Le Croizier Gaël

Anne Lorrain

Sonke Jeroen

Hoyos-Padilla E Mauricio

Galván-Magaña Felipe

Santana-Morales Omar

Aquino-Baleytó Marc

Muntaner-López Gádor

Ketchum James

Block Barbara

Carlisle Aaron

Salvador J Jorgensen

Besnard Lucien

Jung Armelle

Schaal Gauthier

Gaël Le Croizier
email: gael.lecroizier@hotmail.fr

Mauricio E Hoyos Padilla

The Twilight Zone as a Major Foraging Habitat and Mercury Source for the Great White Shark

The twilight zone contains the largest biomass of the world's ocean. Identifying its role in the trophic supply and contaminant exposure of marine megafauna constitutes a critical challenge in the context of global change. The white shark (Carcharodon carcharias) is a threatened species with some of the highest concentrations of neurotoxin methylmercury (MeHg) among marine top predators. Large white sharks migrate seasonally from coastal habitats, where they primarily forage on pinnipeds, to oceanic offshore habitats. Tagging studies suggest that while offshore, white sharks may forage at depth on mesopelagic species, yet no biochemical evidence exists. Here, we used mercury isotopic composition to assess the dietary origin of MeHg contamination in white sharks from the Northeast Pacific Ocean. We estimated that a minimum of 72% of the MeHg accumulated by white sharks originates from the consumption of mesopelagic prey, while a maximum of 25% derives from pinnipeds. In addition to highlighting the potential of mercury isotopes to decipher the complex ecological cycle of marine predators, our study provides evidence that the twilight zone constitutes a crucial foraging habitat for these large predators, Please note that this is an author-produced PDF of an article accepted for publication following peer review. The definitive

Introduction

Many shark populations are declining worldwide in the Anthropocene [START_REF] Baum | Collapse and Conservation of Shark Populations in the Northwest Atlantic[END_REF][START_REF] Myers | Rapid Worldwide Depletion of Predatory Fish Communities[END_REF][START_REF] Ferretti | Shark Baselines and the Conservation Role of Remote Coral Reef Ecosystems[END_REF] , with potential large-scale cascading effects such as changes in abundance, distribution and behavior of prey, that may impact the structure and function of marine ecosystems [START_REF] Heithaus | Predicting Ecological Consequences of Marine Top Predator Declines[END_REF][START_REF] Ferretti | Patterns and Ecosystem Consequences of Shark Declines in the Ocean[END_REF][START_REF] Pimiento | Functional Diversity of Marine Megafauna in the Anthropocene[END_REF] . As an apex predator, the white shark (Carcharodon carcharias) is a key species that exists in low abundance, implying low capacity for population recovery [START_REF] Roff | Decline of Coastal Apex Shark Populations over the Past Half Century[END_REF][START_REF] Hammerschlag | Disappearance of White Sharks Leads to the Novel Emergence of an Allopatric Apex Predator, the Sevengill Shark[END_REF] . Consequently, white sharks are particularly vulnerable to extinction, along with their ecosystem role as apex predators [START_REF] Pimiento | Functional Diversity of Marine Megafauna in the Anthropocene[END_REF] .

As white sharks experience different levels of protection during their migrations (e.g. areas within and beyond national jurisdictions) [START_REF] Harrison | The Political Biogeography of Migratory Marine Predators[END_REF] , understanding more about how they use ocean ecosystems is vital to their protection. Mercury (Hg) is a global pollutant of both anthropogenic and natural origin, of which 80% of atmospheric emissions are deposited in the ocean [START_REF] Horowitz | A New Mechanism for Atmospheric Mercury Redox Chemistry: Implications for the Global Mercury Budget[END_REF] . Once in seawater, a fraction of deposited inorganic Hg is converted trough microbial activity to toxic methylmercury (MeHg) [START_REF] Podar | Global Prevalence and Distribution of Genes and Microorganisms Involved in Mercury Methylation[END_REF] , which is bioaccumulated by aquatic organisms and biomagnified along trophic webs. Due to their long lifespans and high trophic positions, apex predators are particularly prone to MeHg contamination, potentially causing adverse effects on their reproduction, development, behavior and nervous system function [START_REF] Eisler | Mercury Hazards to Living Organisms[END_REF][START_REF] Krey | Assessment of Neurotoxic Effects of Mercury in Beluga Whales (Delphinapterus Leucas), Ringed Seals (Pusa Hispida), and Polar Bears (Ursus Maritimus) from the Canadian Arctic[END_REF][START_REF] López-Berenguer | A Critical Review about Neurotoxic Effects in Marine Mammals of Mercury and Other Trace Elements[END_REF] . Although the impact of MeHg exposure on shark neurophysiology is still poorly understood [START_REF] Ehnert-Russo | Mercury Accumulation and Effects in the Brain of the Atlantic Sharpnose Shark (Rhizoprionodon Terraenovae)[END_REF] , white sharks display some of the highest MeHg concentrations among shark species [START_REF] Mckinney | Global versus Local Causes and Health Implications of High Mercury Concentrations in Sharks from the East Coast of South Africa[END_REF] . MeHg accumulation in white sharks may thus exceed neurotoxicity thresholds proposed for other marine predators [START_REF] Krey | Assessment of Neurotoxic Effects of Mercury in Beluga Whales (Delphinapterus Leucas), Ringed Seals (Pusa Hispida), and Polar Bears (Ursus Maritimus) from the Canadian Arctic[END_REF][START_REF] López-Berenguer | A Critical Review about Neurotoxic Effects in Marine Mammals of Mercury and Other Trace Elements[END_REF] and potentially pose an additional threat to this vulnerable species.

Large white sharks are known to aggregate near coastal seal colonies across the global oceans [START_REF] Huveneers | Future Research Directions on the "Elusive" White Shark[END_REF] . In the Northeastern Pacific, reproductively mature individuals migrate seasonally from aggregation areas in the productive ecosystem of the California Current (e.g. Guadalupe Island in Mexico and Central California in the USA) [START_REF] Jorgensen | Connectivity among White Shark Coastal Aggregation Areas in the Northeastern Pacific[END_REF] , to oceanic habitats in the oligotrophic waters of the North Pacific Gyre [START_REF] Jorgensen | Philopatry and Migration of Pacific White Sharks[END_REF][START_REF] Jorgensen | Eating or Meeting? Cluster Analysis Reveals Intricacies of White Shark (Carcharodon Carcharias) Migration and Offshore Behavior[END_REF] . While the hunting behavior of white sharks on seals in coastal environments has been widely documented [START_REF] Long | White Shark Predation on Four Pinniped Species in Central California WatersGeographic and Temporal Patterns Inferred from Wounded Carcasses[END_REF][START_REF] Hammerschlag | Effects of Environmental Conditions on Predator-Prey Interactions between White Sharks (Carcharodon Carcharias) and Cape Fur Seals (Arctocephalus Pusillus Pusillus) at Seal Island, South Africa[END_REF][START_REF] Brown | Dynamics of White Shark Predation on Pinnipeds in California: Effects of Prey Abundance[END_REF] , little is known about their feeding ecology in the open ocean [START_REF] Domeier | Migration Patterns of White Sharks Carcharodon Carcharias Tagged at Guadalupe Island, Mexico, and Identification of an Eastern Pacific Shared Offshore Foraging Area[END_REF][START_REF] Nasby-Lucas | White Shark Offshore Habitat: A Behavioral and Environmental Characterization of the Eastern Pacific Shared Offshore Foraging Area[END_REF] . Recently, offshore movements of blue and white sharks in the Atlantic Ocean have been linked to oceanic processes and more particularly to mesoscale eddies [START_REF] Braun | Mesoscale Eddies Release Pelagic Sharks from Thermal Constraints to Foraging in the Ocean Twilight Zone[END_REF][START_REF] Gaube | Mesoscale Eddies Influence the Movements of Mature Female White Sharks in the Gulf Stream and Sargasso Sea[END_REF] . The vertical mixing dynamics associated with these structures may facilitate access to deep mesopelagic prey. In the Northeast Pacific Ocean, tagging studies revealed that white sharks perform offshore dives in the mesopelagic zone [START_REF] Jorgensen | Eating or Meeting? Cluster Analysis Reveals Intricacies of White Shark (Carcharodon Carcharias) Migration and Offshore Behavior[END_REF][START_REF] Weng | Migration and Habitat of White Sharks (Carcharodon Carcharias) in the Eastern Pacific Ocean[END_REF] . Foraging in these depths, also called the twilight zone (i.e. between 200 and 1000m deep), enables access to the largest fish biomass in the global ocean [START_REF] Irigoien | Large Mesopelagic Fishes Biomass and Trophic Efficiency in the Open Ocean[END_REF] . Despite the growing number of studies suggesting that it constitutes a crucial foraging habitat for large pelagic predators, no direct evidence of deep water feeding by white sharks has been provided to date in the Northeastern Pacific.

As MeHg production by bacterial transformation is enhanced in deep low oxygen waters [START_REF] Blum | Methylmercury Production below the Mixed Layer in the North Pacific Ocean[END_REF] , MeHg exposure increases with foraging depth in pelagic consumers at both the interspecific [START_REF] Choy | The Influence of Depth on Mercury Levels in Pelagic Fishes and Their Prey[END_REF] and intraspecific scale [START_REF] Madigan | Mercury Stable Isotopes Reveal Influence of Foraging Depth on Mercury Concentrations and Growth in Pacific Bluefin Tuna[END_REF][START_REF] Peterson | Marine Foraging Ecology Influences Mercury Bioaccumulation in Deep-Diving Northern Elephant Seals[END_REF] , when feeding on mesopelagic prey [START_REF] Thompson | Seabirds as Biomonitors of Mercury Inputs to Epipelagic and Mesopelagic Marine Food Chains[END_REF] . Pinnipeds, such as the northern elephant seal (Mirounga angustirostris) targeted by white sharks in the Northeastern Pacific, are predators themselves and can display high MeHg concentrations [START_REF] Peterson | Marine Foraging Ecology Influences Mercury Bioaccumulation in Deep-Diving Northern Elephant Seals[END_REF][START_REF] Peterson | Foraging and Fasting Can Influence Contaminant Concentrations in Animals: An Example with Mercury Contamination in a Free-Ranging Marine Mammal[END_REF] , generally exceeding MeHg levels in pelagic fish, squid [START_REF] Ferriss | Does Trophic Structure Dictate Mercury Concentrations in Top Predators? A Comparative Analysis of Pelagic Food Webs in the Pacific Ocean[END_REF][START_REF] Houssard | A Model of Mercury Distribution in Tuna from the Western and Central Pacific Ocean: Influence of Physiology, Ecology and Environmental Factors[END_REF] , and other mesopelagic prey [START_REF] Monteiro | Mercury Concentrations in Prey Fish Indicate Enhanced Bioaccumulation in Mesopelagic Environments[END_REF] . The high MeHg concentrations found both in pinnipeds and in potential offshore prey raise the question of the relative MeHg exposure associated with different prey, and different foraging depths, during the migratory cycle of white sharks between inshore and offshore habitats.

