Natalia Vélez

Sandra Bessudo

Dalia C Barragán-Barrera

Felipe Ladino

Paco Bustamante

Andrea Luna-Acosta

Mercury concentrations and trophic relations in sharks of the Colombian Pacific

Keywords: Sharks, total mercury, stable isotopes, human health risks, trophic ecology, Colombia Pacific

Sharks are fished for human consumption in Colombia, and fins are exported illegally to international markets. The goal was to identify differences in total mercury (THg) concentrations in fins and muscles of shark species seized in the Buenaventura port (Colombian Pacific), and to assess potential human health risks related to shark consumption.

Introduction

Many shark species are currently threatened, due to the degradation of their habitat, overfishing, bycatch, and especially finning, considered as the main cause of shark population decline worldwide [START_REF] Clarke | Social, Economic, and Regulatory Drivers of the Shark Fin Trade[END_REF][START_REF] Dulvy | Extinction risk and conservation of the world's sharks and rays[END_REF]. Finning is a fishing activity that consists in fishing sharks, removing their fins, and returning the rest of the body to the ocean [START_REF] Clarke | Social, Economic, and Regulatory Drivers of the Shark Fin Trade[END_REF]Hernandez Betancourt et al., 2011;[START_REF] Helfman | Sharks: The Animal Answer Guide[END_REF]. Even if this is an illegal activity in many countries, finning continues on a large scale, and it is estimated that between 26 and 73 million of sharks are traded worldwide annually [START_REF] Clarke | Social, Economic, and Regulatory Drivers of the Shark Fin Trade[END_REF]. This is due to the high price and demand of this resource in Asian markets, particularly in Hong Kong [START_REF] Clarke | Estimates of shark species composition and Numbers associated with the shark fin trade based on Hong Kong auction data[END_REF], where a shark fin costs ~US $42.00 per kilo [START_REF] Jaiteh | The end of shark finning? Impacts of declining catches and fin demand on coastal community livelihoods[END_REF], and a shark fin soup costs between US $250 and US $1800 [START_REF] Nalluri | Methylmercury in dried shark fins and shark fin soup from American restaurants[END_REF]The 8 Restaurant, 2017).

In countries like Colombia, shark is part of food in some coastal locations, but fin soup is not consumed. However, finning is an activity that generates strong incomes due to their high commercial value in the Pacific region [START_REF] Salazar | Comercio internacional de tiburones y rayas en Costa Rica, Panama y Colombia[END_REF]. Fin prices in Colombia are approximately US $40 per kilo, in contrast to shark meat prices of US $1.5 per kilo (Ross [START_REF] Salazar | Comercio internacional de tiburones y rayas en Costa Rica, Panama y Colombia[END_REF]. Between 2005 and 2017, an average of 317,974 kg of sharks were caught in Colombia (Ross [START_REF] Salazar | Comercio internacional de tiburones y rayas en Costa Rica, Panama y Colombia[END_REF], even though in 2013 shark finning was prohibited in Colombia (Rodríguez [START_REF] Ortiz | La Pesca Ilegal Marina en Colombia[END_REF]. Unfortunately, this activity has continued illegally, putting at high risk shark populations (Caldas Aristizabal et al., 2010;[START_REF] Jaiteh | The end of shark finning? Impacts of declining catches and fin demand on coastal community livelihoods[END_REF].

Recent studies suggest that prices of shark fins have fallen sharply since 2012 (Eriksson and Clarke, 2015) due, in part, to the conservation campaigns that have raised awareness of the effects of finning on shark populations [START_REF] Whitcraft | Evidence of Declines in Shark Fin Demand[END_REF] and concerns about food safety [START_REF] Fabinyi | Seafood banquets in Beijing: Consumer perspectives and implications for environmental sustainability[END_REF]. Studies of THg concentrations in shark tissues have reported high concentrations of this metal (e.g., [START_REF] Kim | Species-specific accumulation of methyl and total mercury in sharks from offshore and coastal waters of Korea[END_REF][START_REF] Bourg | Effect of body length, trophic position and habitat use on mercury concentrations of sharks from contrasted ecosystems in the southwestern Indian Ocean[END_REF] that exceed the safety level for human consumption of 1000 ng g -1 ww determined by organizations such as the Food and Agriculture Organization of the United Nations (FAO) and the World Health Organization (WHO) (FAO/WHO, 2011). These have generated a concern about human health risks to shark consumption, leading this distress as a conservation strategy to reduce shark fin demand [START_REF] Who | Exposure to Mercury: A major public health concern[END_REF]Escobar-Sanchez et al., 2010;[START_REF] Fabinyi | Seafood banquets in Beijing: Consumer perspectives and implications for environmental sustainability[END_REF][START_REF] Man | Shark fin, a symbol of wealth and good fortune may pose health risks: the case of mercury[END_REF][START_REF] Nalluri | Methylmercury in dried shark fins and shark fin soup from American restaurants[END_REF]. The main concern is because THg is toxic for humans as it is a cumulative poison that bioaccumulates in the body [START_REF] Matulik | Bioaccumulation and biomagnification of mercury and methylmercury in four sympatric coastal sharks in a protected subtropical lagoon[END_REF]. Because THg is biomagnified by trophic transfers in food webs, top predators such as sharks, generally show very high THg concentrations in their tissues in comparison to other seafood products [START_REF] Nalluri | Methylmercury in dried shark fins and shark fin soup from American restaurants[END_REF].

Because of both legal and illegal gold extraction [START_REF] Tubb | Muddy decisions: gold in the Chocó, Colombia[END_REF][START_REF] Castellanos | Malaria in gold-mining areas in Colombia[END_REF][START_REF] Palacios-Torres | Mercury pollution by gold mining in a global biodiversity hotspot, the Choco biogeographic region, Colombia[END_REF], Colombia is the third country that emits more THg to the environment after China and Indonesia (Telmer and Veiga, 2009), exceeding the amounts issued by the three main gold producers together, minus China, which are Russia, Australia, and the United States (World Gold Council, 2020). The Choco region, which is located in the Colombian North Pacific coast, is the second largest producer of gold in Colombia and it has been detected that 90% of the gold produced comes from alluvial operations [START_REF] Massé | Responsible Business Conduct: Due Diligence in Colombia's Gold Supply Chain Gold Mining in Antioquia[END_REF]. The releases from gold mining may contribute to the THg contamination of the marine environment and consequently of the whole food webs up to sharks. Assessing THg concentrations in shark populations from the Colombian Pacific will allow to know the current contamination status in these species and the ecosystems they exploit and forage on, and also will provide relevant data about potential health risks related to shark consumption.

Materials and methods

Study area

The Buenaventura port is located on the Colombian Pacific coast (Fig. 1). Fisheries on this region are characterized by sustenance fishing marketed in local markets (P´erez-Valbuena, 2007). Particularly for sharks, a large number of by-products such as jaw, vertebrae, meat, and liver are marketed in local markets (Caldas Aristizabal et al., 2010) as ornaments, food, or a nutritional source of omega-3 fatty acids [START_REF] Maggie | Omega-3 fatty acids[END_REF], respectively; however, fins are mostly marketed in international markets [START_REF] Navia | Fishing effects on elasmobranchs from the Pacific Coast of Colombia[END_REF]. These fins are exported illegally mainly from the Buenaventura port to Hong Kong and to China (Ross [START_REF] Salazar | Comercio internacional de tiburones y rayas en Costa Rica, Panama y Colombia[END_REF], so most of shark fin seizures in Colombia take place in this port (Estupiñan-Montaño et al., 2017[START_REF] Salazar | Comercio internacional de tiburones y rayas en Costa Rica, Panama y Colombia[END_REF]. For this reason, samples used for this study came from shark fin seized on the coast of the Buenaventura port.

Shark tissue collection and sample preparation

A total of 175 samples of two different shark tissues were collected: 130 fin and 45 muscle samples. Shark fin and muscle samples seized at the Buenaventura port, were collected by researchers from the Malpelo Foundation and rangers from the Unit of National Natural Parks of Colombia between 2009 and 2013. For the purposes of this study, the seven species of sharks that had the highest collection frequency were selected.

Among the species selected to analyze fin samples, were included: (1) Pelagic Thresher (A. pelagicus) a highly migratory species from the epipelagic zone, which is in the Endangered category (EN) according to the IUCN (Rigby et al., 2019a(Rigby et al., , 2019b)); (2) Pacific Smalltail Shark (C. cerdale), a coastal species that lives in estuarine ecosystems of the continental shelf, in shallow waters and with muddy substrates, cataloged by the IUCN as Critically Endangered (CR) [START_REF] Pollom | Carcharhinus cerdale[END_REF]; (3) Brown Smoothhound (M. henlei), which inhabits mainly in coastal waters and in the open sea on the continental shelves, cataloged as Least Concern (LC) (Pérez-Jiménez et al., 2016a, 2016b); (4) Sicklefin Smoothhound (M. lunulatus), a species that is found near the coast and categorized as LC due mainly to incidental fishing (Pérez-Jiménez et al., 2016a); (5) Scalloped Bonnethead (S. corona), which resides on the continental shelf in shallow estuarine habitats, and is listed as Near Threatened (NT) mainly due to artisanal fishing [START_REF] Mycock | Sphyrna corona. The IUCN Red List of Threatened Species[END_REF]; (6) Scalloped Hammerhead (S. lewini), a coastal and semi-oceanic pelagic species found on continental and insular shelves, and in deeper waters up to 275 m depth, cataloged as Critically Endangered (CR) mainly due to finning (Rigby et al., 2019a); and (7) Bonnethead Shark (S. tiburo), an estuarine species found in shallow bays that is listed as LC mainly due to commercial, recreational, and incidental fisheries [START_REF] Compagno | FAO species catalogue. Vol. 4. Sharks of the world. An annotation and illustrated catalogue of shark species known to date[END_REF][START_REF] Cortés | Sphyrna tiburo. The IUCN Red List of Threatened Species[END_REF]. Additionally, muscle samples were collected for A. pelagicus and S. lewini, two species whose threat status is the most critical (Supplementary Table S1).

