Aurélie Goutte
email: aurelie.goutte@ephe.sorbonne.fr

Yves Cherel

Carine Churlaud

Jean-Pierre Ponthus

Guillaume Massé

Paco Bustamante

Trace elements in Antarctic fish species and the influence of foraging habitats and dietary habits on mercury levels

Keywords: Heavy metals, Nototheniidae, Southern Ocean, Stable Isotopes Highlights:

This study aims at describing and interpreting concentration profiles of trace elements in seven Antarctic fish species (N = 132 specimens) off Adélie Land. Ichthyofauna plays a key role in the Antarctic ecosystem, as they occupy various ecological niches, including cryopelagic (ice-associated), pelagic, and benthic habitats. Firstly, trace element levels in the studied specimens were similar to those previously observed in fish from the Southern Ocean.

Apart from manganese and zinc, concentrations of arsenic, cadmium, copper, iron, mercury (Hg), nickel, selenium and silver differed among fish species. Muscle δ 13 C and δ 15 N values were determined to investigate whether the fish foraging habitats and dietary habits could explain Hg levels. Species and foraging habitat (δ 13 C) were strong predictors for variations of Hg concentrations in muscle tissues. The highest Hg contamination was found in shallow benthic fish compared to cryopelagic and pelagic fish. This pattern was likely due to the methylation of Hg in the coastal sediment and the photodemethylation by ultraviolet radiation in surface waters.

Introduction

Trace elements, from natural and anthropogenic sources are increasingly released in the environment [START_REF] Sen | Anthropogenic Disturbance of Element Cycles at the Earth's Surface[END_REF] and are ultimately deposited in the ocean.

Long-range transport to the open ocean happens through oceanic currents and atmospheric circulation, followed by wet and dry deposition processes [START_REF] Scor Group | GEOTRACES -An international study of the global marine biogeochemical cycles of trace elements and their isotopes[END_REF]. Moreover the ocean plays a critical role in the biogeochemical cycle of trace metals, through chemical and biological reactions in the water column [START_REF] Morel | The biogeochemical cycles of trace metals in the oceans[END_REF][START_REF] Scor Group | GEOTRACES -An international study of the global marine biogeochemical cycles of trace elements and their isotopes[END_REF]. For instance, mercury (Hg) is deposited through the atmosphere in its inorganic form (HgII) and is methylated (Me-Hg) in the ocean, thereby being more bioavailable for marine biota. In that respect, marine ecosystems could be particularly exposed to toxic metals, even in remote and isolated areas [START_REF] Fitzgerald | The case for atmospheric mercury contamination in remote areas[END_REF][START_REF] Ebinghaus | Antarctic springtime depletion of atmospheric mercury[END_REF].

Although the contamination pattern of Arctic marine biota by trace elements has been well described [START_REF] Atwell | Biomagnification and bioaccumulation of mercury in an arctic marine food web: insights from stable nitrogen isotope analysis[END_REF]AMAP, 1998AMAP, , 2011)), such investigations have been less abundant in the Southern Ocean [START_REF] De Moreno | Heavy metals in Antarctic organisms[END_REF][START_REF] Sanchez-Hernandez | Trace element contamination in Antarctic ecosystems[END_REF][START_REF] Bargagli | Environmental contamination in Antarctic ecosystems[END_REF]. Moderate to high levels of trace metals have been reported in Antarctic and subantarctic zooplankton [START_REF] Rainbow | Copper, cadmium and zinc concentrations in oceanic amphipod and euphausiid crustaceans, as a source of heavy metals to pelagic seabirds[END_REF][START_REF] Petri | Trace metal in the crustaceans in the Antarctic Ocean[END_REF], benthic octopuses [START_REF] Bustamante | Cadmium, copper and zinc in octopuses from Kerguelen Islands, Southern Indian Ocean[END_REF], fish [START_REF] Honda | Organ and tissue distribution of heavy metals, and their growth-related changes in Antarctic fish, Pagothenia borschgrevinki[END_REF]Bargagli et al., 1998a,b;[START_REF] Marquez | Metal (Fe, Zn, Mn and Cu) levels in the Antarctic fish Notothenia coriiceps[END_REF][START_REF] Bustamante | Distribution of trace elements in the tissues of benthic and pelagic fish from the Kerguelen Islands[END_REF], seabirds [START_REF] Blévin | Wide range of mercury contamination in chicks of Southern Ocean seabirds[END_REF]Carravieri et al., 2014a) and marine mammals [START_REF] Szefer | Mercury and major essential elements in seals, penguins, and other representative fauna of the Antarctic[END_REF]. This could raise matters of environmental concerns, since some metals, such as Hg, cadmium (Cd) and lead (Pb), cause health problems in vertebrates, including endocrine disruption, DNA damage, immunotoxicity and reprotoxicity (UNEP, 2010a,b;[START_REF] Wolfe | Effects of mercury on wildlife: a comprehensive review[END_REF].On the other hand, some elements (e.g. copper (Cu), iron (Fe), manganese (Mn), nickel (Ni), zinc (Zn)) play essential biological roles, often as cofactors or part of cofactors in enzymes and structural elements of proteins.

