Flavia Dory
email: flavia.dory@imbe.fr

| Laurent Cavalli

Evelyne Franquet

Magalie Claeys-Bruno

| Benjamin Misson

Thierry Tatoni

| Céline Bertrand

Laurent Cavalli

Magalie Claeys-B

Benjamin Mis

Céline Bertrand

Microbial consortia in an ice-covered high-altitude lake impacted by additions of dissolved organic carbon and nutrients

1. High-altitude lakes are sentinels of change. Anticipated increases in inputs of dissolved organic carbon (DOC) from catchments in high-altitude lakes could affect planktonic interactions, especially if inputs occur during the winter ablation phase.

However, the responses of plankton communities to added DOC interacting with nutrients during this period are still not well understood.

2. We sampled under-ice water and used a multifactorial experimental design to investigate the DOC effect on planktonic organisms (phytoplankton and heterotrophic prokaryotic plankton [HPP]) and their interactions during the winter ablation phase. The plankton community was subjected to DOC additions (0, 2, 4, and 6 mg C/L) under two nutrient-availability treatments (natural concentrations O RCI D

or enriched in N and P), two light conditions (dark or light), and two temperature conditions (10 or 18℃).

3. We found HPP to be co-limited by N, P, and C in our microcosms. Added glucose as available C-source for bacterioplankton was highly consumed at the end of the experiments. This consumption was not always related to an increase of the HPP biomass, due to a rising predatory control by ciliates and mixotrophic phytoplankton over bacteria. In dark conditions, the biomasses of both autotrophic and mixotrophic phytoplankton were substantially reduced, and the HPP biomass under DOC and nutrient additions principally depended on the predatory control exerted by ciliates. In light conditions, a diversification of top-down control over bacteria was observed, with the HPP response to DOC and nutrient additions depending on both mixotrophs and ciliates. Moreover, when heterotrophic ciliates and mixotrophs were present together in the experiments, the ciliates replaced the mixotrophs in phagotrophy over bacteria. 4. Our experimental results indicate that DOC inputs can rapidly alter the trophic interactions of the planktonic food web, depending on nutrient limitation in highaltitude lakes. We found decreased commensalistic interactions between bacteria and phytoplankton, but increased competition and predation, after DOC additions.

| INTRODUC TI ON

Oligotrophic high-altitude lakes have been identified as sentinels of change [START_REF] Moser | Mountain lakes: Eyes on global environmental change[END_REF][START_REF] Williamson | Lakes and reservoirs as sentinels, integrators, and regulators of climate change[END_REF] and provide ideal ecosystems for studying the impacts of global change on biodiversity. Lakes in the alpine region are undergoing change driven by climate and anthropogenic factors [START_REF] Smiatek | EURO-CORDEX regional climate model analysis for the greater alpine region: Performance and expected future change[END_REF].

It has been found that atmospheric nutrient deposition of nitrogen (N) and phosphorus (P) is intercepted by mountain catchments [START_REF] Battarbee | Threatened and stressed mountain lakes of Europe: Assessment and progress[END_REF], altering the nutrient limitations in alpine lakes [START_REF] Bergström | Phytoplankton responses to nitrogen and phosphorus enrichment in unproductive Swedish lakes along a gradient of atmospheric nitrogen deposition[END_REF][START_REF] Elser | Nutrient availability and phytoplankton nutrient limitation across a gradient of atmospheric nitrogen deposition[END_REF]. Furthermore, the Alps have a particularly high warming rate: since the late 19th century, they have warmed twice as fast as the global or Northern Hemispheric average [START_REF] Auer | HISTALP-Historical instrumental climatological surface time series of the Greater Alpine Region[END_REF]. Models of climate change also predict increasing extreme precipitation events in the alpine region during the current century [START_REF] Ipcc | working Group I to the fifth assessment report of the intergovernmental panel on climate change[END_REF]. Both the current upward shift of the treeline in alpine regions and the predicted increase in extreme precipitation events could substantially increase inputs to lakes from terrestrial runoff, including dissolved organic carbon (DOC; [START_REF] Ejarque | Climate-induced hydrological variation controls the transformation of dissolved organic matter in a subalpine lake[END_REF][START_REF] Moser | Mountain lakes: Eyes on global environmental change[END_REF].

Increased allochthonous concentrations of DOC have been shown to seriously affect the planktonic food web functioning in aquatic systems. Inputs of allochthonous DOC fuel bacterial respiration and production [START_REF] Soares | Bacterioplankton responses to increased organic carbon and nutrient loading in a boreal estuary-Separate and interactive effects on growth and respiration[END_REF], and reduce bacterial reliance on phytoplankton-produced carbon, particularly in oligotrophic, carbon-limiting ecosystems [START_REF] Medina-Sánchez | Neither with nor without you: A complex algal control on bacterioplankton in a high mountain lake[END_REF].

High quantities of DOC modify bacterial limitation toward a primary limitation by nitrogen (N) and phosphorus (P; [START_REF] Pinhassi | Seasonal changes in bacterioplankton nutrient limitation and their effects on bacterial community composition in the NW Mediterranean Sea[END_REF], leading to direct competition with phytoplankton for these nutrients [START_REF] Carney | Lotic bacterioplankton and phytoplankton community changes under dissolved organic-carbon amendment: Evidence for competition for nutrients[END_REF][START_REF] Hitchcock | Different resource limitation by carbon, nitrogen and phosphorus between base flow and high flow conditions for estuarine bacteria and phytoplankton[END_REF]. Plankton communities dominated by bacteria are thus typically found in lakes with high inputs of allochthonous DOC [START_REF] Jansson | Allochthonous organic carbon and phytoplankton/bacterioplankton production relationships in lakes[END_REF][START_REF] Karlsson | Pelagic energy mobilization and carbon dioxide balance in subarctic lakes in Northern Sweden[END_REF].

Mixotrophic phytoplankton acquire carbon and/or mineral nutrients from bacterial prey, which allows them to eliminate their main competitors for these nutrients [START_REF] Thingstad | On the strategy of 'eating your competitor': A mathematical analysis of algal mixotrophy[END_REF]. Increased DOC concentrations therefore have the potential to directly alter the phytoplankton species assemblage by favouring mixotrophic flagellates relative to autotrophs when the plankton community is dominated by bacteria [START_REF] Jansson | Impact of allochthonous organic carbon on microbial food web carbon dynamics and structure in Lake Örträsket[END_REF].

Interactions between DOC and nutrients alter the net impact of DOC on aquatic systems [START_REF] Hitchcock | Responses of estuarine bacterioplankton, phytoplankton and zooplankton to dissolved organic carbon (DOC) and inorganic nutrient additions[END_REF]. Several studies have reported a nutrient and carbon co-limitation in heterotrophic bacteria, leading to synergetic responses when resources were added concomitantly rather than separately [START_REF] Dorado-García | Quantification of carbon and phosphorus co-limitation in bacterioplankton: New insights on an old topic[END_REF][START_REF] Egli | The concept of multiple-nutrient-limited growth of microorganisms and its application in biotechnological processes[END_REF]. However, inorganic nutrients associated with dissolved organic matter may also stimulate primary productivity through enhanced nutrient availability [START_REF] Deininger | Nitrogen effects on the pelagic food web are modified by dissolved organic carbon[END_REF][START_REF] Kissman | Nutrients associated with terrestrial dissolved organic matter drive changes in zooplankton:phytoplankton biomass ratios in an alpine lake[END_REF]. The generally low concentration of DOC in oligotrophic high-altitude lakes (commonly <1 mg/L, see [START_REF] Laurion | Attenuation of ultraviolet radiation in mountain lakes: Factors controlling the among-and within-lake variability[END_REF] makes these ecosystems highly sensitive to increased DOC inputs [START_REF] Sadro | The effect of an extreme rain event on the biogeochemistry and ecosystem metabolism of an oligotrophic high-elevation lake[END_REF]. Thus, bacteria were found to depend strongly on photosynthetic labile carbon released by algae, i.e. commensalistic interactions, in high-altitude lakes [START_REF] González-Olalla | Climate-driven shifts in algal-bacterial interaction of high-mountain lakes in two years spanning a decade[END_REF][START_REF] Medina-Sánchez | Neither with nor without you: A complex algal control on bacterioplankton in a high mountain lake[END_REF]. However, little is known about the effects on planktonic organisms of a labile carbon source and its interactions with nutrients in high altitude lakes, especially during the ablation phase of the ice-cover period.

In alpine regions, ice cover is a recurrent and prolonged state for lakes, acting as a major physical control on ecosystems [START_REF] Moser | Mountain lakes: Eyes on global environmental change[END_REF][START_REF] Pernica | In the cold light of day: The potential importance of under-ice convective mixed layers to primary producers[END_REF]. [START_REF] Felip | Microbial communities in the winter cover and the water column of an alpine lake: System connectivity and uncoupling[END_REF] distinguish three phases of winter cover: formation, growth, and ablation. Ablation is influenced by water melting from the snowpack in the catchment, correlated with nutrient loading rates and availability in lakes [START_REF] Leydecker | Spatial scaling of hydrological and biogeochemical aspects of high-altitude catchments in the Sierra Nevada, California[END_REF]. Dissolved organic matter of terrestrial origin and a predominantly heterotrophic epilimnion were thus observed immediately after snowmelt in a high-altitude lake of the Sierra Nevada [START_REF] Sadro | The effect of an extreme rain event on the biogeochemistry and ecosystem metabolism of an oligotrophic high-elevation lake[END_REF]. Global change, by affecting the quantity of accumulated snow and the nutrient quality and quantity in the catchment snowpack, could have direct repercussions on ecosystem functioning in these lakes [START_REF] Sadro | Effects of climate variability on snowmelt and implications for organic matter in a high-elevation lake[END_REF].

