Marine Ballutaud

Hilaire Drouineau

Laure Carassou

Gregory Munoz

Xavier Chevillot

Paul Labadie

Hélène Budzinski

Jérémy Lobry
email: jeremy.lobry@irstea.fr

Gabriel Munoz

Pierre Labadie

EStimating Contaminants tRansfers Over Complex food webs (ESCROC): An innovative Bayesian method for estimating POP's biomagnification in aquatic food webs

come

proposes a relevant and innovative TMF estimation method accounting for its many variability sources. The ESCROC model (EStimating Contaminants tRansfers Over Complex food webs), which is implemented in a Bayesian framework, allows for a more reliable and rigorous assessment of contaminants trophic magnification, in addition to accurate estimations of isotopes trophic enrichment factors and their associated uncertainties in food webs. Similar to classical mixing models used in food web investigations, ECSROC computes diet composition matrices using isotopic composition data while accounting for contamination data, leading to more robust food web descriptions.

As a demonstration of the practical application of the model, ESCROC was implemented to revisit the trophic biomagnification of 5 polyfluoroalkyl substances (PFAS) in a complex estuarine food web (the Gironde, SW France). In addition to the TMF estimate and 95% confidence intervals, the model provided biomagnification probabilities associated to the investigated contaminants -for instance, 92% in the case of perfluorooctane sulfonate (PFOS) -that can be interpreted in terms of risk assessment in a precautionary approach, which should prove useful to environmental managers.

Introduction

Increased nutrients, pollutants, and agrochemicals due to industries, urbanization and agriculture exert dramatic impacts on ecosystems [START_REF] Köhler | Wildlife ecotoxicology of pesticides: can we track effects to the population level and beyond?[END_REF][START_REF] Verhoeven | Regional and global concerns over wetlands and water quality[END_REF]. Aquatic ecosystems and, among them, coastal and estuarine ecosystems are particularly vulnerable to these changes: they are increasingly exploited and polluted, and their biodiversity is decreasing [START_REF] Budzinski | Evaluation of sediment contamination by polycyclic aromatic hydrocarbons in the Gironde estuary[END_REF][START_REF] Matthiessen | Contaminants and their effects on estuarine and coastal organisms in the United Kingdom in the late twentieth century[END_REF]. At the individual and population scales, some pollutants can lead to deleterious effects, such as altered metabolism, immunotoxicity, endocrine disruption or neurotoxicity [START_REF] Köhler | Wildlife ecotoxicology of pesticides: can we track effects to the population level and beyond?[END_REF]. This issue is exacerbated by the fact that some pollutants tend to be accumulated by organisms, a process known as bioaccumulation. Bioaccumulation is a fundamental process in environmental toxicology and risk assessment because it controls the internal dose of potential toxicants in individual organisms [START_REF] Arnot | A food web bioaccumulation model for organic chemicals in aquatic ecosystems[END_REF]. Additionally, some contaminants also become ecologically harmful because they accumulate through food webs, a process known as biomagnification. In these instances, pollutants found at low concentrations in natural environments can achieve harmful concentration for high-order organisms including human beings [START_REF] Kelly | Food Web-Specific Biomagnification of Persistent Organic Pollutants[END_REF][START_REF] Köhler | Wildlife ecotoxicology of pesticides: can we track effects to the population level and beyond?[END_REF][START_REF] Van Oostdam | Human health implications of environmental contaminants in Arctic Canada: A review[END_REF]. Studies aquatic ecosystems -marine systems (e.g. [START_REF] Romero-Romero | Biomagnification of persistent organic pollutants in a deep-sea, temperate food web[END_REF][START_REF] Sun | Halogenated organic pollutants in marine biota from the Xuande Atoll, South China Sea: Levels, biomagnification and dietary exposure[END_REF], lakes (e.g. [START_REF] Liu | Residues, bioaccumulations and biomagnification of perfluoroalkyl acids (PFAAs) in aquatic animals from Lake Chaohu, China[END_REF][START_REF] Mazzoni | Trophic transfer of persistent organic pollutants through a pelagic food web: The case of Lake Como (Northern Italy)[END_REF], coastal environments [START_REF] Bodin | PCB, PCDD/F and PBDE levels and profiles in crustaceans from the coastal waters of Brittany and Normandy (France)[END_REF]Loizeau et al., 2001a;Loizeau et al., 2001b;[START_REF] Munschy | Classic and novel brominated flame retardants (BFRs) in common sole (Solea solea L.) from main nursery zones along the French coasts[END_REF] and rivers [START_REF] Lopes | Is PCBs concentration variability between and within freshwater fish species explained by their contamination pathways?[END_REF]-but also in terrestrial environments (e.g. [START_REF] Daley | Aquatic to terrestrial transfer of sediment associated persistent organic pollutants is enhanced by bioamplification processes[END_REF][START_REF] Wang | A review of study on bioaccumulation and biomagnification of persistent organic pollutants in terrestrial food chain using modeling method[END_REF]) demonstrated such biomagnification process occurs for hydrophobic organohalogenated contaminants. Being potentially persistent, bioaccumulative and toxic (due for instance to eurotoxic properties and/or endocrine disruption), Persistent Organic Pollutants (POPs) are of particular concern (see the Stockholm Convention on POPs as amended in 2009 -UNEP, 2009) for human health [START_REF] Belpaire | Contaminants in Eels and their Role in the Collapse of the Eel Stocks[END_REF][START_REF] Berger | Fish consumption as a source of human exposure to perfluorinated alkyl substances in Sweden -Analysis of edible fish from Lake Vättern and the Baltic Sea[END_REF] as well as for animal populations' viability (Gilliers et al., 2006a;Gilliers et al., 2006b;[START_REF] Rochette | Effect of nursery habitat degradation on flatfish population: Application to Solea solea in the Eastern Channel (Western Europe)[END_REF]. In this context, a comprehensive understanding of the ecodynamics of human-induced chemicals in coastal and estuarine ecosystems is needed to better manage the ecological functions associated with these areas.

Potential for bioaccumulation in organisms and biomagnification in food webs differ depending on the investigated contaminants, environmental contexts, and physiological characteristics of species [START_REF] Bodiguel | A dynamic and mechanistic model of PCB bioaccumulation in the European hake (Merluccius merluccius)[END_REF][START_REF] Connolly | p′-DDE bioaccumulation in female sea lions of the California Channel Islands[END_REF][START_REF] Gobas | A model for predicting the bioaccumulation of hydrophobic organic chemicals in aquatic food-webs: application to Lake Ontario[END_REF]. Therefore, accurate in situ assessment of bioaccumulation and biomagnification potential of pollutants in aquatic food webs is required, in order to inform management actions.

Most empirical approaches used to understand trophic transfers of pollutants rely on the estimation of a Trophic Magnification Factor (TMF) from field data [START_REF] Borgå | Trophic magnification factors: Considerations of ecology, ecosystems, and study design[END_REF]. The TMF is used to assess the biomagnification of a given pollutant in a food web and to define environmental quality norms in some instances (see french envrionmental quality norms (NQE) - [START_REF] Migne-Fouillen | Problématique NQE dans le biote et le sédiment[END_REF]. It is usually corresponds to the slope of the statistical regression between the chemical concentration and the trophic level of organisms within a food web. Although TMF is increasingly used to describe trophic dynamics of xenobiotics, its estimates present many uncertainties, reviewed by Borga et al. (2012) and [START_REF] Mackay | Processes influencing chemical biomagnification and trophic magnification factors in aquatic ecosystems: Implications for chemical hazard and risk assessment[END_REF]. Among the manyassumptions, potential bias, pitfalls, and vigilance points reported in these reviews, uncertainty in measurements of contaminant concentrations, temporal or spatial variability of these concentrations, , inter and intraspecific variability in the bioaccumulation process, and uncertainty about the food web structure and trophic levels of individuals were emphasized. Recently, [START_REF] Munoz | Evidence for the Trophic Transfer of Perfluoroalkylated Substances in a Temperate Macrotidal Estuary[END_REF] evaluated different statistical methods to address these above-mentioned sources of uncertainty and bias, based on data on 19 polyfluoroalkyl substances (PFASs) in the Gironde estuarine food web. The statistical approaches compared included linear mixed models from the 'NADA' [START_REF] Lee | NADA: Nondetects and Data Analysis for Environmental Data[END_REF] and 'LMEC' [START_REF] Vaida | lmec: Linear Mixed-Effects Models with Censored Responses[END_REF] R-packages, accounting for censored responses and a random effect 'species', respectively. Both methods however assumed that the trophic level of each individual -and consequently, the structure of the trophic network-are perfectly known, an assumption that rarely verifies in the real world, and particularly not in the Gironde estuary.

Theoretically, estimating the trophic level of a consumer species (or an individual) requires that its diet be estimated, i.e., the proportion, in biomass, of each prey and its respective trophic level, in the overall consumer's diet. This is usually done through stomach content analyses, which reflect the quantitative and qualitative ingestion of species at a specific time, but sometimes raise problems of prey identification, suffers from some biases such as differential digestibility, and requires many samples to be analyzed. Stable isotope analyses represent more integrative records of food intake over longer time scale [START_REF] Post | Using Stable Isotopes to Estimate Trophic Position: Models, Methods, and Assumptions[END_REF] and are now widely used to explore food web structure [START_REF] Boecklen | On the use of stable isotopes in trophic ecology[END_REF][START_REF] Layman | Applying stable isotopes to examine food-web structure: an overview of analytical tools[END_REF]. Stable isotopes of nitrogen are discriminated during digestion and assimilation, leading to an enrichment of the 15 N/ 14 N ratio (δ 15 N) of the consumer with respect to its prey. Since the enrichment factor is generally in the range 3 -4 ‰ [START_REF] Deniro | Influence of diet on the distribution of nitrogen isotopes in animals[END_REF][START_REF] Minagawa | Stepwise enrichment of 15 N along food chains: further evidence and the relation between δ 15 N and animal age[END_REF][START_REF] Peterson | Stable isotopes in ecosystem studies[END_REF], linear regressions can be used to convert stable isotope composition into trophic level [START_REF] Post | Using Stable Isotopes to Estimate Trophic Position: Models, Methods, and Assumptions[END_REF]. This is the usual method chosen to estimate trophic level when investigating contaminant biomagnification [START_REF] Borgå | Trophic magnification factors: Considerations of ecology, ecosystems, and study design[END_REF]. Combined with the consideration of the isotopic ratio of other elements (e.g. 13 C/ 12 C or 34 S/ 33 S), it can be used to estimate the diet of species among a set of potential prey. This is the approach used by MixSIR, SIAR and MixSIAR, the mixing models classically used to estimate a species diet based on its isotopic composition, which is assumed to be a mixture of the isotopic compositions of the different prey [START_REF] Moore | Incorporating uncertainty and prior information into stable isotope mixing models[END_REF][START_REF] Parnell | SIAR: stable isotope analysis in R[END_REF][START_REF] Parnell | Source Partitioning Using Stable Isotopes: Coping with Too Much Variation[END_REF][START_REF] Parnell | Bayesian stable isotope mixing models[END_REF][START_REF] Stock | MixSIAR: Bayesian Mixing Models in R[END_REF]. This approach allows accounting for the uncertainty of stable isotope enrichment factors, and for intra-and interspecific variability. However, since the number of isotopic tracers is small (i.e., usually two) compared to the number of potential prey, isotope mixing models are generally underdetermined [START_REF] Fry | Alternative approaches for solving underdetermined isotope mixing problems[END_REF][START_REF] Phillips | Source partitioning using stable isotopes: coping with too many sources[END_REF][START_REF] Phillips | Best practices for use of stable isotope mixing models in food-web studies[END_REF]. Consequently, precise estimates of enrichment factors must be provided for the mixing model to work, although these estimates are very sensitive parameters [START_REF] Bond | Recent Bayesian stable-isotope mixing models are highly sensitive to variation in discrimination factors[END_REF]. Furthermore, it is not possible to carry out the analysis using those mixing models over a full trophic network but only one predator after another. Finally, since biomagnification and food web analyses are generally carried out into two independent steps, it is usually impossible (or very difficult) to propagate the uncertainty on estimated trophic levels to the estimation of biomagnification factors. For both scientific and management reasons, it is therefore necessary to provide an alternative rigorous method based on sound statistics to evaluate biomagnification factors (TMF) and associated uncertainty.