Ichthyofauna plays a key role in the Antarctic ecosystems, as they constitute a link between lower (copepods, euphausiids) and higher (seabirds, seals) levels of the trophic web [START_REF] Mesa | The role of notothenioid fish in the food web of the Ross Sea shelf waters: a review[END_REF]. Moreover Antarctic fish occupy most of the available ecological niches, including cryopelagic (ice-associated), pelagic, benthic and epibenthic habitats (La [START_REF] Mesa | The role of notothenioid fish in the food web of the Ross Sea shelf waters: a review[END_REF][START_REF] Cherel | Isotopic niches of fishes in coastal, neritic and oceanic waters off Adélie Land[END_REF]. Antarctic fish species are thus appropriate to assess the respective contribution of foraging habitat and diet in both the inter-and intra-specific variations of trace element concentrations. As a result of bioaccumulation and bioamplification processes within trophic webs [START_REF] Atwell | Biomagnification and bioaccumulation of mercury in an arctic marine food web: insights from stable nitrogen isotope analysis[END_REF][START_REF] Morel | The chemical cycle and bioaccumulation of mercury[END_REF]Bargagli et al., 1998a), the concentrations of biomagnifiable trace element are supposed to increase with higher trophic level organisms.

In addition, foraging habitat may shape the levels of exposure to trace metals. Due to the high Hg bioavailability in coastal bottom water around the Antarctic shelf [START_REF] Fitzgerald | Marine biogeochemical cycling of mercury[END_REF], benthic fish species are expected to have higher Hg levels than species foraging in the water column and underneath the sea ice.

The present study was carried out in the Pointe Géologie archipelago, Adélie Land, Antarctica, which contains a rich marine ecosystem with a high density of epibenthic organisms, pelagic fish, seabirds and marine mammals [START_REF] Micol | Long term population trends in seven Antarctic seabirds at Pointe Géologie Terre Adélie[END_REF][START_REF] Gutt | Mega-epibenthic diversity off Terre Adélie (Antarctica) in relation to disturbance[END_REF]. The first goal of this study was to describe the concentrations of 13 trace elements in the liver (silver (Ag), arsenic (As), Cd, cobalt (Co), chromium (Cr), Cu, Fe, Mn, Ni, selenium (Se), vanadium(V), and Zn) and in the muscle (Hg) of seven Antarctic fish species (N = 132 specimens) off Adélie Land. The second objective aims at exploring the influence of feeding strategies in driving Hg variations in Antarctic fish, by interpreting the ratios of stable isotopes of carbon (δ 13 C) and nitrogen (δ 15 N) in fish muscle. In the marine environment, the δ13C values are mainly used to indicate inshore versus offshore, or pelagic versus benthic contribution to food intake. Moreover, consumers are typically enriched in 15 N relative to their food and consequently the δ 15 N values serve as indicators of a dietary habits and trophic position (Vanderklift and Ponsard, 2003).

Materials and methods

Study area, species and sample collection

This study was carried out from the 24 th of April 2010 to 17 th of January 2012 in the Pointe Géologie Archipelago (Adélie Land, Antarctica, 66°40' S, 140°01' E). Table 1 provides general information about the samples analyzed in this study. Pleuragramma antarcticum is the dominant pelagic fish in high-Antarctic waters (La [START_REF] Mesa | The role of notothenioid fish in the food web of the Ross Sea shelf waters: a review[END_REF][START_REF] Mesa | Antarctic silverfish: life strategies of a key species in the high-Antarctic ecosystem[END_REF] and was collected over the continental slope (66°18'S and 141°56'E) from the Research Icebreaker Astrolabe using an Isaacs-Kidd Midwater Trawl (IKMT). The six other species were caught near-shore underneath the sea ice and up to 87-meter-deep in the vicinity of the station.

The cryopelagic [START_REF] Hoshiai | Feeding by the Nototheniid fish, Pagothenia borchgrevinki on the ice-associated copepod, Paralabidocera antarctica[END_REF]) fish Pagothenia borchgrevinki were caught in cracks in the sea ice, using fishing rods at a depth of less than one meter. Most of the benthic species (Notothenia coriiceps, Trematomus bernacchii, T. hansoni, T. pennellii, [START_REF] Gon | Demographic responses to mercury exposure in two closely related Antarctic top predators[END_REF] were caught by using fish traps on the sea bottom, or by paying out line until we felt contact with the bottom and then reeled in just enough to keep our lure from hanging bottom.

The fish Trematomus newnesi, known to feed in the water column or at the undersurface of ice in near shore shallow areas [START_REF] Gon | Demographic responses to mercury exposure in two closely related Antarctic top predators[END_REF], was collected in the water column using a fishing rod. Each fish was identified to the species level based on morphological criteria. Individuals were measured (total length; nearest mm) and weighed (nearest g). These morphometric measures were not taken for the 9 P. antarcticum, because they had head or caudal fin removed while fishing with the IKMT net. Samples of white muscle (N=129) and liver (N=75) were excised and immediately frozen at-80 °C until analysis in the laboratory.

Since amounts of liver samples were limited, it was not possible to analyze both Hg and the 12 other elements in liver samples. Hence, Hg concentrations were determined in muscle samples and the 12 other elements in liver samples.

Trace element analyses.