The under-ice plankton communities of high-altitude lakes can tell us a lot about the effects of inputs of DOC and nutrients. Firstly, plankton communities experience the impact of inputs from the catchment and atmospheric deposition during snowmelt. Secondly, 5. The expected future scenario of global change during the ablation phase is likely to change the balance between heterotrophic and autotrophic processes in planktonic food webs by increasing heterotrophic processes. These changes could have major repercussions on energy transfer from the base to the top of the food chain in high-altitude lakes.

6. Exploring the planktonic response to rapid environmental changes during the ablation phase appears to be crucial in order to determine how vulnerable high-altitude lakes are to future change. under-ice communities should be composed of taxa adapted to more heterotrophic conditions and should therefore show a clear response to DOC inputs. Finally, these communities constitute the inoculum of summer phytoplankton succession [START_REF] Adrian | Effects of ice duration on plankton succession during spring in a shallow polymictic lake[END_REF], so that changes in community structure could significantly impact the biodiversity of high-altitude lakes. However, a clearer picture is needed of how increased allochthonous inputs during the ablation period alter the functioning of high mountain lakes, especially the trophic relationships between phytoplankton and bacterioplankton.

This study investigated a plankton community's response to DOC inputs in interaction with inorganic nutrients during the ablation phase of the ice-covered period. We sampled the natural plankton assemblage under ice in a high-altitude lake and placed it under a dark: light cycle at 10℃ in laboratory microcosms. Then we subjected it to DOC additions under two nutrient-availability conditions (ambient concentrations or enriched by N and P). Glucose was used as DOC because it is a readily available C-source for bacterioplankton. To clarify the phytoplankton-bacterioplankton relationship, a total darkness treatment was realised to target heterotrophic processes, and an 18℃ treatment was realised to accelerate the metabolic processes of planktonic organisms. We hypothesised that: [START_REF] Felip | Microbial communities in the winter cover and the water column of an alpine lake: System connectivity and uncoupling[END_REF] under dark conditions limiting the influence of autotrophs, the addition of DOC should favour heterotrophic bacteria and mixotrophic phytoplankton; and (2) under light conditions, the addition of DOC should have a negative effect on autotrophs but a positive effect on heterotrophic prokaryotic plankton (HPP) and mixotrophs due to competition for nutrients.

| ME THODS

| Water sampling for experiments

Water for experiments was sampled in Lake Cordes, a high mountain lake located in the French Alps, adjacent to the Queyras regional nature park (France, 44°50′42″N, 6°47′20″E). Lake Cordes is situated above the treeline at 2,446 m above sea level. The lake is small (1.8 ha) and shallow (maximum depth = 9 m). The catchment area is large (140 ha), consisting of developed soils and meadows with approximately 60% alpine grass cover. The catchment lithology is mainly metamorphic rock (blue Shales). This lake has been described as oligotrophic by [START_REF] Jacquemin | Growth rate of alpine phytoplankton assemblages from contrasting watersheds and N-deposition regimes exposed to nitrogen and phosphorus enrichments[END_REF], with strong limitation of phytoplankton by N and P. The lake is ice-covered for 7-8 months, from October to June.

Sampling was conducted on 26th April 2019, at the transition from the growth to the ablation phase, when ice cover is usually at maximum thickness [START_REF] Catalan | High mountain lakes: Extreme habitats and witnesses of environmental changes[END_REF]. The lake was reached by ski and the water sampled for experiments by drilling a hole in the snow and in the ice. Water samples totalling 30 L were collected using a Niskin Bottle every metre, in order to sample the entire water column. The sampled water was filtered through a 50µm mesh to exclude larger potential grazers on food web components. This filtered water was then stored in sterilised opaque HDPE 8-L containers, placed in a cool box, and transported to the laboratory as soon as possible (between 5 and 6 hr later).

| Experimental design

| Factors and domain of interest

The aim of this study was to evaluate the effects of DOC and nutrient additions on a plankton community during the ablation phase in a high-altitude lake, particularly on interactions between heterotrophic bacteria and phytoplankton. To explore under-ice phytoplankton community responses, four factors were investigated:

• DOC additions (four treatments): 0, 2, 4, and 6 mg C/L, coded

respectively [0C], [2C], [4C] and [6C].
For the DOC additions, glucose was chosen as the carbon source to ensure that only the influence of the available fraction of DOC inputs was tested. Glucose is commonly used as a source of DOC in other similar microcosm experiments [START_REF] Hitchcock | Responses of estuarine bacterioplankton, phytoplankton and zooplankton to dissolved organic carbon (DOC) and inorganic nutrient additions[END_REF][START_REF] Liao | Interactive effects of ultraviolet radiation and dissolved organic carbon on phytoplankton growth and photosynthesis in Sanya Bay, Northern South China Sea[END_REF]. It was added in relatively low concentrations (+2, +4, and +6 mg/L) consistent with theoretical values for the biodegradable DOC fraction transported into the lake during the ablation period, but sufficient to ensure that, gradually, higher than natural DOC concentrations were reached. The 0C treatments with no glucose addition were used as the DOC-control, for comparison with the DOC additions.

• Nutrient addition (two treatments): ambient-nutrient concentration [0NP] and nitrogen and phosphorus-enriched [NP].

For the nutrient addition, N was added as NH 4 NO 3 to increase N concentrations to 335 µg/L and P was added as KH 2 PO 4 to increase P concentrations to 35 µg/L. The aim was to avoid potential nutrient limitation throughout this experiment, while remaining consistent with natural concentrations of dissolved inorganic nitrogen (DIN) and soluble reactive phosphorus (SRP) [START_REF] Jacquemin | Growth rate of alpine phytoplankton assemblages from contrasting watersheds and N-deposition regimes exposed to nitrogen and phosphorus enrichments[END_REF].

• Temperature (two conditions): [10℃] and [18℃].

The 10℃ temperature was chosen in order to mimic the conditions prevailing at the end of the ablation phase (a surface temperature of 2.79℃ was measured on 9 June 2016 in Lake Cordes, subsequently reaching 10.27℃ on 24 June 2016, personal data). The 18℃ temperature was chosen to enhance heterotrophy and accelerate the metabolic processes of organisms, without representing a threat to the planktonic organisms [START_REF] Jacquemin | Vulnerability of high altitude lakes to climate change[END_REF].

• Light conditions (two conditions): total darkness [Dark] and light:

dark cycle [Light].
The dark condition was intended to target heterotrophic processes while minimising the influence of autotrophs. For the dark condition, microcosms were placed in the dark in growth chambers, surrounded by aluminium. The light condition was designed to mimic light conditions at the end of the ablation phase, after ice-out. For the light condition, microcosms were placed under a circadian cycle (Light: dark cycle = 14:10), at a fixed irradiance (45 ± 2 µmol m -2 s -1 ).

This irradiance was sufficient to avoid light limitation in the microcosms [START_REF] Dubourg | Light and nutrient co-limitation of phytoplankton communities in a large reservoir: Lake Diefenbaker, Saskatchewan, Canada[END_REF][START_REF] Jacquemin | Growth rate of alpine phytoplankton assemblages from contrasting watersheds and N-deposition regimes exposed to nitrogen and phosphorus enrichments[END_REF].

| Design of experiments

The experimental designs are mathematical and statistical techniques that optimise the relevance of the data obtained by quantifying the relationship between output and input variables [START_REF] Box | Statistics for experimenters[END_REF][START_REF] Montgomery | Design and analysis of experiments[END_REF], while reducing the number of experiments required. Contrary to a one-factor-at-a-time approach, the experimental design involves simultaneous variation of all the factors, with a subset of combinations of experiments selected for modelling to estimate the effects of the four factors by considering the interactions between them. This approach, which is widely used in chemical studies, is relatively innovative in ecology.

The aim of this study was to evaluate the influence of DOC addition through interaction effects, i.e. quantifying a change in the effect of one factor according to the value of another factor. We considered the result of each experiment to be a linear combination of the main effects and interaction effects of each dimensionless factor, only taking into account interactions between two factors. This model could be written as:

X1 = DOC, X2 = Nutrients, X3 = Light, X4 = Temperature, b0 = model constant, b iA…C = coefficients for single and interactive effects.
To estimate the coefficients of this linear model, we used a Doptimal design with 24 experiments, which is a subset of the experiments under the full 4*2*2*2 factorial design with 32 experiments.

