Fanny Colas
email: fanny.colas@univ-lyon1.fr

Jean-Marc Baudoin
email: jean-marc.baudoin@ofb.gouv.fr

Patricia Bonin
email: patricia.bonin@mio.osupytheas.fr

Léa Cabrol
email: lea.cabrol@mio.osupytheas.fr

Martin Daufresne
email: martin.daufresne@inrae.fr

Rémy Lassus
email: remy.lassus@inrae.fr

Julien Cucherousset
email: julien.cucherousset@univ-tlse3.fr

Ecosystem maturity modulates greenhouse gases fluxes from artificial lakes

Keywords: Gas fluxes, Ecosystem metabolism, C cycling, Eutrophication, Artificial lakes

Lentic ecosystems play a major role in the global carbon cycling but the understanding of the environmental determinants of lake metabolism is still limited, notably in small artificial lakes.

Here the effects of environmental conditions on lake metabolism and CO2 and CH4 emissio ns were quantified in 11 small artificial gravel pit lakes covering a gradient of ecosystem maturity, ranging from young oligotrophic to older, hypereutrophic lakes. The diffusive fluxes of CO2 and CH4 ranged from -30.10 to 37.78 mmol m -2 d -1 and from 3.05 to 25.45 mmol m -2 d -1 across gravel pit lakes, respectively. Nutrients and chlorophyll a concentrations were negative ly correlated with CO2 concentrations and emissions but positively correlated with CH4 concentrations and emissions from lakes. These findings indicate that, as they mature, gravel pit lakes switch from heterotrophic to autotrophic-based metabolism and hence turn into CO2sinks. In contrast, the emission of CH4 increased along the maturity gradient. As a result, eutrophication occurring during ecosystem maturity increased net emissions in terms of climate impact (CO2 equivalent) due to the higher contribution of CH4 emissions. Overall, mean CO2 equivalent emission was 7.9 g m -2 d -1 , a value 3.7 and 4.7 times higher than values previously reported in temperate lakes and reservoirs, respectively. While previous studies reported that lakes represent emitters of C to the atmosphere, this study highlights that eutrophication may reverse lake contribution to global C budgets. However, this finding is to be balanced with the fact that eutrophication also increased CH4 emissions and hence, enhanced the potential impact of these ecosystems on climate. Implementing mitigation strategies for maintaining intermediate levels of maturity is therefore needed to limit the impacts of small artific ia l waterbodies on climate. This could be facilitated by their small size and should be planned at the earliest stages of artificial lake construction.

Introduction

Due to the large amounts of terrestrial C that they transport, process and store, inland waters are an active component of the global carbon (C) cycle thus potentially affect global climate [START_REF] Cole | Plumbing the global carbon cycle: integrating inland waters into the terrestrial carbon budget[END_REF][START_REF] Tranvik | Lakes and reservoirs as regulators of carbon cycling and climate[END_REF]. During the last decade, a myriad of studies has focused on quantifying CO2 (e.g., [START_REF] Battin | The boundless carbon cycle[END_REF][START_REF] Raymond | Global carbon dioxide emissions from inland waters[END_REF] and CH4 (e.g., [START_REF] Bastviken | Freshwater methane emissions offset the continental carbon sink[END_REF] emissions from inland waters. In particular, lentic inland ecosystems including lakes appeared to be globally significant emitters of CO2 and CH4 to the atmosphere (e.g., [START_REF] Bastviken | Freshwater methane emissions offset the continental carbon sink[END_REF][START_REF] Deemer | Greenhouse Gas Emiss io ns from Reservoir Water Surfaces: A New Global Synthesis[END_REF]DelSontro et al., 2018;[START_REF] Holgerson | Large contribution to inland water CO2 and CH4 emissions from very small ponds[END_REF] justifying their inclusion in IPCC guidelines for national and global inventories of greenhouses gases (GHG) (IPCC, 2019). Nonetheless, current estimates of C emissions from lentic ecosystems are based on extrapolations of average emission rates to global lake surface area.

These estimates vary considerably, ranging from 0.38 to 0.81 Pg C yr -1 (e.g., [START_REF] Cole | Plumbing the global carbon cycle: integrating inland waters into the terrestrial carbon budget[END_REF]DelSontro et al., 2018;[START_REF] Holgerson | Large contribution to inland water CO2 and CH4 emissions from very small ponds[END_REF][START_REF] Tranvik | Lakes and reservoirs as regulators of carbon cycling and climate[END_REF], highlighting the existence of large uncertainties for global estimates that was likely driven by a lack of knowledge of the mechanisms driving emission rate variability (e.g., DelSontro et al., 2018).

Eutrophication is a paramount environmental concern worldwide [START_REF] Carpenter | Predicting responses of chlorophyll and primary production to changes in phosphorus, grazing, and dissolved organic carbon (Reply to comment by Nürnberg)[END_REF][START_REF] Jeppesen | Chapter 6 -Biomanipulation as a Restoration Tool to Combat Eutrophicatio n: Recent Advances and Future Challenges[END_REF], but its role as a driver of the direction and magnitude of GHG flux from/to lentic ecosystems remains unclear. The role of lakes as sources or sinks of C is highly dependent on the balance between primary production and ecosystem respiration (e.g., [START_REF] Cole | Persistence of net heterotrophy in lakes during nutrient addition and food web manipulations[END_REF][START_REF] Jeppesen | Major changes in CO 2 efflux when shallow lakes shift from a turbid to a clear water state[END_REF][START_REF] Prairie | The summer metabolic balance in the epilimnion of southeastern Quebec lakes[END_REF]. Lakes with high loading of organic C tend to be net heterotrophic ecosystems and act as significant sources of C to the atmosphere through respiration (e.g., [START_REF] Andersson | Comparison of a mass balance and an ecosystem model approach when evaluating the carbon cycling in a lake ecosystem[END_REF][START_REF] Hanson | Lake metabolism: relations hips with dissolved organic carbon and phosphorus[END_REF][START_REF] Laas | High-frequency metabolism study in a large and shallow temperate lake reveals seasonal switching between net autotrophy and net heterotrophy[END_REF]. However, the relative importance of organic C load and associated heterotrophic respiration may be offset by a high CO2 uptake by primary producers, especially in lakes with high total phosphorus (TP) concentrations since it is known that TP regulated primary productivity (e.g., [START_REF] Davidson | Eutrophication effects on greenhouse gas fluxes from shallow-lake mesocosms override those of climate warming[END_REF][START_REF] Laas | High-frequency metabolism study in a large and shallow temperate lake reveals seasonal switching between net autotrophy and net heterotrophy[END_REF][START_REF] Yang | Eutrophication influe nces methanotrophic activity, abundance and community structure in freshwater lakes[END_REF]. In some eutrophic lakes, high CO2 uptake by primary producers can turn lakes into net autotrophic ecosystems and hence CO2 sinks [START_REF] Kosten | Climate-dependent CO2 emissions from lakes: Climate-Dependent CO2 Emissions[END_REF][START_REF] Pacheco | Eutrophication reverses whole-lake carbon budgets[END_REF][START_REF] Roland | Variability of carbon dioxide flux from tropical (Cerrado) hydroelectr ic reservoirs[END_REF]). Yet, this holds for a small proportion of lakes while most of them are predominant sources of C. This is because the loading of allochtho no us organic C generally greatly exceeds autochthonous primary production (e.g., [START_REF] Bastviken | Freshwater methane emissions offset the continental carbon sink[END_REF][START_REF] Cole | Persistence of net heterotrophy in lakes during nutrient addition and food web manipulations[END_REF][START_REF] Cole | Carbon dioxide supersaturation in the surface waters of lakes[END_REF][START_REF] Deemer | Greenhouse Gas Emiss io ns from Reservoir Water Surfaces: A New Global Synthesis[END_REF]. The projected increase in lakes eutrophication (e.g., [START_REF] Beaulieu | Eutrophication will increase methane emissions from lakes and impoundments during the 21st century[END_REF] may therefore reverse the global contribution of lakes to global C budget [START_REF] Pacheco | Eutrophication reverses whole-lake carbon budgets[END_REF]. While high primary productivity may decrease CO2 emissions from lakes, it may act oppositely by promoting CH4 emissions, providing labile substrate for methanogenic bacteria and promoting C-rich and oxygen-poor environment (e.g., [START_REF] Sepulveda-Jauregui | Eutrophication exacerbates the impact of climate warming on lake methane emission[END_REF][START_REF] Vachon | Methane emission offsets carbon dioxide uptake in a small productive lake[END_REF]West et al., 2016[START_REF] West | Effects of algal and terrestrial carbon on methane production rates and methanogen community structure in a temperate lake sediment[END_REF][START_REF] Yang | Eutrophication influe nces methanotrophic activity, abundance and community structure in freshwater lakes[END_REF]. This suggests that eutrophication may lead to a decrease in emissions of C from lakes in the form of CO2 but, at the same time, to an increase in emissions of C in the form of CH4. This is an important consideration because CH4 in the atmosphere is up to 34 times more potent as greenhouse gas (GHG) than CO2 over a 100-year time scale (IPCC, 2013) and its individ ua l contribution to total radiative forcing range between 71.8-77.8% when considering aquatic waterbodies (DelSontro et al., 2018a). This indicates that the effects of eutrophication on CH4 emissions can deeply influence lake contribution to global warming.