Freeze-dried samples were powdered and homogenized. The total Hg concentrations in the muscle were determined by analyzing Hg directly with an Advanced Mercury Analyzer (ALTEC AMA 254) on aliquots ranging from 5 to 50 mg of freeze-dried sample weighed to the nearest 0.01 mg [START_REF] Bustamante | Total and organic Hg concentrations in cephalopods from the North Eastern Atlantic waters: Influence of geographical origin and feeding ecology[END_REF]). All analyses were repeated 2-3 times for each sample until having a relative standard deviation < 10%. The analysis of Ag, As, Cd, Co, Cr, Cu, Fe, Mn, Ni, Se, V and Zn were determined in liver samples according to [START_REF] Kojadinovic | Multi-elemental concentrations in the tissues of the oceanic squid Todarodes filippovae from Tasmania and the Southern Indian Ocean[END_REF]. Briefly, 60 to 300 mg samples were microwave digested in a mixture of 6 mL of 65% HNO3 (VWR Quality SUPRAPUR) and 2 mL of 30% HCl (VWR Quality SUPRAPUR), except for the samples with a weight below 100 mg: 3 mL HNO3 and 1 mL HCl. Then the samples were diluted to 50 mL (25 mL for the samples with a weight below 100 mg) with ultrapure water. The 12 elements were then analyzed by Inductively Coupled Plasma Atomic Emission Spectrometry (Varian Vista-Pro ICP-OES) and Mass Spectrometry (ICP-MS II Series Thermo Fisher Scientific). To avoid trace element contamination, all glass and plastic utensils used were soaked in a bath of nitric acid (50 mL in 2 L) for a minimum of 48 h, rinsed in ultrapure water and dried under a laminar hood before use. Accuracy and reproducibility of the preparation were tested by preparing analytical blanks and replicates of lobster hepatopancreas (TORT-2) and dog-fish liver (DOLT-3) reference standards (National Research Council, Canada) along with each set of samples. Results for the certified reference materials were in good agreement with the certified values and recovery rates varied from 83% to 109%. The detection limits (μg•g -1 dry wt) were 0.005 (Hg), 0.02 (Ag, Cd, Co, Cr), 0.1 (Cu, Mn, Se), 0.2 (As), 0.3 (Ni), 0.33 (V), and 3.3 (Fe, Zn). Trace element concentrations are expressed in μg•g -1 dry weight (dw).

Stable isotope analyses

Stable isotopes were determined in muscle samples. After being freeze-dried, samples were ground to a fine powder, lipids were extracted using cyclohexane and carbonates were removed using 1 N HCl. The low C:N mass ratio of the delipidated samples (< 4.0; [START_REF] Post | Getting to the fat of the matter: models, methods and assumptions for dealing with lipids in stable isotope analyses[END_REF]) allowed comparison of the carbon isotopic signature without any deleterious effect due to different lipid contents among individuals and species (Table 1). Relative abundance of 13 C and 15 N were determined with a continuous flow mass spectrometer (Thermo Scientific Delta V Advantage) coupled to an elemental analyzer (Thermo Scientific Flash EA 1112) as detailed in [START_REF] Chouvelon | Revisiting the use of 15 N in meso-scale studies of marine food webs by considering spatio-temporal variations in stable isotopic signatures -The case of an open ecosystem: the Bay of Biscay (North-East Atlantic)[END_REF]. Results are presented in the δ notation relative to Vienna PeeDee Belemnite and atmospheric N2 for δ 13 C and δ 15 N, respectively. Based on replicate measurements of internal laboratory standards (acetanilide), the experimental precision is ±0.15 and ±0.20‰ for δ 13 C and δ 15 N, respectively.

Statistical analyses

All statistical analyses were performed using R software version 3.2.0 (R Development [START_REF] Core | R: A language and environment for statistical computing[END_REF]. Only trace element concentrations that were above the limit of quantification (LoQ) in at least 70% of individuals were included in statistical analyses. Hence Co, Cr and V were not further considered. For the other trace elements, concentrations below the LoQ were substituted using 0.5 X LoQ to avoid missing values distorting the statistical outcomes. T. pennellii was not included in the statistical analyses because only one specimen was collected.

Data were first checked for normality and homogeneity of variances and were log-transformed if necessary. Generalized linear models (GLM) with a normal distribution and an identity-link function were used to test the effects of species and length on log-transformed trace element concentrations. Terms were added sequentially. If necessary, post-hoc tests were conducted using Tukey multiple comparisons of means or pairwise comparisons using Wilcoxon rank sum test and Bonferroni correction.

Pearson or Spearman correlation rank tests were used to test relationships between muscle Hg concentrations and δ 13 C (or δ 15 N) values, or between trace element concentrations.

Since stable isotopes were measured in muscle samples, we did not perform a correlation test between the 12 trace elements measured in liver samples and stable isotopes. Since δ 13 C and δ 15 N were significantly correlated (Spearman's rank correlation, ρ = 0.877, p < 0.001), these explanatory variables were not included in the same models. GLM with a normal distribution and an identity-link function were used to test the effects of species, foraging habitat or dietary habits (inferred from muscle δ 13 C and δ 15 N values, respectively) and the interaction between species and foraging habitat (or dietary habits) on log-transformed Hg concentrations in muscle.

