Christos Panagiotopoulos

Richard Sempere
email: sempere@com.univ-mrs.fr

Ingrid Obernosterer

Laurent Striby

Madeleine Goutx

France Van Wambeke

Sophie Gautier

Raymond Lafont

Richard Sempéré

Bacterial degradation of large particles in the southern Indian Ocean using in vitro incubation experiments

Keywords: Marine particles, Organic carbon, Carbohydrates, Amino-acids, Lipids, Bacterial decomposition, Southern Indian Ocean, Polar Front Zone (PFZ), Sub-Antarctic area (SAr)

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

Introduction

Large (> 60 µm) non-living sinking particles are mainly produced in the upper layers of the ocean (euphotic zone) and consist of biogenic material such as faecal pellets, marine snow, algal and bacterial exudates or exopolymer particles that sink to the sea floor with different rates [START_REF] Fowler | Role of large particles in the transport of elements and organic compounds through the oceanic water column[END_REF][START_REF] Alldredge | Characteristics, dynamics and significance of marine snow[END_REF][START_REF] Turley | Microbial response to the input of fresh detritus to the deepsea bed[END_REF][START_REF] Asper | Rapid coupling of sinking particle fluxes between surface and deep ocean waters[END_REF][START_REF] Alldredge | The abundance and significance of a class of large, transparent organic particles in the ocean[END_REF]. Such material is an active component of the exchange of particulate [START_REF] Martin | VERTEX: Carbon cycling in the northeast Pacific[END_REF] and dissolved [START_REF] Alldredge | Interstitial dissolved organic carbon (DOC) concentrations within sinking marine aggregates and their potential contribution to carbon flux[END_REF] organic material between surface and deep waters of the ocean. During transit in the water column, hydrolytic activity on aggregates by attached bacteria give rise to dissolved organic carbon (DOC) release, which is mainly taken up by free-living bacteria that in turn produce CO 2 through respiration [START_REF] Cho | Major role of bacteria in biogeochemical fluxes in the ocean's interior[END_REF][START_REF] Herndl | Ecology of amorphous aggregations (marine snow) in the northern Adriatic Sea: II. Microbial density and activity in marine snow and its implication to overall pelagic processes[END_REF][START_REF] Karner | Extracellular enzymatic activity and secondary production in free-living and marine-snow-associated bacteria[END_REF]Herndl, 1992, Smith et al., 1992;[START_REF] Hoppe | Evidence for dependency of bacterial growth on enzymatic hydrolysis of particulate organic matter in the mesopelagic ocean[END_REF][START_REF] Sempéré | Microbial decomposition of large organic particles in the Northwestern Mediterranean Sea: an experimental approach[END_REF]. These processes are relevant to the global carbon cycle since they determine how much of organic and inorganic carbon is sequestered in the ocean interior [START_REF] Siegenthaler | Atmospheric carbon dioxide and the ocean[END_REF].

The organic composition of sinking particles has been described mainly for sediment trap material, focusing on carbohydrates [START_REF] Ittekkot | Seasonality in the fluxes of sugars, amino acids, and amino sugars to the deep ocean: Sargasso Sea[END_REF][START_REF] Tanoue | Monosaccharide composition of marine particles and sediments from the Bering Sea and nothern North Pacific[END_REF][START_REF] Hernes | Neutral carbohydrate geochemistry of particulate material in the central equatorial Pacific[END_REF], amino acids [START_REF] Lee | The vertical flux of particulate organic nitrogen in the sea: decomposition of amino acids in the Peru upwelling area and the equatorial Atlantic[END_REF][START_REF] Wakeham | Biogeochemistry of particulate organic matter in the ocean: results from sediment trap experiments[END_REF][START_REF] Lee | Composition and flux of particulate amino acids and chloropigments in equatorial Pacific seawater and sediments[END_REF] and lipids [START_REF] Wakeham | Biogeochemistry of particulate organic matter in the ocean: results from sediment trap experiments[END_REF]Wakeham et al., 1997a;[START_REF] Cailliau | Sedimentation pathways in the indian sector of the Southern Ocean during a production regime dominated by regeneration[END_REF][START_REF] Goutx | High-frequency of labile compounds in the central Ligurian Sea, northwestern Mediterranean[END_REF][START_REF] Kiriakoulakis | Controls on the organic chemical composition of settling particles in the Northeast Atlantic ocean[END_REF], or by using solid state 13 C-NMR spectroscopy [START_REF] Hedges | The molecularly-uncharacterized component of nonliving organic matter in natural environments[END_REF]. Recent studies indicated that bacterial degradation of large marine particles in the water column can be described by a multi-G model [START_REF] Sempéré | Microbial decomposition of large organic particles in the Northwestern Mediterranean Sea: an experimental approach[END_REF], which was initially proposed for sedimentary organic matter [START_REF] Berner | Early diagenesis: a Theoretical Approach[END_REF]Westrich andBerner, 1984, Rabouille et al., 1998). Related studies also demonstrated that particulate organic matter from phytoplankton debris, zooplankton, and axenic cultures of phytoplankton (Henrich and Doyle, 1986;[START_REF] Harvey | Kinetics of phytoplankton decay during simulated sedimentation: changes in biochemical composition and microbial activity under oxic and anoxic conditions[END_REF][START_REF] Nguyen | Protein and amino acid cycling during phytoplankton decomposition in oxic and anoxic waters[END_REF] follows first order kinetics and does not degrade as a single pool. However, very few data are available on the turnover rates of large particles (> 60 µm) as well as the amount of organic material released through these processes in the form of dissolved organic matter.

Therefore, particulate organic material (POM) was collected by using in situ pumps from two localities (Polar front zone: PFZ and Subantarctic region: SAr) in the southern Indian Ocean. The southern Indian Ocean in particular may play a major role in global environmental changes, since it is considered an important sink for atmospheric CO 2 , [START_REF] Metzl | The annual fCO 2 cycle and the air-sea CO 2 flux in the sub-Antarctic Ocean[END_REF], however very few data are available on the degradation of large organic particles that often dominate the recycling of organic matter. Moreover, this region is characterized as the largest "high nutrient low chlorophyll" region, which exhibits elevated productivity only in the Polar Front due to the entrainment of trace elements [START_REF] De Baar | Importance of iron for plankton blooms and carbon dioxide drawdown in the Southern Ocean[END_REF]. In this study the objectives were:

(1) to measure the amount and composition of POM, namely organic carbon, sugars, amino acids and lipids, during bacterial degradation of large (> 60 µm) sinking particles,

(2) to better understand particulate-dissolved organic matter transfer during degradation

(3) to determine bacterial growth efficiency (BGE) during organic matter degradation, (4) to provide turnover rates for sugars, amino acids and lipids found in the particulate organic material, and

(5) to compare data sets between PFZ and SAr for which large differences in particulate material reaching the seafloor have already been reported [START_REF] Rabouille | Recycling of organic matter in Antarctic sediments: a transect through the polar front in the southern Ocean (Indian Sector)[END_REF].

Materials and methods

2.1 Study area. Seawater and particle collection was carried out from January to February 1999 in the southern Indian Ocean in the framework of the Antares-4 (ANTarctic RESearch) project, a French contribution to SO-JGOFS. Two stations typical of the Southern Ocean at these latitudes were sampled, the first one is located in the Polar Front Zone (PFZ: 46°01.22′S; 62°56.70′E) and the other is located in the Sub-Antarctic region (SAr : 44°10.92′S; 63°23.37′E) (Fig. 1; Table 1). The PFZ is located between the Sub-Antarctic Front (SAF) in the north and the Polar Front (PF) in the south. In the upper 200 m, temperature and salinity at PFZ varied from 5 to 10 °C and from 33.69 to 33.94, respectively (Table 1). Water masses in SAr, which is located between the Sub-Tropical Front (STF) in the south and the Agulhas return Front (AF) in the north [START_REF] Park | Cross-frontal exchange of Antarctic Intermediate water and antarctic bottom water in the Crozet Basin[END_REF], were much warmer with temperature ranging from 11 to 14 °C and the corresponding salinity range was 34. 35-34.82 (Table 1). Depth integrated values (0-150 m) of biogenic silica in PFZ averaged 38 mmol m -2 in the PFZ and 25 mmol m -2 in the SAr, whereas integrated primary production (PP) over 0-150 m averaged 28 mmol C m -2 d -1 in the PFZ and 47 mmol C m -2 d -1 in the SAr (Leblanc et al., in press). Integrated total organic carbon (TOC) values (0-150 m) averaged 7474 mmol C m -2 in PFZ and 9642 mmol C m -2 in the SAr, whereas bacterial production averaged 8 mmol C m -2 d -1 in the PFZ and 13 mmol C m -2 d -1 in the SAr (R. Sempéré, unpublished observations).

Sampling.

Large particles (> 60 µm) were collected at 30 and 200 m depth using in situ pumps (Challenger Oceanics) equipped with 60 µm pore-size filters (Nitex, Ø: 142 mm).

Seawater (10 l) was also sampled at the same depths with Niskin bottles and filtered through 0.2 µm pore-size filters (Millipore, Ø: 143 mm; P < 50 mm Hg) in order to remove bacteria and grazers. Prior to filtration, the 0.2 µm pore-size filters were flushed with Milli-Q water (2 l) and 0.5-1 l of seawater in order to minimize contamination (Yoro et al., 1999). This water was used for particle extraction from filters and for batch preparation.

Incubation experiments.

Within 2 hours of particle collection, swimmers were discarded using squeezers and the filters were placed into petri dishes. Particles were then extracted from the filters by washing several times with filtered (0.2 µm) seawater (total volume ~ 200 ml) with a syringe. The mixture was transferred into a 2 l polycarbonate bottle filled (previously washed with 2 % HCl and Milli-Q water) with additional 0.2 µm-filtered seawater and immediately transferred to incubation bottles (500 ml glass bottles; combusted 450 °C); using a peristaltic pump (Perfifill IQ 2000, Jencons Ltd). The particulate material was incubated on board for 7-17 days (longer incubation times would probably induce anoxic conditions) at in situ seawater temperature (5-14 °C) in the dark and swirled following the protocol of [START_REF] Sempéré | Microbial decomposition of large organic particles in the Northwestern Mediterranean Sea: an experimental approach[END_REF] and [START_REF] Arraes-Mescoff | The behavior of Al, Mn, Ba, Sr, REE and Th isotopes during in vitro degradation of large marine particles[END_REF]. The headspace-to-sample ratio inside the incubation bottles was about 240 : 500 ml, which ensured oxic conditions throughout the incubation period.