The relationships between eutrophication, CO2 autotrophy and CH4 emissions are, however, highly context-dependant [START_REF] Deemer | Greenhouse Gas Emiss io ns from Reservoir Water Surfaces: A New Global Synthesis[END_REF]DelSontro et al., 2018a;Ollivier et al., 2019). For instance, DelSontro et al. (2018) reported that TP enrichment decreased CO2 emissions in medium to large-size lakes while it increased emissions in small lakes. In addition, chlorophyll a was positively associated to CH4 emissions, though the strength of this effect was stronger for larger ecosystems (DelSontro et al. 2018). This suggests that the extent to which eutrophication influences greenhouse gas emissions may be dependent on lake morphometr y and highlights the high contribution of small lakes to global C emissions from lentic ecosystems. While they are particularly prone to eutrophication (e.g., Ollivier et al., 2019;[START_REF] Wetzel | Limnology: lake and river ecosystems[END_REF] and extremely abundant worldwide (e.g., [START_REF] Cael | The volume and mean depth of Earth's lakes[END_REF][START_REF] Verpoorter | A global inventory of lakes based on high-resolution satellite imagery[END_REF], small, shallow and artificial lakes remain overlooked compared to natural and large ecosystems (e.g., Peacock et al., 2019;[START_REF] Van Bergen | Seasonal and diel variatio n in greenhouse gas emissions from an urban pond and its major drivers[END_REF]Webb et al., 2019). For instance, C fluxes from gravel pit lakes, artificially formed when gravel pits are excavated at or below the water table [START_REF] Mollema | Water and (bio)chemical cycling in gravel pit lakes: A review and outlook[END_REF], have not been documented yet. Gravel pits lakes are extremely abundant across the globe [START_REF] Mollema | Water and (bio)chemical cycling in gravel pit lakes: A review and outlook[END_REF], notably because more than 890 million tons of gravel are produced globally per year (USGS, 2017).

Gravel pit lakes are usually small (1-100 ha), shallow (2-12 m maximal depth) and distributed in regional clusters experiencing similar climatic conditions. They represent interesting model ecosystems for disentangling the effects of eutrophication on C emissions in small lentic ecosystems. In particular, as they age (defined here as the time since the end of excavatio n), gravel pit lakes tend to switch from oligotrophic to hypereutrophic waterbodies due to increased nutrients concentrations, lake productivity and the sedimentation of detritus includ ing autochthonous material [START_REF] Kattner | Eutrophication of gravel pit lakes which are situated in close vicinity to the river Donau: Water and nutrient transport[END_REF][START_REF] Mollema | Water and (bio)chemical cycling in gravel pit lakes: A review and outlook[END_REF][START_REF] Zhao | Environme nta l determinants of fish community structure in gravel pit lakes[END_REF]. This represents a maturation process [START_REF] Vitousek | Ecosystem succession and nutrient retention: a hypothesis[END_REF] that may be promoted in gravel pit lakes by their disconnection to the rest of the river network and the importance of terrestrial inputs in their functioning [START_REF] Alp | Phenological response of a key ecosystem function to biological invasion[END_REF]. For instance, [START_REF] Zhao | Environme nta l determinants of fish community structure in gravel pit lakes[END_REF] reported a large range of lake productivity (e.g. chlorophyll-a concentration ranging from 0.9 to 58.8 mg l -1 ) in gravel pit lakes. Maturation of these artificial ecosystems is multifaceted process that includes an increased amount of nutrient in the systems (eutrophication), a change in animal communities, an increased ripisylve along the shore as trees grow and a higher intensity of human activities as ecosystems become older [START_REF] Zhao | Environme nta l determinants of fish community structure in gravel pit lakes[END_REF]. Because of their high environmental heterogeneity, gravel pit lakes represent a unique model system to examine the impact of eutrophication on C cycling, while controlling other factors such as climate variability given their very restricted geographical distribution.

In the present study, the effects of eutrophication on gas metabolism and emissions were quantified in 11 gravel pit lakes across a large range of ecosystem maturity to identify the environmental factors driving lakes as C-source or sink. In particular, gravel pit lakes were predicted to shift from net CO2 sources to net CO2 sinks as they mature, mainly due to the increased CO2 uptake by primary producers. Nonetheless, increased CH4 emissions as primary production and nutrient contents increased were predicted. The impacts of gas fluxes from gravel pit lakes on climate were also estimated and were predicted to be dependent on the balance between CO2 and CH4 fluxes and hence, between heterotrophic benthic and the autotrophic water layer metabolism. In addition, and to provide a broader perspective to these results, the values of gas fluxes measured in the present study were compared to values reported in the literature in other temperate lentic ecosystems.

Materials and Methods

Study sites

The study area was located in the Garonne floodplain (south-west of Toulouse, France) that contains more than 1522 ha of gravel pit lakes [START_REF] Saplairoles | Evaluation de l'impact sur la ressource en eaux souterraines de l'exploitation de granulats dans le milie u alluvionnaire de la Garonne[END_REF]. The study was conducted in an area with a large quantity of gravel pit lakes with varying environme nta l conditions [START_REF] Alp | Phenological response of a key ecosystem function to biological invasion[END_REF][START_REF] Stocker | Between-lake variation in the trophic ecology of an invasive crayfish[END_REF][START_REF] Zhao | Environme nta l determinants of fish community structure in gravel pit lakes[END_REF]. From mid-September to mid-October 2017, 11 gravel pit lakes were selected to cover a gradient of ecosystem maturity based on their age that ranged from 12 to 55 years (Fig. 1). Several abiotic and biotic environmental variables were assessed once at three locations within each lake (Table 1). Specifically, a portable multiparameter probe (EXO2, YSI Incorporated, Ohio, USA) was used to determine the depth profiles of temperature, pH, turbidity and conductivity. Nine important physic-chemical variables including variables related to eutrophication (e.g, total phosphorus, total nitrogen, ammonium, phosphate) were measured according to national standards (NF EN ISO 10304-1, 1339; AFNOR NF EN ISO 14911) with water sampled at 1 m depth. Sediments were sampled with an Ekman dredge, sieved, homogenized, and stored in a cooler. Grain size distribution, ash free dry mass and concentrations in organic carbon, TN, TP were subsequently measured (LDA26, Valence, France). Water clarity (Secchi depth) was measured using a Secchi-disk. Chlorophyll a (chla) and Cyanobacteria concentrations were measured directly in the surface water (0.5 m depth) via fluorescence using a portable fluorescence photometer (AlgaeTorch, BBE-Moldaenke, Kiel, Germany). Specifically, the AlgaeTorch measures the fluorescence of algae cells in the water by exciting the algae pigments by 6 coloured LEDs of different wavelengths (i.e., 470, 525 and 610 nm) to obtain a fluorescence spectrum. In parallel, turbidity was determined by measuring the reflection at a wavelength of 700 nm which allows simultaneous turbidity correction during chlorophyll measurement. A standardised zooplankton sample was collected at the water surface in all lakes using a 250 µm mesh net. Samples were sieved and fixed in 100 mL 70 % ethanol. In the laboratory, a 10 mL sub-samples was taken and debris removed from the sample that was oven-dried (60°C for 72 h) and weighted to the nearest mg to estimate zooplankton density (mg.L -1 ). The average value of each variable across the three replicates in each lake was used for subsequent analyses. Additionally, aerial pictures and geographic information system (GIS) analyses were used to calculate the area, the perimeter and the percentage of area covered by riparian vegetation (10-metre buffer around each lake), urbanization and other gravel pit lake dredging (5-km buffer) [START_REF] Zhao | Environme nta l determinants of fish community structure in gravel pit lakes[END_REF]. Lake depth and volume were determined using bathymetry analyses.

Ecosystem maturity gradient

The lakes covered a large range of environmental conditions associated to ecosystem maturity (Table 1), including productivity (e.g., chla ranging from 2.5 to 48.2 µg L -1 ) and water nutrie nt content (e.g., TP ranging from 28.8 to 115.9 µg L-1). The lakes were distributed along a gradient of ecosystem maturity defined using a principal component analyses (PCA) based on environmental conditions in the lakes. The first two dimensions of the PCA accounted for 74.2% of the total inertia (Fig. 2). The main variables positively correlated with PC1 (50.8%) were the concentrations of chla, of nutrients in water and in sediments, lake age and the level of urbanization (see details in Supplementary material, Table A1). The content of minera l matter in sediment, the Secchi depth and the maximal depth were negatively correlated with PC1. Therefore, PC1 axis was used to represent the multifaceted characteristics of ecosystem maturity and the distribution of studied lakes along a maturity gradient based on their rank from the youngest unproductive lake (rank 1; SAB) to the oldest highly productive lake (rank 11, BVI). The main variables positively correlated with PC2 (23.4%) were related to lake hydromorphology including perimeter, surface and shoreline development. The second component discriminated smaller and circular lakes (e.g., LIN, BVI) from larger lakes with more complex shape (e.g. LAM, LAV).

