Nejia Tlig
email: tlig.nejia@yahoo.com

Marie Boye

Tahani Hallek

Pierre Burckel

Maher Gzam

Mohamed Ali Tagorti

Sediment quality and environmental risk assessment in a Mediterranean coastal system using geochemical and multivariate statistical analyses: the case of Boughrara Lagoon (Southeastern Tunisia)

Keywords: Surficial sediments, Metal contamination, Eutrophication, Pyrite, Contamination factor, Risk assessment, Boughrara Lagoon

come

Sediment quality and environmental risk assessment in a

Mediterranean coastal system using geochemical and multivariate statistical analyses: the case of Boughrara Lagoon (southeastern Tunisia)

Introduction

Lagoons are generally considered as the most vulnerable ecosystems in marine coastal environments. With the rapid industrialization, anthropogenic activities have indeed increased the amount of toxic chemicals and metals in coastal ecosystems [START_REF] Zaaboub | Accumulation of trace metals in sediments in a Mediterranean Lagoon: usefulness of metal sediment fractionation and elutriate toxicity assessment[END_REF][START_REF] Hu | Heavy metal concentrations and chemical fractions in sediment from Swan Lagoon, China: Their relation to the physiochemical properties of sediment[END_REF][START_REF] Mosbahi | Response of benthic macrofauna to multiple anthropogenic pressures in the shallow coastal zone south of Sfax (Tunisia, central Mediterranean Sea)[END_REF]. Without any purification treatment, polluted wastewater is discharged into the coastal environment, possibly leading to the accumulation of pollutants, especially of metals, in the exchangeable fraction of surface coastal sediments. The accumulation of these elements including metals in coastal ecosystems poses a serious threat to human health and aquatic environment. Metals are characterized by their long residence time allowing to their accumulation and biomagnification in the food chain [START_REF] Zhao | Distribution and pollution assessment of metals in the intertidal zone environments of typical sea areas in China[END_REF]. Metals accumulated in marine coastal environment sediments may result from anthropogenic sources like industrial wastewater, while rock weathering and erosion are considered as natural sources. For instance, data analysis of contaminants distribution in coastal environment may constitute a crucial tool for predicting and monitoring the status of vulnerable areas and also for the identification of possible sources of contamination (Ferraro et al., 2022;[START_REF] Kükrer | Ecological risk assessment of surface sediments of Çardak Lagoon along a human disturbance gradient[END_REF].

Recently, various renewed scientific focus in marine pollution indicated that coastal environments were highly contaminated by organic and inorganic pollutants and especially by metals [START_REF] Pignotti | Sediment quality assessment in a coastal lagoon (Ravenna, NE Italy) based on SEM-AVS and sequential extraction procedure[END_REF]Çullu et al., 2020;[START_REF] Kükrer | Ecological risk assessment of surface sediments of Çardak Lagoon along a human disturbance gradient[END_REF][START_REF] Lin | Pollution and ecological risk assessment, and source identification of metals in sediment from the Beibu Gulf, South China Sea[END_REF][START_REF] El Zrelli | Surface sediment enrichment with trace metals in a heavily human-impacted lagoon (Bizerte Lagoon, Southern Mediterranean Sea): Spatial distribution, ecological risk assessment, and implications for environmental protection[END_REF]Ferraro et al., 2022;[START_REF] Wang | Distribution and pollution risk assessment of metals in the surface sediment of the intertidal zones of the Yellow River Estuary, China[END_REF]. The Mediterranean Sea is considered as the most threatened ecosystem, subject to significant anthropogenic pressure due to the economic and population development. Several recent studies were carried out to evaluate the pollution in various coasts in Tunisia, since they are subject to high anthropogenic pressures (Kharroubi et al., 2012;[START_REF] Zaaboub | Accumulation of trace metals in sediments in a Mediterranean Lagoon: usefulness of metal sediment fractionation and elutriate toxicity assessment[END_REF][START_REF] Khedhri | Assessment of surface sediment dynamics and response of benthic macrofauna assemblages in Boughrara Lagoon (SW Mediterranean Sea)[END_REF][START_REF] El Zrelli | Biomonitoring of coastal pollution in the Gulf of Gabes (SE, Tunisia): use of Posidonia oceanic seagrass as a bio-indicator and its mat as an archive of coastal metallic contamination[END_REF]Ben Mna et al., 2017;[START_REF] Gargouri | Use of sediment quality indicators for metals contamination and ecological risk assessment in urbanized coastal zones[END_REF][START_REF] Naifar | Spatial distribution and contamination assessment of metals in marine sediments of the southern coast of Sfax, Gabes Gulf, Tunisia[END_REF][START_REF] Mosbahi | Response of benthic macrofauna to multiple anthropogenic pressures in the shallow coastal zone south of Sfax (Tunisia, central Mediterranean Sea)[END_REF][START_REF] Keskes | Dinoflagella tesencystment with emphasis on blooms in Boughrara lagoon (South-Western Mediterranean): Combined effects of trace metal concentration and environmental context[END_REF]Belkahia et al., 2020;Ben Mna et al., 2021;[START_REF] El Zrelli | Surface sediment enrichment with trace metals in a heavily human-impacted lagoon (Bizerte Lagoon, Southern Mediterranean Sea): Spatial distribution, ecological risk assessment, and implications for environmental protection[END_REF]. However, the extent of pollution by metals is not precisely known in the Boughrara lagoon which is located between the southeastern part of Tunisia and Djerba Island, whereas this semi-enclosed lagoon can represent an accumulation basin of pollution. This lagoon has an important economic function, particularly in fishing and halieutic activities.

Indeed, this lagoon receives various wastes from different sources such as soil mining, aquaculture, fishery and industry from the Tunisian chemical group (TCG). Industrial wastewater discharged in the Gabes Gulf is advected by the long-shore current oriented towards the south, causing a large contamination by phosphogypsum, which can be a source of various chemical elements (Cu, Al, P, Cd…) in the Boughrara lagoon [START_REF] Amari | Courantologie, hydrologie et environnements sédimentaires sur le platier de Kerkennah et le littoral de Sfax (Tunisie)[END_REF]Magherbi et al., 1995;[START_REF] Gargouri | Use of sediment quality indicators for metals contamination and ecological risk assessment in urbanized coastal zones[END_REF]. Phosphorous (P) enrichment of phosphogypsum combined with anoxic conditions due to weak circulation in the lagoon can accelerate the phenomenon of eutrophication, leading to serious environmental problems (El Zrelli et al., 2017;[START_REF] Rabaoui | Metal bioaccumulation in two edible cephalopods in the Gulf of Gabes, South-Eastern Tunisia: environmental and human health risk assessment[END_REF]. In this context, citizens of the Boughrara region, especially bathers in summer, have recently observed the appearance of red tides and high fish mortality in the southwestern part of the lagoon, the cause of which remains uncertain.

In addition, metal inputs from the red clay and lead extraction mines upstream of the watersheds could represent other sources of contamination in the lagoon during the flood periods, as well as the erosion of surrounding cliffs. But these potential sources of metal pollutions have not yet been investigated.

Thus, the present study aims to diagnose the state of pollution by various elements like Zn, Pb, Cu, Cd, Fe, Cr, P, Ti and Ca in the Boughrara lagoon, which will serve as a study model to allow a better ecological risk assessment and help improve resource management in anthropized coastal systems. To this end, we made mineralogical and chemical analyses of 25 surficial sediment samples collected in the western side of the Boughrara lagoon and we calculated the contamination factors (CF) for each chemical element. Multivariate statistical analyses combined with geostatistical tests assisted with GIS tools were used to further interpret the data. In order to identify the sources of the pollution in the Boughrara lagoon, analyzed surficial sediments were compared with other sites collected in the Boughrara lagoon watershed. These results will contribute to the establishment of a sediment quality baseline and to the management of the local environment.

Material and methods

Study area

The Boughrara Lagoon is located in the southeastern part of Tunisia (Fig. 1), in the Gulf of Gabes. It covers a total surface area of 500 km 2 between the coordinates 33°28'-33°45'N and 10°40'-10°57'E. The lagoon has been remained geologically stable since the last 125 ka BP [START_REF] Rached | Sedimentary record from Holocene to present-day Southeastern Tunisia: facies, paleoenvironments and climate changes[END_REF]. The average depth is about 4 m, with a maximum of 16 m in the lagoon center. Water communication between the Mediterranean Sea and the lagoon is mainly assured through the Ajim channel (2.5 km wide) in the northern side, since the passage on the eastern side (6 km wide) is closed by an old Roman road. Both the shape and the bathymetry of the lagoon reduce water circulation causing high rates of salinity (Kharroubi, 2012). The Boughrara lagoon is an outlet from the Fjé, Smar and Bou Hamed streams, whose watershed area is estimated to be of 2394 km 2 (Fig. 1). Annual input water into the lagoon is about 11 Mm 3 per year, mainly from these main streams [START_REF] Brahim | La dynamique sédimentaire au voisinage du port de pêche de Zarzis[END_REF].

Sampling procedure

Surface sediments were sampled at 25 sites (Fig. 1) in December 2018 and January 2019 in the middle and the south of the western Boughrara Lagoon, near the three main streams (Fjé, Smar and Bouhamed; Fig. 1).

Sampling sites were chosen because of their geographical locations near the streams, also near the water current flowing from the north and circulating to the south, which carries effluents from industrial and chemical factories. Two additional rock samples were collected in December 2020 in the upper watershed over which the main streams flow: a first sample was collected from the ex-lead mine of Tebaga Mountain and another from the red clay quarry located in the Tejra Esghira Mountain (Fig. 234) in order to characterize the main sources of sediment input in the southwestern part of Boughrara Lagoon and to assess the origin of the marine pollution by metals.

At each station, the exact location was recorded with a GPS and the top 5 cm of sediments were collected using a gravitational core sampler (Van Veen grab). We carefully rinsed the outside of the sampler with water from the sampling station, in order to remove material that could contaminate the sample during transfer.

Samples were transported directly to the laboratory, and they were oven dried at a temperature <60°C to prevent the destruction of the organic matter. Rocks were crushed using an automatic mortar grinder.

Grain size analyses

In order to determine the size distribution of materials, dried samples were passed in dry and wet sieving (using a standard column of AFNOR sieves) to separate the fine (<63 µm) and coarse (>63 µm) sediment fractions. We used a decreasing series of sieve meshes as follows : 2000, 1600, 1250, 1000, 800, 630, 500, 400, 315, 250, 200, 160, 125, 100, 80 and 63 µm. Grain size results are given as a percentage of the refusal mass relative to the total mass of the sample, for each diameter. For each sample, the cumulative curve of the fine and coarse fractions of surficial sediments is presented in a semi-logarithmic plot using the particle diameter and the cumulative percentages of the refusal [START_REF] Folk | Brazos River bar (Texas): a study in the significance of grain size parameters[END_REF]. GRADISAT software version 4.0 was used for grain-size statistical calculations.