Sub-sampling of incubations was performed by collecting aliquots for particulate organic carbon (POC), dissolved organic carbon (DOC), particulate and dissolved sugars, amino acids, and lipid analyses as well as for the determination of bacterial production. The peristaltic pump was used to transfer the aliquots (∼ 50 ml) into four glass bottles (100 ml), corresponding to POC, DOC, sugar, amino acid and lipid measurements. The particulate material was collected on GF/F filters (nominal retention: 0.7 µm) for further determination of POC, amino acids, sugars and lipids and these were stored in the dark (-17°C) prior to analysis on shore. The filtrates passing through the GF/F filters were transferred into duplicate glass vials, closed with Teflon-lined screw caps and stored in the dark (-17°C) for sugar and amino acid analyses.

Samples for DOC were preserved with HgCl 2 (final concentration: 10 mg l -1 ) and stored in the dark at 4 °C [START_REF] Ogawa | Comparison of two methods for measuring dissolved organic carbon in seawater[END_REF]. Dissolved lipids were immediately extracted with chloroform from the filtrates (see below) and stored in the dark under N 2 (-17°C). The standard deviation for the particle distribution, which was determined by measuring POC in five replicates, was 5 % at the start of the incubation. Experimental errors based on duplicate analyses were estimated to be about 10 % for the concentration of each chemical parameter and BP during incubation the experiment. Controls (1 sub-sample for each sampling depth at 30 and 200 m) were prepared by adding HgCl 2 (10 mg l -1 final concentration) to batches containing particles at the start of the experiment and were processed in the same way as above.

2.4 POC and DOC. Filters were processed according to [START_REF] Tan | Carbon isotope ratios of particulate organic matter in the Gulf of St. Lawrence[END_REF], and assayed on a CS analyzer (CS 125-Leco). In preparation for POC analysis, the GF/F filters were covered with a few ml of 2 N H 3 PO 4 and evaporated to dryness at 50 °C for 12 hours to remove inorganic carbon. The filters were then combusted and the CO 2 generated was measured by a non-dispersive infra-red detector, with a standard deviation of 2 %. POC values reported in this study were not corrected for bacterial biomass-C (determined from bacterial abundance) since this represented < 5 % of POC.

DOC was measured by high temperature combustion on a Shimadzu TOC 5000 analyzer, as described in [START_REF] Dafner | Total organic carbon distribution and budget through the Strait of Gibraltar in April 1998[END_REF] and Sempéré et al. (in press). A four point-calibration curve was performed daily with standards prepared by diluting a stock solution of potassium hydrogen phthalate in Milli-Q water. The procedural blank ranged from 4 to 8 µM C and was subtracted from the values presented here. TOC concentrations were estimated by summing POC and DOC.

Particulate sugars (PCHO) and dissolved sugars (DCHO).

Filters were hydrolyzed with 0.1 M HCl at 100 °C for 20 h [START_REF] Burney | Dissolved carbohydrates in seawater. II, A spectrophotometric procedure for total carbohydrate analysis and polysaccharide estimation[END_REF]. On cooling, the aqueous acid was evaporated to dryness in a rotary evaporator and the residue was washed with a small volume of water (200 µl) which was removed by evaporation. The residue was taken up in 2 ml of Milli-Q water and analyzed for PCHO in order to determine the concentrations and composition of combined sugars. Neutral monosaccharide concentrations in hydrolyzed samples were measured by high performance anion exchange chromatography with pulsed amperometric detection (HPAEC-PAD) according to [START_REF] Mopper | Determination of sugars in unconcentrated seawater and other natural waters by liquid chromatography[END_REF] and modified by [START_REF] Panagiotopoulos | Sub-ambient temperature effects on separation of monosaccharides by HPAEC-PAD. Application to marine chemistry[END_REF]. Briefly, monosaccharides were separated on an anion exchange column (Carbopac PA-1, Dionex) by isocratic elution with 19 mM NaOH at 17 °C (column temperature) and detected by an electrochemical detector (Decade, Antec). The detection limit of the method was found to be 25 nM (S/N=3, loop 20 µl). Final PCHO concentrations were expressed as C-equivalents.

Since HPAEC-PAD technique provides variable recovery of individual dissolved monosaccharides in seawater because of the desalting steps [START_REF] Mopper | Determination of sugars in unconcentrated seawater and other natural waters by liquid chromatography[END_REF], dissolved monosaccharides were measured by a colorimetric technique with a detection limit of ~500 nM glucose equivalents [START_REF] Myklestad | A sensitive method for analysis of dissolved mono-and polysaccharides in seawater[END_REF]. Thus, filtrates were hydrolyzed to give an estimate of DCHO similarly as described above [START_REF] Burney | Dissolved carbohydrates in seawater. II, A spectrophotometric procedure for total carbohydrate analysis and polysaccharide estimation[END_REF] for PCHO and measured on a spectrophometer (Perkin Elmer E201 Lambda). Thus, the concentration of DCHO is equivalent to the sum of free and combined dissolved sugars. Total monosaccharide concentrations (TCHO) were estimated by summing PCHO and DCHO. DCHO concentrations were converted to C-equivalents by using a molar conversion factor of six. Final TCHO and PCHO concentrations were expressed as C-equivalents.

2.6 Particulate amino acids (PAA) and dissolved amino acids (DAA). Filters were hydrolyzed using 6 N HCl at 110 °C for 20h [START_REF] Parsons | A manual of chemical and biological methods for seawater analysis[END_REF], then the hydrolyzate was neutralized with 6.1 N NaOH and the amino acids were measured according to [START_REF] Delmas | Dissolved primary amine measurement by flow injection Analysis with o-pthaldialdeyde: Comparison with High-Performance Liquid Chromatography[END_REF] using a peristaltic pump (Gilson) and fluorescence labeling with o-phtaldialdehyde (OPA). The filtrate was used for the analyses of DAA. The concentration of DAA was determined after hydrolysis (6 N HCl, 110 °C, 22 h) and it corresponds to both free and combined dissolved amino acids. Total amino acids (TAA) concentrations were calculated by adding up PAA and DAA (TAA = PAA + DAA). The blanks for the PAA were 0.4-0.5 µM (cv = 13%; n = 3 for the 0.1-1 µM level). The measured concentrations were not corrected for blank values. The detection limit was found at 0.1 µM (0.1-1 µM level) which is consistent with [START_REF] Delmas | Dissolved primary amine measurement by flow injection Analysis with o-pthaldialdeyde: Comparison with High-Performance Liquid Chromatography[END_REF]. Final TAA, PAA and DAA concentrations were expressed as Cequivalents by using a molar conversion factor of four, since this value represents an average calculated for the eight most abundant (78%) amino acids in marine particles [START_REF] Lee | Composition and flux of particulate amino acids and chloropigments in equatorial Pacific seawater and sediments[END_REF].

Particulate lipids (PL) and dissolved lipids (DL)

. PL were extracted from filters according to [START_REF] Bligh | A rapid method of total lipid extraction and purification[END_REF]. Lipid classes, including glyceride lipids (wax esters, triglycerids, glycolipids and phospholipids) and free lipids (fatty acids, alcohols and sterols)

were separated and quantified using a thin layer chromatography-flame ionization detection (TLC-FID) Iatroscan apparatus following the protocol of [START_REF] Striby | Improvement in the Iatroscan thin-layer chromatographic-flame ionization detection analysis of marine lipids. Separation and quantitation of monoacylglycerols and diacylglycerols in standards and natural samples[END_REF]. Dissolved lipids (DL) were liquid-liquid extracted from the filtrate (4 times with 10 ml of chloroform, last extraction at pH < 2) in separatory funnels on board and analyzed on land following the same procedure for PL. Total lipids (TL) consisted of the sum of PL and DL (TL = PL + DL) and were estimated by adding up the individual classes. The detection limit of the method was found to be 4-5 nmol (S/N = 3). Final TL, PL and DL concentrations were expressed as Cequivalents by using an average lipid to carbon mass ratio of 0.7.

Bacterial production (BP)

. BP, the rate of increase of heterotrophic bacterial biomass per unit time (ng C l -1 h -1 ) was estimated from rates of protein synthesis as measured with leucine technique [START_REF] Kirchman | Leucine incoporation as a measure of biomass production by heterotrophic bacteria[END_REF][START_REF] Van Wambeke | Bacterial dynamics during the transition from spring bloom to oligotrophy in the northwestern Mediterranean Sea: relationships with particulate detritus and dissolved organic matter[END_REF]. This technique, widely used in microbial ecology in aquatic waters, is based on the assumption that the rate of protein synthesis is proportional to BP [START_REF] Kirchman | Leucine incoporation as a measure of biomass production by heterotrophic bacteria[END_REF]. At each time point of biodegradation experiment, duplicate samples (4 ml) and a formalin-killed control were incubated with 7.6 nM -[4, 5 3 H]-leucine (specific activity 136 Ci mmol -1 ) and 200 nM of non-radioactive leucine.

Samples were incubated at in situ temperature and in the dark for 3 hours, which was in the linear phase of leucine incorporation. Incubations were stopped with formalin (2 % final concentration), samples were filtered through 0.2 µm cellulose ester filters (GSWP, Millipore)

and then extracted with ice-cold 5 % trichloroacetic acid. Samples were counted in a liquid scintillation counter (Packard 1600 TR). Leucine uptake was thus converted to BP based on a conversion factor of 1.5 kg C per mole incorporated leucine [START_REF] Kirchman | Leucine incoporation as a measure of biomass production by heterotrophic bacteria[END_REF].

Bacterial growth efficiency (BGE).

We determined BGE from TOC decrease and BP increase as follows:

BGE = (IBP/∆TOC) x 100 % (1)
where IBP is the integrated BP over successive time intervals and determined from rates of 3 Hleucine incorporation, and ∆TOC is the amount of TOC utilized during the same time interval.