Mercury (Hg) isotopes present multiple useful signatures due to classical massdependent isotope fractionation (MDF, reported as δ 202 Hg) and unique photochemical massindependent fractionation (MIF, reported as Δ 199 Hg). These properties enable tracing MeHg sources in marine environments [START_REF] Sackett | Mercury Sources and Trophic Ecology for Hawaiian Bottomfish[END_REF][START_REF] Masbou | Hg-Stable Isotope Variations in Marine Top Predators of the Western Arctic Ocean[END_REF][START_REF] Cransveld | Mercury Stable Isotopes Discriminate Different Populations of European Seabass and Trace Potential Hg Sources around Europe[END_REF] . While Hg MDF is the result of various abiotic (e.g. photoreduction, volatilization) [START_REF] Bergquist | Mass-Dependent and -Independent Fractionation of Hg Isotopes by Photoreduction in Aquatic Systems[END_REF][START_REF] Zheng | Mercury Isotope Fractionation during Volatilization of Hg( 0 ) from Solution into the Gas Phase[END_REF] and biotic processes (e.g. methylation, demethylation) 44- 46 , Hg MIF occurs predominantly during photochemical reactions [START_REF] Bergquist | Mass-Dependent and -Independent Fractionation of Hg Isotopes by Photoreduction in Aquatic Systems[END_REF] . In seawater, solar radiations induce a MIF gradient from the surface to depths, which leads to higher Δ 199 Hg values in the photic or epipelagic zone (between 0 and 200m deep) than in the twilight or mesopelagic zone (between 200 and 1000m deep) where light penetration varies from weak to zero [START_REF] Blum | Methylmercury Production below the Mixed Layer in the North Pacific Ocean[END_REF][START_REF] Sackett | Nitrogen, and Mercury Isotope Evidence for the Biogeochemical History of Mercury in Hawaiian Marine Bottomfish[END_REF] . Thus, Δ 199 Hg values constitute a powerful tool to trace the feeding depth of marine predators, for instance discriminating epipelagic from mesopelagic foraging habitats [START_REF] Madigan | Mercury Stable Isotopes Reveal Influence of Foraging Depth on Mercury Concentrations and Growth in Pacific Bluefin Tuna[END_REF][START_REF] Croizier | Mercury Isotopes as Tracers of Ecology and Metabolism in Two Sympatric Shark Species[END_REF] . Importantly, Δ 199 Hg values are conserved between prey and predators, due to the absence of Hg MIF during trophic transfers or metabolic processes [START_REF] Masbou | Hg-Stable Isotope Variations in Marine Top Predators of the Western Arctic Ocean[END_REF][START_REF] Perrot | Natural Hg Isotopic Composition of Different Hg Compounds in Mammal Tissues as a Proxy for in Vivo Breakdown of Toxic Methylmercury[END_REF][START_REF] Kwon | Absence of Fractionation of Mercury Isotopes during Trophic Transfer of Methylmercury to Freshwater Fish in Captivity[END_REF][START_REF] Kwon | Quantifying Mercury Isotope Dynamics in Captive Pacific Bluefin Tuna (Thunnus Orientalis)[END_REF] , which reveals MeHg dietary transfers and therefore predator-prey interactions.

Climate change is predicted to increase MeHg contamination in marine predators, due to increases in seawater temperature and deoxygenation [START_REF] Schartup | Climate Change and Overfishing Increase Neurotoxicant in Marine Predators[END_REF] . A proper characterization of trophic MeHg pathways is therefore needed to foresee the evolution of neurotoxicant levels in species, particularly in predators that influence the function of marine ecosystems.

In this context, this study sought to evaluate the contribution of different prey groups to MeHg contamination in the white shark. Additionally, our aim was to estimate shark foraging depths and assess the existence of trophic interactions between white sharks and mesopelagic prey. To achieve these objectives, we collected dermis and muscle samples from 95 Northeastern Pacific white sharks in the waters surrounding the aggregation site of Guadalupe Island (Mexico), as well as hair samples from juvenile northern elephant seals, which are a primary prey of white sharks foraging in this region [START_REF] Brown | Dynamics of White Shark Predation on Pinnipeds in California: Effects of Prey Abundance[END_REF][START_REF] Jorgensen | Killer Whales Redistribute White Shark Foraging Pressure on Seals[END_REF] . We measured Hg isotope signatures from shark and seal samples, and compared those with potential prey for white sharks obtained from published studies in the Central North Pacific [START_REF] Blum | Methylmercury Production below the Mixed Layer in the North Pacific Ocean[END_REF] and Northeast Pacific [START_REF] Madigan | Mercury Stable Isotopes Reveal Influence of Foraging Depth on Mercury Concentrations and Growth in Pacific Bluefin Tuna[END_REF] . We used a Bayesian mixing model based on Hg isotopes to determine both the trophic MeHg sources and the vertical foraging habitat of white sharks. This innovative chemical tracer approach provides an understanding of contaminant exposure, as well as new insights in the trophic ecology of a key marine top predator.

Materials and methods

Sample collection

White sharks (n = 95) and northern elephant seals (NES, n = 10) were sampled at Guadalupe Island in the Mexican Pacific, between the months of September and November. Shark samples were collected in 2016, 2017 and 2018, and seal samples in 2018. Freeswimming white sharks were attracted with dead baits (Thunnus albacares) near the scientific boat. Samples (dermis and muscle) were taken using a biopsy probe (1 cm diameter) targeting the tissue directly below the dorsal fin [START_REF] Meyer | Simple Biopsy Modification to Collect Muscle Samples from Free-Swimming Sharks[END_REF] . The same device was used to collect NES hair on one of the island's beaches. The biopsy probe was cleaned and rinsed with alcohol before and between samples. After collection, tissue samples were immediately transferred to a -20 °C freezer onboard the vessel. Individual sharks were sexed (based on the presence or absence of claspers) and sized to the nearest 10 cm using visual size estimates. White sharks ranged from 2m to 5m total length (TL) and were composed of juveniles (< 3m TL), subadults (3-3.6m TL for males and 3-4.8m TL for females) and adults (> 3.6m TL for males and > 4.8m TL for females) [START_REF] Domeier | Global Perspectives on the Biology and Life History of the White Shark[END_REF] (SI Appendix, Table S3). Samples were collected from different individuals including 54 females, 34 males and 7 unsexed sharks.

Dermis and muscle tissues come from different sharks. Sex and maturity stage of seals were visually determined. Most seals were juveniles and subadults (SI Appendix, Table S3).

Mercury analyzes

Total Hg (THg) is known to be predominantly in the MeHg form in the dermis and muscle of various shark species [START_REF] Croizier | Mercury Isotopes as Tracers of Ecology and Metabolism in Two Sympatric Shark Species[END_REF][START_REF] Matulik | Bioaccumulation and Biomagnification of Mercury and Methylmercury in Four Sympatric Coastal Sharks in a Protected Subtropical Lagoon[END_REF][START_REF] Pethybridge | Mercury in 16 Demersal Sharks from Southeast Australia: Biotic and Abiotic Sources of Variation and Consumer Health Implications[END_REF][START_REF] De Carvalho | Assessment of Total and Organic Mercury Levels in Blue Sharks (Prionace Glauca) from the South and Southeastern Brazilian Coast[END_REF][START_REF] Bosch | Heavy Metal Accumulation and Toxicity in Smoothhound (Mustelus Mustelus) Shark from Langebaan Lagoon, South Africa[END_REF][START_REF] Nalluri | Methylmercury in Dried Shark Fins and Shark Fin Soup from American Restaurants[END_REF] , aquatic and marine mammal hair [59][60][61] , as well as in pelagic fish muscle and squid mantle [START_REF] Blum | Methylmercury Production below the Mixed Layer in the North Pacific Ocean[END_REF][START_REF] Madigan | Mercury Stable Isotopes Reveal Influence of Foraging Depth on Mercury Concentrations and Growth in Pacific Bluefin Tuna[END_REF] . THg was thus used as a proxy for MeHg concentrations in all the species studied here. Moreover, THg isotope ratios in sharks and seals analyzed in this work, or obtained in pelagic organisms from previous studies [START_REF] Blum | Methylmercury Production below the Mixed Layer in the North Pacific Ocean[END_REF][START_REF] Madigan | Mercury Stable Isotopes Reveal Influence of Foraging Depth on Mercury Concentrations and Growth in Pacific Bluefin Tuna[END_REF] , mainly reflect the isotopic signature of MeHg. Consequently, considering that MeHg (unlike inorganic mercury) is the main Hg form transferred between prey and predators 62,63 , we refer throughout the text to MeHg, although MeHg fraction was not measured in our samples.

Blubber and muscle constitute most of the tissues ingested by sharks when eating a seal, and these tissues may have different integration time than hair. However, NES only feed during offshore foraging trips, fasting completely from food and water when at rookeries, such as Guadalupe Island 64 . This onshore fasting implies that MeHg in all seal tissues may come from the same offshore dietary sources 65 . Moreover, as MeHg isotope ratios are similar between different seal tissues fed a constant diet [START_REF] Perrot | Natural Hg Isotopic Composition of Different Hg Compounds in Mammal Tissues as a Proxy for in Vivo Breakdown of Toxic Methylmercury[END_REF] , and MeHg fraction is high in seal hair 60 , Δ 199 Hg and δ 202 Hg values of THg in NES hair represent a relevant proxy for MeHg isotopic signature in other tissues (e.g. blubber and muscle) 60 .

-Total Hg concentrations Once in the laboratory, samples were lyophilized and homogenized using an electric grinder that was rinsed with alcohol between samples. THg determination was carried out on aliquots (around 10 mg) of homogenized shark and seal samples by combustion, gold trapping and atomic absorption spectrophotometry detection using a DMA80 analyzer (Milestone, USA). THg concentrations in samples are expressed on a dry weight basis (ng•g -1 dw). Only one analysis was performed per sample, but the accuracy and reproducibility of the method were established using two freeze-dried certified biological material: a tuna fish flesh homogenate reference material (IAEA 436, IRMM) and a lobster hepatopancreas reference material (TORT 3, NRCC). The certified values for IAEA 436 (4.19 ± 0.36 μg•g -1 dw, n = 10) were reproduced (measured value: 4.33 ± 0.19 μg•g -1 dw) within the confidence limits. The certified values for TORT 3 (0.292 ± 0.022 μg•g -1 dw) were also reproduced (measured value: 0.286 ± 0.024 μg•g -1 dw, n = 10) within the confidence limits. The detection limit was 0.005 μg•g -1 dw.

