Günce Keziban Orman
email: korman@gsu.edu.tr

Vincent Labatut

Hocine Cherifi

Qualitative Comparison of Community Detection Algorithms

Keywords: Complex Networks, Community Detection, Community Properties, Algorithms Comparison

Community detection is a very active field in complex networks analysis, consisting in identifying groups of nodes more densely interconnected relatively to the rest of the network. The existing algorithms are usually tested and compared on real-world and artificial networks, their performance being assessed through some partition similarity measure. However, artificial networks realism can be questioned, and the appropriateness of those measures is not obvious. In this study, we take advantage of recent advances concerning the characterization of community structures to tackle these questions. We first generate networks thanks to the most realistic model available to date. Their analysis reveals they display only some of the properties observed in real-world community structures. We then apply five community detection algorithms on these networks and find out the performance assessed quantitatively does not necessarily agree with a qualitative analysis of the identified communities. It therefore seems both approaches should be applied to perform a relevant comparison of the algorithms.

Introduction

The use of networks as modeling tools has spread through many application fields during the last decades: biology, sociology, physics, computer science, communication, etc. (see [START_REF] Da Fontura Costa | Analyzing and Modeling Real-World Phenomena with Complex Networks: A Survey of Applications[END_REF] for a very complete review of applied studies). Once a system has been modeled, the resulting network can be analyzed or visualized thanks to some of the many tools designed for graph mining. Such large real-world networks are characterized by a heterogeneous structure, leading to specific properties. In particular, a heterogeneous distribution of links often results in the presence of a socalled community structure [START_REF] Fortunato | Community Detection in Graphs[END_REF]. A community roughly corresponds to a group of nodes more densely interconnected, relatively to the rest of the network [START_REF] Newman | Finding and Evaluating Community Structure in Networks[END_REF]. The way such a structure can be interpreted is obviously dependent on the modeled system. However, independently from the nature of this system, it is clear the community structure conveys some very important information, necessary to a proper understanding [START_REF] Lancichinetti | Characterizing the Community Structure of Complex Networks[END_REF]. Detecting communities is therefore an essential part of modern network analysis. Many different community detection algorithms exist [START_REF] Fortunato | Community Detection in Graphs[END_REF], which can diverge in two ways: first the process leading to an estimation of the community structure, but also the nature of the estimated communities themselves. This raises a question regarding the comparison of these algorithms, from both a theoretical and a practical point of view. Authors traditionally test their community detection algorithms on real-world and/or artificial networks [START_REF] Girvan | Community Structure in Social and Biological Networks[END_REF][START_REF] Lancichinetti | Benchmark Graphs for Testing Community Detection Algorithms[END_REF]. The performance is assessed by comparing the estimated communities with some community structure of reference using a quality (e.g. modularity [START_REF] Newman | Finding and Evaluating Community Structure in Networks[END_REF]) or association (e.g. Normalized Mutual Information [START_REF] Danon | The Effect of Size Heterogeneity on Community Identification in Complex Networks[END_REF]) measure. This single value is then compared with those obtained when applying preexisting algorithms on the same data. The main problem with this approach is its purely quantitative aspect: it completely ignores the nature of the considered community structures. Two algorithms can reach the exact same level of performance, but still estimate very different community structures.

Besides performance evaluation, the data used to perform the tests are also subject to some limitations. For realism reasons, it is necessary to apply the algorithms to real-world networks, but these are not sufficient because 1) reference communities (i.e. ground truth) can rarely be defined objectively, and 2) the topology of the selected networks can hardly be diverse enough to represent all types of systems. Testing on artificial networks can be seen as complementary, because they overcome these limitations. Indeed, a random model allows generating as many networks as desired, while controlling some of their topological properties. The only issue is the realism of the obtained networks, which should mimic closely real-world networks in order to get relevant test results.