Collected samples were preserved in 70% ethanol and stored at -20°C for subsequent laboratory analysis. Following Barragan-Barrera et al. (2019), samples were left on a bench to let alcohol evaporated, then were homogenized, and freeze-dried to perform posterior THg and isotopic analyses [START_REF] Fontaine | Ecological tracers and at-sea observations document the foraging ecology of southern long-finned pilot whales (Globicephala melas edwardii) in Kerguelen waters[END_REF]Barragan-Barrera et al., 2019).

Mercury analyses

THg measurements were conducted using an atomic absorption spectrometer AMA-254 (Altec© Advanced Mercury Analyzer-254). For each sample, at least a minimum of two aliquots of 1 to 5 mg of homogenized dry tissue subsamples were analyzed in order to estimate average THg concentrations [START_REF] Aubail | Use of skin and blubber tissues of small cetaceans to assess the trace element content of internal organs[END_REF][START_REF] Angel-Romero | Mercury Concentrations in Wild Humpback Whales (Megaptera novaeangliae) Sampled in the Colombian Pacific and the Antarctic Peninsula[END_REF]Barragan-Barrera et al., 2019). Some measurements needed to be repeated until having analytical differences below 10%. The analytical quality of the THg measurements by the AMA-254 was evaluated by the analysis of blanks and certified reference material (CRM) TORT-2 (Reference Material of lobster hepatopancreas marine certified by the National Research Council of Canada) at the beginning and at the end of the analytical cycle, and after running the analysis of 15 samples. Blanks were negligible and agreement was considered satisfactory. The CRM measured concentration was 0.305 ± 0.025 μg g -1 (n = 20), with a percentage of average recovery of 104%. THg measurements are presented in ng g -1 on a wet weight basis (ww) and the detection limit was 0.5 ng.

Conversion of dry weight to wet weight in shark fins and muscles

Threshold values defined by regulatory guidelines of health agencies are established in wet weight (ww). However, concentration measurements of contaminants and stable isotope ratios C and N are usually made in dry material in order to avoid differences in results due to variations in water content of the individuals analyzed (Bryan, 1984;[START_REF] Fisk | Using anthropogenic contaminants and stable isotopes to assess the feeding ecology of Greenland sharks[END_REF][START_REF] Cresson | A multitracer approach to assess the spatial contamination pattern of hake (Merluccius merluccius) in the French Mediterranean[END_REF][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]. For this reason, THg concentrations measured in dry weight (dw) in this study were transformed to wet weight (ww) based on the following formula:

𝐶 𝑤𝑤 = 𝐶 𝑑𝑤 × ( 100 -%𝐻 100 ) ,
where Cww and Cdw are concentrations expressed in wet and dry weight respectively, and %H is the percentage of humidity that normally oscillates around 80% for fish species [START_REF] Murray | The Composition of Fish (Torry Advisory Note[END_REF][START_REF] Hislop | Variation in the calorific value and total energy content of the lesser sandeel (Ammodytes marinus) and other fish preyed on by seabirds[END_REF][START_REF] Payne | Proximate composition of some north-eastern Pacific forage fish species[END_REF]Environmental Protection Agency, 2011).

Risk assessment for consumption of shark fins and muscles

THg concentrations of each species in fins and muscles were evaluated considering the maximum limit of THg in fish for human consumption by the Food and Agriculture Organization (FAO) and the World Health Organization (WHO), established as 1000 ng g -1 ww for top predators, such as sharks (FAO/WHO, 2011).

Human health risks derived from the consumption of fins and shark muscles were evaluated based on the non-carcinogenic risk ratio or Target Hazard Quotient (THQ). THQ is a specific dose ratio of a contaminant (in this case THg) at a reference dose level. THQ ≤ 1 indicates that there are no adverse health effects, while THQ > 1 indicates possible adverse health effects (United States Environmental Protection Agency (USEPA), 1989(USEPA), , 2000)). THQ is calculated using the following equation (United States Environmental Protection Agency (USEPA), 1989; [START_REF] Vieira | Mercury, cadmium, lead and arsenic levels in three pelagic fish species from the Atlantic Ocean: Intra-and inter-specific variability and human health risks for consumption[END_REF]:

𝑇𝐻𝑄 = 𝐸𝐹𝑟 × 𝐸𝐷 × 𝐼𝑅 × 𝑀𝐶 𝑅𝑓𝐷 × 𝐵𝑊 × 𝐴𝑇 ,
where THQ is dimensionless; EFr is the frequency of exposure (365 days per year; Storelli et al., 2008); ED is the duration of the exposure (70 years, as the average human life time; Storelli et al., 2008); IR is the rate of food ingestion (33. for an adult between 20 and 65 years and an average weight of 30 kg for a child between one and 19 years [START_REF] Vieira | Mercury, cadmium, lead and arsenic levels in three pelagic fish species from the Atlantic Ocean: Intra-and inter-specific variability and human health risks for consumption[END_REF]; AT is the number of days during which the exposure is averaged (365 days × ED, according to REF). THQ was calculated with the average THg concentration (average THQ) and with the maximum and minimum values of THg concentrations for each species (maximum and minimum THQ, respectively).

Furthermore, the average, minimum, and maximum estimated weekly intake (EWI) of THg was calculated for each species, and these results were compared to the provisional tolerable weekly intake (PTWI) recommended by the Joint FAO/WHO Expert Committee on Food Additives for methylmercury (MeHg), since this organic form represents usually 90% of THg in fish muscles [START_REF] Bloom | On the chemical form of mercury in edible fish and marine invertebrate tissue[END_REF][START_REF] Adams | Mercury levels in four species of sharks from the Atlantic coast of Florida[END_REF] and 70% in fins [START_REF] Garcia Barcia | Mercury and arsenic in processed fins from nine of the most traded shark species in the Hong Kong and China dried seafood markets: The potential health risks of shark fin soup[END_REF]. The Joint FAO/WHO Expert Committee stated that the PTWI is 1.6 ng g -1 body weight (bw) for the most susceptible human population such as children and women of childbearing age to protect an embryo [START_REF] Jecfa | Methylmercury. In: Safety evaluation of certain food additives and contaminants. Report of the 61st Joint FAO/WHO Expert Committee on Food Additives[END_REF]. Regarding the adult population, the committee considers that the intake of THg can be up to two times more (3.2 ng g -1 of body weight) [START_REF] Who | Exposure to Mercury: A major public health concern[END_REF]. The EWI was determined with the following equation [START_REF] Mohammed | Mercury, arsenic, cadmium and lead in two commercial shark species (Sphyrna lewini and Carcharinus porosus) in Trinidad and Tobago[END_REF]:

𝐸𝑊𝐼 = 𝑄 𝑓𝑖𝑠ℎ × 𝑀𝐶 𝐵𝑊 ,
where Qfish is the weekly amount of shark consumed (kg), MC is the concentration of the contaminant in the shark piece consumed (ng g -1 ww), and BW is the human body weight (kg; 60 kg for adults between 20 and 65 years, and 30 kg for children between one and 19 years; [START_REF] Vieira | Mercury, cadmium, lead and arsenic levels in three pelagic fish species from the Atlantic Ocean: Intra-and inter-specific variability and human health risks for consumption[END_REF]. For adults, it was considered a consumption of 37.51 g of fins in a portion of fish soup [START_REF] Man | Shark fin, a symbol of wealth and good fortune may pose health risks: the case of mercury[END_REF] and of 234 g of muscles in a plate (Food and Agriculture Organization (FAO), 2009). For children, knowing that food consumption at this early stage of life is lower than an adult [START_REF] Leung | Growth and nutrition of Hong Kong children aged 0-7 years[END_REF], 37.51 g of fins and 200 g of muscles were considered [START_REF] Man | Shark fin, a symbol of wealth and good fortune may pose health risks: the case of mercury[END_REF]. A rate consumption of one portion per week was considered for both adults and children [START_REF] Man | Shark fin, a symbol of wealth and good fortune may pose health risks: the case of mercury[END_REF].