The linear model was also used to predict the output values for the eight conditions not treated experimentally. The 32 experiments (24 treated experimentally and eight modelled) are interpreted together in our study. All 24 experiments were realised in triplicate, for a total of 72 experiments (Table S1). Each experiment is a combination of one carbon treatment, one nutrient treatment, one temperature condition, and one light condition. The experimental design made it possible to reduce the number of experiments experimentally realised, thereby reducing the quantity of water transported from the lake. All quantitative analyses were realised with the AZURAD software (version Expert, AZURAD SAS, Marseille, France. 2019).

| Experimental set-up

Plankton were first acclimatised overnight in three 10-L sterilised transparent polycarbonate plastic bottles (Nalgene ® ) at 10℃ under the circadian cycle before the start of the experiments. Then, water from each polycarbonate plastic bottle was manually homogenised and transferred to the 72 microcosms. Each microcosm consisted of a 500-ml sterilised transparent polycarbonate plastic bottle (Nalgene ® ) filled with 350 ml of sampled water to allow gas exchanges, according to the protocol used by [START_REF] Jacquemin | Growth rate of alpine phytoplankton assemblages from contrasting watersheds and N-deposition regimes exposed to nitrogen and phosphorus enrichments[END_REF].

Natural planktonic organisms were incubated under the different experimental conditions for 10 days. The microcosms were manually homogenised and randomly displaced inside the growth chamber every day.

| Measurements

| Dissolved organic carbon

Dissolved organic carbon was measured at the initial conditions and at the end of the experiments. Subsamples were filtered through pre-combusted 25-mm diameter glass filters (Whatman GF/F, 0.7 µm), then stored in 24 ml pre-combusted (4 hr at 450℃) glass tubes (Wheaton equipped with Teflon/silicone septa) and preserved with 30 µl of sodium azide solution (1 M NaN 3 ) at +4℃. DOC concentration was determined using a TOC-VCSH analyser (Shimadzu, TOC-V). Consumed DOC was the difference between the initial DOC concentrations after carbon additions and the final DOC concentrations measured at the end of the experiments.

| Anions and cations

Subsamples of water were filtered through precombusted 25mm glass filters (Whatman GFF, 0.7 μm) for estimation of DIN

(DIN = NH + 4 + NO + 2 ⋅ NO 2 -
3 ) and SRP (SRP = PO 3 - 4 ) concentrations at the initial conditions. The dissolved fraction was stored in a 125ml HDPE bottle, placed in a cool box and frozen (-18℃) until analysis.

Dissolved anions and cations were determined by ionic chromatography (Metrohm, 930 Compact IC Flex combined with 863 Compact Autosampler).

| Chlorophyll a

Chlorophyll a concentration was measured at the initial conditions and at the end of the experiments to estimate chlorophyll biomass.

Water was filtered through 47-mm glass filters (Whatman GF/C, 1.2 µm) placed in glass tubes filled with 10 ml of acetone solution (90%) for 24 hr at +4℃ for chlorophyll a extraction. Chlorophyll a concentrations were measured spectrophotometrically (Jasco,

Y = b 0 + b 1A X 1A + b 1B X 1B + b 1C X 1C + b 2A X 2A + b 3A X 3A + b 4A X 4A + b 1A-2A X 1A X 2A + b 1B-2A X 1B X 2A +b 1C-2A X 1C X 2A + b 1A-3A X 1A X 3A + b 1B-3A X 1B X 3A + b 1C-3A X 1C X 3A + b 1A-4A X 1A X 4A +b 1B-4A X 1B X 4A + b 1C-4A X 1C X 4A + b 2A-3A X 2A X 3A + b 2A-4A X 2A X 4A + b 3A-4A X 3A X 4A
V-630) by the Lorenzen method, with correction for pheophytin interference by acidification.

| Phytoplankton

Our analyses distinguished between picophytoplankton (<2 µm size) and larger phytoplankton (>2 µm size), for a finer assessment of trophic functioning [START_REF] Izaguirre | Phytoplankton in Antarctic lakes: Biodiversity and main ecological features[END_REF].

Sub-samples of 1.5 ml were taken at the initial conditions and thereafter every 2 experimental days in the microcosms for picophytoplankton analyses by flow cytometry. Subsamples were fixed with glutaraldehyde (0.25% final concentration) and stored at -80℃ until flow cytometry analysis. Picophytoplankton were characterised and enumerated using an Accuri C6 flow cytometer equipped with a blue laser (488 nm) and running 500 µl of sample at fast speed (66 µl/ min). Data were acquired and analysed using BD Accuri CFlow Plus Analysis software (BD-Biosciences). Picophytoplankton were identified according to size (FSC), complexity (SSC), and fluorescence (emission in the orange and red wavelength ranges, respectively 585 ± 20 and >670 nm). Non-fluorescent polystyrene microspheres (Flow Cytometry Size Calibration Kit, Thermo Fisher Scientific) were used as a size standard. Flow cytometer analysis distinguished between two picophytoplankton groups. Small cells (<2 µm) with high orange fluorescence and low granularity were classified as phycoerythrinrich picocyanobacteria (picocyanobacteria). A picoeukaryote group was identified by its high red and low orange fluorescence, small size (<2 µm) but higher granularity than the picocyanobacteria.

Phytoplankton >2 µm in size were enumerated and identified via microscopy. Phytoplankton communities were analysed before the start and at the end of the experiments. The samples for phytoplankton composition analysis were fixed with alkaline Lugol solution (0.5%) and stored in 150 ml HDPE bottles at +4℃. Phytoplankton counts were performed according to the [START_REF] Utermöhl | Methods of collecting plankton for various purposes are discussed[END_REF] method, at 40-fold magnification under an inverted microscope (Olympus IX 70). Phytoplankton samples were identified at genus level and species level when possible, using appropriate taxonomic guides.

To ensure that picocyanobacteria and cyanobacteria >2 µm were not double counted, we calculated the average size of each of these groups. We estimated the mean size of picocyanobacteria from the average FSC value of their cytometric population. We then used the equation obtained from the linear regression between the size of polystyrene microspheres (Flow Cytometry Size Calibration Kit, Thermo Fisher Scientific) and their respective FSC values. For the unicellular cyanobacteria >2 µm, we measured the length of each cell (n > 30) using NIS Element ® software, then calculated an average length for the group.

| Heterotrophic prokaryotic plankton

Sub-samples of 1 ml were taken at the initial conditions and thereafter every 2 experimental days in the microcosms for HPP analyses by flow cytometry. Subsamples were fixed with glutaraldehyde (0.25% final concentration) and stored at -80℃ until flow cytometry analysis. After thawing, each sample was stained with 1:10,000 (vol/vol) SYBR ® Green II and incubated 20 min in darkness. HPP were characterised and enumerated using an Accuri C6 flow cytometer equipped with a blue laser (488 nm) and running 50 µl of stained sampled at medium speed (35 µl/min). Data were acquired and analysed using BD Accuri CFlow Plus Analysis software (BD-Biosciences). HPP were identified by their small size (low FSC), low complexity (low SSC), high green fluorescence (530 ± 15 nm), and lack of red (>670 nm) fluorescence.

| Cellular carbon biomass calculation

To estimate the carbon biomass of the natural picoplankton organisms, abundance was transformed into carbon content based on the literature. Cell abundance (cells/ml) of HPP was converted to biomass (µg C/L) using 20 fg C/cell as constant conversion factor [START_REF] Ducklow | Bacterial production and biomass in the oceans[END_REF][START_REF] Linacre | Distribution pattern of picoplankton carbon biomass linked to mesoscale dynamics in the southern Gulf of Mexico during winter conditions[END_REF]. The conversion factor for picocyanobacteria was 237 fg C/cell [START_REF] Gerea | Grazing impact and prey selectivity of picoplanktonic cells by mixotrophic flagellates in oligotrophic lakes[END_REF]) and for picoeukaryotes it was 56 fg C/cell [START_REF] Linacre | Distribution pattern of picoplankton carbon biomass linked to mesoscale dynamics in the southern Gulf of Mexico during winter conditions[END_REF]. For phytoplankton >2 µm, biovolume was estimated by shape assimilation to known geometric forms and direct measurement of the main cell dimensions. The mean biovolume was calculated for each class of phytoplankton, then the biovolume was converted into biomass using the particular carbon content defined for each class by [START_REF] Wetzel | Composition and biomass of phytoplankton[END_REF].

| Ciliate abundance estimations

We attempted here to minimise any possible predation by multicellular zooplankton and ciliates by filtering the water at 50 µm.

However, to determine whether any predators had developed in our microcosms, ciliate abundances were estimated via the Utermöhl method [START_REF] Felip | Microbial communities in the winter cover and the water column of an alpine lake: System connectivity and uncoupling[END_REF], under initial conditions and at the end of the experiments.

| Statistical analysis

| Quantitative analysis

The effect of DOC additions in interaction with nutrients, with temperature, and with light was tested using the linear model estimated according to the experimental design. For each output variable, the coefficients of the model were calculated (version Expert, AZURAD SAS, Marseille, France. 2019) using multilinear regressions (see Section 2.2.2). For the eight modelled experiments, data were calculated using the model and the error bars were calculated based on the mean standard errors of the 24 triplicates, with a 95% confidence interval.

| Multivariate analysis

Multivariate analyses to detect changes in phytoplankton community structure were performed on the phytoplankton biomass at the end of the experiment. Multivariate analyses were performed with the vegan package on R software (v. 3.6.3). Because phytoplankton community structure differed strongly between the dark and the light conditions, all multivariate analyses were performed twice, under both dark and light conditions. To visualise the differences in phytoplankton community structure between treatments, we performed a non-metric multidimensional scaling analysis on the Bray-Curtis dissimilarity matrix to depict community structure patterns in two dimensions. To test the hypothesis that DOC addition structured the distribution of phytoplankton communities, permutational multivariate analysis of variance (PERMANOVA) was used with 999 permutations (p = 0.05) with the ADONIS function in R. We carried out a multivariate homogeneity of group dispersion analysis (β diversity) to assess the homogeneity of phytoplankton assemblages within a group of samples [START_REF] Anderson | Multivariate dispersion as a measure of beta diversity[END_REF]. A similarity percentage (SIMPER) analysis was performed to identify which phytoplankton groups govern community dynamics.

| RE SULTS

| Initial conditions

Chemical variables such as DOC, SRP, and DIN were low at the start of the experiments, representative of typical oligotrophic lakes with C/N ratio = 2.5 (Table 1). Plankton biomass was dominated by HPP at the start of the experiments, but phytoplankton biomass showed a value relatively close to that of HPP biomass.