Some properties common to most real-world networks are well-identified: powerlaw distributed degree, small-worldness, non-zero degree correlation and relatively high transitivity [START_REF] Newman | The Structure and Function of Complex Networks[END_REF]. Additionally, networks with a community structure are characterized by a power-law distributed community size [START_REF] Guimerà | Self-Similar Community Structure in a Network of Human Interactions[END_REF]. Several generative models with increasing realism were successively designed [START_REF] Lancichinetti | Benchmark Graphs for Testing Community Detection Algorithms[END_REF] before finally meeting these constraints [START_REF] Lancichinetti | Benchmark Graphs for Testing Community Detection Algorithms[END_REF][START_REF] Orman | A Comparison of Community Detection Algorithms on Artificial Networks[END_REF][START_REF] Orman | The Effect of Network Realism on Community Detection Algorithms[END_REF]. However, recent studies showed other properties besides the community size distribution can be used to characterize real-world community structures [START_REF] Lancichinetti | Characterizing the Community Structure of Complex Networks[END_REF][START_REF] Leskovec | Statistical Properties of Community Structure in Large Social and Information Networks[END_REF], such as community-wise density and average distance, hub dominance, embeddedness. They allow giving a more detailed description of the internal topology of the communities, and of the way they are interconnected.

To our opinion, these new results have two important consequences on the problem of community detection assessment. First, the question to know whether the artificial networks used as benchmark also exhibit these properties arises naturally. But more importantly, it is now possible to perform a qualitative comparison of the communities identified by different algorithms, instead of relying only on a single performance measure. In this article, we try to answer both questions using the realistic generative model LFR [START_REF] Lancichinetti | Benchmark Graphs for Testing Community Detection Algorithms[END_REF] and a representative set of community detection algorithms. In section 2, we review in greater details the properties used to describe community structures in complex networks. In section 3, we shortly present the LFR model and its properties, and introduce an adjustment allowing to improve the realism of the networks it generates. We also review the various approaches used in the literature to define the concept of community, and describe a selection of community detection algorithms from this perspective. In section 4, we first analyze the properties of the generated networks. We then compare the community structures detected by the selected algorithms on these networks. We consider both their similarity to the community structure of interest, and how community properties differ from one algorithm to the other. Finally, we discuss our results and explain how our work could be extended.

Characterization of a Community Structure

Complex networks are often characterized at microscopic and macroscopic levels, i.e. by studying the characteristics of nodes taken individually and of the network considered as a whole, respectively. The microscopic approach focuses on some nodes of interest, and tries to identify which features allow distinguishing them from the rest of the network (degree, centrality, local transitivity, etc.). At the macroscopic level, one can take advantage of the multiplicity of nodes to derive statistics or distributions summarizing some of the network features (degree distribution, degree correlation, average distance, transitivity, etc.). The development of community detection corresponds to the apparition of a mesoscopic level, and highlights the need for adapted tools to characterize the community structure. In this section, we present a selection of the mesoscopic measures recently proposed and indicate how real-world networks behave relatively to them. In some cases, no general observation can be made, and one has to consider the class of the network: communication, biological, social, etc. Note other measures exist besides those described here, such as the network community profile [START_REF] Leskovec | Statistical Properties of Community Structure in Large Social and Information Networks[END_REF] or roles distribution [START_REF] Guimerà | Functional Cartography of Complex Metabolic Networks[END_REF].

The community size distribution is considered as an important characteristic of the community structure. It has been largely studied in real-world networks, and seems to follow a power law [START_REF] Guimerà | Self-Similar Community Structure in a Network of Human Interactions[END_REF][START_REF] Newman | Detecting Community Structure in Networks[END_REF] with exponent ranging from to [START_REF] Palla | Uncovering the Overlapping Community Structure of Complex Networks in Nature and Society[END_REF]. This means their sizes are heterogeneous, with many small communities and only a few very large ones.

The embeddedness measure assesses how much the direct neighbors of a node belong to its own community. It is defined as the ratio of the internal degree to the total degree of the considered node [START_REF] Lancichinetti | Characterizing the Community Structure of Complex Networks[END_REF]: [START_REF] Da Fontura Costa | Analyzing and Modeling Real-World Phenomena with Complex Networks: A Survey of Applications[END_REF] This internal degree is the number of links the nodes has with other nodes from the same community, by opposition to its external degree , which corresponds to connections with nodes located in other communities. The maximal embeddedness of is reached when all the neighbors are in its community ( ), whereas the minimal value of corresponds to the case where all neighbors belong to different communities (

). In real-world networks, a majority of nodes, usually with low degree, have a very high embeddedness. The rest are distributed depending on the considered class: communication, Internet and biological networks exhibit a peak around , whereas social and information networks have a more uniform distribution. In all cases, the whole range of is significantly represented, even small values [START_REF] Lancichinetti | Characterizing the Community Structure of Complex Networks[END_REF].