Stable isotope analysis

Because lipids are present in shark tissues and can alter values of δ 13 C (De Niro and Epstein, 1977), all samples were delipidated before analysis of stable isotopes. For this, three repetitions of lipid removal in 4 ml of cyclohexane were carried out in each sample, stirring for 10 min, 5 min of centrifugation, and finally drying in an oven at a maximum temperature of 45°C (Chouvelon et al., 2011). Then, between 0.2 and 0.4 mg of each delipidated sample were weighted in tin cups. Stable isotope measurements were performed on a Delta V Advantage IRMS isotopic mass spectrometer (Thermo Scientific, Bremen, Germany) coupled to an EA 1112 Flash elemental analyzer (Thermo Scientific, Germany). The reference gas was calibrated with international reference materials including acetanilide and peptone. These two reference materials are passed at the beginning and at the end of the analytical cycle, and after running the analysis of 20 samples. All results were expressed under the notation δ relative to Vienna PeeDee Belemnite and atmospheric nitrogen for δ 13 C and δ 15 N, respectively, according to the following equation [START_REF] Peterson | Stable Isotopes in Ecosystem Studies[END_REF]:

δ𝑋 = [( 𝑅 𝑠𝑎𝑚𝑝𝑙𝑒 𝑅 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 ) -1] × 10 3
where X is δ 13 C or δ 15 N, and R is the isotopic ratio 13 C/ 12 C or 15 N/ 14 N, respectively. Replicate measurements of reference materials (caffeine: USGS61 and USGS62) indicated that analytical errors were <0.15 ‰ for both δ 13 C and δ 15 N. Percentages of elemental composition C and N were also obtained by the elemental analyzer, and calculated C:N ratios were always below 3.5, which indicates a good efficiency of lipid removal (Table 1).

Data analysis

Shapiro-Wilk and Levene tests were performed to evaluate the assumptions of parametric tests (normality and homogeneity of variance, respectively). Transformations were performed so that the data fulfilled these assumptions (logarithmic transformation for THg), and nonparametric tests were performed when this was not possible (δ 15 N and δ 13 C). A oneway ANOVA test followed by a Tukey post-hoc test was used to evaluate significant differences in THg concentrations between species.

A two-way ANOVA followed by a Tukey post-hoc test was used to evaluate significant differences in THg concentrations between tissues. A Kruskal-Wallis test followed by a nonparametric multiple comparison post-hoc test was used to evaluate significant differences in δ 13 C and δ 15 N values between shark species.

A Bayesian approach based on multivariate ellipse metrics (SIBER -Stable Isotope Bayesian Ellipses within the R-siar package; [START_REF] Jackson | Comparing isotopic niche widths among and within communities: SIBER -Stable Isotope Bayesian Ellipses in R[END_REF] was used to assess the overlapping of isotopic niche between species. This analysis generates areas of standard ellipses corrected for small sample sizes (SEAc) that correspond to 40% of the data regardless of the sample size [START_REF] Batschelet | Circular Statistics in Biology[END_REF], which can be compared between species and thus determine differences in the central isotope niche space and the niche superposition [START_REF] Jackson | Comparing isotopic niche widths among and within communities: SIBER -Stable Isotope Bayesian Ellipses in R[END_REF]. The calculation of standard ellipses (SEAc) was performed for the data δ13Cδ 15 N, δ 13 C -THg, and δ 15 N -THg, supported by its associated covariance matrix:

∑ = [ 𝜎 𝑥 2 𝑐𝑜𝑣(𝑥, 𝑦) 𝑐𝑜𝑣(𝑦, 𝑥) 𝜎 𝑦 2 ] ,
which defines the shape and size of the ellipses, and the averages of x and y define the location of the ellipse on the graph [START_REF] Jackson | Comparing isotopic niche widths among and within communities: SIBER -Stable Isotope Bayesian Ellipses in R[END_REF]. To know the degree of niche overlapping, that is, the overlap in the areas of the standard ellipses (SEAc) of the species for each combination of the above parameters, was used the OVERLAP command. This overlap value normally ranges between 0 and 1, and values closer to 1 represent greater overlap. The degree of overlapping was later transformed into percentages for a better visualization of the data [START_REF] Jackson | Comparing isotopic niche widths among and within communities: SIBER -Stable Isotope Bayesian Ellipses in R[END_REF].

Finally, a nonparametric Spearman correlation test was performed to evaluate relationships between δ 13 C -δ 15 N, δ 13 C -THg, and δ 15 N -THg values. All data analyses were performed using the program R 1.1.423 (R Development Core Team, 2014).

Results

THg concentrations in shark fins and muscles

A total of 175 shark samples (130 fins and 45 muscles) were analysed. THg concentrations were measured in all samples (Table 1). Fin THg concentrations were measured in all species, showing significant differences between species (F = 5.55, df = 6, p < 0.05; Table 1, Fig. 2), of which S. lewini showed the highest values (88.56 ± 82.30 ng g -1 ww). Muscle THg concentrations were only measured in A. pelagicus and S. lewini (Fig. 3). S. lewini also showed the highest concentrations (809.29 ± 728.88 ng g -1 ww; Table 1, Fig. 3). These concentrations were significantly higher than fin THg concentrations for both species (F = 114.83, df = 1, p < 0.05, Fig. 3).

Risk assessment for consumption

Average THg concentrations were compared with the maximum permitted level (ML) of THg in predatory fish recommended by the FAO/WHO of 1000 ng g -1 ww (FAO/WHO, 2011). THg fin concentrations were all below to ML (Figs. 2 and3), and only for THg muscle concentrations some individuals of A. pelagicus and S. lewini exceeded the ML by two to almost three orders of magnitude (maximum values of 1893.46 and 2664.66 ng g -1 ww, respectively; Fig. 3).

The minimum, maximum, and average values of the estimated weekly intake (EWI) and the average Target Hazard Quotient (THQ) values were calculated for two age-specific human categories (adults and children). EWI results in fins were below the PTWI for all species (Table 2). However, EWI results in muscles for A. pelagicus and S. lewini exceeded this limit for both age-groups, except for A. pelagicus in adults, which presented a relatively high average but below to the recommended limit (2.21 ng g -1 bw; Table 2). THQ results in fins for both age groups analyzed were <1 while THQ results in muscles of A. pelagicus and S.

lewini were >1 for both age-groups (Table 2).

Trophic interactions

Only fins were analyzed for all seven shark species for ecological niche overlapping. An overlapping of δ 13 C -δ 15 N ellipses among all species was observed, some of them with a greater percentage of overlapping than others (Table 3, Figs. 4A and5A). Particularly, S.

tiburo showed the lowest percentage of shared niche with other species (Table 3, Fig. 5A), while A. pelagicus and S. lewini showed the highest one (Table 3, Fig. 5A).

Results in standard ellipses of δ 13 C-THg and δ 15 N-THg (Tables 4 and5, SEAc: Figs. 5B-C),

showed for the genus Mustelus an important niche segregation in relation to other genera; particularly M. henlei showed lower percentages for δ 13 C-THg and S. tiburo and M. henlei for δ 15 N-THg (Tables 4 and5 showed the smallest ellipse area (13.52 and 15.26, in ‰², respectively, Supplementary Table S2).

Relationship between δ 13 C, δ 15 N and THg concentrations

Fins values of δ 15 N and δ 13 C varied significantly among species (Kruskal-Wallis, X 2 =77.60, df=6, p <0.05 and X 2 =37.46, df=6, p <0.05, respectively), but not varied significantly for THg concentrations. Spearman correlation tests were performed separately for fins and muscles since significant differences were encountered in THg concentrations between fins and muscles. In fins, no significant (p > 0.05) correlations were found between δ 13 C, δ 15 N, and THg, when all species were considered. At species level with fin samples, only a significant positive correlation was found between δ 15 N -THg for S. tiburo (Spearman: r = 0.60, p = 0.01). In muscles, no significant (p > 0.05) correlations were found between δ13C, δ 15 N, and THg, whether considering both species together or species individually.

Discussion

This is the first study that reports THg contamination levels for some of the most representative shark species on the Colombian Pacific, and that describes ecological aspects associated with their trophic ecology, and the partition of ecological and foraging niches.

This information can be of great help for the implementation of future conservation plans and strategies to reduce the trade and export of shark fin in Colombia and other neighboring countries.

Levels of THg concentrations

In the Colombian Pacific, sharks showed moderate THg concentrations in comparison to other studies worldwide ( 6).

Differences in THg concentrations between fins and muscles could be explained by the high affinity that has THg with the thiol sulfuric groups present in the amino acids of muscles,

showing high values for this tissue (Escobar-Sanchez et al., 2010;Pethybridge et al., 2010;[START_REF] O'bryhim | Relationships of mercury concentrations across tissue types, muscle regions and fins for two shark species[END_REF]. However, fins also showed significant high THg concentrations for A. pelagicus and S. lewini, both species threatened according to the IUCN because of finning (Endangered and Critically Endangered, respectively; Rigby et al., 2019aRigby et al., , 2019b)), which concerns about health status of these species.

Effects on human health due to Hg overload and risk assessment

According to FAO/WHO, the THg permitted concentration limit for humans is 1000 ng g -1 ww (FAO/WHO, 2011). Our data showed THg concentrations in fins and muscles below this limit (46.12 and 688.04 ng g -1 ww on average, respectively). However, our results showed that muscles of some individuals of A. pelagicus and S. lewini presented THg concentrations that exceeded this safety limit for consumption.

EWI and THQ risk indexes for muscles of A. pelagicus and S. lewini also showed a risk for human health due to THg consumption in both adults and children. Particularly, the risks for children are greater because they consume three to four times more food in proportion to their body size than adults and, therefore, ingest larger amounts of chemicals per unit of body mass (United States Environmental Protection Agency (USEPA), 2008). However, since the fish ingestion rate in Colombia is unknown, it is possible the fish ingestion rate used is underestimated for the Colombian fishing community, and therefore, more specific studies including local fish and especially shark consumption should be carried out in the future.