-Hg isotopes Aliquots of approximately 10 mg of dry muscle or 20 mg of dry dermis were left over night at room temperature in 3 mL of concentrated bi-distilled nitric acid (HNO3). Samples were then digested on a hotplate for 6h at 85°C in pyrolyzed glass vessels closed by Teflon caps. One mL of hydrogen peroxide (H2O2) was added and digestion was continued for another 6h at 85°C. One hundred µL of BrCl was then added to ensure a full conversion of MeHg to inorganic Hg. The digest mixtures were finally diluted in an inverse aqua regia S1). Duplicate analyzes were performed on a subset of 15 shark samples to assess δ 202 Hg (2SD = 0.12‰) and ∆ 199 Hg (2SD = 0.10 ‰) long-term reproducibility. Measured isotope signatures as well as analytical reproducibility of standards were found to be in agreement with previously published values [START_REF] Blum | Methylmercury Production below the Mixed Layer in the North Pacific Ocean[END_REF][66][67][68] (SI Appendix, Table S1).

Data treatment

Two previous studies analyzed Hg isotopes from pelagic biota in the foraging habitat of Northeast Pacific white sharks (i.e. Central North Pacific [START_REF] Blum | Methylmercury Production below the Mixed Layer in the North Pacific Ocean[END_REF] and Northeast Pacific 32 ) (Figure 1). As Hg isotope ratios decrease with increasing foraging depth [START_REF] Madigan | Mercury Stable Isotopes Reveal Influence of Foraging Depth on Mercury Concentrations and Growth in Pacific Bluefin Tuna[END_REF] , these potential prey were classified in groups according to their vertical feeding habitat based on individual Δ 199 Hg and δ 202 Hg values (SI Appendix, Table S2), using a K-means cluster analysis 69 . This clustering method delineates groups in the dataset by minimizing the sum of the within-group sums of squared-distances, based on Euclidean distance. The number of groups for the partition was defined using the Caliński-Harabasz criterion 70 . Two groups were identified (SI Appendix, Table S2 and Figure S1): a first with higher Δ 199 Hg (2.69 ± 0.45 ‰) and δ 202 Hg (0.83 ± 0.18 ‰) representing epipelagic species ("EPI", n = 21), a second group with lower Δ 199 Hg (1.60 ± 0.31 ‰) and δ 202 Hg (0.40 ± 0.24 ‰) gathering mesopelagic organisms ("MES", n = 35). These groups contain fish and squid species which may be targeted by white sharks or which are representative of a certain foraging depth. As the Hg isotope signature reflects the feeding depth (i.e. where Hg is trophically assimilated), the vertical classification of some species may differ from the literature which uses either the median depth of occurrence [START_REF] Blum | Methylmercury Production below the Mixed Layer in the North Pacific Ocean[END_REF] or to the depth of maximum occurrence [START_REF] Madigan | Mercury Stable Isotopes Reveal Influence of Foraging Depth on Mercury Concentrations and Growth in Pacific Bluefin Tuna[END_REF] . Flying fish were not included in the analysis since only three individuals from a single species would have formed a fourth group due to outlying Δ 199 Hg and δ 202 Hg values caused by direct proximity with the surface [START_REF] Blum | Methylmercury Production below the Mixed Layer in the North Pacific Ocean[END_REF] . Crustaceans were excluded because of their low MeHg fraction which could have biased Hg isotope analyzes [START_REF] Madigan | Mercury Stable Isotopes Reveal Influence of Foraging Depth on Mercury Concentrations and Growth in Pacific Bluefin Tuna[END_REF] , as well as juvenile Pacific bluefin tunas whose signature partially reflect the western Pacific Ocean (outside the white shark distribution) due to recent migration from west to eastern Pacific Ocean waters [START_REF] Madigan | Mercury Stable Isotopes Reveal Influence of Foraging Depth on Mercury Concentrations and Growth in Pacific Bluefin Tuna[END_REF] .

For comparison of Hg isotope ratios between groups, data were first checked for normality (Shapiro-Wilk tests) and homogeneity of variances (Bartlett tests). One-way analyses of variance (ANOVAs) were applied when these conditions were met, followed by Tukey's HSD tests when more than two groups were compared. In the absence of homoscedasticity Welch's ANOVAs with Games-Howell post hoc test were used. When variables followed a normal distribution, Pearson correlation tests were used to investigate the link between shark length and Hg isotope ratios. In the absence of normality, Spearman correlation tests were applied. To assess the relationship between Hg isotope ratios and depth, individual

Δ 199 Hg values in potential pelagic prey (i.e. fish and squids from EPI and MES groups, n = 56) were modeled using a logarithmic regression with depth as explanatory variable. Estimated species depths were taken from previous studies [START_REF] Blum | Methylmercury Production below the Mixed Layer in the North Pacific Ocean[END_REF][START_REF] Madigan | Mercury Stable Isotopes Reveal Influence of Foraging Depth on Mercury Concentrations and Growth in Pacific Bluefin Tuna[END_REF] and correspond either to the median depth of occurrence [START_REF] Blum | Methylmercury Production below the Mixed Layer in the North Pacific Ocean[END_REF] or to the depth of maximum occurrence [START_REF] Madigan | Mercury Stable Isotopes Reveal Influence of Foraging Depth on Mercury Concentrations and Growth in Pacific Bluefin Tuna[END_REF] (SI Appendix, Table S2).

Bayesian stable isotope mixing models were constructed with Δ 199 Hg and δ 202 Hg values to estimate the relative contribution of different prey groups to the MeHg burden in white sharks using the "simmr" package 71 in R. Bayesian approaches use statistical distributions to characterize the uncertainties in food source and consumer isotopic values and in estimated source contributions. Complete formulation of the models is available in the literature 72,73 .

Because Δ 199 Hg values are conserved between diet and consumer fish [START_REF] Kwon | Absence of Fractionation of Mercury Isotopes during Trophic Transfer of Methylmercury to Freshwater Fish in Captivity[END_REF][START_REF] Kwon | Quantifying Mercury Isotope Dynamics in Captive Pacific Bluefin Tuna (Thunnus Orientalis)[END_REF]74 and following prior studies [START_REF] Madigan | Mercury Stable Isotopes Reveal Influence of Foraging Depth on Mercury Concentrations and Growth in Pacific Bluefin Tuna[END_REF] , no trophic discrimination factor (TDF) for Δ 199 Hg was incorporated in the models. However, MeHg demethylation has recently been suggested in shark species, leading to an increase in δ 202 Hg values in sharks compared to their prey [START_REF] Croizier | Mercury Isotopes as Tracers of Ecology and Metabolism in Two Sympatric Shark Species[END_REF] . Although this δ 202 Hg TDF is poorly characterized to date, our models considered different δ 202 Hg TDF ranging from 0 to 1‰, based on previous studies on sharks and aquatic mammals [START_REF] Perrot | Natural Hg Isotopic Composition of Different Hg Compounds in Mammal Tissues as a Proxy for in Vivo Breakdown of Toxic Methylmercury[END_REF][START_REF] Croizier | Mercury Isotopes as Tracers of Ecology and Metabolism in Two Sympatric Shark Species[END_REF]75,[START_REF] Li | Selenium and Stable Mercury Isotopes Provide New Insights into Mercury Toxicokinetics in Pilot Whales[END_REF] .

The source data were incorporated in the mean ± SD form. Models were run with generalist prior distributions and Markov Chain Monte Carlo (MCMC) simulation methods (number of iterations = 100000, size of burn-in = 10000, amount of thinning = 100 and number of MCMC chains = 4). Convergence of the models was checked using Gelman-Rubin diagnostics. In all cases, the Gelman-Rubin diagnostic was 1, indicating good convergence.

All statistical analyses were performed using the open source software R (version 3.6.2, R Core Team, 2020).