2.3. Gas concentrations and fluxes 2.3.1. Dissolved gas concentrations and metabolic balances Depth profiles of dissolved methane (CH4), dioxide carbon (CO2) and oxygen (O2) concentrations were measured once at three locations within lakes (i.e., at littoral area, center and deepest area) for capturing the heterogeneity of lakes. In particular, CH4 and CO2 concentrations were measured using submersible gas sensors (Mini CH4 TM , Mini CO2 TM , ProOceanus, Nova Scotia, Canada) operating through diffusion of dissolved gases from liquids through a supported semi-permeable membrane to a non-dispersive infrared detector (NDIR). Dissolved O2 concentrations were measured using a portable multiparameter probe (EXO2, YSI Incorporated, Ohio, USA). Dissolved gas concentrations were measured during 15 minutes every 0.5 m depth. In addition, temperature, pressure, and humidity of the internal gas were determined to correct the gas concentration measurement. The solubility coefficients of [START_REF] Weiss | Carbon dioxide in water and seawater: the solubility of a non-ideal gas[END_REF] and [START_REF] Yamamoto | Solubility of methane in distilled water and seawater[END_REF] were then used to calculate the dissolved concentrations of CO2 and CH4, respectively. Because there was no significant variation on gas concentratio ns across depth (P-value > 0.05), the entire profiles were used to calculate the water column gas concentration (average of 0.5-m interval profiles values) for each replicate. The mean surface concentrations were then expressed as a concentration differential (Δgas in µM) from elevatio n and temperature corrected saturation values (named hereafter 'departures from saturation'). Gas saturation was calculated using atmospheric concentrations of 407.8 ppm for CO2 and 1869 ppb for CH4 (Source: WMO Global Atmosphere Watch). The average value of dissolved gas concentrations and metabolic balance using the three replicate in each lake was used for subsequent analyses 2.3.2. Atmospheric gas emissions Atmospheric gas emissions were determined for CO2 and CH4. CO2 flux across air-water interface were estimated using two floating chambers (FC; volume: 47 L; area: 0.24 m 2 ; water penetration: 6 cm). The FC were covered with reflective alumina tape to minimize interna l heating. The FC were equipped with a vent on the top to equalize the air pressure in the chamber with the atmospheric pressure before starting the measurements and with a floating structure (PVC tube ø 90 cm). CO2 concentrations within the FC were measured continuously using a non-dispersive infrared (NDIR) spectroscopy logger (ELG CO2, SenseAir, Delsbo, Sweden) (details in [START_REF] Bastviken | Cost-effic ie nt approaches to measure carbon dioxide (CO 2) fluxes and concentrations in terrestrial and aquatic environments using mini loggers[END_REF]. For each lake, the two FC were deployed three times from the center of lake. The FC were left drifting during measurement to avoid creation of artific ia l turbulence. Each deployment was run over about 15 minutes after an equilibration period with opened vent for 5 minutes. Before starting new deployment, the chamber was lifted, vented for 5 min, and then replaced on the water. Diffusive CO2 flux at the air-water interface (mmol m - 2 day -1 ) were calculated according to:

𝐹 𝐶𝑂2 = 𝑆. 𝑡. 𝑉 𝐹𝐶 (𝑉 𝑚 × 𝐴) (1)
Where S is the slope of the linear regression of gas concentration in the chamber versus time (ppm.min -1 ), t is a conversion factor of minutes into days (1440 min d -1 ), VFC is the volume of the chamber, Vm is the gas molar volume at ambient temperature and pressure and A is the area of the chamber. Fluxes derived from chamber deployments were kept only when the linear regression exhibited R 2 > 0.8 and a significant slope (P-value < 0.05).

Then, gas exchange coefficients for CO2 (kCO2) expressed in m d -1 were derived from concomitant measurements of gas flux and partial pressure in air (pCO2a) and in surface water (pCO2w) expressed in atmosphere following:

𝑘 𝐶𝑂2 = 𝐹 𝐶𝑂 2 𝐾 𝑜 .(𝑝𝐶𝑂 2𝑤 -𝑝𝐶𝑂 2𝑎 ) (2)
where Ko is the solubility of CO2 in water expressed in mole l -1 atm -1 at surface water temperature of given lake [START_REF] Weiss | Carbon dioxide in water and seawater: the solubility of a non-ideal gas[END_REF].

The kCO2 was normalized to a Schmidt number of 600 at 20°C according to [START_REF] Jähne | On the parameters influencing air-water gas exchange[END_REF]:

𝑘 600 𝐶𝑂2 = 𝑘 𝐶𝑂2 ( 600 𝑆𝑐 𝐶𝑂2,𝑇 ) -𝑛 (3)
Where ScCO2, T is the Schmidt number for CO2 at a given temperature. N=2/3 was used for wind speed at 10 m < 3.7 m s -1 [START_REF] Jähne | On the parameters influencing air-water gas exchange[END_REF].

Then, k600 CO2 in a given lake was used to extrapolate the gas exchange coefficient for CH4 as follows:

𝑘 𝐶𝐻4 = 𝑘 600 𝐶𝑂2 (600 𝑆𝑐 𝐶𝐻4, 𝑇 ⁄ ) -𝑛 (4)
The diffusive flux of CH4 at the air-water interface was then computed following the equation proposed by [START_REF] Cole | Atmospheric exchange of carbon dioxide in a low-wind oligotrophic lake measured by the addition of SF6[END_REF]:

𝐹 𝐶𝐻4 = 𝑘 𝐶𝐻4 (𝐶 𝑤 -𝐶 𝑒𝑞 ) (5)
Where FCH4 is the flux at the air-water interface for CH4 (mmol m -2 day -1 ), kCH4 is the gas exchange coefficient (m day -1 ), Cw is the concentration of CH4 in water (mmol m -3 ), and Ceq is the theoretical concentration of CH4 in water if the water phase was in equilibrium with the atmosphere (mmol m -3 ).

To integrate the contributions of both CO2 and CH4 fluxes in total GHG emissions from the 11 gravel pit lakes, the emission terms were expressed in C and CO2 equivalent (CO2eq). For this purpose, diffusive fluxes were previously converted into g m -2 d -1 and a global warming potential for CH4 of 34 was taken assuming a period of 100 years and no carbon feedback loop (IPCC, 2013).

Benthic gas fluxes

An optically clear acrylic benthic chamber mounted on a stainless steel frame was used for estimating benthic fluxes of O2, CO2 and CH4. The chamber was configured to have 10 cm of chamber walls buried inside the sediment. The chamber was equipped at the top with a data logger of dissolved oxygen concentration and temperature (hobo U26, onset), a stirrer, three non-return check valves and a PVC tubing (6 mm outer diameter, 4 mm inner diameter) inserted through cable glands. The stirrer (5-7 rpm) was mounted at approximately 15 cm above the sediment and was used for mixing chamber water during the deployment. The two non-return valves placed at the corners of the chamber allowed the water to drain into the chamber during the immersion. The small non-return valve in the center allowed water to enter inside the chamber during water sampling. Deployments usually started between 08:30 and 09:30 AM by slowly lowering the chamber to the sediment on a rope tethered to a float from a small boat.

The chamber was placed at approximately 4 m from the shoreline. During the incubatio n, approx. 1 m of water remained over the chamber. The incubation period was 5-6 h during which oxygen concentrations and temperature were recorded every 5 minutes and water was sampled every 20 minutes. Water samples were collected using 50 mL syringes with three-way stopcocks connected to the end of the PVC tubing equipped with a luer-lock syringe valve. 15 mL of water was injected into pre-evacuated 21 mL-serum bottles previously filled with 6 g of NaCl (final saturation concentration) to inhibit microbial activity before analysis [START_REF] Bastviken | Freshwater methane emissions offset the continental carbon sink[END_REF]. Then, a headspace was created at the lab, and CO2 and CH4 concentrations in the headspace were measured by GC-MS (gas chromatograph CompactGC, GASTM, Global Analyser Solutions equipped with GS-Carbon plot column (Agilent), coupled to mass spectrometer detector in ionisation mode ISQ, THERMO) after desorption (simultaneo us autosampler-desorber TriPlus 300, Thermo). The benthic flux (Fsed) for each gas was then calculated as follows:

𝐹 𝑠𝑒𝑑,𝑔𝑎𝑠 = 𝑆×𝑉 𝐵𝐶 ×𝑡 𝐴 𝐵𝐶 (6)
Where S is the slope of the linear regression of dissolved gas concentration in the benthic chamber versus time (µmol m -3 h -1 ), t is a conversion factor of hours into days (24 h d -1 ), VBC is the volume of water in the benthic chamber (0.0405 m 3 ) and ABC is the surface area of the sediment enclosed in the chamber (0.2025 m 2 ). Fluxes derived from chamber deployments were kept only for linear regression with R 2 > 0.8 and a significant slope.

Comparisons with existing emission data

A literature survey of studies quantifying CO2 and CH4 diffusive emissions from temperate lentic ecosystems was performed. A total of 31 references (see details in Supplementar y Material Table A2) were collected and a total of 1026 emissions estimates obtained. Only summer-autumn measurements were considered to allow comparison with the present study.

For some references, values provided were expressed in CH4-C or CO2-C. These values were converted using 1.34 and 3.66 conversion factors, respectively. All CO2-equivalent values (expressed in g CO2 m -2 d -1 ) presented in this study were calculated using the global warming potentials (GWPs) of CH4 at the 100 year (1 g CH4 = 34 g CO2) time-scales (IPCC, 2013).

2.5.Statistical analyses

The relationships between dissolved gas concentrations, gas emissions and environme nta l gradients defined according the coordinates of sites on the PCA axes were examined using Spearman's rank correlation coefficient. Partial least-squares (PLS) regressions [START_REF] Abdi | Partial least square regression (PLS regression)[END_REF] were then performed to identify environmental variables significantly associated to gas concentrations and emissions. Cross-validation was used for selecting the optimal number of components that minimize the prediction errors (RMSE). The variable importance in projection (VIP) coefficients were calculated to classify the predictors according to their explanatory power of the dependent variable. Predictors with VIP larger than 1 are the most relevant for explaining the dependent variable [START_REF] Eriksson | Introduction to Multi-and Megavariate Data Analysis Using Projection Methods[END_REF][START_REF] Tenenhaus | La régression PLS: théorie et pratique[END_REF]. Then, specific relationships between gas concentrations and environmental variables were examined using linear models. For all parametric analyses, normal distribution and homoscedasticity were checked. All statistical analyses were performed using R software (R Development Core Team, 2008) using FactoMineR [START_REF] Lê | FactoMineR: An R Package for Multivariate Analys is[END_REF] and PLS [START_REF] Mevik | The pls Package: Principal Component and Partial Least Squares Regression in R[END_REF] packages.

