and autotrophic assimilation, and denitrification (Taylor and Townsend 2010, Wymore et al 2016, Dupas et al 2017, Maranger et al 2018, Stutter et al 2018, Gao et al 2021. For example, average concentrations of Nitrate (NO 3 )-N at catchment outlets are explained by both upstream agricultural N inputs and retention in the catchment (Frei et al 2020, Ebeling et al 2021b. Macronutrient concentrations at catchment outlets typically vary on the intra-annual scale, which translates to pronounced variability of the rOC:rN, rN:rP, and rOC:rP, ratios and possible changes in nutrient limitation (Abbott et al 2018, Dupas et al 2018. This intra-annual variability is known to be a consequence of the discharge-mediated temporally variable mixing of different water sources with different stoichiometric ratios (Dupas et al 2018), but also of the seasonal retention processes in streams (Rode et al 2016, Dehaspe et al 2021. Given the interlinkages of OC, N, and P inputs and cycles at the catchment scale, we propose to go one step further by looking not at separate C:N, N:P, and C:P ratios but at joint riverine reactive C:N:P ratios. We use ternary plots of the reactive C:N:P ratios (figure 1), which allows us to depict and detect macronutrient depletion relative to (micro-)organismic demands in contrast to separate investigations of C:N, C:P, and N:P ratios (Graeber et al 2021). Furthermore, studying reactive C:N:P ratios (rOC:rN:rP) enables us to understand better how nutrient export is jointly shaped by catchment-internal biogeochemical processes and the mixing of different water sources. In this paper, we investigate reactive C:N:P ratios of water exported from catchments-to assess to their first-order controls and compare them to the stoichiometrical demands of key microbial processes.
We analyze this for 574 German catchments (3-123 000 km 2 ), influenced to a varying degree by a long history of human impacts (Ebeling et al 2021a). Specifically, we hypothesize that (I) average reactive C:N:P ratios in agriculturally-impacted catchments show a stoichiometric imbalance towards high rN and/or rP export relative to the Redfield ratio (Redfield 1934) due to excessive N inputs from fertilizer application and wastewater. (II) Furthermore, we hypothesize rOC:rN:rP at the catchment outlet to show distinct intra-annual variability that can be linked to key hydrological and biogeochemical processes within the catchment. We further discuss the underlying processes that shape both average and intra-annual variability of rOC:rN:rP at the catchment scale and their implications for in-stream biological processes within the river network and in receiving water bodies. We furthermore believe that this study has the potential to serve as a stepping stone for further hypothesis-driven research.

Data selection
To assess the spatial and temporal variability of rOC, rN, and rP ratios exported from catchments, we use data from 574 German catchments compiled by Ebeling et al (2022). First, we approximate each of the reactive nutrient fractions with total organic C (TOC), dissolved inorganic N (DIN = NO 3 -N + NH 4 -N), and soluble reactive phosphorus (SRP), respectively, measured at the catchment outlet at bi-weekly or monthly frequencies. Only a part of the bulk OC (2%-45%, Stutter et al (2018)) is bioavailable (in the following, referred to as reactive symbolized by the prefix r), and this is well known to be a function of land cover (Stutter et al 2018), discharge levels (Hosen et al 2021a), river network residence time (Hosen et al 2021b) and nutrient availability . We approximate the rOC/bulk TOC ratios (b OC ) of each catchment based on its land cover, considering different b OC values for different land covers: where f is the fraction of the catchment covered by the subscripted land cover. b OC values for different land covers are based on Stutter et al (2018) (table S2). The distribution of b OC ranges from 10% to 20% with a median of 16% (figure S1). While Stutter et al (2018) refer to dissolved OC (DOC), we apply their rDOC/bulk DOC ratio to the more available parameter TOC as both are strongly correlated (figure S2), and 86% of the TOC is dissolved. Furthermore, DIN and SRP do not include all biologically reactive fractions of N and P (Graeber et al 2021), leading to potential under-estimations of reactive N and P, which we acknowledge and discuss in section 3.2 (also figure S3). The catchments used in this study were chosen to allow the analysis of average intraannual behavior, excluding inter-annual variabilities such as trends or extreme events (see supplementary information, section S1 for the criteria).
In short, we selected (near stationary) time series of at least seven years with concurrently measured TOC, DIN, and SRP concentrations between 2000 and 2015. A total of 444 of these selected catchments have delineated boundaries with available catchment characteristics (Ebeling et al 2022). We used the median b OC (16%) for catchments without available characteristics (n = 130). The studied catchments range in their drainage area from 3 to 123 000 km 2 (mean = 3741 km 2 ). While we use DIN for our analyses, in 80% of the catchments, the average sampled DIN is dominated (>90%) by NO 3 -N ( figure S4).