Results and Discussion

MeHg exposure during the nearshore season

In white sharks sampled at Guadalupe Island, Hg isotope values were higher in dermis (Δ 199 Hg = 1.66 ± 0.22‰ and δ 202 Hg = 1.15 ± 0.27‰) compared to muscle (Δ 199 Hg = 1.54 ± 0.18‰ and δ 202 Hg = 0.88 ± 0.25‰) (Figure 2, Figure 3). While δ 202 Hg can vary between tissues due to Hg metabolism [START_REF] Li | Selenium and Stable Mercury Isotopes Provide New Insights into Mercury Toxicokinetics in Pilot Whales[END_REF][START_REF] Bolea-Fernández | High-Precision Isotopic Analysis Sheds New Light on Mercury Metabolism in Long-Finned Pilot Whales (Globicephala Melas)[END_REF] , Δ 199 Hg values are not affected by trophic transfer or biological processes, leading to similar Δ 199 Hg values between the different tissues of a consumer with a constant diet [START_REF] Perrot | Natural Hg Isotopic Composition of Different Hg Compounds in Mammal Tissues as a Proxy for in Vivo Breakdown of Toxic Methylmercury[END_REF][START_REF] Kwon | Absence of Fractionation of Mercury Isotopes during Trophic Transfer of Methylmercury to Freshwater Fish in Captivity[END_REF]74,[START_REF] Li | Selenium and Stable Mercury Isotopes Provide New Insights into Mercury Toxicokinetics in Pilot Whales[END_REF] . However, Δ 199 Hg values may fluctuate between organs if MeHg exposure changes over time and if tissues exhibit contrasting integration times due to different turnover rates. For instance, arctic seabirds displayed higher Δ 199 Hg values in feathers compared to blood, reflecting seasonal dietary changes and different integration times for MeHg exposure among tissues [START_REF] Renedo | Seabird Tissues As Efficient Biomonitoring Tools for Hg Isotopic Investigations: Implications of Using Blood and Feathers from Chicks and Adults[END_REF] . In the Northeast Pacific, white sharks are primarily concentrated along the west coast of North America from late summer to early winter while the rest of the year they migrate into oceanic habitats [START_REF] Jorgensen | Philopatry and Migration of Pacific White Sharks[END_REF][START_REF] Domeier | Migration Patterns of White Sharks Carcharodon Carcharias Tagged at Guadalupe Island, Mexico, and Identification of an Eastern Pacific Shared Offshore Foraging Area[END_REF][START_REF] Weng | Migration and Habitat of White Sharks (Carcharodon Carcharias) in the Eastern Pacific Ocean[END_REF][START_REF] Carlisle | Using Stable Isotope Analysis to Understand the Migration and Trophic Ecology of Northeastern Pacific White Sharks (Carcharodon Carcharias)[END_REF] . In aggregation sites such as Guadalupe Island, white sharks have been shown to feed mainly on pinniped species such as sea lions, fur seals and elephant seals [START_REF] Long | White Shark Predation on Four Pinniped Species in Central California WatersGeographic and Temporal Patterns Inferred from Wounded Carcasses[END_REF][START_REF] Brown | Dynamics of White Shark Predation on Pinnipeds in California: Effects of Prey Abundance[END_REF] while in the open Pacific ocean they are thought to consume pelagic prey [START_REF] Carlisle | Using Stable Isotope Analysis to Understand the Migration and Trophic Ecology of Northeastern Pacific White Sharks (Carcharodon Carcharias)[END_REF][START_REF] Jaime-Rivera | Feeding and Migration Habits of White Shark Carcharodon Carcharias (Lamniformes: Lamnidae) from Isla Guadalupe Inferred by Analysis of Stable Isotopes Δ15N and Δ13C[END_REF] , even if targeted species remain largely unidentified [START_REF] Domeier | Migration Patterns of White Sharks Carcharodon Carcharias Tagged at Guadalupe Island, Mexico, and Identification of an Eastern Pacific Shared Offshore Foraging Area[END_REF][START_REF] Nasby-Lucas | White Shark Offshore Habitat: A Behavioral and Environmental Characterization of the Eastern Pacific Shared Offshore Foraging Area[END_REF] . Using carbon and nitrogen stable isotopes (δ 13 C and δ 15 N), previous studies suggested that muscle and dermis have different turnover rates in sharks [START_REF] Carlisle | Using Stable Isotope Analysis to Understand the Migration and Trophic Ecology of Northeastern Pacific White Sharks (Carcharodon Carcharias)[END_REF][START_REF] Li | Quantifying Ontogenetic Stable Isotope Variation between Dermis and Muscle Tissue of Two Pelagic Sharks[END_REF][START_REF] Prebble | Limited Latitudinal Ranging of Juvenile Whale Sharks in the Western Indian Ocean Suggests the Existence of Regional Management Units[END_REF] . Moreover, dermis δ 13 C and δ 15 N values of white sharks sampled along the coast of California closely resembled isotopic composition of local pinnipeds, suggesting that dermis displays a faster incorporation rate from prey than muscle tissues, and reflects more recent foraging activity northern elephant seal (NES) (Figure 2, Figure 3). However, Bayesian mixing models estimated that the NES contribution to shark MeHg exposure was higher in dermis than in muscle (e.g. 46% versus 25% without δ 202 Hg TDF, respectively) (Figure 4). In accordance with previous conclusions based on δ 13 C and δ 15 N values [START_REF] Carlisle | Using Stable Isotope Analysis to Understand the Migration and Trophic Ecology of Northeastern Pacific White Sharks (Carcharodon Carcharias)[END_REF] , Hg isotopes support the hypothesis of a shorter integration time in dermis compared to muscle, as dermis Hg isotope values indicate these tissues are more influenced by the recent consumption of pinnipeds at Guadalupe Island. Importantly, these results reveal that seals represent a significant source of MeHg exposure for white sharks during the nearshore season, accounting for half of MeHg in dermis.

MeHg origin at the scale of the entire migration cycle

Skeletal muscle tissue is believed to integrate dietary MeHg over durations of approximately 1,000 days based on Δ 199 Hg values of captive Pacific bluefin tuna (Thunnus orientalis), which were fed a controlled diet [START_REF] Kwon | Quantifying Mercury Isotope Dynamics in Captive Pacific Bluefin Tuna (Thunnus Orientalis)[END_REF] . This slow turnover time, in a metabolically active fish species with similar physiology traits to white sharks [START_REF] Bernal | Review: Analysis of the Evolutionary Convergence for High Performance Swimming in Lamnid Sharks and Tunas[END_REF][START_REF] Donley | Convergent Evolution in Mechanical Design of Lamnid Sharks and Tunas[END_REF] , enables determining the average origin of MeHg exposure across the entire migratory cycle of white sharks, including both oceanic and coastal seasons. Using muscle δ 13 C and δ 15 N values, it has been previously suggested that during the coastal season, northeast Pacific white sharks in California have approximately twice the prey consumption rate compared to when they are offshore [START_REF] Carlisle | Using Stable Isotope Analysis to Understand the Migration and Trophic Ecology of Northeastern Pacific White Sharks (Carcharodon Carcharias)[END_REF] .

Despite previous results suggesting juvenile elephant seals (NES) are one of the main prey for white sharks near pinniped colonies such as Guadalupe Island [START_REF] Long | White Shark Predation on Four Pinniped Species in Central California WatersGeographic and Temporal Patterns Inferred from Wounded Carcasses[END_REF][START_REF] Brown | Dynamics of White Shark Predation on Pinnipeds in California: Effects of Prey Abundance[END_REF][START_REF] Jorgensen | Killer Whales Redistribute White Shark Foraging Pressure on Seals[END_REF][START_REF] Klimley | The Hunting Strategy of White Sharks (Carcharodon Carcharias) near a Seal Colony[END_REF] , their Hg signature differed significantly from that of sharks (Figure 2, Figure 3). Because Δ 199 Hg values decrease with depth, lower Δ 199 Hg values in white sharks may indicate deeper foraging depths compared to juvenile NES 65 . In addition, high δ 202 Hg values are commonly observed in mammals and are thought to reflect in vivo demethylation of MeHg [START_REF] Perrot | Natural Hg Isotopic Composition of Different Hg Compounds in Mammal Tissues as a Proxy for in Vivo Breakdown of Toxic Methylmercury[END_REF][START_REF] Li | Selenium and Stable Mercury Isotopes Provide New Insights into Mercury Toxicokinetics in Pilot Whales[END_REF][START_REF] Bolea-Fernández | High-Precision Isotopic Analysis Sheds New Light on Mercury Metabolism in Long-Finned Pilot Whales (Globicephala Melas)[END_REF] , which probably sets NES apart from other prey groups and white sharks. Consequently, according to Bayesian mixing models based on Hg isotope tracers, the NES contribution to MeHg levels in shark muscle was estimated to be 25% maximum (Figure 4B). Lipid reserves represent major sources of metabolic energy in marine predators that have very high energetic requirements related to long migrations [START_REF] Del Raye | Travelling Light: White Sharks (Carcharodon Carcharias) Rely on Body Lipid Stores to Power Ocean-Basin Scale Migration[END_REF][START_REF] Pethybridge | Fatty Acid and Energy Density Profiles of White Sharks: Insights into the Feeding Ecology and Ecophysiology of a Complex Top Predator[END_REF] . To cover energy needs related to undertaking long migrations, white sharks are hypothesized to rely primarily on the blubber of marine mammals during the inshore season [START_REF] Del Raye | Travelling Light: White Sharks (Carcharodon Carcharias) Rely on Body Lipid Stores to Power Ocean-Basin Scale Migration[END_REF][START_REF] Moxley | Non-Trophic Impacts from White Sharks Complicate Population Recovery for Sea Otters[END_REF][START_REF] Hoyos-Padilla | Contrasts in the Movements and Habitat Use of Juvenile and Adult White Sharks (Carcharodon Carcharias) at Guadalupe Island, Mexico[END_REF] . Indeed, fat can exceed 40% of the total body mass in juvenile NES 64 , which are believed to be a preferred prey for white sharks due to their high energy supply [START_REF] Jorgensen | Killer Whales Redistribute White Shark Foraging Pressure on Seals[END_REF][START_REF] Klimley | The Hunting Strategy of White Sharks (Carcharodon Carcharias) near a Seal Colony[END_REF] . As MeHg primarily binds to thiol-containing amino acids in proteins [START_REF] Thera | Tissue Content of Thiol-Containing Amino Acids Predicts Methylmercury in Aquatic Invertebrates[END_REF][START_REF] Lemes | Methylmercury Speciation in Fish Muscle by HPLC-ICP-MS Following Enzymatic Hydrolysis[END_REF][START_REF] Harris | The Chemical Form of Mercury in Fish[END_REF] , blubber which is mainly composed of lipids generally contains low MeHg levels in seals [START_REF] Gmelch | Risk-Benefit Assessment of Monomethylmercury and Omega-3 Fatty Acid Intake for Ringed Seal Consumption with Particular Emphasis on Vulnerable Populations in the Western Canadian Arctic[END_REF] . Thus, despite a presumed high feeding rate during the inshore season [START_REF] Carlisle | Using Stable Isotope Analysis to Understand the Migration and Trophic Ecology of Northeastern Pacific White Sharks (Carcharodon Carcharias)[END_REF] , low MeHg levels in pinniped blubber may be responsible for the limited contribution of NES to the global MeHg exposure for white sharks (Figure 4B). Electronic tags have rapidly increased our knowledge on marine predator movements [START_REF] Block | Tracking Apex Marine Predator Movements in a Dynamic Ocean[END_REF][START_REF] Hussey | Aquatic Animal Telemetry: A Panoramic Window into the Underwater World[END_REF][START_REF] Skomal | Movements of the White Shark Carcharodon Carcharias in the North Atlantic Ocean[END_REF] and revealed that many perform large migrations from forage rich coastal realms to offshore oceanic areas traditionally considered deserts [START_REF] Jorgensen | Eating or Meeting? Cluster Analysis Reveals Intricacies of White Shark (Carcharodon Carcharias) Migration and Offshore Behavior[END_REF][START_REF] Domeier | Migration Patterns of White Sharks Carcharodon Carcharias Tagged at Guadalupe Island, Mexico, and Identification of an Eastern Pacific Shared Offshore Foraging Area[END_REF] . Recently, these types of movements have been linked to ocean physics and more specifically to mesoscale eddies, which induce regional penetration of warm surface waters to depths of up to 800m [START_REF] Braun | Mesoscale Eddies Release Pelagic Sharks from Thermal Constraints to Foraging in the Ocean Twilight Zone[END_REF] .