Model selection was based on Akaïke's Information Criteria adjusted for small sample sizes (AICc). The model with the lowest AICc value was considered to be the most accurate. Models with AICc values differing by less than 2 have a similar level of support in the data, and the model including the least number of parameters was regarded as the most accurate, according to the principle of parsimony (Burnham and Anderson, 2002).

Results

Trace element concentrations for each fish species were detailed in Tables 2 and3.

Concentrations of trace elements in liver, except for Mn and As, were strongly and positively correlated (Table 4). By contrast, concentrations of Hg in muscle were not correlated to other trace elements, except a strong correlation between Hg in muscle and Cd in liver (Table 4).

Ag, As, Cd, Cu, Fe, Hg, Ni and Se, but not Mn and Zn, significantly differed among Antarctic fish species (Table 5).Significantly higher Hg levels (p < 0.05 for all post-hoc tests) were found in T. bernacchii compared to P. antarcticum, P. borchgrevinki, T. newnesi, and N. coriiceps; and in N. coriiceps and T. hansoni compared to P. antarcticum, P. borchgrevinki, and T. newnesi.

After taking into account species-differences, the majority of trace element concentrations were not related to fish length. Concentrations of As, Cd, Hg and Se significantly increased with fish length (Table 5). It should however be noticed that slopes' estimates ranged between 0.002 and 0.008 (Table 5) and were thus closed to 0. Since standard errors were even smaller (0.001 for all tests), we concluded that concentrations of As, Cd, Se in liver and Hg in muscle slightly increased with length in Antarctic fish.

Hg concentrations in muscle were significantly and positively correlated to both δ 13 C and δ 15 N values in muscles (Spearman correlation, ρ = 0.719 and 0.714, respectively, p < 0.001 for both tests). Models were ranked to disentangle the influence of species, foraging habitat (δ 13 C), dietary habits (δ 15 N) and interactions on Hg concentrations in fish muscles (Table 6).

Models including species as covariate (models 1-5, Table 6) had the highest AICc, corroborating the strong species-differences in Hg concentrations. In addition, models including δ 13 C values as covariate (models 1 and 2, Table 6, Fig. 1) had the highest AICc weight (91%) and thus presented the best fit to the data set. Models including species and δ 15 N values as covariates (models 4 and 5, Table 6, Fig. 2) had a lower AICc than the model including only species and did not explain well the variation in Hg levels (AICc weight: 2%). Model 1 (Table 6) described Hg concentrations as a function of species, δ 13 C, and the interaction between species and δ 13 C, had the highest level of support in the data, but its AICc value differed by less than 2 with model 2 (no interaction effect). According to the principle of parsimony, the most accurate model is model 2: Hg concentrations in muscles were explained by species differences and increased with increasing δ 13 C values (Fig. 1).

Discussion

Comparison with other species and Antarctic areas

Our results fall within the range of trace metals levels for several fish species from the Antarctic Ocean [START_REF] Sanchez-Hernandez | Trace element contamination in Antarctic ecosystems[END_REF]. The present study could be further compared with a previous study that investigated the concentrations of trace elements in the liver, kidney and muscle of eight fish species from the subantarctic Kerguelen Islands [START_REF] Bustamante | Distribution of trace elements in the tissues of benthic and pelagic fish from the Kerguelen Islands[END_REF].

Antarctic fish (this study) had slightly lower Hg concentrations in muscle (ranges in µg•g -1 dw; pelagic species: 0.02-0.24 vs 0.15-0.48; benthic species: 0.06-0.80 vs 0.03-1.51), similar Cd (0.95-19.0 vs 0.82-52.1), slightly higher Cu (2.45-35.3 vs 0.9-24.7), and higher concentrations in liver than sub-Antarctic fish [START_REF] Bustamante | Distribution of trace elements in the tissues of benthic and pelagic fish from the Kerguelen Islands[END_REF]. The slight differences in trace element concentrations between fish species from Adélie Land and Kerguelen Island could be attributed to a geographical gradient in the oceanic distribution and bioavailability of trace elements [START_REF] Cossa | Mercury in the southern ocean[END_REF]). Lower Hg levels in higher latitude organisms were also recently observed in closely related seabird species (the South Polar Skua Catharacta maccormicki from Adélie Land vs the Brown Skua C. lonnbergi from the subantarctic Kerguelen Archipelago, [START_REF] Gon | Demographic responses to mercury exposure in two closely related Antarctic top predators[END_REF]. Furthermore, wide-ranging wandering albatrosses showed a pronounced latitudinal effect, with birds feeding in northern subtropical waters having higher blood Hg concentrations than those feeding further south (Carravieri et al. 2014b).

Species differences and relationships with length

After taking into account species-differences, the majority of trace element concentrations were not related to fish length. Concentrations of As, Cd, Hg and Se significantly increased with fish length (Table 5). It should however be noticed that slopes' estimates ranged between 0.002 and 0.008 (Table 5) and were thus closed to 0. Since standard errors were even smaller (0.001 for all tests), we concluded that concentrations of As, Cd, Se in liver and of Hg in muscle slightly increased with length in Antarctic fish.