Although fins are exported to external markets, muscles can be consumed by adults and children of local communities of the Colombian Pacific [START_REF] Fuentes-Gandara | Human health impacts of exposure to metals through extreme consumption of fish from the Colombian Caribbean Sea[END_REF]. THg released into the environment by both natural and anthropogenic origins, this last one increased rapidly in Colombia due to gold mining during the last decade (Güiza and Aristizabal, 2013), accentuates a public health problem. Therefore, and following guidelines of European Commission and FAO/WHO, we suggest that daily consumption of A. pelagicus and S. lewini is not safe for human health and should be regulated especially for children (Falco et al., 2006). These findings have also conservation implications, because A. pelagicus and S. lewini have been reported as the most exploited species in the Colombian Pacific coast [START_REF] Caballero | Application of multiplex PCR approaches for shark molecular identification: Feasibility and applications for fisheries management and conservation in the Eastern Tropical Pacific[END_REF].

Amplitude and overlapping patterns of ecological niche

Regarding the amplitude and overlapping patterns, only fin samples were considered since this tissue has been already employed in stable isotope and fatty acid analyzes in sharks [START_REF] Every | Comparison of fin and muscle tissues for analysis of signature fatty acids in tropical euryhaline sharks[END_REF][START_REF] Rangel | Resource partitioning between two young-of-year cownose rays Rhinoptera bonasus and R. brasiliensis within a communal nursery inferred by trophic biomarkers[END_REF], revealing feeding habits and habitat use over periods of time of more than a year due to its slow turn-over rate [START_REF] Malpica-Cruz | Tissue-specific isotope trophic discrimination factors and turnover rates in a marine elasmobranch: empirical and modeling results[END_REF]. Niche overlap of all species is not 100% in terms of trophic level (δ 15 N). It was possible to identify three groups in which the first was M. henlei with the highest average of δ 15 N, the second was S. tiburo with the lowest average of δ 15 N, and the third group was the rest of the species that had a high overlap in terms of δ 15 N (A. pelagicus, C. cerdale, M. lunulatus, S. corona, and S. lewini). The first group seems to have prey of relatively higher trophic level, while the second group appears to have prey of relatively lower trophic level, even though generally the δ 15 N results are low for all the individuals. Previous studies on the diet of M. henlei and S. tiburo indicate that these species feed both on small fishes and crustaceans, which could explain these results [START_REF] Cortés | Diet, feeding habits and diet feeding chronology of the bonnethead shark, Sphyrna tiburo, in southwest Florida[END_REF]Pérez-Jiménez et al., 2016a, 2016b).

δ 13 C values in fins ranged between -15.64 and -14.83 ‰. Although values for all the species were similar even for standard ellipses of δ 13 C and THg, we suggest the existence of two shark groups in terms of habitat use. One group was only represented by S. tiburo (mean = -15.64 ‰) while remaining species formed the other group (range = -15.50 and -14.62 ‰).

δ 13 C values of shark species in this study were relatively high, indicating coastal habits [START_REF] Hussey | Fin-icky samples: an assessment of shark fin as a source material for stable isotope analysis[END_REF], with the exception of S. tiburo that showed a wide range of δ 13 C values, suggesting a wider foraging area. This result differs from other studies for most shark species analyzed here, such as S. lewini, which usually inhabits pelagic zones when they are adults, for their development, growth, and foraging [START_REF] Compagno | FAO species catalogue. Vol. 4. Sharks of the world. An annotation and illustrated catalogue of shark species known to date[END_REF]Estupiñan-Montaño et al., 2009, 2017[START_REF] Estupiñán-Montaño | Stable isotope evidence for movements of hammerhead sharks Sphyrna lewini, connecting two natural protected areas in the Colombian Pacific[END_REF]. Because the Colombian Pacific mangroves are known as suitable areas for shark species during their first years [START_REF] Quintanilla | Conservation Genetics of the Scalloped Hammerhead Shark in the Pacific Coast of Colombia[END_REF] and considering the relatively low δ 15 N results, these results reinforce also the hypothesis that the S. lewini specimens analyzed in this study were juveniles feeding in coastal habitats.

Overall, δ 13 C results suggest also a niche overlap in coastal areas for all the studied individuals, which could lead to a competition for food between these species. However, the significant differences found in isotopic relationships between δ 15 N and THg, suggests diet differences among individuals analyzed (Maya [START_REF] Meneses | Trophic overlap between blue sharks (Prionace glauca) and shortfin makos (Isurus oxyrinchus): Trophic linkages between two shark species in the Eastern Pacific Ocean food web[END_REF]. For instance, S. lewini prefers cephalopods, while M. lunulatus consumes more stomatopods (Estupiñan-Montaño et al., 2009;Galvan-Magaña et al., 2013). These diet differences could thus allow coexistence of species in coastal areas, as has been reported for several shark species (Maya [START_REF] Meneses | Trophic overlap between blue sharks (Prionace glauca) and shortfin makos (Isurus oxyrinchus): Trophic linkages between two shark species in the Eastern Pacific Ocean food web[END_REF], even in other Colombian areas such as Malpelo Island (Estupiñan-Montaño et al., 2017). These results are also supported by SIBER-based analyses of the standard ellipses between δ 13 C and δ 15 N (with the exception of S. tiburo, see Fig. 5A).

Shark ecological patterns: implications for conservation

This study was limited by the origin of the samples, since they correspond to seizures, in which most of them were only fins already cut off from the sharks, which makes it impossible to know other important biological variables such as size. However, isotopic data showed insights about age of individuals analyzed in this study. The generally low δ 15 N results suggest that individuals analyzed in this study could be juveniles (Estupiñan-Montaño et al., 2009;[START_REF] Torres-Rojas | Feeding habits of the scalloped hammerhead Sphyrna lewini, in Mazatlán waters, southern Gulf of California, Mexico[END_REF]. Considering both, relatively low δ 15 N and relatively high δ 13 C values, these results reinforce also the hypothesis that most specimens analyzed in this study were juveniles feeding in coastal habitats.

Our findings suggest therefore two worrisome hypotheses: 1) most individuals collected, particularly A. pelagicus and S. lewini, were juveniles, and 2) biggest Colombian sharks fishing activity is concentrated in coastal areas. However, [START_REF] Payan | Caracterización y comportamiento histórico de la pesca de elasmobranquios en el Pacífico colombiano[END_REF] identified the pelagic zone as the most visited by the fishing fleet in the Colombian Pacific, where there is a greater incidental capture of elasmobranchs. Nevertheless, our findings suggest the potential shark fishing in coastal areas, likely in a small scale. The possibility of fishing coastal young Chondrichthyes or adults during their reproductive period should be considered as an important issue for fisheries management in Colombia and probably other neighboring countries with similar practices [START_REF] Quintanilla | Conservation Genetics of the Scalloped Hammerhead Shark in the Pacific Coast of Colombia[END_REF], in order to maintain the population growth of these species that are in some state of threat. Particularly in the Colombian Pacific, a marine connectivity has been detected for adults and neonates of S.

lewini between oceanic and coastal waters in Malpelo Island and the Sanquianga National Natural Park, respectively [START_REF] Quintanilla | Conservation Genetics of the Scalloped Hammerhead Shark in the Pacific Coast of Colombia[END_REF]Estupiñan-Montaño et al., 2021).

Therefore, potential extension of Marine Protected Areas mainly in coastal areas, or the inclusion of marine corridors between coastal and oceanic areas should be considered as an important measure to protect sharks in Colombia (Estupiñan-Montaño et al., 2021).

Survival of juveniles is particularly important for shark conservation [START_REF] Cortés | Incorporating uncertainty into demographic modelling: application to shark populations and their conservation[END_REF]. Sharks are highly vulnerable to increased mortality rates due to their slow growth, late age of sexual maturation, low reproduction rate, and an important parental investment in young pups [START_REF] Ferretti | Loss of large predatory sharks from the Mediterranean Sea[END_REF]. Juveniles are generally segregated from adults in coastal waters as breeding areas, a strategy that is supposed to improve survival by providing shelter from predation and prey abundance [START_REF] Heupel | Shark nursery areas: concepts, definition, characterization and assumptions[END_REF]. However, these areas, which are generally found in estuarine and mangroves ecosystems [START_REF] Nakano | The biology and ecology of the blue shark, Prionace glauca[END_REF], are the most affected in Colombia by THg contamination due to anthropogenic activities, as has been reported, in South Baja California (Mexico) [START_REF] Maz-Courrau | Bioaccumulation and biomagnification of total mercury in four exploited shark species in the Baja California Peninsula, Mexico[END_REF]. This coastal contamination could also affect adult sharks during pregnancy period because it has been reported that females are capable of carrying out excretion processes by transferring part of their bioaccumulated THg to their embryos (Cadena-Cardenas, 2004;Pethybridge et al., 2010;[START_REF] Man | Shark fin, a symbol of wealth and good fortune may pose health risks: the case of mercury[END_REF]. These situations may be happening in the Colombian Pacific coast.