Mesoscale eddies are hypothesized to improve access to deep-sea mesopelagic prey for blue sharks (Prionace glauca) [START_REF] Braun | Mesoscale Eddies Release Pelagic Sharks from Thermal Constraints to Foraging in the Ocean Twilight Zone[END_REF] and white sharks [START_REF] Gaube | Mesoscale Eddies Influence the Movements of Mature Female White Sharks in the Gulf Stream and Sargasso Sea[END_REF] in the Atlantic Ocean, by releasing them from thermal constraints and reducing the physiological costs of thermoregulation, respectively.

Although the twilight zone contains the largest fish biomass in the global ocean [START_REF] Irigoien | Large Mesopelagic Fishes Biomass and Trophic Efficiency in the Open Ocean[END_REF] , so far there has not been direct evidence of trophic connections between white sharks and mesopelagic organisms in the Pacific Ocean. Here, Δ 199 Hg values in white shark tissues were similar to mesopelagic (MES) prey (Figure 2, Figure 3), which we estimated to be the main MeHg source for white sharks, accounting for a minimum of 52% of dermis MeHg and 72% of muscle MeHg (Figure 4A and4B). These results align with previous observations revealing higher MeHg exposure associated with deeper foraging depths in pelagic fish from the Pacific Ocean [START_REF] Choy | The Influence of Depth on Mercury Levels in Pelagic Fishes and Their Prey[END_REF][START_REF] Madigan | Mercury Stable Isotopes Reveal Influence of Foraging Depth on Mercury Concentrations and Growth in Pacific Bluefin Tuna[END_REF] . Indeed, MeHg concentrations in Pacific waters are known to increase with depth [START_REF] Munson | Mercury Species Concentrations and Fluxes in the Central Tropical Pacific Ocean[END_REF]100 , driven by the production of MeHg below the mixed layer [START_REF] Blum | Methylmercury Production below the Mixed Layer in the North Pacific Ocean[END_REF] . As Δ 199 Hg values are not modified during MeHg trophic transfer (29-32), our results demonstrate strong evidence that white sharks actively feed on mesopelagic organisms, revealing the existence of trophic interactions that have been suspected for over a decade [START_REF] Domeier | Migration Patterns of White Sharks Carcharodon Carcharias Tagged at Guadalupe Island, Mexico, and Identification of an Eastern Pacific Shared Offshore Foraging Area[END_REF][START_REF] Nasby-Lucas | White Shark Offshore Habitat: A Behavioral and Environmental Characterization of the Eastern Pacific Shared Offshore Foraging Area[END_REF] . Finally, Δ 199 Hg values in white shark muscle indicate an exposure to MeHg having undergone weak photochemical degradation in the twilight zone (i.e. low values, Figure 5). As NES are not the main contributor to overall MeHg exposure (Figure 4B), and as white shark distribution during the coastal season is confined bathymetrically primarily to the photic zone (i.e. above 200m) [START_REF] Jorgensen | Eating or Meeting? Cluster Analysis Reveals Intricacies of White Shark (Carcharodon Carcharias) Migration and Offshore Behavior[END_REF][START_REF] Domeier | Migration Patterns of White Sharks Carcharodon Carcharias Tagged at Guadalupe Island, Mexico, and Identification of an Eastern Pacific Shared Offshore Foraging Area[END_REF][START_REF] Weng | Migration and Habitat of White Sharks (Carcharodon Carcharias) in the Eastern Pacific Ocean[END_REF][START_REF] Hoyos-Padilla | Contrasts in the Movements and Habitat Use of Juvenile and Adult White Sharks (Carcharodon Carcharias) at Guadalupe Island, Mexico[END_REF] , the low Hg MIF observed in shark tissues strongly suggests a dominant MeHg origin from offshore deep waters. This conclusion is supported by observed diving behaviors in oceanic habitats, where white sharks frequently reached 500m [START_REF] Jorgensen | Eating or Meeting? Cluster Analysis Reveals Intricacies of White Shark (Carcharodon Carcharias) Migration and Offshore Behavior[END_REF][START_REF] Weng | Migration and Habitat of White Sharks (Carcharodon Carcharias) in the Eastern Pacific Ocean[END_REF] and occasionally 1,000m [START_REF] Domeier | Migration Patterns of White Sharks Carcharodon Carcharias Tagged at Guadalupe Island, Mexico, and Identification of an Eastern Pacific Shared Offshore Foraging Area[END_REF][START_REF] Gaube | Mesoscale Eddies Influence the Movements of Mature Female White Sharks in the Gulf Stream and Sargasso Sea[END_REF]101 .

Hg isotopes to interpret white shark movements and habitat use

Contrasting habitat use was previously identified between juvenile and adult white sharks at Guadalupe Island [START_REF] Hoyos-Padilla | Contrasts in the Movements and Habitat Use of Juvenile and Adult White Sharks (Carcharodon Carcharias) at Guadalupe Island, Mexico[END_REF] , which could potentially influence MeHg exposure and therefore Hg isotope signatures. Juvenile white sharks at Guadalupe Island remained close to the shore and in shallow water (i.e. primarily between the surface and 50m depth), probably to avoid adults patrolling in deeper water (up to 200m depth) in search for an opportunity to attack seals [START_REF] Hoyos-Padilla | Contrasts in the Movements and Habitat Use of Juvenile and Adult White Sharks (Carcharodon Carcharias) at Guadalupe Island, Mexico[END_REF] . Moreover, juveniles and adults have different thermal preferences, with adults being more tolerant to colder waters, likely due to an increase in thermal inertia and thermoregulatory abilities with ontogeny [START_REF] Hoyos-Padilla | Contrasts in the Movements and Habitat Use of Juvenile and Adult White Sharks (Carcharodon Carcharias) at Guadalupe Island, Mexico[END_REF][START_REF] Skomal | Movements of the White Shark Carcharodon Carcharias in the North Atlantic Ocean[END_REF]102 . This higher thermal tolerance could result in vertical niche expansion for adult sharks, increasing exposure to MeHg with lower isotope ratios [START_REF] Blum | Methylmercury Production below the Mixed Layer in the North Pacific Ocean[END_REF] . Although both juvenile and adult sharks were considered in our study (SI Appendix, Table S3), Δ 199 Hg and δ 202 Hg values did not vary with body length for any of the two tissues analyzed (Pearson or Spearman correlation tests, p > 0.05). Thus, our results do not provide support for an effect of habitat use or thermal tolerance on foraging depth, and subsequent MeHg exposure, for white sharks over 2 meters in total length. Alternatively, both juveniles and adult sharks could have access to the same mesopelagic prey that migrate to the surface at night, facilitated by the very steep bathymetry and oceanic nature of Guadalupe Island [START_REF] Hoyos-Padilla | Contrasts in the Movements and Habitat Use of Juvenile and Adult White Sharks (Carcharodon Carcharias) at Guadalupe Island, Mexico[END_REF] .

During the seasonal offshore migration, northeast Pacific white sharks occupy a pelagic zone referred to as the "White Shark Café", also known as "Shared Offshore foraging Area" (SOFA), located in the North Pacific Sub-Tropical Gyre halfway between Hawaii and the coasts of Mexico [START_REF] Jorgensen | Philopatry and Migration of Pacific White Sharks[END_REF][START_REF] Domeier | Migration Patterns of White Sharks Carcharodon Carcharias Tagged at Guadalupe Island, Mexico, and Identification of an Eastern Pacific Shared Offshore Foraging Area[END_REF]101 . The reason why a large number of white sharks congregate in this area remains unanswered, and the two main hypotheses proposed relate to reproduction or feeding [START_REF] Jorgensen | Eating or Meeting? Cluster Analysis Reveals Intricacies of White Shark (Carcharodon Carcharias) Migration and Offshore Behavior[END_REF][START_REF] Weng | Migration and Habitat of White Sharks (Carcharodon Carcharias) in the Eastern Pacific Ocean[END_REF][START_REF] Domeier | Global Perspectives on the Biology and Life History of the White Shark[END_REF] . Pronounced sex-based structure in the diving behavior of white sharks has been identified within the Café [START_REF] Jorgensen | Eating or Meeting? Cluster Analysis Reveals Intricacies of White Shark (Carcharodon Carcharias) Migration and Offshore Behavior[END_REF] . If foraging was the only activity, the significant differences in depth occupancy between sexes 20 should be reflected by contrasting Δ 199 Hg values. Indeed, in the Café region, females mainly perform diel vertical migrations (DVM) peaking in the upper 200 meters during the night, while they occupy a water layer between 350 and 500m depth during the day (Figure 5). By contrast, males initially exhibit a mix of DVM and rapid oscillatory diving (ROD) behavior, then increasingly focus on ROD at depths between the surface and 200m (day and night), before returning to the coast [START_REF] Jorgensen | Philopatry and Migration of Pacific White Sharks[END_REF][START_REF] Jorgensen | Eating or Meeting? Cluster Analysis Reveals Intricacies of White Shark (Carcharodon Carcharias) Migration and Offshore Behavior[END_REF] . We found that muscle Δ 199 Hg and δ 202 Hg values did not differ between sexes (ANOVAs, p > 0.05), suggesting no difference in mean foraging depth between females and males at the scale of the entire migration cycle. Only a slight difference in Δ 199 Hg values was found in the more rapidly integrating dermis tissue, with lower values for females compared to males (ANOVA, p = 0.048). Since none of the previous studies has identified differences in diving behavior between males and females at Guadalupe Island [START_REF] Domeier | Migration Patterns of White Sharks Carcharodon Carcharias Tagged at Guadalupe Island, Mexico, and Identification of an Eastern Pacific Shared Offshore Foraging Area[END_REF][START_REF] Nasby-Lucas | White Shark Offshore Habitat: A Behavioral and Environmental Characterization of the Eastern Pacific Shared Offshore Foraging Area[END_REF][START_REF] Hoyos-Padilla | Contrasts in the Movements and Habitat Use of Juvenile and Adult White Sharks (Carcharodon Carcharias) at Guadalupe Island, Mexico[END_REF] or along the California coast [START_REF] Jorgensen | Eating or Meeting? Cluster Analysis Reveals Intricacies of White Shark (Carcharodon Carcharias) Migration and Offshore Behavior[END_REF][START_REF] Weng | Migration and Habitat of White Sharks (Carcharodon Carcharias) in the Eastern Pacific Ocean[END_REF]103 , the lower Δ 199 Hg values in the females' dermis likely reflects the fact that females arrive later at Guadalupe Island compared to males [START_REF] Domeier | Migration Patterns of White Sharks Carcharodon Carcharias Tagged at Guadalupe Island, Mexico, and Identification of an Eastern Pacific Shared Offshore Foraging Area[END_REF][START_REF] Hoyos-Padilla | Contrasts in the Movements and Habitat Use of Juvenile and Adult White Sharks (Carcharodon Carcharias) at Guadalupe Island, Mexico[END_REF] . At the moment of sample collection, females had spent less time in the insular habitat. Their dermis, which is mainly influenced by recent MeHg exposure, would therefore reflect to a stronger degree the offshore season, during which both sexes dive deeper and may assimilate MeHg with lower Δ 199 Hg values than in the waters surrounding Guadalupe Island [START_REF] Domeier | Migration Patterns of White Sharks Carcharodon Carcharias Tagged at Guadalupe Island, Mexico, and Identification of an Eastern Pacific Shared Offshore Foraging Area[END_REF][START_REF] Nasby-Lucas | White Shark Offshore Habitat: A Behavioral and Environmental Characterization of the Eastern Pacific Shared Offshore Foraging Area[END_REF] . Regarding DVM performed by both sexes, previous studies agree that it may reflect a foraging behavior following the diel vertical migration of the deep scattering layer (DSL), a community of mesopelagic fish and squid that rise near the surface at night and occupy the twilight zone during the day [START_REF] Jorgensen | Eating or Meeting? Cluster Analysis Reveals Intricacies of White Shark (Carcharodon Carcharias) Migration and Offshore Behavior[END_REF][START_REF] Nasby-Lucas | White Shark Offshore Habitat: A Behavioral and Environmental Characterization of the Eastern Pacific Shared Offshore Foraging Area[END_REF] . In the Café, the estimated depth at the top of this layer is 460m during the day 101 , which corresponds both to the layer occupied by white sharks engaged in daytime DVM [START_REF] Jorgensen | Eating or Meeting? Cluster Analysis Reveals Intricacies of White Shark (Carcharodon Carcharias) Migration and Offshore Behavior[END_REF] and matches the Δ 199 Hg values found in white shark tissues (Figure 5). The White Shark Café is thought to support considerable mesopelagic biomass [START_REF] Domeier | Global Perspectives on the Biology and Life History of the White Shark[END_REF] . Although DVM is not restricted to the Café and is performed throughout the entire offshore range of white sharks [START_REF] Jorgensen | Eating or Meeting? Cluster Analysis Reveals Intricacies of White Shark (Carcharodon Carcharias) Migration and Offshore Behavior[END_REF] , they may preferentially use this offshore ecosystem to target deep mesopelagic prey, as suggested in other regions [START_REF] Gaube | Mesoscale Eddies Influence the Movements of Mature Female White Sharks in the Gulf Stream and Sargasso Sea[END_REF] . While through ROD behavior males could also target the DSL which rises to the 200m zone at night [START_REF] Jorgensen | Eating or Meeting? Cluster Analysis Reveals Intricacies of White Shark (Carcharodon Carcharias) Migration and Offshore Behavior[END_REF] , daytime ROD appears incompatible with the Δ 199 Hg values found in white shark tissues (e.g. around 1.5 ‰ in muscle), which would correspond to a daytime feeding depth of over 350m (Figure 5). Alternatively, this behavior is similar to the vertical movements of Atlantic Bluefin tuna (Thunnus thynnus) at their breeding grounds 104 and has previously been proposed as a potential mating activity [START_REF] Jorgensen | Eating or Meeting? Cluster Analysis Reveals Intricacies of White Shark (Carcharodon Carcharias) Migration and Offshore Behavior[END_REF][START_REF] Weng | Migration and Habitat of White Sharks (Carcharodon Carcharias) in the Eastern Pacific Ocean[END_REF] .