Phytoplankton biomass was dominated by large diatoms such as

Fragilaria sp. (32%), picocyanobacteria (25%), chrysophytes-mainly Dinobryon sp.-(19%), and dinoflagellates (15%). Unicellular cyanobacteria >2 µm also represented a non-negligible proportion of the phytoplankton biomass.

| Consumed DOC at the end of experiments

The DOC consumed at the end of the experiments varied according to DOC interaction with nutrients (p < 0.001), with temperature (p < 0.001), or with light (p < 0.001). DOC consumed increased according to the glucose gradient in almost all the four conditions of temperature*light (Figure 1). In DOC-control treatments (0C), DOC was consumed in the dark but was in excess in the light at the end of the experiments, whatever the temperature. However, DOC was consumed more when glucose was added at 18℃ than at 10℃, whatever the light condition. Finally, DOC was consumed more when glucose was added in combination with nutrient addition (NP) than in nutrient-ambient treatments (0NP).

| Heterotrophic prokaryotic plankton

Interactions between DOC and nutrients (p = 0.009), DOC and temperature (p < 0.001), and DOC and light (p = 0.017) had significant effects on HPP biomass assessed at the end of the experiments.

Under the 10°C_dark condition, addition of DOC increased HPP biomass compared to DOC-control treatments (Figure 2). Under the 10°C_light condition, addition of DOC increased HPP biomass compared to DOC-control in the ambient-nutrient treatments. HPP biomass decreased with DOC addition compared to 0C at 18°C_dark in the NP treatments, and at 18°C_light in both the 0NP and the NP treatments.

Moreover, interactions between nutrient addition and temperature affected HPP biomass (p < 0.001). At the end of the experiments, N and P additions increased HPP biomass at 10℃ but not at 18℃. However, nutrient addition had a positive effect on HPP biomass at 18℃ as well, until the sixth day of the experiments (Figure 3; Table S2). This was followed by a strong decline in HPP biomass until the end of the experiments. in the microcosms at 10℃, regardless of light condition (Figure 4).

| Ciliates

However, ciliates developed at 18℃ when DOC was added either alone or in combination with nutrients. A particularly strong increase in ciliate abundance was observed when DOC was added at concentrations of 4 and 6 mg/L (4C and 6C). At 18℃, in the 4C_NP and 6C_NP treatments, ciliate abundance was higher in the dark than in the light at the end of the experiments.

| Chlorophyll biomass

There were significant effects from interactions between carbon and nutrients (p < 0.001), carbon and temperature (p < 0.001), and carbon and light (p < 0.001) on chlorophyll biomass at the end of the experiments. In dark conditions, chlorophyll biomass was below the initial concentration of 1.01 µg/L in almost all treatments. The exceptions were the treatments at 10℃ at 2C_0NP and 6C_0NP, where chlorophyll biomass reached 1.52 and 1.31 µg/L, and at 18℃ at 0C_NP, where chlorophyll biomass reached 1.89 µg/L (Figure 5). In light conditions, chlorophyll biomass increased more strongly in DOC-controls than under DOC additions, except at 10℃ in the 0NP treatments. This effect was more pronounced at 18℃ in nutrient-enriched conditions, where chlorophyll biomass increased by 7.9 µg/L in the DOC-control but only between 4.5 and 5.1 µg/L after DOC additions.

Chlorophyll biomass was strongly correlated with final total phytoplankton biomass (Pearson's correlation, Cor = 0.91, p < 0.001).

| Shifts in phytoplankton community structure

There were significant effects from interactions between carbon and nutrients (p = 0.003), carbon and temperature (p < 0.001), and carbon and light (p = 0.006) on total phytoplankton biomass at the end of the experiments. Permutational multivariate analysis of variance did not reveal any change in community composition under DOC addition alone, neither in the dark nor in the light.

However, ADONIS analyses showed that the interaction between DOC and nutrients led to significant differences in community structure under the different carbon*nutrients treatments, both in light (r 2 = 0.54, F = 5.4, p = 0.001) and in dark conditions (r 2 = 0.30, F = 1.9, p = 0.006). Moreover, significant differences in community structure were also detected under the different DOC*temperature conditions, both in light (r 2 = 0.51, F = 4.7, p = 0.001) and in dark conditions (r 2 = 0.41, F = 3.2, p = 0.001; Table S3). with increasing DOC (SIMPER analysis): chrysophytes (37%), picocyanobacteria (27%), diatoms (19%), cyanobacteria >2 µm (5%), and dinoflagellates (6%). Concerning the size of the two groups of cyanobacteria, the calculated and measured lengths were highly different between the groups: the mean size of the cyanobacteria >2 µm was 5.04 ± 0.86 µm, and the mean size of the picocyanobacteria was 1.5 ± 0.03 µm (data not shown).

Interactions between carbon and nutrients (p < 0.001), carbon and temperature (p < 0.001), and carbon and light (p < 0.001) were

shown at the end of the experiments to have significantly affected picophytoplankton biomass, mainly composed of picocyanobacteria (Table S4; Figure S1). Moreover, each interaction between DOC and temperature, light, and nutrients at the 10th experimental day was representative of the other experimental days. The addition of DOC had a negative effect on picocyanobacteria biomass in all conditions of temperature*light, except in the 10°C_dark condition (Figure 6). In the 10°C_light condition, picocyanobacteria biomass decreased with DOC addition only when nutrients were added to the microcosms (NP). In the 18°C_dark and 18°C_light conditions, picocyanobacteria biomass decreased with DOC addition at 4C and 6C in both NP and 0NP treatments.

| D ISCUSS I ON

The ablation phase is a crucial period in the functioning of high altitude lakes [START_REF] Felip | Microbial communities in the winter cover and the water column of an alpine lake: System connectivity and uncoupling[END_REF], because allochthonous inputs can directly affect the food web [START_REF] Kissman | Nutrients associated with terrestrial dissolved organic matter drive changes in zooplankton:phytoplankton biomass ratios in an alpine lake[END_REF] and therefore govern summer plankton communities. This study sought to assess how planktonic organisms respond to the joint addition of DOC and nutrients during the winter ablation phase in a high-altitude lake. We At the end of the experiments, glucose was consumed in the dark conditions, and more glucose was consumed when nutrients and glucose were added together. Moreover, we found an effect of interaction between DOC and nutrients on HPP biomass. At 10℃, this interactive effect resulted in a higher HPP biomass when nutrients and DOC were added together than under single additions of DOC or nutrients, evidence of co-limitation of HPP by C, N, and P. Several previous studies also deduced that there was co-limitation by nutrients and carbon in microbial communities of oligotrophic lakes [START_REF] Vidal | Carbon and phosphorus regulating bacterial metabolism in oligotrophic boreal lakes[END_REF], finding stronger responses to combined resources than to single-nutrient additions. Particularly in arctic and alpine lakes, bacterial growth appears to be highly limited by low natural concentrations of inorganic nutrients and organic carbon [START_REF] Bertoni | Susceptibility of bacterioplankton to nutrient enrichment of oligotrophic and ultraoligotrophic lake waters[END_REF][START_REF] Granéli | Phosphorus limitation of bacterial growth in high Arctic lakes and ponds[END_REF].

By contrast, we did not observe any positive effect of DOC additions on HPP biomass in our microcosms at 18℃ in the dark conditions, neither when added alone nor when combined with nutrients.

Ciliate abundance in our microcosms was stimulated by DOC addition at 18℃, especially under combined additions of DOC and nutrients. The strong decline in HPP biomass from the 6th day until the end of the experiments at 18℃ further supports increased predatory pressure from ciliate development in our microcosms. Therefore, the observed HPP response to DOC additions at 18℃ was probably the result of strong predation by ciliates. Ciliates are acknowledged to be major consumers of bacteria [START_REF] Ameryk | The dependence between bacterial production and environmental conditions in the Gulf of Gdańsk[END_REF]. In earlier mesocosm experiments, flagellates and ciliates were found to increase following DOC additions [START_REF] Blomqvist | Effects of additions of DOC on pelagic biota in a clearwater system: Results from a whole lake experiment in northern Sweden[END_REF] via a transfer of bacterial production up to these predators. Our findings support the idea that the presence of ciliates acts as a major control of HPP biomass. Moreover, the magnitude of the predatory control increased considered by several studies as a possible adaptation to permanent ice-cover in Antarctic lakes [START_REF] Marshall | The balance between photosynthesis and grazing in Antarctic mixotrophic cryptophytes during summer[END_REF].