The concentrations of Hg in muscle, and of Ag, As, Cd, Cu, Fe, Ni, and Se in liver greatly differed among fish species collected off Adélie Land, Antarctica. Since all individuals were collected in the same area, the Pointe Géologie Archipelago and were not migratory species, regional discrepancies should be excluded. Other possible explanations include interspecific differences in i) exposure to trace elements, and especially in variation of these metals bioavailability across the water column [START_REF] Cossa | Mercury in the southern ocean[END_REF], ii) diet and trophic level according to biomagnification processes in Antarctic trophic web (Bargagli et al., 1998a), iii) mechanisms related to the kinetics of trace elements that are absorption, biotransformation, and excretion (e.g. [START_REF] Spry | A kinetic method for the measurement of zinc influx in vivo in the rainbow trout, and the effects of waterborne calcium on flux rates[END_REF] and iv) individual parameters (sex, growth, body condition, life cycle, [START_REF] Al-Yousuf | Trace metals in liver, skin and muscle of Lethrinus lentjan fish species in relation to body length and sex[END_REF]. The two last hypotheses were not tested due to the lack of appropriate individual information and the need for experimental monitoring.

Because of food resource partitioning within Antarctic notothenioid fish assemblage (e.g. [START_REF] Barrera-Oro | Analysis of dietary overlap in Antarctic fish (Notothenioidei) from the South Shetland Islands: no evidence of food competition[END_REF], low proportion of prey overlap among species may explain differences in trace element concentrations. Isotopic signatures were used to disentangle the respective contribution of foraging habitats and dietary habits in driving variations in muscle Hg concentrations.

Concerning an accumulation of trace elements during growth, this study highlighted a slight increase of As, Cd, Hg and Se concentrations with length and no significant relationship between Ag, Cu, Fe, Mn, Ni, Zn and length. In the open scientific literature, relationships between trace element levels and fish sizes are mostly non-significant or have negative slopes (e.g. [START_REF] Al-Yousuf | Trace metals in liver, skin and muscle of Lethrinus lentjan fish species in relation to body length and sex[END_REF][START_REF] Canli | The relationships between heavy metal (Cd, Cr, Cu, Fe, Pb, Zn) levels and the size of six Mediterranean fish species[END_REF][START_REF] Merciai | Trace metal concentration and fish size: Variation among fish species in a Mediterranean river[END_REF], except for Hg (e.g. Chouvelon et al., 2014). Since Me-Hg likely binds with sulfhydryl groups of muscular proteins, Hg shows slow elimination rates in muscles and accumulates with aging in fish (Chouvelon et al., 2014). Our data only reveal a slight increase of Hg with length, which could be due to a limited range of fish size and thus age.

Foraging habitats

We postulated that foraging habitat would shape Hg contamination in Antarctic ichthyofauna. In agreement with the hypothesis, the most contaminated fish were the shallow benthic species (T. bernacchii, T. pennellii, N. coriiceps, T. hansoni, Gon and Heemstra 1990) and the less contaminated fish were the cryopelagic (P. borchgrevinki, [START_REF] Hoshiai | Feeding by the Nototheniid fish, Pagothenia borchgrevinki on the ice-associated copepod, Paralabidocera antarctica[END_REF]), pelagic (P. antarcticum, La Mesa et al. 2004;[START_REF] Mesa | Antarctic silverfish: life strategies of a key species in the high-Antarctic ecosystem[END_REF] and semipelagic (T.

newnesi, [START_REF] Gon | Demographic responses to mercury exposure in two closely related Antarctic top predators[END_REF] species. Furthermore, muscle δ 13 C values were used to confirm the influence of foraging habitat on individual Hg concentrations. Except for P. antarcticum, all specimens were collected near-shore, so the δ 13 C values mainly reflect inshore/benthic versus offshore/pelagic contribution to food intake. Our results on δ 13 C values were consistent with previous investigations of the isotopic niches of fish species in Adélie Land [START_REF] Cherel | Isotopic niches of fishes in coastal, neritic and oceanic waters off Adélie Land[END_REF]. Our model selection highlighted that Hg concentrations in muscles differed among species and increased with δ 13 C values. Three fish species shared low and highly similar profile of Hg and δ 13 C values: P. antarcticum, P. borchgrevinki and T. newnesi.

Although they differ in their ecological niche (pelagic, cryopelagic and semipelagic, respectively), they are pelagic feeders, thus exhibiting low δ 13 C values and appeared to be poorly Hg-contaminated. N. coriiceps and T. hansoni exhibited non-significantly different Hg levels, although N. coriiceps were more benthic (higher δ 13 C values) than T. hansoni. At last, T. bernacchii had the highest Hg levels and the more benthic life style according to its δ 13 C. This result strongly corroborates the hypothesis stating that Hg is more bioavailable for coastal benthic organisms, because of the production of Me-Hg in sediments [START_REF] Fitzgerald | Marine biogeochemical cycling of mercury[END_REF]).

Moreover, photodemethylation by ultraviolet radiation provides a further mechanism for Me-Hg removal in surface waters [START_REF] Lehnherr | Methylation of inorganic mercury in polar marine waters[END_REF], and a lower Hg bioavailability for surface feeders, such as P. antarcticum, P. borchgrevinki and T. newnesi. Hence foraging habitat strongly shapes Hg load in Antarctic ichthyofauna.