The present work aimed at presenting such alternative method combining both biomagnification and food web analyses into a single model. We assume that using contaminants as additional diet tracers within trophic networks could mitigate the issue of underdetermination of mixing models. Conversely, incorporating the inference of trophic levels within biomagnification analysis allows propagating the uncertainty over trophic levels when estimating biomagnification factors such as TMF. Diet tracers such as isotopes can then be used to estimate contaminant transfers. Our model aims at (1) accounting for most of the sources of variability listed above on both biomagnification and isotopic fractionation, (2) estimating diets and related uncertainty for all predators of the food web at once, (3) estimating the biomagnification of contaminants and related uncertainty. Our model, named ESCROC (EStimating Contaminants tRansfers Over Complex food webs), is based on a generic mixing model, similar to those used for deriving diet composition from isotopic data, but allows incorporating contamination measures.

To illustrate the relevance of this model, a large dataset describing the occurrence of a family of Persistent Organic Pollutants (POPs) in the Gironde estuary was used. Located on the French Atlantic coast, in SW France and largest estuary in Western Europe [START_REF] Lobry | Structure of the Gironde estuarine fish assemblages: a European estuaries comparison perspective[END_REF], the Gironde estuary case study is especially relevant since POPs are now an increasing issue in this area [START_REF] Munoz | Evidence for the Trophic Transfer of Perfluoroalkylated Substances in a Temperate Macrotidal Estuary[END_REF][START_REF] Tapie | PBDE and PCB contamination of eels from the Gironde estuary: From glass eels to silver eels[END_REF]. Among those substances, the target selected compounds were polyfluoroalkyl substances (PFASs). Few studies have addressed the contamination of estuarine food webs by these emerging contaminants (de Vos et al., 2008;Naile et al., 2012;[START_REF] Munoz | Evidence for the Trophic Transfer of Perfluoroalkylated Substances in a Temperate Macrotidal Estuary[END_REF]). As the dataset was previously described and analyzed by [START_REF] Munoz | Evidence for the Trophic Transfer of Perfluoroalkylated Substances in a Temperate Macrotidal Estuary[END_REF] with a set of various modelling approaches, this would also allow a comparison of the outcomes provided by the ESCROC model with those obtained with more traditional methods.

Material and methods / description of the model

Context on TMF estimation

Basis of TMF estimation

Basically, TMF estimation consists in assessing the average factor of change in contaminant concentration per Trophic Level (TL). In that sense, it is similar to the enrichment factor in isotopic analysis. Considering biomass distribution in aquatic food webs as well as contaminants transfer efficiencies, the relationship between contaminant concentrations [C] and TL has an exponential form [START_REF] Borgå | Trophic magnification factors: Considerations of ecology, ecosystems, and study design[END_REF]. Therefore, TMF estimations are based on the linear regression between Logtransformed contaminant concentrations Log 10 [C] and TL. The TMF is subsequently obtained as 10 b , with b being the slope of the linear regression (Eq. 1, Figure 1) usually estimated from simple regression models.

Log 10 [C]=a + bTL

Eq. 1

Modifications to improve TMF estimation calculation were however recently proposed to better account for different sources of uncertainty and variability. For instance, [START_REF] Munoz | Evidence for the Trophic Transfer of Perfluoroalkylated Substances in a Temperate Macrotidal Estuary[END_REF] suggested to use linear mixed models with censored data (to take into account non-detected data), with random effects to integrate both inter-specific variabilities in physiological properties, errors in chemical concentration measurements and potentially low sampling effort.. These methods however still assumed that trophic levels were perfectly known.

If initially, the trophic positions of organisms in the food webs were directly assessed using stable N isotope ratios (δ 15 N), most recent studies (see Borga et al. 2012 or for instance [START_REF] Munoz | Evidence for the Trophic Transfer of Perfluoroalkylated Substances in a Temperate Macrotidal Estuary[END_REF] refined the estimation of trophic position by using integer-based TL. The TL of a primary producer being fixed to 1 by convention, a primary consumer has a TL of 2. Thus, for secondary consumers, the trophic level of a particular individual (TL i see Eq. 2) is estimated using the difference between its own stable N isotope ratio (δ 15 N i , obtained using tissue measures of 15 N/ 14 N) and a source isotope ratio δ 15 N base at the base of the food web weighted by the trophic enrichment between TLs (∆ 15 N). Different sources for benthic and pelagic food chains (δ 15 N base1 and δ 15 N base2 ) are often considered in marine coastal and/or estuarine environments, to reflect the complexity of trophic food webs in those systems. Each individual has to be allocated to one or the other of these food chains through an α coefficient (from totally benthic: α=1 to totally pelagic α=0), which has to be fixed a priori using expert knowledge on species' feeding ecology and food web structure.

TL i = 2+ [δ 15 N i -{αδ 15 N base1 +(1-α)δ 15 N base2 }] ∆ N 15 Eq. 2
Then, a linear mixed model has to be fitted for each food web (benthic and pelagic) independently, by selecting species based on α values For species feeding on both pelagic and benthic preys and sources, α values can be comprised between 0 and 1. When α>0.5 species are allocated to benthic food chain and to the pelagic one for α<0.5 for pelagic.

Estimating trophic levels is therefore not straightforward, and subjected to multiple sources of uncertainty, including measurements of δ 15 N of individuals and sources at the basis of the food web, and estimations of α values associated to each species considered in the food web. Moreover, while a linear increase in δ 15 N with TL probably oversimplified the mechanism of isotope discrimination [START_REF] Hussey | Rescaling the trophic structure of marine food webs[END_REF] and equation 2 is not necessarily relevant in a situation where trophic chains are intertwined in complex interaction trophic networks.

ESCROC modeling framework

The proposed model (ESCROC) was developed in a Bayesian framework. The Bayesian theorem allows

(1) combining objectively different core metrics accounting for their sensitivity and variability and (2)

providing rigorous uncertainty quantification.

The approach in ESCROC was based on the same conceptual framework as stable isotope mixing models such as MixSIAR [START_REF] Parnell | Bayesian stable isotope mixing models[END_REF][START_REF] Stock | MixSIAR: Bayesian Mixing Models in R[END_REF]. In such models, consumer species are assumed to feed on a combination of prey items (or sources) that are all known, and that the isotopic composition y i,e,t of an individual i of species e for tracer t results from the combined isotopic composition of the assimilated prey items.

Model formulation

In ESCROC, we combine isotope values and contaminant concentrations (in log scale) as chemical tracers of food web structure.

We can therefore describe the mean concentration Y of a tracer t for a species e as a combination of its consumed prey (p) concentrations. In lieu of raw tracer concentrations, scaled values were used by subtracting the average value and dividing by the standard deviation: y 𝑖,𝑒,𝑡 ′ = ( y i,e,t -𝑦 𝑡 ̅ ) 𝜎 𝑡 ⁄ ) so that all tracers share a common scale. This facilitates the integration of prioris and statistical inference of the model [START_REF] Bolker | Strategies for fitting nonlinear ecological models in R, AD Model Builder, and BUGS[END_REF].

Based on stable isotope mixing model assumptions, the tracer composition of a predator was calculated using the tracer compositions of its prey items: As ESCROC is implemented in a Bayesian framework, priors can be defined for unknown parameters.

Y e,
Priors, corresponding to possible a priori distributions of the parameters, can be constructed using knowledge from various sources (expert knowledge, meta-analyses, other field data…). In the absence of external knowledge, uninformative or weakly informative priors can be built.

Y e,t as described in Eq3 therefore corresponds to a weighted average of the prey tracer compositions (with weights corresponding to the importance of the prey in the predator's diet and to the concentration of the tracer in the prey), to which we added an enrichment and a species effect. If q p,t are equal among prey items, equation 3 simplifies to: Similarly, the variance of the values of the tracer t for a species e, denoted V e,t , can be calculated from the variances of the different prey:

Y e,t =
V e,t = ∑ (ρ e,p 2 •q p,t 2 •V p,t )
p∈prey(e)

[∑ (ρ e,p •q p,t )

p∈prey(e) ] 2 + B t

Eq. 5

With B t a variable to add potential noise at each trophic level.

If the concentration parameters 𝑞 𝑝,𝑡 are all equals, then the equation simplifies to:

V e,t = ∑ (ρ e,p 2 •V p,t )
p∈prey(e)

+ B t

In equation 3, if Y e,t is the concentration of a contaminant (in log10 scale) and assuming that all concentration parameters are equal (as in equation 4), then ∆ t corresponds to the enrichment in contaminant between a prey and its predator, i.e., the enrichment along the food web when trophic level increases by 1. Consequently, it corresponds to the slope of the line in Figure 1 and we obtain ∆ t =log 10 (TMF).

The measured values of a given tracer on a given dataset are supposed to follow a Normal law whose parameters are calculated from previous equations. We thus assume that the distribution of the tracer t value, for an individual i of the species e can be written as:

y i,e,t ~Normal(Y e,t ,V e,t )
Eq. 6

In case of the concentration measurement of a given tracer is null or not reliable for analytical reasons (e.g. below the detection threshold of a given measurement method), it can be considered as a left-censored data. The cumulative distribution of the normal distribution is thus used instead of the density of probability.

Model calibration and priors construction

We propose here a selection of possible priors that can be implemented for most of the model applications, but adaptation can be made in relation with available data or expert knowledge.

Selection of priors for main parameters

Priors can be supplied for the enrichment factors either on the transformed scale or on the original scale. Informative priors for Nitrogen and Carbon TEF (∆ N and ∆ C see Eq. 3) can be inferred from the literature (e.g. [START_REF] Post | Using Stable Isotopes to Estimate Trophic Position: Models, Methods, and Assumptions[END_REF]. For instance, these priors can be implemented as follows:

Δ N ~Normal(3,1) Eq. 7

Δ C ~Normal(0,1) Eq. 8 corresponding to a TEF value for N around 3 and around 0 for C.