Moreover, even though cyanobacteria >2 µm are considered strictly photoautotrophic in freshwater [START_REF] Reynolds | Ecology of phytoplankton[END_REF], glucose assimilation has been observed in some filamentous species in a deep mesotrophic perialpine lake [START_REF] Zotina | Photoheterotrophy and lightdependent uptake of organic and organic nitrogenous compounds by Planktothrix rubescens under low irradiance[END_REF] and in several genera of cyanobacteria in a Siberian saline lake [START_REF] Quesada | Heterotrophic capability of a metalimnetic plankton population in saline Lake Shira (Siberia, Khakasia)[END_REF]. Our results suggest that unicellular cyanobacteria >2 µm could also have played a role in glucose consumption in the dark in our microcosms.

Thus, contrary to our expectations, we found that mixotrophs were not particularly favoured by DOC additions in the dark and that bacterivory by mixotrophs had only a minor impact on the HPP response to DOC addition. Mixotrophy is known to be an advantageous strategy in light-limiting and nutrient-limiting environments, despite a higher energetic cost compared to the obligate autotrophic or heterotrophic metabolism [START_REF] Mitra | The role of mixotrophic protists in the biological carbon pump[END_REF]. Acquiring carbon and/or mineral nutrients from bacterial prey allows mixotrophs to eliminate their main competitors for these nutrients, called the eating your competitor strategy by [START_REF] Thingstad | On the strategy of 'eating your competitor': A mathematical analysis of algal mixotrophy[END_REF]. However, it was also experimentally demonstrated that mixotrophic bacterivory on picoplankton was light-dependent (Fischer et al., 2017). This dependency has been interpreted as a need for energetic photosynthesis to support phagotrophy [START_REF] Li | Mixotrophy in Gyrodinium galatheanum (Dinophyceae): Grazing responses to light intensity and inorganic nutrients*[END_REF].

Overall, DOC additions stimulated HPP biomass in the dark, particularly when combined with addition of nutrients because of the co-limitation of HPP by C, N, and P. However, our results did not confirm our hypothesis regarding mixotrophic phytoplankton. When the influence of commensalistic and competitive interactions between phytoplankton and bacteria were reduced, ciliate predatory control was the major control of the HPP response to DOC addition. Multivariate analyses also revealed significant effects on the phytoplankton community from interactions between the DOC*nutrients treatments and between the DOC*temperature treatments. These interactive effects resulted in increased biomass of chrysophytes after combined DOC and nutrient addition at 10℃ alone.

Our results reflected a diversification of top-down control in the light conditions, with potential ingestion of HPP by mixotrophs at 10℃ under combined additions of DOC and nutrients. In the light conditions, mixotrophic phytoplankton and ciliates competed for the same prey in our microcosms. Previous studies reported competition between mixotroph and heterotrophic bacterivores for prey in the light (Fischer et al., 2017). Although temperature optima differ between species, most ciliates tolerate a relatively wide range of temperatures, with high growth rates at high temperatures [START_REF] Weisse | Freshwater ciliates as ecophysiological model organisms-lessons from Daphnia, major achievements, and future perspectives[END_REF]. Moreover, the metabolic theory of ecology predicts that the heterotrophic metabolism will respond more strongly to rising temperature than the autotrophic metabolism [START_REF] Rose | Does low temperature constrain the growth rates of heterotrophic protists? Evidence and implications for algal blooms in cold waters[END_REF]. Our results show that DOC additions stimulated the mixotrophic strategy of eating your competitor at 10℃ when nutrients were added to the microcosms, while prey ingestion by ciliates replaced ingestion by mixotrophs at a higher temperature.

| Competition processes with autotrophs

We found a strong decrease in picocyanobacteria biomass with DOC additions in the light, except at 10℃ without nutrients. Previous studies reported a competitive advantage of heterotrophic bacteria over picocyanobacteria, especially after carbon inputs [START_REF] Drakare | Competition between picoplanktonic cyanobacteria and heterotrophic bacteria along crossed gradients of glucose and phosphate[END_REF][START_REF] Liao | Interactive effects of ultraviolet radiation and dissolved organic carbon on phytoplankton growth and photosynthesis in Sanya Bay, Northern South China Sea[END_REF]. We therefore suggest that the observed decrease ciliates and mixotrophs could not be determined from our experiments. As in the dark, the predatory control exerted by ciliates on HPP biomass was the major control at the higher temperature.

| Primarily nutrient limitation and commensalistic interaction

We found that DOC concentrations increased in the DOC-control treatments in the light conditions, but not in the dark, which indicates two indirect results: (1) phytoplankton-derived carbon was produced in the light; and (2) control by phytoplankton-derived carbon was severely limited in the dark at the end of the experiments. Moreover, HPP biomass in the dark conditions revealed that HPP were able to develop with added nutrients alone, evidence of limitation primarily by N and P of the HPP in our microcosms.

Due to the generally low DOC concentrations in high-altitude lakes, heterotrophic bacteria are known to be primarily carbon-limited in these environments [START_REF] Carrillo | The interaction of phytoplankton and bacteria in a high mountain lake: Importance of the spectral composition of solar radiation[END_REF][START_REF] Durán | Changes in the phytoplankton-bacteria coupling triggered by joint action of UVR, nutrients, and warming in Mediterranean highmountain lakes[END_REF][START_REF] Medina-Sánchez | Patterns of resource limitation of bacteria along a trophic gradient in Mediterranean inland waters[END_REF]. Nevertheless, limitation primarily by nutrients and co-limitation by C of bacteria was previously observed in an oligotrophic mountain lake [START_REF] Dorado-García | Quantification of carbon and phosphorus co-limitation in bacterioplankton: New insights on an old topic[END_REF]. This pattern of co-limitation was explained by the autotrophic nature of the ecosystem, where carbon derived from phytoplankton was sufficient to support bacterial demands. In our experiments, while the initial phytoplankton biomass was slightly smaller than the HPP biomass,

  Interactions between DOC and nutrients (p = 0.003), and DOC and temperature (p < 0.001) significantly affected ciliate abundance at the end of the experiments. Very few ciliates developed TA B L E 1 Mean values of the main chemical and biological variables measured in the initial experimental conditions

F I G U R E 1

 1 Dissolved organic carbon (DOC) consumed at the end of each experiment. Concentrations are shown for each DOC*nutrient treatment under the four temperature*light conditions. Error-bars represent standard error (n = 3). High values indicate lower concentrations at the end of the experiments than at initial conditions, while negative values indicate higher concentrations at the end of the experiments than at initial conditions At the end of the experiments, five phytoplankton groups accounted for 94% of differences in community structure observed

For

  the mixotrophic taxa, DOC addition had a positive effect on the relative biomass of mixotrophic phytoplankton, depending on taxonomic groups, conditions of temperature*light, and nutrient addition. The relative biomass of chrysophytes increased with DOC addition in the 10°C_light condition in the NP treatments. The relative biomass of cryptophytes increased weakly with DOC addition in the 18°C_dark condition at 6C compared to DOC-controls, in both 0NP and NP treatments (Figure S2). The relative biomass of dinoflagellates increased weakly with DOC addition in the 18°C_dark condition in 0NP treatments. Finally, the relative biomass of cyanobacteria >2 µm increased with DOC addition when nutrients were added to the microcosms, in all temperature*light conditions except the 10°C_dark condition.

F

  Heterotrophic prokaryotic plankton (HPP) biomass at the end of experiments. Biomass is shown for each dissolved organic carbon (DOC)*nutrient treatment under the four temperature*light conditions. Error-bars represent standard error (n = 3) specifically used a multifactorial experimental design to focus on the phytoplankton-bacterioplankton relationship.

F

  Heterotrophic prokaryotic plankton (HPP) biomass per experimental day. Biomass is shown for each dissolved organic carbon (DOC)*nutrient treatment under the four temperature*light conditions. Error-bars represent standard error (n = 3) substantially with changing environmental conditions, and overtook the bottom-up effect of DOC and nutrients on HPP biomass. 4.1.2 | Phytoplankton response to DOC and nutrients in the dark Both chlorophyll and phytoplankton biomass were substantially lower in the dark, indicating a strong reduction of phytoplanktonic influence in these experimental conditions. Due to this very low biomass, we did not observe a clear response to the DOC additions in the dark from either mixotroph or autotroph phytoplankton. There was only a slight tendency to increased biomass of cyanobacteria >2 µm and of cryptophytes biomass under DOC and nutrient additions at 18℃. Although weak, this tendency confirms that cryptophytes are capable of prey ingestion in darkness (McKie-Krisberg et al., 2015),

F

  Ciliate abundances at the end of experiments. Abundances are shown for each dissolved organic carbon (DOC)*nutrient treatment under the four temperature*light conditions. Error-bars represent standard error (n = 3) 4.2 | DOC and nutrient additions in light conditions 4.2.1 | Diversification of top-down controls in the light As in the dark conditions, HPP biomass increased only at 10℃ with DOC additions, but only when DOC was added alone. Moreover, the increase of ciliates at 18℃ and the decrease of HPP biomass from the sixth day until the end of the experiments at 18℃ suggested the same predatory control by ciliates over HPP in the light conditions.