Overall, Hg isotopes confirm that mesopelagic foraging occurs in the Café, but do not exclude the possibility that other behaviors such as mating could take place in this area.

In the context of climate change, global warming is expected to expand oxygenminimum zones (OMZs) by reducing oxygen supply to the ocean 105,106 . Microbial MeHg production is enhanced in mesopelagic zones, which are located in sub-thermocline oceanic waters, where oxygen concentration is low and organic matter is intensively remineralized [START_REF] Blum | Methylmercury Production below the Mixed Layer in the North Pacific Ocean[END_REF]107,108 . Thus, the expansion of the MeHg production zone suggests that MeHg exposure could increase for mesopelagic organisms and consequently for their predators such as white sharks. In addition, strong modifications in global mesopelagic biogeographic structure are predicted by the end of this century. More precisely, the mesopelagic biomass is expected to decrease in the North Pacific Tropical Gyre, including the offshore foraging habitat of northeast Pacific white sharks 109 . This study highlights the importance of the mesopelagic compartment in the diet of marine apex predators, such as white sharks. A reduction in the mesopelagic biomass could therefore alter trophic supply to sharks and / or lead to a modification of their migration patterns towards more productive offshore areas, which could alter the location or function of their potential mating area. These climatedriven changes should be carefully considered to avoid potential extinction of white sharks and their ecological roles over the next century [START_REF] Pimiento | Functional Diversity of Marine Megafauna in the Anthropocene[END_REF] . for the COFAA and EDI fellowships.

Tables and figures

Graphical abstract S2). Two offshore diving behaviors of white sharks are figured: the "rapid oscillatory diving" (ROD) behavior occurring between 0 and 200m (day and night) and the daytime "diel vertical migration" (DVM) behavior from 350 to 500m [START_REF] Jorgensen | Eating or Meeting? Cluster Analysis Reveals Intricacies of White Shark (Carcharodon Carcharias) Migration and Offshore Behavior[END_REF] . According to the ∆ 199 Hg variation in potential prey, the signature of white shark corresponds to a feeding on organisms living over 350 meters deep during the day, which matches daytime DVM but not daytime ROD. Table S2: Hg isotope signatures in pelagic fish and squids from the foraging habitat of northeast Pacific white sharks, obtained in previous studies [START_REF] Blum | Methylmercury Production below the Mixed Layer in the North Pacific Ocean[END_REF][START_REF] Madigan | Mercury Stable Isotopes Reveal Influence of Foraging Depth on Mercury Concentrations and Growth in Pacific Bluefin Tuna[END_REF] . Species were classified in two groups (i.e. epipelagic or mesopelagic) according to individual Δ 199 Hg and δ 202 Hg values. Estimated species depths of occurrence are presented as described in the literature and correspond either to the median depth of occurrence (Blum et al., 2013) [START_REF] Blum | Methylmercury Production below the Mixed Layer in the North Pacific Ocean[END_REF] or to the depth of maximum occurrence (Madigan et al., 2018) [START_REF] Madigan | Mercury Stable Isotopes Reveal Influence of Foraging Depth on Mercury Concentrations and Growth in Pacific Bluefin Tuna[END_REF] . "n" refers to the number of individuals per species or group.

( 3 HNO3: 1

 31 HCl, 20 vol.% MilliQ water) to reach a nominal Hg concentration of 1 ng•g -1 . Two types of certified reference materials (NRC TORT-3 and ERM-BCR-464) and blanks were prepared in the same way as tissue samples. Mercury isotope compositions were measured by multi-collector inductively coupled plasma mass spectrometry (MC-ICP-MS, Thermo Finnigan Neptune Plus) with continuous-flow cold vapor (CV) generation using Sn (II) reduction (CETAC HGX-200). Hg isotope composition is expressed in δ notation and reported in parts per thousand (‰) deviation from the NIST SRM 3133 standard, which was determined by sample-standard bracketing according to the following equation: δ XXX Hg (‰) = [ ( ( XXX Hg/ 198 Hg)sample / ( XXX Hg/ 198 Hg)NIST 3133 ) -1 ] X 1000 where xxx represents the mass of each mercury isotope. δ 202 Hg represents Hg MDF, and ∆ notation is used to express Hg MIF by the following equation: ∆ xxx Hg (‰) = δ xxx Hg -(δ 202 Hg X a) , where a = 0.252, 0.502 and 0.752 for isotopes 199, 200 and 201, respectively. Total Hg in the diluted solutions was monitored by MC-ICP-MS using 202 Hg signals: mean recoveries of 101 ± 13% (n = 105) for samples and 95 ± 7% (n = 16) for certified reference materials were found. Hg levels in blanks were below the detection limit. Reproducibility of Hg isotope measurements was assessed by analyzing UM-Almadén (n = 20), ETH-Fluka (n = 20) and the biological tissue procedural standards NRC TORT-3 (n = 6) and ERM-BCR-464 (n = 10) (SI Appendix, Table

  courtesies extended to us by personnel of the University of California, Davis, Centro Interdisciplinario de Ciencias Marinas (CICIMAR), Secretaria de Marina, Comisión de Areas naturals Protegidas (CONANP), Island Conservation (GECI), Horizon Charters, Islander Charters, Solmar V, Club Cantamar and local fishermen from Guadalupe Island. The laboratory analyses were financially supported by the French National Research Agency project ANR-17-CE34-0010 MERTOX (PI David Point). White shark and elephant seal samples were collected under permits from the Secretaría del Medio Ambiente y Recursos Naturales (SEMARNAT): OFICIO NUM.SGPA/DGVS/07052/16 in 2016, OFICIO NUM.SGPA/DGVS/06673/17 in 2017 and OFICIO NUM.SGPA/DGVS/004284/18 in 2018. White shark samples were exported from Mexico under the CITES permit (number MX007) of the Universidad Nacional Autónoma de México and imported in France under the CITES permit (number FR75A) of the Muséum National d'Histoire Naturelle. We thank Laure Laffont and Jérôme Chmeleff for expert management of the OMP mercury and mass spectrometry facilities. Felipe Galvan-Magaña thanks the Instituto Politécnico Nacional (IPN)

Figure 1 :

 1 Figure 1: Map of the spatial distribution of white sharks (white hatched lines) in the Northeast Pacific Ocean. White shark and northern elephant seal samples were collected at Guadalupe Island (*) for the present study. Hg isotope signatures in pelagic organisms were obtained from two previous studies: green and red sampling locations for Blum et al. (2013) 30 and Madigan et al. (2018) 32 , respectively.

Figure 2 :

 2 Figure 2: Boxplots of Hg isotope values in white shark tissues and potential prey groups: epipelagic prey (EPI, n = 21), mesopelagic prey (MES, n = 35), northern elephant seals (NES, n = 10), white shark dermis (WSd, n = 65) and white shark muscle (WSm, n = 30). Groups are ordered by decreasing Δ 199 Hg values. Different letters indicate significant differences between groups (Δ 199 Hg: Welch's ANOVA with Games-Howell post hoc test, δ 202 Hg: ANOVA followed by Tukey's HSD test; p < 0.05).

