Y Letourneur
email: yves.letourneur@unc.nc

Sources of organic matter in an atypical phytoplankton rich coral ecosystem, Marquesas Islands: composition and properties

The purpose of this work is to characterize several potential sources of organic matter (OM) in the Marquesas Islands, French Polynesia, and to understand how these sources contribute to OM pools. Stable isotope (δ13C and δ15N) and fatty acid (FA) compositions of OM potential sources (algal turf, benthic macroalgae, detrital terrestrial plants (DTP), phytoplankton) and OM pools (sediment (SOM) and particulate organic matter (POM)) were studied in coastal areas in Nuku Hiva Island. Isotope compositions of marine POM (δ13C = -22.5 ± 0.8 ‰; δ15N = 12.1 ± 1.1 ‰) and SOM (δ13C = -19.1 ± 0.9 ‰; δ15N = 14.4 ± 0.5 ‰) highlighted that OM sources at the base of the local food web had unusually high δ15N values. Potential FA markers of diatoms and/or cyanobacteria (20:5ω3 and 16:1ω7) were found in these two OM pools. In addition, coastal SOM also displayed FA markers of bacteria, macroalgae and terrestrial plants. For marine POM, potential macroalgae FA markers were recorded (18:2ω6 and 16:2ω4). The stable isotope mixing model highlighted the major contribution of phytoplankton to the coastal SOM (62%), followed by benthic macroalgae (32%), whereas marine POM was mainly composed of a mixture of algal turf and phytoplankton in similar averaged proportions (38%) but presenting wide variations. Our results as a whole strongly suggest that pelagic-benthic coupled processes drive the characteristics and properties of OM sources.

INTRODUCTION

The ever-increasing pace of anthropogenic and climatic stressors has motivated a widespread interest in understanding the contribution of species to ecosystem functioning. This stems from the concern that a loss of species may correspond to a net loss of ecosystem productivity. However, understanding the mechanisms that maintain ecosystem productivity also require a definition of the major sources of energy and nutrients that fuel the entire ecosystem [START_REF] Bierwagen | Trophodynamics as a tool for understanding coral reef ecosystems[END_REF].

In coastal ecosystems, the high diversity of sources available to primary consumers complicates the characterization of the food web and the understanding of energy flows [START_REF] Mann | Production and use of detritus in various freshwater, estuarine and coastal marine ecosystems[END_REF]. Carbon sources may be of continental or marine origin. Moreover, they can come from coastal, pelagic or deep waters, and from living organisms or detrital matter [START_REF] Gazeau | The European coastal zone: characterization and first assessment of ecosystem metabolism[END_REF][START_REF] Bode | Phytoplankton and macrophytes contributions to littoral food webs in the Galician upwelling estimated from stable isotopes[END_REF]. Food webs in coastal areas are often supported by phytoplankton [START_REF] Bode | Phytoplankton and macrophytes contributions to littoral food webs in the Galician upwelling estimated from stable isotopes[END_REF]). However, in several ecosystems, benthic production or the inputs from the terrestrial realm can also be major contributors to the organic matter (hereafter OM) pools [START_REF] Riera | Isotopic Determination of food sources of Crassostrea gigas along a trophic gradient in the Estuarine Bay of Marennes-Oléron[END_REF][START_REF] Briand | Major sources of organic matter in a complex coral reef lagoon: Identification from isotopic signatures (δ 13 C and δ 15 N)[END_REF]. Changes in the major source of nutrient may influence the primary production of coastal system with potential implications for the functioning of the ecosystem [START_REF] Liénart | Dynamics of particulate organic matter composition in coastal systems: Forcing of spatio-temporal variability at multi-systems scale[END_REF]. The pool of nutrient can be altered by several drivers of natural and anthropogenic origin. For example, nutrients can be altered by variation in the anthropogenic inputs or changes of the water mixing regime (D 'Angelo and Wiedenmann 2014). Global climate change may also have an important effect by modifying the exchanges of organic matter at the interface between ocean and land [START_REF] Liénart | Dynamics of particulate organic matter composition in coastal systems: Forcing of spatio-temporal variability at multi-systems scale[END_REF]. For example, the input of the Particulate Organic Matter (hereafter POM) carried by rivers may dramatically change if water flow or seasonality are affected. Therefore, defining the vulnerability of coastal ecosystems requires an understanding of the basal organic matter that fuel the ecosystem.

Among coastal ecosystems, coral reefs are complex semi-open ecosystems. This complexity arises from the high species diversity and the large biomass typical of these systems [START_REF] Choat | The trophic status of herbivorous fishes on coral reefs -II. Food processing modes and trophodynamics[END_REF]). High diversity corresponds to myriads of potential trophic interaction [START_REF] Hubert | Community assembly and diversification in Indo-Pacific coral reef fishes[END_REF], which in turn makes it complex to describe the topology and functioning of coral reef food webs [START_REF] Frisch | Trophic ecology of large predatory reef fishes: energy pathways, trophic level, and implications for fisheries in a changing climate[END_REF].

Benthic primary producers may be important carbon sources for coral reef food webs, although numerous species also rely on oceanic production (plankton) [START_REF] Wyatt | Particulate nutrient fluxes over a fringing coral reef: Source-sink dynamics inferred from carbon to nitrogen ratios and stable isotopes[END_REF][START_REF] Bourg | The same but different: stable isotopes reveal two distinguishable, yet similar, neighbouring food chains in a coral reef[END_REF].

The type of resource that mainly contribute to the productivity of coral reefs partly depends on environmental (e.g. sea surface temperature, nutrient concentrations) and hydrodynamic conditions. These benthic and pelagic potential food sources are moreover available as mixtures of OM pools, their proportions depending on their abundance and their export capacity (degradation, consumption and rejection by feces, etc.). Indeed, POM is a mixture made of both living (e.g. bacteria, phytoplankton) and non-living matter (e.g. detritus, fecal pellets, clays) [START_REF] Volkman | Chemical and biological studies of particulate organic matter in the ocean[END_REF][START_REF] Briand | Major sources of organic matter in a complex coral reef lagoon: Identification from isotopic signatures (δ 13 C and δ 15 N)[END_REF].

This POM contributes significantly to coral ecosystem nutrient budgets and plays an important role in the transfer of organic matter between the land and the ocean [START_REF] Sorokin | Plankton of the central Great Barrier Reef: Abundance, production and trophodynamic roles[END_REF][START_REF] Wyatt | Particulate nutrient fluxes over a fringing coral reef: relevant scales of phytoplankton production and mechanisms of supply[END_REF]. Sedimentary organic matter (SOM) is another OM pool potentially composed of the same sources as POM, with the addition of macroalgae fragments, meiofauna and/or microphytobenthos [START_REF] Wyatt | Particulate nutrient fluxes over a fringing coral reef: Source-sink dynamics inferred from carbon to nitrogen ratios and stable isotopes[END_REF][START_REF] Briand | Major sources of organic matter in a complex coral reef lagoon: Identification from isotopic signatures (δ 13 C and δ 15 N)[END_REF]. These differences of composition between SOM and POM, as well as a different bacterial activity, may lead to different signature of carbon and nitrogen stable isotopes.

The Marquesas Islands are a unique case among tropical coral ecosystems. The archipelago almost devoid of coral reefs. Coral communities may be locally abundant, but they are in the form of scattered colonies with low diversity [START_REF] Benzoni | Les coraux peu profonds (Cnidaria, Anthozoa, Scleractinia) des Îles Marquises[END_REF]. The surface waters around the Marquesas have high concentrations of nutrients; those of nitrate (NO3 -) and phosphate (PO4 -) are higher than 1 μM and 0.3 μM, respectively [START_REF] Martinez | Environnement océanique des Marquises[END_REF]. These concentrations are one hundred times higher than those measured in the South Pacific subtropical gyre [START_REF] Martinez | Environnement océanique des Marquises[END_REF]. This nutrient richness promotes the development of a significant phytoplankton biomass around the Marquesan coasts, with an average of 0.2 μg.l -1 of Chl-a over the year [START_REF] Martinez | Environnement océanique des Marquises[END_REF]. The richness of the Marquesan marine waters seems to be linked to a particular local enrichment mechanism, likely due to current disturbance related to the island topography(the so called "island effect"; [START_REF] Raapoto | Modeling the wake of the Marquesas Archipelago[END_REF]). These characteristics may imply a particular model of coastal trophic functioning, probably supported mainly by pelagic primary production.

Trophic markers such as stable isotopes (SI), fatty acids (FA) are useful tools to determine the flows of carbon in coastal ecosystems. In addition, C:N ratio provides information about the quality of the OM. Carbon (C) and nitrogen (N) isotope compositions are commonly used to describe the organic matter and to determine the flows of energy in coastal food webs [START_REF] Peterson | Stable isotopes as tracers of organic matter input and transfer in benthic food webs: a review[END_REF][START_REF] Letourneur | Identifying carbon sources and trophic position of coral reef fishes using diet and stable isotope (δ 15 N and δ 13 C) analyses in two contrasted bays in Moorea, French Polynesia[END_REF][START_REF] Wyatt | Particulate nutrient fluxes over a fringing coral reef: Source-sink dynamics inferred from carbon to nitrogen ratios and stable isotopes[END_REF][START_REF] Briand | Complex food webs in highly diversified coral reefs: Insights from δ 13 C and δ 15 N stable isotopes[END_REF]. For example, the δ 13 C values may distinguish benthic and pelagic carbon sources [START_REF] Peterson | Stable isotopes as tracers of organic matter input and transfer in benthic food webs: a review[END_REF]. Nitrogen isotope compositions are often used to estimate the consumers' trophic positions [START_REF] Post | Using stable isotopes to estimate trophic position: models, methods, and assumptions[END_REF]; however, in some cases the detection of 15 N-enriched components may also provide information on the possible occurrence of upwelling [START_REF] Liu | The eastern tropical Pacific as a source of 15 N-enriched nitrate in seawater off southern California[END_REF]. Isotope mixing models enable estimation of the relative contribution of isotopically different OM sources in a mixture (e.g. consumer tissue, OM pools; [START_REF] Parnell | Source partitioning using stable isotopes: Coping with too much variation[END_REF]. Fatty acid analysis can also be a reliable method to trace food sources in food webs. FAs are carbon-rich compounds that are ubiquitous in all organisms, but some FAs are biosynthesized de novo only by specific organisms at the base of the food chain (e.g. bacteria, diatoms, macroalgae, vascular plants; [START_REF] Koussoroplis | Nutritional importance of minor dietary sources for leaping grey mullet Liza saliens (Mugilidae) during settlement: insights from fatty acid δ 13 C analysis[END_REF], and are poorly metabolized by the consumers, making these FAs good trophic markers. As a result, FAs may help to characterize and to trace the organic matter within food webs [START_REF] Koussoroplis | Nutritional importance of minor dietary sources for leaping grey mullet Liza saliens (Mugilidae) during settlement: insights from fatty acid δ 13 C analysis[END_REF].