The time interval corresponded to the initial phase of bacterial increase (log phase).

Results

Water column concentrations of POC of large particles (< 60 µm) ranged in both stations from 4.33 to 17.6 nM (Table 1) and are roughly 3 orders of magnitude lower than that reported for suspended POC (> 0.7 µm GF/F filters) at the same stations (1.5-17.8 µM; Leblanc et al., in press). Assuming a sinking velocity of 100 m d -1 [START_REF] Wakeham | Biogeochemistry of particulate organic matter in the ocean: results from sediment trap experiments[END_REF][START_REF] Alldredge | Characteristics, dynamics and significance of marine snow[END_REF], these concentrations roughly correspond to a theoretical organic carbon sinking flux at 200 m of 0.43 (SAr) and 0.57 (PFZ) mmol C m -2 d -1 (Table 1). These values are about two orders of magnitude lower than the POC produced from integrated (0-150 m) primary production (28 -47 mmol C m -2 d -1 , Leblanc et al., in press). These flux estimates are likely to be somewhat low because the particles were probably not completely extracted from the in situ pump filters (removal efficiency was estimated to be about 80 %). Poor estimation of the sinking velocity is also very likely. However, they indicate rapid degradation of organic matter in surface waters, and particularly in SAr judging from the relative ratio POC-flux against PP (POC-flux SAr x PP -1 = 0.009; POC-flux PFZ x PP -1 = 0.02).

Organic carbon concentrations during the experiment

For all series, initial concentrations of dissolved constituents (DOC and others) in the incubation bottles were systematically higher (228-488 µMC) than in the water column (45-75 µMC; Table 1) indicating that dissolution and/or bacterial decomposition of POC, started as soon as the particles were washed from the filters and diluted in filtered seawater. This transfer from the particulate to the dissolved phase occurred prior to the commencement of the incubation experiments (t=0) and is consistent with previous studies [START_REF] Sempéré | Microbial decomposition of large organic particles in the Northwestern Mediterranean Sea: an experimental approach[END_REF][START_REF] Arraes-Mescoff | The behavior of Al, Mn, Ba, Sr, REE and Th isotopes during in vitro degradation of large marine particles[END_REF]. Hence, TOC concentrations in batches are likely to better represent the decay of POM. During experiment preparation, DOC concentrations in the 0.2 µm-filtered seawater (see Materials and Methods) were initially slightly higher (+5 µM C) than those determined in discrete samples collected by Niskin bottles (Table 1) at the same station probably because of slight contamination during filtration. This value compared to those released from particulate material (228-488 µM C) at t = 0 or before the beginning of the experiments may, therefore, be considered to be negligible. This source of contamination probably comes from the organic material that constitutes the filter and it is very difficult to eliminate it completely (Yoro et al., 1999). This trend was not observed for amino acids, sugars and lipids, for which we found similar concentrations as in the water column.

In the PFZ 30 m and 200 m biodegradation experiments, TOC concentrations decreased by 32 % and 38 % of their initial concentrations, respectively, whereas the corresponding decreases were 43 % and 50 % for the SAr biodegradation experiments, suggesting higher lability of > 60 µm particles in the SAr (Table 2

Amino acids, sugars and lipids concentrations during the experiment

At the beginning of the incubation TAA comprised 29-40 % of TOC (200-30 m) for PFZparticles and ~10 % of TOC for SAr-particles indicating significant differences in the particle chemical composition between the two sites (Fig. 4). By the end of the time course experiment, TAA represented 23 % and 12-14 % of TOC for the PFZ-and SAr-particles, respectively (Fig. 4). At the PFZ, TAA concentrations decreased by 61 % of their initial concentration at 30 m and by 54 % at 200 m (Table 2). At SAr-particles, TAA concentrations decreased by only ~30 % of the initial concentration at both depths. Therefore, total amino acids compounds appeared to be largely degraded during the time course experiment.

At the beginning of the biodegradation experiments, TCHO comprised 8-9 % and 15-19% of TOC of the particles (200-30 m) at PFZ and SAr , respectively (Fig. 4). By the end of the time course experiment, TCHO represented 9-13 % and 17-19 % of TOC of the PFZ and SArparticles, respectively (at both depths, see Fig. 4). In PFZ-30 m experiment, TCHO concentrations decreased by 18 % of their initial concentration at 30 m and 15 % at 200 m. In the SAr experiment, TCHO concentrations decreased by 37-50 % of the initial concentrations (Table 2).

At t=0, TL comprised 7-17 % and 2-3 % of TOC of PFZ and SAr-particles, respectively (Fig. 4) indicating that the contribution of TL to TOC also varied between the two areas studied as did amino-acids and sugars. By the end of the experiment, TL represented 4-10 % of TOC for PFZ and accounted 3-5 % of TOC for SAr-particles for both depths (Fig. 4), whilst TL concentrations decreased by ~ 64 % and by 14-30 % of their initial concentrations for PFZ and SAr, respectively (Table 2).

BP and BGE

In all samples, we observed an increase in BP during the first 2-7 days and a decrease thereafter until the end of the experiment (Figs. 2 and3). The increase in BP was closely coupled with the decrease in TOC concentration. Our results showed that BP peaks observed at PFZ for both depths were rapidly reached within the first two days, whereas at Sar, maximum BP was reached after 4 days for both depths. BGE values were calculated for all samples at the end of the exponential growth of BP and ranged from 10 to 21 %, with slightly lower values for 30 m samples than 200 m samples for both stations (Table 2). The decline in BP after a few days at both sites and depths suggests that most of labile carbon was rapidly exhausted.

Alternatively, the effect of nutrient exhaustion in the bottles or flagellate grazing on bacteria cannot be excluded [START_REF] Newell | Rate of degradation and efficiency of conversion of phytoplankton debris by marine micro-organisms[END_REF][START_REF] Harvey | Kinetics of phytoplankton decay during simulated sedimentation: changes in biochemical composition and microbial activity under oxic and anoxic conditions[END_REF]. Unfortunately, during incubation experiments we did not collect sample aliquots for further nutrient measurements. However, we believe that our incubation system was not nutrient limited because ambient nutrient concentrations area high (Leblanc et al., in press). On the other hand, as explained in materials and methods section, swimmers were discarded from filters. Additional information using epifluorescence microscopy did not show a significant number of heterotrophic flagellates at the beginning of the experiment, whereas only few of them were observed at the end the experiment and were responsible for the bacterial biomass decrease (Figs. 2,3).

Degradation and mineralization rates of organic matter

Organic matter degradation and mineralization rates (k) were calculated for both fractions (particulate and total) for amino acids, sugars and lipids as well as for organic carbon according to the formula [START_REF] Amon | Bacterial utilization of different classes of dissolved organic matter[END_REF]:

k = (C init -C fin ) x (t) -1 x (C init ) -1 (2)
where:

-C ini is the initial concentration of any constituent -C fin is the final concentration of any constituent -t is the incubation time All rates were normalized to the initial concentration at the incubation in order to provide a better measurement of the proportion of total or particulate fraction of each biochemical class that is readily available for bacterial consumption. Calculated values of k for both stations and depths were: 0.022-0.072 d -1 for TOC, 0.021-0.047 d -1 for TAA, 0.003-0.053 d -1 for TCHO, 0.010-0.048 d -1 for TL (Table 3). A comparison between the different particulate pools revealed that PAA (0.038-0.14 d -1 ) were the most rapidly degraded by bacteria followed by PL (0.030-0.10 d -1 ) and PCHO (0.016-0.049 d -1 ).

It should be noted that the degradation rates of particulate material do not correlate with those of the total fractions because decomposition of particulate material produces dissolved compounds or submicronic particles (< 0.7 µm) which are not completely consumed by bacteria during the incubation time [START_REF] Sempéré | Microbial decomposition of large organic particles in the Northwestern Mediterranean Sea: an experimental approach[END_REF]. Thus, mineralization rates of total organic pool (such as k TOC ) are related to changes from organic to mineral state (i.e. CO 2 )

while degradation rates of POM (such as k POC ) are rather related to bacterial degradation as well as a transfer from particulate to dissolved state.

Discussion

Mechanisms of particle decomposition

Incubation of large particles showed a rapid response of bacteria to the input of labile organic material. Rapid breakdown of organic matter occurred during the first two days, after which rates slowed, presumably reflecting the degradation and mineralization of less labile compounds. Throughout the experimental period the labile fraction of consumed POC (ΔPOC;

Table 2) was higher at 30 m (24-45 %) than at 200 m (21-22 %) at both sites, indicating that the organic matter of large particles at 200 m was more degraded than at 30 m at the time of sampling. Our results showed that DOC concentrations in the biodegradation experiments were much higher (228-488 µMC) than those found in the water column (45-75 µMC) indicating that sinking marine aggregates are potentially a source of DOC to the water column [START_REF] Alldredge | Interstitial dissolved organic carbon (DOC) concentrations within sinking marine aggregates and their potential contribution to carbon flux[END_REF]. These results are consistent with the paradigm that POC degradation is the result of ectoenzymatic activity of attached bacteria [START_REF] Karner | Extracellular enzymatic activity and secondary production in free-living and marine-snow-associated bacteria[END_REF][START_REF] Smith | Intense hydrolytic enzyme activity on marine aggregates and implications for rapid particles dissolution[END_REF] producing high (>1 kDa) molecular weight dissolved organic compounds [START_REF] Amon | Bacterial utilization of different classes of dissolved organic matter[END_REF][START_REF] Skoog | Aldoses in various size fractions of marine organic matter: Implications for carbon cycling[END_REF]. The latter are further enzymatically degraded to smaller molecules (500-1000 Da) that are partly transported across the bacterial membrane [START_REF] Saier | Molecular dynamics in biological membranes[END_REF]Hedges et al., 2000 and references therein).

