The CO2‐equivalent balance of freshwater ecosystems is non‐linearly related to productivity

Eutrophication of fresh waters results in increased CO2 uptake by primary production, but at the same time increased emissions of CH4 to the atmosphere. Given the contrasting effects of CO2 uptake and CH4 release, the net effect of eutrophication on the CO2‐equivalent balance of fresh waters is not clear. We measured carbon fluxes (CO2 and CH4 diffusion, CH4 ebullition) and CH4 oxidation in 20 freshwater mesocosms with 10 different nutrient concentrations (total phosphorus range: mesotrophic 39 µg/L until hypereutrophic 939 µg/L) and planktivorous fish in half of them. We found that the CO2‐equivalent balance had a U‐shaped relationship with productivity, up to a threshold in hypereutrophic systems. CO2‐equivalent sinks were confined to a narrow range of net ecosystem production (NEP) between 5 and 19 mmol O2 m−3 day−1. Our findings indicate that eutrophication can shift fresh waters from sources to sinks of CO2‐equivalents due to enhanced CO2 uptake, but continued eutrophication enhances CH4 emission and transforms freshwater ecosystems to net sources of CO2‐equivalents to the atmosphere. Nutrient enrichment but also planktivorous fish presence increased productivity, thereby regulating the resulting CO2‐equivalent balance. Increasing planktivorous fish abundance, often concomitant with eutrophication, will consequently likely affect the CO2‐equivalent balance of fresh waters.

However, eutrophication can change the CO 2 -equivalent balance by methanogenic microbes in the sediments transforming a fraction of the CO 2 fixed by autochthonous primary production into CH 4 (Grasset et al., 2018;West, Coloso, & Jones, 2012).
Eutrophication consequently has two opposite effects on the CO 2 -equivalent fluxes, inducing both increased CO 2 uptake from the atmosphere, but also enhanced CH 4 release to the atmosphere (DelSontro, Beaulieu, & Downing, 2018). However, the effect of productivity on the overall CO 2 -equivalent balance of freshwater ecosystems is rarely considered. The only study published to date reports a negative effect of productivity on the CO 2 -equivalent emission of shallow-water mesocosms (Davidson et al., 2015), but did not measure CH 4 emission via bubbles (ebullition), which typically is a major CH 4 emission pathway Davidson et al., 2018), and was further comprised of only two levels of productivity. This study could as such not answer the question of how far a shift in ecosystem productivity, which is the typical situation in natural systems (Rineau et al., 2019), may affect the CO 2 -equivalent balance.
Autochthonous primary production in fresh waters is not only controlled by inorganic nutrient supply but also by food web structure (Carpenter et al., 2001). Animals often have indirect effects on biogeochemical processes, sometimes with a large impact on GHG emissions (Schmitz et al., 2014). For instance, increasing planktivorous fish abundance, often concomitant to eutrophication (Jeppesen, Peder Jensen, SØndergaard, Lauridsen, & Landkildehus, 2000;Moss et al., 2011), can increase primary production and thus CO 2 uptake by photosynthesis by reducing grazing pressure from zooplankton (Atwood et al., 2013;Cole et al., 2000;Schindler et al., 1997). On the other hand, fish may reduce CH 4 emission from fresh waters through top-down control of zooplankton that graze on CH 4 oxidizers (Devlin, Saarenheimo, Syväranta, & Jones, 2015). The overall effect of food web structure on the CO 2 -equivalent balance of freshwater ecosystems has not yet been investigated.
Only a fraction of the CH 4 that is produced in anoxic sediments reaches the atmosphere, primarily due to aerobic CH 4 oxidation by CH 4 -oxidizing bacteria. Between 45% and 100% of the produced CH 4 in lake sediments could be lost by oxidation (Bastviken, 2009), mainly during CH 4 transport by diffusion across the oxic-anoxic interface in the sediment or in the water column. Recent studies show that the responses to drivers such as temperature and nutrients are different for CH 4 production and CH 4 oxidation (Fuchs, Lyautey, Montuelle, & Casper, 2016;Sepulveda-Jauregui et al., 2018). This implies that the balance between CH 4 oxidized and CH 4 produced, and thus the proportion of the produced CH 4 that is emitted by diffusion to the atmosphere might change along environmental and climatic gradients. Accordingly, the CO 2 -equivalent balance of fresh waters may vary in complex ways across productivity gradients in response to the combined effects of CO 2 fixation and mineralization, food web effects, and production as well as oxidation of CH 4 .
To determine how the CO 2 -equivalent balance depends on productivity, we set up a total of 20 mesocosms, two at each of the 10 nutrient levels (total phosphorus [TP] from 39 to 939 µg/L), and one at each nutrient level was stocked with fish. We hypothesized that CH 4 emission will increase exponentially and CO 2 will decrease linearly with productivity, such that the CO 2 -equivalent emission will have a minimum along a productivity gradient. In addition, we hypothesized that the presence of fish reduces emissions of CO 2 and CH 4 due to reduction of zooplankton grazing on phytoplankton and CH 4 oxidizers.