Organic matter sources with high nutritional quality have an important functional role. For example, compounds such as essential fatty acids (EFAs) are known to be essential for the achievement of many physiological processes [START_REF] Arts | Essential fatty acids" in aquatic ecosystems: a crucial link between diet and human health and evolution[END_REF][START_REF] Koussoroplis | Nutritional importance of minor dietary sources for leaping grey mullet Liza saliens (Mugilidae) during settlement: insights from fatty acid δ 13 C analysis[END_REF]. The ratio of polyunsaturated to saturated fatty acids (PUFAs/SFAs) may also be an indicator of the quality of potential food sources [START_REF] Dalsgaard | Fatty acid trophic markers in the pelagic marine environment[END_REF][START_REF] Meziane | Fate of mangrove organic matter along a subtropical estuary: Small-scale exportation and contribution to the food of crab communities[END_REF]) and provides information on the relative quantity of fresh natural OM such as phytoplankton compared to detritus [START_REF] Biandolino | Preliminary investigation on the phytoplankton contribution to the mussel diet on the basis of fatty acids analysis[END_REF]. A low ratio indicates a poor quality of the resource [START_REF] Moynihan | Spatial and temporal dynamics of nano-and pico-size particulate organic matter (POM) in a coastal megatidal marine system: Dynamics of nano-and pico-POM[END_REF]. The quantity of EFAs such as 20:4ω6, 20:5ω3 and 22:6ω3 (i.e. arachidonic, eicosopentaenoic and docosahexaenoic acids, respectively) may also be used to assess the nutritional quality of the lipid fraction. Finally, the C:N ratio also provides information about the quality of the organic matter and is thus an essential metric to understand the use of different OM sources by primary consumers. For marine OM, ratios ~5-7 indicate high nutritional quality (i.e. fresh material), due to the presence of a significant amount of amino acids [START_REF] Danovaro | Deep-sea ecosystem response to climate change: the eastern Mediterranean case study[END_REF]). Higher C:N ratios reflect the degradation of compounds rich in nitrogen, so ratios higher than 12 characterize refractory organic matter [START_REF] Hedges | Compositions and fluxes of particulate organic material in the Amazon River[END_REF]. Primary consumers can preferentially select sources with a higher nitrogen content, providing better nutritional quality [START_REF] Jacquin | The reproductive response of the sea urchins Paracentrotus lividus (G.) and Psammechinus miliaris (L.) to a hyperproteinated macrophytic diet[END_REF][START_REF] Schaal | Trophic significance of the kelp Laminaria digitate (Lamour.) for the associated food web: a between-sites comparison[END_REF] and likely assimilate these food sources in a much easier way. This multi-trophic markers approach therefore enables discrimination between the different food sources fueling a food web. Using this approach, we have tested the hypothesis that, in this region characterized by high nutrient concentrations and plankton biomass, organic matter of pelagic origin provides significant support for the coastal ecosystems. Thus, the first aim of this study is to characterize the main organic matter sources at the base of a Marquesan coastal ecosystem by investigating the carbon and nitrogen stable isotope compositions, the C:N ratio and FA compositions in macroalgae, algal turf, detrital terrestrial plant (DTP) material, phytoplankton, sediment and particulate OM. Our second aim is to quantify the relative contributions of the different primary producers to the particulate and sedimentary organic matter pools.

MATERIAL AND METHODS

Studied site

The study was carried out in August 2016 (cold, dry season) and in March 2017 (warm, wet season) in the southeast part of Nuku Hiva, Marquesas Archipelago (7°50'-10°35'S, 138°25'-140°50'O), French Polynesia (Figure 1). Rainfall, although unstable, is usually more regular and abundant from January to August [START_REF] Laurent | Le climat aux îles Marquises[END_REF]. The intensification of the trade winds during the austral winter accentuates the surface currents. This phenomenon, combined with the slight decrease in surface water temperatures, results in a seasonal increase in vertical mixing and thus nutrient enrichment of the surface water layers [START_REF] Raapoto | Modeling the wake of the Marquesas Archipelago[END_REF]. During the sampling, the mean water temperatures were 27.6 °C in August and 29.2 °C in March.

The marine seafloor is dominated by rocky habitats, characterized mainly by steep scree slopes of volcanic rock, but also by soft-bottom habitats, algae groves, coral habitats and caves. The benthic community is composed mainly of algal turf, macroalgae (mostly calcified and encrusting), scattered coral colonies and sponges. This assemblage of organisms reflects an environment with strong hydrodynamic conditions [START_REF] Payri | La macroflore marine des îles Marquises[END_REF].

Sampling

Organic matter sources were sampled at five stations in shallow waters (from 0.5 to 20 m): three coastal sites (C1, C2 and C3), a river mouth site (R) and an 'oceanic' site (P). Only POM and phytoplankton were collected at station P due to high depth, ~150-200 m) (Figure 1). The river has a low flow, from ~0.5 to ~3.0 m 3 .s -1 , depending on rainfall, and low nutrient concentrations (0.5-1.0 mol.l -1 NO3 -and 0.4-1.0 mol.l -1 NH4 + for instance; Fey et al. unpublished data). Sampling was performed by targeting the OM sources that potentially constitute the food web basis, including the OM pools (i.e. POM and SOM). More specifically, eleven different macrophytes (algal turf and macroalgae, n = 73) and DTP material (i.e. tree leaves) transported by the river (n = 16) were collected by hand and placed in hermetic bags. Algal turfs and macroalgae were collected on the pebbles found at each site.

They were scraped carefully from the substratum and sorted by taxonomical groups: turf, Rhodophyta, Ochrophyta and Chlorophyta. Algal turfs are a complex assemblage dominated by filamentous algal species and may represent a major OM source on coral reefs [START_REF] Vermeij | The effects of nutrient enrichment and herbivore abundance on the ability of turf algae to overgrow coral in the Caribbean[END_REF][START_REF] Letourneur | Identifying carbon sources and trophic position of coral reef fishes using diet and stable isotope (δ 15 N and δ 13 C) analyses in two contrasted bays in Moorea, French Polynesia[END_REF][START_REF] Briand | Major sources of organic matter in a complex coral reef lagoon: Identification from isotopic signatures (δ 13 C and δ 15 N)[END_REF]. Among the macroalgae, four taxa were sampled for Rhodophyta, two for Ochrophyta and two others for Chlorophyta (see Results section). Macroalgae were cleared of their epiphytes to avoid potential confusion in the results.

The POM of the subsurface water (< 1 m, n = 49) were also sampled: 1 to 4 liters of water were vacuum-filtered through a pre-combusted (500 °C, 6 h) and pre-weighed glass fiber filter (0.7 µm porosity GF/F, Whatman ® ). Surface POM isotope compositions are often used as a proxy of those of phytoplankton in oceanic ecosystems. However, in an area subjected to river inputs, surface water POM may be influenced by OM of terrestrial or detrital origin, and there may be a significant difference between POM and phytoplankton isotope compositions [START_REF] Harmelin-Vivien | Comparison of C and N stable isotope ratios between surface particulate organic matter and microphytoplankton in the Gulf of Lions (NW Mediterranean)[END_REF]. We thus analyzed POM (i.e. phytoplankton, plus various kind of organic particles) and phytoplankton sensu stricto. In this paper, the term 'phytoplankton' refers to the categories of nano-(2-20 µm), and microplankton (20-63, and 63-200 µm) fractions that were separated through sieving, thus having a larger size range than in most comparable studies (usually 63-180 μm) and taking into account the abundance of nano-plankton in Marquesan waters [START_REF] Dolan | The 'neutral' community structure of planktonic herbivores, tintinnid ciliates of the microzooplankton, across the SE Tropical Pacific Ocean[END_REF]). During POM collection, micro-zooplankton (100 -300 µm) may be captured [START_REF] Wyatt | Particulate nutrient fluxes over a fringing coral reef: Source-sink dynamics inferred from carbon to nitrogen ratios and stable isotopes[END_REF]. Although its contribution to the POM composition is usually relatively low [START_REF] Sorokin | Plankton of the central Great Barrier Reef: Abundance, production and trophodynamic roles[END_REF], an effort was made to remove all detected organisms in addition to filtering water with a 200 μm-mesh sieve.

Sediment organic matter (SOM) was sampled at the bottom substrate (< 5 cm, n = 47). Large particles such as stones, shells, etc. were removed from these samples. All samples were kept in ice chests during sampling and (except for POM) immediately stored at -20°C until further analyses.

Biochemical analyses

Stables isotopes

All samples except filters were freeze-dried and ground to fine powder with an agate mortar and pestle. The POM and phytoplankton collected on filters were scraped off with a scalpel. Inorganic carbonates (shells, spikes, etc.) have higher δ 13 C values than organic carbon. As a result, a contamination of samples by carbonates can bias the value of the isotope composition of a food source or a consumer [START_REF] Pinnegar | Differential fractionation of δ 13 C and δ 15 N among fish tissues: implications for the study of trophic interactions[END_REF]. Therefore, samples potentially containing carbonates (i.e. POM, SOM, encrusting algae and phytoplankton) were acidified prior to measurement of δ 13 C values. Filters were acidified using HCl fumes for 4 hours under vacuum. The other samples were acidified in glass vials by stepwise addition of 0.5 mol.l -1 or 2 mol.l -1 HCl (for algae and SOM, respectively), until cessation of bubbling. These samples were then dried at 60°C using a dry block heater, homogenized with ultrapure water, freeze-dried and ground again. Measurements of δ 15 N values were carried out on raw samples.

Approximately 1 mg of powder was weighed into a tin cup (8 x 5 mm) for vegetal/animal samples, ~15 mg for SOM and ~3 mg for POM, using a precision balance (ADAM PW124 ® , d= 0.0001 g). Carbon and nitrogen isotope compositions and C:N ratios of all samples were determined using an elemental analyzer (Flash EA 2000, Thermo Scientific ® , Milan, Italy) coupled with a continuous-flow isotope ratio mass spectrometer (Delta V Plus, Thermo Scientific ® , Bremen, Germany) via a Conflo IV interface.

Analyses were carried out at the LIENSs stable isotope facility of the University of La Rochelle, France.

Isotope compositions are expressed in the δ notation as deviations from the standard reference materials (N2 in air for δ 15 N and Vienna Pee Dee Belemnite for δ 13 C, according to the formula:

δX = [( R sample R standard -1)] × 1000
where X is 13 C or 15 N, R is the ratio corresponding to 13 C: 12 C or 15 N: 14 N (proportion of heavy to light isotope). Calibration was done using reference materials (USGS-24, -61, -62, IAEA-CH6, -600 for carbon; USGS-61, -62, IAEA-N2, -NO-3, -600 for nitrogen). The analytical precision of the measurements was <0.15‰ for carbon and nitrogen based on analyses of USGS-61 and USGS-62 used as laboratory internal standards. Overall, this represents 239 stable isotope measures (96 samples of OM pools and 143 primary producers).

Fatty acids

Fatty acid analyses were conducted for both seasons on subsamples of SOM, river and marine POM, terrestrial detritus, three Rhodophyta species (Ceratodictyon scoparium, Pterocladiella caerulescens and Peyssonnelia spp.), algal turf and phytoplankton. Four samples were analyzed for each OM source, except phytoplankton for which the available material was not sufficient (n= 2).