A non-informative prior can be used for the enrichment factors of all tracers corresponding to PFAS concentrations:

∆ 𝑡 ′ ~Normal(0,10) Eq. 9

Finally, non-informative priors can be used for other parameters (residual variation and random effect) of model formulation (Eq. 3 and Eq. ):

B t ~Inverse Gamma(0.01,0.01) Eq. 10 σ t ~Uniform(0.01,10) Eq. 11

Diet matrix

Information on trophic interactions should be implemented in the model. At first, we can only specify if a prey p can be predated by a consumer e based on the evidence of predator-prey relationships using field data.

An uninformative prior for the dietary contribution of prey p for consumer e (ρ e,p see Eq. 3) can then be constructed by assuming that it follows a Dirichlet distribution: {ρ e,1 ,…,ρ e,n }~Dirichlet({λ e,1 ,…,λ e,n }) Eq. 12

where λ e,p = 1 if e feeds on p and λ e,p = 0 otherwise; n being the number of species in the considered food web.

Informative priors can be implemented if external data, such as stomach contents, are available.

However, considering the implementation framework, trophic loops cannot be included in the food web description.

Constructing priors for tracer values using data

Average tracer compositions of predators are calculated from prey tracer compositions. However, if a species does not have prey (e.g. primary producers), or if some prey of a species are not present in the dataset (i.e., no contamination data or isotopic measurements), it is necessary to provide priors for this species. We will see in the case study how an informative prior can be constructed. However, in the absence of external data, a weakly informative prior can be implemented as follows:

Y e,t ~Normal (0,10) Eq. 13

V e,t ~Gamma (0.01,0.0) Eq. 14

Outputs and Implementation

Outputs

Main outputs of ESCROC consist in posterior distributions of the estimated parameters. Three main types of outputs can be obtained from ESCROC: diet compositions of each consumer of the investigated food web, enrichment factors for each tracer, and TMF estimates (with associated credibility interval).

As a mixing model, ESCROC allows estimating a distribution of the proportion of each prey in the diet of the predators in the investigated food web.

Furthermore, by considering posterior distribution of enrichment factors (see Eq. 3, Figure 4) for N and C isotopic ratios, ESCROC allowed re-estimating TEF values, which are usually empirically fixed in the literature on isotope-based trophic studies, with aforementioned uncertainty. TEF can indeed be estimated using the median of the distribution and 2.5% and 97.5% quantiles, providing associated 95%-credibility intervals. In the same way, estimated posterior distributions of enrichment factors for contaminants can be used to estimate TMFs and associated credibility intervals. In this case, TMFs corresponds to 10 ∆t . Similarly, an estimation of TMFs can be provided using the median of the distribution and bounds of the 95%-credibility interval, computed from 2.5% and 97.5%-quartiles.

Associated with TMF estimates, the probability of a contaminant to be biomagnified in the investigated food web can then be computed by estimating the probability of ∆ t to be positive (i.e.

corresponding to a TMF value greater than 1).

Implementation

ESCROC was implemented using the R software (R Development Core Team, 2006) and the integrated development environment (IDE) R-studio (the model being run using coda and runjags packages). For the Bayesian part of the model, the JAGS language was used [START_REF] Plummer | rjags: Bayesian Graphical Models using MCMC[END_REF]. The model convergence can be checked using Gelman and Rubin tests [START_REF] Brooks | General Methods for Monitoring Convergence of Iterative Simulations[END_REF][START_REF] Gelman | Inference from Iterative Simulation Using Multiple Sequences[END_REF]. A first beta version of the R-package (escrocR) implementing the method is available on GitHub (https://github.com/Irstea/escroc). It can be cited as follows:

Hilaire Drouineau, Marine Ballutaud and Jeremy Lobry (2018). EscrocR: a R package implementing the model ESCROC. R package version 0.0.0.9000.

Illustrative example: PFAS in the Gironde estuarine food web

In this illustrative example, the method was applied to a dataset on PFAS contamination in the Gironde estuarine food web. The main aims were to estimate (1) TMF values for a set of PFAS previously described and analyzed [START_REF] Munoz | Evidence for the Trophic Transfer of Perfluoroalkylated Substances in a Temperate Macrotidal Estuary[END_REF]), (2) enrichment factors of two isotopes of nitrogen and carbon and (3) the diets of all species within the trophic network.

Dataset

Data used in this study are taken from [START_REF] Munoz | Ecodynamique des composés poly-et perfluoroalkylés dans les écosystèmes aquatiques[END_REF] and [START_REF] Munoz | Evidence for the Trophic Transfer of Perfluoroalkylated Substances in a Temperate Macrotidal Estuary[END_REF]. Samples were collected between May and November 2012 in the mesohaline zone of the Gironde estuary. Amongst the initial dataset of 147 biological samples from 18 species or group of species, a subset of data was used comprising 138 samples from 16 species, for which both isotopic data (δ 15 N and δ 13 C) and PFAS concentrations were available. We selected 5 PFAS (L-PFOS, FOSA, PFOA, PFNA and PFUnDA, see Table S1) based on their occurrence in biota samples, the existence of censored data (considering PFAS with different proportions of censored data), the TMF values previously estimated, and the variety of chemical structures (ie., fluoroalkyl chain length or functional group -Table 1).

Specific priors

The priors for diet compositions were directly built from the trophic network illustrated in Figure 2.

For two groups (gammarids and copepods), instead of using uninformative prior as proposed in equations 13 and 14, we built an informative prior to take advantage of pre-existing data on nitrogen and carbon isotopic ratios (David, unpublished data). We specified a normal prior parameterized with the mean and the standard errors in pre-existing available tracer composition data: Eq. 17

Y e,

Outputs and model implementation

We set q p,t =1 for all species in the model. We also computed an index α e for each predator to compare to the α values (see section 2.1.1) arbitrarily assigned in the Munoz et al. dataset (2017). For gammarids and copepods, we set α e =0 (pelagic), and we set α e =0 (benthic) for nereids and crabs.

The model was fitted using a MCMC (Monte Carlo Markov Chain) method. Three chains were used in parallel with 1 million preliminary iterations -burnin -followed by 150,000 iterations to assess posterior distributions. We run the model with JAGS software version 4.1.0 and check convergence using the Gelman-Rubin diagnostic (gelman.test< 1.05).

Results

Model calibration and convergence

Values of Gelman indices confirmed the model convergence for 68 parameters out of 70. The only two parameters for which the model did not converge corresponded to tracer composition of prey items with 100% of censored data.

The model fitted observations as suggested by the plot of predicted posterior distributions of mean species tracer composition against observed values (Figure 3).

Outputs

Diet compositions

Diet compositions were estimated for each predator of the Gironde estuarine food web for which both isotope and PFAS data were available (see Figure 4 as an example). A global diet matrix can then be obtained by compiling all the diet values estimated by ESCROC using both N and C isotopic ratios and the 5 PFAS concentrations (Table 2).

For most species, the coefficients relating the species to the pelagic and benthic food webs were rather consistent with the expert knowledge used in [START_REF] Munoz | Evidence for the Trophic Transfer of Perfluoroalkylated Substances in a Temperate Macrotidal Estuary[END_REF] though the model tends to consider less species as benthic (Table 3). Those results confirm that it is very difficult to separate species into a set of two independent food-webs, as required by usual TMF estimation methods.

Enrichments and TMF

TEF values and the associated uncertainty were estimated, as well as TMFs estimates and biomagnification probabilities (Figure 4 and Table 4).

Non-informative priors were used for the PFAs enrichment factors, as highlighted by the flat curve lines in Figure 4. In these cases, ESCROC provided informative posterior estimates for contaminants TMFs. Conversely, informative priors based on literature were used for isotopes TEFs. Although the estimated posterior distribution appeared consistent for δ 15 N, it was significantly different for δ 13 C even if the classical value used in the literature and in our prior definition (TEF = 0) is comprise in the posterior credibility interval.

Discussion

4.1 Limits and benefits of the ESCROC model formulation

Bayesian framework, a priori information and uncertainty propagation

ESCROC was implemented in an innovative and flexible Bayesian framework to estimate TMFs and associated uncertainty. This modeling approach presents several advantages.

Unlike frequentist methods previously mentioned (e.g. linear models and mixed models), the Bayesian framework allows to account rigorously for uncertainty propagation in measurements (e.g., TL estimates) to TMF estimates. [START_REF] Starrfelt | Estimating trophic levels and trophic magnification factors using bayesian inference[END_REF], for instance, recommended the use of Bayesian inference to account for measure uncertainty in contaminants concentrations and isotope ratios (δ 15 N), as well as for variability and uncertainty related to TL estimates, in order to improve the precision of TMF estimations. ESCROC goes even further, by providing credibility intervals for all parameters, in particular for contaminants TMFs and isotopes TEFs. By doing so, ESCROC represents a noteworthy methodological advance as compared to traditional methods for TMF estimation.

Based on both a contaminant propagation model and an isotope mixing model, ESCROC combines and enriches both modeling approaches. The contaminant propagation model therefore benefits from integrated diet estimations. As such, TMF estimates are of more generic nature, as they no longer depend on a pre-specified trophic chain structure that the model user provides (and usually simplify).

This model rather accounts for the whole food web complexity at once, and provides generic TEF estimates. Similar to widely-used mixing models [START_REF] Parnell | SIAR: stable isotope analysis in R[END_REF][START_REF] Parnell | Source Partitioning Using Stable Isotopes: Coping with Too Much Variation[END_REF][START_REF] Parnell | Bayesian stable isotope mixing models[END_REF][START_REF] Stock | MixSIAR: Bayesian Mixing Models in R[END_REF], ESCROC allows estimating diet compositions in investigated food webs (See Supplementary Materials S2 for a preliminary comparison of both approaches). It allows going even further than classical mixing models. Indeed, using contaminants in addition to isotopes data increases the number of chemical tracers and allow the estimation of isotope enrichment factors, a significant improvement as compared to the use of fixed a priori -values from the literature (usually from Post ( 2002)), values which are known to not perform as well in various environmental contexts or for contrasted food webs). Furthermore, our modelling approach partly addresses some of the recommendations listed by [START_REF] Hussey | Rescaling the trophic structure of marine food webs[END_REF] for estimating isotope discrimination. The full Bayesian estimation framework indeed provides a pragmatic and very flexible estimation of enrichment factors. The framework is thus generic and can be applied in all ecosystem contexts.

Furthermore, a random effect 'Species' is added in the model. Thus, although the TEF and TMF estimation are still considered globally constant through the food web, they are modulated species by species. By doing this, ESCROC did not specifically consider that isotope discrimination varies with trophic position but it allowed the estimations to vary for every species.

In the Gironde estuarine case study, the TEF for δ 13 C estimated from ESCROC considerably differs from the one in literature. This is mostly explained by the fact we used data from studies on marine environments to compute the prior distribution while estuarine ecosystems are usually enriched on continental organic carbon which signature is different. However the model allowed not only estimating more accurately the TEF distribution for δ 13 C in the estuarine context but the estimates remains consistent with the reference literature (e.g. [START_REF] Post | Using Stable Isotopes to Estimate Trophic Position: Models, Methods, and Assumptions[END_REF]. This result further highlights the need for accurate TEF estimates based on the best available knowledge, as already advocated in multiple reviews of isotope-based ecological studies [START_REF] Martinez Del Rio | Isotope ecology ten years after a call for more laboratory experiments[END_REF][START_REF] Layman | Applying stable isotopes to examine food-web structure: an overview of analytical tools[END_REF][START_REF] Bastos | Are you what you eat? Effects of trophic discrimination factors on estimates of food assimilation and trophic position with a new estimation method[END_REF].