| Mesocosm setup
Twenty white opaque high density polyethylene mesocosms of 2 m height and 1 m diameter were deployed in the mesotrophic hard water µm mesh (to remove large plankton and algal colonies), and about 80 L of surface sediment sampled from Erken at 15 m depth 1 week before. TP and total nitrogen (TN) concentration were set to 10 different levels, and of the two mesocosms receiving the same nutrient addition, one mesocosm was stocked with two juvenile crucian carp (Carassius carassius) individuals, which reflects the crucian carp density of natural populations (Holopainen & Pitkänen, 1985). The diet of juvenile crucian carp consists of zooplankton and Chrionomidae (Penttinen & Holopainen, 1992), and they were therefore expected to exert the hypothesized top-down control on zooplankton abundance and grazing. The experiment was run for 1 year and 3 months to allow for new detritus to deposit on the sediment and thus affect methanogenesis.
Zooplankton inoculates (approximately 13 individuals L −1 ), obtained from tows with a 100 µm plankton net were added to the mesocosms.
Fish were added to 10 of the mesocosms during spring and summer (July-October 2017 and May-September 2018) and were removed during winter by hand-netting in order to avoid death because of low oxygen during ice cover. The mesocosms were shaded with black plastic sheets placed on the outside of walls to limit periphyton growth.
In order to allow for all autochthonous organic carbon to reach the sediment and contribute to methanogenesis, the mesocosm walls were scraped every 4 weeks during the ice-free period to detach periphyton.

| Nutrient gradient establishment
A gradient of TP concentration in the water column with 10 different levels was set: background TP concentration of lake Erken (no addition), 40,60,80,100,150,200,400,600, and 1,000 µg/L, spanning from mesotrophic to hypereutrophic. Each target concentration was set for two mesocosms, and one mesocosm was stocked with fish during the ice-free period, while the other mesocosm was without fish. TN concentrations were calculated to obtain an N/P atomic ratio of 16, allowing other algae than N-fixing bacteria to colonize the mesocosms (TN target concentration between 0.45 and 11.29 mg/L). Monopotassium phosphate (KH 2 PO 4 ) and ammonium nitrate (NH 4 NO 3 ) were added to adjust to the TP and TN target concentrations on the first day, every 2 weeks during the ice-free period, and every 4 weeks during the icecovered period. No nutrients were added in the lowest nutrient treatment to keep the background concentration. Over summer 2018, the mean TP values varied between 39 ± 35 (SD) µg/L for the no addition treatments and 939 ± 381 (SD) µg/L for the highest nutrient treatments. An extremely high TP value of 1,000 µg/L can be encountered in fresh waters and it is consequently appropriate to include it in our eutrophication gradient to cover the most extreme cases of eutrophication (DelSontro et al., 2018).