Lipids were extracted following [START_REF] Meziane | Inter-specific and geographical variations in the fatty acid composition of mangrove leaves: Implications for using fatty acids as a taxonomic tool and tracers of organic matter[END_REF], and using 30 mg of freeze dried material for tree leaves, algae and phytoplankton, 1 g for SOM and 5 to 20 mg for POM. An internal standard, tricosanoic acid (23:0), was added in each sample before extraction to calculate the final concentrations of fatty acid methyl esters (FAME) following their separation by gas chromatography analysis (Varian 3800-GC), using a flame ionization detector. Identification of each FAME was done by comparing retention times with those of a commercial standard (Supelco ® ) and confirmed using a mass spectrometer coupled to a gas chromatograph (Varian 450-GC; Varian 220-MS). Fatty acid concentrations are expressed as percentages (%) of total FA or absolute concentrations (mg.g -1 ).

The FA were classified according to their degree and type of unsaturation i.e. saturated fatty acids (SFAs; e.g. 14:0, 16:0 and 18:0), monounsaturated fatty acids (MUFAs; e.g. 16:1ω7 and 18:1ω9), polyunsaturated fatty acids (PUFAs; e.g. 20:4ω6, 20:5ω3 and 22:6ω3 ; having a terminal end omega-3 (ω3) or omega-6 (ω6) indicates essential fatty acids: EFAs) and branched fatty acids (BrFAs; e.g. iso-15:0 and anteiso-15:0).

Quality indicators

C:N ratios were calculated for all OM sources sampled. For fatty acids, the ratios of polyunsaturated to saturated fatty acids (PUFAs/SFAs) were also calculated [START_REF] Biandolino | Preliminary investigation on the phytoplankton contribution to the mussel diet on the basis of fatty acids analysis[END_REF][START_REF] Moynihan | Spatial and temporal dynamics of nano-and pico-size particulate organic matter (POM) in a coastal megatidal marine system: Dynamics of nano-and pico-POM[END_REF].

Statistical analyses and models

Statistical analysis

Differences in mean δ 13 C values, δ 15 N values, C:N ratios and fatty acid functional groups (e.g., MUFAs, PUFAs) according to the potential OM sources (e.g. POM, phytoplankton, etc.) were tested using two-way analyses of variance (ANOVA; F) after assumption of normality. Data homogeneity was tested using the Levene test. A Kruskal-Wallis test (KW) was performed when the variances were heterogeneous. Significant results were tested with a post-hoc Tukey test for ANOVA or a Mann-Whitney pairwise permutation test for the Kruskal-Wallis test. A Student test (t) or Wilcoxon test (W)

was used when comparison between two means was necessary. All tests were considered significant when p-value < 0.05.

A principal component analysis (PCA) was performed to explore the links between the different fatty acid percentages and the samples of OM pools. This PCA was performed using the 25 individual FAs measured displaying an average proportion greater than 1 % within at least one group of samples.

The statistics and graphical representations were performed using R version 3.4.4 (R Core Team 2018).

Bayesian mixing model

The isotope composition of an organic matter pool can be considered as the result of the mixture of the isotope composition of the different sources [START_REF] Phillips | Mixing models in analyses of diet using multiple stable isotopes: a critique[END_REF][START_REF] Phillips | Source partitioning using stable isotopes: coping with too many sources[END_REF]. The contributions of the different sources to the pools of OM (i.e. POM, SOM) were determined using the Bayesian mixing model SIAR [START_REF] Parnell | Source partitioning using stable isotopes: Coping with too much variation[END_REF]) using the isotope compositions of the two elements (C and N). Models were run for 200,000 iterations, the burn-in was set up at 50,000 iterations and a onefifteenth thinning was applied. This model provides ranges of solutions of the different proportions of sources to explain the isotope composition of a mixture, here the POM or the SOM. The trophic fractionation factor (TFF) can significantly influence the model's output [START_REF] Bond | Recent Bayesian stable-isotope mixing models are highly sensitive to variation in discrimination factors[END_REF].

However, in this study, the TFF was set at 0 because no consumption process is involved in OM pools, as only the mixture of the different OM sources was considered [START_REF] Briand | Major sources of organic matter in a complex coral reef lagoon: Identification from isotopic signatures (δ 13 C and δ 15 N)[END_REF].

RESULTS

Stable isotope analyses

Seasonal and spatial variations of δ 13 C and δ 15 N values

The detrital terrestrial plant material samples had similar carbon and nitrogen isotope compositions between warm and cold seasons (Figure S1, p = 0.320). δ 15 N values of algal turf were similar between sites and seasons (p = 0.067), but their δ 13 C values displayed spatio-temporal variations (i.e. site C3 in warm season; p < 0.05; Figure S1). No significant differences were observed between sites for the δ 13 C of macroalgae (p > 0.05) while δ 15 N differed between sites (C1 vs. C2; p < 0.01) and between seasons (C2; p< 0.001) (Figure S1). Isotope composition of phytoplankton was more variable: we detected seasonal difference for δ 15 N in both coastal and oceanic samples (higher δ 15 N values of ~ 2.5-3.0 ‰ during the warm season, Figure S1). During the cold/dry season, phytoplankton had similar δ 13 C and δ 15 N between coastal sites (C1-3) (p > 0.05, and all samples from coastal sites were significantly more enriched in 13 C and 15 N than oceanic phytoplankton (p < 0.001). During the warm/wet season, oceanic phytoplankton had a lower δ 15 N value than coastal phytoplankton from site C1 and a higher δ 13 C value than coastal phytoplankton from sites C2-C3 (p < 0.001).

Even if some seasonal and spatial patterns were observed, primary producers had a rather clustered isotopic composition that was clearly distinguishable from that of phytoplankton (Figure 2; Figure S1).

Thus, to facilitate the subsequent analysis, primary producer samples from the two seasons were pooled.

In this case, coastal and oceanic phytoplankton had similar isotope compositions (δ 13 C and δ 15 N; p > 0.05), these were therefore pooled under the common name 'Phytoplankton' (Phyto; Figure 2, Table 1).

Pools of organic matter (POM and SOM) exhibited strong differences in carbon and nitrogen isotope compositions between marine and river mouth sites (p < 0.01), for both seasons (Figure S1). For SOM, river and coastal samples both had similar isotope compositions from one season to another (p > 0.05).

Among POM, river POM displayed seasonal differences both in δ 13 C and δ 15 N values (p < 0.001 and < 0.01, respectively). Oceanic POM had slightly different δ 15 N values between the two seasons (p < 0.001), but no difference was observed for δ 13 C values (p = 0.990). Coastal POM samples had similar isotope composition between sites and seasons (p > 0.05) (Figure S1). Thus, coastal and oceanic POM samples were pooled into 'marine POM' (M-POM) in the rest of the study.

Characteristics of organic matter sources based on their isotope compositions

Terrestrial sources (river POM, river SOM and DTP) were both depleted in 13 C and 15 N; on average δ 13 C values varied from -29.5 to -24.3 ‰ and δ 15 N values from 1.9 to 6.2 ‰ (Table 1, Figure 2). Isotope compositions of marine OM sources (OM pools and primary producers) were more enriched in 13 C and 15 N, and ranged from -23.9 to -12.7 ‰ for δ 13 C values, and 10.9 to 15.0 ‰ for δ 15 N values (Table 1).

Coastal SOM presented higher δ 13 C and δ 15 N values (-19.1 ± 0.9 ‰ and 14.4 ± 0.5 ‰, respectively)

than M-POM (-22.5 ± 0.8 ‰ and 12.1 ± 1.1 ‰, respectively; p < 0.001; Table 1). Among marine primary producers, algal turf was the most 13 C-depleted (-23.9 ± 1.7 ‰), and macroalgae were the most 13 Cenriched (-16.4 ± 2.0 ‰), especially Cladophoropsis sudanensis (Table 1, Figure 2). For δ 15 N values, phytoplankton had the highest values (15.0 ± 1.8 ‰) and macroalgae the lowest (11.6 ± 0.9 ‰). By taking into account both primary producers and OM pools, some similarities of isotope compositions could be highlighted. Phytoplankton and coastal SOM had similar δ 15 N values (p = 0.270), as well as macroalgae and M-POM (p = 0.07). Regarding the δ 13 C values, all food sources had different carbon isotope compositions (p < 0.001), except algal turf and R-SOM (p = 0.25; Figure 2).

Among OM pools, C:N ratios were lower overall for SOM compared to POM, but only significantly different between coastal SOM and marine POM, with 5.3 ± 2.9 and 7.1 ± 1.3, respectively (p < 0.001; Table 1). For primary producers, DTP and algal turf exhibited the highest and most variable values, with 15.5 ± 33.6 and 18.1 ± 16.0, respectively. Generally, macroalgae exhibited C:N values that oscillated around 10 (Table 1) and that were similar between species (p > 0.05). Finally, phytoplankton had the lowest mean ratio among the primary producers, with 5.6 ± 1.6 (p < 0.001). This C:N ratio was similar to that obtained for the coastal SOM (p = 0.056).

Fatty acids

In this study, thirty-three fatty acids were detected at concentrations > 1 % of the total FA identified (57 FAs) in at least one of the OM sources considered (Table 2). Saturated fatty acid (SFAs) contributions were dominant in all samples, ranging from ~43 % to ~65 % (Table 2).

The monounsaturated fatty acid (MUFAs) percentages were highly variable and relatively close from one sample to another (p = 0.180), extremum being ~15 % and ~24 % for algal turf and coastal SOM, respectively. Overall, branched fatty acids (BrFAs) represented the lowest contribution to the total FAs (less than 5 %), except for river and coastal SOM with ~10 % in both cases (Table 2). Conversely, phytoplankton showed the lowest average value for this fatty acid category, with ~1.3 %. Nevertheless, primary producers had significantly lower BrFA percentages than OM pools (p < 0.001; Table 2).

PUFAs had a wide range of percentages, the highest mean contribution being for phytoplankton (~39 %)

and the lowest for the river SOM (~9 %). However, no clear trend was observed between primary producers and OM pools, only detrital terrestrial plant material displayed a significantly higher PUFA contribution than R-SOM, C-SOM and M-POM (p < 0.05; Table 2).

Among SFAs, the 16:0 fatty acid contributed the most to the overall percentage, ranging from ~19 % (DTP) to ~53 % (Macroalgae; Table 2). The predominant monounsaturated fatty acid (MUFAs) was the 16:1ω7 in phytoplankton, coastal SOM and river POM (Table 2). Fatty acid 18:1ω9 exhibited a higher contribution in all other samples (Table 2). The PUFAs 18:3ω3 and 18:2ω6 contributed the most to the total FAs in the DTP samples (Table 2). Amongst essential fatty acids (EFAs), 20:4ω6 exhibited higher percentages in macroalgae species than in algal turf or phytoplankton (Table 2). In OM pools, relatives contributions of this EFA were maximum in coastal SOM (~3.2 %) whereas contributions 20:5ω3 and 22:6ω3 were much higher in phytoplankton, (> 13 % of total FAs ; Table 2).Algal turf and macroalgae bear the highest relative contribution of 20:5ω3 following phytoplankton (~4.4 % for (Table 2).

Phytoplankton samples were more concentrated in FA than the other samples, with > 40 mg.g -1 .. The lowest concentrations were measured in sediment samples both for river and coastal SOM (Table 2).