Dietary habits

Since Hg is efficiently biomagnified along food webs [START_REF] Atwell | Biomagnification and bioaccumulation of mercury in an arctic marine food web: insights from stable nitrogen isotope analysis[END_REF][START_REF] Morel | The chemical cycle and bioaccumulation of mercury[END_REF]Bargagli et al., 1998a), higher trophic level species were assumed to exhibit higher Hg levels than lower trophic level species. This pattern was clearly established for subantarctic seabird communities (Carravieri et al., 2014a). In the present study, fish Hg concentrations increased with muscle δ 15 N values, but the strength of the correlation was not as pronounced as the link between Hg levels and δ 13 C values. This could be due to many non-mutually exclusive explanations. Firstly, the δ 15 N values in Antarctic fish species reflect not only trophic position, but also foraging habitats. Coastal/inshore benthic fish had higher 15 N values than cryopelagic and pelagic consumers, mainly because baseline δ 15 N values are higher in inshore/benthic than offshore/pelagic ecosystems (e.g. [START_REF] Chouvelon | Revisiting the use of 15 N in meso-scale studies of marine food webs by considering spatio-temporal variations in stable isotopic signatures -The case of an open ecosystem: the Bay of Biscay (North-East Atlantic)[END_REF]. Secondly, as expected [START_REF] Cherel | Isotopic niches of fishes in coastal, neritic and oceanic waters off Adélie Land[END_REF], δ 15 N vary little among the studied Antarctic fish species [9.2-13.3‰]. This poor variability did not allow a clear relationship between Hg concentrations and trophic levels to be established. Thirdly, benthic fishes are considered as trophic generalists and opportunistic feeders [START_REF] Gon | Demographic responses to mercury exposure in two closely related Antarctic top predators[END_REF][START_REF] Mesa | The role of notothenioid fish in the food web of the Ross Sea shelf waters: a review[END_REF], which results in poor inter-specific δ 15 N variations and thus precludes describing strong positive relationship between trophic levels and Hg levels.

To conclude, foraging habitat (benthic vs pelagic) and to a lesser extent, dietary habits and age, were strong predictors of variations in muscle Hg levels.

Table 1. Sample data, including scientific names of species, sample size (N), sampling period (start and end, dd-mm-yy), habitat, total water depth (in m), sample collection depth, fishing gear, total length (TL, mean ± SD, in mm) and mass (mean ± SD, in g).

Table 2. Mean ± standard deviation of stable isotopes (δ 13 C and δ 15 N) in muscle and mean ± standard deviation and range Hg in muscle (µg•g -1 dw) of 129 specimens representing seven different species.

Table 3. Mean ± standard deviation and range of trace elements in liver (µg•g -1 dw) in 75 specimens representing six different species. Table 5: Effects of species and length on log-transformed concentrations of trace elements in liver and muscle samples, using GLM with a normal distribution and an identity-link function. P. antarcticum and T. pennellii were excluded from these analyses due to the absence of morphometric data and low sample size respectively. When the correlation between a trace element concentration and length was significant, the slope's estimate and standard error (SE) was provided.

Table 6. AICc model ranking for Hg concentrations (log-transformed, N = 121) in muscle in relation to fish species (6 species, T. pennellii was not included because only one specimen was fished), δ 13 C (as a proxy of foraging habitat, inshore/benthic vs offshore/pelagic) and δ 15 N (as a proxy of dietary habits). Abbreviations: k: number of parameters; AICc: Akaike's Information Criteria adjusted for small sample-size values; ΔAICc: difference between AICc and min(AICc); w(AICc): AICc weights, i.e. weight of evidence interpreted as a proportion.

Table 4 :

 4 Pearson or Spearman correlation matrix between trace element concentrations in Antarctic fish (* p 0.05, ** p < 0.01, *** p < 0.001)

Figure 1 :Figure 2 :

 12 Figure1: Positive correlation between muscle Hg concentrations (mean ± standard deviation, μg•g -1 dw) and δ 13 C (mean ± standard deviation, ‰) in fish species off Adélie Land, Antarctica

Acknowledgments

We thank C. Robineau and J. Lanshere who helped with collecting fish, and M. Brault-Favrou and G. Guillou for running stable isotope analysis. This article benefited greatly from the comments of two anonymous reviewers. This work was logistically supported by the French Institute Paul-Emile Victor (IPEV project number 1010, ICELIPIDS, G. Massé) and was financially supported by the European Research Council (ICEPROXY, project number 203441), the ANR project POLARTOP (ANR-10-CESA-0016) and the Contrat de Projet Etat Région (CPER 13).


Rahimeh Shahin Gelareh
email: shahin.gelareh@unv-artois.fr

Neamatian Monemi
email: monemi@isima.fr

Frédéric Semet
email: frederic.semet@ec-lille.fr

Rahimeh Neamatian Monemi

Capacitated Hub Routing Problem in Hub-and-Feeder Network Design: Modeling and Solution Algorithm

Keywords: Hub Location, Location Routing, Branch-and-Bound, Benders Decomposition

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Introduction

In this paper, we address a new hub location and routing problem. The Bounded Cardinality Capacitated Hub Routing Problem (BCCHRP) aims to determine the minimum total times transportation system to transfer goods from origins to destinations through hubs. More precisely, given a set origin-destination (O-D) pairs defined on a set of nodes, we have to partition this set into a subset of hub nodes and a subset of non-hub nodes and to design a network including arcs between hubs and directed routes serving non-hub nodes rooted at hubs. From each hub, one directed route at most can be performed by a vehicle with a limited capacity. The number of hubs used must lie within a minimum and maximum hubs. Transhipment takes place at hub nodes where freight is transferred from the hub-level transporters to the vehicles performing routes. The limited vehicle capacity influences the allocation of non-hub nodes to hub nodes.