| Water analyses
Water samples were taken from each mesocosm every 2 weeks during the ice-free period, every 4 weeks otherwise, for nutrient and dissolved organic carbon (DOC) analyses. Water was collected with a 1 m long plastic tube to get integrative samples of the water column. TP concentration was measured using the ammonium molyb- with a Shimadzu TOC-L TNM-L analyzer. Turbidity, pH, temperature, dissolved oxygen, and Chlorophyll a (Chla), were conjointly measured with a multiprobe (EXO2 Multiparameter Sonde, YSI) at 50, 100 and 125 cm below the water surface. In addition, dissolved oxygen was automatically measured every 10 min with oxygen probes (mini-DO2T PME) at a depth of 25-30 cm below water surface.

| Zooplankton sampling
Zooplankton samples were taken from the integrated water sample used for the water analyses. Five liters of water was filtered through 55 µm and zooplankton was immediately preserved with Lugol's solution and later analyzed using an inverted microscope (

| Primary producer biomass
Phytoplankton biomass was calculated from the Chla (µg/L) measurements in the water column by assuming a C:Chla ratio of 40 (g:g; Lorenzen, 1968). Periphyton biomass was measured using plastic strips, made of the same material as the mesocosms, that were attached to the walls of the mesocosms and reached the full depth down to the sediment. The strips were scraped every 4 weeks during the ice-free period, and biomass was upscaled from the width of the strip (7 cm) to the full diameter of the mesocosm. Samples were dried at 50-60°C, grinded manually into a fine powder with a mortar and a pestle, acidified with HCl 5% and encapsulated in tin capsules for total organic carbon and nitrogen analysis with a C/N elemental analyzer (Costech Analytical Technologies Inc.). The total primary producer biomass in the mesocosms (g C mesocosm −1 ) was calculated by summing periphyton and phytoplankton biomass. Sediment was sometimes also visibly present on the periphyton strips and thus increased the overall estimation of periphyton C content. However, this contamination was likely to be similar among treatments and negligible for high nutrient treatments since sediment C content was low (7% wt, data not shown) in comparison to periphyton C content (algal C content is typically around 20%-50% wt).

| Net ecosystem production
Dissolved oxygen automatic measurements at 10 min intervals were used to estimate net ecosystem production (NEP in mg O 2 L −1 hr −1 ) according to Cole et al. (2000) as follows: with DO the dissolved O 2 concentration in mg/L and air water exchange in mg O 2 L −1 hr −1 : z the mixing depth of the system was assumed to be the total water depth (1.65 m) as no stratification was observed in the mesocosms.
DO sat in mg/L was defined according to Benson and Krause Jr. (1984): with T in Kelvin. with Sc the Schmidt number of O 2 according to Wanninkhof (1992).
We chose n = 1/2 since the water surface in the mesocosms was often not smooth.
NEP is expressed in mmol O 2 m −3 day −1 in the rest of the manuscript for comparisons with literature.

| CO 2 and CH 4 diffusive fluxes
CH 4 and CO 2 concentrations in the water were measured every 2 weeks during the ice-free period, and every 4 weeks during ice cover, with the headspace method (Cole & Caraco, 1998), by sampling 30 ml of surface water in each mesocosm and equilibrating 1 min with 10 ml of atmospheric air. The gas samples were then transferred to another syringe and analyzed within 24 hr with a gas chromatograph equipped with a flame ionization detector (Agilent Technologies, 7890 A GC system). CO 2 and CH 4 concentrations were calculated from their concentrations in the headspace, the volume of water, and the specific gas solubility of CO 2 (Weiss, 1974) and CH 4 (Yamamoto, Alcauskas, & Crozier, 1976). The diffusive fluxes of CO 2 and CH 4 from the water to the atmosphere were calculated according to Cole and Caraco (1998): where F is the flux in mmol m −2 day −1 , K T is the gas transfer velocity in m/day calculated according to Equation (4), C is the gas concentration in µmol/L, P sat is the atmospheric gas concentration in µatm and K H is Henry's constant in mol L −1 atm −1 .
Daily CO 2 and CH 4 fluxes over summer 2018 were estimated from single daytime measurements in water sampled between 9 a.m. and 11 a.m. Over summer 2017, however, CO 2 concentration was also measured at night (between 3 a.m. and 5 a.m.) at three dates (August, September and October), and the nighttime concentrations of CO 2 were found to be very close to the daytime concentrations measured between 9 a.m. and 11 a.m. (for the three dates, average of the slope = 1.1 and average of the R 2 = .86, data not shown). In May, June and July, the nights are very short (<6 hr) and not completely dark at this latitude, which probably limits the daily variation in CO 2 . We consequently assumed that daily variation in CO 2 concentration was low over summer and that a single CO 2 concentration measurement can be representative of its daily concentration.