Additionally, prior knowledge incorporation is a really significant advantage of both ESCROC and MixSIAR approaches [START_REF] Parnell | Source Partitioning Using Stable Isotopes: Coping with Too Much Variation[END_REF][START_REF] Parnell | Bayesian stable isotope mixing models[END_REF]. Indeed, the Bayesian framework is especially well-adapted to integrate a priori information such as expert knowledge or external datasets. For instance, in the present case study, external information about copepods isotopic composition were combined in an informative prior as available data were uncertain. Similarly, expert knowledge and food web data (such as stomach contents) could have been used to compute more informative prior on trophic interactions, instead of using an uninformative prior for the contribution of each prey in each consumer diet.

Computing TMF and associated bioaccumulation probabilities

Although the initial purpose of the model was to compute TMF estimates and associated uncertainty, the ECROC modeling approach provides a comprehensive framework for the understanding of contaminants transfers in a complex food web. In relation with the Bayesian framework used, ECSROC indeed provides a biomagnification probability, which corresponds to the probability of a particular contaminant to be biomagnified in the investigated food web. This innovative feature is especially relevant for risk assessment. In fact, this probability directly expresses the risk a manager would take by classifying a given contaminant as "biomagnifiable" in a given food web. As such, ESCROC model represents an important tool to support decision making. For instance, estimated thresholds of risks could be used to define contamination levels for which additional monitoring is required, as well as levels for which specific management measures appear mandatory.

Limitations

Despite the aforementioned advances and advantages, ESCROC modeling approach also presents two major limitations.

First, considering the implementation framework, trophic loops cannot be considered in the food web description, although such phenomena may exist in nature. We can cite cannibalism as an illustrative example, a process relatively common in aquatic food webs, in which adult consumers sometimes prey upon juveniles from the same species [START_REF] Livingston | Trophic organization in coastal systems[END_REF]). In our case example, we assumed such flows to be be negligible or, at least much weaker than direct prey-predator trophic flows. This assumption seems reasonable with regards to available knowledge on food webs in our study system (see for instance [START_REF] Lobry | Diversity and stability of an estuarine trophic network[END_REF][START_REF] Selleslagh | Trophic functioning of estuarine ecosystems along a gradient of anthropogenic pressures: a French case study with emphasis on a small and low impacted estuary[END_REF][START_REF] Tecchio | The mosaic of habitats of the Seine estuary: Insights from food-web modelling and network analysis[END_REF] for French estuaries).

Another limitation of the ESCROC modeling approachlies in technical aspects. First, computing time can reveal quite long depending on food web complexity and computer devices used. Second, data about multiple tracers need to be included to avoid any underdetermination issues, as TMFs and TEFs are estimated together and at the whole trophic network scale, SSince, the number of tracers (either isotopes or contaminants) should be large enough to avoid any underdetermination issue. This implies considerable efforts in sample collection, preparation, and chemical analysis, an even higher than for a classical mixing model such as MixSIAR.

Diagnosis about PFAS in the Gironde estuary

The computed TMF values of the five investigated PFAS are not significantly greater than 1 with a αrisk at 95%. This implies that, considering the results of the present study, none of the five investigated contaminants can be considered as 'biomagnifiable' in the Gironde estuarine food web.

However, when considering the biomagnification probabilities associated with TMF estimates, results are more contrasted. The diagnosis actually depends on the risk-level a manager is ready to accept.

For instance, if a risk-level was fixed to 30% in a precautionary approach, PFUnDA, FOSA, and more particularly L-PFOS would be considered to be biomagnified in the food web with 72%, 86% and 92% of certainty, respectively (Table 4). These considerations give sense to the computation of biomagnification probabilities within the ESCROC modeling tool.

Our ESCROC-based diagnosis about PFAS contamination in the Gironde estuarine food web are slightly different from previous assessment from [START_REF] Munoz | Evidence for the Trophic Transfer of Perfluoroalkylated Substances in a Temperate Macrotidal Estuary[END_REF]. In the latter study, the 5 investigated contaminants were considered to have been magnified at both the benthic chain and the whole food web levels, whereas only one TMF estimates (FOSA) was greater than one when considering the pelagic chain. Differences between [START_REF] Munoz | Evidence for the Trophic Transfer of Perfluoroalkylated Substances in a Temperate Macrotidal Estuary[END_REF] and our interpretation probably arises from differences in the methodological approaches. First, pelagic and benthic data were combined in ESCROC's estimates as well as in the Munoz's pooled estimates (Table S17 in [START_REF] Munoz | Evidence for the Trophic Transfer of Perfluoroalkylated Substances in a Temperate Macrotidal Estuary[END_REF]. As we saw in section 3.2.1, such combination is probably more realistic than separating benthic and pelagic food chains, and this difference can lead to significant contrasts in TMF estimates. Second, the Bayesian model formulation provides a better integration of uncertainty propagation than traditional linear models. This leads to greater associated uncertainties and larger credibility intervals than the confidence intervals estimated with the LMEC method used in [START_REF] Munoz | Evidence for the Trophic Transfer of Perfluoroalkylated Substances in a Temperate Macrotidal Estuary[END_REF] consideration, although such a method can still be seen as a simple and useful approach to perform comparative studies for comparing biomagnification of selected chemicals in a given ecosystem.

Nevertheless, the results obtained in the present study also plead for a precautionary approach when interpreting contaminant transfer data, and for using biomagnification probabilities rather than TMF values alone.

Perspectives for the ESCROC modeling approach

More than an innovative estimation framework for TMFs in complex food webs, ESCROC can also be (2016) underlined that: "Diet estimates for functional groups can also be obtained from stable isotopic analyses using Bayesian isotopic mixing models." By providing rigorous estimates of diet matrices (and associated uncertainty) based on chemical tracers (eventually combined with expert knowledge and/or external information), diet composition estimates from ESCROC modeling could so be used to calibrate diet matrices in mass-balanced food web models.

Other perspectives could also relate to mass-balance equations (similar than the ones used in Ecopath) which could also be implemented in the ESCROC model formulation, in order to provide an innovative modeling framework of 'biomass propagation'. This would allow a very integrated view of Anchovy 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Common seabass 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Spotted seabass 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Flounder 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Goby 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Meagre 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Mullet 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Sole 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Sprat 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 White shrimp 0.00 0.08 0.23 0.00 0.00 0.17 0.00 0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Brown shrimp 0.00 0.09 0.00 0.00 0.00 0.16 0.00 0.13 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Mysids 0.41 0.38 0.15 0.00 0.83 0.11 0.06 0.00 0.00 0.49 0.54 0.00 0.00 0.00 0.00 0.00 Gammarids 0.12 0.29 0.19 0.71 0.17 0.09 0.00 0.47 0.59 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Copepods 0.46 0.00 0.13 0.00 0.00 0.10 0.94 0.00 0.41 0.51 0.46 1.00 0.00 0.00 0.00 0.00 Nereis 0.00 0.06 0.28 0.05 0.00 0.35 0.00 0.12 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Crab 0.00 0.00 0.00 0.22 0.00 0.00 0.00 0.07 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1

  viewed as an improved mixing model for food web analyses. Considering more chemical tracers than the classical N and C isotopes indeed clearlyimproves diet matrix estimations. Results obtained for the Gironde estuarine food web are in line with those previously obtained by[START_REF] Pasquaud | A preliminary investigation of the fish food web in the Gironde estuary, France, using dietary and stable isotope analyses[END_REF] and[START_REF] Pasquaud | Determination of fish trophic levels in an estuarine system[END_REF] using both stomach contents and isotope data, and by[START_REF] Lobry | Diversity and stability of an estuarine trophic network[END_REF] using literature compilation and mass-balance modeling. Moreover, in the ESCROC modeling approach presented herein, tracers are contaminants, but other kind of isotopes (e.g. δ 34 S) can be used as well.As highlighted by[START_REF] Mackay | Processes influencing chemical biomagnification and trophic magnification factors in aquatic ecosystems: Implications for chemical hazard and risk assessment[END_REF], several processes related for instance to hydrophobicity or rates of biotransformation and growth can influence contaminant biomagnification. However, as far as they biomagnify, any type of tracer can be used in the ESCROC modeling framework. In their Best practice in Ecopath with Ecosim food-web models for ecosystem-based management,Heymans et al.

Figure 3 .

 3 Figure 3. Predicted posterior distributions (boxplot) and observations (points) of tracer values by species. Values are scaled (see text for details)

Figure 5 .

 5 Figure 5. Graphical representation of priors (curves in red) and posteriors (histograms in black) distributions of enrichment factors for each investigated tracer (d15N: δ 15 N, d13C: δ 13 C, and contaminants concentrations: L-PFOS, FOSA, PFOA, PFNA

  Note that the model does not work if two species are both prey and predator of each other because equations 3 or 4 become circular.

	∑ (ρ e,p •Y p,t )	+ ∆ t ' +E e,t with E e,t ~N(0,s t 2 )	Eq. 4
	p∈prey(e)

Table 1 .

 1 Data summary with Average [Min; Max] values for each tracer (5 PFAS, d13C and d15C). n: number of samples on which contaminants and isotopes were measured for each species. -1 corresponds to censored values (i.e. values below the limit of quantification for each specific contaminant). Contaminant concentrations are given in ng g -1 wet weight of the whole-body (from 2