  in picocyanobacteria could be due to competition between HPP and picocyanobacteria for nutrients. Added to the competition with HPP, picocyanobacteria can also suffer predation by mixotrophs and ciliates. In shallow oligotrophic lakes, ingestion of picocyanobacteria by mixotrophic flagellates was recently observed[START_REF] Gerea | Grazing impact and prey selectivity of picoplanktonic cells by mixotrophic flagellates in oligotrophic lakes[END_REF], notably by chrysophytes in subalpine lakes[START_REF] Weisse | Light affects picocyanobacterial grazing and growth response of the mixotrophic flagellate Poterioochromonas malhamensis[END_REF]. F I G U R E 5 Chlorophyll biomass at the end of experiments. Concentrations are shown for each dissolved organic carbon (DOC)*nutrient treatment under the four temperature*light conditions. Error-bars represent standard error (n = 3) Unfortunately, our experiments did not enable us to determine the proportions of the decrease in picocyanobacteria explained by competition with HPP and by predation by bacterivores. Contrary to the picocyanobacteria, the biomass of the cyanobacteria >2 µm increased with combined additions of DOC and nutrients in the light. As in the dark, this increase indicates that the cyanobacteria >2 µm were capable of carbon assimilation and depended on a sufficient stoichiometric C: NP ratio to develop in the light conditions. Overall, DOC additions in the light stimulated the biomass of HPP and mixotrophs, and predation by mixotrophs acted as a strong top-down control of HPP biomass at 10℃. While DOC addition decreased autotrophic picocyanobacteria, the proportions of this decrease explained by competition with HPP and by predation by

  it may have been sufficient to generate limitation of HPP primarily by N and P and co-limitation by C. Despite stronger limitation by nutrients than by carbon, an increase in HPP biomass was observed in our microcosms after DOC additions. This could be interpreted as a release from HPP dependency on photosynthetic carbon excreted by phytoplankton, i.e. a decrease in commensalistic interactions between HPP and phytoplankton.F I G U R E 6 Phytoplankton groups relative biomass and total absolute biomass (black points) at the end of experiments. Biomass is shown for each dissolved organic carbon*nutrient treatment under the four temperature*light conditions

DATA AVA I L A B I L I T Y S TAT E M E N T

The datasets generated and analysed during the current study are available from the corresponding author on reasonable request.

| Ecological implications

Our results support previous findings that DOC inputs can greatly alter the food web in high-altitude lakes [START_REF] Kissman | Nutrients associated with terrestrial dissolved organic matter drive changes in zooplankton:phytoplankton biomass ratios in an alpine lake[END_REF], particularly if they occur during the ablation phase. Our results suggest that DOC inputs during the ablation phase, depending on nutrient limitation, may rapidly alter the trophic interactions between heterotrophic bacteria and phytoplankton. These changes are likely to involve decreased commensalistic interactions between bacteria and phytoplankton but increased competition with autotrophic picocyanobacteria, and an increase and diversification of predatory top-down controls over bacteria. Since the winter communities constitute the inoculum of the summer succession in high-altitude lakes [START_REF] Adrian | Effects of ice duration on plankton succession during spring in a shallow polymictic lake[END_REF], rapid changes in trophic relationships between bacteria and phytoplankton can have major repercussions on the general functioning of lakes. While bacteria would benefit more than phytoplankton from labile DOC inputs in a future scenario of global change, higher predatory control over bacteria is also expected. Thus, our findings support a future scenario of global change involving modifications in the balance of heterotrophic versus autotrophic processes toward higher heterotrophy during the ablation phase in high-altitude lakes. The predicted change will vary according to: [START_REF] Felip | Microbial communities in the winter cover and the water column of an alpine lake: System connectivity and uncoupling[END_REF] the characteristics of the dissolved organic matter, i.e. nutrient content, lability of the carbon source, and proportion of humic coloured substances; (2) type of top-down control, such as predation by zooplankton or ciliates; and (3) the composition of phytoplankton assemblages, including the proportion of mixotrophic phytoplankton.

ACK N OWLED G M ENTS

We are grateful to Eric Meineri and to members of the French Biodiversity Office for their help in the field. DOC analyses were carried out by the Mediterranean Institute of Oceanography. Data used in this study were partly produced through the technical facilities of the Biological and Chemical Analysis (IMBE, Marseille) by David Brinvillier. We thank Marjorie Sweetko for improving the English of this manuscript. Flavia Dory received a PhD fellowship from the Ministère de l'Enseignement Supérieur et de la Recherche and this paper is part of her Ph.D.

CO N FLI C T O F I NTE R E S T

The authors declare no conflicts of interest.

S U PP O RTI N G I N FO R M ATI O N

Additional supporting information may be found online in the Supporting Information section.

How to cite this article


Claire Dune

Anthony Remazeilles

Eric Marchand

Christophe Leroux

Vision-based grasping of unknown objects to improve disabled persons autonomy

This paper presents our contribution to vision based robotic assistance for people with disabilities. The rehabilitative robotic arms currently available on the market are directly controlled by adaptive devices, which lead to increasing strain on the user's disability. To reduce the need for user's actions, we propose here several vision-based solutions to automatize the grasping of unknown objects. Neither appearance data bases nor object models are considered. All the needed information is computed on line. This paper focuses on the positioning of the camera and the gripper approach. For each of those two steps, two alternative solutions are provided. All the methods have been tested and validated on robotics cells. Some have already been integrated into our mobile robot SAM.

I. INTRODUCTION

This work relates to robotic assistance for disable people, where autonomous robotic systems are designed to compensate for a human motor disability. We propose solutions for the grasping of any object within a domestic environment such as an apartment. Providing a robust, generic and easy-to-use solution to improve the user's interaction with their personal environment would largely increase their autonomy.

Contrary to an industrial environment [START_REF] Sanz | Grasping the not-so-obvious: vision-based object handling for industrial applications[END_REF], the domestic environment is highly unstructured. Thus, the robotic system needs exterioceptive sensors to adapt its behavior to the current situation. Vision sensors are almost always used: this sensor is quite cheap, the acquired information is very rich, and it can even be directly used as feedback for the user.

A. State of the art

Before starting a grasping procedure, a robotic system first needs to extract information on the object from the visual input. In order to handle any object shape and appearance, it is necessary to make some assumptions on the situations the robot can handle.

Some approaches propose to constrain the possible locations for the object. For example, [START_REF] Hauck | Visual determination of 3d grasping points on unknown objects with a binocular camera system[END_REF] assumes that the scene is known and uses a simple image difference with the known background to localize the object. The project FRIEND II reduces the grasping area to a tactile tray fixed on an instrumented wheelchair [START_REF] Volosyak | Rehabilitation robot FRIEND II -the general concept and current implementation[END_REF].

Since the user would like to operate anywhere in his home, it is difficult to constrain the grasping place ; assumptions must then be made on the objects themselves. Some solutions rely on a data base of objects which is used to recognize the scene observed by the camera. In [START_REF] Kragic | Vision for robotic object manipulation in domestic settings[END_REF], the object recognition and pose estimation is performed by comparing SIFT descriptors [START_REF] Lowe | Distinctive image features from scale-invariant keypoints[END_REF] and color histograms with the database. Object tracking methods like [START_REF] Liefhebber | Vision-based control of the manus using SIFT[END_REF][START_REF] Dionnet | Robust stereo tracking for space robotic applications[END_REF] suppose that an object model is known (respectively a sparse 3D model and a structured one).

Instead of requiring the knowledge of all possible objects several methods propose to infer the object characteristics or shape in order to get a set of object categories that are then used to guide the robot toward the grasping position. In [START_REF] Saxena | Robotic grasping of novel objects using vision[END_REF], a set of rendered 3D models are used as a training database. A supervised learning stage enables an object to be associated with one of the five obtained categories, and from there selects the best grasping position. The MOVAID project [START_REF] Taddeucci | Experiments in synthetic psychology for tactile perception in robots: steps towards implementing humanoid robots[END_REF] uses a mixed fuzzy logic/neural network module to select the best grasping position.

Naturally, the user expects to be able to grasp any object in his environment. Nevertheless, no machine learning or object recognition technique can succeed in handling every kind of object. It is thus necessary to provide solutions to deal with unknown objects, at least as a complement to these methods. In this context, several approaches propose to infer the object characteristics from its observed shape. The 2D structure of the object can be used to determine the grasping position, such as its skeleton [START_REF] Hauck | Visual determination of 3d grasping points on unknown objects with a binocular camera system[END_REF] or its 2D moments [START_REF] Sanz | Grasping the not-so-obvious: vision-based object handling for industrial applications[END_REF]. Some approaches rely on implicit 3D functions to model the object's 3D shape, using active vision to refine the estimated parameters [START_REF] Whaite | Autonomous exploration driven by uncertainty[END_REF][START_REF] Flandin | Visual data fusion for objects localization by active vision[END_REF].

In most of the robotic systems, the camera is embedded onto the arm gripper (eye-in-hand configuration) and the object is supposed to be directly within the camera field of view (FOV). Nevertheless, the perception of the environment around the arm is strongly restricted, and there is little chance that the above requirement is met, especially when the arm is mounted on a mobile unit. Few methods address this problem. It is usually solved by using an external additional camera (eyeto-hand configuration). In [START_REF] Horaud | Camera cooperation for achieving visual attention[END_REF] an initialization step ensures that a moving object detected by the eye-to-hand camera falls within the embedded camera's FOV. [START_REF] Kragic | Vision for robotic object manipulation in domestic settings[END_REF] adds a wide FOV stereo rig to orientate an eye-in-hand stereo rig toward the object direction.