Species such as S. lewini are mobile and migrate in periods of rain constantly through the East Tropical Pacific Corridor between the islands of Cocos, Galapagos, and Malpelo [START_REF] Bessudo | Residency of the scalloped hammerhead shark (Sphyrna lewini) at Malpelo Island and evidence of migration to other islands in the Eastern Tropical Pacific[END_REF]. Since this corridor is a marine-protected area (MPA), it is possible that this regional conservation efforts carried out would be threatened by this THg contamination, in addition to coastal overfishing of juveniles and/or adults during their reproductive period. Further studies are needed to continue monitoring the THg exposure in sharks and local communities along the Colombian Pacific coast, as well as effective management of shark fishing in coastal areas, in order to guarantee their conservation in the long term.

Conclusions and recommendations

This study contributed to assess the status of THg contamination of shark populations, and knowledge of the trophic ecology of A. pelagicus, C. cerdale, M. henlei, M. lunulatus, S. corona, S. lewini, and S. tiburo in the Colombian Pacific. Overall, it was found that THg concentrations vary according to the species and were moderate, in comparison to other studies. However, ML, EWI, and THQ results suggested human health risks to shark consumption, which is a warning signal for consumers, especially for children and pregnant women. In addition, isotope analyses results suggested that coastal areas have the highest capture of sharks, which would be affecting the growth of shark populations. This information helps to understand the role of these shark species that are the most affected by overfishing and finning in this area of the country, with the aim of providing useful information to develop management and conservation plans for these species. Furthermore, the identification of key habitats like foraging areas can be also important evidence for ideal conservation and management policies such as potential extension of MPAs or creation of marine corridors.

It is recommended for future studies to include molecular analyses to complement the information obtained in this study such as sex identification, to assess if females accumulate higher THg concentrations than males, which could increase risks of THg transfer to the neonates (Cadena-Cardenas, 2004;Pethybridge et al., 2010;[START_REF] Man | Shark fin, a symbol of wealth and good fortune may pose health risks: the case of mercury[END_REF]. Additionally, shark size information would help explain possible bioaccumulation processes [START_REF] Delshad | Mercury concentration of the whitecheek shark, Carcharhinus dussumieri (elasmobranchii, chondrichthyes), and its relation with length and sex[END_REF][START_REF] Maz-Courrau | Bioaccumulation and biomagnification of total mercury in four exploited shark species in the Baja California Peninsula, Mexico[END_REF][START_REF] Man | Shark fin, a symbol of wealth and good fortune may pose health risks: the case of mercury[END_REF][START_REF] Kim | Species-specific accumulation of methyl and total mercury in sharks from offshore and coastal waters of Korea[END_REF], since adult sharks tend to accumulate more THg in their tissues than juveniles (Escobar-Sanchez et al., 2011).

THg levels found here are an important issue for shark conservation, so pollution management should be considered as one of the most important issues for future management plans in Colombia or at regional level. Finally, for future investigations, the exact geographical fishing points would help to identify the areas of greatest threat of overfishing and finning for sharks in the Colombian Pacific and therefore prioritize fishing management plans for these areas.

Acknowledgements

  International authorities such as FAO/WHO (Food and Agriculture Organization/World Health Organization) and Colombian agencies such as Invima (National Institute for Food and Drug Surveillance) are responsible for controlling these limits of THg in food and informing the population about the possible risks of THg in human health. Findings on this sense may also contribute to improve conservation and management strategies for shark populations that have been carried out in the Colombian Pacific, such as the National Action Plan for the Conservation and Management of Sharks, Rays, and Chimaeras of Colombia (PAN-Tiburones Colombia) (Caldas Aristizabal et al., 2010). Confirmation of THg concentrations in shark tissues from Colombia, could be used as a conservation strategy to reduce their international demand and national overfishing. Therefore, for this study we assessed: (1) THg concentrations in fins and muscles of seven shark species seized in the Buenaventura port (Colombian Pacific), which include the Pelagic Thresher (Alopias pelagicus), Pacific Smalltail Shark (Carcharhinus cerdale), Brown Smoothhound (Mustelus henlei), Sicklefin Smoothhound (Mustelus lunulatus), Scalloped Bonnethead (Sphyrna corona), Scalloped Hammerhead (Sphyrna lewini), and Bonnethead Shark (Sphyrna tiburo); (2) potential human health risks related to fin and muscle consumption of any of these species; and (3) trophic ecology of the seven species of sharks by analyzing trophic interactions and possible overlaps of their ecological niche using chemical tracers of habitat and diet (δ 13 C and δ 15 N, respectively). Assessing trophic ecology and monitoring of THg in sharks captured in the Colombian Pacific and seized in the Buenaventura port, represents important precautionary measures to facilitate shark conservation in Colombia and neighboring countries.

  4 10 -3 kg per day per person for the world; Food and Agriculture Organization (FAO), 2009); MC is the THg shark tissue concentration (mg/kg); RfD is the oral reference dose (3.0 10 -4 mg/kg/day for THg; Nadal et al., 2008; United States Environmental Protection Agency (USEPA), 2010); BW is the human body weight (kg): for this research, it was assumed an average body weight of 60 kg

  , Fig. 5B in purple, Fig. 5C in dark blue and purple). Conversely, most of the species showed a considerable niche overlap for these results (Figs. 5B-C), in which M. lunulatus and S. corona presented the highest percentage values for δ 13 C-THg and M. lunulatus the highest values for δ 15 N-THg (Tables4 and 5, Fig.5Bin neon green and neon blue, Fig.5Cin neon green). Likewise, for both δ 13 C-THg and δ 15 N-THg, S. lewini showed the largest ellipse area(229.45 and 168.14, in ‰², respectively), while M. lunulatus

Figure 1 .

 1 Figure 1. Map of study area showing Buenaventura, where is located the Buenaventura port in the Colombian Pacific coast. Sources: IGAC, modified for this study.

Fig. 2 .

 2 Fig. 2. THg concentrations (ng g -1 ww) in fins of seven shark species of the Colombian Pacific: Alopias pelagicus (red), Carcharhinus porosus (yellow), Mustelus henlei (neon green), Mustelus lunulatus (mint green), Sphyrna corona (blue), Sphyrna lewini (purple) and Sphyrna tiburo (pink). The upper and lower ends of the boxes are the quartiles, the vertical lines are the maximum and minimum, the bold line represents the average and the points are the outliers. The horizontal lines are the paired combinations with significant differences (*: p <0.05).

Fig. 3 .

 3 Fig. 3. Fin (blue) and muscle (grey) THg concentrations (ng g -1 ww) in Alopias pelagicus and Sphyrna lewini individuals of the Colombian Pacific. The upper and lower ends of the boxes are the quartiles, the vertical lines are the maximum and minimum, the bold line represents the average and the points are the outliers. The dotted horizontal line represents the limit of maximum consumption of Hg in predatory fish recommended by the FAO/WHO (2011). The horizontal lines are the paired combinations with significant differences (*: p < 0.05).

Fig. 4 .

 4 Fig. 4. Relationship (mean ± SD) between carbon and nitrogen isotopic signatures (‰) and THg concentrations (ng g -1 ww) in fins for seven shark species of the Colombian Pacific, including: Alopias pelagicus (red), Carcharhinus porosus (yellow), Mustelus henlei (neon green), Mustelus lunulatus (mint green), Sphyrna corona (blue), Sphyrna lewini (purple) and Sphyrna tiburo (pink). (A) represents relationship between δ 13 C and δ 15 N, (B) δ 13 C and THg and (C) δ 15 N and THg.

Fig. 5 .

 5 Fig. 5. Standard ellipses for corrected sample sizes (SEAc) of carbon and nitrogen isotopic signatures (‰) and THg concentrations (ng g -1 ww) in fins for seven shark species of the Colombian Pacific, including: Alopias pelagicus (red), Mustelus lunulatus (neon green), Sphyrna lewini (dark green), Sphyrna tiburo (dark blue), Mustelus henlei (purple), Carcharhinus porosus (orange) and Sphyrna corona (neon blue). (A) represents relationship between δ 13 C and δ 15 N, (B) δ 13 C and THg and (C) δ 15 N and THg.

  Table6) likely related to tissue samples being from juvenile sharks (see discussion Section 4.3). In muscles, these concentrations were similar to THg measurements reported for several shark species in the Pacific coast of Costa Rica, in the Mexican Pacific coast, in the Southeastern United States Caribbean coast, and in the Southwest Indian Ocean[START_REF] Maz-Courrau | Bioaccumulation and biomagnification of total mercury in four exploited shark species in the Baja California Peninsula, Mexico[END_REF][START_REF] Bergés-Tiznado | Mercury and selenium in muscle and target organs of scalloped hammerhead sharks (Sphyrna lewini) of the Gulf of California: dietary intake, molar ratios, loads, and human health risks[END_REF][START_REF] Kiszka | Plasticity of trophic interactions among sharks from the oceanic south-western Indian Ocean revealed by stable isotope and mercury analyses[END_REF][START_REF] Sandoval-Herrera | Mercury levels in muscle tissue of four common elasmobranch species from the Pacific coast of Costa Rica, Central America[END_REF][START_REF] O'bryhim | Relationships of mercury concentrations across tissue types, muscle regions and fins for two shark species[END_REF] (Table

Table 1 .

 1 Total mercury (THg in ng g -1 ww) concentration, stable isotopes ratios (δ 13 C and δ 15 N in ‰), C and N ratio (C:N) in sharks of the Colombian Pacific. Means and standard deviations were calculated (Mean ± SD). NA: data not available.