Results

2.6.Metabolic balance and gas emissions

Dissolved gas concentrations in the water column varied moderately among the studied lakes, ranging from 259.7 to 403.1 µM for O2, from 5.2 and 39.9 µM for CO2 and from 1.97 to 4.42 µM for CH4 (Table 2). CH4:CO2 molar ratio ranged from 0.07 to 0.68 among lakes (mean ± SD: 0.27 ± 0.18) suggesting predominance of aerobic respiration in the water column and/or strong methanotrophic activities. Five mature lakes were oversaturated with O2 and undersaturated with CO2 suggesting an epilimnetic net autotrophy (Fig. 3A). The least mature lake was undersaturated with O2 and oversaturated with CO2 suggesting net heterotrophy of water column (Fig. 3A). The other lakes were oversaturated with both O2 and CO2. The five lakes exhibiting net autotrophy of water column were CO2 sinks (Fig. 3B). The others lakes were CO2 sources. All lakes were CH4 sources with a relatively broad range of saturation levels (2.0 -4.8 µM ; Fig. 3B). The least mature lake showed highest departure from saturation for CO2 but lowest for CH4. CO2 and CH4 emission fluxes ranged from -30.10 to 37.78 mmol m -2

d -1 and from 3.05 to 25.45 mmol m -2 d -1 , respectively (Table 2). Except for one lake, the fluxes mirrored the patterns obtained by the departure from saturation (Fig. 3). Five lakes were sinks of CO2 but sources of CH4. The six other lakes were sources of both CO2 and CH4. Total net emissions ranged from -0.21 to 0.60 g C m -2 d -1 (Fig. 4) and from 2.6 to 12.8 g CO2eq m -2 d -1 .

The net emissions fluxes were negatively correlated with the gradient of ecosystem maturity when expressed in C equivalents (rho = -0.85, P = 0.002), but positively correlated when expressed in CO2-equivalents (rho = 0.61, P = 0.052).

2.7.Coupling benthic-pelagic metabolism

Benthic gas fluxes were successfully computed on six and eight lakes for O2 and CO2, respectively (Table 2). They ranged from -93. 3, R 2 of 0.56 for CO2, 0.59 for CH4, 0.61 for FCO2, 0.87 for FCH4).

Atmospheric gas emissions had overall the same explanatory variables than dissolved gas concentration. The most influential variables (VIP > 1.0) for CO2 concentrations and emissio ns were chla and DOC concentrations, lake depth, nutrient concentrations in the water (TP, TN), urbanization level and TOC contents in sediments (Fig. 5). In particular, CO2 concentratio ns and emissions decreased with increased values of chla, nutrients, DOC and TOC concentratio ns and urbanization. Conversely, deeper lakes exhibited higher CO2 concentrations and emissio ns.

Additionally, positive relationship between CO2 concentrations in the water column and CO2 fluxes from sediments was detected. CH4 concentrations and emissions exhibited opposite relationships with environmental parameters than those described for CO2 concentrations and emissions. In particular, CH4 concentrations and emissions increased with nutrient and TOC contents in sediments and urbanization but decreased with lake depth (Fig. 5). Additiona lly, atmospheric CH4 emissions increased with the concentrations in chla.

Comparison of emissions with other temperate lentic ecosystems

A comparison with values reported in the literature about GHG emissions in other freshwater (natural and artificial) ecosystems in temperate climate was performed (see details in Supplementary material, Table A2). This comparison revealed that the studied gravel pit lakes generally emitted more CO2-equivalent (supported by higher CH4 emission contribution) than natural ecosystems such as lakes and ponds. In particular, CO2-equivalent emissions from the studied gravel pit lakes were about 3.7 times and 1.5 times higher than emissions from natural lakes and ponds belonging to the same climatic zone (Fig. 6), respectively. CH4 and CO2equivalent emissions from gravel pit lakes were overall similar to emissions reported for other temperate small artificial-waterbodies such as urban and farm ponds (CH4: 195 mg m -2 d -1 ; CO2eq: 7.8 g m -2 d -1 , in average).

Discussion

3.1.Switching from heterotrophy to autotrophy when increases ecosystem maturity

Eutrophication of aquatic ecosystems is key facet of future ecosystem changes [START_REF] Beaulieu | Eutrophication will increase methane emissions from lakes and impoundments during the 21st century[END_REF] and its consequences on C cycling in aquatic ecosystems remains unclear, and this is particularly true for small, artificial lakes. In the present study, lake productivity (i.e. eutrophication) increased quickly after artificial lake construction, with some lakes being hypereutrophic after 26 years [START_REF] Carlson | A trophic state index for lakes1[END_REF][START_REF] Wetzel | Limnology: lake and river ecosystems[END_REF]. This gradient of ecosystem maturity was accelerated by human activities as suggested by the positive correlation between variables related to lake productivity (e.g., TP concentrations), lake age and urbanization level.

Consistently with previous studies, increased chlorophyll a concentration (likely due to increased nutrient loadings) was negatively correlated with CO2 concentrations and emissio ns from lakes (e.g., [START_REF] Li | Methane and CO2 emissions from China's hydroelectric reservoirs: a new quantitative synthesis[END_REF][START_REF] Pacheco | Eutrophication reverses whole-lake carbon budgets[END_REF]. As they mature, lakes shifted from heterotrophic to autotrophic-based metabolism due to the CO2 uptake by primary producers. As they turned into a CO2 sink, more C buried in lake sediments, as suggested by the negative relationships between the total organic C contents in sediments and both CO2 concentratio ns and efflux. As observed previously, eutrophication may reverse lake contribution to global C budget [START_REF] Pacheco | Eutrophication reverses whole-lake carbon budgets[END_REF], in particular in the small ecosystems. Nonetheless, this finding contrasts with some studies reporting that small lakes globally strong emitters of CO2 (e.g., [START_REF] Holgerson | Large contribution to inland water CO2 and CH4 emissions from very small ponds[END_REF], especially when eutrophic (DelSontro et al., 2018a;Ollivier et al., 2019). The extent to which eutrophication affects the direction and magnitude of CO2 emissions from lakes is likely dependent on the balance between the rates of primary productivity and the input of terrestrial C, substrate of heterotrophic respiration. Here, the young gravel pit lakes exhibited high CO2 concentrations and emissions probably because, even in small quantities (average DOC concentrations < 3 mg L -1 ), allochthonous C subsidies exceeded autochthonous C-CO2 consumption limited by low nutrient concentrations (as already described for many oligotrophic lakes, e.g., [START_REF] Biddanda | Dominance of bacterial metabolism in oligotrop hic relative to eutrophic waters[END_REF][START_REF] Del Giorgio | Respiration rates in bacteria exceed phytoplankton production in unproductive aquatic systems[END_REF][START_REF] Depew | Production and Respiration in Lake Erie Plankton Communities[END_REF]. Furthermore, a coupling between sediment respiration and CO2 concentrations in water column of young lakes was observed, likely promoted by the shallow depth of the lakes. This suggests that sediment respiration may be a major driver of CO2 oversaturation in young gravel pit lakes [START_REF] Kortelainen | Sediment respiration and lake trophic state are important predictors of large CO2 evasion from small boreal lakes[END_REF]. Conversely, eutrophicatio n led to an uncoupling between benthic heterotrophic metabolism and water column autotrophy suggesting that CO2 uptake by primary producers offset the CO2 efflux from sediments. The overweight of primary producers' CO2 uptake over ecosystem respiration is likely favored by low inputs of terrestrial materials to gravel pit lakes. Indeed, even if DOC concentratio ns increased in concert with primary productivity along the maturity gradient, they remained overall low among gravel pit lakes (< 6 mg L -1 , except for one lake, LAM, with DOC = 17.5 mg L -1 ). Several studies reported that switching from net autotrophy to net heterotrophy occurred at DOC concentrations higher than 6-10 mg L -1 (e.g., [START_REF] Andersson | Comparison of a mass balance and an ecosystem model approach when evaluating the carbon cycling in a lake ecosystem[END_REF][START_REF] Hanson | Lake metabolism: relations hips with dissolved organic carbon and phosphorus[END_REF][START_REF] Prairie | The summer metabolic balance in the epilimnion of southeastern Quebec lakes[END_REF]. Consequently, it is likely that here, increase in DOC concentrations was not enough for maintaining heterotrophy along the maturity gradient.