The contribution of this paper is twofold. First, we introduce the problem, and propose a polynomial mixed integer linear model. Second, we describe a hybrid exact algorithm combining branchand-cut methodology and Benders decomposition. The efficiency of the approach is assessed on a various testbed.

Rodriguez-Martìn et al. [START_REF] Inmaculada Rodríguez Martín | A branch-and-cut algorithm for the hub location and routing problem[END_REF] studied a similar problem. In their article, the number of hub nodes is fixed and the capacity restriction is on the maximum number of non-hub nodes served on a route. They proposed a mathematical model and a branch-and-cut approach to solve instances up to 50 nodes. The model and the cuts are based on a previous work devoted to the Plant Cycle Location Problem (PCLP) [START_REF] Labbé | A branch-and-cut algorithm for the plant-cycle location problem[END_REF]. Other related papers are the followings. Gelareh et al. [START_REF] Gelareh | Huband-spoke network design and fleet deployment for string planning of liner shipping[END_REF] proposed a mixed integer linear programming formulation and a Lagrangian relaxation for the simultaneous design of network and fleet deployment of a deep-sea liner service provider (p-String Planning Problem (pSPP)). Cetiner et al. [START_REF] Selim C ¸etiner | Hubbing and routing in postal delivery systems[END_REF] described a multiple allocation hub location and routing problem applied to postal delivery. Again for similar applications, Wasner et al. [START_REF] Wasner | An integrated multi-depot hub-location vehicle routing model for network planning of parcel service[END_REF] proposed a model where direct connections between non-hub nodes are allowed. de Camargo et al. [START_REF] Saraiva De Camargo | A new formulation and an exact approach for the many-to-many hub location-routing problem[END_REF] tackled a similar problem where the route lengths are bounded. They proposed a Benders decomposition approach. Last, Nagy et al. [START_REF] Nagy | The many-to-many location-routing problem[END_REF] addressed a hub location routing problem with capacity constraints where pick-up points and delivery points are served on distinct routes.

Solution methodology

First, we propose a mixed integer linear model where 2-index variables are associated with the design decisions and 4-index variables are associated with the fractions of flows traversing inter-hub or nonhub arcs for all O-D pairs. Design variables are binary while flow variables are continuous. The model has two sets of constraints: network design constraints and flow routing constraints. To strengthen the linear relaxation of this model, we present several valid inequalities involving the design variables, some of them being similar to those proposed by Rodriguez-Martìn et al. [START_REF] Inmaculada Rodríguez Martín | A branch-and-cut algorithm for the hub location and routing problem[END_REF].

Then, we describe our solution method which is based on a Benders decomposition scheme. The master problem includes the network design constraints while the subproblem includes the flow routing constraints and the linking constraints. The master problem includes also some valid inequalities which are relaxed versions of the capacity constraint imposed on each route. Other cuts are added dynamically. To accelerate the convergence, we use a heuristic based on local searches to generate feasible solutions and add the corresponding cuts to the master problem.

When no violated inequality can be identified, we generate Benders cuts. Due to capacity constraints on routes, the subproblem is still a capacitated multi-commodity flow problem parameterized in the design imposed by the master problem. In some cases, we show that the subproblem can be decomposed into one subproblem per O-D. This leads to disaggregated cuts which can improve the lower bound significantly. In addition, by exploiting symmetry, a mechanism is designed that, under certain conditions, allows extracting a relative interior point of the master problem polytope which is used later on in generating non-dominated cuts from the subproblem.

Computational experiments

Based on a testbed generated from the well-known Australian Post (AP) dataset (see [START_REF] Ernst | Solution algorithms for the capacitated single allocation hub location problem[END_REF]), we conducted two types of computational experiments. First, we solved the proposed model with CPLEX 12.6.1 with a time limit of 36000 seconds. Results are reported in Table 1. The first column reports the instance name in the format nN pP α where N is the number of nodes, P is the maximum number of hub nodes, and α represents the factor of economies of scale on inter-hub arcs varying in {0.7, 0.8, 0.9}. The second column indicates CPU times elapsed during the LP solution. The next column reports the LP objective function values followed by a column for the LP statuses. The next column report the number of hub nodes 'Nhubs' in the LP solution. In columns 'TimeIP' and 'IPobj', we report the CPU times for IP solution and the objective function values, respectively. The subsequent column reports the number of nodes processed in the branch-and-bound algorithm before termination criteria is met. The column 'IPStatus' reports the termination criterion that has been met for every instance. The next column reports the optimality gaps when CPLEX terminated.