	3	Munoz et al., 2017).
	4
		Species	(ng g -1 ) L-PFOS	(ng g -1 ) FOSA	(ng g -1 ) PFOA	(ng g -1 ) PFNA	(ng g -1 ) PFUnDA	(‰) δ 13 C	(‰) δ 15 N	n
		Anchovy	3.58 [1.6;6.3]	1.52 [0.9;2.2]	0.12 [-;0.1]	0.25 [0.0;0.1]	0.31 [-;0.2]	-18.71 [-19.4;-18.2]	7.99 [8.8;12.0]
		Brown shrimp	6.57 [3.8;8.0]	3.75 [1.5;5.4]	0.37 [0.3;0.5] 1.44 [0.8;2.1]	0.51 [0.5;0.6] -18.07 [-18.7;-17.1] 12.60 [11.5;13.3]
		Common seabass	6.68 [3.0;14.3]	1.39 [0.4;2.2]	0.30 [-;0.2]	0.39 [0.1;0.5]	0.63 [0.3;1.4] -17.58 [-19.8;-15.7] 12.65 [10.7;15.0]
		Copepods	1.24 [0.8;1.6]	0.33 [0.3;0.4]	0.31 [0.1;0.5] 0.56 [-;0.1]	0.32 [0.1;0.2] -23.43 [-26.4;-21.6]	9.04 [10.6;13.1]
		Crabs	2.42 [1.8;3.0]	0.22 [0.2;0.2]	2.42 [1.7;3.0] 1.40 [0.8;2.3]	0.31 [-;0.4]	-14.84 [-15.8;-13.3]	6.03 [7.9;10.1]
		Flounder	5.71 [0.7;21.7]	0.90 [0.1;3.8]	0.40 [-;1.6]	1.18 [0.2;7.9]	0.73 [0.1;1.9] -18.00 [-23.8;-14.1] 10.53 [10.7;15.2]	13
		Gammarids	2.36 [1.5;2.8]	0.52 [0.4;0.7]	1.00 [0.3;2.1] 0.48 [0.3;0.6]	0.44 [0.4;0.5] -22.51 [-24.2;-19.4]	9.10 [8.4;9.1]
		Goby	2.35 [2.0;2.4]	0.18 [0.2;0.2]	-	[-;-]	0.14 [0.1;0.2]	0.41 [-;0.4]	-19.21 [-19.2;-19.0] 11.53 [11.2;11.8]
		Meagre	4.39 [2.5;10.7]	3.30 [2.3;5.4]	-	[-;-]	0.34 [-;0.3]	0.39 [0.2;0.8] -16.89 [-18.4;-16.3] 14.19 [13.1;14.8]	12
		Mullet	2.53 [0.8;4.0]	0.36 [0.1;0.8]	-	[-;-]	0.36 [-;0.3]	0.94 [-;4.0]	-21.55 [-28.2;-16.5] 10.11 [8.7;13.6]	12
		Mysids	3.14 [2.4;3.8]	1.20 [0.9;1.5]	0.86 [0.1;0.1] 0.15 [0.1;0.2]	0.15 [0.1;0.2] -21.35 [-22.8;-19.9] 10.75 [8.2;13.3]
		Nereis	2.90 [2.0;21.0]	0.59 [0.4;0.8]	5.21 [3.6;8.2] 6.01 [3.7;8.3]	0.49 [0.1;0.3] -16.40 [-18.2;-15.2]	4.85 [9.9;10.7]
		Oyster	0.52 [0.1;0.1]	0.74 [0.4;0.8]	0.16 [-;0.0]	0.11 [-;0.0]	0.16 [-;0.0]	-19.66 [-21.2;-18.7]	7.86 [6.1;8.5]
		Scrobicularia	0.31 [0.2;0.5]	0.27 [0.2;0.3]	0.26 [-;0.0]	0.31 [0.0;0.0]	0.49 [0.0;0.1] -16.25 [-17.5;-15.5]	7.65 [7.6;7.7]
		Sole	9.12 [0.7;19.2]	1.22 [0.1;2.4]	0.83 [0.0;2.5] 3.73 [0.2;11.8]	0.47 [0.1;1.3] -14.19 [-20.8;-14.3] 13.11 [11.1;14.9]	31
		Spotted seabass	4.87 [2.2;10.5]	2.22 [1.0;4.2]	0.41 [-;0.7]	0.27 [-;0.7]	0.39 [0.1;1.0] -16.45 [-20.1;-14.8] 13.78 [11.8;15.4]	28
		Sprat	1.64 [0.3;3.8]	3.03 [1.7;4.7]	-	[-;-]	0.15 [-;0.1]	-	[-;-]	-17.19 [-17.4;-16.8] 11.60 [11.3;11.9]
		White shrimp	3.02 [2.7;3.0]	3.24 [2.7;3.6]	0.39 [0.3;0.4] 0.39 [0.3;0.4]	0.42 [0.3;0.5] -14.00 [-20.9;-19.4]	8.00 [10.5;11.2]

Table 2 .

 2 Diet matrix of the Gironde estuarine food web. Each value corresponds to the proportion of the prey in line in the diet of the predator in column. It was computed as the median value of the proportion of each of the listed preys in the diet composition of the predators estimated by ESCROC using both N and C isotopic ratios and 5 PFAS concentrations.

	Prey	Predators	Anchovy	Common seabass	Spotted seabass	Flounder	Goby	Meagre	Mullet	Sole	Sprat	White shrimp	Brown shrimp	Mysids	Gammarids	Copepods	Nereis	Crab

Table 4 .

 4 Estimates and associated 95% -credibility interval of isotopes TEF and contaminants TMF in the investigated Gironde estuary food web with associated biomagnification probabilities.[START_REF] Munoz | Evidence for the Trophic Transfer of Perfluoroalkylated Substances in a Temperate Macrotidal Estuary[END_REF] are TMF values via LMEC methods when pooling all samples. See text for details.

	Tracers	Median	Bounds of the 95% credibility interval	Biomagnification probability	Munoz et al. (2017)
	Isotopes TEF
	δ 15 N	2.76	1.55	3.80	NA
	δ 15 C	1.60	-0.23	3.09	NA
	Contaminants TMF
	L-PFOS	1.65	0.77	3.28	0.92	1.5 [1.5;1.6]
	FOSA	2.29	0.48	6.50	0.86	1.9 [1.9;2.0]
	PFOA	0.28	0.04	1.50	0.06	2.0 [1.9;2.1]
	PFNA	0.69	0.13	4.22	0.32	1.5 [1.4;1.6]
	PFUnDA	1.30	0.47	3.02	0.72	1.1 [1.0;1.2]

Table S 1

 S . List of PFAS compounds targeted in the present study

	Acronym Compound name	Molecular formula
	L-PFOS	acid n-perfluoro-1-octanesulfonic	C 8 F 17 SO 3 H
	FOSA	perfluorooctane sulfonamide	C 8 F 17 SO 2 NH 2
	PFOA	perfluoro-n-octanoic acid	C 7 F 15 COOH
	PFNA	perfluoro-n-nonanoic acid	C 8 F 17 COOH
	PFUnDA perfluoro-n-undecanoic acid	C 10 F 21 COOH

Figure 2. Synoptic diagram of the Gironde estuarine food web (from Pasquaud et al., 2010)

Acknowledgments

This study has been carried out with financial support from the French National Research Agency (ANR) in the frame of the Investments for the future Programme, within the Cluster of Excellence COTE (ANR-10-LABX-45). We would like to thank Marc Babut for early discussions and insights on this subject.

aquatic ecosystem food webs, with simultaneous estimations of biomass, contaminants, and isotopes transfers.. Table 3. α e coefficients (1=benthic, 0=pelagic) estimated by the model (quantiles of the posterior distributions) for the different species and comparison with the values estimated a priori by Muñoz et al. (2017)

S2. Comparisons between ECSROC and MixSIAR

As an illustrative example, we calibrated MixSIAR to estimate the sole diet, using the same data that were used to fit ESCROC.

To be consistent with our ESCROC approach (see text for details),

-We used exactly the same isotope data -We used exactly the same a prior for diet composition than in ESCROC -We used two alternative priors for N and C TEFs (∆ N and ∆ C in Eq 7 and 8 in the text)

o First, we used exactly the same priors as in ESCROC (see Eq. 7 and 8 in the text):

o Second, we used priors corresponding to the TEF posterior distributions from ESCROC (see Figure 5 in the text)

Then, we also fitted ESCROC, but, contrary to the article, using only C and N (i.e., ignoring contaminants concentrations) data to directly compare with MixSIAR outputs. Note that with such a limited dataset, ESCROC is likely to be underdetermined.

The results presented in the figure S2 below are based on the direct plotting of the posterior distributions for both ESCROC and MixSIAR. They first highlight that:

(1) Adding contaminants in ESCROC allows to better discriminate the proportions of the main prey in the sole diet (Figures S2 A andC).

(2) Using the posterior distribution of TEF from ESCROC, MixSIAR provides very similar results to ESCROC (Figures S2 A andD).

(3) Using naive priors for TEF and using posterior distributions from ESCROC in MixSIAR provide quite different diet estimates (Figures S2 B and D). This is due to the fact that the naive prior is rather different from the posterior distribution (especially for C). This underlines that MixSIAR is especially sensitive to TEF prior specifications.

Outputs from ESCROC and MixSIAR (Figures S2 C andD) are different but not contradictory. Actually, they mainly differ in the proportion of white shrimps in the sole's diet. However, the prosterior density is very flat and rather uninformative for this particular species in the MixSIAR outputs and does not allow to really conclude on the proportion of this shrimp in the sole's diet. Indeed, most of the ESCROC simulated results could correspond to the MixSIAR posterior distribution.

Although based on the same transfer equations, these differences between ESCROC and MixSIAR could be explained by:

(1) the fact that ESCROC estimates are computed for the whole food web at one time. This allows using mutual information to compute more accurate estimates.

(2) the use of a random effect 'Species' Thus, although the TEF and TMF estimation are still considered globally constant through the food web, they are modulated species by species. By doing this, we did not specifically consider that isotope discrimination varies with Trophic Position but we allowed the estimation to vary for every species.

(3) a different way to account for uncertainty in both models. In particular, posterior sources and consumers' isotope compositions are computed in ESCROC using both observation data and


Cédric Colomban

Evgeny V Kudrik

Pavel Afanasiev

Alexander B Sorokin
email: alexander.sorokin@ircelyon.univ-lyon1.fr

Oxidative defluorination reactivity of µ-nitrido diiron tetraphenylporphyrin complex

Keywords: Diiron complexes, porphyrin, µ-nitrido, C-F bonds, defluorination, XANES, EXAFS

Transformation of organofluorine compounds by oxidation pathways is rare in chemistry and biology since C-F bonds formed by the most electronegative element should react with electrondeficient oxidizing species. Recently, we have shown that µ-nitrido diiron phthalocyanine complexes efficiently catalyze oxidative defluorination of poly-and perfluoroaromatics by H 2 O 2 . Herein, we studied their more biologically relevant porphyrin counterpart, µ-nitrido diiron(III,IV) tetraphenylporphyrin complex (TPP)Fe III (µN)Fe IV (TPP) in stoichiometric and catalytic reactions with a series of fluorinated aromatic compounds under oxidation conditions. Addition of hexafluorobenzene to (TPP)Fe III (µN)Fe IV (TPP) in the presence of t-butylhydroperoxide led to the formation of high-valent µnitrido diiron(IV,IV) porphyrin cation radical complex (TPP)F-Fe IV (µN)Fe IV -F(TPP +⸱ ). This complex was isolated and its structural and electronic properties were investigated by spectroscopic methods (EXAFS, XANES, EPR, UV-vis). Replacement of t BuOOH with H 2 O 2 oxidant resulted in the catalytic defluorination of selected heavily fluorinated aromatic compounds with high conversions (50-98 %), TON (1768-4825) and defluorination degrees (71-98 %). The scope of oxidative defluorination with (TPP)Fe III (µN)Fe IV (TPP) was extended to perfluorinated olefins exemplified by perfluoroallylbenzene.

The perfluorinated double bond was more reactive compared with perfluorinated aromatic moiety providing C 6 F 5 CF 2 COOH and C 6 F 5 COOH products. The properties of µ-nitrido diiron tetraphenylporphyrin in homogeneous and heterogeneous catalytic defluorination were compared with those of its phthalocyanine counterpart.