Mineralogy

Mineralogical characterization (type and quantification of mineral phases) of the fine fraction was conducted for each sample using X-ray diffractometry. X-ray analyses were performed with a diffractometer (PANALYTICAL X'PERT PRO) using a copper anticathode. The resulting spectra were processed using High Score plus. Many corrections were recommended, followed by smoothing. Peak identification was based on the software database and on the diffraction angle (dƟ) of each mineralogical phase [START_REF] Lutterotti | Quantitative phase analysis[END_REF].

Scanning electron microscopy

Images were taken in the fine fraction using a focused ion beam-scanning electron microscope (SEM) of type FEG-FIB-SEM AURIGA 40 ZEISS. Samples were dehydrated prior to all SEM analyses. Before placing the samples under the microscope, the powder was metallized with gold. This instrument allowed reconstructing the sample topography and provided a sub-nanometer scale resolution fitted with Zeiss Gemini column.

Total particulate carbon and nitrogen

A CHN elemental analyzer (Flash 2000 Organic Elemental Analyzer, Thermo scientific) was used to determine the concentrations of total particulate carbon (TPC) and total particulate nitrogen (TPN) in the surficial sediments [START_REF] Eksperiandova | Estimation of metrological characteristics of the element analyzer EuroVector EA-3000 and its potential in the single-reactor CHNS mode[END_REF]. The samples were dried and well homogenized to ensure the homogeneity of the material analyzed. Samples were weighed (about 4 mg) in tin containers and introduced into the combustion reactor. After the combustion, the analyte gases are carried in a helium flow to a layer containing copper, and finally carbon and nitrogen are detected by a Thermal Conductivity Detector (TCD) [START_REF] Eksperiandova | Estimation of metrological characteristics of the element analyzer EuroVector EA-3000 and its potential in the single-reactor CHNS mode[END_REF]. The analyzer was calibrated using a certified standard (BBOT) (about 1-3 mg). The results were calculated as percentages of particulate carbon relative to the total mass of the analyzed sample.

Determination of metal concentrations in the sediments

About 0.2 g of dried sediment was mixed with 1 ml of hydrofluoric acid in Teflon bombs and left enclosed in ultrasonic bath for 30 min. Then, 1 ml of quartz distilled nitric acid (6 N) was added. The mixture was heated for 12-24 hours at a temperature of 100-130°C (closed Teflon beaker). Next, it was heated at a temperature of 180-200°C to evaporate the acid (opened Teflon beaker). The residue obtained was mixed with 3 ml of quartz distilled hydrochloric acid (6 N) and the mixture was heated for 12-24 hours (closed Teflon beaker). Then, the Teflon plug was opened and the mixture was heated at a temperature of 180-200°C until evaporation of the acid.

The HCl heating and evaporation step were repeated until a clear solution was obtained. For each digestion program, a blank was prepared with an equal amount of acids. Finally, we added 3 ml of HNO3 (40%) to the dried residue. The solution was consequently diluted in MilliQ water to a final volume of 60 ml. A 0.5 ml aliquot of the diluted sample was collected, and diluted to 12.5 ml with HNO3 (2%) [START_REF] Berthod | Mantle xenolith-bearing phonolites and basanites feed the active volcanic ridge of Mayotte (Comoros archipelago, SW Indian Ocean)[END_REF]. Elemental concentrations were assessed using an Agilent 7900 quadruple ICP-MS. Elements with masses between that of sodium ( 23) and arsenic (75), as well as silver (107), cadmium (111) and gadolinium ( 157), were all measured by using a collision-reaction cell with helium gas (5 mL/min) to eliminate polyatomic interferences. The remaining elements were measured without collision gas. Scandium, indium and rhenium internal-standards were added after inline mixing with the samples to correct for signal drift and matrix effects. Two sets of multielement calibration standards (one for major and one for trace elements) were analyzed to confirm and model (through simple linear regression) the linear relationship between signal and concentration. The model was then used to convert measured sample counts to concentrations. Reported uncertainties were calculated using error propagation and considering the combination of standard deviation on replicated consecutive signal acquisitions (n=3), internal-standard ratio and blank subtraction. The non-linear term (internal-standard ratio) was linearized using a first-order Taylor series expansion to simplify error propagation [START_REF] Jochum | Reference values following ISO guidelines for frequently requested rock reference materials[END_REF]. Elemental concentrations are expressed in ppm of dry weight. Detection limits for Cu, Zn, Co, Cd, Pb, Mn, Fe, Al, P, Ca and Ti were, respectively, 0.030, 0.258, 0.020, 0.039, 0.007, 0.018, 0.037, 0.146, 2.040, 0.67 and 0.28 ppb. Cr concentrations were less than the detection limit. To verify the analytical accuracy of the metals, we used the standard reference materials BHVO-1 [START_REF] Gladney | Compilation of Elemental Concentration Data for USGS BHVO-1, MAG-1, QLO-1, RGM-1, SCo-1, SDC-1, SGR-1 and STM-1[END_REF]. Results showed good agreement between the certified and the measured values for all analyzed metals. Recovery percentages for metal contents in sediment were 101,107,96,76,73,78,72,53,145,107, and 56 % for respectively Fe, Al, Mn, P, Co, Cu, Zn, Cd, Pb, Ca and Ti.

Assessment of sediment quality

The contamination factor (CF) was calculated to assess the degree of pollution in the Boughrara lagoon. CF is used to describe the contamination of a toxic substance in the environment [START_REF] Hakanson | An ecological risk index for aquatic pollution control. A sedimentological approach[END_REF], and it was calculated as follows:

𝐶𝐹 !"#$% = 𝐶 !"#$% 𝐶 &$'()*+,-.
Where Cmetal is the metal concentration measured in the sediment sample and CBackground is the background value of this metal. Since no background values in the soils of the Boughrara lagoon were available, the concentrations in the Upper Continental Crust (UCC) reported by [START_REF] Wedepohl | The composition of the continental crust[END_REF] were used as the background crustal values.

The following criteria were used to describe the level of the contamination: if CFmetal < 1, then the contamination is considered low; it is moderate if 1 < CFmetal < 3; considerable if 3 < CFmetal < 6; and very high if CFmetal > 6 [START_REF] Hakanson | An ecological risk index for aquatic pollution control. A sedimentological approach[END_REF].

Statistical analysis

In order to explore the spatial distribution of metals in the sediments of the Boughrara lagoon and to visualize potential metal sources, all contents were mapped in the GIS-based software ArcGIS 10.2 from Esri (the Environmental Systems Research Institute Inc). A multivariate statistical method was also used to identify samples with similar elemental composition, and to interpret the contamination pattern and distribution of all parameters. For this purpose, the compositional data analysis (CoDA) was applied with the chemical element concentrations analyzed in the surficial sediments (Cu, Zn, Co, Cd, Pb, Mn, Fe, Al and P) by using RStudio software. Indeed, CoDA is a statistical method useful for simultaneous analysis of several elemental ratios by reducing a large number of variables to a few unrelated components [START_REF] Aitchison | The statistical analysis of compositional data[END_REF][START_REF] Xu-Yang | Compositional data analysis (CoDA) as a tool to evaluate a new low-cost settling-based PM 10 sampling head in a desert dust source region[END_REF].

Results

Mineralogy and grain size distribution

Near the 3 streams, the sediment coarse fraction (> 63 µm) mainly constituted of sand represented more than 90% of the total mass of the sample with, respectively, 94.4%, 89.9%, 92.2%, 95.7%, 93.1% and 95.3% at stations P7, B6, B7, B8, B9 and B10 (Table 1). For these samples, the curves of the sediment size distribution were skewed (S-shaped), indicating homogeneity of the very coarse sand (Fig. 4). By contrast, the sediment fine fraction (< 63 µm) was much more significant in the water inflows from the Ajim channel, as it represented 39 to 69% of the total sample mass (Table 1) at stations C3, C4, C5, C6, C8, C9, C10 and C11 with, respectively, 39.3%, 65.9%, 69.2%, 50.6%, 45.7%, 52.3%, 40.97% and 51.9%. The semi-logarithmic curves of the sediment size distribution presented a parabolic shape in this area (Fig. 4), indicating heterogeneity of the fine fraction, in which remains of shells were found to be dominant.

The X-ray diffraction analyses of the surficial sediments highlighted the presence of many minerals like quartz, calcite, aragonite and some types of clay (Fig. 5). Samples located near the Fjé and Smar streams (stations P1, P3, P7 and B6-B10) presented a simple mineralogical composition, with dominance of quartz XRD-peaks (SiO2; ICSD: PAN 98-015-4289). Near the Bou Hamed stream (stations B2-B3), the most important peak was for evaporates (gypsum and halite), whereas illite-smectite was less abundant. Near the Ajim channel (stations C6-C11) the main peaks were for calcium carbonate (CaCO3; ICSD: PAN 98-004-0107), with significant peaks in particular for calcite, magnesium-calcite and dolomite. Mica and illite-smectite were also present in this area.

In order to confirm the mineralogical analyses, sediment powders have been also observed using scanning electron microscopy. Three types of clay have been observed, which were illite-smectite, chlorite and mica (stations P1, C1 and C3) (Fig. 6a-b). Furthermore, a rhombohedral shape for quartz was identified in the samples near the three streams. Coccoliths, and diatoms and their silica-frustules were identified in the southwestern part of the lagoon (Fig. 6c-d). Pyrite mineral (FeS2) in euhedral form was also identified (stations P1, P3, C1 and C3).

Spatial distribution of metals and phosphorus in surficial sediments

The concentrations of Cu, Zn, Co, Cd, Pb, Mn, Fe, Al, Ca, Ti and P in surficial sediments of the Boughrara Lagoon are reported in Table 3. Ti and Ca were used to identify the main origin of sediment in the studied lagoon. The spatial distribution of measured elements showed highest concentrations in the southwestern part of the lagoon (Fig. 7). The ranges of concentrations varied significantly between the different elements, decreasing in the order of Fe > Al > Mn > P > Zn > Cu > Pb > Co > Cd, with mean concentrations of, respectively, 1.63%, 1.2%, 414 ppm, 377 ppm, 86.6 ppm, 40.9 ppm, 34.7 ppm, 4.7 ppm and 0.5 ppm. The highest concentrations were observed near the three main streams (Fjé, Smar and Bou Hamed) with 4.9% for Fe, 2.4% for Al, 1469 ppm for Mn, 826 ppm for P, 244.8 ppm for Zn, 173.3 ppm for Pb, 134.3 ppm for Cu, 12.9 ppm for Co, and 2.2 ppm for Cd.

Zinc and Cu presented similar features, with high values at stations B3 and B9 of respectively, 131 ppm and 134 ppm for Cu, 245 ppm and 244 ppm for Zn (Fig. 7). Cobalt and Cd also showed a similar spatial distribution, with the highest concentrations at stations B8-B9 with 12.90 ppm for Co and 2.24 ppm for Cd (Fig. 7). Concerning Pb concentrations, its highest concentration of 173 ppm was observed near the Bou Hamed stream at station B3 (Fig. 7). The spatial distribution of Mn was similar to that of Fe, with high values near the Fjé and Smar streams (Fig. 7). The maximum concentrations of Mn and Fe were recorded at station B8 with, respectively, 1469 ppm and 4.9%. Aluminum and phosphorus concentrations also showed a similar distribution (Fig. 7) with high values observed near the Bou Hamed stream at station B3, with 3.2% for Al and 826 ppm for P. The concentrations of Cd were much lower than those of the other metals values, ranging from 0.1 to 2.2 ppm, with a maximum at station B8. The enrichment in metals (Pb, Fe, Mn, Zn, Cu and Al) detected with the measurement of high concentrations was further confirmed by the calculations of their relatively high contamination factor (CF) (Table 4).