Eutrophication increases CH4 emissions

In contrast with CO2 fluxes, atmospheric CH4 fluxes exhibited positive relationships with nutrients (TP, TN) and organic material contents in sediments, and DOC and chlorophyll a concentrations in water, suggesting that eutrophication promoted CH4 emissions. Conversely, CH4 fluxes were negatively correlated with lake depth. This could reflects that higher depth leads to higher potential oxidation capacity of CH4 produced in the sediments before reaching the atmosphere (e.g., Bastviken et al., 2004). Yet, this could also be explained by the accumulation of organic matter in the water and in the sediments through sinking, resulting in a reduced water depth, along the ecosystem maturation (e.g., Staehr et al., 2010). In particular, highly productive autotrophic systems produce substantial organic detritus since about 15-35% of dead phytoplankton settles to sediments [START_REF] Baines | Relationships between Suspended Particulate Matter and Sinking Flux along a Trophic Gradient and Implications for the Fate of Planktonic Primary Production[END_REF]. This accumulation of easily degradable phytoplankton-derived organic substrate (e.g., West et al., 2016[START_REF] West | Effects of algal and terrestrial carbon on methane production rates and methanogen community structure in a temperate lake sediment[END_REF] tends to promote C-rich and oxygen-depleted environment favouring CH4 production (e.g., Bastviken et al., 2004;Delsontro et al., 2018;[START_REF] Borrel | Production and consumption of methane in freshwater lake ecosystems[END_REF][START_REF] Sepulveda-Jauregui | Eutrophication exacerbates the impact of climate warming on lake methane emission[END_REF][START_REF] West | Effects of algal and terrestrial carbon on methane production rates and methanogen community structure in a temperate lake sediment[END_REF]. Additionally, a positive correlation between the CH4 concentration and nutrie nt contents (notably TP) in sediments of gravel pit lakes was found. The link between CH4 production and nutrient content in sediments has been paid less attention. Here, the positive relationship could merely reflect enhanced primary production in pelagic waters, since TP content in sediments increased with lake productivity. Enhanced TP content in sediments may in turn fuel methanogenesis of accumulated organic C by methanogenic archae (e.g., Adhya et al., 1998;Alphenaar et al., 1993). CH4 benthic fluxes could not be succesfully measured in most lakes, even those exhibiting high CH4 concentrations in the water column. That is likely due to methodological biases associated with the benthic chambers (e.g., short incubation time, CH4 oxidation occurring at the sediment water-interface inside the benthic chamber). Nonetheless and consistently with several studies, most of the CH4 produced in sediments (~93% based on the two lakes with successful measurement of benthic methanogenesis) was oxidized before reaching the atmosphere (e.g., [START_REF] Bastviken | Methane as a source of carbon and energy for lake pelagic food webs[END_REF][START_REF] Yang | Eutrophication influe nces methanotrophic activity, abundance and community structure in freshwater lakes[END_REF]. This oxidation was likely promoted by well-oxygenated water of the gravel pit lakes. Despite this, the small part of CH4 escaping oxidation outweighed the primary producers' CO2 uptake along the maturatio n gradient. This stronger contribution of CH4 emissions is particularly since CH4 has a global warming potential (GWP) approximately 34 times higher than that of CO2 (IPCC, 2013). As a result, while the lakes turned into a CO2-sink as they matured, the increased CH4 emissions due to eutrophication led to the increase of atmospheric C flux when expressed in CO2 equivalents.

Furthermore, these measurements of CH4 emissions are probably underestimated because ebullition was not measured, despite being an important CH4 efflux mechanism in shallow and eutrophic lakes (Bastviken et al., 2004;DelSontro et al., 2016;[START_REF] Huttunen | Fluxes of methane, carbon dioxide and nitrous oxide in boreal lakes and potential anthropogenic effects on the aquatic greenhouse gas emissio ns[END_REF][START_REF] Mcginnis | Fate of rising methane bubbles in stratified waters: How much methane reaches the atmosphere?[END_REF]. Moreover, lateral CH4 transport (DelSontro et al., 2018b;[START_REF] Fernández | On the methane paradox: Transport from shallow water zones rather than in situ methanogenesis is the major source of CH4 in the open surface water of lakes[END_REF] or CH4 production in the oxic water layers by cyanobacteria [START_REF] Bižić | Aquatic and terrestrial cyanobacteria produce methane[END_REF][START_REF] Günthel | Photosynthesis-dr ive n methane production in oxic lake water as an important contributor to methane emiss io n[END_REF], or within anaerobic microniches associated to suspended particles [START_REF] Bianchi | Strictly aerobic and anaerobic bacteria associated with sinking particulate matter and zooplankton fecal pellets[END_REF][START_REF] Grossart | Microbial methane production in oxygenated water column of an oligotrophic lake[END_REF] or through methylphosphonate metabolism by planktonic microbes [START_REF] Khatun | Aerobic methane production by planktonic microbes in lakes[END_REF][START_REF] Wang | Methylphosphonate metabolism by Pseudomonas sp. populations contributes to the methane oversaturation paradox in an oxic freshwater lake[END_REF]) cannot be excluded [START_REF] Peeters | Sediment fluxes rather than oxic methanogenesis explain diffusive CH 4 emissions from lakes and reservoirs[END_REF]. Yet, the balance between autotrophy (mainly in water column) and respiration (mainly in sediment), both influenced by maturity, seems clearly determine the total flux of GHG from gravel pit lakes.

3.3.Perspectives

This study provides first insights on autumn emissions in gravel pit lakes and highlights the importance of CH4 emissions from mature ecosystems. In particular, gravel pit lakes studied here, similarly to others man-made small ecosystems (e.g., farm and urban ponds), generally emitted more CO2-equivalent (supported by higher CH4 emission contribution) than lakes, ponds and reservoirs ecosystems. This is probably because these small and shallow artific ia l ecosystems tend to be highly productive (e.g., [START_REF] Ortiz-Llorente | Comparison of biogenic methane emissio ns from unmanaged estuaries, lakes, oceans, rivers and wetlands[END_REF]Webb et al., 2019) and hence, exhibit frequent phytoplankton and cyanobacteria blooms that may fuels CH4 production rates (e.g., [START_REF] Günthel | Photosynthesis-dr ive n methane production in oxic lake water as an important contributor to methane emiss io n[END_REF]West et al., 2016). Since gravel pit lakes are made in terrestrial ecosystems (considered as C sinks), GHG emissions, in particular the CH4 ones, can be considered as a direct consequence of the construction of the waterbody (concept of net emissions, [START_REF] Prairie | Greenhouse Gas Emissions from Freshwater Reservoirs: What Does the Atmosphere See?[END_REF]. Considering their potential high number in the landscape of many countries, small artificial waterbodies should be integrated in the future estimates of regional and global C emissions from inland waters. The present study included a limited number (n = 11) of gravel pit lakes and a more complete survey is still needed to fully estimate their contribution. This is particularly important to quantify annual emissions of gravel pit lakes since it is likely that benthic and epilimnetic metabolisms as well as resulting gas flux vary between seasons and years (e.g., [START_REF] Jeppesen | Major changes in CO 2 efflux when shallow lakes shift from a turbid to a clear water state[END_REF][START_REF] Laas | High-frequency metabolism study in a large and shallow temperate lake reveals seasonal switching between net autotrophy and net heterotrophy[END_REF]. In particular, considering that the magnitude of sediment respiration and the epilimnetic metabolism are strongly regulated by primary production, one might expect a switch from net autotrophy to net heterotrophy during the winter season due to a reduced phytoplankton growth [START_REF] Marshall | General patterns in the seasonal development of chlorophyll a for temperate lakes[END_REF]. A long-term survey is therefore needed to fully characterize the dynamics of GHG fluxes and the extent to which gravel pit lakes are C sink or sources over time. It would be also interesting to assess the organic C stored in sediments that can potentially be considered as an offset to net C emissions [START_REF] Prairie | Greenhouse Gas Emissions from Freshwater Reservoirs: What Does the Atmosphere See?[END_REF]. Finally, a crucial avenue of research is to identify the extent to which the switch from heterotrophy to autotrophy is regulated by biotic interactions and the structure of food webs (e.g., [START_REF] Atwood | Predator-induced reduction of freshwater carbon dioxide emissions[END_REF][START_REF] Cole | Persistence of net heterotrophy in lakes during nutrient addition and food web manipulations[END_REF][START_REF] Davidson | Eutrophication effects on greenhouse gas fluxes from shallow-lake mesocosms override those of climate warming[END_REF]. A previous study on the same gravel pit lakes showed changes in fish communities from an initial biomass of pioneer and predator species (e.g., European perch) in young lakes to higher biomass of cyprinids species in mature and eutrophic lake [START_REF] Zhao | Environme nta l determinants of fish community structure in gravel pit lakes[END_REF], probably driven by fishery management. Changes in fish community compositio n (including planktivorous fishes) along the maturation gradient may strongly control the zooplankton community, which, as primary consumers of phytoplankton, might have an effect on primary productivity (e.g., [START_REF] Carpenter | Predicting responses of chlorophyll and primary production to changes in phosphorus, grazing, and dissolved organic carbon (Reply to comment by Nürnberg)[END_REF]. Here, zooplankton biomass exhibited no significant changes along the maturity gradient. However, a lack of complete survey cannot rule out changes in species composition or abundance along the maturity gradient. It is likely that both controls (i.e., by food web and eutrophication) exert here in concert and that the increased primary production due to eutrophication is accelerated in lakes where the biomass of predatory fish is reduced. Further researches will be needed to disentangle the relative importance of both controls.

Conclusion

This study demonstrated that eutrophication increased CO2 sequestration in small and shallow lakes by increasing the relative importance of primary productivity compared to ecosystem respiration. Nevertheless, eutrophication also increased net GHG emissions in terms of climate impact by providing labile organic matter for enhanced CH4 production. Consequently, gravel pit lakes turned into CO2-sinks along the ecosystem maturity gradient but also into hotspots of CH4 emissions. Additionally, since CH4 emissions increased as gravel pit lake mature, mitigation strategies are urgently needed to maintain intermediate levels of eutrophication by limiting nutrient inputs, using biomanipulation or removing sediments. By providing a first insight into the biogeochemical functioning of gravel pit lakes, this study confirms recent evidences on the important role of small artificial waterbodies on global C cycling. Further studies are therefore needed to assess the GHG emissions and their environmental drivers in small artificial ecosystems in order to accurately estimate their global contribution to C budgets.

are grateful to the anonymous reviewers for their suggestions that have significantly improved the quality of the manuscript. This study was financially supported by the French Agency for Biodiversity (STABLELAKE project; IFLAC project).