Derivation and visualization of C:N:P ratios
We calculated the long-term median and monthly median concentrations (figure S5) and the coefficient of variation (CV) of the concentration time series for each catchment and compound. The rOC:rN:rP ratios (as visualized in the ternary plots) are calculated relative to the Redfield ratio (C:N:P = 106:16:1, (Redfield 1934) as follows: with DIN, SRP, and TOC as the observed concentrations (mmol l −1 ) in a given sample. b P and b N describe the nutrients bioavailability. For b N and b P we assume 100%, but also tested values larger than 100%, considering that SRP and DIN are only a part of the reactive N and P pools (figure S3, section S4). The molar rOC:rN:rP ratio of a given sample matching the Redfield ratio is located in the center of the ternary plot (black circle, figure 1(a)) as the Redfield normalized concentrations of all nutrients (rOC RFC , rN RFC and rP RFC ) are equal to 33.3%. If a sample has more rN relative to rOC and rP, rN RFC would be larger than 33.3%, and rP RFC and rOC RFC would be lower. Furthermore, the ternary plot does not only allow visualizing C:N:P ratios, but also their comparison to ecologically relevant ratios, such as the C:N ratio below which denitrification is carbon limited (C:N = 1) (Taylor and Townsend 2010) or N or P depletion for lake and marine phytoplankton biomass production (Guildford and Hecky (2000), figure 1(b)).
We selected the Redfield ratio as a well-known biologically relevant ratio corresponding to the mean nutrient ratio in marine phytoplankton (Redfield 1934). Similar global ratios also have been reported for benthic algae (Hillebrand and Sommer 1999) and bacterial biomass in lakes and soils (Cleveland and Liptzin 2007), indicating that stoichiometric imbalances found in relationship to the Redfield ratio are relevant at the ecosystem-or catchment scale.

Classification of catchment stoichiometry
2.3.1. Classification of the median reactive C:N:P ratios To assess the stoichiometric balance, we classified each catchment according to its median reactive C:N:P ratio. We call a catchment 'depleted' of a nutrient if its Redfield normalized concentration is below 20% and further allow for depletion by two elements (co-depletion) and a no-depletion case (Jarvie et al 2018). Using this definition, we split the ternary diagram into seven classes ( figure 1(a)). As the 20% threshold limit chosen here is moderately high, and the precise physical meaning of this limit requires further investigation, we also investigate the spatial patterns of absolute RFC values (figure S6).

Classification of the intra-annual reactive C:N:P variability
To assess the temporal variability of the abovementioned stoichiometric balance, we developed the dist metric, which quantifies the total distance between monthly reactive C:N:P ratios in the ternary diagram (i.e. the circumference of the 'loop' , figure 1(b)). We calculate the dist metric as follows where x i , y i are the Cartesian coordinates (for projection, see equations (S1) and (S2)) of the Redfieldnormalized rOC, rN, rP concentrations of the month i. The maximal distance between two points in the ternary diagram is 100, meaning that the maximal dist value is 1100 (for more details, see section S3).

Linkage to catchment characteristics
To link the observed reactive C:N:P patterns to the biogeochemical cycles of C, N, and P, we use catchment characteristics provided by Ebeling et al (2022). We focus on a core set of characteristics, which they have shown to capture the main sources and sinks of rOC, rN, and rP (Ebeling et al 2021b). Those are the topographic wetness index (TWI-source of OC), P emissions from WWTPs (P wwtp, source of rP), the fraction of agricultural land cover (f agric -source of rN), and the fraction of sedimentary aquifer material (f sedim , sink of rN via high potential for denitrification in the aquifer). To investigate the overall strength of monotonic correlations between catchment characteristics, nutrient concentrations, RFC concentrations, and dist, we use Spearman's rank correlation coefficient ρ implemented in the Python package SciPy (Virtanen et al 2020).