The PCA ran on FA concentrations of the four primary producer categories (i.e. macroalgae, algal turf, phytoplankton and terrestrial detritus) well reflected these FA distributions within producers (Figure 3a).

Regarding the nutritional quality indices, phytoplankton displayed the best PUFAs/SFAs ratio and percentage of EFAs (20:5ω3, 22:6ω3 and 20:4ω6), with 0.90 ± 0.15 and 30.95 ± 3.57 %, respectively (Table 2). The other categories of samples did not clearly stand out compared to the others, only DTP and river SOM had PUFAs/SFAs ratios that were significantly different, with 0.68 ± 0.27 and 0.16 ± 0.10, respectively (p < 0.05). The remaining groups had ratios close to 0.30.

The first two principal components of the PCA run on marine OM pools (i.e. M-POM and C-SOM) accounted for 46.4 % of the total variation in the data set (Figure 3b). 18:3ω3, 18:1ω7, 14:0, iso-15:0, anteiso-15:0 and 20:4ω6 fatty acids were the variables contributing the most to the first axis, while 24:0, 16:2ω4, 18:0, 17:0, 16:1ω7 and 20:5ω3 contributed more to the second axis. The PCA results highlighted three main groups of samples. Firstly, marine POM samples are linked to elevated percentages of 12:0, 14:0, 18:2ω6, 22:6ω3 and 16:2ω4 fatty acids (Figure 3b). Then two other groups among coastal SOM samples stand out. One group of individuals is clearly linked to 24:0, 17:0 and 18:0 fatty acids, while the others are related to 18:3ω3, 18:1ω7, 20:4ω6, 16:1ω7 and 20:5ω3 fatty acids (Figure 3b). The PCA highlighted the strong correlations between some FAs, such as 18:1ω7 and 20:4ω6, 16:1ω7 and 20:5ω3, 24:0 and 17:0, iso-16:0 and iso-17:0 (Figure 3b).

Mixing model

Phytoplankton was clearly the most important source contributing to the mean composition of the coastal SOM, with ~62 % (Figure 4a). Macroalgae represented the second major source of carbon in the C-SOM, with ~ 32 %. Mean contributions from other potential OM sources were almost negligible, with ~4 % for algal turf and below 1 % for sources of terrestrial origin (R-POM, R-SOM and DTP).

Algal turf and phytoplankton were both the main contributors to the marine POM, with ~ 38 % on average in both cases (Figure 4b). However, the violin plots bimodal distributions of these primary producers illustrates a 'joint uncertainty' regarding their relative mean contribution to the M-POM, which can vary from ~5-10 to ~65-70%. River POM, river SOM, DTP and benthic macroalgae had lower proportions, with mean contributions ranging from ~5% to ~7%.

DISCUSSION

Isotope compositions

The carbon isotope compositions of the sources of OM is generally within the ranges commonly observed in the literature [START_REF] Briand | Major sources of organic matter in a complex coral reef lagoon: Identification from isotopic signatures (δ 13 C and δ 15 N)[END_REF]. However, some sources revealed a remarkable deviation from expected values. While benthic primary producers are usually more enriched in 13 C than pelagicprimary producers [START_REF] Peterson | Stable isotopes as tracers of organic matter input and transfer in benthic food webs: a review[END_REF], in our study algal turf has lower δ 13 C values than phytoplankton (-23.9 ± 1.7 ‰ and -20.5 ± 0.6 ‰, respectively). Algal turf is generally among the most 13 C-depleted macrophytes, but generally has higher δ 13 C values than marine POM or phytoplankton [START_REF] Letourneur | Identifying carbon sources and trophic position of coral reef fishes using diet and stable isotope (δ 15 N and δ 13 C) analyses in two contrasted bays in Moorea, French Polynesia[END_REF][START_REF] Briand | Major sources of organic matter in a complex coral reef lagoon: Identification from isotopic signatures (δ 13 C and δ 15 N)[END_REF][START_REF] Briand | Complex food webs in highly diversified coral reefs: Insights from δ 13 C and δ 15 N stable isotopes[END_REF]. Despite a wide variability of δ 13 C values, the main groups of primary producers are clearly distinct from each other (Fig. 2). Nitrogen isotope compositions clearly distinguish land-based sources (δ 15 N values of 1.8 ± 2.3 ‰ and 6.2 ± 0.8‰, for DTP and river SOM, respectively) from marine sources (δ 15 N values of 11.6 ± 0.9 ‰ and 15.0 ± 1.8 ‰ for macroalgae and phytoplankton, respectively), as the latter are more enriched in 15 N. Our study highlights that primary producers had much higher δ 15 N values than those commonly observed in other coral ecosystems, even in the Pacific.

Taking benthic primary producers as a reference, the  15 N values recorded in the Marquesas Islands displayed differences of about 10 ‰ and 8 ‰ compared to New Caledonia and Moorea, respectively [START_REF] Letourneur | Identifying carbon sources and trophic position of coral reef fishes using diet and stable isotope (δ 15 N and δ 13 C) analyses in two contrasted bays in Moorea, French Polynesia[END_REF][START_REF] Briand | Major sources of organic matter in a complex coral reef lagoon: Identification from isotopic signatures (δ 13 C and δ 15 N)[END_REF]. These high  15 N values are probably related to an enrichment in 15 N of the nitrogen nutrient pool (i.e. nitrites, nitrates and/or ammonium). Knowing that phytoplankton is abundant throughout the year in the Marquesas Islands [START_REF] Martinez | Environnement océanique des Marquises[END_REF], nitrogen utilization by phytoplankton would probably lead to an increase in the  15 N values in the residual nutrient pool [START_REF] Savoye | Dynamics of particulate organic matter δ 15 N and δ 13 C during spring phytoplankton blooms in a macrotidal ecosystem (Bay of Seine, France)[END_REF]. Consequently, the nitrogen isotope compositions of primary producers incorporating these remaining nutrients would also rise. This assumption could be consistent if the nitrogen stock was not large enough to support the primary producers' needs. However, the waters surrounding the Marquesas have relatively high nutrient concentrations [START_REF] Martinez | Environnement océanique des Marquises[END_REF]), which does not presuppose a lack of nutrients.

Fatty acids

The results obtained for marine OM pools (POM and SOM) are relatively similar to those found in other Pacific ocean studies [START_REF] Liénart | Dynamics of particulate organic matter in a coastal system characterized by the occurrence of marine mucilage-A stable isotope study[END_REF]. These OM pools are characterized by a strong contribution of the SFAs (~ 62 and 50 % TFAs), and a small contribution of the MUFAs (~ 17 and 24 % TFAs) and branched fatty acids (~ 4 and 9 % TFAs). PUFAs, however, have a higher contribution 2). PCA (Fig. 3) separates OM pools into three groups, reflecting compositional differences between marine POM and two groups for coastal SOM. These results highlight contributions of various PUFAs such as 22:6ω3 (often found in dinoflagellate), 16:2ω4 (a marker for diatoms or algae), 18:2ω6 (suggesting OM derived from macroalgae or vascular plants) and some SFAs (12:0, 14:0 and 16:0) to marine POM [START_REF] Budge | Lipid biogeochemistry of plankton, settling matter and sediments in Trinity Bay, Newfoundland. II. Fatty acids[END_REF][START_REF] Arts | Essential fatty acids" in aquatic ecosystems: a crucial link between diet and human health and evolution[END_REF]). Thus, these FA markers indicate that the marine POM would consist of a mixture of different primary producers, both benthic and pelagic and potentially of terrestrial origin as well. For coastal SOM, one group exhibits contributions mainly from MUFAs and PUFAs. In the same way as for the POM, FAs markers found for this OM are likely to come from marine and terrestrial sources. 20:5ω3 and 16:1ω7 are indeed known to be markers of diatoms [START_REF] Budge | Lipid biogeochemistry of plankton, settling matter and sediments in Trinity Bay, Newfoundland. II. Fatty acids[END_REF][START_REF] Dalsgaard | Fatty acid trophic markers in the pelagic marine environment[END_REF][START_REF] Liénart | Dynamics of particulate organic matter in a coastal system characterized by the occurrence of marine mucilage-A stable isotope study[END_REF], 20:4ω6 of Rhodophyta [START_REF] Jaschinski | Seasonal variation in carbon sources of mesograzers and small predators in an eelgrass community: stable isotope and fatty acid analyses[END_REF]) and 18:3ω3 of OM derived from macroalgae or vascular plants [START_REF] Meziane | Inter-specific and geographical variations in the fatty acid composition of mangrove leaves: Implications for using fatty acids as a taxonomic tool and tracers of organic matter[END_REF]). The FAs 18:1ω7 and anteiso-15:0 may indicate the presence of bacteria in this group [START_REF] Dalsgaard | Fatty acid trophic markers in the pelagic marine environment[END_REF]. But the orientation of variables representing the branched fatty acids (iso-17:0, iso-16:0 and iso-15:0) in the PCA suggests the presence of bacteria within the two coastal SOM groups (Figure 3). Marine heterotrophic bacteria are known to colonize settling particulate matter following plankton blooms, and can be abundant in sediments [START_REF] Dalsgaard | Fatty acid trophic markers in the pelagic marine environment[END_REF]. However, the second group of coastal SOM samples had contributions of relatively more degraded organic material, as suggested by the high contributions of SFAs (24:0, 17:0 and 18:0; [START_REF] Wakeham | Compositions and transport of lipid biomarkers through the water column and surficial sediments of the equatorial Pacific Ocean[END_REF]. This result suggest a qualitative degradation of these samples with the help of a bacterial blooming related most likely to a storage problem of samples.. A similar trend was observed in another study, with diatom markers 16:1ω7 and 20:5ω3 found in highest proportions in sediments rather than marine POM, and conversely for the dinoflagellates marker (22:6ω3; Richoux and Froneman 2008). The analysis of our primary producers gives results in agreement with designated FA markers in the literature, with major observations of fatty acids such as 20:4ω6 in benthic algae, 18:2ω6 and 18:3ω3 in detrital terrestrial plants, 16:1ω7, 20:5ω3 and 22:6ω3 in phytoplankton.