INTRODUCTION

µ-Nitrido diiron macrocyclic complexes have attracted attention of many research groups due to their unusual structure and properties [START_REF] Floris | The Porphyrin Handbook[END_REF][START_REF] Summerville | [END_REF][3][4][5][6][7][8][9][10][11][12]. In recent years, µ-nitrido diiron phthalocyanine complexes have emerged as powerful catalysts for demanding oxidation reactions [13][14][15][16] including oxidation of methane [17][18][19][20][21][22][23][24], ethane [25][26] and other hydrocarbons [27][28][29]. Related diiron N-bridged complexes based on porphyrin [19] and porphycene [30] platforms have been also reported as catalysts for challenging methane oxidation. The strong oxidizing properties of µ-nitrido diiron macrocyclic complexes have been associated with their ability to form high-valent oxo species using hydrogen peroxide or m-chloroperbenzoic acid as oxygen sources [14,[19][20][21]. The resulting ultra high-valent transient species are very strong oxidants that can be characterized by spectroscopic methods at very low temperatures [14,19]. In the course of our studies we have found that µ-nitrido diiron phthalocyanine complexes in combination with peroxides are capable of performing the oxidative dehalogenation of chlorinated [31][32] and even poly-and perfluorinated aromatic compounds [33]. This defluorination activity under oxidative conditions was retained when one phthalocyanine ligand was replaced with porphyrazine macrocycle [34]. Oxidative activation of aromatic C-F bonds is unusual and deserves further discussion.

The chemistry of C-F bonds remains a fundamental challenge because of their unique properties such as the bond strength, high chemical and thermal stability, low polarity and weak intermolecular interactions. Due to their particular features, fluorinated organic compounds find increasing use in a great variety of the large-scale practical applications, e.g., around 25 % of pharmaceuticals and 40 % of agrochemicals currently used contain fluorine atoms [35]. Therefore, the activation and transformation of C-F bonds are of great importance [36][37][38][39][40]. Owing to the strongest electronegativity of fluorine, the activation of C-F bonds typically involves electron-rich species such as low-and zerovalent transition metal complexes, powerful reductants and strong nucleophiles [36][37][38][39][40][41]. In this context, the cleavage of C-F bonds in oxidative conditions mediated by transition metal complexes is a particular reaction [42][43] because the C-F bonds formed by the most electronegative element should react with electron-deficient oxidizing species.

The examples of oxidative defluorination activity are rare and are essentially stoichiometric reactions or intramolecular defluorination of supporting ligands. Bis(µ-oxo)dicopper(III) complexes with pyridine ligands prepared by the reaction of dicopper(I) precursors with O 2 at -90°C performed defluorination of sodium 2-fluorophenolates in stoichiometric manner providing catehols with 21-62 % yields based on the amount of bis(µ-oxo)dicopper(III) complex [44]. This reaction is favored in the presence of acids such as Sc(CF 3 SO 3 ) 3 , B(C 6 F 5 ) 3 or DMF⸱CF 3 SO 3 H and mechanistically resembles defluorination of 2-fluorophenols mediated by flavin adenine dinucleotide-containing phenol hydroxylases [45]. Intramolecular defluorination of supporting ligand was observed in tetranuclear iron complexes [LFe 3 (PhPz) 3 OFe](OTf) 2 (PhPz = 3-phenylpyrazolate) and its fluorinated analog [LFe 3 (F 2 ArPz) 3 OFe](OTf) 2 (F 2 ArPz = 3-[2,6-difluorophenyl]pyrazolate) upon the treatment with PhIO or n Bu 4 NIO 4 [46,47]. The hydroxylation of bridging pyrazolate ligand occurred with a 8:1 C-F/C-H selectivity [48]. Related manganese complex showed a lower defluorination activity and cleaved the C-H bond preferentially [49]. Non-heme iron(IV) oxo complexes can often undergo an intramolecular hydroxylation of arene ligand instead of desired intermolecular oxidation of substrates. To mitigate this intramolecular ligand oxidation, Goldberg and co-workers have replaced four C-H bonds in the aromatic ligand fragments with C-F bonds [50]. This modification has allowed for trapping of the Fe IV =O active species at low temperature which underwent intramolecular defluorination accompanied by the formation of Fe-OAr bond [50,51].

Hirobe and co-workers have published the elimination of fluorine substituent from p-fluorophenol performed by mononuclear iron meso-tetrakis (2,6-difluorophenyl)porphyrin in combination with m-CPBA to afford p-benzoquinone with a TON of 3.3 [52].

As mentioned above, we have recently achieved the transformation of aromatic C-F bonds under oxidative conditions provided by µ-nitrido diiron tetra-tert-butylphthalocyanine complex, (Pc)Fe III (µ-N)Fe IV (Pc), and peroxide oxidant [33].

Using H 2 O 2 as the oxidant, a variety of per-and polyfluorinated aromatic compounds with different substitution pattern including highly recalcitrant C 6 F 6 , C 6 F 6 CF 3 and C 6 F 5 OH were defluorinated with high conversions and high turnover numbers. Noteworthy, the striking reactivity of (Pc)Fe III (µ-N)Fe IV (Pc) -H 2 O 2 system was even observed in water, providing up to 4825 C-F bond cleavages per catalyst molecule [33].

The remarkable properties of µ-nitrido diiron phthalocyanine -H 2 O 2 system in the oxidative transformation of highly fluorinated aromatics raise the question on the role of the nature of the macrocyclic ligand. It should be noted that cytochrome P-450 having iron porphyrin in the active site is a very poor catalyst for oxidative transformation of heavily fluorinated aromatics [53]. In the search of increased activity for the oxidation of polyhalogenated aromatics, genetically engineered P-450 mutants have been prepared but no notable improvement has been yet achieved [54]. In this context, it would be much of interest to explore N-bridged diiron complexes with a more biologically relevant porphyrin ligands. Here we report a comparative investigation of catalytic properties of µ-nitrido diiron tetraphenylporphyrin, (TPP)Fe III (µ-N)Fe IV (TPP) (Fig. 1), in the oxidative defluorination of representative fluoroaromatic compounds and extension of the reaction scope to perfluorinated olefins. The high-valent F-(TPP)Fe IV (µ-N)Fe IV (TPP +. )-F complex involved in the defuorination process was isolated and its structural and electronic properties were determined by X-ray absorbtion spectroscopy (EXAFS and XANES).

EXPERIMENTAL Equipement and methods

UV-vis spectra of solutions were recorded on a Perkin-Elmer Lambda 35 or Agilent 8453 spectrophotometers. Infrared spectra were obtained using a Bruker Vector 22 FTIR spectrometer using KBr pellets. 1 H and 19 F NMR spectra were acquired on a Bruker Avance HD (400 MHz) spectrometer at room temperature. The reaction products were identified by GC-MS method (Hewlett Packard 5973/6890 system; electron impact at 70 eV, He carrier gas, 30 m x 0.25 mm HP-INNOWax capillary column, polyethylene glycol (0.25 µm coating).

The mass spectra of the complexes were recorded on a MicroTOF Q II, a quadrupole time of flight (Q-TOF) mass spectrometer (Bruker Daltonics, Bremen), equipped with a cold spray ionization source with a spray voltage of 5 kV. XAS experiments were carried out at the SAMBA beamline of the SOLEIL synchrotron facility. The Fe K-edge spectra were measured in the transmission mode, using a Si(111) crystal monochromator. The spectra were aligned by putting the energy of the first inflection point for the reference Fe foil K-edge at 7112 eV. Scattering amplitudes and phases were calculated using FEFF6 software [55] on the basis of crystallographic structures of tetraphenylporphyrin iron chloride for the in-plane macrocycle and iron phthalocyanine dimer for the Fe-N-Fe fragment. The data were treated with ATHENA [56] and VIPER [57] programs. Curve fitting was carried out alternatively in the R and k spaces.

Coordination numbers (CN) were fixed according to the structural models of molecules, with the exception of Fe-Fe and Fe-F neighbors. For the former multiple scattering is important because of linearity of the Fe-N-Fe fragment whereas for the latter we did not have a priori information on the coordination number. Interatomic distances (R), distance variances (σ 2 ), and energy shifts (ΔE 0 ) were used as fitting parameters. Distance variances and amplitude factor S 0 2 were decorrelated from the CNs, using fitting of the spectra multiplied by different powers of k, as described in the previous work [58]. Constraints were imposed on the fitting variables to remain in physically reasonable ranges.

The quality of fitting was evaluated using the values of variance and goodness.

Materials

All fluorinated comppounds [hexafluorobenzene (99%), pentafluorophenol (99%), 1,2-difluorobenzene (98+%), perfluroro(allylbenzene) (97%) and pentafluorobenzoic acid (99%)] were purchased from Alfa Aesar and were used as received without further purification. Hydrogen peroxide (35 %) and 70 % aqueous t BuOOH solution were obtained from Sigma-Aldrich. Tetraphenylporphyrin (Sigma-Aldrich, 95 %) was purified by column chromatography (SiO 2 , CH 2 Cl 2 ). Iron tetraphenylporphyrin chloride and iron tetra-p-tert-butylporphyrin chloride were prepared according to published protocol [59]. µ-Nitrido diiron porphyrins were prepared according to published procedure [START_REF] Summerville | [END_REF].

Preparation of supported catalyst

(TPPFe) 2 N (7 mg, 5.2 μmol) was dissolved in 20 mL of CH 2 Cl 2 and 520 mg of carbon (HSAG 300, specific surface -300 m 2 /g) was added into solution. The resulting mixture was stirred for 6 h at room temperature and the solvent was evaporated under reduced pressure. The solid material was dried in vacuum at room temperature for 1 h and at 60 °C for 6 h. The complex loading was 10 μmol/g.

Preparation of [(TPP)Fe IV (µ-N)Fe IV (TPP)]F2

Protocol A. N-bridged diiron meso-tetraphenylprophyrin (TPP)Fe III (µ-N)Fe IV (TPP) (10 mg, 7.4 µmol) was dissolved in 12.5 mL of the C 6 F 6 /THF (1:4) mixture and 200 µL of a 70% aqueous solution of t BuOOH (1.4 mmol) was added to the solution. The resulting mixture was stirred at 60°C for 3 hours, then the solvent and the excess of oxidant were evaporated under reduced pressure at 40°C and the solid was dried in vacuum.

Protocol B.

N-bridged diiron meso-tetraphenylprophyrin (TPP)Fe III (µ-N)Fe IV (TPP) (5mg, 3.7 µmol) was dissolved in 3 mL of the C 6 F 6 /C 6 F 5 H (1:5) mixture and 100 µL of a 70% aqueous solution of t BuOOH (0.7 mmol) was added to the solution.

The resulting mixture was stirred at 60°C for 2 h. The solvent and the excess of the oxidant was evaporated under reduced pressure at 40°C and the solid was dried in vacuum.

Typical procedure for catalytic reactions with perfluorinated aromatic compounds

A 3 mL Teflon reactor was charged with 2 mL CD 3 CN containing perfluorinated substrate (0.1 M), H 2 O 2 (typically 1.6 M) and catalyst (0.4 mM). The catalyst : substrate : oxidant ratio was 1: 250 : 4000. The reaction mixture was stirred at 60°C for 15 h. The products were identified and quantified by GC-MS and 19 F NMR techniques. Turnover numbers (TON) were caculated as the molar amount of F -formed per mole of catalyst. Defluorination degree is the ratio of the amount of F -formed during reaction with respect to the total amount of fluorine in the converted substrate. The TON values and defluorination degrees were determined from 19 F NMR spectra of the reaction mixtures after reactions.