Spatial variability of median reactive C:N:P ratios
The vast majority of the studied catchments (94%, figure 2(b)) exhibited rOC depletion (19%), rP depletion (6%) or co-depletion of rOC and rP (69%). A minority (3%) of the catchments revealed rN depletion or no depletion. An rN & rP co-depletion was not found in any catchment of the study area. Depletion of rN occurred in one catchment, implying an overall imbalance towards excess rN. This was further supported by the fact that most catchments had rN RFC values >40% (figure 2(e)). Here, we only include DIN and SRP as rN and rP due to the lack of monitoring data for organic N and P fractions. With this, we ignore the potential contribution of reactive dissolved organic N and P (Graeber et al 2021). However, our conclusions on the dominance of rOC, rP, and co-depletion of rOC and rP do not change, even in a scenario with high concentrations of reactive dissolved organic N and P (figure S3 for details). The spatial patterns of the depletion classes suggested that catchment landscape features exert a first-order control on average reactive C:N:P ratios ( figure 2(a)). While rOC-depleted catchments are grouped in South Western Germany, non-carbondepleted catchments (rN, rP, rN & rP, or no depletion) are grouped in North Eastern Germany. Other regions are mostly covered by rP & rOC co-depleted catchments. We found that the catchment characteristics which dominantly control mean nutrient concentrations (Ebeling et al 2021b) are primarily responsible for the spatial distribution of the depletion classes. We linked a high topographical wetness index (TWI, 90th percentile, Musolff et al (2018))-catchments with flat topography and high upstream contributing area-to higher rOC RFC values (figure 2(d), table S2: Spearman's ρ = 0.58). High rOC concentrations were also found to be correlated to the TWI in previous studies (Musolff et al 2018, Ebeling et al 2021b, which were interpreted as an indicator for near-stream rOC sources, such as well-connected riparian wetlands. Note that catchments with high rOC RFC are rN and rP depleted and cluster in Eastern Germany around Berlin (see also figures S6(a)-(c)), an area rich in wetlands (figure S7(a)) due to the existence of a primal valley after the last ice age (Graeber et al 2012(Graeber et al , 2015 However, many catchments with high TWIs are still relatively depleted in rOC. This is likely since depletion is a relative term and more potent sources of rN from agriculture can obfuscate the signal from rOC sources ( figure 2(d)). Additionally, the prediction of riparian For rN, previous studies suggest that both the agricultural input and the subsurface denitrification capability of a catchment exert first-order control on average concentrations (Wherry et al 2021, Ebeling et al 2021b. Apart from the nearsurface denitrification capabilities, the composition of catchment aquifers (either sedimentary or non-sedimentary) affects their subsurface denitrification capability, with sedimentary aquifers having much more favorable conditions (Knoll et al 2020). The rN RFC in sedimentary and non-sedimentary aquifer catchments show a positive relationship with agricultural land cover, but the sedimentary aquifer catchments often show lower rN RFC values with similar proportions of agricultural land cover. This confirms the previously mentioned two dominant interacting controls. Furthermore, rN RFC in non-sedimentary catchments is mostly >50%, even at low agricultural land cover shares (figure 2(e), white data points). However, one must consider that RFC values are normalized concentrations and that high rN RFC does not necessarily coincide with high (absolute) rN concentrations (figures S6(h)-(j)) but can also be caused by low rOC and rP concentrations.
The rP RFC values show a moderate positive relationship (ρ = 0.43, table S9) with estimated P emissions from WWTPs ( figure 2(g)). This illustrates that the fraction of P exports stemming from point sources is not necessarily dominant (Westphal et al 2019) and that a variety of other biogeochemical processes (e.g. sorption and desorption, release, assimilation) or diffuse source P input can control average P export from catchments (Withers and Jarvie 2008).

Intra-annual variability of reactive C:N:P ratios
The reactive C:N:P ratios showed a marked intra-annual variability. This variability is highly heterogeneous among the catchments, with some being almost static and some covering large parts of the ternary area and switching between different depletion classes (figures 3(a) and (b)).

Intra-annual variability of depletion classes
Considering annual median values, rP & rOC codepletion (69%) and rOC-depletion (19%) are the dominant depletion classes demonstrating both the temporal and spatial stability of the imbalance towards rN across the study area ( figure 3(b)). However, from spring (March, April, May) to summer (June, July, August), rP & rOC co-depletion decreases while rOC depletion increases. The nodepletion class also peaks during summer. This process is reversed during the fall. Depletion and codepletion classes containing rN are more dominant during summer and fall (September, October, and November), but make up only a small fraction (max. 2% during August). In comparison, the fraction of rP-depleted catchments stays constant throughout the year and rOC depletion peaks during July (35%).