A mean of 96 % (range 78-109 %; Table 4) of the degraded POC fraction, was attributed to the degradation of characterizable compounds that constitute POC (sum of PAA, PCHO, PL). This percentage is much higher than their initial contribution in POC (22-68 %; Fig. 5),

indicating that attached bacteria preferentially degraded particulate characterizable compounds (PCC) in > 60 µm particles. This is confirmed by the relatively high degradation rates for amino acids and lipids at both sites (Table 3) and the significant decreases of the % weight contributions of these pools to POC by the end of the experiment (Fig. 5). On the other hand, a preference for the PCC in the degraded POC fraction is not very evident when examining TOC mineralization. Indeed, only in PFZ 30 m experiment, did bacteria preferentially mineralize the total characterizable compounds (ΔTCC/ ΔTOC = 105 %; Table 4), which is confirmed by the significant decrease of this characterized fraction (i.e. TAA + TCHO + TL) by the end of the experiment (from 65 to 42 %; Fig. 4). In the other experiments, bacteria mineralized the TCC in more or less the same proportion as in the initial composition (SAr 30 m : ΔTCC/ ΔTOC = 30 % for a initial composition of 31 %; PFZ 200 m : ΔTCC/ ΔTOC = 50 % for a initial composition of 45 %; SAr 200 m : ΔTCC/ ΔTOC = 19 % for a initial composition of 28 % ;

Table 4, Fig. 4). Our results also showed that TCC contributed ~ 38 % (mean of the four experiments) of the TOC pool by the end of the experiments indicating that the composition of TOC becomes more uniform (Fig. 4). This is consistent with the findings of Wakeham et al. (1997b), who found that TCC contributed 24 % and 20 % to the organic carbon in deep-water particles and surface sediments, respectively.

Efficiency of organic carbon utilization

In the present study bacteria apparently turned over 32-38 % and 43-50 % of TOC in the PFZ and SAr biodegradation experiments within ca 14 days, mainly during exponential growth, indicating that mineralization of particles is more effective in SAr than in PFZ. The BGE values, calculated for the log growth phase, ranged from 10 to 21 %, resulting in high CO 2 production, i.e. 79-90 % of the assimilated carbon was respired by heterotrophic bacteria (Table 2). These BGE values are consistent with those reported for sinking particles in the water column (Smith et al., 1995: 9 to 17 %;Sempéré et al., 2000: 3-31 %) as well as for detrital aggregates incubated with deep-sea bacterial communities (Turley and Lochte, 1990: 5 to 80 %). A comparison of the two stations revealed similar BGE values, indicating that bacterial energy requirements may be similar despite different physical, biological and chemical processes at both sites (See study area; [START_REF] Rabouille | Recycling of organic matter in Antarctic sediments: a transect through the polar front in the southern Ocean (Indian Sector)[END_REF]Leblanc et al., in press).

Degradation and mineralization rates of organic matter

Numerous studies of organic carbon decomposition have been undertaken for different matrices of organic matter, yielding rates ranging from less than a day to years. The wide range of values reported for POC degradation or TOC mineralization (Westrich and Berner, 1984;[START_REF] Turley | Microbial response to the input of fresh detritus to the deepsea bed[END_REF][START_REF] Sun | Laboratory studies of oxic and anoxic degradation of chlorophyll-α in Long Island Sound sediments[END_REF][START_REF] Harvey | Kinetics of phytoplankton decay during simulated sedimentation: changes in biochemical composition and microbial activity under oxic and anoxic conditions[END_REF][START_REF] Harvey | Kinetics of phytoplankton decay during simulated sedimentation: changes in lipids under oxic and anoxic conditions[END_REF][START_REF] Rabouille | Recycling of organic matter in Antarctic sediments: a transect through the polar front in the southern Ocean (Indian Sector)[END_REF][START_REF] Sempéré | Microbial decomposition of large organic particles in the Northwestern Mediterranean Sea: an experimental approach[END_REF] might be due to the origin of particles or to different incubation times (i.e longer incubation times yield slower rates), incubation temperatures, oxic or anoxic conditions, static or continual flow systems, as well as different applied models (first-order vs multi-G models or linear vs exponential models). For instance, [START_REF] Sempéré | Microbial decomposition of large organic particles in the Northwestern Mediterranean Sea: an experimental approach[END_REF] found that mineralization rates of > 10 µm Mediterranean particles were well fitted by a 2G-model. By applying equation 2 (Section 3.4) to the results of [START_REF] Sempéré | Microbial decomposition of large organic particles in the Northwestern Mediterranean Sea: an experimental approach[END_REF] rates for the degradation of Mediterranean particles ranging from 0.021 to 0.041 d -1 are determined, which are of the same order as those in the present study (Table 3). On the other hand, [START_REF] Harvey | Kinetics of phytoplankton decay during simulated sedimentation: changes in biochemical composition and microbial activity under oxic and anoxic conditions[END_REF] and [START_REF] Harvey | Kinetics of phytoplankton decay during simulated sedimentation: changes in lipids under oxic and anoxic conditions[END_REF], using a 1G-model, estimated degradation rates for individual chemical fractions (i.e sugars, amino acids and lipids) during a phytoplankton decay. Their values ranged from 8.2 y -1 (k lipids ) to 34.2 y -1 (k sugars ) and were obtained for an incubation period of 45-77 days. However, if their results

were calculated according to equation 2 (Section 3.4), they would range from 2.92 to 8.03 y -1 , again in the same order as the present study. Small differences between these results might be explained by the mathematical approach used for the calculations (i.e linear -TOC decrease this study vs exponential -TOC decrease based on the model used by [START_REF] Harvey | Kinetics of phytoplankton decay during simulated sedimentation: changes in biochemical composition and microbial activity under oxic and anoxic conditions[END_REF]Harvey and[START_REF] Harvey | Kinetics of phytoplankton decay during simulated sedimentation: changes in lipids under oxic and anoxic conditions[END_REF]). Differences in the incubation times (7-17 vs 45-77 days) and in the nature of material may also explain the differences as well.

Mineralization rates of TOC in 200 m samples were higher in SAr than in PFZ waters, although the theoretical sinking fluxes at this depth were 0.43 and 0.57 mmol C m -2 d -1 , respectively (Tables 1 and3). We are aware a single result taken from experimental work where they may be significant errors, both experimental and analytical cannot be used to explain variations in the annual particle fluxes at these stations. However, these results

indicate that organic carbon of sinking particles could be more rapidly remineralized in the The most striking feature of this kinetic study is that in PFZ, mineralization rates of amino acids and lipids associated with > 60 µm particles were two to ten fold higher than sugars (k TAA = 0.032-0.047 d -1 ; k TL = 0.037-0.048 d -1 versus k TCHO = 0.003-0.014 d -1 respectively ; Table 3), whereas mineralization rates of sugars were higher than those of amino acids and lipids in > 60 µm particles in SAr (Table 3). Moreover sugars were more efficiently consumed in SAr than in PFZ experiments (37 and 50 % of their initial amount versus 15 and 18 %, respectively; Table 2). Figure 6 shows significant positive relationships between TL and TCHO in PFZ as well as TAA and TCHO in the time series samples from PFZ and SAr biodegradation experiments. Absence of correlation between TCHO and TL in SAr could not be explained in this study. Such relationship implies that bacteria utilized lipids, sugars and amino acids in the same proportion during the time course of the biodegradation experiment. Additionally, higher slopes of TL and TAA against TCHO confirms that in PFZ bacteria associated to > 60 µm particles preferentially consumed lipids and amino acid rather than sugars. It is important to note that the initial composition of > 60 µm particles in SAr was particularly carbohydrate rich and lean in other components such as lipids and amino acids (Fig. 4). Clearly these results indicate that the way that bacteria used the different fractions of particles was influenced by their initial chemical composition. On the other hand, our results showed that the PAA pool was more rapidly degraded (0.038-0.14 d -1 ) than the PL (0.030-0.10 d -1 ) and PCHO (0.016-0.049 d -1 ) pools for all biodegradation experiments (Table 3). These results are consistent with the initial and final distribution of PAA in POC (Fig. 5) and indicate that dissolution processes from particulate to dissolved phase occurred more intensively with respect to amino acids rather than sugars and lipids, suggesting higher ectoenzymatic activities of proteins compared to those of sugars and lipids [START_REF] Smith | Intense hydrolytic enzyme activity on marine aggregates and implications for rapid particles dissolution[END_REF].

Chemical composition of > 60 µm particles

Recent studies indicated that sugars, amino acids and lipids accounted for 80 % of the organic carbon in particles exported from the euphotic zone (Wakeham et al., 1997b), with the highest contribution by amino acids (Lee et al., 2000, 60 %) followed by lipids (Wakeham et al., 1997a, 15 %) and carbohydrates (Hernes et al., 1996, 5 %). In the present study, these components accounted only 28-65 % of organic carbon (see initial composition of TOC, Fig. 4). One possible explanation is that in situ pumps collect a wide spectrum of particle sizes including large and small (and already degraded) particles, whereas sediment traps, which were used in previous studies collect only fast large sinking particles (that are probably less degraded). Alternatively, these results may be due to natural variability or to the assumptions made for the carbon conversion factors. Our results also showed that the total uncharacterized carbon (TUC) fraction was higher at 200 m (55 % PFZ; 72 % SAr) than at 30 m (35 % PFZ; 69 % SAr), which is in agreement with previous investigations (Wakeham et al., 1997b;[START_REF] Hedges | The molecularly-uncharacterized component of nonliving organic matter in natural environments[END_REF].

The initial chemical composition of > 60 µm particles varied markedly between the two sites. Our results indicated that the fraction of TOC that could be attributed to the main characterized biochemical classes (amino acids, lipids and sugars) was higher in the PFZparticles (65 % at 30 m and 45 % at 200 m) than in the SAr-particles (31 % at 30 m and 28 % at 200 m) (Fig. 4). Amino acids were predominant (200 m) or relatively abundant (30 m) in PFZ-particles (29-40 % of TOC), whereas carbohydrates were relatively more abundant in SAr surface waters (15-19 % of TOC). Since amino acids are typical of fresh algal detritus and are more rapidly degraded than other biochemical classes [START_REF] Harvey | Kinetics of phytoplankton decay during simulated sedimentation: changes in biochemical composition and microbial activity under oxic and anoxic conditions[END_REF][START_REF] Harvey | The chemical composition and cycling of particulate and macromolecular dissolved organic matter in temperate estuaries as revealed by molecular organic tracers[END_REF]) their high relative abundance in PFZ suggests that particles were initially less degraded in PFZ waters than in the SAr waters.