B. Our system philosophy

Our robotic system has been designed to observe the following constraints: (i) no assumption is made on the scene structure surrounding the object to grasp, (ii) no a priori information on the object appearance (no 3D model, no image database) is used (iii) the user's actions are reduced to a minimum.

In this paper, we propose two alternate solutions to address situations where the object is not directly inside the embedded camera FOV (section II). We then investigate the automatic positioning of the arm in front of the object (section III).

Since there is not a unique solution to perform visionbased grasping, it is possible to provide several concurrent methods, with different physical architectures and algorithmic assumptions. The best solution can then be selected depending on the user's situation, and his personal preferences.

The current design of our robot SAM [START_REF] Remazeilles | SAM: a robotic butler for handicapped people[END_REF] is a result of discussions with end users, especially from the APPROCHE 1 group. One of their main concerns was to avoid creating a bulky wheelchair: some users were indeed complaining about the increased size of a wheelchair with an embedded arm, preventing them from moving freely in their apartment [START_REF] Eftring | Technical results from manus user trials[END_REF].

SAM (see Fig. 1) is made of a mobile platform (MPM470 2 ) and a MANUS arm 3 . The mobile unit offers ready-to-use solutions for self-localization and navigation (thus we suppose in this paper that the desired object is reachable by the arm). The MANUS arm is the most widespread arm within the rehabilitation field [START_REF] Alqasemi | Wheelchairmounted robotic arms: analysis, evaluation and development[END_REF]. The user interacts with the robot through a remote HMI designed to minimize the user's action.

II. ARM ORIENTATION TOWARD THE OBJECT DIRECTION

The very first step to start any vision-based grasping is to get the object within the embedded camera FOV. We propose to use an eye-to-hand camera to get a global view of the environment. A single click on this view gives SAM enough information to move its eye-in-hand camera so that it's FOV holds the object. Two alternative solutions are described, using respectively a catadioptric sensor and a pinhole camera.

A. Arm positioning with a catadioptric sensor

The appeal of an omnidirectional camera is that a single acquisition gives a 360 • view of the environment. The mirror in our sensor has been worked out to get a vertical FOV wide enough to see an object from the floor up to 1.30 m high [START_REF] De Chaumont | Omnidirectional mirror design: multiple linear ring-windows viewing[END_REF].

The omnidirectional camera is mounted on the MANUS shoulder (see Fig. 2(a)), i.e. its first joint. The direction of the first axis remains constant within the panoramic view. Furthermore, there is a direct mapping between an image xcoordinate x qp and the corresponding first joint angle q p . Let x q0 be the constant first joint projection onto the panoramic view. Then the motion to perform, such that this joint points toward the selected direction, is:

∆ q = 2π x M x qp -x q0 , (1)
where x M denotes the horizontal length of the panoramic view.

1 association promoting the use of robotics platform by disabled people 2 designed by Neobotix: http://www.neobotix.de 3 designed bu ExactDynamics: http://www.exactdynamics.nl/ The eye-in-hand camera's optical axis is to be aligned with the axis passing the optical centers of the two cameras, so that the embedded camera acts as if it was rigidly linked to a virtual axis centered on the base frame. As soon as this alignment is achieved, the motion to perform to see the direction indicated by the user with the embedded camera is:

q * 0 = q 0 + ∆ q -(q c -q 0 ) = 2q 0 + 2π x M ∆ x -arctan xc yc , (2)
where (x c , y c ) are the embedded camera frame center coordinates expressed in the base frame. This method ensures that the vertical 3D line going through the indicated point is centered in the eye-in-hand view. Figures 3 and4 illustrate this method. The left image of Fig. 3 is the initial embedded camera FOV. The desired object (a coffee box) is not visible. Fig. 4 is the panoramic view provided to the user. The right picture of Fig. 3 is the view given by the camera after the positioning of the arm onto the object.

This method has been assessed and verified during one month within four French medical centers 4 , by 24 valid and 20 tetraplegic people. Even though the user feedback was globally positive, some constraints were considered as drawbacks by some people. The first complaint was that the image resolution is not sharp enough, especially on the lower part of the image-corresponding to the central area of the acquired view, described by fewer pixels. Another complaint was that this solution does not control the gripper's height, and may need additional user action to adjust the gripper vertically to see the object.

B. Arm positioning with an eye-to-hand pinhole camera

In this section, the eye-to-hand imaging is done by a pinhole camera. Given the user's click on this view and the calibration of the system, the object coordinates along the x and y axes within the eye-to-hand camera frame are directly obtained. However, the depth of the object remains unknown, and thus we get a set of candidate positions within the eye-in-hand camera frame corresponding to an epipolar line. The method proposed here consists of scanning this line with the eye-inhand camera and detecting the location of the object by image processing [START_REF] Dune | One click focus with eye-inhand/eye-to-hand cooperation[END_REF].

1) Surfing on the epipole: The geometrical relations describing a scene observed by two cameras can be summarized by the essential matrix 2 E 1 :

2 p 2 E 1 1 p = 0, (3)
which indicates that the point corresponding to the clicked point 1 p belongs to a line in the eye-in-hand view, the epipolar line 2 E 1 1 p. The essential matrix is directly defined by the relative position of the two cameras. Thus, if the defined line is scanned by the second camera, the corresponding point 2 p will necessarily be observed.

The epipolar line is scanned using visual servoing. Visual servoing aims to reduce the difference e s = ss * between a visual feature value s observed by a camera, and its desired value s * . This minimization is performed by moving the camera with a velocity deduced from [START_REF] Chaumette | Visual servo control, part I: Basic approaches[END_REF]:

τ c = -λL + s e s , ( 4
)
where λ is a positive scalar, and L s is the interaction matrix linking the variation of the feature position to the motion of the camera. In order to scan the line, we use a redundant control law involving two tasks. The first task, e 1 , controls the orientation of the camera (i.e. the arm) so that the epipolar line stays horizontal and centered in the embedded view, while the second task, e 2 , handles the camera motion along this line.

The control law is [START_REF] Chaumette | Visual servo control, part I: Basic approaches[END_REF]:

τ c = -λ 1 L 1 + e 1 -λ 2 P L 2 + e 2 (5)
The redundancy framework ensures that the epipolar line centering (primary task) remains satisfied by requiring the line covering task to operate onto the null space of L 1 .

2) Bayesian object detection: The visual appearance of the object is defined by the region around the user's click in the eye-to-hand view. The object's location is thus obtained by comparing this description with the ones acquired by the eyein-hand camera during the line scanning.

The reference and all the candidate zones are characterized by SIFT descriptors [START_REF] Lowe | Distinctive image features from scale-invariant keypoints[END_REF], and each couple reference-candidate view is searched for matches. Each match gives a confidence in the underlying object depth. Finally the depth having the highest score is associated with the object. The object is finally brought back to the eye-in-hand camera FOV.

3) Experimental results: This method has been applied experimentally and validated on a robotic cell (the experimental setup is displayed on fig. 5). Figure 6 presents views before, during and after the arm navigation. The object is always correctly brought inside the camera FOV.

III. GRASPING UNKNOWN OBJECTS

Both of the previous stages ensure that the camera positioning requirement (defined at the end of Sec. I-A) is met. This section proposes two different solutions for the autonomous object grasping. The first one (section III-A), based on a stereo virtual visual servoing, can handle textured objects. The grasping strategy consists in servoing the translational degrees of the arm to bring the gripper in front of the object. The second one, based on an active estimation of the object shape (section III-B) leads to a more accurate grasping position, but needs an additional exploration step.

A. Stereovision-based object grasping

This first solution compensates for the lack of information on the object to grasp by embedding a stereo rig on the gripper (see Fig. 7). It relies on a tracking method estimating at each iteration the object pose within the camera frame, in order to guide the arm just in front of the object. This pose estimation uses the virtual visual servoing framework that reuses the principle of visual servoing (see eq. ( 4)). The description made in [START_REF] Dionnet | Robust stereo tracking for space robotic applications[END_REF] uses contours as visual information ; in our case, we consider Harris points.

1) Sparse Object Model estimation: The virtual visual servoing needs an object model to realize the estimation of the object pose ; information that we do not have. Thus, an estimation of this model has to be performed on-line. The advantage of a stereo rig is that 3D information can be directly extracted without moving the arm.

The input of the process is a box surrounding the object defined by the user on a remote display-which can be done in only two image clicks. First, Harris points are extracted from the region of interest, and their relatives are searched within the second view ; we use the differential tracker KLT [START_REF] Shi | Good features to track[END_REF]. Thanks to the stereo rig calibration, a sparse 3D model of the object can then be built.

2) Vision-based arm positioning: During the motion, the points are tracked in each optical flow with KLT. The pose estimation is done with a stereo implementation of the virtual visual servoing, as in [START_REF] Dionnet | Robust stereo tracking for space robotic applications[END_REF].

The grasping strategy consists of controlling the translational velocities of the arm to move toward the object while centering the box's centroid. Its desired position is about 200 mm from the gripper frame, i.e. about 5 cm from the gripper's fingers. 3) Experiments: Figure 8 illustrates the tracker behavior on a classical object. The box defined by the user is correctly tracked even when the object undergoes rotations.