In Table 1, one observes that the LP bound is rather weak. In the LP relaxation, there is a tendency towards opening maximum possible number of hubs (in the fractional sense). While for n = 10 the instances were solved in less than one hour, for n = 15, optimality could not be proven within 10 hours.

Our initial computational experiments show that using our solution hybrid solution approach, we As a rule, the number of nodes processed is very moderate and most instances are solved to optimality. For two instances we have numerical issues that led to failures. The efforts to avoid such numerical instabilities by tuning different parameters and tolerances were not successful. In order to avoid numerical issues we have set the gap tolerance to 0.5%. One observes that the optimality is subject to the user-defined tolerance gap. The number of feasibility Benders cuts corresponds to the iterations where infeasible solution has been encountered. These numbers are also very small. It means that the number of iterations with no (or very minimal) improvement in the lower bound is quite small.

Table 1 :

 1 Computational experiments with the 2-index model.can solve to optimality up to n = 20. The first column in Table2indicates the instance name. The second and third columns reports CPU times and the best incumbent value found. The column 'Nnodes' report the number of nodes processed in the course of solution process. The column 'CplexStatus' reports the CPLEX status upon termination. The column 'Gap(%)' reports the termination gaps (the LB is also reported when the method failed). The next two columns represent number of feasibility Benders cuts ('#F. Cuts') and number of optimality Benders cuts ('#O. Cuts').

	instance	TimeRoot	LPobj	LPStatus	Nhubs	TimeIP	IPobj	Nnodes	IPStatus	Gap (%)
	n10 p3 0.9	3	2219.32	Optimal	3	1974	3395.63	15905	Optimal	0.00
	n10 p3 0.8	3	2160.99	Optimal	3	2177	3315.81	19729	OptimalTol	0.01
	n10 p3 0.7	3	2097.88	Optimal	3	3371	3235.99	50926	OptimalTol	0.01
	n15 p3 0.9	8	5998.29	Optimal	3	36009	14461.60	2923	AbortTimeLim	56.71
	n15 p3 0.8	8	5863.59	Optimal	3	36017	14702.10	4661	AbortTimeLim	56.97
	n15 p3 0.7	10	5699.74	Optimal	3	36016	11842.20	4305	AbortTimeLim	48.50
	n15 p4 0.9	25	5568.42	Optimal	4	36035	10785.20	5615	AbortTimeLim	43.16
	n15 p4 0.8	21	5419.25	Optimal	4	36030	9594.57	5072	AbortTimeLim	37.67
	n15 p4 0.7	1-	5240.83	Optimal	4	36025	10425.50	6505	AbortTimeLim	44.79
	n15 p5 0.9	20	5203.81	Optimal	5	36021	9122.92	4391	AbortTimeLim	37.44
	n15 p5 0.8	17	5039.83	Optimal	5	36023	7381.18	7004	AbortTimeLim	23.58
	n15 p5 0.7	20	4852.73	Optimal	5	36027	7885.72	7149	AbortTimeLim	32.88

Table 2 :

 2 Computational experiments with the Benders decomposition.

	instance	Time (sec.)	Obj. Val.	#Nodes	CplexStatus	Gap(%)	#F. Cuts.	#O. Cuts.
	n10 p3 0.9	14	3395.63	0	Optimal	0.37	0	696
	n10 p3 0.8	14	3315.81	0	Optimal	0.42	0	617
	n10 p3 0.7	17	3235.99	0	OptimalTol	0.09	0	785
	n15 p3 0.9	398	11244.20	9	OptimalTol	0.19	3	3009
	n15 p3 0.8	1395	11255.74	25	OptimalTol	0.27	3	6465
	n15 p3 0.7	929	11120.20	47	OptimalTol	0.41	4	5681
	n15 p4 0.9	899	9067.25	84	OptimalTol	0.00	1	2690
	n15 p4 0.8	883	10170.06	39	OptimalTol	0.41	0	4706
	n15 p4 0.7	1073	10683.44	97	OptimalTol	0.37	9	6039
	n15 p5 0.9	1615	7387.35	231	Optimal	0.00	0	2364
	n15 p5 0.8	591	7143.31	46	Optimal	0.00	0	1989
	n15 p5 0.7	626	6899.27	68	Optimal	0.00	0	1581
	n20 p3 0.9	28673	24935.81	288	OptimalTol	0.25	10	13250
	n20 p3 0.8	-	-	114	failed	22.07%(LB = 19509.37)	-	-
	n20 p3 0.7	15307	5548.09	965	OptimalTol	0.46	33	747
	n20 p4 0.9	15767	21585.40	184	Optimal	0.00	0	9202
	n20 p4 0.8	14432	21284.45	107	OptimalTol	0.48	3	13217
	n20 p4 0.7	-	-	199	failed	30.57%(LB = 15169.85)	-	-
	n20 p5 0.9	19051	17441.26	301	Optimal	0.00	0	6676
	n20 p5 0.8	19572	17624.70	247	OptimalTol	0.24	16	5694
	n20 p5 0.7	6470	16933.63	51	Optimal	0.00	0	5984
	n20 p6 0.9	98991	17274.12	1525	AbortUser	31.33	0	10308
	n20 p6 0.8	46695	16922.59	719	AbortUser	31.01	0	10462
	n20 p6 0.7	27531	15738.56	275	OptimalTol	0.41	0	16339