	Species	Tissue	n	THg	δ 15 N	δ 13 C	C:N
				Mean ± SD	Mean ± SD	Mean ± SD	Mean ± SD
		Fins	30	88.07 ± 97.66	13.05 ± 0.56	-15.14 ± 0.74	3.04 ± 0.14
	Alopias pelagicus
		Muscles	25	566.78 ± 337.07	14.19 ± 0.52	-16.99 ± 0.60	3.34 ± 0.15
		Fins	9	45.56 ± 25.40	13.64 ± 0.47	-14.65 ± 0.80	2.81 ± 0.72
	Carcharhinus porosus
		Muscles	NA	NA	NA	NA	NA
		Fins	25	23.45 ± 15.27	14.16 ± 0.56	-15.50 ± 0.45	3.08 ± 0.38
	Mustelus henlei
		Muscles	NA	NA	NA	NA	NA
	Mustelus lunulatus	Fins	20	18.38 ± 11.76	13.14 ± 0.39	-14.81 ± 0.35	2.52 ± 0.72
		Muscles	NA	NA	NA	NA	NA
	Sphyrna corona	Fins	10	24.10 ± 16.16	12.74 ± 0.42	-14.62 ± 0.30	3.09 ± 0.07
		Muscles	NA	NA	NA	NA	NA
		Fins	19	88.56 ± 82.30	13.61 ± 0.63	-14.83 ± 0.88	2.66 ± 0.71
	Sphyrna lewini
		Muscles	20	809.29 ± 728.88	15.46 ± 0.67	-16.09 ± 0.85	3.34 ± 0.14
	Sphyrna tiburo	Fins	17	34.69 ± 32.10	12.31 ± 0.56	-15.64 ± 0.96	3.04 ± 0.64
		Muscles	NA	NA	NA	NA	NA

Table 2 .

 2 Estimated weekly intake (EWI) and Target Hazard Quotient (THQ) for seven shark species of the Colombian Pacific. The provisional tolerable weekly intake (PTWI) recommended by the Joint FAO/WHO Expert Committee (2004) is 1.6 ng g -1 bw for children and 3.2 ng g -1 bw for adults. THQ values >1 indicate possible adverse effects for human health.

	Age group Species	Tissue	Mean EWI (µg/kg)	Min EWI -Max EWI (µg/kg)	Mean THQ	Min THQ -Max THQ
		A. pelagicus	Fins Muscles	0.11 3.78	0.01 -0.68 0.13 -12.62	0.33 2.10	0.03 -2.03 0.07 -7.03
		C. porosus Fins	0.06	0.02 -0.13	0.17	0.05 -0.37
	Children	M. henlei	Fins	0.03	0.01 -0.09	0.09	0.03 -0.28
	(1-19 years)	M. lunulatus Fins	0.02	0.01 -0.07	0.07	0.03 -0.21
	30 kg	S. corona	Fins	0.03	0.01 -0.08	0.09	0.04 -0.24
		S. lewini	Fins Muscles	0.11 5.40	0.02 -0.40 0.30 -17.76	0.33 3.00	0.07 -1.20 0.17 -9.89
		S. tiburo	Fins	0.04	0.01 -0.16	0.13	0.02 -0.47
		A. pelagicus	Fins Muscles	0.06 2.57	0.00 -0.34 0.09 -8.58	0.16 1.05	0.01 -1.01 0.04 -3.51
		C. porosus Fins	0.03	0.01 -0.06	0.08	0.03 -0.19
	Adult	M. henlei	Fins	0.01	0.00 -0.05	0.04	0.01 -0.14
	(25-65 years)	M. lunulatus Fins	0.01	0.01 -0.04	0.03	0.02 -0.10
	60 kg	S. corona	Fins	0.02	0.01 -0.04	0.04	0.02 -0.12
		S. lewini	Fins Muscles	0.06 3.67	0.01 -0.20 0.21 -12.08	0.16 1.50	0.03 -0.60 0.08 -4.94
		S. tiburo	Fins	0.02	0.00 -0.08	0.06	0.01 -0.24

Table 3 .

 3 Overlapping percentage of corrected standard ellipses (SEAc) of δ 13 C and δ 15 N in fins of seven shark species of the Colombian Pacific, including: Alopias pelagicus, Mustelus lunulatus, Sphyrna lewini, Sphyrna tiburo, Mustelus henlei, Carcharhinus porosus and Sphyrna corona.

	Species	A. pelagicus	M. lunulatus	S. lewini	S. tiburo	M. henlei	C. porosus	S. corona
	A. pelagicus	*	88.6	29.4	9.7	0.7	23.2	65.9
	M. lunulatus	31.4	*	18.6	0.0	0.0	16.5	33.1
	S. lewini	42.3	75.2	*	0.0	36.7	92.8	17.8
	S. tiburo	13.2	0.0	0.0	*	0.0	0.0	9.7
	M. henlei	0.4	0.0	16.5	0.0	*	6.6	0.0
	C. porosus	23.9	48.1	66.6	0.0	10.6	*	1.1
	S. corona	21.7	30.8	4.1	2.3	0.0	0.3	*

Table 4 .

 4 Percentage of overlap (in %) of corrected standard ellipses (SEAc) of δ 13 C vs THg for fins of seven shark species of the Colombian Pacific, including: Alopias pelagicus, Mustelus lunulatus, Sphyrna lewini, Sphyrna tiburo, Mustelus henlei, Carcharhinus porosus and Sphyrna corona.

	Species	A. pelagicus M. lunulatus	S. lewini	S. tiburo	M. henlei	C. porosus	S. corona
	A. pelagicus	*	100.0	68.8	40.6	37.4	67.4	90.9
	M. lunulatus	6.5	*	4.9	7.9	4.6	7.1	58.8
	S. lewini	76.0	83.8	*	27.8	9.1	87.8	99.7
	S. tiburo	19.9	59.8	12.3	*	100.0	41.3	30.2
	M. henlei	4.0	7.5	0.9	21.9	*	12.0	0.0
	C. porosus	18.1	29.1	21.3	22.6	29.9	*	42.1
	S. corona	6.6	65.9	6.6	4.5	0.0	11.5	*

Table 5 .

 5 Percentage of overlap (in %) of corrected standard ellipses (SEAc) of δ 15 N vs THg for fins of seven shark species of the Colombian Pacific, including: Alopias pelagicus, Mustelus lunulatus, Sphyrna lewini, Sphyrna tiburo, Mustelus henlei, Carcharhinus porosus and Sphyrna corona.

	Species	A. pelagicus	M. lunulatus	S. lewini	S. tiburo	M. henlei	C. porosus	S. corona
	A. pelagicus	*	66.2	39.2	30.7	0.0	22.3	81.7
	M. lunulatus	6.3	*	4.5	0.0	0.0	4.1	26.3
	S. lewini	40.9	49.3	*	0.0	24.2	95.7	9.0
	S. tiburo	10.5	0.0	0.0	*	0.0	0.0	45.0
	M. henlei	0.0	0.0	3.9	0.0	*	16.7	0.0
	C. porosus	5.9	11.5	24.3	0.0	25.9	*	0.0
	S. corona	11.8	40.2	1.3	19.2	0.0	0.0	*

Table 6 .

 6 Total mercury (THg) concentrations (ng g -1 ww) in fins and muscles of shark species reported in the literature and in this study.

	Species	N	THg (mean ± SD)	Tissue	Region	Reference
	S. zygaena	37	7	Fins	Baja California Sur, Mexico Escobar-Sanchéz et al. (2010)
	C. melanopterus	26	1100 ± 770	Fins	Korean Pacific Ocean	Kim et al. (2016)
	Prionace glauca	15	2300 ± 1100 Fins	Korean Pacific Ocean	Kim et al. (2016)
	A. pelagicus	13	1500 ± 510	Fins	Korean Pacific Ocean	Kim et al. (2016)
	C. longimanus	4	530 ± 790	Fins	Korean Pacific Ocean	Kim et al. (2016)
	S. zygaena	3	1600 ± 900	Fins	Korean Pacific Ocean	Kim et al. (2016)
	M. manazo	2	320 ± 140	Fins	Korean Pacific Ocean	Kim et al. (2016)
	S. tiburo	18	8 ± 6	Fins	Southeastern United States O'Bryhim et al. (2017)
	C. porosus	12	67.3 -2368.4 Fins	Trinidad and Tobago	Mohammed & Mohammed (2017)
	S. lewini	10	301.6 -1465.8 Fins	Trinidad and Tobago	Mohammed & Mohammed (2017)
	C. albimarginatus	26	56 -32	Fins	Revillagigedo Archipelago Le Croizier et al. (2020)
	C. albimarginatus	28	63 -48	Fins	Clipperton Atoll	Le Croizier et al. (2020)
	A. pelagicus	30	88.07 ± 97.66 Fins	Colombian Pacific Coast	This study
	C. porosus	9	45.56 ± 25.40 Fins	Colombian Pacific Coast	This study
	M. henlei	25	23.45 ± 15.27 Fins	Colombian Pacific Coast	This study
	M. lunulatus	20	18.38 ± 11.76 Fins	Colombian Pacific Coast	This study
	S. corona	10	24.10 ± 16.16 Fins	Colombian Pacific Coast	This study
	S. lewini	19	88.56 ± 82.30 Fins	Colombian Pacific Coast	This study


Guillaume Merle
email: merle@lurpa.ens-cachan.fr

Jean-Marc Roussel
email: roussel@lurpa.ens-cachan.fr

ALGEBRAIC MODELLING OF FAULT TREES WITH PRIORITY AND GATES

Keywords: Fault trees, minimal cut sets, temporal gates, algebraic approach

This paper presents a formal framework allowing to extend the simplification of static fault trees to fault trees built with gates PRIORITY AND. The laws which make these simplifications possible have been demonstrated thanks to a homogeneous algebraic definition of each gate studied. These definitions use a mathematical model of events able to take into account their order of appearance. The processing of an example points out the possibilities offered by this algebraic framework dedicated to non-repairable faults.