Indicators of OM quality

In this study, the sources with the highest quality were sedimentary OM (river and coastal), phytoplankton and marine POM. Their C:N ratios between 5 and 7 (Table 1) suggest the presence of a significant amount of amino acids [START_REF] Danovaro | Deep-sea ecosystem response to climate change: the eastern Mediterranean case study[END_REF]). However, regarding quality indices obtained with FA analysis, phytoplankton is significantly of much higher quality (Table 2). The highest percentage of essential fatty acids was indeed measured in the latter (30.95 ± 5.57 %), moreover its PUFAs/SFAs ratio indicates fresher OM than the other sources. Among OM pools, coastal SOM and POM have a similar quality based on their C/N ratios and FA quality indices, which is likely related to the fact that fresh phytoplankton represents a very important contribution to SOM composition (i.e. see mixing model data). This clearly indicates the important trapping of phytoplankton into the sediment and the importance of the benthic-pelagic coupling in the functioning of this ecosystem. Among OM pools, even if coastal SOM has a lower C:N ratio than marine POM, their nutritional quality cannot be differentiated based on FA quality indices. The C:N ratios higher than 12 measured in algal turf and freshwater macrodetritus (DTP) indicates a lower nutritional quality of these sources, with a higher content of refractory organic matter [START_REF] Hedges | Compositions and fluxes of particulate organic material in the Amazon River[END_REF]. Benthic macroalgae OM also does not appear as a food resource of very good quality, based on its C:N ratios around 10. Thus, comparing all sources, the OM pools had lower C:N ratios than the benthic primary producers (macroalgae and algal turf),

indicating that OM pools may be relatively more nutritious. Interestingly, although less important than for phytoplankton, the EFAs found in algal turf and macroalgae represent a high proportion of their PUFAs (Table 2). Therefore, despite their relatively poor quality in terms of nitrogen supply, marine macroalgae could be interesting food sources for consumers to supplement their needs in essential fatty acids [START_REF] Arts | Essential fatty acids" in aquatic ecosystems: a crucial link between diet and human health and evolution[END_REF]. The marine POM and phytoplankton C:N ratios correspond to those obtained in other studies in temperate and tropical areas (~ 6.5 for POM, between 6 and 10 for phytoplankton; [START_REF] Savoye | Dynamics of particulate organic matter δ 15 N and δ 13 C during spring phytoplankton blooms in a macrotidal ecosystem (Bay of Seine, France)[END_REF][START_REF] Cresson | Spatio-temporal variation of suspended and sedimentary organic matter quality in the Bay of Marseilles (NW Mediterranean) assessed by biochemical and isotopic analyses[END_REF].

Composition of OM pools

The Bayesian mixing model highlighted that coastal SOM is mostly made of phytoplankton, followed by macroalgae. Phytoplankton is known as a significant contributor to SOM through the sinking of dead phytoplankton [START_REF] Cresson | Spatio-temporal variation of suspended and sedimentary organic matter quality in the Bay of Marseilles (NW Mediterranean) assessed by biochemical and isotopic analyses[END_REF]. Composition of marine POM is also influenced by phytoplankton, but with average contributions of smaller amplitude than for coastal SOM (~38 %).

Phytoplankton is not the major contributor in this case, and algal turf fragments also represent an important contribution to POM (~38 %). However, it is likely erroneous to look only at these average contributions, due to the bimodal distributions displayed on the violin plots for algal turf and phytoplankton (Fig. 4). This bimodal distribution means that, if the algal turf contribution is at the top of its probability range, then the contribution of phytoplankton is likely to be at the bottom of its probability range, and vice versa. In contrast to other studies [START_REF] Harmelin-Vivien | Comparison of C and N stable isotope ratios between surface particulate organic matter and microphytoplankton in the Gulf of Lions (NW Mediterranean)[END_REF][START_REF] Letourneur | Identifying carbon sources and trophic position of coral reef fishes using diet and stable isotope (δ 15 N and δ 13 C) analyses in two contrasted bays in Moorea, French Polynesia[END_REF], our results did not indicate any clear influence of river organic matter on marine POM. The greater macroalgae relative contribution observed for SOM (compared to POM) could be explained by a coarser fragmentation of macroalgae, these staying less easily in suspension than algal turf fragments.

A lower degradation rate would probably favors the trapping of OM derived from benthic macroalgae in sediment over a longer period. It is also plausible that other organisms or compounds, which are difficult to collect, may influence the composition of OM pools. In our case, according to the results obtained with the fatty acids analyses (see above), bacteria probably influence the OM pools' compositions. Additional analyses highlighted high abundances of cyanobacteria, mostly

  than in the literature, with ~ 16 % for both POM and SOM (e.g. POM: ~ 9 % -Liénart et al. 2016; SOM: ~ 7 % -Liénart et al. 2018). Essential fatty acids represent ~ 4 to 6 % of TFAs comprising PUFAs (Table

FiguresFigure 1 .

 1 Figures

Figure 2 .

 2 Figure 2. δ 13 C vs δ 15 N mean values of OM sources, both seasons pooled. Grey circles represent primary producers and triangles represent river OM pools. Black squares represent marine POM and coastal SOM. Error bars indicate standard deviations. Codes are detailed in Table1.

Figure 3 .

 3 Figure 3. (A) Projection of variables (fatty acid trophic marker percentages) and individuals (primary producers) on the first two components resulting from the principal component analysis (PCA). Only FAs displaying an average proportion greater than 1 % within at least one group of primary producer samples and with cos² > 0. 4 are presented.. (B) Projection of variables (fatty acid trophic marker percentages) and individuals grouped by category (C-SOM and marine POM) on the first two components resulting from the principal component analysis (PCA). Only FA displaying an average proportion greater than 1 % within at least one group of samples and with cos² > 0.2 are presented. Numbers in brackets indicate the percentage of the total variance explained by each axis. Eigenvalues histogram of the different components result from the PCA.

Figure 4 .

 4 Figure 4. Relative importance of different OM sources in the composition of (a) coastal sedimentary organic matter (C-SOM) and (b) marine particulate organic matter (M-POM). DTP: Detrital terrestrial plants material; Phyto: Phytoplankton; R-POM: river particulate organic matter. Violin plots represent the posterior distribution shape of the data (density estimation) in grey; Boxplots represent median, interquartile ranges (white box), credibility intervals (thin line) and outliers (black dots).

Table 1 .

 1 Isotope compositions (δ 13 C and δ 15 N values) and C/N ratios of organic matter (OM) sources (mean ± SD). Data from cold and warm seasons are pooled. POM: particulate organic matter, SOM: sedimentary organic matter.

				Code	n	δ 13 C (‰)	δ 15 N (‰)	C/N
	OM Pools	POM SOM	River Marine River Coastal	R-POM M-POM R-SOM C-SOM	11 38 17 30	-27.2 ± 0.9 -22.5 ± 0.8 -24.3 ± 1.2 -19.1 ± 0.9	4.4 ± 0.5 12.1 ± 1.1 6.2 ± 0.8 14.4 ± 0.5	13.0 ± 3.8 7.1 ± 1.3 5.2 ± 4.9 5.3 ± 2.9
		Detrital terrestrial plants	DTP	16	-29.5 ± 1.7	1.9 ± 2.3	15.5 ± 33.6
		PHYTOPLANKTON	Phyto	49	-20.5 ± 0.6	15.0 ± 1.8	5.6 ± 1.6
		MACROALGAE	Algae	41	-16.4 ± 2.0	11.6 ± 0.9	9.9 ± 4.6
		Chlorophyta			6	-13.8 ± 2.1	11.9 ± 0.7	11.2 ± 2.2
			Ulva sp.	Ulva	2	-16.0 ± 0.3	12.8 ± 0.3	10.4 ± 0.3
	Primary producers	Cladophoropsis sundanensis Ochrophyta Lobophora obscura Lobophora spp. Rhodophyta Pterocladiella caerulescens	Clsu Loob Losp Ptca	4 7 4 3 28 11	-12.7 ± 1.5 -15.9 ± 1.9 -16.9 ± 1.4 -14.6 ± 1.8 -17.1 ± 1.4 -17.2 ± 1.0	11.5 ± 0.2 12.0 ± 0.9 12.7 ± 0.2 11.0 ± 0.4 11.4 ± 0.9 11.3 ± 1.2	11.6 ± 2.7 10.9 ± 5.0 10.1 ± 1.9 11.9 ± 8.2 9.3 ± 4.8 7.3 ± 5.0
		Ceratodictyon variabile	Ceva	4	-17.9 ± 0.5	11.7 ± 0.2	11.8 ± 0.8
		Ceratodictyon scoparium	Cesc	8	-17.1 ± 0.9	11.1 ± 0.7	8.4 ± 5.0
		Peyssonnelia spp.	Pesp	5	-16.2 ± 2.7	11.9 ± 0.8	13.3 ± 3.3
		ALGAL TURF		Turf	32	-23.9 ± 1.7	12.9 ± 0.6	18.1 ± 16.0

Table 2 .

 2 Fatty acid (FA) composition percentages and total concentrations (% of total identified fatty acids and total concentrations in mg.g -1 , mean ± SD) of OM sources (primary producers and pools). Only FAs displaying an average proportion greater than 1 % within at least one group of samples are presented. DTP: detrital terrestrial plants, POM: particulate organic matter, SOM: sedimentary organic matter, SFAs: saturated FAs, MUFAs: monounsaturated FAs, PUFAs: polyunsaturated FAs, BrFAs: branched FAs. For SOM, the term 'coastal' rather than 'marine' is used because no SOM sample was collected at the oceanic site (see text).

			Primary producers					OM pools
	Fatty acids (%)	DTP	Algal turf	Macroalgae Phytoplankton	River	SOM	Coastal	River	POM	Marine
		n = 9	n = 9	n = 15	n = 2	n = 6			n = 18	n = 4	n = 12
	Saturated
	12:0	0.47 ± 0.34	0.31 ± 0.29	0.41 ± 0.23	0.19 ± 0.04	1.13 ± 0.93	0.58 ± 0.57	1.27 ± 0.54	1.78 ± 1.05
	14:0	1.82 ± 1.16	3.56 ± 1.18	5.31 ± 1.89	10.54 ± 0.81	3.69 ± 3.16	3.37 ± 0.69	6.81 ± 0.65	13.94 ± 2.57
	15:0	0.41 ± 0.28	1.10 ± 0.92	0.82 ± 0.24	1.05 ± 0.17	1.24 ± 0.91	1.29 ± 0.42	1.77 ± 0.58	1.61 ± 0.41
	16:0	19.51 ± 6.70 44.26 ± 10.81 52.95 ± 9.72	23.14 ± 2.70	29.95 ± 4.81	27.95 ± 6.18	28.51 ± 3.21 30.01 ± 5.05
	17:0	1.00 ± 0.56	1.13 ± 0.38	0.65 ± 0.30	1.19 ± 0.08	3.33 ± 2.17	3.70 ± 2.79	4.75 ± 4.96	2.10 ± 1.26
	18:0	7.50 ± 4.37	5.46 ± 1.49	4.52 ± 1.99	6.32 ± 0.03	17.59 ± 7.47	9.74 ± 6.24	12.62 ± 3.24 10.37 ± 3.09
	20:0	2.43 ± 2.42	0.32 ± 0.10	0.25 ± 0.13	0.37 ± 0.006	1.07 ± 0.29	0.73 ± 0.39	0.83 ± 0.14	0.86 ± 0.28
	21:0	1.41 ± 3.66	0.02 ± 0.03	0.02 ± 0.04	0.04 ± 0.06	0		0.06 ± 0.16	0.07 ± 0.14	0.10 ± 0.11
	22:0	4.31 ± 4.05	0.39 ± 0.22	0.26 ± 0.11	0.41 ± 0.07	1.82 ± 1.34	1.40 ± 2.67	1.11 ± 0.27	0.85 ± 0.28
	24:0	10.65 ± 20.48	0.62 ± 0.15	0.30 ± 0.26	0.25 ± 0.07	1.85 ± 0.57	1.22 ± 0.52	1.28 ± 0.17	0.86 ± 0.40
	Σ SFAs	45.29 ± 8