Ecosystem maturity modulates greenhouse gases fluxes from artificial lakes

Fanny Colas 1* , Jean-Marc Baudoin

  8 to 26.4 mmol m -2 d -1 for O2 and from -54.4 to 228.0 mmol m -2 d -1 for CO2. Except for two lakes that exhibited benthic primary production (BVI, SOA), most of lakes exhibited benthic fluxes suggesting sediment respiration (O2 consumption, CO2 release). CH4 fluxes from sediment were successfully computed only for two lakes exhibiting methanogenesis (BIR: 140.8 mmol m -2 d -1 and LAV 178.7 mmol m -2 d -1 ), while in the other lakes models were not significant or R 2 <0.80. Six lakes showed benthicpelagic metabolism coupling, i.e. atmospheric emissions of CO2 by lakes exhibiting sediment respiration and conversely influx of CO2 at the air-water interface by lakes exhibiting benthic primary production. Uncoupling between benthic and surface metabolism was observed in two lakes exhibiting a net autotrophy of the water column. ~15% of CO2 and only ~7% of CH4 produced in sediments were emitted to the atmosphere.2.8. Environmental drivers of gas concentrations and emissionCO2 concentrations and emissions decreased significantly along the gradient of ecosystem maturity (rho = -0.83, P = 0.003; rho = -0.74, P = 0.013; respectively) whereas CH4 emissio ns and the CH4:CO2 molar ratio significantly increased (rho = 0.73, P = 0.01; rho = 0.78; P = 0.007; respectively). Variability in CO2 and CH4 concentrations and fluxes were overall well explained by the model (Table

Fig. 1 :Fig. 2 :

 12 Fig.1: Map of the 11 gravel pit lakes in the Garonne floodplain (south-west of Toulouse, France).

Fig. 3 :Fig. 4 :Fig. 5 :Fig. 6 :

 3456 Fig. 3: Relationship between (A) CO 2 and O 2 departure from saturation (mean ± SD) and (B) CO 2 and CH 4 departure from saturation (µM) in the studied gravel pit lakes. Dots are filled based on the level of

Table A1 :

 A1 2,3 , Patricia Bonin 4 , Léa Cabrol 4,5 , Martin Daufresne 6 , Rémy Lassus 6,7 and Julien Cucherousset 7 1 Univ Lyon, Université Claude Bernard Lyon 1, CNRS, ENTPE, UMR 5023 LEHNA, F-69622, Villeurbanne, France Pearson correlation coefficients of the environmental variables on the first (PC1) and second (PC2) axis. PC1 and PC2 explained 50.8% and 23.4% of the total variance, respectively.

	2 Pôle R&D « ECLA », Aix-en-Provence, France.
	3 OFB, Direction de la Recherche et de l'Appui Scientifique, Aix-en-Provence, France
	4 Aix Marseille Univ., Universite de Toulon, CNRS, IRD, MIO UM 110, 13288, Marseille,
	France
	5 Institute of Ecology and Biodiversity (IEB), Faculty of Sciences, Universidad de Chile,
	Santiago, Chile
	6 Inrae, Aix Marseille Univ, RECOVER, Aix-en-Provence, France
	7 UPS, CNRS, IRD, Université de Toulouse, UMR 5174, Laboratoire Évolutio n et Diversité
	Biologique (EDB), Université de Toulouse, 118 route de Narbonne, 31062 Toulouse, France.
	Only significant variables were displayed (P-value < 0.05)
	Variable	PC1 (50.8%) PC2 (23.4%)
	AGE	0.803
	SUR *	0.865
	PER	0.931
	maxDE	-0.660
	SLD *	0.863
	UrA	0.754
	Temp	0.737
	Secc	-0.774
	TP	0.897
	TN	0.681
	DOC	0.614
	TOC	0.929
	Chla	0.901
	Cya	0.833
	AFDM	-0.881
	TOCsed	0.871
	Nsed	0.880
	Psed	0.696

Table A2 :

 A2 Literature synthesis of CO2 and CH4 diffusive emissions from temperate lentic ecosystems. Values presented are mean (ranges) and were extracted from different studies. Only summer-autumn or dry season measurements were considered. * For these references, values provided were expressed in CH4-C or CO2-C and converted using 1.34 and 3.66 conversion factors, respectively. All CO2-equivalent values (expressed in g CO2 m -2 d -1 ) presented in this study were calculated using the global warming potentials (GWPs) of CH4 at the 100 year (1 g CH4 = 34 g CO2) time-scales(IPCC, 2013). 'FC' refers to floating chambers and 'TBL' to thin boundary layer. a median values instead of means. Bold values represents mean and range values for each ecosystem type.

	Reservoir		0.66	0.50	0.68	FC	Demarty et al., 2009
	Reservoir		0.1 (-0.002 -0.31)	2.9 (0.2 -10.6)	0.20 (0.05 -0.38)	FC	Bastien et al., 2009
	Reservoir		0.28 (0.1 -0.69)	0.28 (0.1 -0.7)	0.29 (0.1 -0.69)	TBL	Diem et al., 2012
	Reservoir		0.12	17.3	0.71	FC	Fearnside, 2002
	Reservoir			43.3		TBL	Descloux et al., 2017
	Reservoir		0.75 (0.3 -1.2)			TBL	Morales-Pineda et al.,
	Ecosystem type Reservoir Reservoir	n	CO2 flux (g m -² d -1 ) 7.07	CH4 flux (mg m -² d -1 ) 0.34 4.1 (2.9 -5.8)	CO2eq flux (g m -² d -1 ) 7.01	2016* Mosher et al., 2015 Method References TBL TBL Maeck et al., 2013
	Reservoir Natural Lake Reservoir		1.95 1.34 (-0.2 -7.1)	13.7 7.9 (0.3 -36.6) 10.6 (0.3 -43.3)	2.41 1.66 (0.06 -7.01)	TBL FC	Li et al., 2018* Bastviken et al., 2004*
	Lake Farm Pond		1.94 1.82	6.06 114.2	2.14 5.70	TBL TBL	Casper et al., 2000 Webb et al., 2019
	Lake Farm Pond		-0.09 (-0.4 -0.03) 1.07	115.5	11.12	TBL FC	Kelly et al., 2001* Ollivier et al., 2019
	Lake Farm Pond		0.84 1.5 (1.1 -1.8)	15.6 114.9 (114.2 -115.5) 8.4 (5.7 -11.1) 1.37	FC	Bartosiewicz et al., 2015
	Lake Lake Urban Pond Lake Urban Pond Lake Urban Pond Lake Urban Pond		1.64 0.75 2.29 0.62 1.21 (-0.1 -2.3) 0.8 (-)	35.6 0.46 (0.19 -0.87) 30.3 35.3 129 5.76 165.9 16.5 (0.5 -35.6) 108.4 (30.3 -165.9)	2.74 1.29 3.49 0.81 2.11 (0.8 -3.5) 1.3 (-)	TBL FC TBL FC FC TBL FC	Li et al., 2018* Peacock et al., 2019 West et al., 2016* Grinham et al., 2018 DelSontro et al., 2016 Ortega et al., 2019 Whitfield et al., 2011
	Pond Stormwater pond		1.50	22.6 362.4	13.82	FC FC	Duc et al., 2013 Gorsky et al., 2019
	Pond Pond		7.96 3.48	8.02 26.7	8.23 4.39	FC FC	Glaz et al., 2016 a ** Bergen et al., 2019*
	Pond		2.51	67.4	4.8	FC	DelSontro et al., 2016
	Pond		1.01	46.2	2.58	FC	Burger et al., 2016 a
	Pond		3.7 (1.0 -8.0)	34.2 (8.0 -67.4)	5.0 (2.6 -8.2)
	Artificial
	Reservoir		0.71 (-1.0 -3.1)	17.04 (0.1 -70.7)	1.29 (0.1 -3.4)	FC	Tremblay, 2005*
	Reservoir		0.66 (0.2 -1.3)	6.8 (3.0 -11.0)	0.90 (0.6 -1.4)	FC	St. Louis et al., 2000
	Reservoir		1.89 (0.7 -6.4)	14.5 (5.8 -30.5)	2.38 (0.8 -7.5)	FC	Bevelhimer et al., 2016
	Reservoir		-0.15 (-1.2 -1.2)	6.23 (3.2 -9.5)	0.06 (-1.0 -1.6)	FC	Soumis et al., 2004
	Reservoir		2.01	10.49	2.37	TBL	Jacinthe et al., 2012

Gravel pit lakes -0.049 (-1.32 -1.66) 233.0 (48.9 -408.2) 7.9 (2.6 -12.8)

	FC	Present study

Table 1 :

 1 Environmental characteristics (minimum, mean and maximum values) of the 11 studied gravel pit lakes.

	1 SLO = (maxDE / Distance from banks) x 100
	2 SLD = PER / (2√πSUR) according to Hutchinson (1957)
	*variables included in partial least squares models. δ log-transformed variables. ξ inverse transformation.

Table 2 :

 2 Gas concentrations (mean ± SD) and fluxes at the interfaces surface water/air (mean ± SD) and sediment/water for the 11 gravel pit lakes . Lakes are ordered according to level of maturity from the youngest to the oldest lake. For kCO2 the number in brackets indicates the number of measurements with floating chambers used for calculating k. n.s. indicates invalidated data because models were not significant or R 2 < 0.80. Δgas indicates the departures from saturation.