| CH 4 ebullitive flux
Bubble traps consisting of a 50 ml syringe standing just below the water surface and attached to 20 cm wide inverted funnel (Davidson et al., 2018;Huttunen, Lappalainen, Saarijärvi, Väisänen, & Martikainen, 2001) were used to collect CH 4 bubbles. The transparent syringes were covered by an opaque light-grey cap to prevent biofilm growth on the surface of the syringe and were cleaned at each sampling. The bubble traps remained permanently in the mesocosms and were sampled every 2 weeks during the ice-free period, every 4 weeks otherwise, when gas was visibly accumulating in the bubble traps. The gas was transferred to a syringe and analyzed within 24 hr with the gas chromatograph. The ebullitive flux of CH 4 (in mmol m −2 day −1 ) was calculated as the amount of CH 4 (mmol) divided by the surface of the funnel in m 2 and the number of days between two consecutive measurements. The volume of the trapped gas exceeded the volume of the syringe at one occasion for mesocosm I with fish (13/06/18) and mesocosm I without fish (14/08/18; A being the lowest nutrient treatment and J the highest), resulting in an underestimation of ebullition flux for these two treatments.

| CH 4 oxidation
Two different methods were used to quantify CH 4 oxidation, the fraction of the CH 4 produced in sediment that was oxidized in situ was calculated from δ 13 C-CH 4 measurements, and the potential CH 4 oxidation rate was calculated from aerobic incubation of the mesocosm water. Details on the potential CH 4 oxidation rates are given in the supplementary material.
The fraction of CH 4 oxidized in situ was calculated from δ 13 C of CH 4 in mesocosm surface water and δ 13 C of anaerobically produced CH 4 in a sediment incubation. δ 13 C-CH 4 in surface water samples was measured at two dates (13/08/18 and 11/09/18) in each mesocosm. CH 4 gas samples were obtained with the headspace method by equilibrating 90 ml of surface water with 20 ml of N 2 in 120 ml syringes for 2 min. The gas samples were stored in , the fractionation factor, is assumed to be 1.02 (Bastviken et al., 2002), δ 13 CH 4, oxidized is the δ 13 C of CH 4 in surface water that has undergone oxidation through the sediment and water column, and δ 13 CH 4, newly formed the δ 13 C of CH 4 before oxidation. Some studies use δ 13 C-CH 4 measurements from gas bubbles or bottom waters to estimate δ 13 CH 4, newly formed (Barbosa et al., 2018;Thottathil, Reis, Giorgio, & Prairie, 2018) but it is then not possible to exclude that oxidation has already occurred in the sediment or during gas transport. We consequently used δ 13 C of CH 4 produced during an anoxic sediment incubation as δ 13 CH 4, newly formed (Zhang, Yu, Fan, Ma, & Xu, 2016) to calculate the fraction of anaerobically produced CH 4 in the sediment that is oxidized. In an open system at steady state, CH 4 production is supposed constant and CH 4 as well as the products of CH 4 oxidation can leave freely, while in closed systems, CH 4 and oxidation products accumulate (Barbosa et al., 2018;Bastviken et al., 2002). Values often >1 were also reported in floodplains and lakes (Barbosa et al., 2018;Bastviken et al., 2002;Thottathil et al., 2018) suggesting that the assumptions for open systems might not always be valid in natural systems. We consequently chose to use the fraction of CH 4 oxidized in closed systems as a conservative measurement of CH 4 oxidation in the rest of the manuscript.