.78 63.14 ± 10.14 65.81 ± 11.42 43.80 ± 3.51 64.71 ± 14.92 50.64 ± 11.98 59.67 ± 9.07 62.26 ± 10.21 Monounsaturated

	16:1ω9	1.39 ± 1.77	1.82 ± 0.83	1.01 ± 0.65	0.18 ± 0.05	0.40 ± 0.13	1.81 ± 1.06	0.84 ± 0.43	1.17 ± 0.73
	16:1ω7	1.03 ± 0.87	3.49 ± 1.80	3.45 ± 2.23	7.62 ± 0.66	2.56 ± 1.73	7.82 ± 5.39	5.55 ± 4.36	5.19 ± 2.59
	16:1ω5	0.47 ± 0.64	0.35 ± 0.19	0.69 ± 0.62	0.21 ± 0.008	1.29 ± 0.85	0.85 ± 0.42	0.44 ± 0.22	0.38 ± 0.29
	18:1ω9	5.46 ± 3.19	4.39 ± 2.06	5.36 ± 2.54	3.62 ± 0.52	5.16 ± 3.30	5.57 ± 3.18	4.12 ± 2.75	5.45 ± 2.79
	18:1ω7	3.52 ± 3.86	2.73 ± 1.30	2.71 ± 1.30	2.61 ± 0.23	2.55 ± 1.29	5.13 ± 3.03	1.92 ± 0.61	2.43 ± 1.48
	22:1ω11	2.23 ± 6.57	0.02 ± 0.03	0.03 ± 0.05	0.02 ± 0.03	0	0.03 ± 0.06	0.003 ± 0.007 0.02 ± 0.05
	22:1ω9	3.97 ± 11.15	0.07 ± 0.09	0.18 ± 0.12	0.26 ± 0.05	0.54 ± 0.63	2.46 ± 7.48	0.99 ± 1.97	0.48 ± 0.76
	Σ MUFAs	21.13 ± 15.03 14.59 ± 4.93	14.56 ± 5.89	15.41 ± 0.03	16.19 ± 7.86 24.44 ± 10.82 15.07 ± 9.91 17.15 ± 7.36
	Polyunsaturated
	16:2ω6	1.51 ± 2.26	0.34 ± 0.28	0.25 ± 0.35	0.16 ± 0.02	0.90 ± 1.26	1.88 ± 2.44	2.50 ± 3.64	1.77 ± 2.09
	16:2ω4	0.09 ± 0.11	0.35 ± 0.21	0.31 ± 0.29	0.76 ± 0.16	0.58 ± 0.91	0.73 ± 0.68	1.54 ± 1.29	1.52 ± 1.23
	18:2ω6	9.24 ± 4.90	1.70 ± 1.04	1.42 ± 0.64	1.54 ± 0.26	1.37 ± 0.87	1.22 ± 0.40	1.84 ± 1.43	2.05 ± 1.07
	18:3ω3	13.77 ± 12.72	0.50 ± 0.26	0.55 ± 0.48	0.52 ± 0.15	1.88 ± 1.29	1.15 ± 0.28	0.65 ± 0.36	0.72 ± 0.29
	20:4ω6	0.28 ± 0.33	4.89 ± 2.59	6.35 ± 4.93	2.69 ± 0.03	0.45 ± 0.46	3.23 ± 2.11	0.65 ± 0.47	0.69 ± 0.56
	20:5ω3	0.75 ± 2.00	4.42 ± 2.45	4.32 ± 3.04	13.23 ± 2.58	0.46 ± 0.80	2.33 ± 2.15	1.37 ± 0.53	1.77 ± 0.95
	22:2ω9	0.12 ± 0.29	0.06 ± 0.11	0.04 ± 0.13	0.01 ± 0.01	1.72 ± 3.90	0.07 ± 0.18	0.20 ± 0.40	0
	22:4ω6	0.38 ± 0.54	7.36 ± 20.90	0.20 ± 0.17	0.23 ± 0.07	0.06 ± 0.12	0.24 ± 0.18	5.14 ± 5.14	0.67 ± 1.63
	22:5ω6	0.19 ± 0.30	1.96 ± 1.57	1.35 ± 0.79	1.15 ± 0.21	1.26 ± 1.30	1.30 ± 2.90	1.88 ± 1.32	2.73 ± 2.06
	22:5ω3	0	0.26 ± 0.24	0.12 ± 0.19	1.17 ± 0.006	0	0.32 ± 0.51	0.03 ± 0.06	0.07 ± 0.07
	22:6ω3	0.38 ± 0.56	0.69 ± 0.37	0.49 ± 0.37	15.03 ± 0.96	0	0.55 ± 0.47	0.48 ± 0.20	1.78 ± 1.25
	Σ PUFAs	30.25 ± 11.49 19.21 ± 5.70	17.51 ± 6.86	39.25 ± 3.23	9.10 ± 4.74	15.51 ± 5.28	20.95 ± 2.75 15.80 ± 4.78
	Branched
	15:0anteiso	0.42 ± 0.56	0.23 ± 0.09	0.17 ± 0.12	0.14 ± 0.03	1.28 ± 0.51	1.21 ± 0.65	0.89 ± 0.44	0.61 ± 0.11
	15:0iso	0.97 ± 1.23	0.82 ± 0.30	0.59 ± 0.22	0.34 ± 0.06	3.18 ± 1.10	3.74 ± 1.17	1.16 ± 0.47	0.92 ± 0.60
	16:0iso	0.57 ± 0.84	0.53 ± 0.28	0.28 ± 0.16	0.16 ± 0.006	3.57 ± 4.30	1.70 ± 1.03	0.62 ± 0.59	0.57 ± 0.42
	17:0anteiso	0.24 ± 0.35	0.18 ± 0.07	0.45 ± 0.72	0.07 ± 0.03	1.16 ± 0.30	0.74 ± 0.46	0.26 ± 0.18	0.81 ± 2.06
	17:0iso	0.51 ± 0,48	0.76 ± 0.21	0.43 ± 0.17	0.38 ± 0.02	1.66 ± 0.49	1.32 ± 0.32	0.69 ± 0.11	0.87 ± 0.19
	Σ BrFAs	3.27 ± 3.51	3.05 ± 0.57	2.12 ± 1.15	1.30 ± 0.02	10.01 ± 3.27	9.41 ± 2.69	4.03 ± 1.53	4.71 ± 2.44
	Σ FA (mg.g -1 ) 2.85 ± 2.99	0.54 ± 0.24	1.30 ± 0.95	41.00 ± 14.76	0.007 ± 0.003 0.019 ± 0.020	1.12 ± 0.68	3.25 ± 3.08

Acknowledgements

This work is a part of the first author's PhD work, funded by the LabEx "Corail" (project RETROMAR). We would like to thank the Centre Plongée Marquises (X. Curvat "Pipapo", J. Augereau, M. Edragas and D. Taupotini), the Délégation à la Recherche de la Polynésie française, the mayor and people of Nuku Hiva for their support. We are also grateful to C. Berthe, F. Boulileret, R. Sauze, D.

Lecchini and M. Taquet for their field assistance. We thank the staff of the CRIOBE for logistical support and laboratory assistance, especially C. Sidobre, and B. Espiau, and N. Thiney for her invaluable help for FAs analyses in Paris, Muséum National d'Histoire Naturelle. Thanks to M. Paul, a native English-speaker, for improving the English of the article. Gaël Guillou is acknowledged for running stable isotope analyses. We also thank the anonymous referees for their useful and constructive comments that allowed us to improve the article.

Synechococcus spp., during the warm season (results not shown). These organisms are very small (0.5 to 1.8 µm), therefore it is possible that they were not captured in a representative manner in the size class < 20 µm (taken into account in this study). [START_REF] Haas | Effects of coral reef benthic primary producers on dissolved organic carbon and microbial activity[END_REF] estimated that reefs dominated by algal turf and macroalgae will support 2 to 3 times as much microbial abundance in the water column as coral or crustose algae dominated reefs.

CONCLUSIONS

Our findings suggest that the most important food sources available for primary consumers in this system consist of organic matter principally derived from phytoplankton, with complements of macroalgae and algal turf. OM sources of terrestrial origin had a very minor influence. In addition, phytoplankton was characterized by the best nutritional quality, with low C:N ratio and high essential fatty acid contributions to total FAs, which are important for physiological processes. These characteristics make this OM source particularly attractive for primary consumers. This suggests that the supply of labile organic matter in the system results from a pelagic-benthic coupling. Our study also highlights an atypical Marquesan baseline, marine primary producers having significantly higher δ 15 N values than those observed in other South Pacific areas. However, further research is needed to examine the processes leading to the enrichment in 15 N in primary producers. It would be interesting to measure δ 15 N values in nitrate pools and to follow the nutrient inputs over a long time period. A better knowledge of the bacterial processes occurring in Marquesan waters could also provide useful clarification.

Compliance with ethical standards

This research received no specific grant from any funding agency, commercial or not-profit sectors.

The authors declare that they have no conflicts of interest. No benthic/coral habitat was disturbed during this research. Because this work did not use animals, no international, national, local and/or institutional guidelines for sampling was applicable. Supplementary figure 1. δ 13 C vs δ 15 N values of OM sources, with sites and seasons. For sites: C1 in red, C2 in yellow, C3 in green, P in blue and R in pink. Circles represent the cold/dry season and triangles the warm/wet season. Among C-Phyto (coastal phytoplankton) and O-Phyto (oceanic phytoplankton), '<20' indicate phytoplankton fraction smaller than 20 μm, '20' the fraction 20-63 µm, and '63' the fraction 63-200 µm. Codes are detailed in Table 1.


Daniel Balouek
email: daniel.balouek@inria.fr

Hélène Coullon
email: helene.coullon@imt-atlantique.fr

Dynamic Adaptation of Urgent Applications in the Edge-to-Cloud Continuum

Keywords: Urgent Computing, Computing Continuum, Dynamic Adaptation, Decentralized System

The integration of Urgent Computing is essential in order to adhere to stringent time and quality constraints of emerging distributed applications, hence facilitating efficient decision-making processes in numerous fields. Adaptation of such applications to produce outcomes within the desired confidence range and defined time interval can be of great benefit, especially in distributed and heterogeneous execution contexts. This study provides a justification for the necessity of dynamic adaptation in applications that are time-sensitive. Furthermore, we present our viewpoint on time-sensitive applications and undertake a thorough analysis of the underlying principles and challenges that need to be resolved in order to accomplish this goal. This research aims to provide a comparative analysis of our suggested vision for adaptation in contrast to the existing literature. We provide a comprehensive explanation of the architectural framework that we plan to construct, and conclude with discussing some on-going challenges.