This technique has been integrated into SAM, and intensively tested during clinical evaluations and several demonstrations. Figure 9 shows a variety of textured objects that have been correctly tracked and grasped. Figure 10 This method presents two main advantages: (i) it is very easy to launch: only two user clicks are needed to define the box (ii) no 3D a priori information is required, since all the needed data is automatically extracted from the visual input. Furthermore, the initialization step is not time consuming: once the user has defined the box, the sparse model is estimated in around 100 ms, and the arm guidance toward the object starts almost directly.

However, this grasping strategy fails when the grasping position should be associated to the object's shape and pose, e.g. an object lying on a table or with special features (tea cup with an handle).

In order to obtain a more suited strategy, it is then necessary to extract more information on the object.

B. Rough 3D shape estimation by active vision

The definition of a better grasping position implies to estimate the object shape on-line. We suggest that the objective here is not to get an accurate object reconstruction, but rather Fig. 11. Quadric fitting scheme. Within each view, the real object shape projection (in yellow) is approximated by a conic (in green). The projection of the estimated quadric is in red. The optimization process consists in reducing the difference between the quadric projections and the measured conics. to gather enough information, i.e. the pose the rough size of the object, to allow a manipulator to grasp it by aligning the gripper with its minor axis while being perpendicular to its major axis.

This approach is based on contour analysis and on implicit 3D reconstruction methods [START_REF] Dune | Active rough shape estimation of unknown objects[END_REF]. 3D shapes are represented by quadrics. They have the nice property of projecting on an image plane in conics, which provide compact representations that are easy to extract. The reconstruction scheme is the following: get several views of the object at different camera locations, track the conics in the acquired views, and use the parameters of the conics to estimate by minimization the parameters of the corresponding quadric (see Fig. 11). The quality of the reconstruction obviously relies on the locations of each acquired views. Hence we also propose to use active vision in order to determine the next best view.

1) Contour extraction: Active contours are used to extract the points of the object's edge [START_REF] Kass | Snakes: Active contour models[END_REF]. We use a parametric formulation of the active contour [START_REF] Brigger | B-spline snakes: a flexible tool for parametric contour detection[END_REF] which is more robust than the classical formulation based directly on point motion. The use of such techniques adds two assumptions: (i) the object is entirely seen in every view (it is ensured by the active vision step, see III-B.4), (ii) the object can be segmented from the scene without resorting to either prior knowledge about its appearance or to an a priori known model.

As an input, the active contour algorithm needs an initial box almost surrounding the object. This information can be provided by the method used to get the object inside the embedded camera FOV (see previous section). Note that one click is even sufficient. Indeed, if the click is almost at the center of the object, the scale of the box can be automatically obtained by studying the object intrinsic scale [START_REF] Lindeberg | Feature detection with automatic scale selection[END_REF].

In each view, the active contours extraction gives a set of 2D image points x = (x, y, 1) (in green in fig. 11) that belong to the apparent contour of the object.

2) Conic parameters estimation: The points extracted by the active edge detector are then used to estimate the corresponding C 3×3 conic parameters such that [START_REF] Zhang | Parameter estimation techniques: A tutorial with application to conic fitting[END_REF]:

g(x, c) = x Cx, (6)
This computation is performed for each considered view, and the obtained C j conic parameters are stored along with the corresponding camera positions.

3) Quadric representation: This step consists of estimating the quadric parameters whose projection best fits the data stored in the previous step.

The equation of a quadric expressed in the Cartesian reference frame, R w , is such that:

h w ( w X, w Γ) = w X w Γ w X, (7)
where w X = (X w , Y w , Z w , 1) are the homogeneous 3D coordinates of a contour point expressed in R w , and w Γ is the symmetric positive matrix associated with the quadric. Given an estimation of the quadric parameters w Γ and the camera calibration (extrinsic and intrinsic parameters), we can compute the corresponding projections Ĉ in every view taken by the eye-in-hand camera. Thus, the quadric parametrization that best fits the observed object shape is the one that minimizes the error between the measured conics C and the projected ones, Ĉ. This quadric is obtained by minimizing the following cost function:

f ( w Γ) = ij (ĉ ij -c ij ) 2 σ ij , (8)
where i ∈ [0, 5] is the index of the i th conic parameter and j ∈ [0, N ] the index of the j th view.

As in [START_REF] Whaite | Autonomous exploration driven by uncertainty[END_REF], we can solve this problem using non-linear minimization techniques. In order to cope with potential noise in the edge points extraction, we propose to us a robust Levenberg-Marquartd minimization algorithm [START_REF] Vetterling | Numerical Recipes in C++: The Art of Scientific Computing[END_REF].

4) Active vision to cope with ambiguities: The quality of the estimation of the quadric parameters strongly depends on the different views used to describe the object. For instance, views taken too closely to eachother will provide a bad estimation of the quadric.

Active vision is used to define the best camera position to describe the object. [START_REF] Whaite | Autonomous exploration driven by uncertainty[END_REF] proposed to use the uncertainty of the parameter estimation to control the camera displacement. They highlight the link between the uncertainty and the covariance matrix on the quadric parameters resulting from the optimization process. The basic idea is to move the camera to the position that generates the most information about the most poorly estimated parameters.

Instead of computing the minimum of the determinant of the covariance matrix like in [START_REF] Whaite | Autonomous exploration driven by uncertainty[END_REF], we select the next best view by minimizing the Froebenius norm of the covariance matrix. It is indeed less time consuming and has the advantage of avoiding the local minima that occur as soon as one of the parameters is well estimated.

Here, we face a non linear minimization problem without analytic Jacobian computation. Thus the optimisation is done with the Simplex method of Nelder and Mead [START_REF] Vetterling | Numerical Recipes in C++: The Art of Scientific Computing[END_REF].

This method is used to compute the translational components of the camera velocity. The rotational component is deduced by visual servoing [START_REF] Espiau | A new approach to visual servoing in robotics[END_REF], so that the projection of the centroid of the estimated quadric remains in the center of the image plane.

5) Experimental results: A frame attached to the object can be computed directly from the parameters of the estimated quadric, as shown in Figure 12.

At the end of the reconstruction process, the gripper is aligned with the object frame using 3D servoing and then moved toward the object in order to grasp it. The quadric parameters can be continuously refined until gripper closure. Since our reconstruction process is directly based on object contour extraction in the images, the solution is very fast, allowing us to compute the object shape in real time and to use it in a closed-loop grasping task. The proposed solution is fully generic and works for any roughly convex object. We are currently integrating this grasping procedure on the SAM platform (current experiments use the Afma6 arm).

IV. CONCLUSION This paper has presented different solutions to orientate a robotic arm in the direction of an object and then to grasp it. In all the techniques proposed, we have minimized the assumptions on the grasping environment and on the object appearance, so that the system can handle a wide range of situations. The use of our solutions does not require the user to have any technical expertise, and needs a very small number of clicks. Furthermore, the solutions for the two problems addressed can easily be combined, depending on the robot structure, the user need, and/or convenience. Some of these techniques have been evaluated by disabled subjects with a static robot. We are preparing evaluations involving a mobile unit. The methods validated on robotic cells are currently integrated on SAM, and will be soon tested by the envisioned end-users.

Fig. 1 .

 1 Fig. 1. SAM: a Manus arm mounted onto the MPM470 mobile platform.

Fig. 2 .

 2 Fig. 2. Panoramic-based arm positioning: (a) the omnidirectional camera mounted onto the MANUS first axis, (b) the panoramic-embedded camera's relation when the second one is correctly aligned.

Fig. 3 .

 3 Fig. 3. Panoramic-based arm positioning: images acquired by the embedded camera before and after the motion.

Fig. 4 .

 4 Fig. 4. Panoramic view provided to the user before the arm positioning. Red crosses: positions that can not reach the first joint. White line: first axis position. Blue line: initial FOV of the camera (left picture of Fig 3). Green line: desired camera direction, given by the user with one click. After the arm positioning, the embedded camera gives the right picture of Fig 3.

Fig. 5 .

 5 Fig. 5. Experimental setup, with a cluttered scene. The red line, defined by the user click, is the epipolar line that is covered by the embedded camera.

Fig. 6 .

 6 Fig. 6. Method illustration : (a) eye-to-hand view, with the user click (b) initial eye-in-hand view, with the current epipolar line in green and its desired position in red, (c) view during line scanning, (d) final FOV of the camera.

Fig. 7 .

 7 Fig.7. Stereo rig used to bring the gripper just in front of the object. When the cameras are too close to the object, a blind forward motion is performed so that the object enters the gripper. This is detected by an optical barrier (b). The gripper is then closed, applying a pressure controlled by load cells (c).

Fig. 8 .

 8 Fig. 8. Cup tracking. Only the right image is shown. The first view is the initial one where the box has been defined.

Fig. 9 .

 9 Fig. 9. Example of objects correctly grasped (cards, can, book, bottle).

  illustrates the positionbased control of the arm. It shows the classical exponential decrease of the error.

Fig. 10 .

 10 Fig. 10. Visual servoing on the card box (see Fig. 9): object center position error (in mm) vs iteration.

Fig. 12 .

 12 Fig. 12. Object reconstruction results: the two first images are examples of active contours. Last image illustrates the final object frame estimation. The blue and red arrays are respectively the major and minor axis of the object.

CRF Coubert, CHU Reims, Center Calvé at Berck sur Mer, and CHU Raymond Poincaré at Garches