Samples collected from the red clay quarry (S1) and the lead-zinc deposits (S2) were highly enriched in metals (Table 3). The red clay quarry (S1) was particularly enriched in Fe, Al, Mn, P, Cd, and Pb with concentrations of, respectively, 6.6%, 7.1 %, 351.4 ppm, 13063.98 ppm (Table 3). In the lead-zinc deposits (S2), Pb, Zn, Cd and Fe displayed the highest concentrations of, respectively, 307587.7 ppm, 77558.9 ppm, 682.1 ppm and 2.9% for Fe (Table 3).

Total particulate carbon and nitrogen in surficial sediments

The relative abundance of total particulate carbon (TPC) in the surficial sediments was relatively low, ranging from 1% to 13%, with an average value of 7%. The minimum and maximum TPC relative abundance were observed at stations C1 and B6, respectively (Table 2). The relative abundance of total particulate nitrogen (TPN) was even lower compared to TPC, with maximum and minimum values of, respectively, 0.8% at station C1 and 0.1% at station B7.

Compositional data analysis (CoDA)

Based on the compositional data analysis (CoDA) tool, the projection of 9 variables of chemical elements (8 metals and phosphorus) and 17 individuals of surficial sediments was plotted in Figure 9. Percentages of variability explained by the first two components were 65% for comp.1 and 21% for comp.2, a total of 86%. This biplot highlighted the presence of three different groups to classify the surficial sediments in the lagoon.

The first group (A) contains samples near the Bou Hamed stream (B2, B3, P1 and P3), which were enriched in Pb and Cu. The second group (B) contained samples near the Fjé and Smar streams that were enriched in Fe, Mn and Co. Finally, the third group (C) included the samples located in the water inflows from the Ajim channel (C1, C2, C8, C9, C10, and C11) and were enriched in P and Al.

Furthermore, the biplot achieved with a selection of 4 metals as variables (Cd, Zn, Pb, and Cu) that combined our results and those recorded in the Gulf of Gabes (El Zrelli, 2015), suggested similar enrichment, mainly in Cu and Pb, in the southwestern of the lagoon and near the Gabes port (Fig. 10). In this compositional biplot, the first two axes explained 91% of the total variance, with 80% for comp.1 and 11% for comp.2.

Discussion

Main sediment input

Samples located near the water inflows from the Ajim channel were dominated by the fine fraction (<63 µm) which is enriched with carbon. This enrichment observed at stations C1-C11 can indicate a high biological production [START_REF] Luczak | Simple standard procedure for the routine determination of organic matter in marine sediment[END_REF][START_REF] Aleksandrov | Biological production and eutrophication of Baltic Sea estuarine ecosystems: the Curonian and Vistula Lagoons[END_REF]. Furthermore, the elemental ratios of Fe/Ca and Ti/Ca were relatively low in this area (Fig. 8) due to comparatively high concentrations of calcium (Table 3). Such high levels of calcium are generally associated with carbonate fraction that specifies the biogenic autochthonous source [START_REF] Plewa | Geochemical distribution patterns as indicators for productivity and terrigenous input off NW Africa[END_REF][START_REF] Affouri | Extreme flood event reconstruction spanning the last century in the El Bibane Lagoon (southeastern Tunisia): a multi-proxy approach[END_REF]. The TPC/TPN ratios ranged between 10 and 44, with a mean of 23 (Table 2). The highest values were found at stations C2 and C11 influenced by the water inflows from the Mediterranean Sea. Here, the relative enrichment in TPC correlated with high percentages of mud in the fine fraction (Tables 12) which can point out a marine origin of the particulate matter. A relatively high abundance of mud rich in gastropods and mollusks was also recently recorded in the center of the lagoon and near the Ajim channel [START_REF] Keskes | Dinoflagella tesencystment with emphasis on blooms in Boughrara lagoon (South-Western Mediterranean): Combined effects of trace metal concentration and environmental context[END_REF].

Near the three streams, the granulometric analyses showed the predominance of the coarse fraction and a relatively high abundance of quartz as detected with SiO2 XRD-peaks, all suggesting continental inputs (aeolian and fluvial) to surficial sediments in these areas. High values of Fe/Ca and Ti/Ca ratios were also observed in the southwestern side of the Boughrara lagoon (Fig. 8) due to relatively low Ca concentrations (Table 3), confirming an allochthonous lithogenic source. For all samples near the three main streams, the TPC/TPN ratios were low (stations P1-B6) which confirms the terrestrial origin of sediment input.

Contamination and ecological risk assessment of chemical elements

Background on chemical contamination

Surficial sediments of the southwestern part of the Boughrara lagoon were characterized by high concentrations of metals, especially by Pb, Fe, Mn, Cu and Zn. Phosphorus concentrations were also very high, ranging between 77 ppm and 888 ppm, similar to what was observed by [START_REF] Keskes | Dinoflagella tesencystment with emphasis on blooms in Boughrara lagoon (South-Western Mediterranean): Combined effects of trace metal concentration and environmental context[END_REF] in the Boughrara lagoon (Table 5).

Cupper concentrations recorded in the surficial sediments of the Boughrara lagoon (7.64-134.26 ppm) were also similar to those reported by Keskes et al. (2020) of 3.8-161.2 ppm. Cadmium, Cu and Zn concentrations recorded in this study were in a similar range than those reported by Kharroubi et al. (2012) in the Boughrara lagoon with values of, respectively, 0.11-2.23 ppm, 8-134 ppm and 29-245 ppm in this study and 0-3.1 ppm, 14-56 ppm and 39-119 ppm in Kharroubi et al. (2012) (Table 5). The concentrations of Fe and Mn in the sediments were much higher in the southwestern sediments (this study) compared to those located in the North of the lagoon (Kharroubi et al., 2012) with values of, respectively, 4881-48802 ppm and 68-1469 ppm in this study and 8320-9580 ppm and 59-99 ppm in Kharroubi et al. (2012) (Table 5). High Fe concentrations were also previously recorded in the western part of the Boughrara lagoon [START_REF] Keskes | Dinoflagella tesencystment with emphasis on blooms in Boughrara lagoon (South-Western Mediterranean): Combined effects of trace metal concentration and environmental context[END_REF], but these concentrations were lower than the maximum values obtained in our study (Table 5).

Compared to other coastal lagoons threatened by anthropogenic pressure such as the Bizerte Lagoon in Tunisia [START_REF] El Zrelli | Surface sediment enrichment with trace metals in a heavily human-impacted lagoon (Bizerte Lagoon, Southern Mediterranean Sea): Spatial distribution, ecological risk assessment, and implications for environmental protection[END_REF]Ben Mna et al., 2017), the Ghar El Melh Lagoon in Tunisia [START_REF] Oueslati | Cycles biogéochimiques des métaux lourds dans les sédiments marins de la lagune de Ghar El Melh[END_REF]) and the Manzala Lagoon in Egypt (Abu [START_REF] Khatita | Distribution and ecological risk assessment of heavy metals in the sediment cores from Manzala lagoon, Egypt[END_REF], the concentrations of Fe in the sediments were higher in this study, except for values obtained in the Ghar El Melh Lagoon [START_REF] Oueslati | Cycles biogéochimiques des métaux lourds dans les sédiments marins de la lagune de Ghar El Melh[END_REF]) (Table 5).

Distribution, origin and degree of contamination by chemical elements

The contamination factor (CF) values for Pb ranged between 3 and 6 near Bou Hamed (stations P3 and B9; Table 4), indicating a considerable level of contamination. The CF value of Pb was 10.2 at station B3 near Bou Hamed stream (Table 4), indicating a very high contamination by Pb. For Cu, the CF values were higher than 6 at stations P3, B3, B8 and B9, indicating a very high level of contamination. Copper and Zn had a similar spatial distribution showing highest values in the sediments near the the Bou Hamed and Smar streams (Fig. 7). Like Cu, the enrichment by Zn was confirmed with CF values ranging between 3 and 6 at stations P3, B3 B8 and B9 indicating a considerable degree of contamination.

The CF values calculated for Fe ranged between 1 and 3 at stations B3, B6 and B7 with values of, respectively, 1.1, 1.3 and 1.6, indicating a moderate degree of contamination. Here, Fe concentrations were slightly higher than concentrations in the Upper Continental Crust (UCC) [START_REF] Wedepohl | The composition of the continental crust[END_REF], and they were much higher than those reported in the same lagoon by [START_REF] Keskes | Dinoflagella tesencystment with emphasis on blooms in Boughrara lagoon (South-Western Mediterranean): Combined effects of trace metal concentration and environmental context[END_REF] and Kharroubi et al. (2012). Results similar to those of Fe were obtained for Mn, with CF values ranging between 1 and 3 with values of 1.9, 1.8, 2.8, 2 and 1.5 at stations P7, B6, B8, B9 and B10, respectively. Near the Fjè and Smar streams, the CF values of Cd were higher than 6 at stations P1, P3, B3, B8, B9, C1, C6 and C10 indicating a very high level of contamination by Cd in these areas.

The CF values for P were generally lower than 1 (Table 4) indicating that this area is not contaminated by P, but phosphorous concentrations were higher than those obtained in Kharroubi et al. (2012).

Compared to other coastal regions in Tunisia, the Boughrara lagoon has already been reported to have a high level of contamination by metals like Pb, Fe, Mn, Al, Cu, Cd and Cr [START_REF] Gargouri | Heavy metal concentrations in the surface marine sediments of Sfax Coast, Tunisia[END_REF]Kharroubi et al., 2012;Elzrelli et al. 2017;[START_REF] Keskes | Dinoflagella tesencystment with emphasis on blooms in Boughrara lagoon (South-Western Mediterranean): Combined effects of trace metal concentration and environmental context[END_REF]Elzrelli et al., 2021), and our study confirmed these contaminations. In view of these results and by comparing with the previous studies, three possible sources of pollutants can be identified. The first potential source is phosphogypsum discharges, pumped from the chemical industry of Gabes, which are very enriched in P, Cu, Cd and Co. This source of pollution was also proposed by Kharroubi et al. (2012) by comparing metal concentrations analyzed in surficial sediments with those obtained in phosphogypsum effluents. The second anthropogenic source concerned Pb and Zn, and it was probably due to the transportation of Pb from the Pb ex-mine by Fjé, Smar and Bouhamed streams to the Boughrara Lagoon. The third source which caused Fe enrichment can be related to both natural (cliff weathering) and anthropogenic (stream inputs from Tejra red clay quarry) precursors.