Introduction

Recent years have witnessed an increase in global emergencies, from pandemics that claim lives and livelihoods to risks of flooding and food harvesting challenges brought on by climate change. Society at large is wrestling with these pressing challenges, which warrant for solutions guided by science [START_REF] Peleg | The covid-19 pandemic challenge to the all-hazards approach for disaster planning[END_REF]. Advanced information and communication technologies, such as IoT, Artificial Intelligence, big data analytics, and super computers (e.g., Clouds, High Performance Computing), have been proven to be more and more helpful in predicting scenarios' outcomes early enough to prevent disastrous situations or lessen their harmful effects. During the COVID-19 pandemic, supercomputers and data systems have worked together with unprecedented efficiency, from understanding the structure of the SARS-CoV-2 virus to modeling its spread, from therapeutics to vaccines, from medical response to managing the virus's impacts [START_REF] Friji | A generalized mechanistic model for assessing and forecasting the spread of the covid-19 pandemic[END_REF][START_REF] Alashhab | Impact of coronavirus pandemic crisis on technologies and cloud computing applications[END_REF]. Similarly, the VESTEC European FET project fuses super computers and real-time data for urgent decision-making [START_REF] Brown | The role of interactive super-computing in using hpc for urgent decision making[END_REF].

Urgent computing aims at facilitating scientific applications that leverage distributed data sources to support critical decision-making in a timely manner. Overall, urgent applications consist of the identification of events from distributed data sources and the triggering of appropriate reactions to accelerate response [START_REF] Leong | Towards a general definition of urgent computing[END_REF][START_REF] Gibb | The technologies required for fusing hpc and real-time data to support urgent computing[END_REF]. The time scales of the underlying processes vary from days in case of social unrest events, to hours in flood protection systems, to minutes in ship safety, and to seconds in earthquakes or tsunamis [START_REF] Boukhanovsky | Urgent computing for decision support in critical situations[END_REF]. The time available for decision support therefore varies in different application domains. An urgent application is typically modeled as a workflow of components exchanging discrete or continuous flows of data.

Low-latency connections and distributed servers, illustrated by the Edge-to-Cloud Continuum (Computing Continuum, or Continuum for short), are demonstrating new potential for urgent computing. Running applications on an aggregation of resources spanning the edge of the network, where data are generated, to the cloud and HPC resources at the network's core, is an opportunity for steering computations and numerical models to help reduce latency while increasing flexibility [START_REF] Balouek-Thomert | Harnessing the computing continuum for urgent science[END_REF][START_REF] Kumar | Coding the computing continuum: Fluid function execution in heterogeneous computing environments[END_REF]. For example, the Tactile Internet is expected to enable the matching of specific needs in one physical location with the best skill in another location. Building on 5G-like connectivity and haptic encoders, this technology will require an end-to-end latency below 1ms with minimal outage [START_REF] Van Den Berg | Challenges in Haptic Communications Over the Tactile Internet[END_REF][START_REF] Aijaz | Realizing the Tactile Internet: Haptic Communications over Next Generation 5G Cellular Networks[END_REF]. Due to these requirements, the Computing Continuum is an excellent enabler for urgent applications due to its holistic approach that exploits end-users, resources, and services at the logical extreme of the network and throughout the data path [START_REF] Balouek-Thomert | Towards a computing continuum: Enabling edge-to-cloud integration for data-driven workflows[END_REF] [START_REF] Beckman | Harnessing the computing continuum for programming our world[END_REF].

The realization of urgent applications presents specific requirements and constraints due to the nature and distribution of the data, the complexity of the models involved, the stringent error thresholds, and the strict time constraints. Identifying and mapping various user concerns (such as functional and nonfunctional requirements, restrictions for response time, solution quality, data resolution, cost, energy use, etc.) against a heterogeneous and dynamic environment warrant the design of adaptation mechanisms. Examples of such adaptations are choosing suitable workflow components and services, modifying application parameters, modifying the connections between components of the workflow, changing the required constraints when provisioning resources (e.g., CPU, RAM, network, etc.) Such mechanisms must be able to address cost/benefit trade-offs of the application. This paper proposes a vision of how adaptation mechanisms can be natively handled when designing urgent applications across the Continuum. The remainder of the paper is organized as follows: Section 2 gives a motivating use-case for our vision with an Early Earthquake Warning (EEW) workflow, which combines data streams from geo-distributed seismometers and high-precision GPS stations to detect large ground motions; Section3 presents our vision of urgent applications through the modeling of both the development and management aspects; Section 4 presents elements of solutions and open challenges around our vision, and finally, Section 5 concludes this work.

Motivating use case

In this section, we introduce the Earthquake Early Warning use case that motivated this work. We also discuss the challenges associated with executing distributed applications on the Computing Continuum.

Earthquakes are among the most destructive natural disasters. Networks of distributed seismic instruments on various scales are used for earthquake detection. Earthquake Early Warning (EEW) systems provide earthquake alerts before the shaking damage of a seismic event reaches sensitive areas, giving governments and communities a time window of seconds to minutes to take protective actions.

EEW can be described as a classification problem in which high-frequency seismic data stream from multiple sensors are processed to infer classes indicating the magnitude of the seismic event in a timely manner. Related efforts include novel algorithms recently developed to locate earthquakes and to calculate their magnitudes using P-and S-wave energy [START_REF] Liang | A virtual sub-network approach to earthquake early warning[END_REF]. Recently, ShakeAlert proposed detecting and disseminating EEW alerts using smartphones, relying on the fact that they have become ubiquitous to the public [START_REF] Rochford | Myshake: Using humancentered design methods to promote engagement in a smartphone-based global seismic network[END_REF][START_REF] Kohler | Earthquake Early Warning ShakeAlert 2.0: Public Rollout[END_REF].

EEW is a workflow typically composed of four components: (1) the preprocessing component that collects and cleans raw data obtained from sensors; (2) the classification component that relies on window-based processing to gather measurements streamed by each sensor, and performs classification on this streamed data; (3) the prediction component that filters and aggregates the data streams by regions using a bag-of-words representation to calculate the final prediction of eventual seismic events; (4) the alert component that is responsible for broadcasting alerts based on class predictions (normal activity, medium earthquake, or large earthquake). Some of these components may run continuously somewhere in the Continuum, but when initial seismic waves are detected, this complete workflow has to be deployed in a timely manner.

Traditionally, EEW is executed in a fully centralized fashion with data from sensors being sent to clouds (private or public) which is compatible with a static way of designing the application. However, this vision of EEW will not withstand potential destruction or unavailability of the infrastructure (fault tolerance), and thus is not reliable. Instead, we would like to leverage heterogeneous geographically distributed resources across the Continuum, which requires applications to adapt dynamically their codes, communication protocols, etc. according to the dynamically chosen hosting resource. For instance, if deployed within the Cloud, the prediction component can leverage heavy stream processing frameworks such as Flink, whereas if deployed at the Edge on small devices, low-level C libraries and MPI would be preferable.

In previous work [START_REF] Fauvel | A Distributed Multi-Sensor Machine Learning Approach to Earthquake Early Warning[END_REF][START_REF] Balouek-Thomert | Mdsc: modelling distributed stream processing across the edge-to-cloud continuum[END_REF] we proposed moving part of the sensor data processing toward the Edge to speed up detection and enhance fault tolerance. Figure 1 illustrates this static Edge deployment. However, if we have shown that different versions of the application running on different parts of the Continuum may have different behaviors, we did not address the automatic and dynamic adaptation of the application.

… … …

Data Production

By-Sensor Processing By-Region Processing Broadcasting Alerts

Fig. 1. An illustration of Distributed MultiSensor Earthquake Early Warning usecase (DMSEEW), previously proposed in [START_REF] Balouek-Thomert | Harnessing the computing continuum for urgent science[END_REF]. Seismic sensors located in the Edge send measurements to gateways in the network which preprocess that data. Those preprocessed data are sent to cloud servers which complete that data processing and eventually broadcast earthquake alerts.

We use Figure 2 (extracted from [START_REF] Balouek-Thomert | Mdsc: modelling distributed stream processing across the edge-to-cloud continuum[END_REF]) to further illustrate the need for adaptation in this use-case. Figure 2 presents the latency resulting from processing one seismic event in a previous evaluation of our EEW implementation [START_REF] Balouek-Thomert | Mdsc: modelling distributed stream processing across the edge-to-cloud continuum[END_REF]. Using the gros cluster on the Grid'5000 experimental testbed, we deployed a prototype of the application under different network configurations: a 10Gb link between the Edge and Fog layers, and different links (2G, 3G, 10 Gb) between the Fog and the Cloud layers. Edge designates that each component is executed on a separated layer of the Continuum whereas Cloud-only means all components are executed on the Cloud. Of course, when running in the Edge or at the Cloud level, the components also have to be adapted (e.g., libraries, frameworks, etc.). The performance of the application is influenced by two factors: the network and the bottlenecks resulting from the interaction between the different libraries (in the context of the current paper, components). The different values were obtained in separated experiments to understand the behavior of the application under different conditions. Currently, there is no mechanism to switch from one configuration to another based on availability of the infrastructure and the events occurring in the system, but also there is a need to consider the cost and feasibility of the operations when such reconfiguration is needed, which motivates the need for adaptation mechanisms.

Our vision of Urgent Computing

First, we see the Continuum as an external infrastructure offered by a provider. We consider that we do not have to handle this Continuum but instead that the Continuum is offering APIs to ask for resources (e.g., virtual or physical machines). In particular, we think that, in addition to the usual Cloud APIs that provides a type of resource as well as specific features (RAM, CPU, GPU etc.), one can also provision specific geographical locations in the Continuum.

Definition 1. We model an urgent application as a pair (D, M), where D is specified by the application developers (functional and nonfunctional developers), and M is specified typically by DevOps engineers or system administrators to manage the application deployment and life-cycle (i.e., adaptation).

This vision follows the one presented in [START_REF] Coullon | Component-based distributed software reconfiguration: A verification-oriented survey[END_REF], a survey on component-oriented reconfiguration.

Development part of an urgent application

Definition 2. The development of an urgent application D is a tuple (C, P, m, p i , p c ) with:

-C the set of software components available for the application, some of them being produced by the current developer, others being made available from the community; -P the set of patterns or strategies of service assemblies; m a labeled finite state machine that indicates from which to which pattern in P the application may switch at runtime and under which conditions; p i the initial pattern in P ; p c the current pattern in P . Definition 3. A pattern p ∈ P is defined as an assembly of components (C p , L p ) where C p ⊆ C is the set of component instances in the pattern, and L p is the set of connections or links between components.

In urgent applications, the nature of the connections is typically data-driven, and thus the assembly of components can be considered as a dataflow or a workflow. However, we want to add configurations to the links between components, under the form of connectors in the CBSE literature [START_REF] Coullon | Component-based distributed software reconfiguration: A verification-oriented survey[END_REF], or service-mesh approaches [START_REF] Ganguli | Challenges and opportunities in performance benchmarking of service mesh for the edge[END_REF][START_REF] Li | Service mesh: Challenges, state of the art, and future research opportunities[END_REF]. For example, we may want to redirect 50% of data to one component or another dynamically according to events. Hence, a link is configurable in our vision of urgent components. A component is associated with a set of variables V c to model the component (state, behavior, parameters), thus representing either the static or dynamic knowledge (modeling) on each component. These variables can then be used within constraints C c st that should be satisfied on a set of variables. One typical constraint that we consider at the level of the component is the geographical location of the component.