| Statistical analyses
The effects of TP concentration and fish presence on productivity (NEP) and C fluxes (total CH 4 and CO 2 emissions) and the fraction of CH 4 oxidized were tested with analysis of covariance (lm function with fish presence as a categorical variable). The relationships between C fluxes (total CH 4 and CO 2 emissions, CO 2 -equivalent balance), the fraction of CH 4 oxidized, potential CH 4 oxidation rate, productivity (NEP), primary producer biomass and zooplankton biomass were tested with linear first-order regressions and polynomial models (lm function). All models were based on the averages of the C fluxes, NEP and primary producer biomass over summer 2018 for each mesocosm (n = 20) because averages were considered more robust and integrative of the whole period, and indicative of the overall treatment effects regardless of any temporal variability. Furthermore, as we did not see any consistent temporal patterns for C fluxes and NEP ( Figures S3, S4 and S6), we preferred to choose the simpler models with averages rather than the more complex mixed-effect models that also show a positive effect of productivity on CH 4 emissions and a negative effect on CO 2 emissions (Table S1). All variables except the fraction of CH 4 oxidized and NEP were log-transformed (natural logarithm) before modeling to normalize distributions and decrease the effect of extreme values. Before log-transformation, a constant was added to CO 2 emissions, CO 2 -equivalent balance (180 mg CO 2 m −2 day −1 ) and to potential CH 4 oxidation rates (1 mg L −1 day −1 ) to make all values positive. For CO 2 emissions and CO 2 -equivalent balance, the minimum values were −175 and −168 mg CO 2 m −2 day −1 , respectively, the addition of 180 was chosen to give the best data normalization (according to Shapiro tests and histogram plots of the data). The accuracy of the models was assessed by visualizing the residuals and the observed against predicted data. When comparing several polynomial models, the best model was chosen according to the Akaike information criterion. Thresholds of the polynomial model between CO 2 -equivalent balance and NEP were determined by the "optim" function that returns parameters that minimize a function.
All statistical analyses were performed with the R software (R Core Team, 2016).

| Relationships between C fluxes, productivity and primary producer biomass
As expected, total CH 4 emissions (diffusive + ebullitive) increased with productivity while CO 2 emissions decreased ( Figure 1; Table 1).
until a threshold at high productivity (NEP = 32 mmol O 2 m −3 day −1 ) after which the CO 2 -equivalent balance decreased again with increasing productivity (Figure 1; Table 1). Eight out of nine mesocosms having NEP values between 5 and 18 mmol O 2 m −3 day −1 acted as CO 2 -equivalent sinks (CO 2 -equivalent balance <0) while all mesocosms with higher or lower productivity acted as CO 2 -equivalent sources (Figure 1). In accordance with these observations, a polynomial model between the CO 2 -equivalent balance and productivity F I G U R E 1 Relationships between total CH 4 emissions (a), CO 2 emissions (b) and the CO 2 -equivalent balance (c) in mg CO 2 m −2 day −1 and productivity (net ecosystem production). 180 mg CO 2 m −2 day −1 is added before log-transformation to CO 2 emissions and the CO 2 -equivalent balance to make values strictly positive. See Table 1 for the statistics of the linear and polynomial regressions (black lines). The red points refer to the treatments with fish addition (n = 10) and the green points correspond to the treatments without fish (n = 10). Error bars represent standard errors. The dotted line corresponds to C fluxes = 0  ), and C fluxes. All fluxes are logged (natural logarithm) and a constant is added before log-transformation to make CO 2 emissions and CO 2 -equivalent balance positive. All models are performed on averaged values over summer 2018 (n = 20, average for 9 dates for C fluxes and 117 dates for NEP). When choosing between different polynomial models, the best model was selected according to the lowest Akaike information criterion.