INTRODUCTION

A fault tree is a standardized well-known model used in engineering to express graphically what the causes of an undesired/catastrophic event are (IEC 2006) [START_REF] Vesely | Fault Tree Handbook with Aerospace Applications[END_REF]. A fault tree is often built top-down starting from the undesired event. All the intermediate events which contribute to the undesired event are expanded recursively. The recursion ends with the basic events, which represent the finest level of abstraction chosen for the study. Each analysed event -top or intermediate event -is connected to its causessub-events -by a gate. An AND gate indicates that all sub-events are necessary to trigger the analysed event; for an OR gate, only one sub-event is necessary.

The rules of Boolean algebra are commonly applied to restructure fault trees to simpler, equivalent forms. Amongst them, the minimal cut set form allows quantitative and qualitative evaluations to be performed in a straightforward manner [START_REF] Vesely | Fault Tree Handbook with Aerospace Applications[END_REF]. Qualitative analysis identifies single failures or events that alone can cause the top event to occur. Quantitative analysis consists of the determination of top event probabilities and basic event importances.

In the Fault Tree Handbook [START_REF] Vesely | Fault Tree Handbook[END_REF]), a distinct gate was defined to allow priorities between events: temporal gate PRIORITY AND (PAND). In addition to the condition of gate AND, one input event must occur before the other one for its output event to occur. However, Boolean algebra cannot take into account this sequence of events since events are modelled by Booleans. Consequently, the fault trees using this gate could not be simplified with the laws of Boolean algebra.

The aim of this paper is to define a homogeneous and unambiguous formal framework able to give gate PAND a semantics which would allow the determination of the laws necessary to simplify fault trees. In order to preserve the coherence with the current results, the framework proposed must necessarily give gates OR and AND a semantics allowing to determine the laws commonly used for the calculation of minimal cut sets.

This paper mainly focuses on the formal framework proposed. Section 2 deals with the detailed presentation of the problem and the hypotheses made. The formal framework, described in section 3, relies on the mathematical definition of the elements present in a fault tree: events, gates, . . . This definition allowed us to establish the laws necessary to the simplification of fault trees. The application of these laws is illustrated in section 4.

PROBLEM

In this paper, the term fault is used to refer to fault tree events in order to avoid the confusion between the concept of event used in fault trees and the concept used in discrete event systems.

Let us consider the fault tree in figure 1. Its top fault is s, its basic faults are a, b, c, d, and its intermediate faults are m, n, p, q. This fault tree contains five gates -three OR gates, one AND gate and one PAND gate -whose definitions proposed in the Fault Tree Handbook [START_REF] Vesely | Fault Tree Handbook[END_REF]

B Q Ä B Q © A BEFORE B ⇔ from figure IV-12
Table 1. Definitions of the gates studied

Dugan 2004) -that trigger the top fault, as well as its probability to appear. These state-based models are mainly timed Petri nets, in [START_REF] Adamyan | Sequential failure analysis using counters of petri net models[END_REF], or Markov chains, in [START_REF] Coppit | Formal semantics of models for computational engineering: a case study on dynamic fault trees[END_REF]. Deterministic and Stochastic Petri Nets are also used in [START_REF] Kaiser | State/event fault trees -a safety analysis model for software-controlled systems[END_REF]) to analyse quantitatively state/event fault trees, which combine elements of fault tree analysis, Markov chains and state automata. In [START_REF] Buchacker | Modeling with extended fault trees[END_REF], an alternative solution to temporal gates is studied with Extended fault trees taking into account repairable components and allowing stochastic dependencies thanks to stochastic Petri nets.

The proposed approach is purely algebraic, as in [START_REF] Walker | Pandora: The time of priority-and gates[END_REF]. It aims at defining the set of laws which is necessary to simplify fault trees with PAND gates upstream, in order to make the state-based models presented above simpler. This paper deals with the trees containing the three gates presented in table 1, whose definitions come from [START_REF] Vesely | Fault Tree Handbook[END_REF].

A definition can be commented upon: as stated in [START_REF] Coppit | Formal semantics of models for computational engineering: a case study on dynamic fault trees[END_REF], the term "BEFORE" is ambiguous: it is not clear whether the term is considered strictly -A must appear before B occurs -or not strictly -A must appear before B occurs or at the same time as B occurs.

The hypotheses for this paper are as follows:

• the class of faults studied is limited to nonrepairable -persistent -faults. • there is no restriction on the order of appearance of the faults. Two basic faults can appear simultaneously. • the term "BEFORE" is considered strictly.

This hypothesis is the same as that in [START_REF] Walker | Pandora: The time of priority-and gates[END_REF].

Taking these hypotheses into account, the expected behaviour of the three gates studied can be represented with timing diagrams. They dis-play the behaviour of output Q according to the behaviour of inputs A and B. The three cases to consider are as follows: A appears before B appears, A appears at the same time as B appears, A appears after B has appeared.

The expected behaviour of the three gates studied is shown in table 2. Table 2. Expected behaviour in the case of non-repairable faults

FORMAL FRAMEWORK PROPOSED

The aim of this work is to determine the laws necessary to simplify fault trees containing PAND gates. Consequently the gates of a fault tree were formalized thanks to a mathematical description, to obtain an algebraic form adapted to this kind of calculation. For the sake of clarity during the modelling phase, each concept and element present in a fault tree were mathematically defined. Section 3.1 deals with this. The mathematical model of gates OR and AND, together with the list of the laws which were demonstrated thanks to it, is presented in section 3.2. Section 3.3 deals with operation "BEFORE" defined in order to model gate PAND. The algebraic model of the three gates studied is given in section 3.4.

Mathematical definition of fault tree concepts

3.1.1. Non-repairable faults In the case of nonrepairable or persistent faults, the knowledge of the date of appearance of a fault allowed us to describe the fault without any ambiguity, provided the occurrence of a fault is considered as instant.

Before that date, the fault is absent; at that date and after that date, the fault is present. Taking these hypotheses into account, a non-repairable fault is shown in the timing diagram in figure 2.

s 6 - 0 1 t s a(t) d(a)
s a(t i ) Fig. 2. A non-repairable fault From a mathematical point of view, a nonrepairable fault is a piecewise right-continuous function on R + ∪{+∞}, whose range is B = {0,1}, and which allows at most a single change of value -a single discontinuity. This function has the following characteristics:

• it is worth 0 as long as there is no fault • it is worth 1 as soon as the fault has appeared -at the instant noted d(a) on the timing diagram in figure 2 Let F nr be the set of non-repairable faults. F nr contains two elements that are special since they are constant. The always-present fault is noted e: ∀t ∈ R + ∪ {+∞}, e(t) = 1. The never-occurring fault is noted : ∀t ∈ R + ∪ {+∞}, (t) = 0.

Definition 1. (Date of appearance of a fault).

The date of appearance of a fault a is the instant t at which fault a appears. This date is noted d(a).

In

Fault functions

A fault tree describes how basic faults must combine to form the top fault. From a mathematical point of view, the top fault can be considered as the image of the n-tuple of the basic faults by the fault function whose expression is the considered fault tree.

Definition 3. (Fault function).

A fault function of order n is an application from (F nr ) n -→ F nr with n ∈ N * .

Let Ψ n = {f : (F nr ) n -→ F nr } be the set of the fault functions of order n. Ψ n contains two fault functions that are special because they are constant. These fault functions are noted and ⊥ and are defined as follows. Henceforth, A is any n-tuple (a 1 , a 2 , . . . , a n ) of (F nr ) n .

Definition 4. (Function ).

is the fault function which associates the always-present fault e to any n-tuple A ∈ (F nr ) n : :

(F nr ) n -→ F nr (a 1 , a 2 , . . . , a n ) -→ e
Definition 5. (Function ⊥). ⊥ is the fault function which associates the never-occurring fault to any n-tuple A ∈ (F nr ) n : ⊥ :

(F nr ) n -→ F nr (a 1 , a 2 , . . . , a n ) -→ Definition 6. (Equivalent fault functions). Let f and g be two elements of Ψ n . Fault functions f and g are equivalent -noted f ∼ g -if and only if ∀A ∈ (F nr ) n , f (A) ≈ g(A).

Comment: The concepts of fault and fault function are both mathematically described by functions, but these functions are of different natures:

• faults are functions from R + ∪ {+∞} → B
whose set is noted F nr • fault functions are functions from (F nr ) n → F nr whose set is noted Ψ n

Expression of a fault function

A fault tree is the expression shown in a graphical form of a fault function defined on the n-tuple of the basic faults present in that tree. The fault tree shown in figure 1 The simplification of the tree consists of finding an equivalent expression of the fault function free of redundant parts.