Alternatively, different planktonic populations might explain variations in the chemical composition as indicated above. Biological observations indicated that diatoms (partly dissolved) as well as dinoflagellates were relatively more abundant (particularly PseudoNitszschia sp.) in SAr, which is confirmed by particulate lipid analyses (data not shown) whereas PFZ was characterized by an important accumulation of coccoliths of Michaelsaisia sp. (Leblanc et al., in press).

Other investigations reported higher potential dissolution rates of biogenic silica (Leblanc et al., in press) and higher BP in surface waters (0-150 m) of the SAr compared to the cold waters of the PFZ (unpublished observations). It is well known that organic matter decomposition is related to silica dissolution [START_REF] Lewin | The dissolution of silica from diatoms walls[END_REF][START_REF] Bidle | Accelerated dissolution of diatom silica by marine bacterial assemblages[END_REF], which is controlled by temperature [START_REF] Nelson | Production and dissolution of biogenic silica in the ocean : revised global estimates, comparison with regional data and relationship to biogenic sedimentation[END_REF] as well as by bacterial activity [START_REF] Bidle | Accelerated dissolution of diatom silica by marine bacterial assemblages[END_REF]. Therefore, we suggest that > 60 µm particles in SAr are depleted in amino acids and lipids because they were more degraded at the time of collection, due to the high dissolution rate of the silica frustules as well as the higher BP and temperature, encountered in these waters (Table 1). Conversely, colder temperatures and lower bacterial activity in the PFZ probably prevent extensive dissolution of dead diatoms and subsequent amino-acid and lipid consumption by bacteria. This is in consistent with other investigations indicating that PFZ waters are particularly enriched in biogenic silica compared to POC (Leblanc et al., in press).

The higher abundance of carbohydrates in > 60 µm particles in SAr waters could derive from different macromolecular material that is resistant to bacterial degradation, but is measurable by conventional analysis [START_REF] Hedges | Evidence for non-selective preservation of organic matter in sinking marine particles[END_REF]. Refractory organic or inorganic matrices may shield intrinsically labile organic substances [START_REF] Knicker | 13 C and 15 N NMR spectroscopy investigation on the formation of fossil algal residues[END_REF] which may then persist much longer than other organic compounds, such as proteins and lipids.

Conclusions

The main results concerning > 60 µm particles degradation in the two sites examined (PFZ, SAr) in the southern Indian Ocean obtained by bulk analysis of POC, DOC, amino acids, sugars and lipids as well as bacterial production measurements are summarized below :

• Bacteria preferentially degraded PCC (PCC = PAA + PCHO + PL) in a high percentage (96 %).

• By the end of the experiment, the composition of particles became uniform and the sum of biochemicals analyzed (sugars, amino acids and lipids) contributed ~ 36 % of the TOC pool.

• During the experiments, 32-38 % and 43-50 % of TOC were mineralized and considered as labile material in the PFZ and SAr, respectively. This material was utilized with a bacterial growth efficiency (BGE) of 10-21 % (PFZ) and 12-17 % (SAr), indicating that 79-90% of the incorporated carbon from large particles was respired as CO 2 .

• This study revealed that the initial relative abundance of the three main classes of organic matter, including amino acids, lipids and sugars, greatly varied between SAr and PFZ, with sugars being more abundant in than in PFZ-particles (8-9 % of TOC). Additionally, a kinetic model indicated that in PFZ mineralization rates of amino acids and lipids were two to ten fold higher than those of sugars, whereas the opposite was the case in the SAr biodegradation experiments. These results strongly suggest that bacterial decomposition of organic matter is influenced by its initial chemical composition.

• The differences observed in initial particle composition and mineralization rates between the two sites (PFZ and SAr) may be best explained by the higher dissolution processes of silica as well as by higher temperatures and BP in SAr waters.

These observations suggest that both processes (different origin of particles and selective biodegradation) may act together and affect the composition of sinking material to the ocean interior. Our study suggests that bacteria rapidly mineralized a higher proportion of sinking particles leaving the euphotic layer in SAr rather than in PFZ waters. Therefore it is not surprising that there is little material reaching the sea-floor in SAr compared to PFZ [START_REF] Rabouille | Recycling of organic matter in Antarctic sediments: a transect through the polar front in the southern Ocean (Indian Sector)[END_REF]. The coupling of colder temperatures, high biogenic silica and lower mineralization rates at PFZ, probably can facilitate the > 60 µm particles to reach the sea-floor in this region. Theoretical sinking fluxes at 200 m depth for > 60 µm particles were calculated according to the formula:

F = v x C
where: F: is the calculated flux v: is the sinking velocity (m s -1 ) C: is the concentration (nM)

  SAr (depth ~ 5000 m) water column than in PFZ (depth ~ 4000 m), being consistent with the work of Rabouille et al. (1998) who showed higher POC flux deposited at the sediment-water interface in PFZ than in SAr.

Figure captions Figure 1 .

 captions1 Figure captions

Figure 2 .

 2 Figure 2. Time course responses of particulate and total fractions of organic carbon, amino acids,

Figure 3 .

 3 Figure 3. Time course responses of particulate and total fractions of organic carbon, amino acids,

Figure 4 .

 4 Figure 4. Carbon contributions of characterized biochemicals to TOC at the beginning and end of

Figure 5 .

 5 Figure 5. Carbon contributions of characterized biochemicals to POC at the beginning and end of

Figure 6 .

 6 Figure 6. Concentrations (µM C) of total lipids (a) and amino acids (b) versus total sugars in the

  Figure1

  ; Figs.2 and 3). In controls experiments (HgCl 2 -poisoned samples), BP was not detectable; we observed slight variation of TOC (≤ 10 %) indicating that adsorption of POC and/or DOC on the bottle walls played a minor role in the TOC variations. POC concentrations in PFZ, for both 30 and 200 m samples decreased by 45 % and 21 % of their initial concentrations, respectively. At both depths for SAr-particles, POC concentrations decreased by only ~23 % of the initial concentration (Table2; Figs.2 and 3). The greatest decrease in TOC and POC concentrations were observed during the first two days (Figs.2 and 3). Hence there was a sharp decrease of POC concentrations, by 323 µM C

(36 % of initial POC) after 1 day at PFZ-30 m, 69 µM C (19%) after 1 day at PFZ-200 m, 46 µM C (10%) after 2 day at SAr-30 m and 54 µM C (32 %) after 1 day at SAr-200 m, thereafter concentrations decreased more slowly until the end of the incubation.

  Wakeham, S.G., Hedges, J.I.,Lee, C., Peterson, M.L., Hernes, P.J., 1997a. Compositions and transport of lipid biomarkers through the water column and surficial sediments of the equatorial Pacific Ocean.Deep-Sea Research II 44, 2131-2162.

	Wakeham, S.G., Lee, C., Hedges, J.I., Hernes, P.J., Peterson, M.L., 1997b. Molecular
	indicators of diagenetic status in marine organic matter. Geochimica et Cosmochimica Acta
	61, 5363-5369.
	Westrich, J., Berner, R., 1984. The role of sedimentary organic matter in bacterial sulphate
	reduction: the G model tested. Limnology and Oceanography 29, 236-249.
	Yoro, S.C., Panagiotopoulos, C., Sempéré, R., 1999. Dissolved organic carbon
	contamination induced by filters and storage bottles. Water Research 33, 1956-1959.

Table 1 :

 1 Summary of particle sampling conditions and in situ seawater characteristics.

	PFZ: Polar Front Zone ; SAr : Sub-Antarctic region.
	Station	PFZ		SAr
	Location	46°01.22′S; 62°56.70′E	44°10.92′S; 63°23.37′E
	Sampling depth (m)	30	200	30	200
	Date of sampling	18/01/99	21/01/99	06/02/99	08/02/99
	Seawater temperature (°C) *	9	5	14	12
	Salinity	33.69	33.94	34.35	34.82
	POC (> 60 µm) (nM)	17.6	5.7	6.2	4.3
	In situ TOC (µM) **	52	45	75	59
	In situ BP (ng C l -1 h -1 ) **	44.6	3.6	153	4.4
	Flux (mmol C m -2 d -1 )		0.57		0.43
	Biogenic silica (mmol m -2 ) ***	38		25
	PP (mmol C m -2 d -1 ) ***	28		47
	* Seawater temperature at the sampling depth.

** R. Sempéré, unpublished observations. *** Integrated values (0-150 m) according to

Leblanc et al. (in press

).

Table 2 :

 2 Bacterial growth efficiencies (BGE%) calculated from TOC utilization and integrated bacterial production (IBP) calculated for the log phase of the exponential growth and net

	variations of different pools of organic carbon (∆TOC, ∆POC, ∆TAA, ∆PAA, ∆TCHO,
	∆PCHO, ∆TL, ∆PL) expressed as percentages of initial amount of organic carbon. ∆% was
	calculated according the formula: ∆% = (final concentration -initial concentration)/ initial
	concentration.
	Sample	Incubation period (d) BGE %				Biochemical fractions
				OC		AA		CHO
				TOC	POC TAA	PAA	TCHO PCHO
	PFZ 30 m	13	10	-32	-45	-61	-95	-18	-21
	200 m	17	21	-38	-21	-54	-65	-15	-30
	SAR 30 m	14	12	-43	-24	-30	-88	-50	-54
	200 m	7	17	-50	-22	-29	-95	-37	-34

Table 3 :

 3 Degradation (POC, PAA, PCHO, PL) and mineralization (TOC, TAA, TCHO, TL) rates determined in biodegradation experiments according to the equation (2). Units in µmol C l -1 d -

	1 /µmol C init l -1
		PFZ		SAr
	Biochemical fraction	30 m	200 m	30 m	200 m
	k TOC	0.024	0.022	0.030	0.072
	k POC	0.034	0.012	0.017	0.031
	k TAA	0.047	0.032	0.021	0.041
	k PAA	0.073	0.038	0.062	0.14
	k TCHO	0.014	0.003	0.035	0.053
	k PCHO	0.016	0.018	0.038	0.049
	k TL	0.048	0.037	0.010	0.021
	k PL	0.050	0.034	0.030	0.10