Environmental consequences of metal contamination

As a part of the Gulf of Gabes, the Boughrara lagoon has become one of the most polluted ecosystems in this region. Previous studies have already suggested that the Gulf of Gabes is highly contaminated by organic and inorganic pollutants [START_REF] Darmoul | Pollution dans le golfe de Gabès (Tunisie): bilan de six années de surveillance[END_REF][START_REF] Rabaoui | Assessment of metals pollution in the gulf of Gabes (Tunisia) using four mollusk species[END_REF][START_REF] El Zrelli | Heavy metal contamination and ecological risk assessment in the surface sediments of the coastal area surrounding the industrial complex of Gabes city, Gulf of Gabes, SE Tunisia[END_REF][START_REF] El Zrelli | Biomonitoring of coastal pollution in the Gulf of Gabes (SE, Tunisia): use of Posidonia oceanic seagrass as a bio-indicator and its mat as an archive of coastal metallic contamination[END_REF], leading to a significant degradation of the environment.

The accumulation of metals by various marine species and its biomagnification in the food chains cause many serious human threats [START_REF] Annabi-Trabelsi | Concentrations of trace metals in phytoplankton and zooplankton in the Gulf of Gabès, Tunisia[END_REF]. Many authors attributed these threats to either the high metallic marine pollution or radio-chemical wastes like phosphogypsum (Dethlefsen, 1989;[START_REF] Ayadi | Assessment of contaminated sediment by phosphate fertilizer industrial waste using pollution indices and statistical techniques in the Gulf of Gabes (Tunisia)[END_REF][START_REF] El Zrelli | Biomonitoring of coastal pollution in the Gulf of Gabes (SE, Tunisia): use of Posidonia oceanic seagrass as a bio-indicator and its mat as an archive of coastal metallic contamination[END_REF].

Since metals can be bioaccumulated in the tissues of marine biota, some marine species can even serve as bioindicators of metal pollution in coastal environments [START_REF] Rainbow | Trophic transfer of trace metals from the polychaete worm Nereisdiversicolor to the polychaete N. virens and the decapod crustacean Palaemonetesvarians[END_REF][START_REF] Zhou | Enhanced H2 adsorption in isostructural metal-organic frameworks with open metal sites: strong dependence of the binding strength on metal ions[END_REF]. For instance, various species of mollusks (like Pinna nobilis and P. radiate) and gastropods (like G. ardens and P. cearulea) of the Gulf of Gabes, especially of the Boughrara lagoon, have shown to be highly contaminated by metals (Cd, Zn, Cu, Al, Pb,…) [START_REF] Rabaoui | Metal bioaccumulation in two edible cephalopods in the Gulf of Gabes, South-Eastern Tunisia: environmental and human health risk assessment[END_REF], El Zrelli et al., 2017).

Eutrophication phenomenon in the Boughrara Lagoon

We detected the presence of pyrite (FeS2) for the first time in the sediments of the Boughrara Lagoon. Pyrite precipitation (pyritization) is a result of sulfate and Fe (oxy-)hydroxides reduction in anoxic conditions [START_REF] Sabadini-Santos | Organic matter and pyritization relationship in recent sediments from a tropical and eutrophic bay[END_REF]. For instance, the hydrogen sulfide (H2S) generated during early diagenesis in anoxic sediments can precipitate as authigenic sulfide minerals, like pyrite [START_REF] Morse | Analysis and distribution of iron sulfide minerals in recent anoxic marine sediments[END_REF]. The high inputs of sulfate-rich phosphogypsum and Fe-rich red clays into the lagoon likely favored the formation of pyrite. Anyway, the presence of pyrite that we detected in these sediments when it had not been reported in previous studies indicated a preservation of pyrite which can only be explained by an increase of anoxic conditions in the lagoon. The occurrence of red tides and algae bloom reported in the southwestern part of the Boughrara lagoon indeed indicated eutrophication of the lagoon that can lead to the development of hypoxicanoxic conditions (Fig. 11). Increasing anthropogenic pressures combined with the extremely low renewing of the waters in the lagoon (0.4% of renewing daily) that leads to the inevitable stagnation of the waters and the stronger stratification of the water-column [START_REF] Ali | Investigation on possible chemical pollution of the Boughrara lagoon, south of Tunisia, by chemical wastes[END_REF][START_REF] Ben Aoun | Investigation on possible chemical pollution of the Boughrara lagoon, south of Tunisia, by chemical wastes[END_REF]Kharroubi et., al 2012[START_REF] Brahim | La dynamique sédimentaire au voisinage du port de pêche de Zarzis[END_REF], Atoui et., al 2017and 2020, Ciglenečki et al., 2020[START_REF] Pagano | Planktonic responses to hydrodynamic forcing in coastal ecosystems in the context of climatic and anthropogenic change[END_REF] were likely the causes of the eutrophication of the lagoon and the development of anoxic conditions. Eutrophication phenomenon can lead to many environmental threats in the lagoon like the proliferation of macro-algae and the development of tolerant species. This would have a drastic impact on the social-economic development of the village of Boughrara.

Conclusion

Coastal marine systems are subject to increasing anthropogenic pressures and various chemical pollutions that can threaten aquatic ecosystems and human health. It is therefore becoming urgent to develop pollution monitoring tools in order to preserve resources and biodiversity in these environments. The lagoon of Boughrara constitutes a privileged study site for developing these pollution indicators since it constitutes a semi-closed basin in which the phosphogypsum discharges from a chemical industry and the metal inputs from an ex-Pb mine and a red clay quarry can accumulate.

Our study showed that the central-western part of the lagoon was influenced by the advection of the Mediterranean waters through the Ajim channel and, there, the sediments were enriched in P, Cd, Cu and Co, due to the accumulation of phosphogypsum released by the chemical industry in the Gulf of Gabes. However, the contamination by Cd and Cu was estimated to be low in this area, on the contrary to the radiochemical phosphogypsum that can have a profound deleterious impact on the environment and health.

In the south-western part of the lagoon, continental inputs carried by three main streams were prevalent and the surficial sediments were highly enriched in Pb, Zn and Cu in the southern part of the lagoon and in Fe, Mn and Co in the southwestern part, due to the inputs from the ex-Pb mine and the red clay quarry, and to the cliff weathering. In these areas, the degree of contamination by Pb, Cd, Zn and Cu was found to be very high to considerable, which can have serious toxic effects. Furthermore, pyrite deposits were detected in the surficial sediments of the lagoon, likely resulting from the high inputs of sulfate-rich phosphogypsum and Fe-rich red clays, combined with the eutrophication and increasing anoxia of the lagoon. Systematic monitoring of metal and mineral levels in the sediments of marine coastal systems will therefore make it possible to better assess the level of metal contamination and the degree of anoxia of these systems sensitive to anthropogenic pressures. It is a prerequisite for preserving the water-resource quality and the marine biodiversity.

Author Contribution

Nejia TLIG contributed to data interpretation and wrote the major manuscript. Marie BOYE contributed to writing and revising the manuscript. Tahani HALLEK contributed to sampling and data collection. Pierre BURCKEL contributed to analyses. Maher GZAM contributed to sampling. Mohamed Ali TAGORTI revised the manuscript. All authors reviewed and approved the final version to be published. Table 1. Grain size distribution in the sediment samples in the Boughrara Lagoon (% of coarse and fine fractions)

Figure captions

Stations

Fig. 1

 1 Fig.1 Localisation of Boughrara Lagoon and GIS Slope Map (in degrees) of the southeastern of Tunisia classified into four classes (top right panel), location of surficial sediments stations in the southwestern Boughrara Lagoon and location of samples collected from Tejra quarry (S1) and from the ex-lead mine (S2) (low right panel) Fig.2 Ex-lead deposit and location of the sample site (red star and rectangle) in Tebaga Mountain (south of Tunisia) highlighting the predominance of Pb and Zn minerals.Fig.3 Red clay collected from Tejra Esghira quarry (south of Tunisia; yellow rectangle) Fig.4 Cumulative semi-logarithmic curves of sediment size distribution in the Boughrara Lagoon Fig.5 X-Ray diffractograms of the surficial sediments in the Boughrara Lagoon, at stations P7 (upper panel), C3 (middle panel) and B3 (lowest panel). QZ= quartz, Ca= calcite, I= illite, M= mica, Pyr= pyrite, Dol= dolomite, Ca-Mg= magnesium-calcite Fig.6 SEM images of sediment samples in the Boughrara Lagoon with (a) clay minerals, (b) quartz, (c) coccolithes, (d) diatoms, (e) and (f) pyrite mineral Fig.7 Distributions of the concentrations of the chemical elements (Cu, Zn, Co, Cd, Mn, Fe, Al, Pb and P) in the surficial sediments of the Boughrara Lagoon (concentrations in ppm) Fig.8 Cross-plot of Fe/Ca versus Ti/Ca ratios (ratios in ppm/ppm) in the surficial sediments in the Boughrara Lagoon (Plewa et al., 2012, Affouri et al., 2017) Fig.9 Compositional data analysis (CoDA) biplot of surficial sediments in the Boughrara Lagoon for 9 chemical variables (8 metals and phosphorus) with comp.1 = 65% and comp.2 = 21%. Area A regroups samples near Bou Hamed stream, Area B contains the samples near Fjé stream and Area C the samples located in the water inflows from the Ajim channel Fig.10 Compositional data analysis (CoDA) biplot of the surficial sediments analyzed in the present study (in blue) and in the Gulf of Gabes (in red) by El Zrelli (2015) for 4 variables of metals (Cd, Zn, Pb, Cu) with comp.1 = 80% and comp.2 = 11 % Fig.11 A graphic illustration of the water column stratification showing environmental risks in Boughrara Lagoon: a, b and d: biota mortalities; C: algae bloom, e: diatoms, f: coccolith, g and h: pyrite mineral

Fig. 3

 3 Fig.1 Localisation of Boughrara Lagoon and GIS Slope Map (in degrees) of the southeastern of Tunisia classified into four classes (top right panel), location of surficial sediments stations in the southwestern Boughrara Lagoon and location of samples collected from Tejra quarry (S1) and from the ex-lead mine (S2) (low right panel) Fig.2 Ex-lead deposit and location of the sample site (red star and rectangle) in Tebaga Mountain (south of Tunisia) highlighting the predominance of Pb and Zn minerals.Fig.3 Red clay collected from Tejra Esghira quarry (south of Tunisia; yellow rectangle) Fig.4 Cumulative semi-logarithmic curves of sediment size distribution in the Boughrara Lagoon Fig.5 X-Ray diffractograms of the surficial sediments in the Boughrara Lagoon, at stations P7 (upper panel), C3 (middle panel) and B3 (lowest panel). QZ= quartz, Ca= calcite, I= illite, M= mica, Pyr= pyrite, Dol= dolomite, Ca-Mg= magnesium-calcite Fig.6 SEM images of sediment samples in the Boughrara Lagoon with (a) clay minerals, (b) quartz, (c) coccolithes, (d) diatoms, (e) and (f) pyrite mineral Fig.7 Distributions of the concentrations of the chemical elements (Cu, Zn, Co, Cd, Mn, Fe, Al, Pb and P) in the surficial sediments of the Boughrara Lagoon (concentrations in ppm) Fig.8 Cross-plot of Fe/Ca versus Ti/Ca ratios (ratios in ppm/ppm) in the surficial sediments in the Boughrara Lagoon (Plewa et al., 2012, Affouri et al., 2017) Fig.9 Compositional data analysis (CoDA) biplot of surficial sediments in the Boughrara Lagoon for 9 chemical variables (8 metals and phosphorus) with comp.1 = 65% and comp.2 = 21%. Area A regroups samples near Bou Hamed stream, Area B contains the samples near Fjé stream and Area C the samples located in the water inflows from the Ajim channel Fig.10 Compositional data analysis (CoDA) biplot of the surficial sediments analyzed in the present study (in blue) and in the Gulf of Gabes (in red) by El Zrelli (2015) for 4 variables of metals (Cd, Zn, Pb, Cu) with comp.1 = 80% and comp.2 = 11 % Fig.11 A graphic illustration of the water column stratification showing environmental risks in Boughrara Lagoon: a, b and d: biota mortalities; C: algae bloom, e: diatoms, f: coccolith, g and h: pyrite mineral

  Figure 1

  Figure 11

Table 2 .