Absolute intra-annual variability of reactive C:N:P ratios
To consider intra-annual movement both across and inside the single depletion classes, we use the dist metric (equation (5)), which quantifies intraannual reactive C:N:P variability in each catchment ( figure 4(a)). We refer to catchments with low dist values as stoichio-static and those with higher values as stoichio-dynamic ( figure 4(a)). We classify all sites with a dist value <33 (total intra-annual movement of reactive C:N:P ratios is less than one-third of a single edge length of 100 in the ternary diagram) as stoichio-static. Our results show that this is the case for 40% (n = 231) of all investigated catchments.
Stoichio-static catchments tend to have higher rN median concentrations, lower rN CVs, and low rOC medians. Stoichio-dynamic behavior, in contrast, can be linked to high rN and rP CVs ( figure 4(b)). For the dist value, rN CV and median concentrations show the strongest monotonous relationships (ρ = 0.57 and −0.48). We interpret this as follows: As rN is, according to the Redfield ratio, the overly abundant nutrient, its variability controls the rOC:rN:rP ratios. With rN inputs exceeding the plant and microbial uptake and the catchment's retention capabilities for decades, rN can accumulate in different parts of the catchment, which may lead to high in-stream concentrations during the entire year and over the long term , Ebeling et al 2021a, Winter et al 2022. Year-round high rN concentrations can in turn overrule intra-annual variability of rOC and rP, leading to low variability of rOC:rN:rP ratios (low dist values). Previous studies have linked the intra-annual variability of in-stream nitrate concentrations to denitrification in the subsurface or riparian zones (Zhi and Li 2020, Ebeling et al 2021b). Riparian zone denitrification would explain the positive relationship between dist and median rOC concentrations as riparian zones are well suited for supplying OC to streams (Laudon et al 2012). This is further supported by the spatial distribution of dist which is high in North-Eastern Germany (figure S11), which in turn is characterized by a high abundance of wetlands (Graeber et al 2012). Algae in stream and water bodies are also known for retaining significant amounts of rN during summer (Ritz andFischer 2019, Yang et al 2021) and increasing TOC concentrations (Hardenbicker et al 2016). This also potentially explains the inverted relationships between the CVs of rOC and rN with dist, as depicted in figure 4(b). However, CV of rP is also positively correlated with dist, but weaker (ρ CVrN vs dist = 0.57 versus ρ CVrP vs dist = 0.38), probably due to most catchments having lower rP concentrations compared to rN and rOC.
While we noticed a systematic relationship between median concentration levels and dist for rOC and rN, this is not the case for rP (figure 4(c)). A fundamental limitation of this study was the uncertainty regarding the exact amount of bioavailable nutrients for the investigated catchments. However, we found that different parameterizations of bOC do not significantly change the picture of the overall imbalance of catchment exports towards rN (figure S8). We likely underestimated the reactive N and P fractions but cannot assess how much this would drive the results towards more or fewer N imbalances. However, even if we assume rP is 150% of the measured SRP concentrations, the imbalance toward high rN persists ( figure S3). Furthermore, the Redfield ratio we used to normalize our concentration data (equations (2)-(4)) does not represent bacterial stoichiometry. However, using a ratio specifically for bacteria did not change the overall results (figure S9).