RESULTS AND DISCUSSION

Preparation of [(TPP)Fe IV (µ-N)Fe IV (TPP +⸱ )]F2

(TPP)Fe III (µN)Fe IV (TPP) was synthesized according to published procedure [START_REF] Summerville | [END_REF] and was spectroscopically characterized as previously reported [START_REF] Summerville | [END_REF]19]. According to the protocol previously reported for µ-nitrido diiron phthalocyanine complex [33] (TPP)Fe III (µN)Fe IV (TPP) was incubated with C 6 F 6 in the presence of t BuOOH. It should be noted that the choice of the co-solvent is important for the preparation of the high-valent complex with axial fluoride ligands. The reaction with t BuOOH and C 6 F 6 cannot be performed in the presence of chlorinated co-solvent (e.g. CH 2 Cl 2 ) because of possible formation of the corresponding chloride complex [(TPP)Fe IV (µ-N)Fe IV (TPP +⸱ )]Cl 2 [31].

When the reaction was carried out in the C 6 F 6 /THF mixture (1:4), the UV-vis bands of the initial (TPP)Fe III (µN)Fe IV (TPP) at 383, 410 and 533 nm were replaced by the bands at 408, 531 and 564 nm (Fig. 2). The disappearance of a S = 1/2 EPR signal with g factor of 2.155 and 2.008 and the appearance of the symmetric and narrow signal at g = 2.0037 implies the presence of the cation-radical at porphyrin ligand and Fe IV Fe IV configuration.

The 19 F NMR spectrum of the complex showed one signal at -129 ppm indicating the presence of fluoride anion. All these observations are compatible with the formation of the target [(TPP)Fe IV (µ-N)Fe IV (TPP +⸱ )]F 2 complex. However, upon isolation of this complex from the reaction mixture containing THF, evolution of the complex into a new EPRsilent species showing UV-vis bands at 418 and 538 nm was observed. These changes suggest the one-electron reduction of the [(TPP)Fe IV (µ-N)Fe IV (TPP +⸱ )]F 2 complex to [(TPP)Fe IV (µ-N)Fe IV (TPP)]F. To avoid this transformation, [(TPP)Fe IV (µ-N)Fe IV (TPP +⸱ )]F 2 was prepared using a C 6 F 6 /C 6 F 5 H mixture (1:5). The resulting complex was studied by X-ray absorbtion spectroscopy (XAS) and its structural and electronic properties were compared with those of the initial (TPP)Fe III (µN)Fe IV (TPP) and one-electron reduced [(TPP)Fe IV (µ-N)Fe IV (TPP)]F complexes.

Fe K-edge extended X-Ray absorption fine structure (EXAFS)

Core hole spectroscopies using synchrotrone radiation such as Extended X-ray Absorption Fine Structure (EXAFS) and X-ray Absorption Fine Structure (XANES) provide valuable information on the structure and electronic properties of high-valent iron complexes [60]. Comparison of the Fe K-edge EXAFS spectra of (TPP)Fe III (µN)Fe IV (TPP) (1), [(TPP)Fe IV (µ-N)Fe IV (TPP)]F (2) and [(TPP)Fe IV (µ-N)Fe IV (TPP +⸱ )]F 2 (3) shows the retention of the µ-nitrido dimer topology in all three complexes (Fig. 3). The high-quality EXAFS fitting data showing the average interatomic distances are presented in Table 1.

Table 1. Results of the EXAFS fitting for the Fe-K edge spectra of the complexes (TPP)Fe III (µN)Fe IV (TPP) (1), [(TPP)Fe IV (µ-N)Fe IV (TPP)]F (2) and [(TPP)Fe IV (µ-N)Fe IV (TPP +⸱ )]F 2 (3). The ratio of interatomic axial Fe-N and Fe-Fe distances close to 2 as well as strong contributions from the Fe-N-Fe multiple scattering paths indicate nearly perfect linearity of the Fe-N-Fe core in all three structures. The Fe-N bridge distance of 1.68 Å in 1 deduced from the EXAFS data coincides nicely with the Fe-N bridge length of 1.6794(4) Å prevously determined by X-ray diffraction [19]. The distance between iron atoms in µ-nitrido dimer is quite short (3.36 Å) indicating a significant  interaction between the aromatic macrocycles.The successive oxidation of 1 to 2 and to 3 leads to a slight contraction of the molecule. Both the axial Fe-N-Fe fragment and the Fe-N bonds in the FeN 4 inplane unit shrink by 0.02-0.04 Å leading to a noticeable shift of the first FT peak (Fig. 2a). Importantly, no additional ligand is covalently attached to the iron atoms upon oxidation of 1 to 2 suggesting outer-sphere location of the fluoride anion. In the complex 3 the amplitude of the first FT peak is increased in agreement with the presence of a covalently bound fluoride ligand at each iron atom (Table 1, Fig. 3a). A high-quality fit of the EXAFS spectrum of 3 for the two first coordination spheres provided the structure shown in Fig. 4 in which a fluoride ligand is coordinated with each iron center at the distance of 1.92 Å.

Scatterer atom CN R σ 2 (Å 2 ) ΔE 0 (eV) b 1 R= 0.

X-ray absorption near-edge structures (XANES)

The shape and position of the main jump and of the pre-edge peak in the XANES spectra depend on the iron oxidation state and geometry of the iron scatterer. The pre-edge feature is more characteristic and sensitive to the change in the oxidation state and coordination of iron center. The energy of the main edge jump is 7122.9, 7123.8 and 7125.2 eV for the complexes 1, 2 and 3, respectively, corresponding to the decrease of electronic density on iron atom in this sequence. In agreement with this conclusion, the white line intensity increases in the same sequence, from 1 to 3 (Fig. 5). The initial (TPP)Fe III (µN)Fe IV (TPP) complex has a broad pre-edge peak at 7113.7 eV. Apparently, it consists of two components but the less intense low-energy component is merged with the more intense high-energy one and their resolution is difficult (Fig. 5, inset). In [(TPP)Fe IV (µ-N)Fe IV (TPP)]F, the pre-edge peak clearly splits into two components and shifts to a higher energy (7114.5 eV). The energy shift occurs because of the increase of the iron oxidation state. The low-energy component becomes visible because of depopulation of the low-lying energy 3d Fe level. At the same time the pre-edge intensity decreases due to the symmetrization of iron environment and a decrease of s-p covalent mixing. In [(TPP)Fe IV (µ-N)Fe IV (TPP +⸱ )]F 2 , the pre-edge maximum is further shifted to higher energy (7115.3 eV) and its relative intensity further decreased (Fig. 5, inset). This behavior is very similar to that previously observed in our previous studies involving µ-nitrido diiron phthalocyanine dimers [14,31,33,61]. Thus, the analysis of XANES and pre-edge feature confirms the oxidation states of iron in 1-3. The complex 1 is an initial (TPP)Fe III (µN)Fe IV (TPP) dimer, the complex 2 is a [(TPP)Fe IV (µ-N)Fe IV (TPP)]F with outer-sphere fluoride counteranion and the complex 3 is a [(TPP)Fe IV (µ-N)Fe IV (TPP +⸱ )]F 2 complex with axial fluoride anions that further decreases the electronic density on the iron center.

Catalytic oxidation of perfluorinated aromatic compounds mediated by (TPP)Fe III (µN)Fe IV (TPP)

The high-valent [(TPP)Fe IV (µ-N)Fe IV (TPP +⸱ )]F 2 was proposed to be an intermediate in the oxidative defluorination of fluoroaromatics [33,42]. When t BuOOH oxidant is used, this oxidized complex is stable under reaction conditions and can be isolated in high yield. To achieve a catalytic reaction, [(TPP)Fe IV (µ-N)Fe IV (TPP +⸱ )]F 2 should be reduced to the initial (TPP)Fe III (µN)Fe IV (TPP) complex. In our previous studies involving µ-nitrido diiron phthalocyanine complexes, the replacement of t BuOOH by H 2 O 2 resulted in catalytic defluorination reaction since the reduction of the high-valent fluorine complex by H 2 O 2 and regeneration of the initial µ-nitrido dimer closed the catalytic cycle [33,42] (Fig. 6). 2). a Reaction conditions: 0.4 mM catalyst, 0.1 M substrate, 1.6 M H 2 O 2 ; air, 60°C, 15 h. Conversions and F -yields were determined by 19 F NMR. b Turnover numbers (TON) were calculated as the molar amount of F -formed per mole of the catalyst. c Defluorination degree is the ratio of the amount of F -formed to the total amount of fluorine in the converted substrate.

Octafluorotoluene bearing strong electron-withdrawing CF 3 group exhibited comparable 20 % conversion and TON of 180 (Table 2, entry 5). The replacement of fluorine substituent with electron-donating group resulted in higher conversion. For instance, the conversion of pentafluoroanisole achieved 61 % (Table 2, entry 4). p-Difluorobenzene was more reactive than the ortho-substituted analog: 73 and 50 % conversions, and TON of 360 and 91 %, respectively (Table 2, entries 2,3). Importantly, the (TPP)Fe III (µ-N)Fe IV (TPP) -H 2 O 2 catalytic system was also active in the oxidation of perfluorinated olefins examplified by perfluoroallylbenzene (Table 2, entry 6). Perfluoroallylbenzene combining fluorinated aromatic cycle and fluorinated olefinic group is a useful substrate to probe the selectivity of defluorination reaction. Interestingly, in this case different reaction selectivity was observed and heptafluorophenylacetic and pentafluorobenzoic acids were obtained as principal products (Scheme 2). Consequently, perfluorinated olefinic fragment exhibited significantly higher activity in the defluorination reaction compared to aromatic C-F bonds. This reactivity of perfluorinated olefins is in agreement with proposed mechanism of defluorination where the epoxidation is the first step of oxidative defluoluorination [33,62]. Heptafluorophenylacetic and pentafluorobenzoic acids are then obtained by the cleavage of the epoxide fragment accompanied by defluorination.

Then, we have compared the catalytic activity of µ-nitrido diiron porphyrin and phthalocyanine complexes in the homogeneous oxidation of hexafluorobenzene (Table 3). In order to check the effect of tert-butyl substituents of macrocycle the corresponding p-tert-butyl substituted porphyrin complex was also evaluated. 3 shows that µ-nitrido diiron porphyrin and phthalocyanine complexes exhibit a comparable catalytic activity in terms of conversion. However, phthalocyanine catalyst is more efficient in terms of turnover number and defluorination degree indicating higher activity in the transformation of the intermediate fluorinated products.

Analysis of Table

Noteworthy, FeSO 4 operating via Fenton chemistry in the presence of H 2 O 2 was completely inactive in the reaction with C 6 F 6 .