 2 Percentages of total particulate carbon (C) and nitrogen (N) relative of the mass of the analyzed samples (in %) and particulate C:N ratios in the surficial sediments of the Boughrara lagoon

		%fine fraction (Ø<63 µm) %coarse fraction (63 µm<Ø<2 mm)
	P1	23.5	76.5
	P3	22.30	77.7
	P7	5.60	94.4
	B2	31.14	68.86
	B3	29.20	70.8
	B6	10.1	89.9
	B7	7.80	92.2
	B8	4.3	95.7
	B9	6.90	93.1
	B10	4.70	95.3
	C1	31.52	68.48
	C2	29.60	70.4
	C3	39.26	60.74
	C4	65.90	34
	C5	69.20	30.6
	C6	50.6	40.4
	C8	45.70	55.3
	C9	52.3	47.7
	C10	40.97	59.03
	C11	51.9	48.1

Table 4 .

 4 Contamination factor values calculated for metals and phosphorus in the surficial sediments of the Boughrara Lagoon and reported in the upper continental crust (UCC) by[START_REF] Wedepohl | The composition of the continental crust[END_REF]

	Stations	Fe	Mn	Al	P	Zn	Cu	Co	Cd	Pb
	P1	0.2	0.3	0.13	0.5	0.9	1.7	0.2	8.3	1.8
	P3	0.4	0.5	0.19	0.9	4.1	8.0	0.3	23.8	4.9
	P7	0.2	1.9	0.14	0.7	1.7	2.2	0.8	2.9	1.9
	B2	0.2	0.2	0.11	0.4	0.8	1.3	0.2	7.3	1.5
	B3	1.1	0.3	0.17	1.2	4.7	9.2	0.4	20.4	10.2
	B6	1.3	1.8	0.25	0.5	1.4	1.7	0.8	2.2	1.3
	B7	1.6	0.7	0.30	0.3	0.8	0.9	0.4	2.2	0.8
	B8	0.7	2.8	0.10	0.8	4.7	9.4	1.1	8.4	2.5
	B9	0.2	2.0	0.13	0.9	2.9	6.0	0.9	6.9	4.3
	B10	0.6	1.5	0.41	0.4	1.2	1.3	0.6	2.1	0.9
	C1	1.0	0.1	0.13	0.5	0.9	1.9	0.2	11.2	0.6
	C2	0.5	0.3	0.13	0.5	0.7	0.9	0.2	4.8	0.4
	C6	0.2	0.2	0.12	0.4	0.7	1.4	0.2	8.6	2.1
	C8	0.2	0.3	0.11	0.3	0.8	0.7	0.2	3.9	0.5
	C9	0.2	0.2	0.09	0.3	0.6	0.5	0.1	4.2	0.3
	C10	0.2	0.2	0.12	0.4	0.9	1.0	0.2	5.8	0.5
	C11	0.2	0.2	0.10	0.3	0.6	0.6	0.1	4.2	0.3
	Element concentrations UCC (in ppm) (Wedepohl. 1995)	30890	527	77440	655	52	14.3	11.6	0.1	17

Acknowledgements

We are deeply grateful to Dr. Pascale BESSON, Stephan BORENSZTAJN and Clément DEMASY at IPGP (France) for their help and assistance with the geochemical and SEM analyses, and to Dr. Yahya MOUMNI at University of Gabes for his contribution to the sampling missions.

Funding

This work was supported by a LEFE-CYBER project of the French INSU-CNRS coordinated by Dr. Marie BOYE and by an exchange international grant from the University of Gabes (Tunisia).

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data Availability

The datasets generated during and/or analyzed during this study are available from the corresponding author on reasonable request.


domain: sdv sde

text:
Nathalie Cheviron
email: cheviron@versailles.inra.fr

Christelle Marrauld

Virginie Grondin

Helen Vecten

Sabine Houot

Antonio Bispo

Cécile Grand

Laurence Galsomiès

Christian Mougin

Long-term effect of organic amendments on soil enzymatic activities

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

MATERIALS AND METHODS

For each treatment, the Qualiagro site (INRA and Veolia Environment collaboration) comprised four replicates of plots (45 m x 10 m, 450 m 2 ). The treatments were: no organic amendment (CON), farmyard manure (FYM), biowaste compost (BIO), co-compost of green wastes and sludge (GWS) and municipal solid waste compost (MSW)(Figure 1). The present study was managed on plots with optimal mineral nitrogen fertilization. In the site, the luvisol was a silt loam comprising 15% clay, 78% silt, and 7% sand. Its initial pH value was 6.9 and initial organic matter was 1.8%. During the past twenty years, the average annual precipitations amounted to 582 mm, and the average annual temperature was 11°C. The soils were collected at different times (at T0, then 6 and 18 months after amendments from) 2011 to 2013 at a depth of 0-10 cm. Samples were sieved through a 5 mm mesh, and stored at 12 °C before use. Soil water content was determined by drying 5 g of soil at 105 °C for 48 H.0 Phosphatase, b-glucosidase, arylsulfatase, and urease activities were performed in microplate according to modified protocols [16,17,18,19] less than 48 hours after sample collection. Briefly, hydrolases were measured in triplicates in 4 g soil samples mixed during 10 min at 250 rpm with 25 ml water. For phosphatase, b-glucosidase and arylsulfatase activities, soil solutions were incubated with specific substrates (Sigma chemicals) (Tab.2). Reaction was stopped with 0,5 M CaCl 2 and 0,1 M Tris at pH 12. For urease activity, soil solutions were mixed with 0,4 M urea. NH 4 formed was revealed with ammonium salicylate and ammonium cyan rate (Hach reagents). After the reactions, each plate was centrifuged 5 min at 2000 g, and absorbance was measured on a microplate reader Genius (SAFAS). The amounts of p-nitrophenol (PNP) and NH 4 Cl formed were obtained by the absorbance at 405 nm and 610 nm. 1998,2000,2002,2004,2006,2007,2009

Cheviron

  Nathalie 1,P , Marrauld Christelle 1 , Grondin Virginie 1 , Vecten Helen 1 , Houot Sabine 2 , Bispo Antonio 3 , Grand Cécile 3 , Galsomiès Laurence 3 , Mougin Christian 1 (1) INRA, Unité PESSAC 78026 Versailles, FR -(2) INRA/AGROPARISTECH, UMR Environnement et Grandes Cultures, 78850 Thiverval-Grignon, FR -(3) ADEME, 49004 ANGERS cedex 01, FR Average physico-chemical characteristics of organic amendments applied in

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  fresh weight; dw, dry weight; OC, organic carbon content; ON, organic nitrogen content ; C/N tot , organic C to total N ratio b The excess mineralized carbon after 91 days in the soil-organic amendment mixtures was expressed as a percentage of the amendment organic C applied during incubation (after subtracting mineralized C of the control treatment)CONCLUSIONSOrganic amendments have noticeable long-term-effects on enzymatic activities. Soil microbial processes are sensitive indicators for monitoring changes of soil biological properties due to amendments by organic waste and for assessment of Organic Matter status . with (*). QUALIAGRO (Feucherolles -Yvelines; France), is a long-term experiment network to observe and understand the effects of OWP amendments on cropped soils to investigate the environmental impacts of recycling organic residues on soil biochemical properties, as well as the possible resilience of the agrosystems, to assess cost/benefit balance, and to improve agricultural practices. Since 1998The level of b-Glucosidase, Phosphatase and Urease activities increases depending on the nature of the amendment, more especially on the status of organic matter added, its availability and degradability. -Arylsulfatase activity does not respond to these amendments -Organic amendments could promote stability of enzymes which could strongly affect soil quality FYM exogen microorganism input, very degradable MWS high biodegradability, very thin, rapidly incorporated and mineralised GWS: pool of degradable (sludge), and few degradable (Green Wastes) BIO: contains lots recalcitrant organic coumponds; thin mineralisation, poor disponibility of nitrogen


Eloi Mehr

André Lieutier

Fernando Sanchez Bermudez

Vincent Guitteny

Nicolas Thome

Matthieu Cord

Éloi Mehr

Manifold Learning in Quotient Spaces

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Manifold learning and generative models are major research topics to learn from a dataset a latent space representing the input space [4,[START_REF] Koller | Probabilistic Graphical Models: Principles and Techniques -Adaptive Computation and Machine Learning[END_REF]. They are useful tools, not only to grasp the hidden structure of the data, but also to generate new plausible data, either by sampling or by nonlinear interpolation, or to complete missing information by inferring unobserved variables.

In this work we focus on manifold learning of 3D shapes. Such data is often represented in a high-dimensional real vector space X. Manifold learning aims at representing the data by learning an embedding in a low-dimensional space. However, explicit representations of 3D shapes (point clouds, voxels, meshes, CAD1 models) are given through coordinates and therefore in a given pose. These natural representations carry two pieces of information: the "intrinsic geometry" of the shape, i.e. its geometry up to rigid transformations, together with the pose information itself. While mathematically clear, intrinsic geometries are the quotient of X by the action of the group of rigid transformations, following Kendall's shape spaces [18], the quest for simple and parsimonious explicit representations of them remains elusive. To "disentangle" both pieces of information, and learn an explicit representation of intrinsic geometry, one possibility consists in seeing the shape as a metric space, either through heat kernel (or Laplacian) based signatures [23,[START_REF] Sun | A concise and provably informative multi-scale signature based on heat diffusion[END_REF] or, in the case of a point cloud, by giving Euclidean distances between each pair of points. While interesting for some applications, these representations are not parsimonious. One could also suggest rotationinvariant spherical harmonics [START_REF] Kazhdan | Rotation invariant spherical harmonic representation of 3d shape de-scriptors[END_REF], but getting rid of pose information in them makes us lose most geometric information.