Figure 3 :

 3 Figure 3: Individual ∆ 199 Hg and δ 202 Hg values for white shark dermis (WSd, n = 65) and muscle (WSm, n = 30). Standard ellipse areas at 50%, 75% and 95% are figured. Hg isotope compositions of potential prey groups are displayed as mean (± SD): epipelagic prey (EPI, n = 21), mesopelagic prey (MES, n = 35) and northern elephant seals (NES, n = 10).

Figure 4 :

 4 Figure 4: Estimated contributions (%) based on Hg isotope values of different prey groups in the Hg burden in A) dermis and B) muscle of white sharks. Hg contributions were evaluated by considering different trophic discrimination factors (TDF) for δ 202 Hg ranging from 0 to 1 ‰. EPI: epipelagic prey; MES: mesopelagic prey; NES: northern elephant seals. Bayesian mixing models indicated a minimum Hg contribution of 52% from MES in shark dermis (A) and 72% in shark muscle (B). Maximum Hg contribution from NES was 46% in shark dermis (A) and 25% in shark muscle (B). Maximum Hg contribution from EPI was 6% in shark dermis (A) and 3% in shark muscle (B).

Figure 5 :

 5 Figure 5: Mean ∆ 199 Hg value in white shark muscle from this study (∆ 199 Hg = 1.54‰, n = 30, red vertical line) and 95% confidence interval (grey band) from a logarithmic model fitted to ∆ 199 Hg values as a function of depth (R² = 0.45, p < 0.001) in potential pelagic prey from the literature[START_REF] Blum | Methylmercury Production below the Mixed Layer in the North Pacific Ocean[END_REF][START_REF] Madigan | Mercury Stable Isotopes Reveal Influence of Foraging Depth on Mercury Concentrations and Growth in Pacific Bluefin Tuna[END_REF] (i.e. fish and squids from epipelagic and mesopelagic groups, n = 56; SI Appendix, TableS2). Two offshore diving behaviors of white sharks are figured: the "rapid oscillatory diving" (ROD) behavior occurring between 0 and 200m (day and night) and the daytime "diel vertical migration" (DVM) behavior from 350 to 500m[START_REF] Jorgensen | Eating or Meeting? Cluster Analysis Reveals Intricacies of White Shark (Carcharodon Carcharias) Migration and Offshore Behavior[END_REF] . According to the ∆ 199 Hg variation in potential prey, the signature of white shark corresponds to a feeding on organisms living over 350 meters deep during the day, which matches daytime DVM but not daytime ROD.

Figure S1 :

 S1 Figure S1:Hg isotope signatures in pelagic fish and squids from the foraging habitat of northeast Pacific white sharks, obtained in previous studies[START_REF] Blum | Methylmercury Production below the Mixed Layer in the North Pacific Ocean[END_REF][START_REF] Madigan | Mercury Stable Isotopes Reveal Influence of Foraging Depth on Mercury Concentrations and Growth in Pacific Bluefin Tuna[END_REF] . Species were classified in two groups (i.e. epipelagic or mesopelagic) according to individual Δ 199 Hg and δ 202 Hg values.

Table S1 :

 S1 Summary (mean ± 2SD) of δ 202 Hg and ∆ 199 Hg values measured in certified reference materials (CRM).

	CRM	n	δ 202 Hg (‰)	∆ 199 Hg (‰)	Reference
	UM-Almadén	20	-0.57 ± 0.10 -0.03 ± 0.08 -0.57 ± 0.05 -0.02 ± 0.03	This study Blum et al., 2013
	ETH-Fluka	20	-1.41 ± 0.12 0.10 ± 0.06 -1.44 ± 0.12 0.07 ± 0.05	This study Jiskra et al., 2017
		10	0.70 ± 0.10 2.29 ± 0.06	This study
	BCR 464		0.73 ± 0.14 2.29 ± 0.09	Masbou et al., 2013
			0.69 ± 0.06 2.40 ± 0.06	Blum et al., 2013
	TORT 3	6	0.09 ± 0.16 0.65 ± 0.06 0.13 ± 0.12 0.69 ± 0.10	This study Li et al., 2016 68

Species n Species δ 202 Hg (‰) Species Δ 199 Hg (‰) Group Group n Group δ 202 Hg (‰) Group Δ 199 Hg (‰)

	Common name Depth (m) Common dolphinfish Species Reference Coryphaena hippurus Blum et al., 2013 50	3	0.84 ± 0.08	3.48 ± 0.50	Epipelagic (EPI)	21	0.83 ± 0.18	2.69 ± 0.45
	Chub mackerel	Scomber japonicus	Madigan et al., 2018	38	2	1.15 ± 0.27	2.96 ± 0.10	Epipelagic (EPI)
	Yellowfin tuna	Thunnus albacares	Blum et al., 2013	50	3	0.88 ± 0.12	2.76 ± 0.04	Epipelagic (EPI)
	Skipjack tuna	Katsuwonus pelamis	Blum et al., 2013	150	3	0.63 ± 0.04	2.71 ± 0.08	Epipelagic (EPI)
	South american pilchard	Sardinops sagax	Madigan et al., 2018	38	2	0.87 ± 0.02	2.43 ± 0.45	Epipelagic (EPI)
	Jack mackerel	Trachurus symmetricus Madigan et al., 2018	38	2	0.74 ± 0.07	2.39 ± 0.27	Epipelagic (EPI)
	Bigeye tuna	Thunnus obesus	Blum et al., 2013	250	3	0.71 ± 0.07	2.37 ± 0.17	Epipelagic (EPI)
	Pacific saury	Cololabis saira	Madigan et al., 2018	25	3	0.92 ± 0.18	2.31 ± 0.21	Epipelagic (EPI)
	Barracudina	Magnusidis atlantica	Madigan et al., 2018	188	3	0.73 ± 0.08	1.95 ± 0.14	Mesopelagic (MES)	35	0.40 ± 0.24	1.60 ± 0.31
	Opalescent inshore squid	Doryteuthis opalescens Madigan et al., 2018	25	2	0.58 ± 0.36	1.94 ± 0.16	Mesopelagic (MES)
	Swordfish	Xiphias gladius	Blum et al., 2013	375	3	0.57 ± 0.12	1.88 ± 0.07	Mesopelagic (MES)
	Opah	Lampris guttatus	Blum et al., 2013	225	3	0.54 ± 0.13	1.87 ± 0.07	Mesopelagic (MES)
	Lantern fish	Myctophidae indet.	Madigan et al., 2018	63	2	0.64 ± 0.06	1.82 ± 0.11	Mesopelagic (MES)
	Squid	Onychoteuthis spp.	Madigan et al., 2018	300	2	0.49 ± 0.00	1.76 ± 0.04	Mesopelagic (MES)
	Humbolt squid	Dosidicus gigas	Madigan et al., 2018	80	3	0.53 ± 0.16	1.64 ± 0.13	Mesopelagic (MES)
	Lantern fish	Bolinichthys distofax	Blum et al., 2013	590	4	0.12 ± 0.12	1.45 ± 0.13	Mesopelagic (MES)
	Boreopacific armhook squid Gonatopsis borealis	Madigan et al., 2018	550	3	0.32 ± 0.23	1.40 ± 0.21	Mesopelagic (MES)
	Clawed armhook squid	Gonatus onyx	Madigan et al., 2018	600	3	0.32 ± 0.04	1.37 ± 0.46	Mesopelagic (MES)
	Squid	Abraliopsis spp.	Madigan et al., 2018	450	1	0.45 ± 0.00	1.37 ± 0.00	Mesopelagic (MES)
	Squid	Chiroteuthis calyx	Madigan et al., 2018	750	3	0.17 ± 0.11	1.35 ± 0.06	Mesopelagic (MES)
	Lantern fish	Bolinichthys longipes	Blum et al., 2013	388	3	0.11 ± 0.14	1.10 ± 0.16	Mesopelagic (MES)

Table S3 :

 S3 Global data set of the shark and seal samples analyzed in this study.

Acknowledgments

Gaël Le Croizier was supported by a postdoctoral grant from the French National Research Institute for Sustainable Development (IRD) and the ISblue "Interdisciplinary graduate School for the blue planet" project (ANR-17-EURE-0015). The project was funded by Alianza WWF-TELCEL, The Annemberg Foundation, International Community Foundation, Fins Attached Marine Research and Conservation, The Watermen Project, Pfleger Institute of Environmental Research and Shark Diver. Field work was greatly facilitated through