Given the high defluorination efficiency of µ-nitrido dimers in combination with H 2 O 2 , we have further compared porphyrin and phthalocyanine dimers in heterogeneous reactions. To this aim (TPP)Fe III (µ-N)Fe IV (TPP) and (Pc t Bu 4 )Fe III (µ-N)Fe IV (Pc t Bu 4 ) were supported onto carbon with the catalyst loading of 10 µmol/g and supported catalysts were evaluated in the catalytic defluorination of pentafluorophenol and pentafluorobenzoic acid in water using a catalyst:substrate:oxidant ratio of 1:1000:26000 (Table 4). Efficient defluorination reactions were observed with both supported catalysts at 0.1 mol% catalyst loading providing high conversions (50-98 %), TON (1768-4825) and defluorination degrees (71-98 %) (Table 4). Such high efficiencies highlight the benefits of both porphyrin and phatalocyanine-based catalysts for defluorination of recalcitrant perfluorinated substrates. However, phthalocyanine catalyst was more efficient than its porphyrin counterpart.

(Pc t Bu 4 )Fe III (µ-N)Fe IV (Pc t Bu 4 )/carbon and (TPP)Fe III (µ-N)Fe IV (TPP)/carbon carried out the oxidation of pentafluorophenol with conversions of 98 and 84 %, turnover numbers of 4825 and 3535, and defluorination degrees of 98 and 84 %, respectively. The similar trend was observed in the oxidation of pentafluorobenzoic acid.

CONCLUSION

The chemistry of C-F bonds has received a significant attention for practical and fundamental reasons. Fluorinated organic compounds are increasingly used as pharmaceuticals, agrochemicals, special products and in material chemistry. They are particularly inert and their transformation is very challenging. To activate C-F bonds formed by the most electronegative element, the electron-rich species, e.g., zero-and low-valent transition metal complexes, strong reductants and electrophiles are usually used. Transformation of C-F bonds via oxidation pathways is rare in chemistry and biology since it involves the reaction of C-F bonds with electron-deficient oxidizing species. In this context, efficient oxidative defluorination of perfluorinated aromatic compounds performed by µ-nitrido diiron tetrapyrrolic complexes is a very particular reaction. Initially, iron phthalocyanine-based µ-nitrido dimers have been studied as catalysts for this unusual reaction. To extend the library of efficient defluorination catalysts, it is of much interest to explore other macrocyclic supporting ligands for µ-nitrido diiron scaffold.

Herein, we have evaluated defluorination properties of µ-nitrido diiron tetraporphyrin complex. First, a stable highvalent diiron complex [(TPP)Fe IV (µ-N)Fe IV (TPP +⸱ )]F 2 with fluoride anions, coordinated in the axial position of each iron site at the distance of 1.92 Å according to EXAFS data, was obtained by the reaction of (TPP)Fe III (µ-N)Fe IV (TPP) with C 6 F 6 in the presence of t BuOOH oxidant. This complex exhibits a symmetric and narrow EPR signal at g = 2.0037 indicating the cation-radical at porphyrin ligand and Fe(IV)Fe(IV) formulation. The comparison of XANES data of three complexes in the different oxidation states confirms this conclusion. The 19 F NMR spectrum showed one signal at -129 ppm confirming the presence of fluoride anion.

We demonstrated that the (TPP)Fe III (µ-N)Fe IV (TPP) complex in combination with H 2 O 2 mediate efficient oxidative transformation of C 6 F 6 , C 6 F 5 CF 3 , C 6 F 5 OCH 3 , 1,2-and 1,4-difluorobenzenes providing 20-73 % conversions, turnover numbers of 91-360 and defluorination degrees ranging from 28 to 99 %. The defluorination reaction was further extended to perfluorinated olefins examplified by perfluoroallylbenzene. Perfluorinated olefin moiety showed a higher reactivity in the defluorination reaction than aromatic C-F bonds. Heptafluorobenzeneacetic and pentafluorobenzoic acids were obtained as principal products via the cleavage of epoxidized double bond.

The catalytic properties of (TPP)Fe III (µ-N)Fe IV (TPP) in defluorination were compared with those of phthalocyanine counterpart (Pc t Bu 4 )Fe III (µ-N)Fe IV (Pc t Bu 4 ) in homogeneous reaction with C 6 F 6 and heterogeneous reactions with C 6 F 5 OH and C 6 F 5 COOH. While both complexes showed almost comparable activity in homogeneous oxidation of C 6 F 6 , the (Pc t Bu 4 )Fe III (µ-N)Fe IV (Pc t Bu 4 ) supported on carbon was notably more efficient in terms of conversion, turnover number and defluorination degree in the oxidation of C 6 F 5 OH and C 6 F 5 COOH than the porphyrin-based counterpart. These results indicate that the Fe-N-Fe structural feature plays an essential role in the catalytic activity but the nature of the macrocyclic ligand can also modify the catalytic properties. This opens up a way to further optimize the catalyst by the appropriate tuning of the supporting macrocyclic ligand of µ-nitrido dimer.

Comparison of the EXAFS data for [(TPP)Fe IV (µ-N)Fe IV (TPP +⸱ )]F 2 with porphyrin ligand and [(Pc t Bu 4 )Fe IV (µ-N)Fe IV (Pc t Bu 4 +⸱ )]F 2 with phthalocyanine ligand shows that the Fe-F bond is shorter in porphyrin complex: 1.92 Å vs 1.99 Å [33] in phthalocyanine counterpart. Thus, the Fe-F bond in the phthalocyanine complex [(Pc t Bu 4 )Fe IV (µ-N)Fe IV (Pc t Bu 4 +⸱ )]F 2 is elongated and hence weaken compared to that of porphyrin complex [(TPP)Fe IV (µ-N)Fe IV (TPP +⸱ )]F 2 . Consequently, one can suggest that the high-valent phthalocyanine complex should be more amenable to the reduction by H 2 O 2 which is the important step in the catalytic cycle. This can explain the higher reactivity of µ-nitrido diiron phthalocyanine (Pc t Bu 4 )Fe III (µ-N)Fe IV (Pc t Bu 4 ) in the oxidative defluorination of fluoroaromatis.

The use of the µ-nitrido diiron macrocyclic complex -H 2 O 2 oxidation system can be considered as a novel approach for transformation of fluorinated aromatics including perfluorinated compounds. Taking into account the high efficiency, availability of these cheap catalysts in bulk amounts as well as mild reaction conditions and tolerance to air and water, this method seems to be particularly promising in the environmental context, in particular, for disposal of heavily fluorinated [33,42] and chlorinated [32] compounds which are recalcitrant to biodegradation and current depollution methods. Rapidly increasing large-scale production and using of fluorinated organic compounds in various applications coupled with their exceptional stability in the environment make consider these compounds as emerging pollutants of increasing concern. The development of practical methods for their disposal is therefore of great importance. We believe that further development of catalytic systems based on available µ-nitrido diiron complexes and industrially relevant hydrogen peroxide will help to find a solution of this environmental issue.

Fig. 1 .

 1 Fig. 1. The structure of µ-nitrido diiron tetraphenylporphyrin, (TPP)Fe III (µ-N)Fe IV (TPP). The X-ray structure was previously described in ref. 19.

Fig. 2 .

 2 Fig. 2. UV-visible spectra of (A) the initial (TPP)Fe III (µN)Fe IV (TPP) complex in a 1:4 C 6 F 6 /THF mixture; (B) the [(TPP)Fe IV (µ-N)Fe IV (TPP +⸱ )]F 2 complex obtained after incubation of (TPP)Fe III (µN)Fe IV (TPP) in a 1:4 C 6 F 6 /THF mixture in the presence of t BuOOH; (C) the [(TPP)Fe IV (µ-N)Fe IV (TPP)]F complex isolated from the reaction mixture containing THF. meso-Phenyl substituents of the porphyrin macrocycles are omitted for clarity.

Fig. 3 .

 3 Fig. 3. (a) Fourier transforms of the (TPP)Fe III (µN)Fe IV (TPP) (1), [(TPP)Fe IV (µ-N)Fe IV (TPP)]F (2) and [(TPP)Fe IV (µ-N)Fe IV (TPP +⸱ )]F2 (3); and FT EXAFS fits of 1 (b), 2 (c) and 3 (d).

FeFig. 4 .

 4 Fig. 4. EXAFS structure of [(TPP)Fe IV (µ-N)Fe IV (TPP +⸱ )]F2 (3) showing the first and second coordination spheres. Phenyl groups are omitted for the simplicity of presentation.

Fig. 5 .

 5 Fig. 5. XANES of the (TPP)Fe III (µN)Fe IV (TPP) (1), [(TPP)Fe IV (µ-N)Fe IV (TPP)]F (2) and [(TPP)Fe IV (µ-N)Fe IV (TPP +⸱ )]F2 (3).

Fig. 6 .HFScheme 1 .

 61 Fig. 6. Proposed catalytic cycle of defluorination reaction.

Scheme 2 .

 2 Scheme 2. Catalytic transformation of perfluoro(allylbenzene) by (TPP)Fe III (µ-N)Fe IV (TPP) -H2O2 system in CD3CN.

Table 2 .

 2 Homogeneous oxidative defluorination of fluorinated aromatics by (TPP)Fe III (µ-N)Fe IV (TPP) -H 2 O 2 system in CD 3 CN. a

	Entry	Substrate	Conversion, %	TON b	Defluorination degree, % c
	1	hexafluorobenzene	25	128	35
	2	1,4-difluorobenzene	73	360	99
	3	1,2-difluorobenzene	50	91	47
	4	pentafluoroanisole	61	155	28
	5	octafluorotoluene	20	180	83
	6	perfluoroallylbenzene	68	779	46

Table 3 .

 3 Comparison of the catalytic properties of µ-nitrido diiron complexes in the oxidative defluorination of C 6 F 6 with H 2 O 2 . a For reaction conditions see footnote of Table 2. b From ref. 33.

	Entry	Catalyst	Conversion, %	TON	Defluorination degree,
					%
	1	(TPPFe) 2 N	25	128	35
	2	( tBu TPPFe) 2 N	30	138	32
	3 b	( tBu PcFe) 2 N	29	226	52
	4	FeSO 4	no reaction	-	-
	a

Table 4 .

 4 Comparison of supported µ-nitrido diiron complexes in the transformation of water-soluble fluorinated aromatics in D 2 O. a

	Entry	Catalyst	Conversion, %	TON	Defluorination degree, %
	Pentafluorophenol
	1	(TPPFe) 2 N-carbon	84	3535	84
	2 b	( tBu PcFe) 2 N-carbon	98	4825	98
	Pentafluorobenzoic acid
	3	(TPPFe) 2 N-carbon	50	1768	71
	4 b	( tBu PcFe) 2 N-carbon	76	2950	78
	a Reactions were carried out in D 2 O with 20 mg (0.2 µmol) of supported catalyst, 0.1 M substrate, 2.6 M H 2 O 2 ; air, 60°C, 15 h. Conversions and F -yields were determined by 19 F NMR.

b

From ref.

33.

Acknowledgements

This research was supported by Agence National de Recherche (ANR, France, grant ANR-16-CE29-0018-01), by CNRS (PICS project 6295) and Russian Foundation of Basic Research (RFBR, project 14-03-91054). C.C. is grateful to Région Rhône-Alpes for PhD fellowship. We thank the Synchrotron Soleil (SAMBA beamline, Gif-sur-Yvette, France) for provision of synchrotron radiation facility.