TA B L E 1
First-order and polynomial regressions between C fluxes (total CH 4 emissions, CO 2 emissions and the CO 2equivalent balance in mg CO 2 m −2 day −1 ), productivity (NEP in mmol O 2 m −3 day −1 ), and TP (µg/L) with presence of fish as a categorical variable identified two thresholds at NEP = 5 and 19 mmol O 2 m −3 day −1 at which the mesocosms shifted from source to sink and then back again from sink to source ( Figure 1; Table 1).
Productivity was strongly correlated to primary producer biomass ( Figure 2; Table S2) and primary producer biomass correlated in similar ways as productivity to total CH 4 and CO 2 emissions and to the CO 2 -equivalent balance ( Figure S7; Table S3). In the highest productivity treatments, phytoplankton constituted most of the primary producer biomass, and in the other treatments periphyton often dominated ( Figure S8).

| Food web structure and nutrient effect on productivity and C fluxes
Both nutrient concentrations and the presence of fish had a positive effect on primary productivity, thereby regulating CO 2 and CH 4 emissions and the resulting CO 2 -equivalent balance ( Figure 2; Table S2). The presence of fish induced a trophic cascade and increased productivity through a decrease in zooplankton abundance (Atwood et al., 2013;Schindler et al., 1997;Schmitz et al., 2014; Figure 2; Table S2). Nutrient concentrations and the presence of fish had a positive effect on CH 4 emissions and a negative effect on CO 2 emissions (Table 1; Figure S9). The direct effect of nutrients on CO 2 emissions was however not significant probably because two mesocosms (J and H) with high nutrient concentrations and low productivity had sometimes a high respiration ( Figure S9; Figure S4).

| Relationship between CH 4 oxidation, productivity and food web structure
The fraction of CH 4 that was oxidized increased with productivity ( Figure 3) and primary producer biomass, and decreased with Copepoda biomass ( Figure S10; Table S4). However, when CH 4 oxidation was correlated to both fish presence and nutrient concentration, the effect of fish was not significant, suggesting that the presence of fish did not directly enhance CH 4 oxidation (Table S4).