In this paper we propose a strategy to bridge the gap between pre-processing of 3D datasets using co-analysis tech-niques and 3D manifold learning. We introduce a quotient model that allows to directly learn the manifold in the space of the geometry, independently of the pose of the input 3D shape in the dataset (see Figure 1). To produce this parsimonious intrinsic geometry representation, we design a variant of the autoencoder [14,33], called quotient autoencoder (abbreviated QAE), based on a dedicated loss function working in the quotient space X/G, where G is a group, typically the group of rotations. Our method, by some economy principle, allows a shared pose to emerge by implicitly constraining the decoder to select a pose at the reconstruction stage. To further support this behavior, we introduce a specific orbit pooling in our encoder. We also derive a training scheme adapted for both discrete and continuous transformation groups.

We provide empirical results to demonstrate that our QAE is more efficient than a vanilla autoencoder trained with data augmentation. We also provide several experiments to highlight the ability of our QAE to automatically co-align shapes, and we illustrate realistic interpolations of misaligned shapes. Additionally, we show that our framework can be extended to non-rigid transformations with other applications, such as feature matching.

Background

Autoencoders. Given a dataset representing samples from a same class, e.g. a dataset of cars, autoencoders [14,33] aim at learning a mapping, modeled as a feedforward deep neural network, between the original input space and a low-dimensional space. Moreover, autoencoders also learn a reverse mapping from the latent space to the original input space. They can notably be used to perform realistic non-linear interpolation, extract meaningful features in the data, compress the data into a compact representation, complete a partial shape, or sample new shapes (see [3] and also [START_REF] Kingma | Auto-encoding variational Bayes[END_REF][START_REF] Rezende | Stochastic backpropagation and approximate inference in deep generative models[END_REF] for extensions to a variational framework).

Co-alignment of shapes. Co-alignment consists in aligning a dataset of 3D models in a common frame. Many drawbacks are inherent to the existing methods. Some require manual supervision such as [START_REF] Wang | Active co-analysis of a set of shapes[END_REF]. Others like [START_REF] Averkiou | Autocorrelation descriptor for efficient co-alignment of 3d shape collections[END_REF]7] are based on symmetries and correlations analysis, or try to minimize a continuous energy as reviewed in [START_REF] Tam | Registration of 3d point clouds and meshes: A survey from rigid to nonrigid[END_REF]. These methods are not adapted to shapes exhibiting high geometrical or topological variability. Some methods also need very clean meshes to be able to compute accurate features, as in [START_REF] Averkiou | Autocorrelation descriptor for efficient co-alignment of 3d shape collections[END_REF]. Moreover, most of the approaches compute the alignment by a pairwise matching of each sample in the dataset with respect to a reference mesh, but are not able to leverage the whole dataset at once to compute a consistent frame.

3D generative learning. Several recent works in unsupervised learning have been dedicated to 3D shapes. [START_REF] Wu | 3d shapenets: A deep representation for volumetric shapes[END_REF] presents a convolutional deep belief network, which is used for shape completion and recognition tasks. Autoencoers have also been used, for instance in [START_REF] Girdhar | Learning a predictable and generative vector representation for objects[END_REF], where additionally to a 3D autoencoder a CNN is learned to predict the latent vector from an image. [35] extends this idea by replacing the autoencoder with a generative adversarial network (see [START_REF] Goodfellow | Generative adversarial nets[END_REF]), and adds a variational regularization term to the 2D prediction CNN. [31] learns a CNN which predicts an arrangement of cuboids which fits the input voxelic model. These works exploit voxelic models, with a resolution limited to 32 3 . Other works have tried to extend 3D learning to more intrinsic representations, such as point clouds.

[15] learns a probabilistic graphical model, based on point clouds in correspondence. However, all described methods assume the shapes of the input dataset to be co-aligned, or augment the dataset to learn this variability.

Invariance in deep learning. Our work is also closely related to the study of invariance in deep neural networks, an important topic in deep learning. Usual pooling units in CNNs allow local translation invariance, but deeper work has been done since to achieve better invariance properties. [16] proposes to learn a CNN locally invariant to scale changes, by applying the same convolution at different scales and aggregating the results with a max pooling unit. [START_REF] Gens | Deep symmetry networks[END_REF] extends this idea by introducing deep symmetry networks. This work generalizes the invariance property of pooling units to any symmetry group, but still needs to discretize the generating set of the group. Global invariance can be achieved using a global aggregation layer, as explained in [9,[START_REF] Laptev | TI-POOLING: transformation-invariant pooling for feature learning in convolutional neural networks[END_REF]. All the considered transformations are passed to the same network, and then aggregated using max pooling. The same technique was already used in [28] to learn rotation-invariant features for 3D recognition. [START_REF] Laptev | TI-POOLING: transformation-invariant pooling for feature learning in convolutional neural networks[END_REF] points out that the global aggregation enjoins the network to learn a canonical instance position of the inputs.

Our work generalizes the idea developed in [START_REF] Laptev | TI-POOLING: transformation-invariant pooling for feature learning in convolutional neural networks[END_REF] to manifold learning, especially in the 3D context. It learns a more representative embedding of the intrinsic geometry than vanilla autoencoders when the shapes in the dataset are not co-aligned. It also naturally leads to a co-alignment algorithm able to leverage the whole dataset at once. Finally, our framework is generic enough to handle a larger class of invariance group than just translation and rotation groups, or discrete symmetry groups.

Quotient autoencoder (QAE)

Autoencoder limitations

Let D = {x i ∈ X | i ∈ 1,
n } be a dataset of n shapes representing objects of a same class. Each shape x i is represented as a vector in a m-dimensional vector space X. In our work, X represents shapes as 3D binary occupancy voxels grids or 2D depth maps, but the idea is generic and could be extended to point clouds for example following [10,[START_REF] Qi | Pointnet: Deep learning on point sets for 3d classification and segmentation[END_REF].

We define the encoder f w : R m → R p and the decoder g w ′ : R p → R m , parameterized by weights w and w ′ , where p ≪ m is the dimension of the latent space. Encoder and decoder are usually deep feedforward neural networks. The vanilla autoencoder (AE) g w ′ • f w is classically trained by optimizing a reconstruction error

E ae (w, w ′ ) = n i=1 d(x i , g w ′ • f w (x i )) , (1)
where d(x, y) is a loss function, comparing the input sample and the sample reconstructed by the autoencoder, such as the usual squared L 2 loss x -y 2 2 . One of the main issues when applying AEs for learning 3D shape representations is that the shapes are not necessarily co-aligned in a common frame. Shapes can have arbitrary poses, as we do not make any assumption on the frame of each shape in the dataset. An option consists in pre-processing the dataset to align the 3D models. However, state-of-the-art automatic co-alignment algorithms are prone to mistakes, as mentioned in section 2. Another option is to directly learn AEs on non-aligned models. To model pose variability, vanilla AEs rely on brute force data augmentation techniques, which consist in applying random transformations to each input sample. The main drawback with data augmentation is that it decreases the modeling power of the network, leading to a decreased performance in terms of reconstruction quality. Indeed, the latent space is less expressive w.r.t. the geometry of the shapes when they are not aligned, as the AE has to encode the orientation variability in addition to the intrinsic shape variability.

QAE overview

To overcome these limitations, we introduce a new model for unsupervised learning of 3D shapes denoted as quotient autoencoder (QAE). The overall architecture of the proposed QAE scheme is shown in Figure 2. The core idea is to augment the autoencoder with a new quotient loss bringing invariance w.r.t. to a group of transformations, e.g. rotations (subsection 3.3). To fully learn in the quotient space and be transformation-invariant we add an orbit pooling layer to the encoder (subsection 3.4). Finally, we derive a training scheme based on error backpropagation to learn all network parameters, which is applicable to both discrete and continuous transformations groups (subsection 3.5).

Formally, let G be a group, e.g. the group of rotations. G is naturally acting on X by the group action (h, x) → h.x, with h ∈ G and x ∈ X, where h.x is the rotation h applied to the shape x. We learn an autoencoder in the quotient space X/G, namely the manifold of the geometries of shapes, independently of their orientation. Thus, the latent space of the QAE is entirely dedicated to the embedding of the intrinsic geometry, leading to a better reconstruction. The intrinsic geometry of a shape x is exactly its orbit x under the group action: x = {h.x | h ∈ G} (two identical shapes with different orientations have the same orbit, the orbit loses the pose information but keeps all geometric information). Our QAE is able to learn on the quotient dataset D = {x i ∈ X | i ∈ 1, n } itself. We extend our framework to non-rigid transformations in subsection 5.1.

Quotient loss

We modify the usual autoencoder model in order to directly learn in a quotient space, as described previously. The main idea of the QAE is to replace the loss d of the Equation (1) with its induced quotient loss

d(x, y) = inf h∈G d(h.x, y) , (2)
which gives the new QAE reconstruction error

E qae (w, w ′ ) = n i=1 inf h∈G d(h.x i , g w ′ • f w (x i )) . (3)
The infimum appearing in the reconstruction error in Equation (3) allows the QAE to reconstruct the input up to any transformation from G (training part in Figure 2), and thus to focus only on the geometry unlike a vanilla AE. We expect the decoder to be more efficient if it can align all the outputs, since it can dedicate all its capacity to reconstruct similar spatial features at the same place regardless of the input's orientation. Since the loss of the QAE is invariant by any transformation of G applied to the input, the error of the QAE does not take into account the orientation of the output. Thus, the best way for the decoder to exploit all its capacity is to specialize all its neurons to reconstruct the shapes in a common frame. Let's take the example of a dataset of chairs. It is easier for the decoder to reconstruct the legs of each chair in the same region of the output space, and similarly for all other parts. Of course, the output frame of the QAE has no reason to be a canonical frame (legs at the bottom, back at the top). The co-alignment capacity of the QAE is experimented in subsection 4.3.

In the case where the actions of G are isometries for a distance d (like the action of rotations), d(x, y) is also equal to inf h∈G d(x, h.y) and then d defines a distance on X/G (see Proposition 1 in the supplementary material for a proof and [25] for an introduction to quotient topology).

Orbit pooling

In the QAE, the latent features f w (h.x) and f w (h ′ .x) of two inputs h.x and h ′ .x differing only by a transformation of G are likely to be different (unless the QAE perfectly learns such invariance by itself). We propose to explicitly support the latent vector invariance w.r.t. G, in order to have a full quotient architecture additionally to the quotient loss.

To this end, we add an aggregation layer, that we call orbit pooling, at the end of the encoder f of our network (see Figure 2). That is, for each input x of the QAE, we randomly sample several transformations h j ∈ G (or all the transformations if G is finite), and we pass all the transformed inputs h j .x i to the same shared encoders f (blue networks in Figure 2), and for each latent vector z j = f (h j .x i ) we build the aggregated latent vector z by taking the element-wise maximum2 along each dimension, that is z l = max j (z j ) l . This process, already studied in the context of supervised learning in [START_REF] Laptev | TI-POOLING: transformation-invariant pooling for feature learning in convolutional neural networks[END_REF]28], allows the latent vector to capture the shape x modulo the transformation group G, and thus to be much more robust. Indeed, f w (x i ) now depends only on x i and not the full input x i itself, that is it depends on x i independently of the transformations of G, namely independently of the original frame of x i . Thus, the energy can now be elegantly rewritten wholly in the quotient space3 as

E qae (w, w ′ ) = n i=1 inf y∈xi d(y, g w ′ • f w (x i )) , (4)
which shows that it depends solely on x i and not x i . As a result the QAE learns directly on the quotient dataset D itself, namely in the quotient space X/G. Our orbit pooling provides a global invariance w.r.t. to any group G, as it travels the orbit of the shape to pool a global invariant feature, which is different from the usual max-pooling units in CNNs that provide only local invariance for translations.