Table 4 :

 4 Net variations (in µM C) of the different pools of organic carbon (∆TOC, ∆POC, ∆TAA, ∆PAA, ∆TCHO, ∆PCHO, ∆TL, ∆PL) calculated according to the formula: ∆ = (final concentration -initial concentration). ∆POC (µM C) ∆PAA (µM C) ∆PCHO (µM C) ∆PL (µM C) ∆PCC/∆POC ∆TOC (µM C) ∆TAA (µM C) ∆TCHO (µM C) ∆TL (µM C) ∆TCC/∆TOC

	PFZ 30 m	437	324	9	143	109 %
	PFZ 200 m	114	87	8	16	98 %
	SAr 30 m	111	55	50	6	100 %
	SAr 200 m	37	24	3	2	78 %
	PFZ 30 m	474	332	19	146	105 %
	PFZ 200 m	263	97	9	25	50 %
	SAr 30 m	346	24	77	2	30 %
	SAr 200 m	235	13	26	5	19 %

∆PCC : is the sum of ∆PAA + ∆PCHO + ∆PL ∆TCC : is the sum of ∆TAA + ∆TCHO + ∆TL

Acknowledgements

We are grateful to A. Bianchi, R. Fukuda, K. Leblanc, K. Mopper and D. Delmas and two anonymous reviewers for comments on the manuscript and fruitful discussions. Our thanks to the captain and crew of Marion Dufresne for excellent service at sea as well as to Jacques Le Fèvre (leader of the Antares project) and M. Denis (chief scientist of Antares-4 oceanographic cruise). We also thank Catherine Jeandel, Claudie Bournot-Marec, and Laurent Coppola for help with particle collection and batch preparations during the cruise. This research was supported by France-PROOF Antares-4 project. Financial support for C.P. came from the Alexander S. Onassis Public Benefit Foundation, Greece.


Grimaldo Silva

Anne-Hélène Olivier

Armel Crétual

Julien Pettré

Thierry Fraichard

Human inspired effort distribution during collision avoidance in human-robot motion

Recent works in the area of human robot motion showed that behaving in a human-like manner allows a robot to reduce global cognitive effort for people in the environment. Given that collision avoidance situations between people are solved cooperatively, this work models the manner in which this cooperation is done so that a robot can replicate their behavior. To that end, hundreds of situations where two walkers have crossing trajectories were analyzed. Based on these human trajectories involving a collision avoidance task, we determined how total effort is shared between each walker depending on several factors of the interaction such as crossing angle, time to collision and speed. To validate our approach, a proof of concept is integrated into ROS with Reciprocal Velocity Objects (RVO) in order to distribute collision avoidance effort in a human-like way.

I. INTRODUCTION

Consider a robot whose goal is to reach a particular target. In between its current position and its goal, this robot can encounter an unbounded number of static and dynamic obstacles. Our focus in this work lies on the interaction behavior when avoiding dynamic obstacles, specifically people. We are interested in studying how a robot should move among people, what we define as a Human Robot Motion (HRM) problem. In the context of HRM, it is not sufficient to only guarantee collision-free motions [START_REF] Fraichard | Inevitable collision states-a step towards safer robots?[END_REF]. The main objective is to provide robots with human-like behavior when avoiding collision with people, which can involve a broad range of concepts such as social spaces [START_REF] Lindner | Towards a formalization of social spaces for socially aware robots[END_REF] and legibility concerns [START_REF] Lichtenthaler | Influence of legibility on perceived safety in a virtual human-robot path crossing task[END_REF], in what we call an appropriate motion.

In the present work, we focus on one characteristic of human-human interaction during collision avoidance that is the mutual sharing of the adaptations performed to solve a collision [START_REF] Olivier | Collision avoidance between two walkers: Role-dependent strategies[END_REF]. We aim at better understanding the contribution of each walker to avoid a collision, which is expressed in terms of the amount of change in both desired energy and time to the goal, what we call collision avoidance effort. We hypothesize that replicating this human behavior in a robot would imply that people will be able to rely on their implicit *This work is partially supported by the Brazilian National Counsel of Technological and Scientific Development (CNPq) and the LabEx PERSYVAL-Lab (ANR-11-LABX-0025-01) funded by the French program Investissement d'avenir. 1 Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LIG, 38000 Grenoble, France 2 Lab. Mouvement Sport Santeé (M2S), UFRAPS, Université Rennes 2-ENS Cachan, Avenue Charles Tillon, CS24414, 35044 Rennes, France 3 INRIA, Centre de Rennes Bretagne Atlantique, Campus Universitaire de Beaulieu, 263 avenue du Général Leclerc, 35042 Rennes, France E-mail: jose.jgrimaldo@gmail.com, armel.cretual@univ-rennes2.fr, {anne-helene.olivier, julien.pettre, thierry.fraichard}@inria.fr natural behavior when avoiding a collision with a robot [START_REF] Vassallo | How do walkers behave when crossing the way of a mobile robot that replicates human interaction rules?[END_REF]. This could be an advantage given that human-like motion has been shown to reduce planning effort for all the people in the environment [START_REF] Carton | Measuring the effectiveness of readability for mobile robot locomotion[END_REF]. In this context it is also worth noting that people tend to choose collision avoidance strategies based on situational factors, such as heading, rather than personal characteristics [START_REF] Knorr | Influence of person-and situation-specific characteristics on collision avoidance behavior in human locomotion[END_REF] such as gender or personality -or lack thereof in case of a robot.

Recent works have studied the proportional contribution to avoid a collision in perpendicular crossing scenarios between two walkers [START_REF] Olivier | Collision avoidance between two walkers: Role-dependent strategies[END_REF]. They found that there is a statistically significant difference in the amount of contribution performed by each walker to reduce the perceived risk of future collision. This contribution is done by adapting their respective trajectories depending on their role in the collision avoidance: the walker who arrives second at the crossing performed more adaptation than the walker who arrives first. Authors explained this as a consequence of the asymmetric shape of personal space. To further expand these results for a wider range crossing angles (not just perpendicular) and also to better characterize this behavior, our work presents a model designed from the evaluation of hundreds of collision avoidance situations between two walkers.

Our approach is composed of two core components that are a result of this evaluation. The first component is a definition of collision avoidance effort, while the other component is a representation of the effort distribution based on a number of situational factors that describe a given collision situation. These components are tested using the Robot Operating System (ROS) with Reciprocal Velocity Objects (RVO) [START_REF] Claes | Collision avoidance under bounded localization uncertainty[END_REF] to simulate the navigation of both people and robot. However, instead of RVO's standard equal share, our approach is used to predict the amount of contribution to avoid a collision that is expected from each agent.

To our knowledge, this is the first work that explicitly accounts, based on empirical data from walkers in collision avoidance situations, for the manner in which a person expects the effort to be shared in a given scenario.

A. Outline of the paper

In Sec. II, the state-of-the-art is presented and previous works are contrasted with our method. Our first contribution, a measure of collision avoidance effort for a given trajectory, is presented in Sec. III. This measure and the manner in which people distribute it in a given collision situation are then modeled based on the evaluation of hundreds of collision avoidance scenarios in Sec. IV. To evaluate the impact of these changes in actual trajectories, simulated experiments are done into ROS using RVO in Sec. V. Finally, the conclusion is presented in Sec. VI.

II. State-of-the-art and contributions

Understanding and replicating human behavior has been a common trend in recent human-robot motion research. To that effect, many human-like models have been used to allow a robot to replicate or account for a person's behavior. For example, in [START_REF] Cosgun | Anticipatory robot path planning in human environments[END_REF], a robot is able to predict how standing people that are inadvertently blocking its way will react to its motion, that is, in which manner they will allow the robot to pass and how much effort this requires. This allows a robot to pass through regions that would have been hard or impossible otherwise. This is done through the use of the Social Force Model (SFM) [START_REF] Zanlungo | Social force model with explicit collision prediction[END_REF] to calculate people's reaction (as a group or individual) to a particular robot plan.

For situations when people are already in motion, in [START_REF] Shiomi | Towards a socially acceptable collision avoidance for a mobile robot navigating among pedestrians using a pedestrian model[END_REF] a robot navigated inside a shopping mall using an approach also based on SFM. However, in their work, the amount of contribution that each person did to avoid a collision to the robot was not compared to a people-only baseline. To better quantify the amount of change in a person's motion caused by the robot, in [START_REF] Ferrer | Proactive kinodynamic planning using the extended social force model and human motion prediction in urban environments[END_REF], a measure, called social work, was used as an additional cost for each candidate trajectory to the robot's goal. Such formulation allows one to give precedence to trajectories that have smaller impact on the motion plan of nearby people.

In the aforementioned works, the impact of a robot trajectory in a person (or group) is minimized without accounting for people's expectations. However, in [START_REF] Olivier | Collision avoidance between two walkers: Role-dependent strategies[END_REF] it was shown that humans walkers mutually solved the collision avoidance task but their contribution is not symmetric. In particular, in an orthogonal crossing situation, a person who will arrive second at the crossing contributes more than the other to avoid the collision in terms of motion adaptation. Therefore, attempting to solve a collision situation by simply minimizing the impact in a person's original motion plan would lead to a robot behavior that is not human-like. In our work the expectations of people concerning their contribution to avoid a collision in a given situation are defined in the context of the current collision scenario, accounting for situational factors such as: crossing angle, crossing order and time to collision.

In our previous work, presented in [START_REF] Silva | Human robot motion: A shared effort approach[END_REF], the definition of effort was based on progression to the goal i.e. the faster one arrives at the goal the better. This implies, for most cases, that one preferred speed should be its maximum speed. This is not sufficient to properly explain human behavior, as people do not walk at their maximum speed and furthermore often accelerate (or decelerate and change heading) [START_REF] Olivier | Collision avoidance between two walkers: Role-dependent strategies[END_REF] to avoid a collision. Moreover, the effort distribution in [START_REF] Silva | Human robot motion: A shared effort approach[END_REF] does not account for several situational factors such as crossing angle and time to collision. We considered these factors because they may have an influence on the perceived future risk of collision for a given situation. Obviously, on one hand, time to collision indicates how soon the collision will occur. On the other hand, the crossing angle may change how the future distance of closest approach is projected in the personal space of the walker. Indeed, personal space was shown to be elliptical during human locomotion [START_REF] Gérin-Lajoie | The negotiation of stationary and moving obstructions during walking: anticipatory locomotor adaptations and preservation of personal space[END_REF], this can change the threshold in which a person perceives their personal as being invaded when crossing through different angles. These factors (among others) and their impact are accounted for in this work, which is based on empirical results obtained from people in collision avoidance situations.