The link between a fault tree and a fault function is the same as between a Boolean expression and a Boolean function. This link is as follows:

• a Boolean function can be represented by many Boolean expressions • two Boolean expressions are equivalent if they represent the same Boolean function • the link between two equivalent Boolean expressions depends on the laws established for operations defined on the set of Boolean functions [START_REF] Grimaldi | Discrete and Combinatorial Mathematics[END_REF] By analogy to Boolean expressions and Boolean functions, fault trees have been simplified by using the laws established for the operations defined on the set of fault functions.

σ i : (F nr ) n -→ F nr (a 1 , a 2 , . . . , a i , . . . , a n ) -→ a i
Each leaf of the fault tree presented in figure 1 is one of the four basic fault functions.

Operations OR and AND

Be f, g, h ∈ Ψ n .

Definition of operations OR and AND

These operations model the behaviour of gates OR and AND shown in table 2. Definition 9. (Operation OR).

+ : Ψ n × Ψ n -→ Ψ n (f, g) -→ f + g
f + g being defined, for all A ∈ (F nr ) n , by:

(f + g)(A) =      f (A) if d (f (A)) < d (g(A)) g(A) if d (f (A)) > d (g(A)) f (A) if d (f (A)) = d (g(A))
Definition 10. (Operation AND).

.

: Ψ n × Ψ n -→ Ψ n (f, g) -→ f.g
f.g being defined, for all A ∈ (F nr ) n , by:

(f.g)(A) =      g(A) if d (f (A)) < d (g(A)) f (A) if d (f (A)) > d (g(A)) f (A) if d (f (A)) = d (g(A))
Comment: These definitions appear to privilege f with regard to g when d(f (A)) = d(g(A)); that is not the case, since operations OR and AND have been demonstrated as being commutative.

3.2.2. Laws of operations OR and AND These two definitions allowed the demonstration of the following 14 laws:

f + g ∼ g + f (1) f.g ∼ g.f (2) f + (g + h) ∼ (f + g) + h (3) f.(g.h) ∼ (f.g).h (4) f + f ∼ f (5) f.f ∼ f (6) f + (g.h) ∼ (f + g).(f + h) (7) f.(g + h) ∼ (f.g) + (f.h) (8) f + (f.g) ∼ f (9) f.(f + g) ∼ f (10) f + ⊥ ∼ f (11) f. ∼ f (12) f + ∼ (13) f.⊥ ∼ ⊥ (14)
The obtention of laws 1 to 10 was mandatory in order to guarantee that this formal framework could replace the classical Boolean algebra for the calculation of the minimal cut sets of static fault trees with non-repairable faults.

The main benefit of this formal framework is to allow the definition of a new operation to take into account the sequence order between faults.

Operation BEFORE

This operation was introduced to model the concept of priority between faults on which the definition of gate PAND depends.

¡ : Ψ n × Ψ n -→ Ψ n (f, g) -→ f ¡ g
f ¡ g being defined, for all A ∈ (F nr ) n , by:

(f ¡ g)(A) = f (A) if d (f (A)) < d (g(A)) ⊥(A) if d (f (A)) ≥ d (g(A))
3.3.2. Laws of operation BEFORE The definition of these three operations allowed us to determine the 14 following laws:

f + (f ¡ g) ∼ f (15) g + (f ¡ g) ∼ f + g (16) f.(f ¡ g) ∼ f ¡ g (17) f + ((f ¡ g).h) ∼ f (18) f ¡ (g + h) ∼ (f ¡ g).(f ¡ h) (19) (f + g) ¡ h ∼ (f ¡ h) + (g ¡ h) (20) f ¡ (g.h) ∼ (f ¡ g) + (f ¡ h) (21) (f.g) ¡ h ∼ (f ¡ h).(g ¡ h) (22) (f ¡ g).(g ¡ h).(f ¡ h) ∼ (f ¡ g).(g ¡ h) (23) (f ¡ g).(g ¡ f ) ∼ ⊥ (24) f ¡ f ∼ ⊥ (25) f ¡ ⊥ ∼ f (26) ⊥ ¡ f ∼ ⊥ (27) f ¡ ∼ ⊥ (28)
The algebraic definition of this operation was one of the objectives of this work. The homogeneous framework defined above thus allows the modelling and algebraic manipulation of fault trees with PAND gates.

Algebraic model of the gates

Ä B Q Ä B Q Q ∼ A+B Q ∼ A.B Q ∼ B.(A ¡ B)
Table 3. Algebraic model of gates OR, AND and PAND Regarding gate PAND, the following simplified form can be found:

Q ∼ (A.B).(A ¡ B) (2,4) ∼ B.(A.(A ¡ B)) (17) ∼ B.(A ¡ B)

SIMPLIFICATION OF FAULT TREES WITH PAND GATES

Determining laws 15 to 28 was the operational objective of this work. Combined with laws 1 to 14, they allow the simplification of the fault trees which contain gate PAND. These laws are sufficient to analyse any fault tree which does not contain imbricated combinations of PAND gates -i.e. PAND gates whose input sub-trees contain PAND gates.

In order to simplify any tree containing PAND gates whatever its structure, the development laws of forms f ¡ (g ¡ h) and (f ¡g)¡h are mandatory.

The simplification of a fault tree consists in:

(1) expressing the output of each gate according to its inputs, thanks to the algebraic model given in table 3 (2

CONCLUSION

The first contribution of this work is the definition of a homogeneous and unambiguous framework for the formalization of gate PAND. This framework allowed us to determine the laws necessary to the simplification of fault trees containing PRI-ORITY AND gates. The hypotheses made were as follows: basic faults are non-repairable faults, they can appear simultaneously, and the notion of priority is considered strictly.

On-going work deals with determining the developed forms of the two laws presented in section 4, which will allow the simplification of fault trees with PAND gates compositions.

In the short term, the consequences of the hypothesis made on priority -strict priority -will be studied by developing a new operation for which the output fault would also occur if both input faults occur simultaneously, as it was supposed in [START_REF] Coppit | Formal semantics of models for computational engineering: a case study on dynamic fault trees[END_REF]. The extension of the work to other temporal gates -such as gate SEQ [START_REF] Coppit | Formal semantics of models for computational engineering: a case study on dynamic fault trees[END_REF] -is also planned.

  regards to the always-present fault and the never-occurring fault, d(e) = 0 and d( ) = +∞. Definition 2. (Simultaneous faults). Let a and b be two elements of F nr . Faults a and b are simultaneous -noted a ≈ b -if and only if they have the same date of appearance: d(a) = d(b).

  is the graphical representation of the fault function which associates the top fault s to the quadruple of basic faults (a, b, c, d). Definition 7. (Equivalent trees). Two fault trees are equivalent if and only if they describe the same fault function or two equivalent fault functions.

  3.1.4. Mathematical model of fault tree elementsEach kind of gate of a fault tree is characterized by an operation on a set of fault functions. It is the set of the fault functions defined on the ntuple of the basic faults present in the fault tree. The top fault and each intermediate fault are the images of the n basic faults by a fault function. In the interest of homogeneity, each leaf of the tree should also be considered as a fault function. That fault function is special since the image of the ntuple of basic faults by that function is the basic fault having the same name.Definition 8. (Basic fault function). The basic fault functions are the n fault functions of order n σ i -with i ∈ {1, 2, . . . , n} -defined by:

  3.3.1. DefinitionThe expected behaviour of the composition of f and g by operation BEFOREnoted f ¡g -is illustrated by the timing diagrams in figure3-Case 1: d (f (A)) < d (g(A)), Case 2: d (f (A)) = d (g(A)), Case 3: d (f (A)) > d (g(A)). Expected behaviour for (f ¡ g)(A)Definition 11. (Operation BEFORE).

Fig. 4 .

 4 Fig. 4. Fault Tree equivalent to Fault Tree in figure 1

  are recalled in table 1.

					Symbol	Definition from (Vesely et al. 1981)
					OR	The output fault occurs only if one
					or more of the input faults occur.
					from figure IV-2
					The output fault occurs only if all
					ÄND	the input faults occur.
					from figure IV-5
					PRIORITY
			s
		m		n	q
	m a	p	m		m d
	a		m b	m a	m c
	Fig. 1. Fault Tree with a temporal gate
	Under this form, this fault tree cannot be directly
	exploited due to redundant parts. When fault
	trees are static, i.e. trees only containing OR and
	AND gates, the only knowledge of the state of the
	basic faults -failing or not -is sufficient to sim-
	plify these trees. For the tree in figure 1, sub-tree
	m can be reduced to leaf a by using the following
	simplification law: a + (a.b) = a. When fault trees
	are dynamic, e.g. trees containing temporal gates,
	only knowing the state of the faults is no longer
	sufficient since the gates also refer to the order
	of appearance of the faults -cf. definition 3 of
	table 1. As the Boolean model of a fault does not
	contain this kind of information, the classical laws
	of Boolean algebra cannot produce a solution.
	Much work has been carried out to give an op-
	erational semantics to temporal gates. Some au-
	thors convert temporal fault trees into state-based
	models to determine the basic fault sequences -or
	minimal cut sequences, as suggested in (Tang and

AND

Ä

  Table 3 recalls the elements of table 1 and presents the algebraic model associated with each gate.

	OR Gate	AND Gate	PAND Gate
	Q
	A	B