Although our QAE encoder now requires to sample the orbit, the decoder only takes one aggregated latent vector for the whole orbit from one input. Thus, our QAE is effectively twice faster than a vanilla AE to process all augmented data. Overall, the QAE is not necessarily faster to train (see subsection 4.2), because gradient updates are more frequent with a vanilla AE, and the QAE loss landscape is different.

QAE training

As detailed in section 4, we rely on deep convolutionnal neural networks (ConvNets) for implementing QAE encoder and decoder. Thus, we aim at deriving a continuous optimization scheme based on error backpropagation for efficiently training all network parameters (w, w ′ ). In this context, the main challenge is to be able to compute the gradient ∇ w,w ′ E qae (w, w ′ ) in Equation (3).

The straightforward strategy we adopt in the first place is to discretize G into a finite group G ′ (which is a subgroup of G), so that the infimum becomes actually a minimum. If we replace G with the finite subgroup

G ′ = {h 1 , • • • , h k }, the loss becomes min h∈G ′ d(h.x i , g w ′ • f w (x i )) . (5)
The minimum in Equation ( 5) is differentiable almost everywhere w.r.t. (w, w ′ ), which leads to a direct application of backpropagation for training this discrete QAE version.

In the more general continuous case, we assume that G is a Lie group, parameterized by a continuous finitedimensional vector h. Under mild assumptions on the group G (for instance if G is compact and the group action is continuous), the infimum in Equation (3) is actually a minimum, reached in h x (w, w ′ ), that we can compute with gradient descent or Gauss-Newton (comparisons are made in subsection 5.2). However, the computation of the gradient of the quotient loss becomes more challenging. If we define L x : ((w, w ′ ), h) → d(h.x, g w ′ • f w (x)), and

L x : (w, w ′ ) → L x ((w, w ′ ), h x (w, w ′ )), then ∇ w,w ′ d(x, g w ′ • f w (x)) = ∇ L x (w, w ′ ) . (6)
A priori it would require to compute the derivatives of h x w.r.t. (w, w ′ ). Indeed, unlike the discrete case, even an infinitesimal change in (w, w ′ ) modifies h x , whereas it is constant almost everywhere in the discrete case.

Fortunately, we can take advantage of the envelope theorem [START_REF] Bishop | Pattern Recognition and Machine Learning[END_REF] to simplify the gradient computation. Indeed, we have ∇ h L x ((w, w ′ ), h(w, w ′ )) = 0 by definition of h, so

∇ L x (w, w ′ ) = ∇ w,w ′ L x ((w, w ′ ), h(w, w ′ )) + J hx (w, w ′ ) T ∇ h L x ((w, w ′ ), h(w, w ′ )) = ∇ w,w ′ L x ((w, w ′ ), h(w, w ′ )) . (7)
The intuition behind this simplification is that the second-order terms which vanish in the gradient computation make it possible to consider h constant during the backpropagation, as in the discrete case.

Semi-supervised learning

If a small subset of co-aligned shapes is available, we can leverage it in order to reinforce the co-alignment effect of the QAE. We can also use this co-aligned dataset to force the alignment in its orientation, instead of letting the QAE co-align in an arbitrary (random) position. To achieve this goal, we first pre-train the chosen architecture of the QAE (including the orbit pooling layer) with a regular nonquotient loss (i.e. the loss of a vanilla autoencoder in Equation (1)). Then, we fine-tune the QAE architecture on the remaining misaligned dataset using the quotient loss. We validate the significant boost in terms of co-alignment performances of this strategy in subsection 4.3.

Experiments

Experimental setup

We evaluate our model on the ShapeNet dataset [6], which contains a few thousands 3D models for several categories. We focus on chairs, planes, and cars, as these categories exhibit complex geometries and are of primary interest for the CAD industry. Each 3D model is represented as a mesh in the dataset, aligned in a common frame for each category. For each mesh we compute a 2D depth map (in a representative view) of size 64×64 and a 3D volumetric occupancy binary grid of size 32 3 , following a standard protocol (e.g. [START_REF] Choy | 3dr2n2: A unified approach for single and multi-view 3d object reconstruction[END_REF][START_REF] Wu | 3d shapenets: A deep representation for volumetric shapes[END_REF]). We experiment the QAE on both 2D depth maps and 3D voxels grids to illustrate its performances.

We explore the discrete QAE with the rotations (continuous QAE is experimented in subsection 5.2). We train the 2D QAE with a discretized subgroup of SO(2) made of 36 rotations . Besides, CAD models are generally designed such that their 3 main directions are aligned with the frame's axes, but we do not know which direction corresponds to x, y, or z axis, as it depends on each 3D model and the conventions used by the designer. So we decided to experiment the 3D QAE not on SO(3) but on the group of the 24 rotational symmetries which leave the cube unchanged (the octahedral group), in order to be representative of a practical use case. Indeed, we also prove the relevance of the approach with chairs extracted from the SketchUp 3D Warehouse [START_REF]Google 3d warehouse[END_REF]. These chairs are designed in different frames, but all these frames can be aligned up to a transformation from the octahedral group, showing that real datasets can be representative of our hypothesis. Both 2D and 3D datasets have been misaligned, in order to compare with the vanilla autoencoder. To be consistent the misalignment in 3D is done by applying a random rotation of the octahedral group.

We build a 2D and a 3D deep convolutional architecture for the QAE, detailed in the supplementary material. We compare with vanilla autoencoders with the same architectures, except that there is no orbit pooling. As both groups are finite, we can provide the full orbit of rotated shapes to the orbit pooling layer instead of doing a random partial orbit pooling. We adopt the usual squared L 2 loss for the distance d, and train all the autoencoders as denoising autoencoders (with a classical independent Bernoulli noise layer at the input of the encoder, see [32]). We split each category into training, evaluation and test datasets containing respectively 80%, 15% and 5% of the samples. In all experiments we use ADAM optimization [19].

Reconstruction and quantitative experiments

planes chairs cars 2D 3D 2D 3D 2D 3D AE 1 0.14 0.48 0.32 2.2 0.56 0.67 AE 2 0.12 0.44 0.28 2.0 0.52 0.60 QAE 0.10 0.36 0.22 1.9 0.45 0.48 Table 1: Reconstruction errors on each 2D (depth maps) and 3D (voxels) test dataset for the vanilla autoencoder without data augmentation (AE 1), with data augmentation on rotations (AE 2), and the QAE with the pooling of all rotated inputs (QAE).

The first experiment is dedicated to the comparison of our QAE versus a vanilla autoencoder. We train the QAE on the three misaligned datasets, both in 2D and 3D. We also train two vanilla autoencoders with the same architecture than the QAE, one with the same dataset as for the QAE, and another with an augmented dataset including all allowed rotations for each shape in order to let the vanilla autoencoder learn by itself the rotation variability.

The results are summarized in Table 1. These results prove that the QAE achieves a lower reconstruction error compared to a vanilla autoencoder, even with data augmentation (AE2 in the table). Indeed, the latent space being dedicated to model the intrinsic geometric variability of the data, the capacity of the QAE is larger than the vanilla one.

Our QAE beats the vanilla autoencoder on all three datasets both in 2D and 3D, mostly with a significant margin up to a 20% decrease in the reconstruction error relative to AE2 (e.g. 3D cars, 3D planes, 2D chairs). The QAE is just slightly better only on the 3D chairs dataset. We mainly explain such a difference by the nature of the dataset, since 3D chairs have a very complex structure harder to learn, as proved by the high reconstruction error for both the QAE and the autoencoder. Figure 3 evinces that the lower reconstruction error of the QAE effectively corresponds to a visually better reconstruction. Indeed, the reconstructions from the vanilla autoencoder do not exhibit a sharp geometry, such as wheels or body, unlike the QAE which provides a more detailed shape. Notice that the QAE does not reconstruct the shape in its original frame, but co-aligns the shapes. This side effect, raised in subsection 3.3, is studied in subsection 4.3. We also experiment the influence of the orbit pooling on the learning performance. Figure 4 shows the different training curves on the chairs depth maps, and validates the introduction of the orbit pooling explained in subsection 3.4. Indeed, we observe that without the orbit pooling layer (blue curves) the QAE does not beat the vanilla autoencoder (black curves). Nevertheless, with a full pooling (red curves) the QAE reaches a much smaller reconstruction error (0.21 vs 0.28 on the validation set after 200 epochs). Moreover, the partial orbit pooling strategy, instead of pooling over all the transformations of the discretized group, is also validated by the plots (green curves, loss of 0.24 on the validation set after 200 epochs). With this partial pooling we achieve a substantial faster training than with the full pooling (200 epochs take 2h01m in the first case vs 54m in the latter) while still getting a reconstruction error far below the vanilla autoencoder with data augmentation.

Shapes co-alignment

The QAE is also able to reconstruct most of the shapes in a common frame, as illustrated in Figure 5 for the 2D QAE and in Figure 6 for the 3D QAE, providing a new coalignment algorithm with several advantages. It can deal with shapes exhibiting a large geometric variability, and is able to automatically co-align any new data on the fly in real-time once the QAE has been learned. For each input x, we simply replace x with h x .x where h x = arg min h∈G d(h.x, g • f (x)).

For the depth maps datasets, all chairs have been correctly co-aligned in the same frame by the QAE, just as cars (see Table 2). In 3D the diversity of the shapes does not allow the QAE to naturally co-align all the data in a single orientation. Among the 24 possible rotations, two are used by the QAE to reconstruct the input shape. The QAE internally clusters the dataset in two parts, which leads to two different orientations for each cluster (see Figure 6). It is not easy to see a clear semantic meaning of each cluster for the chairs, but very clearly the QAE has learned on the planes dataset to separate the aircrafts with low aspect ratio4 from the aircraft with high aspect ratio (see second row in Figure 6), without any error.

As explained in subsection 3.6, we can use a small pre-processed dataset with aligned shapes in order to constrain the QAE and improve the co-alignment performance. We pre-train the QAE with an aligned dataset containing 5% of the total number of shapes of the whole training dataset, and we fine-tune with the remaining non-aligned 95% shapes. Results are summarized in Table 2, we see that the semi-supervised approach yields a great improvement in co-alignment results. 3D chairs and cars are almost all perfectly co-aligned. Results are a bit inferior with planes, as it is a smaller dataset with more geometric ambiguities, especially with a resolution of 32 3 . Besides, the experiment shown in Figure 5 also proves that the QAE does more than a simple PCA alignment, since it is able to co-align chairs which are wider than high (last two columns), proving that the QAE has really learned a hidden structure specific to the chairs. We point out that these uncommon chairs have been specifically generated to test the robustness of our approach, and thus are not representative of the initial dataset. Although the QAE has never seen wide chairs it is still able to co-align them.