Our work brings novel contributions in the area of humanrobot motion. We present a definition of collision avoidance effort in order to describe scenarios in terms of total effort and also its distribution among people. Furthermore, we also present this as a human-like model for robots that explicitly accounts for situational factors such as crossing angle, crossing order and time to collision. This allows one to define what are the situations in which more effort is expected and also how changes in one or more factors affect the effort distribution.

III. Effort-based trajectory cost function

In this section, we describe the cost of a given trajectory in terms of energy and time. This cost is used to calculate the collision avoidance effort which allows one to estimate the relative effort performed by each agent in a collision avoidance interaction.

A person walking towards his/her goal dedicates a certain amount of energy to reach it, the amount of energy dedicated, for his/her chosen speed, tends to be optimal [START_REF] Zarrugh | Optimization of energy expenditure during level walking[END_REF]. Furthermore, the total energy required for a given trajectory

π p = p p (0), p p (1), • • • , p p (t), • • • , p p (n) with each position p(t) = (x p (t), y p (t)) ∈ R × R,
is defined in the context of our work, based on [START_REF] Zarrugh | Optimization of energy expenditure during level walking[END_REF], as

E(π p ) = n ∑ t=1 32 + 0.0050v p (t) 2 (1)
which represents a quadratic cost function in terms of speed v p (t) at time t for the trajectory π p in meters per minute. It returns the cost in terms of calories per minute per kilogram.

A. Describing trajectories in terms of time and energy

A person going towards its goal without any obstacle, dynamic or otherwise, might choose what is defined as an optimal-speed walk [START_REF] Zarrugh | Optimization of energy expenditure during level walking[END_REF] which refers to the most energy efficient (in terms of calories) walking speed for a given person. Empirical evidence found that this value for an average person is of 80 m/min or 1.33 m/s [START_REF] Zarrugh | Optimization of energy expenditure during level walking[END_REF]. For a robot, finding the most human-like trajectory, at least in terms of energy efficiency, to a given goal could be defined simply as

π * π = arg min π r ∈Π r E(π r ) (2)
where Π r is the set of admissible trajectories of robot r to its goal -trajectories that are both safe (collision-free) and appropriate.

Outside of the optimal-speed walk, in terms of energy spent per meter walked, there are always two speeds that spend the same total energy: one faster than optimal-speed walking and one slower. Walking faster means smaller time to goal while walking slower can allow for greater safety, exploration and also etiquette. In this sense, at least for the task of goal reaching without obstacles there is no incentive to walking slower than the optimal-speed walk.

In the case where dynamic obstacles with potential collision risk are involved, more specifically people, one can increase or reduce their speed and also change their heading to avoid a collision. This in turn can change their original balance between the amount of energy invested and the time to the goal. This trade-off is important in the sense that it can allow even for an energy inefficient action to be justified as it helps minimize global energy cost to avoid a collision. This time and energy trade-off for a person can be represented as a trajectory cost function

Γ : [R 2 , • • • , R 2 ] → R
and represents the cost of a trajectory (with fixed time step), defined as

Γ(π p ) = E(π p ) + ζ p (v des p ) • T (π p ) (3)
where T (π p ) is the time required to execute this trajectory and v des p is the desired speed choice for a person, which is not necessarily the most energy efficient, in case there are no obstacles to its goal. Moreover, ζ : R → R is a function of a given speed that returns a value which makes a given time energy trade-off optimal only when the agent p arrives at the goal with the desired energy and time. That is, even in cases where the agent arrives earlier to the goal while using more energy or when it arrives later while using less energy, the value of Γ(π p ) will not be minimum. Thus, for a given v des p the value of ζ (v des p ) that makes this chosen time energy trade-off optimal for Eq. 3 can be pre-calculated for any speed. The shape of the time energy trade-off function, given ζ , is showcased in Fig. 1.

The value ζ p (v des p ) is of fundamental importance for our formulation given that it defines the willingness of a person to spend energy to reach their goal sooner. For instance, if ζ is defined as zero, the agent will prefer the most costefficient speed. On the other hand, higher values of ζ (v des p ) progressively indicate to the agent that higher energy costs are worth, up to a point, in order to arrive sooner to his goal.

Each person has a different trajectory energy cost function and thus a different ζ (v des p ). Several ways are being considered to approximate an individual trajectory energy cost, such as using height and gender as predictors, but in the current iteration of our formulation, the most energyefficient speed is set as a grand average found in empirical tests in the literature [START_REF] Zarrugh | Optimization of energy expenditure during level walking[END_REF].

B. Collision avoidance effort

As we established in Eq. 3, to reach a goal while avoiding a collision an agent is forced to change its time energy tradeoff to non-optimal values. This change is what we define as collision avoidance effort. Let ∆E(π p ) and ∆T (π p ) represent, respectively, the change in energy and time between the current Γ(π p ) and the optimal time energy trade-off from an ideal situation without obstacles -the baseline. Thus, we represent collision avoidance effort as p ) in case one walks straight to the goal without obstacles. Thus, for each case the minimal value is reached only when the agent arrives at his goal at the desired time using the desired amount of energy. Thus, in case a person accelerates, decelerates or move its heading away from the goal in order to avoid a collision its value will not ever be minimal.

F(π p ) = ∆Γ(π p ) = ∆E(π p ) + ζ (v des p ) • ∆T (π p ) (4)
The value F(π p ) will only be minimal when the person arrives in his goal with both the desired time and energy.

In this case, F(π p ) will be zero.

Given the aforementioned formulation, the effort distribution coefficient (EDC) of a given agent p, that is, their contribution to collision avoidance in relation to another agent q, represented as α p,q , can be directly calculated using

α p,q = F(π p ) F(π p ) + F(π q ) (5)
IV. Human-like effort distribution For a robot, when avoiding collision with a person it is necessary to account for social expectations instead of an approach based on, for instance, the minimization of total effort to avoid a collision. For example, a person that is coming from behind another one generally does not expect the person in front to collaborate in order avoid the collision, even if they are aware of each other. Moreover, depending on the crossing order, relative speed and relative position between people the distribution of effort to avoid a collision won't be necessarily equal.

In this section, we estimate the value of α r,p for the robot r based on situational factors that describe a given collision situation. This is done by analyzing hundreds of collision avoidance scenarios, particularly the trajectories for each person, which are required to calculate F(π p ). This allows us to estimate α r,p by establishing a relationship between the situational factors that describe a given situation and the actual collision avoidance effort distribution.

A. Behavior of people during collision avoidance

To understand the behavior of people when avoiding collisions among each other, we first designed an experiment involving interactions between two walkers having crossing trajectories. Participants volunteered to perform the experiment and our study conforms the declaration of Helsinki. The experiments were composed of over 450 runs divided near equally into five different crossing angles: 30 • , 60 • , 90 • , 120 • and 150 • . Several filters were used into the data to remove data with too much noise and situations without collision avoidance behavior, after which 202 runs remained for analysis.

The area designed for the experiment is equal to a square with length twelve. As can be seen in Fig. 2, there are occluding walls each with three meters in length at the middle of each square side that are oriented towards its center. The walls are meant to separate participants in such way that they are not able to see all other participants at the same time. This allows walkers to reach a comfort speed and a stable state before interacting with the other walker. Participants were told to reach the opposite side of the experiment area at comfort speed and were informed that they will interact with another walker.

The observation zone in which we concentrate our attention is a circular region with three meters radius in the center of the square. This region is meant to provide sufficient space so that subjects can adapt their speed and orientation during collision avoidance.

Each run of a collision avoidance scenario involves four participants, however only two at a time will ever enter the observation zone at each run. This is necessary as in some crossing scenarios a person may see another one as soon as they are into their initial positions, as such, it is necessary to add some uncertainty to avoid possibly altering their behavior. The non-participants, as can be see in Fig. 2, won't enter the observation zone and thus do not participate in the collision avoidance.

The synchronization of the participants initial position and start time is done automatically in order to allow for several different collision situations.

B. Roles during collision avoidance

The information provided in the experimental evaluation of human behavior, detailed in Sec. IV-A, and in accordance to the work of [START_REF] Olivier | Collision avoidance between two walkers: Role-dependent strategies[END_REF], two main roles depending on the crossing order can be identified. Participants are able to identify their future crossing order early in the interaction since few inversions occur within the interaction [START_REF] Olivier | Collision avoidance between two walkers: Role-dependent strategies[END_REF], [START_REF] Knorr | Influence of person-and situation-specific characteristics on collision avoidance behavior in human locomotion[END_REF]. This can be done using the optic variable named bearing angle β and its derivative, both variables are shown in Fig. 3. The rate of change of a given β (its derivative) can be a strong indicator of potential collision. This was established in [START_REF] Cutting | How we avoid collisions with stationary and moving obstacles[END_REF], where a rigorous study of the role of β and its derivative β was made. The derivative of the bearing angle also determines the crossing order, which represents two main roles during collision avoidance: who crosses first and who crosses last. As such, two important conclusions have been reached by analyzing β and its derivative during a situation involving a potential collision [START_REF] Cutting | How we avoid collisions with stationary and moving obstacles[END_REF]:

• when β r,p is diverging over time i.e. going away from the center of the field view, the agent r is crossing first; • conversely when β r,p is converging over time i.e. going towards the center of the field of view, the agent r is crossing last.

The role of crossing order in a collision situation has been subject of much research. In particular, in [START_REF] Olivier | Collision avoidance between two walkers: Role-dependent strategies[END_REF] for the case of 90 • crossing angle it was shown that the person who is crossing first in average contributes less to avoid a collision than who crosses last. Fig. 4: Proportion of effort that was done by the person who crosses first with respect to total effort required to avoid a collision. In situations that require higher total collision avoidance effort its distribution shift the majority of the effort towards the last crosser. Boxplots in blue indicate that there is a significant difference between the contribution of the first crosser and last crosser (p-value<0.05) and in red indicate no significant difference (p-value>0.05). Values are considered outliers when outside 99.3% coverage.