Implications for biogeochemical processing
In this study, we found a prevalent imbalance of catchment nutrient export ratios towards rN excess and rOC and rP depletion relative to the Redfield ratio, which persists throughout Germany (figures 2 and 3). Experimental studies show that the imbalance between rOC & rP depletion and rN excess reduces the assimilation of N into stream microbial biomass (Graeber et al 2021), and rOC depletion may limit hyporheic nitrate and phosphate (Stutter et al 2020, Sunjidmaa et al 2022 and whole-stream nitrate uptake (Wymore et al 2016). Furthermore, our analysis shows that in most catchments (78%), the rOC: rN ratios are less than 1, implying the C limitation of denitrification (Hansen et al 2016). A considerable percentage of catchments (19%) is characterized by a rOC: rN ratio close (i.e. ∓0.5) to the stoichiometry of denitrification (molar DOC: nitrate-N = 1, figures 1, 3 and S10 Taylor andTownsend 2010, Hansen et al 2016). Only 22% of catchments (figure S10) have an rOC: rN ratio greater than 1 implying N limitation. Regarding the diagnosis of nutrient limitation, one should consider that our results are based on calculations that can diverge from other methods, such as bio-assays (Cook et al 2019). Concerning the highly N and P polluted investigated streams and rivers, our results indicate that human-induced imbalances of C:N:P ratios likely decrease their capability to process and retain the excess rN, mainly in the form of nitrate-N. For inland waters and downstream marine ecosystems, insufficient natural OC sources (e.g. due to a decrease in wetlands as a consequence of drainage) and too much fertilization along the river networks likely results in increased input of rN (Taylor and Townsend 2010, Hansen et al 2016, Stutter et al 2018. In the seasonal C:N:P movement, we detected a substantial shift from higher rN: rP ratios in winter to lower rN: rP ratios in summer across the study area (figure 3). For downstream situated rivers, lakes, and marine waters, the load and the ratio of the rN and rP delivered from catchments may control lake eutrophication-the nutrient-induced increase in phytoplankton productivity-which is linked to anoxia, toxic algae blooms, and other deleterious effects (Paerl et al 2016). Moreover, Guildford and Hecky (2000) found N control of eutrophication in the lake and marine waters only at molar N:P ratios below approximately 20, which, even in summer, is only reached in few catchments in our study (<2% of the long-term means, <2% of the summer means, see also figure 3). In contrast, the majority (53%) of catchments export rN: rP ratios >50 throughout all seasons, which may result in severe P limitation of downstream phytoplankton production (Guildford and Hecky 2000). In lakes, the competition for nutrients by heterotrophs and autotrophs has also been shown to be controlled by the availability of rOC due to its dual role as a heterotrophic food source and its brownification effects (Carpenter et al 1998, Hanson et al 2003, where the availability of rOC had even more significant effects on competition than substantial increases in temperature (Feuchtmayr et al 2019). Here, rOC depletion may have shifted German lakes towards dominance of biomass production by autotrophs (phytoplankton) and reduced the importance of microbial heterotrophs (e.g. bacterioplankton). Similarly, the rOC depletion in German catchments results in a shift toward higher autotrophic, algal biomass production and higher production to respiration ratios in streams (Oviedo-Vargas et al 2013). In consequence C:N:Pinduced shifts in ecosystem metabolism could have cascading effects on the aquatic food webs and the role of German inland waters in the global carbon cycle.

Conclusion
This study presents the first large-scale, systematic assessment of reactive C:N:P ratios across river networks. We find that reactive nutrient exports of catchments are imbalanced towards excess N compared to well-known microbial stoichiometric requirements. This causes rOC and rP depletion conditions to prevail across time and space. The fact that not only agricultural catchments show this pattern illustrates the ubiquity of excess rN in anthropogenically influenced landscapes. In contrast to our expectation, we show that not all catchments show an evident intraannual variability in reactive C:N:P ratios, but some are stoichio-static. We link stoichio-static behavior to high nitrate concentrations with little variability throughout the year, which may mask changes in nutrient ratios that could have been caused by the variability of reactive organic C and reactive P concentrations. Our findings reveal the severe extent of the reactive C:N:P ratios in German rivers influenced by agricultural and wastewater effluents. Those effects on the reactive C:N:P ratios likely have strong consequences for (i) catchment nutrient retention due to the stoichiometry of the key biological processes and (ii) for alterations in the integrity and functioning of rivers, lakes, and marine ecosystems. However, the ecological effects of the human-induced changes in catchment-scale stoichiometry require further assessments, especially studies on the combined macronutrient effects on ecological status and biological nutrient processing, which are scarce for all aquatic ecosystems. Our results also show the necessity to include all three macronutrients in monitoring efforts and the need to consider N, P, and C in a more holistic catchment and aquatic ecosystem management.

Data availability statement
The data that support the findings of this study are openly available at the following URL/DOI: https://doi.org/10.4211/hs.0ec5f43e43c349ff818a8d5 7699c0fe1.

Acknowledgments
This study has been funded by the Helmholtz-International Research School 'Trajectories towards Water Security' (TRACER,, and by the Integration Platform 'Freshwater resources' (4th period of Program-oriented Funding, Helmholtz Association of German Research Centres)." PE was funded by the Deutsche Forschungsgemeinschaft-DFG, the Grant Number DFG 392886738. Financial supports for SY were provided by the Helmholtz Climate Initiative Project (www.helmholtz-klima.de) and by the Center for Advanced Systems Understanding, Helmholtz Zentrum Dresden-Rossendorf.