A non-functional service is a piece of software responsible for features not related to the functional aspect of the component, for instance how the component communicates (i.e., communication protocol), handles privacy, or energy etc. Services are deployed (instantiated) from types known in advance, and thus one service can be switched to another if compatible. At the level of one component, this catalog of services should be quite small. It is offered by the developer. Both the elements of S f and S nf are considered as configurable. Functional and non-functional services will typically change their configuration according to the constraints imposed by the infrastructure. For instance, if placed in an IoT device, the urgent component communicates through the LoRa protocol and optimizes the energy consumption rather than the performance. As a consequence the non-functional service responsible for communications may be modified, and the version of the functional service may need to be a downgraded version.

Each service is also associated with a set of variables V s modeling their parameters, state, behavior, etc., and these variables can then be used within constraints C s st that should be satisfied on a set of variables. For example, we could have a constraint on the amount of memory required by a service. Definition 5. A service is defined as a tuple (t, V s , C s st ), where t is the type of the service, V s is the set of variables of the service, and C s st is the set of constraints to satisfy for the service.

Management part of an urgent application

The management M of an urgent application is a complex task responsible for deploying and then adapting the application dynamically at run-time accord-ing to events. However, because of scalability and fault tolerance issues when considering urgent cases, the management cannot be considered as a centralized process.

We model the management of the application as a set of controllers C t , one around each component in C involved in the application. Each controller is responsible for an autonomic infinite loop MAPE-K [START_REF] Kephart | The vision of autonomic computing[END_REF] for its own component: monitoring the component and its environment (through sensors, infrastructure, or application instrumentation); deciding which new configuration should be targeted according to the monitoring knowledge (inference through constraints, by applying rules and policies); planning an adaptation program to move from the current to the targeted configuration (writing a program to modify the state of the component [START_REF] Chardet | Predictable Efficiency for Reconfiguration of Service-Oriented Systems with Concerto[END_REF][START_REF] Chardet | Toward Safe and Efficient Reconfiguration with Concerto[END_REF]); and execute this plan (i.e., program). Controllers, by being local to one component, have the possibility of adapting locally if isolated from the rest of the application, but in a normal context neighbor controllers can collaborate to take better decisions [START_REF] Alidra | SeMaFoR -Self-Management of Fog Resources with Collaborative Decentralized Controllers[END_REF].

It is assumed that each controller component operates on its own unique time scale, independent from the others. For example, monitoring can be an ongoing process, whereas analysis of the data that has been acquired most likely occurs only on occasion. Both processes are used to analyze the information that was collected. The planning is done on a consistent basis or in reaction to changes, and the executions are done as a direct result of the planning. Definition 6. The management of an urgent application M is a tuple (C t , P, m, p i , p c ) where C t is the set of controllers, P , m, p i , and p c respectively the same set of patterns, state machine, initial and current patterns as in D.

Definition 7. Two controllers are neighbors if their components are connected in the current pattern (graph, assembly) p ∈ P of the urgent application. The neighbors of a controller are denoted neighbors(c t ). Definition 8. A controller c t ∈ C t is a piece of software responsible for running an autonomic infinite loop MAPE-K [START_REF] Kephart | The vision of autonomic computing[END_REF] for its own component, denoted component(c t ).

We denote by X ct the local projection of any piece of the above knowledge in (D, M) to a controller c t ∈ C t . A local projection contains the information that relates to the local component that is controlled, and the neighbor components in the current pattern p ∈ P . Definition 9. The local knowledge (K) of each controller c t is composed of a subpart of the application model (D, M) as follows:

in D, the local projection of the set of components C ct ; in M, the local projection of the set of controllers C ct t ; for both D and M, the local projection of the set of patterns P ct , and the initial and current patterns p ct i and p ct c ; for both D and M, the labeled state machine m. The local projections of a pattern can be seen as a subgraph of the overall component assembly that contains as vertices

component(c t ) ∪ neighbors(component(c t )) (1)
As always in distributed systems, we assume that the knowledge shared by controllers is consistent, which is a challenging issue to address. However, to facilitate the global consistency in our modeling, we use a local projection on the local component and its neighbors. The labeled state machine m, which represents the rules under which an urgent application may change its pattern, is the only piece of knowledge that is centralized in this vision. This state machine is given by the developer. However, as will be discussed in the challenges of this paper, it is possible that m change through time, in which case a consistent vision of m is difficult to guarantee.

A controller can adapt many aspects related to an urgent component such as:

(1) change the constraints of the component related to the Continuum C c st ; (2) change the versions of the services within the component while respecting the composability (compatibility of output/input data) (S f , S n f ); (3) change the configuration of the services of a component (t, V s , C s st ); (4) change the current pattern p c to another one by following m, thus changing the topology between components and involved components; (5) change the configuration of the link between components; and (6) spawn, or ask for the destruction of a neighbor component. The "urgent" nature of the domain makes adaptation sensitive to time, which will be discussed in the challenges.

Elements of solution and open scientific challenges

As detailed in the previous section, each controller of a component handles a local autonomic loop MAPE-K. However, the loops cannot be strictly local and requires to collaborate with their neighbors so that the overall application does not deviate from a stable state. In particular, the (A), (P) and (E) steps require collaborations between controllers by exchanging some elements of their local knowledge (K) and by reaching a consensus in their decisions [START_REF] Alidra | SeMaFoR -Self-Management of Fog Resources with Collaborative Decentralized Controllers[END_REF]. For instance, if deciding locally to apply a switch of pattern, the decision should spread across all the controllers and should be compatible for all controllers. We give some elements of solutions in the rest of this section.

(K)nowledge -In our vision the first element to study is how to concretely model the programming and management of urgent applications. We think we can build our vision on three domains of the literature. First, we think that leveraging modern workflow engines based on the FaaS paradigm (Function-asa-Service), such as Argo workflows1 , or other engines adapted to heterogeneous workflows [START_REF] Cadorel | Handling heterogeneous workflows in the cloud while enhancing optimizations and performance[END_REF], is an interesting starting point to model urgent applications. Second, this vision of an urgent application as a workflow of components will have to be coupled with the service-oriented and microservices-oriented trend (e.g., REST, gRPC, GraphQL APIs). In particular, in our vision each component of the workflow is divided into services. Third, we think we will have to model the variability of components and services composing urgent applications with the help of feature models. Feature models are used in software engineering to capture the various configurations that can be selected or enabled in a software system. A feature model consists of a set of features, relationships between features, and constraints on their combinations. Features represent distinct functionalities, or behaviors that can be included or excluded in the software system. Coupling these three domains is not trivial and requires a software-engineering-oriented study. For example, coupling feature models with workflows has been studied in the past [START_REF] Acher | Managing Variability in Workflow with Feature Model Composition Operators[END_REF], as well as coupling feature models and micro-services [START_REF] Sousa | Automated setup of multi-cloud environments for microservices applications[END_REF], but the three of them together is a new challenge.

(A)nalysis -The second element to study is how to decide which local configuration to target according to internal and external events and to some degree of knowledge from neighboring controllers. In particular, if all controllers take a local decision, will the decisions be compatible , and how to make sure of it? We think that the three domains could be combined to handle this aspect. First, we think that distributed algorithms such as consensus, gossip, and leader election algorithms [START_REF] Lamport | The byzantine generals problem[END_REF][START_REF] Alidra | SeMaFoR -Self-Management of Fog Resources with Collaborative Decentralized Controllers[END_REF] could be helpful to reach a convergence between controllers in their decisions. Second, we think that auto-stabilizing versions of these algorithms ccould be important to avoid too many communications but still guarantee the convergence (stabilization) of the overall system [START_REF] Altisen | Introduction to Distributed Self-Stabilizing Algorithms[END_REF]. Third, we think that because of the huge variability when adapting urgent application (large search space), and because of the urgent nature of the decisions, machine learning could be of interest. In particular, perhaps reinforcement learning and federated learning could be studied so that decisions become better through time and so that learning models are trained in a distributed fashion among the controllers. We also think that a learning approach could be supplemented with more traditional approaches to solve satisfaction problems such as constraint solvers or SAT/first-order logic solvers to keep a certain level of explainability in the decision.

(P)lanning and the (E)xecution -In order to tackle many controllers, each with its own autonomic loop, we need languages to define adaptation actions (e.g., changing the pattern, changing internal behaviors of components or services, changing the links between components, etc.), and an associated engine to run these actions in a decentralized fashion. Indeed, if each controller takes its own decision, controllers are not independent because components are connected together, thus requiring some coordination when applying changes. For example, if updating one component, thus requiring it be interrupted, the components that depend on it have to adapt temporarily their own behavior.

In the literature planning and executing an adaptation is often referred as a reconfiguration problem: a reconfiguration language offers programming support to structure and expresses the actions to perform to change the system state; a reconfiguration engine executes and coordinates actions [START_REF] Chardet | Toward Safe and Efficient Reconfiguration with Concerto[END_REF][START_REF] Chardet | Predictable Efficiency for Reconfiguration of Service-Oriented Systems with Concerto[END_REF]; and a reconfiguration inference system automatically generates the set of actions to apply (the plan) [START_REF] Robillard | SMT-Based Planning Synthesis for Distributed System Reconfigurations[END_REF] according to the current and target configurations as inputs. However, existing solutions are mainly centralized in the literature [START_REF] Coullon | Component-based distributed software reconfiguration: A verification-oriented survey[END_REF][START_REF] Alidra | SeMaFoR -Self-Management of Fog Resources with Collaborative Decentralized Controllers[END_REF].

Moreover, the usual reconfiguration systems in the literature do not tackle the reconfiguration of the links between components of the system [START_REF] Coullon | Component-based distributed software reconfiguration: A verification-oriented survey[END_REF]. For this reason, we think that concepts of service-mesh [START_REF] Li | Service mesh: Challenges, state of the art, and future research opportunities[END_REF][START_REF] Ganguli | Challenges and opportunities in performance benchmarking of service mesh for the edge[END_REF] could be of interest to couple with the usual reconfiguration solutions.

Conclusion

Urgent applications are of significant interest in the literature due to the increase of global challenges. The availability of data and pervasive computing promise potential for supporting timely decision-making across the Computing Continuum. In this paper, we presented a vision for modeling urgent applications, with a particular focus on adaptation aspects across heterogeneous and geo-distributed resources. Building on an earthquake early warning motivating use-case, we propose an approach based on component-based reconfiguration. We expect the realization of this vision to impact cyber-infrastructures and similar shared sensors platform in a way that will manage time-sensitive applications and associated requirements with few assumptions during the design of applications.

Fig. 2 .

 2 Fig.2. Latency resulting from processing one seismic event under different applications and infrastructure scenarios, extracted from[START_REF] Balouek-Thomert | Mdsc: modelling distributed stream processing across the edge-to-cloud continuum[END_REF].

FFig. 3 .Definition 4 .

 34 Fig.3. An illustration of m, an object (state machine) modeling from which to which pattern the urgent application can switch. The pattern on the left is the initial pattern. In this example the initial pattern cannot be reached after a first switch.

Fig. 4 .

 4 Fig. 4. An illustration of a pattern with five components and their associated controllers (one color per controller). The colored lines under components represent the local projection of the controller associated with the color, in other words the knowledge of each controller. For instance, the controller of the component B (purple) has knowledge of components A, C and E represented by purple lines.

https://argoproj.github.io/argo-workflows/