	Lakes

Table 3 :

 3 Loadings of the PLS analyses explaining the variability in gas concentrations (CO2, CH4) and emissions (FCO2, FCH4) among gravel pit lakes. Coefficients (Coef.) and loadings (Load.) are provided only for parameters with VIP > 0.7. Highly influential variables (VIP > 1.0) and loadings values > 0.3 are displayed in bold. n.a. represents 'not analyzed'. Parameter names are provided in the Table1.

	Y	CO2		FCO2		CH4 (µM)		FCH4
	Components 1		1		1			2
	r 2 Y	0.56		0.61		0.59			0.87
	Parameter	VIP Coef.	Load. VIP	Coef.	Load. VIP	Coef.	Load. VIP	Coef.	Load.
	Chla	1.55 -1.378 -0.42 1.36 -3.320 -0.37 <0.7			1.21	0.779 -0.51
	CH4	<0.7		<0.7		n.a			n.a.
	DOC ξ	1.52 1.345	0.41 1.74 4.231	0.47 0.81 -0.067 -0.23 0.74 -0.476 -0.23
	FsedCO2	1.04 0.923	0.28	<0.7		n.a			n.a
	maxDE	1.34 1.184	0.36 1.40 3.406	0.37 1.11 -0.092 -0.32 1.29 -0.835 -0.32
	Nsed δ	<0.7		<0.7		1.04 0.086	0.30 1.05	0.678	0.30
	Psed	<0.7		<0.7		1.58 0.130	0.46 0.73	0.440	0.25
	SLD	<0.7		<0.7		0.99	0.083	0.29	<0.7
	SUR	0.72 0.635	0.19	<0.7		0.74	0.061	0.21	<0.7
	Temp	<0.7		<0.7		1.26 0.104	0.36 <0.7
	TN δ	1.10 -0.975 -0.29 1.08 -2.627 -0.29 <0.7			<0.7
	TOCsed ξ	1.18 1.045	0.32 1.13 2.757	0.30 1.49 -0.123 -0.43 1.60 -1.028 -0.43
	TP δ	1.26 -1.115 -0.34 1.26 -3.069 -0.34 <0.7			0.75 0.481 -0.51
	UrA δ	1.17 -1.034 -0.31 1.44 -3.495 -0.38 1.02 0.084	0.29	1.79	1.156	0.29

δ log-transformed variables. ξ inverse transformation.

Acknowledgments

We are grateful to Lucie Buchet, Tiphaine Perroux, Corinne Valette and the graviere team for fieldwork and laboratory assistance. The OMICS platform at the Mediterranean Institute of Oceanography (M.I.O) where biogaz analyses were performed, is in compliance with ISO9001-2015. We also thank lake owners and managers for access to the gravel pit lakes. The authors


Muhammad Mahajne

Oscar Volij

Pairwise consensus and Borda rule

Keywords: Consensus, Borda rule, scoring rules JEL codes: D71, D72 Pairwise consensus and Borda rule Consensus, Borda rule, scoring rules. JEL Classification Numbers: D71, D72

We say that a preference profile exhibits pairwise consensus around some fixed preference relation, if whenever a preference relation is closer to it than another one, the distance of the profile to the former is not greater than its distance to the latter. We say that a social choice rule satisfies the pairwise consensus property if it selects the top ranked alternative in the preference relation around which there is such a consensus. We show that the Borda rule is the unique scoring rule that satisfies this property.

Introduction

We study a standard setting of social choice, in which there is a set of social alternatives and a group of voters, each of which has a preference relation over this set. A social choice rule selects a subset of alternatives for every preference profile. * Mahajne acknowledges financial support from Université de Lyon (project INDEPTH Scientific Breakthrough Program of IDEX Lyon) within the program Investissement d'Avenir (ANR-16-IDEX-0005). † Univ. Lyon, UJM Saint-Etienne, CNRS, GATE L-SE UMR 5824, F-42023 Saint-Etienne, France. mahajnah@gate.cnrs.fr. Declaration of Interest: None. ‡ Ben Gurion University, Beer-Sheba, Israel. ovolij@bgu.ac.il. Declaration of Interest: None.

1

The class of scoring rules is a well-known special class of social choice rules, in which each individual assigns a fixed list of K scores to the set of K alternatives, according to their positions in his preference relation, and select those alternatives with the maximal sum of scores. The Borda rule is an instance of a scoring rule.

A major goal of social choice theory is to examine and characterize social choice rules by means of desirable properties. In this paper, we present a new property, called the pairwise consensus property, and show that the Borda rule is the unique scoring rule that satisfies it. [START_REF] Young | An axiomatization of Borda's rule[END_REF] has characterized the class of scoring rules by the axioms of Anonymity, Neutrality, Reinforcement and Continuity. Along with these axioms, the new property characterizes the Borda rule.

Roughly speaking, a preference profile exhibits pairwise consensus around some preference relation ≻ 0 , if whenever a preference relation ≻ is closer to ≻ 0 than another one ≻ ′ , the more in agreement are the preferences in the profile with ≻ than with ≻ ′ .

Here, the level of agreement of a preference profile to a given preference relation is measured by the well-known Kemeny distance.1 Our first result states that the highest ranked alternative in the preference relation around which there is such a consensus, must be a Condorcet winner.

Based on the above concept, we define the pairwise consensus property of social choice rules. A social choice rule satisfies this property if whenever a preference profile exhibits pairwise consensus around a preference relation ≻ 0 , the rule selects the highest ranked alternative in ≻ 0 . Our main result states that the Borda rule is the only scoring rule that satisfies the pairwise consensus property. [START_REF] Chebotarev | Characterizations of scoring methodsfor preference aggregation[END_REF] survey several existing characterizations of the Borda rule. In particular, we can mention [START_REF] Young | An axiomatization of Borda's rule[END_REF] who characterizes the Borda rule as the unique rule that satisfies Neutrality, Consistency, Faithfulness and having the Cancellation property, and the [START_REF] Nitzan | A further characterization of Borda ranking method[END_REF], that axiomatizes the Borda rule, by means of these axioms, but by replacing Faithfulness by Monotonicity.

The paper is organized as follows. Section 2 contains basic definitions. In Section 3 we define the concept of pairwise consensus and the pairwise consensus property, and prove our main result.

Let A = {a 1 , ...., a K } be a set of K alternatives. Let P be the set of complete, transitive and antisymetric binary relations on A. We will refer to the elements of P as preference relations. For preference relation ≻, when we write ≻= (a 1 , a 2 , ..., a K ) we mean that a 1 is placed first in ≻, and so on. Let N be the set of non-negative integers, which represent the names of the potential voters. For any finite set V ⊆ N of voters, a preference profile is an assignment of a preference relation to each voter in V .

A social choice rule is a function that assigns a nonempty subset of alternatives to each preference profile. A social choice rule is anonymous if it is invariant to the names of the voters. In this paper, we consider only anonymous social choice rules, thus a preference profile can be summarized by a list π = (≻ 1 , ...., ≻ N ) of preference relations where N is the number of voters.

A special class of anonymous social choice rules consists of the scoring rules. A scoring rule is characterized by K-tuple S = (S 1 , S 2 , ..., S K ) of non-negative scores with S 1 ≥ S 2 ≥ ... ≥ S K and S 1 > S K . Given a preference profile π, each voter i = 1, ..., N assigns S k points to the alternative that is ranked k-th in his preference relation, for k = 1, ..., K. The scoring rule associated with the scores S, denoted by F S , chooses the alternatives with the maximum total score. Many well-known social choice rules are instances of scoring rules. For example, the plurality rule is the scoring rule associated with the scores (1, 0, ..., 0). The inverse plurality rule is the scoring rule associated with scores (1, ..., 1, 0). More generally, for 1 ≤ t ≤ K -1, the t-approval rule is the scoring rule associated with the scores (1, ..., 1, 0, ..., 0) in which the first t scores equal 1 and the last (K -t) scores equal 0. Lastly, the Borda rule is the scoring rule associated with the scores (K -1, K -2, ..., 1, 0).

Let d : P 2 → R be the inversion metric on P, which is defined as follows:

d(≻, ≻ ′ )
is the number of pairs of alternatives in A that are ranked differently by ≻ and ≻ ′ . Formally, the inversion metric is defined by

d(≻, ≻ ′ ) = |(≻ \ ≻ ′ )| where ≻ \ ≻ ′ = {(a, b) ∈ A 2 : a ≻ b and b ≻ ′ a}.
We can use the metric d to compare preference relations according to their "close-Example 1. Let the set of alternatives be A = {a, b, c}. The set P contain six preference relations, given by: , b, a). Consider the preference ≻ 1 . It can be checked that the distances of each preference in P to ≻ 1 , according to the inversion metric, are given by

≻ 1 = (a, b, c), ≻ 2 = (a, c, b), ≻ 3 = (b, a, c), ≻ 4 = (c, a, b), ≻ 5 = (b, c, a), ≻ 6 = (c
d(≻ 1 , ≻ 1 ) = 0 d(≻ 2 , ≻ 1 ) = d(≻ 3 , ≻ 1 ) = 1 d(≻ 4 , ≻ 1 ) = d(≻ 5 , ≻ 1 ) = 2 d(≻ 6 , ≻ 1 ) = 3
For any preference profile π = (≻ 1 , . . . , ≻ N ) and any preference relation ≻∈ P, we denote by

d π (≻) = N ∑ n=1 d(≻ n , ≻)
the Kemeny distance of π to ≻. It is the sum of the distances to ≻ of the voters' preferences.

Pairwise consensus

We now introduce the concept of pairwise consensus of preference profiles around a preference relation. Later, we will define the strong pairwise consensus property of social choice rule.