Science of The Total Environment 2014, 496, 644-648. https://doi.org/10.1016/j.scitotenv.2014.04.107. (59) Eccles, K. M.; Littlewood, E. S.; Thomas, P. J.; Chan, H. M. Distribution of Organic and Inorganic Mercury across the Pelts of Canadian River Otter ( Lontra Canadensis). Sci Rep 2019, 9 (1), 1-11. https://doi.org/10.1038/s41598-019-39893-w. (60) Pinzone, M.; Acquarone, M.; Tessier, E.; Bérail, S.; Amouroux, D.; Das, K. Hg Speciation and Stable Isotopic Composition in Marine Mammals: New Insights and Perspectives. 2019. (61) Bechshoft, T.; Dyck, M.; St. Pierre, K. A.; Derocher, A. E.; St. Louis, V. The Use of Hair as a Proxy for Total and Methylmercury Burdens in Polar Bear Muscle Tissue. Science of The Total Environment 2019, 686, 1120-1128. https://doi.org/10.1016/j.scitotenv.2019.06.087. (62) Wang, W.-X.; Wong, R. S. K. Bioaccumulation Kinetics and Exposure Pathways of Inorganic Mercury and Methylmercury in a Marine Fish, the Sweetlips Plectorhinchus Gibbosus. Marine Ecology Progress Series 2003, 261, 257-268. https://doi.org/10.3354/meps261257. (63) Kehrig, H. A.; Seixas, T. G.; Baêta, A. P.; Malm, O.; Moreira, I. Inorganic and Methylmercury: Do They Transfer along a Tropical Coastal Food Web? Marine Pollution Bulletin 2010, 60 (12), 2350-2356. https://doi.org/10.1016/j.marpolbul.2010.08.010. (64) Crocker, D. E.; Champagne, C. D.; Fowler, M. A.; Houser, D. S. Adiposity and Fat Metabolism in Lactating and Fasting Northern Elephant Seals. Adv Nutr 2014, 5 (1), 57-64. https://doi.org/10.3945/an.113.004663. (65) Boeuf, B. J. L.; Morris, P. A.; Blackwell, S. B.; Crocker, D. E.; Costa, D. P. Diving Behavior of Juvenile Northern Elephant Seals. Can. J. Zool. 1996, 74 (9), 1632-1644. https://doi.org/10.1139/z96-181. (66) Masbou, J.; Point, D.; Sonke, J. E. Application of a Selective Extraction Method for Methylmercury Compound Specific Stable Isotope Analysis (MeHg-CSIA) in Biological Materials. J. Anal. At. Spectrom. 2013, 28 (10), 1620-1628. https://doi.org/10.1039/C3JA50185J. (67) Jiskra, M.; G. Wiederhold, J.; Skyllberg, U.; Kronberg, R.-M.; Kretzschmar, R. Source Tracing of Natural Organic Matter Bound Mercury in Boreal Forest Runoff with Mercury Stable Isotopes. Environmental Science: Processes & Impacts 2017, 19 (10), 1235-1248. https://doi.org/10.1039/C7EM00245A. (68) Li, M.; Schartup, A. T.; Valberg, A. P.; Ewald, J. D.; Krabbenhoft, D. P.; Yin, R.; Balcom, P. H.; Sunderland, E. M. Environmental Origins of Methylmercury Accumulated in Subarctic Estuarine Fish Indicated by Mercury Stable Isotopes. Environ. Sci. Technol. 2016, 50 (21), 11559-11568. https://doi.org/10.1021/acs.est.6b03206. (69) Hartigan, J. A.; Wong, M. A. Algorithm AS 136: A K-Means Clustering Algorithm. Journal of the Royal Statistical Society. Series C (Applied Statistics) 1979, 28 (1), 100-108. https://doi.org/10.2307/2346830. (70) Caliński, T.; Harabasz, J. A Dendrite Method for Cluster Analysis. Communications in Statistics 1974, 3 (1), 1-27. https://doi.org/10.1080/03610927408827101. (71) Parnell, A. C. Simmr: A Stable Isotope Mixing Model. R Package Version 0.3. See Https://CRAN.R-Project.Org/Package=simmr. 2016. (72) Parnell, A. C.; Phillips, D. L.; Bearhop, S.; Semmens, B. X.; Ward, E. J.; Moore, J. W.; Jackson, A. L.; Grey, J.; Kelly, D. J.; Inger, R. Bayesian Stable Isotope Mixing Models. Environmetrics 2013, 24 (6), 387-399. https://doi.org/10.1002/env.2221. (73) Stock, B. C.; Jackson, A. L.; Ward, E. J.; Parnell, A. C.; Phillips, D. L.; Semmens, B. X. Analyzing Mixing Systems Using a New Generation of Bayesian Tracer Mixing Models. PeerJ 2018, 6, e5096. https://doi.org/10.7717/peerj.5096. (74) Feng, C.; Pedrero, Z.; Gentès, S.; Barre, J.; Renedo, M.; Tessier, E.; Berail, S.; Maury-Brachet, R.; Mesmer-Dudons, N.; Baudrimont, M.; Legeay, A.; Maurice, L.; Gonzalez, P.; Amouroux, D. Specific Pathways of Dietary Methylmercury and Inorganic Mercury Determined by Mercury Speciation and Isotopic Composition in Zebrafish (Danio Rerio). Environ. Sci. Technol. 2015, 49 (21), 12984-12993. https://doi.org/10.1021/acs.est.5b03587.

Supplementary information (SI)

The twilight zone as a major foraging habitat and mercury source for the great white shark.

Gaël Le Croizier* 1 , Anne Lorrain 2 , Jeroen E Sonke 1 , Mauricio Hoyos-Padilla* [START_REF] Ferretti | Shark Baselines and the Conservation Role of Remote Coral Reef Ecosystems[END_REF][START_REF] Heithaus | Predicting Ecological Consequences of Marine Top Predator Declines[END_REF] , Felipe Galván-Magaña [START_REF] Ferretti | Patterns and Ecosystem Consequences of Shark Declines in the Ocean[END_REF] , Omar Santana-Morales [START_REF] Pimiento | Functional Diversity of Marine Megafauna in the Anthropocene[END_REF] , Marc Aquino-Baleytó [START_REF] Ferretti | Shark Baselines and the Conservation Role of Remote Coral Reef Ecosystems[END_REF][START_REF] Ferretti | Patterns and Ecosystem Consequences of Shark Declines in the Ocean[END_REF] , Edgar E Becerril-García [START_REF] Ferretti | Shark Baselines and the Conservation Role of Remote Coral Reef Ecosystems[END_REF][START_REF] Ferretti | Patterns and Ecosystem Consequences of Shark Declines in the Ocean[END_REF]


Bishal Sharma
email: bishal.sharma@univ-eiffel.fr

Paola Pellegrini
email: paola.pellegrini@univ-eiffel.fr

Joaquin Rodriguez
email: joaquin.rodriguez@univ-eiffel.fr

Neeraj Chaudhary
email: neeraj.chaudhary@railconcept.fr

Real-time train rescheduling for connecting trains

Keywords: Real-time traffic management, Train connections, Station capacities

Introduction

Real-time Rail Traffic Management Problem (rtRTMP) consists in adjusting train timetables in the presence of disturbances, where pre-defined train timetables become infeasible. It does so by employing appropriate control measures, such as re-timing, re-ordering, and re-routing. To address this issue and assist dispatchers, several optimization strategies have been proposed in the literature [START_REF] Cacchiani | An overview of recovery models and algorithms for real-time railway rescheduling[END_REF]. Several connecting trains run throughout the day, allowing passengers to transfer from one train to another. Trains may get delayed when there is a perturbation in the network. A minimum amount of time is allotted for connections called minimum connection time. Reducing the minimum connection time between trains is one option to limit delay propagation. This is often possible thanks to buffers existing in the timetable, provided a minimum connection time is always ensured.

We propose two enhancements to the existing rtRTMP model RECIFE-MILP [START_REF] Pellegrini | Optimal train routing and scheduling for managing traffic perturbations in complex junctions Transportation Research Part B : Methodological[END_REF] to allow passenger transfers and limit delay propagation exploiting connections. We aim to minimize the total delay of all the trains in the system. We also examine the impact of the two enhancements on the solution time of the model. minimum is sufficient to allow the transfer. On the other hand, we can consider the minimum connection time as dependent on the specific platforms chosen : if two close platforms are chosen, the minimum connection time can be short, otherwise it has to be longer and longer as the distance between platforms increases.

This paper proposes two enhancements to the MILP model [START_REF] Pellegrini | Optimal train routing and scheduling for managing traffic perturbations in complex junctions Transportation Research Part B : Methodological[END_REF] concerning those two approaches. We demonstrate the applicability of the proposed enhancements using total train delay as the objective to be minimized. To the best of our knowledge, this is the first study considering rerouting of connecting trains in a station to allow passenger transfers, while using a microscopic representation of the railway infrastructure.

Enhancement algorithm

As mentioned in Section 2,in the Classic RECIFE-MILP (CR) model [START_REF] Pellegrini | Optimal train routing and scheduling for managing traffic perturbations in complex junctions Transportation Research Part B : Methodological[END_REF], a minimum connection time is imposed for pairs of connecting trains stopping at a station. This time is independent of the platforms used by the trains : whatever the choice, CR imposes that the receiving train does not depart before the feeding train arrives plus the fixed minimum connection time. To ensure that passenger transfers are possible, this minimum connection time must be set to the Minimum Walking Time Distance (MWTD) between the two farthest platforms where the connecting trains may stop. Hence, short buffer times are available : given a feeder train arrival (A) and a receiving train departure (D) times in the timetable, the buffer is equal to their difference minus MWTD (D -A -MWDT). As a consequence, delay propagation may be strong. However, with this model, full rerouting flexibility is kept.

In the First Enhancement (FE) that we propose, we presume that the Minimum Connection Time (MCT) is less than MWDT. For two connecting trains, we consider the pair of platforms separated by a minimum walking time greater than MCT to be incompatible : in the model, we introduce constraints forbidding the trains to simultaneously choose these platforms. Compared to the CR, this enhancement may reduce delay propagation thanks to the larger buffer time (D -A -MCT > D -A -MWDT). However, rerouting flexibility is reduced, and this may have a negative effect on delay propagation. The final impact of the FE will depend on the value chosen for MCT, i.e., on the chosen solution for the trade-off between increased buffer time and reduced rerouting flexibility.

In the Second Enhancement (SE) we propose, we consider the MCT for two connecting trains MCT as an additional variable of the problem dependent on the platforms actually chosen. This value is the minimum walking time distance between the specific platforms. In the model, this is done by adding variables and constraints linking platforms and possible MCTs. Compared to the classic RECIFE-MILP model, this enhancement will reduce the buffer time unless two farthest platforms are actually chosen for connection. Thus, it may reduce delay propagation while ensuring full rerouting flexibility. This comes at the cost of a more difficult model due to the additional variables.

We compare the relative performance of RECIFE-MILP implementing the CL, FE and SE models which will also depend on the characteristics of the instances to be tackled. For example, the number of platforms in a station or the number of trains to be dealt with will likely have an impact on performance. In this paper, we compare the performance based on the following characteristics : Reduction of total delay of trains and solution time.

Problem descriptionIn this paper, we extend the Mixed-Integer Linear Programming (MILP) formulation at the basis of the state-of-the-art RECIFE-MILP algorithm[START_REF] Pellegrini | Optimal train routing and scheduling for managing traffic perturbations in complex junctions Transportation Research Part B : Methodological[END_REF] to include passenger connections. The RECIFE-MILP allows solving rtRTMP instances to optimality while taking into account all possible alternative routes that are physically present in the infrastructure of interest. In addition, it also considers microscopic representation of infrastructure with routes divided into track circuits.Train routing, timing and ordering decisions are the problem variables to be fixed to create a feasible timetable. In large station areas, several alternative routes are typically available for each train. They may allow for two trains with passenger connections to be placed at various platforms within the station. A minimum amount of time is allotted for connections, passenger can transfer from one train to another. In RECIFE-MILP, the elapse of this minimum time is ensured between the arrival of the feeding train and the departure of the receiving one. To preserve the transfer practical feasibility, it has to be set considering a walking time which allows passengers to move between the two farthest platforms that can be used by the trains. When the feeding train gets late to the station, the imposition of the minimum connection time may bring delay propagation, unless sufficient buffer exists. By reducing the connection time, delay propagation can be reduced as well. We consider two approaches to shorten it. On the one hand, we can set a short minimum connection time and limit the set of platforms available for the trains to the ones that are very close to each other, and for which the set