C. Variability in effort distribution

Let π first and π last be, respectively, the first and last crosser trajectories. Based on the analysis of the whole dataset with people in pairwise interaction to avoid a collision, that was done for each of these roles for all crossing angles, paired ttests show that the last crosser contributed more to collision avoidance task when the combined total, that is F(π first ) + F(π last ), is between 0.55 and 0.165 (p-value<0.05). There was no significant difference in the low effort condition in the interval between 0 and 0.55. Thus, whenever a relatively small amount of effort is necessary to avoid a collision the distribution of effort varies without bound between both people, as shown in Fig. 4.

Although a clear reason for this behavior is not apparent, one possible explanation is that crossing order is less relevant in smaller crossing angles, such as 60 • , which in our experiments required, in average, less collision avoidance effort. This can be seen in Fig. 5, where the difference in effort distribution between the first and last crosser is comparatively small in comparison to other crossing angles.

D. Avoiding collision in non-trivial cases

The proportion of collision avoidance effort required for the person crossing last increases in correlation with the total amount of effort in a given collision avoidance scenario, as was shown in Fig. 4. Thus it is necessary to determine what are the conditions that engender higher or smaller effort in a given collision avoidance scenario.

To explain the effort of a given collision scenario we model it based on four variables: crossing angle φ , difference in speed, deviation from baseline bearing angle z r,p = β r,pφ r,p 2 and time to collision; the time to collision represents the amount of time in which a collision will happen in case no change in the velocity vector is made. Some of these variables can be visualized in Fig. 3.

Both the difference in people speed and z are calculated in relation to the first crosser. Thus, for each crossing angle we fit the data to a Generalized Linear Model (GLM), with a Binomial distribution and a Logit link function. The GLM was chosen, instead of a linear regression, as it allows for constant change in predictors (situational factors) to be able to cause non-constant change in response. This is important as the increase in total collision avoidance effort causes a non-constant increase in the proportion of effort done by the last crosser.

A GLM model was fitted to the data of the first and of the last crosser (p-value<0.05). Do note that these p-values are valid only within the region where effort is bigger than 0.035, given that the spread of effort distribution when absolute collision avoidance effort is small would be too high to allow for reliable prediction.

An example of effort difference between first and last crosser can be seen in Fig. 5, where the evaluated model indicates that, in average, the upper bound for effort invested by the first crosser remains nearly constant while the last crosser effort increases unbounded as the collision avoidance problem becomes more difficult. The cases of highest effort happens whenever the current crossing order is not respected e.g. one agent yields when it should pass first, as can be seen in the lower left of each individual surface in Fig. 5. Do note that, as stated in Sec. IV-C, in cases which require relatively small amounts of total effort the spread of the effort distribution is high, as such, the effort distribution in these cases is not consistent with the values predicted by our generalized linear model.

E. Discussion

The manner in which people share effort is consistent over situations with high total collision avoidance effort. Our model allows a robot to evaluate situational factors in order to estimate how effort is distributed among roles. The focus on these factors is inspired on recent works which highlight the importance of situational factors (instead of personal characteristics) in explaining collision avoidance behavior [START_REF] Knorr | Influence of person-and situation-specific characteristics on collision avoidance behavior in human locomotion[END_REF]. Although this model can be applied to multiple people by considering each possible pair-wise interaction separately, this could generate unrealistic behavior when dealing with groups of people.

There are other factors that can affect the effort distribution which were not accounted for in this work. For instance, the gender of a person may affect both the degree of collaboration [START_REF] Van Basten | Exploiting motion capture to enhance avoidance behaviour in games[END_REF], the size of a person's personal space and also group organization [START_REF] Costa | Interpersonal distances in group walking[END_REF], which may impact overall behavior. Moreover, a person may decide to yield to a child or an older person even if situational factors indicate that passing first is the expected behavior, in what can be called a polite behavior. V. Experiments in ROS using RVO

The simulated experiments were performed with two main goals in consideration. One is to evaluate if the chosen situational factors are consistent to explain common collision scenarios, while the other helps to validate if the generated effort distribution is consistent with observed data.

A. Finding effort distribution in terms of RVO Consider a situation where two agents q and p, with desired velocities v des q and v des p need to avoid a collision with each other. In this case, RVO finds the smallest change in the relative velocity (v des qv des p ) that avoids a collision between them [START_REF] Van Den Berg | Reciprocal n-Body Collision Avoidance[END_REF], this is given by u as u = ( arg min

v∈∂ VO τ q|p v -( v des q -v des p ) ) -( v des q -v des p ) (6)
where ∂ VO τ q|p is the set of changes in relative velocity that are in the threshold between collision and no collision -the minimum change in relative velocity that avoids a collision.

Commonly, RVO shares the change in relative velocity equally between the two agents [START_REF] Van Den Berg | Reciprocal n-Body Collision Avoidance[END_REF], that is, 1 2 u for each. However, when an agent represents a model of a person's behavior this is not always the correct approach. As such, our work tackles the problem of mapping how much an agent should contribute to avoid a collision into α, that is used instead of the equal share. To that end, given the effort defined in Eq. 4, each agent goal and situational factors of all agents, calculating the k that translates to the desired effort distribution in terms of RVO is trivial.

Another issue is the large spread of effort distribution in small collision avoidance effort situations. Given that RVO requires effort to be reciprocal, it's not evident how to translate this optional cooperative effort into its model. Thus, collision avoidance scenarios that require smaller total collision avoidance effort are set to have equal effort distribution while when total collision avoidance increases the effort distribution is shifted to the actual model-based effort distribution value. Thus, let EDC = α r,p , we represent the desired behavior as

f (π p , π q ) = 1
1 + e -γ(T (π p )+F(π q )-c)

RVO-EDC(π p , π q ) = 0.5 + (EDC -0.5) f (π p , π q ) (8) where c = 0.03 and γ = 260 are defined based on the empirical data as to allow for smooth transition from equal distribution to using EDC depending on the total collision avoidance effort.

B. Simulated experiments

In the simulated experiments, the person and the robot are simulated using the same robot model. Furthermore, in order to simulate human speed, the desired speed is set as 1.3 m/s and 1.5 m/s as maximum speed for the two agents. Using these agents, tests were executed three times for each of these crossing angles: 60 • , 90 • , 120 • and 180 • . However, in the case of 60 • the examples produced diverged little from standard RVO as the effort distribution in our method approximated equal share.

The first step in the evaluation of our model is to demonstrate the impact of effort distribution in generated trajectories. To that end, the results of the comparison between collaborative and non-collaborative agents are presented in Fig. 6. These results show that the manner in which effort is distributed significantly changes generated trajectories.

The second step of our model requires establishing a comparison between predicted effort distribution in our simulated cases with the baseline obtained from the dataset. For the 90 • experiments, the last crosser tended to change their heading in order to avoid a collision. In our tests, the actual effort distribution was at most within five percentage point difference from the one indicated in our model. This indicates that our implementation is able to translate the RVO-EDC to an appropriate value for a given collision avoidance effort distribution. In contrast, in the 120 • experiments, see Fig. 7b, agents tended to change their speed (heading is slightly changed), in this case, in our model, the first crosser accelerates less and the last crosser decelerates more.

In order to evaluate if the agent in front does not share collision avoidance effort as expected from our model, in Fig. 8 the 180 • case is tested. In all tests performed, the expected behavior is obtained where the agent in front does not participate in the collision avoidance.

VI. CONCLUSIONS

People do not always share collision avoidance effort in the same manner, factors such as time to collision and crossing angle affect the proportion each role (first and last crosser) is responsible for. In this work, based on hundreds of collision avoidance situations between people, we evaluated what factors influence the collision avoidance effort distribution in several distinct scenarios. From this, a definition of collision avoidance effort was created and also a model capable of predicting effort distribution. The model shows a clear increase in the relative proportion of effort for the last crosser as the effort increases.

The model was tested in simulated experiments and its result reveals a difference in generated behavior when compared to standard RVO. This difference is more pronounced when a given collision situations requires higher amounts of collision avoidance effort.

It is important to highlight that other factors can influence the manner in which a robot should share effort to others. For instance, a robot can and should yield to a child, given that its awareness of social rules and expectations is not certain when it comes to collision avoidance, even when situational factors would indicate otherwise. As future work, we intend to develop navigation strategies that are better able to represent this non-mandatory cooperation that is present in collision avoidance behavior between people, adding concepts such as politeness in its decision making.

Fig. 1 :

 1 Fig. 1: Change in the time energy trade-off function in accordance to change in ζ p (v desp ) in case one walks straight to the goal without obstacles. Thus, for each case the minimal value is reached only when the agent arrives at his goal at the desired time using the desired amount of energy. Thus, in case a person accelerates, decelerates or move its heading away from the goal in order to avoid a collision its value will not ever be minimal.

Fig. 2 :

 2 Fig.2: Experiment area is a square with twelve meters in length. The red circle has six meters of diameter and represents the zone of observation where collision avoidance analysis is made. The circle is virtual. This particular situation represents a scenario with 150 • crossing angle.

Fig. 3 :

 3 Fig. 3: Collision situation between r and p, where crossing angle φ , bearing angle β and its derivative β are shown. The z is calculated based on bearing and crossing angle. Also note that z r,p = -z p,r . Arrows indicate a velocity vector.

Fig. 5 :

 5 Fig. 5: Collision avoidance effort surface, given time to collision of three seconds, for first and last crosser for two crossing angles.

  (a) Effort shared between agents. Both change trajectory. (b) First crosser does all effort to avoid collision.

Fig. 6 :

 6 Fig. 6: Impact of different ways to distribute effort in the generated trajectories.

Fig. 7 :

 7 Fig. 7: Last crosser collision avoidance effort proportion comparison between actual people and simulated data. Human trajectories are in red, simulated trajectories with our method are in blue.

Fig. 8 :

 8 Fig. 8: Behavior when crossing angle is 180 • . Agent in front is three times slower and does not contribute in avoiding the collision.