Given a preference profile π = (≻ 1 , . . . , ≻ N ) and two alternatives a, b ∈ A, we denote by

µ π (a → b) = |{n ≤ N : a ≻ n b}|
the number of voters that prefer a to b. Note that the Borda count of alternative a ∈ A for a preference profile π = (≻ 1 , . . . , ≻ N ) is given by BC(a) = ∑ b∈A µ π (a → b). Also note that the Kemeny distance of π to ≻∈ P can be written as

d π (≻) = ∑ a≻b µ π (b → a).
Definition 1. A preference profile π exhibits pairwise consensus around preference relation a ≻ 0 if for all pairs of preference relations ≻, ≻ ′ ∈ P,

d(≻, ≻ 0 ) < d(≻ ′ , ≻ 0 ) =⇒ d π (≻) ≤ d π (≻ ′ ) with strict inequality if ≻=≻ 0 .
This concept of consensus is similar to the concept of level-1 consensus introduced in Mahajne, [START_REF] Mahajne | Level r consensus and stable social choice[END_REF]. In order to exhibit consensus around a preference relation ≻ 0 , both concepts require from a preference profile the fulfillment of certain condition. This condition says that the closer to ≻ 0 a preference relation is, the more similar (in some well-defined way) this preference relation should be to the preference profile. Whereas level-1 consensus measure similarity in terms of the number of voters that have the relevant preference relation, pairwise consensus measures it in terms of the Kemeny distance.

It is not the case that every preference profile exhibits pairwise consensus around some preference relation. However, when such consensus exists, it is around one and only one preference relation.

d π (≻ 1 ) = d(≻ 1 , ≻ 1 ) + d(≻ 1 , ≻ 1 ) + d(≻ 6 , ≻ 1 ) = 3 d π (≻ 2 ) = d(≻ 1 , ≻ 2 ) + d(≻ 1 , ≻ 2 ) + d(≻ 6 , ≻ 2 ) = 4 d π (≻ 3 ) = d(≻ 1 , ≻ 3 ) + d(≻ 1 , ≻ 3 ) + d(≻ 6 , ≻ 3 ) = 4 d π (≻ 4 ) = d(≻ 1 , ≻ 4 ) + d(≻ 1 , ≻ 4 ) + d(≻ 6 , ≻ 4 ) = 5 d π (≻ 5 ) = d(≻ 1 , ≻ 5 ) + d(≻ 1 , ≻ 5 ) + d(≻ 6 , ≻ 5 ) = 5 d π (≻ 6 ) = d(≻ 1 , ≻ 6 ) + d(≻ 1 , ≻ 6 ) + d(≻ 6 , ≻ 6 ) = 6
It can also be checked that, there is pairwise consensus around ≻ 1 .

The following claim presents an important feature of consensus.

Claim 1. If π = (≻ 1 , . . . , ≻ N ) exhibits pairwise consensus around ≻ 0 , then the firstranked alternative in ≻ 0 is a Condorcet winner.

Proof. Assume w.l.o.g. that ≻ 0 = (a 1 , a 2 , . . . , a K ). We need to show that for any alternative a k ̸ = a 1 , we have that µ π (a 1 → a k ) ≥ µ π (a k → a 1 ).

For k = 1, 2, . . . , K. Let ≻ k = (a 2 , a 3 , . . . , a k , a 1 , a k+1 . . . , a K ) be the preference relation that is obtained from ≻ 0 by moving alternative a 1 from the first rank to the

kth rank. We have that d(≻ 0 , ≻ k-1 ) < d(≻ 0 , ≻ k ) for k = 2, . . . , K. Since π ∈ P n exhibits pairwise consensus around ≻ 0 , we must have that d π (≻ k-1 ) ≤ d π (≻ k ). But d π (≻ k ) = N ∑ n=1 d(≻ n , ≻ k ) = ∑ 1<j≤k µ π (a 1 → a j ) + ∑ i<j (i,j)̸ =(1,2),...,(1,k) µ π (a j → a i ) Therefore, 0 ≤ d π (≻ k ) -d π (≻ k-1 ) = µ π (a 1 → a k ) -µ π (a k → a 1 ).
Definition 2. We say that choice rule F has the strong pairwise consensus property if F selects the top-ranked alternative according to ≻ whenever π ∈ P n exhibits pairwise consensus around ≻.

The following theorem is our main result.

Theorem 1. The Borda rule is the unique scoring rule that satisfies the pairwise consensus property.

Proof. We first show that the Borda rule satisfies pairwise consensus. Recall that if π ∈ P n exhibits pairwise consensus around ≻ 0 , then for all ⊁ =≻ 0 , we have that

d π (≻ 0 ) < d π (≻).
Assume that π ∈ P n exhibits pairwise consensus around ≻ 0 = (a 1 , . . . , a j , . . . , a K ). Fix a j ̸ = a 1 . We will show that BC(a 1 ) > BC(a j ). Note that

BC(a 1 ) -BC(a j ) = ∑ a k ̸ =a 1 µ π (a 1 → a k ) - ∑ a k ̸ =a j µ π (a j → a k ) = ∑ a k ̸ =a 1 µ π (a 1 → a k ) -(n -µ π (a 1 → a k )) 2 - ∑ a k ̸ =a j µ π (a j → a k ) -(n -µ π (a j → a k )) 2 = ∑ a k ̸ =a 1 µ π (a 1 → a k ) -µ π (a k → a 1 ) 2 - ∑ a k ̸ =a j µ π (a j → a k ) -µ π (a k → a j ) 2
Therefore, it is enough to show that

X := ∑ a k ̸ =a 1 [µ π (a 1 → a k ) -µ π (a k → a 1 )] - ∑ a k ̸ =a j [µ π (a j → a k ) -µ π (a k → a j )] > 0 Note that X = ∑ a k ̸ =a j [µ π (a 1 → a k ) -µ π (a k → a 1 )] + ∑ a k ̸ =a j [µ π (a k → a j ) -µ π (a j → a k )] = ( K ∑ k=1 [µ π (a 1 → a k ) -µ π (a k → a 1 )] + K ∑ k=j+1 [µ π (a k → a j ) -µ π (a j → a k )]
)

+ ( j-1 ∑ k=1 [µ π (a k → a j ) -µ π (a j → a k )] ) (1)
Consider the following preference relations: ≻ = (a 1 , . . . , a j-1 , a j+1 , . . . , a K , a j )

≻ ′ = (a 2 , . . . , a j-1 , a j , a j+1 , . . . , a K , a 1 )

Preference ≻ is obtained from ≻ 0 by moving a j to the last place. Preference ≻ ′ is obtained from ≻ 0 by moving a 1 to the last place. As a result, d(≻ 0 , ≻) < d(≻ 0 , ≻ ′ ).

Since there is consensus around ≻ 0 , we have that

d π (≻ ′ ) -d π (≻) ≥ 0. Since d π (≻ ′ )-d π (≻) = K ∑ k=1 [µ π (a 1 → a k ) -µ π (a k → a 1 )]+ K ∑ k=j+1 [µ π (a k → a j ) -µ π (a j → a k )]
we have that the the expression within the first pair of brakets in (1) is non-negative.

Consider now the following preference relation:

≻ ′′ = (a j , a 1 , a 2 , . . . , a j-1 , a j+1 , . . . , a K )
Preference relation ≻ ′′ is obtained from ≻ 0 by moving a j to the top. It is clear that d(≻ 0 , ≻ 0 ) < d(≻ 0 , ≻ ′′ ). Therefore, since there is consensus around ≻ 0 , we have

d π (≻ ′′ ) -d π (≻ 0 ) > 0. Since d π (≻ ′′ ) -d π (≻ 0 ) = [µ π (a 1 → a j ) -µ π (a j → a 1 )] + j-1 ∑ k=2 [µ π (a k → a j ) -µ π (a j → a k )] = j-1 ∑ k=1 [µ π (a k → a j ) -µ π (a j → a k )]
we have that the the expression within the second pair of brakets in (1) is positive.

Therefore,

X = ( d π (≻ ′ ) -d π (≻) ) + ( d π (≻ ′′ ) -d π (≻ 0 ) ) > 0.
We now show that any scoring rule other than the Borda rule fails to satisfy pairwise consensus. It is enough to show this for K = 3. So, let now K = 3 and let S = (S 1 , S 2 , S 3 ) be a scoring rule distinct from Borda. Without loss of generality assume that the scores associated with S are 1, p and 0, for some 0 ≤ p ≤ 1 such that p ̸ = 1/2. Consequently, as a corollary of our result we obtain that the Borda rule is the only social choie rule that satisfies Young's axioms and the pairwise consensus property. It would be interesting to see if other rules can be characterized by means of some similar notions of the consensus property.

Assume first that

Example 2 .

 2 Continuing with Example 1, consider the following profile of 3 individuals: π = (abc, abc, cba). We obtain that µ π (a → b) = µ π (a → c) = µ π (b → c) = 2, and the Kemeny distances d π (≻), for ≻∈ P, are given by

  p < 1/2 and consider the following preference profile π, along with the associated d π function.≻ # of voters d π (≻)It can be seen that there is consensus around abc and that the score awarded by S to the three alternatives are given by However, for p < 1/2, we have that S(b) > S(a) whenevern > 1 -p 1 -2p8Similarly, assume that p > 1/2 and consider the following preference profile π, with the associated d π function.It can be seen that there is consensus aroun abc and that the score awarded by S to the three alternatives are given by p > 1/2, we have that S(b) > S(a) whenever n > p 2p -1[START_REF] Young | An axiomatization of Borda's rule[END_REF] has characterized the class of scoring rules as the only social choice rules that satisfy the axioms of anonymity, neutrality, reinforcement and continuity.

SeeKemeny and Snell (1962).