| D ISCUSS I ON
Our study is the first to report a non-linear relationship between freshwater productivity (or primary producer biomass) and the net ecosystem CO 2 -equivalent balance. This novel result means that eutrophic freshwater ecosystems have the potential to act as CO 2 -equivalent sinks, but these sinks are fragile since a small increase or decrease of productivity can turn them again into a for which the studied freshwater ecosystems shifted from CO 2equivalent sources to sinks and then returned to being CO 2equivalent sources. In other fresh waters than the ones studied here, different environmental conditions can shift the thresholds.
For example, higher import of dissolved inorganic carbon or higher mineralization of imported organic matter can lead to higher CO 2 emissions (Duarte & Prairie, 2005;Hanson et al., 2004) for the same level of productivity and shift the U-shaped relationship between CO 2 -equivalent balance and productivity upwards. In the same way, in temperate and tropical ecosystems higher temperatures can have a positive effect on CH 4 emissions (Davidson et al., 2018;Yvon-Durocher et al., 2014) and are also likely to shift the U-shaped relationship upwards. This implies that the narrow interval of being a CO 2 -equivalent sink may be even narrower, and the CO 2 -equivalent sink action may disappear completely if the minimum value of CO 2 -equivalent balance is positive. Accordingly, we suggest a general pattern of CO 2 -equivalent balance across freshwater productivity gradients, shaped by the contrasting effects of productivity on CO 2 and CH 4 fluxes. However, the specific positions of thresholds and the magnitude of the CO 2 -equivalent emissions is likely to differ among different fresh water types and climate zones. Our findings are not directly applicable to shallow fresh waters colonized by aquatic plants because in addition to providing substrates for CH 4 production, aquatic plants have other complex effects on CH 4 fluxes that would need to be addressed (e.g., CH 4 oxidation in the rhizosphere, CH 4 transport through plant tissues; Davidson et al., 2018;Kosten et al., 2016;Schütz, Schröder, & Rennenberg, 1991). The extent to which the experimentally derived qualitative pattern depicted in Figure 4 manifests quantitatively in various types of lake ecosystems, that is, which levels of productivity represent thresholds of which levels of CO 2equivalent balance, is therefore unknown and probably variable, and should be the subject of further studies.
Our results indicate that the positive top-down effect of planktivorous fish on productivity decreased CO 2 emissions, in accordance with several studies (Atwood et al., 2013;Cole et al., 2000;Schindler et al., 1997), and increased CH 4 emissions. For CH 4 emissions, this is in apparent contradiction with a recent study showing reduced CH 4 emissions from lakes where fish were present through top-down control of zooplankton that graze on methane oxidizers (Devlin et al., 2015). However, in the latter study the lake was highly rich in humic matter, and the fish addition may not have increased CH 4 production because primary production may have been light-limited in the dark-stained water.
In our study, even if CH 4 emissions increased with productivity, at the same time the fraction of CH 4 oxidized also increased with productivity, hence counteracting CH 4 emissions ( Figure 3; Table S4). We consequently attribute the flattening of the increase in total CH 4 emissions and the decrease in CO 2 -equivalent balance towards the highest productivity levels ( Figure 1)  oxidation. In our study, the strong correlation between primary producer biomass and the fraction of CH 4 oxidized ( Figure S10; Table S4), indicates that light shading by primary producers could enhance CH 4 oxidation. Furthermore, the presence of fish and the associated decrease in zooplankton (Figure 2) could release the grazing pressure on the CH 4 oxidizing bacteria (Devlin et al., 2015), thereby increasing CH 4 oxidation ( Figure S10; Table S4), as we hypothesized. Fish F I G U R E 4 Conceptual CO 2 -equivalent balance of fresh waters along a productivity gradient. The figure depicts the significant polynomial relationships between C fluxes and productivity, measured in 20 freshwater mesocosms (Table 1). Total CH 4 emissions (diffusive + ebullitive) increased while CO 2 emissions decreased with productivity. CO 2 -equivalent balance, calculated as the sum of CH 4 and CO 2 emissions, had a U-shaped relationship with productivity up to a threshold in hypereutrophic systems.
The studied freshwater ecosystems acted as CO 2 -equivalent sinks within a narrow range of productivity. The range of productivity for which systems can act as CO 2 -equivalent sinks is likely to differ, or even disappear for different fresh water types and different climatic zones can also directly enhance CH 4 oxidation via sediment reworking (i.e., bioturbation) and increasing O 2 supply to sediment (Oliveira Junior et al., 2019) but this does not seem to be the case in our study because CH 4 oxidation was not significantly correlated to the presence of fish (Table S4). The food web structure and eutrophication had consequently antagonistic effects on CH 4 emissions. Primarily, and most visibly, the presence of fish and nutrient enrichment increased CH 4 emissions via their positive effect on productivity. On the other hand, they also increased CH 4 oxidation most likely via an increase in primary producer biomass and/or a decrease in zooplankton abundance. Importantly, our results suggest that CH 4 oxidation could play an important role for the CO 2 -equivalent balance of freshwater ecosystems, calling for more studies on the drivers and magnitude of CH 4 oxidation in natural systems.
We show for the first time that eutrophication can alter the CO 2 -equivalent balance of freshwater ecosystems in a non-linear way, and have a negative or a positive feedback on climate depending on the magnitude of productivity increase. In contrast, a recent study used exponential relationships between CO 2 , CH 4 and Chla or TP to predict a future increase of freshwater CO 2equivalent emission due to eutrophication (DelSontro et al., 2018).
This difference in productivity and CO 2 -equivalent emission relationships may arise from spatial disconnection of measurements; while our data describe the effect of productivity on the balance of CO 2 and CH 4 , the other study used published data from different systems to derive separate relationships for CO 2 and CH 4 , and can therefore not reflect any combined effect within a single ecosystem ( Figure 4). The experimental evidence presented here calls for studies on natural systems that investigate both the CO 2 and CH 4 balance over a gradient of productivity, not the least since the thresholds between a negative to a positive feedback on climate are susceptible to differ between fresh water types and climatic zones. 2017-00635).

DATA AVA I L A B I L I T Y S TAT E M E N T
The data that support the findings of this study are available from the corresponding author upon reasonable request.