Figure 7 demonstrates an application of our 3D coalignment to a practical case. The first row shows that different chairs from the 3D Warehouse of SketchUp are not necessarily designed in a common frame, but they are all designed so that their main axes are aligned with the x, y, z axes. Thus, there are 24 possible design conventions. Our algorithm allows to straighten all theses meshes in a common frame. To find the transformation needed to co-align each mesh, we voxelize them and co-align the voxelizations with the 3D QAE. An interesting application of the co-alignment provided by our QAE is the possibility to interpolate the geometry of two shapes which are originally misaligned, as illustrated in Figure 8. Shapes interpolation is done by a linear interpolation of the corresponding latent vectors, and thus the interpolation is done non-linearly in the original space.

The classical interpolation with a vanilla autoencoder, despite having been trained with shapes with arbitrary orientations, is not able to disentangle the pose from the geometry. Instead of rotating the chair and interpolating the geometry, we see that the interpolation seems to perform a kind of optimal transport of one depth map to the other. As a result the interpolated chairs are not realistic. On the contrary, the interpolation in the latent space of the QAE interpolates the geometry independently of the orientation of the initial shapes, leading to realistic interpolations of chairs.

Quotient by non-rigid deformations

Extension of the QAE

The QAE framework we described in section 3 can be applied to a set of non-rigid transformations G, without any modification. It is not even compulsory for G to be a group, but then we may lose some important properties (for instance X/G is not a quotient space anymore).

We can parametrize non-rigid transformations by RBF

Experiment on feature matching

We aim to learn a reference space where all the shapes share a common representation. Once the data is aligned in the reconstructed space, we can match the input shapes by morphing the reconstructed shapes to the original ones. This allows to backpropagate features for instance, as experimented now on chairs depth maps.

We train the QAE on our RBF-based continuous set of non-rigid transformations, with an orbit pooling of 12 random transformed inputs. The optimization of the infimum appearing in the Equation ( 2) is done with Gauss-Newton, where the normal equation is solved with conjugate gradient. We compare it to a basic gradient descent in Figure 9, showing that Gauss-Newton optimization is more efficient (0.41 vs 0.60 for the validation loss). Since depth is less relevant here, training was done on occupancy masks in order to optimize the learning.

Figure 10 shows how we can match features across different shapes by retargeting common points on the learned reference space. Reconstructed shapes (first row) do not look like plausible chairs, as it is not an objective in this experiment, the main goal being to match the shapes in a common space. To perform feature matching we pick a set of points (green marks in the bottom left chair) and warp them in the corresponding reconstructed shape. We copy these warped points across all the reconstructed shapes (red marks of the first row, they all have the same coordinates over the different shapes) and retarget them into the original input shapes (blue marks of the second row).

Conclusion

In this work we introduce a new deep autoencoder model to learn a quotient manifold, in a fully unsupervised framework. Our QAE encompasses a new quotient loss, and an orbit pooling, in order to learn in the quotient space itself. We also explain how this new architecture can be trained for both discrete and continuous transformations. We show that our autoencoder quotiented by rotations leads to a better representation of the intrinsic geometry. Especially, we provide quantitative results proving that the QAE is more efficient than a vanilla autoencoder trained with data augmentation. We also illustrate the ability of the QAE to automatically co-align shapes, leading to other interesting applications such as geometric interpolations of misaligned shapes. We finally extend our model to non-rigid transformations, as illustrated by our feature matching experiment.

Figure 1 :

 1 Figure1: Misaligned dataset is learned in the space of 3D shapes quotiented by rotations, thus the quotient autoencoder focuses on the intrinsic geometry only. As a result it reconstructs better than a vanilla autoencoder, and is also able to co-align the shapes.

Figure 2 :

 2 Figure 2:The QAE takes as input a shape and samples its orbit in order to aggregate the latent vectors of each transformed input via the orbit pooling. The encoders share their weights. The quotient loss is the infimum over the distances of the decoder output to each shape of the input orbit. In the figured3achieves this minimum. This new architecture can still be trained with backpropagation.

Figure 3 :

 3 Figure 3: The first row shows the original depth maps, the second row the reconstruction with the vanilla autoencoder trained with data augmentation, the third row the reconstruction with the QAE.

Figure 4 :

 4 Figure 4: The dashed (resp. solid) curves represent the training (resp. validation) loss. Black: vanilla autoencoder with data augmentation in rotations. Red: QAE with full pooling of all 36 rotated inputs. Green: QAE with partial pooling of 12 random rotated inputs. Blue: QAE without orbit pooling. Vertical lines show elapsed training times for each case.

Figure 5 :

 5 Figure 5: The first row shows input chairs, the second row the chairs reconstructed by the QAE, the third the original input chairs with the orientation given by the QAE. Last two columns represent specifically generated wider chairs, very different from the training dataset, to illustrate the robustness of the QAE.

Figure 6 :

 6 Figure 6: Orientations given by the QAE applied to chairs and planes. The QAE automatically co-aligned on 2 orientations among 24, depending on an internal clustering learned by the QAE.

Figure 7 :

 7 Figure 7: The first row shows meshes from SketchUp 3D Warehouse in their original frame, the second row shows the same meshes straightened with our 3D QAE.

Figure 8 :

 8 Figure 8: The first row shows several interpolations between two chairs with a vanilla autoencoder trained with data augmentation. The second row displays the same interpolation with the QAE.

Figure 9 :

 9 Figure 9: The dashed (resp. solid) curves represent the training (resp. validation) loss for the continuous QAE. The blue curves display the QAE loss where h(w) is obtained with a gradient descent with 25 iterations, and the red (resp. green) curves display the QAE loss where h(w) is computed with 10 (resp. 15) iterations of Gauss-Newton, each one being solved with 5 (resp. 10) iterations of conjugate gradient.

Figure 10 :

 10 Figure 10: All the red marks have the same coordinates. They are retargeted on each original chair to match the green marks with each blue mark on the second row. Retargeting of feature points is shown on the original depth maps.

Table 2 :

 2 Co-alignment errors for the QAE trained on a completely misaligned dataset, and the co-alignment results for the QAE pretrained on a small aligned dataset. The alignment error is given by one minus the greatest number of co-aligned shapes over the total number of shapes, on the misaligned test set.

Computer assisted design.

An aggregation function of L latent vectors of dimension p is a function δ : (R p ) L → R p whose main properties are that δ is invariant under permutation, and δ(h, h, , h) = h for any h ∈ R p .

 3 Notice that the loss in Equation (2) inf h∈G d(h.x i , g w ′ • fw(x i )) can actually be rewritten inf y∈x i d(y, g w ′ • fw(x i )).

The aspect ratio of a wing is the ratio of its span to its mean chord.


Sylvie Nelieu

Ghislaine Delarue

Elodie Ollivier

Pierre Awad

Christian Mougin

Céline Pelosi

Evaluation of epoxiconazole bioavailability in soil to the earthworm Aporrectodea icterica

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Context Context

 In soils, sorption processes limit the bioavailability of organic contaminants to organisms. This bioavailability restriction depends on the target o rganism, soil properties and several processes varying with time [1].  Little attention has been paid to this bioavailability to earthworms even if they are key-organisms for the health of terrestrial ecosystem, as they influence soil structure and chemistry.  Earthworms can be threatened by contaminants such as the persistent fungicide epoxiconazole (EPX), which has a chronic toxicity towards the resistant earthworm Eisenia fetida at a concentration close to the recommended dose. It could thus affect sensitive earthworm species found in cultivated fields, such as Aporrectodea icterica [2].

Objective and approach Objective and approach

 Propose and apply a mild extraction method to estimate the environmental (bio)availability of epoxiconazole (EPX) for earthworms A. icterica.

Step 1. Test of the method sensitivity to soil sorption capacities: the mild extraction yield should vary with organic matter content, soil texture and aging.

-Sublethal effects of epoxiconazole on earthworms

Conclusions Conclusions

• The mild extraction method based on hydroxypropyl--cyclodextrine, chosen to evaluate epoxiconazole availability in soil, fulfilled the criteria of the ISO 17402 norm [6].

• Extraction yields were demonstrated to be sensitive to soil sorption capacities and to aging.

• The mild extraction method mimicked efficiently the earthworm's uptake.

• In these experiments, the earthworms A. icterica were not sensitive to the presence of epoxiconazole.

Weight gain GST activity Total protein content

In this study EPX did not caused significant effects on earthworms, in contradiction with previous experiments [ GST: Formation of reduced glutathione complex with chloro-dinitrobenzene [3] Experimental Experimental Protein content: Bicinchoninic acid method [4] Freeze GST: Formation of the reduced glutathione complex with chloro-dinitrobenzene [3]

Step 2 . 1 -

 21 Exploration of the relationship between EPX concentration in exposed A. icterica and available in soil: the relation should be linear, with a slope close to 1. Step 3. Determination of EPX effects on A. icterica: sublethal effects should be observed. Soil sorption capacities and aging effects on the epoxiconazole availability 2 -Relationship between concentrations in soil and in earthworms EPX bioavailability for earthworm is efficiently determined by the mild extraction method. The mild extraction method allowed determining an EPX available concentration proportional to the total one, in all tested conditions. Organic matter ↘ availability Loamy texture ↘ availability Aging ↘ availability n=3, ANOVA with p=0,05 on contact time for the 8 conditions Linear relation (R 2 0.98) Slope close to 1 (0.96)

  Publication: S. Nélieu, G. Delarue, E. Ollivier, P. Awad, F. Fraillon, C. Pelosi. Evaluation of epoxiconazole bioavailability in soil to the earthworm Aporrectodea icterica. Environ. Sci. Pollut. Res. (2016) 23, 2977-2986.

  available in soil (µg/g) [EPX]total soil (µg/g) 7 days, with earthworms 7 days, w/o earthworms 28 days, with earthworms 28 days, w/EPX in earthworm, µg/g) -Log (EPX available in soil, µg/g)

  or loamy soil (sieved 2 mm) Mixed or not with organic matter (horse dung, 10% dry weight) Formulated (Opus®) or pure EPX 1, 3 or 10 fold recommended dose (D1, D3, D10) Contact time: 7, 28 or 56 days (dark, 15 ± 2°C) /MS analysis -UHPLC on Acquity BEH C18 column -Electrospray interface, positive ionisation mode -Waters Acquity TQD mass spectrometer -MRM detection (330 > 121 and 332 > 121, at 22 eV collision energy)

available vs total EPX in earthworm tissue vs available

	56 days, n=3, Mann-Whitney test p=0,05
	5, Poster MO258].
	EPX toxicological bioavailability for earthworms could not be
	correlated to chemical determinations of environmental availability
	or environmental bioavailability.

EPX

Acknowledgments Acknowledgments

This work was supported by INRA, Department Environment and Agronomy (Pari Scientifique AdVerPe), and by grants from Région Ile-de-France for UHPLC-MS-MS analyses. Biochemical analyses were achieved on the platform Biochem-Env, a service of the « Investment d'Avenir » infrastructure AnaEE France, overseen by the French National Research Agency (ANR) (ANR-11-INBS-0001).