The density of a community is defined as the ratio of links it actually contains, noted , to the number of links it could contain if all its nodes were connected. In the case of an undirected network, the latter is , where is the number of nodes in the community, and we therefore get . When compared to the overall network density, the density allows assessing the cohesion of the community: by definition, a community is supposed to be denser than the network it belongs to. The scaled density is a variant obtained by multiplying the density by the community size [START_REF] Lancichinetti | Characterizing the Community Structure of Complex Networks[END_REF]:

(2)
If the considered community is a tree, it has only links, and . If it is a clique (completely connected subgraph), then and we have . The scaled density therefore allows charactering the structure of the community. Some real-world networks such as the Internet or communication networks have essentially tree-like communities. On the contrary, for other classes like social and information networks, the scaled density increases with the community size. Finally, biological networks exhibit a hybrid behavior, their small communities being tree-like whereas the large ones are denser and close to cliques [START_REF] Lancichinetti | Characterizing the Community Structure of Complex Networks[END_REF].

The distance between two nodes corresponds to the length of their shortest path. When averaged over all pairs of nodes in a community, it allows assessing the cohesion of this community. In real-world networks, small communities ( ) are supposedly small-world, which means the average distance should increase logarithmically with the community size [START_REF] Lancichinetti | Characterizing the Community Structure of Complex Networks[END_REF]. For larger communities, the average distance still increases, but more slowly, or even stabilizes for certain classes like communication networks. A small average distance can be explained by a high density (social), the presence of hubs (communication, Internet), or both (biological, information).

From a community structure perspective, a hub is a node connected to many of the other nodes belonging to the same community. The presence of a central hub in a community can be assessed using the hub dominance measure, which corresponds to the following ratio:

(3)

The numerator is the maximal internal degree found in , and the denominator is the maximal degree theoretically possible given the community size. The hub dominance therefore reaches when at least one node is connected to all other nodes in the community. It can be only if no nodes are connected, which is unlikely for a community. In real-world networks, the behavior of this property depends on the considered class. For communication networks, it is close to the maximum for all community sizes, meaning hubs are present in all communities. Considering their communities are sparse and tree-like, one can conclude they are star-shaped. Other classes do not have as many hubs in their large communities, which is why their hub dominance generally decreases with community size increase [START_REF] Lancichinetti | Characterizing the Community Structure of Complex Networks[END_REF].

Methods

Our experiment is two-stepped: first we generate a set of artificial networks and study the realism of their community-related topological properties; second we apply a selection of community detection algorithms on these networks and analyze the properties of the community structure they estimate. In this section, we first describe the LFR model we applied during the first step, which supposedly allows generating the most realistic networks in terms of overall properties (degree distribution, smallworldness, etc.) [START_REF] Lancichinetti | Benchmark Graphs for Testing Community Detection Algorithms[END_REF][START_REF] Orman | A Comparison of Community Detection Algorithms on Artificial Networks[END_REF][START_REF] Orman | The Effect of Network Realism on Community Detection Algorithms[END_REF]. Then, we shortly describe the community detection algorithms we selected, and explain how they differ on the way they handle the concept of community.

Network Generation

Only a few models have been designed to generate networks possessing a community structure. Girvan and Newman seemingly defined the first one [START_REF] Girvan | Community Structure in Social and Biological Networks[END_REF], which produces networks taking roughly the form of sets of small interconnected Erdős-Rényi networks [START_REF] Erdõs | On Random Graphs[END_REF]. Although widely used to test and compare community detection algorithms, the Girvan-Newman method is limited in terms of realism [START_REF] Lancichinetti | Benchmark Graphs for Testing Community Detection Algorithms[END_REF], mainly because the degree is not power-law distributed and the communities are small, few, and even-sized. Several variants were defined, allowing to produce larger networks and communities with heterogeneous sizes [START_REF] Fortunato | Community Detection in Graphs[END_REF][START_REF] Danon | The Effect of Size Heterogeneity on Community Identification in Complex Networks[END_REF][START_REF] Pons | Computing Communities in Large Networks Using Random Walks[END_REF]. More recently, a different approach appeared, based on a rewiring process [START_REF] Lancichinetti | Benchmark Graphs for Testing Community Detection Algorithms[END_REF][START_REF] Bagrow | Evaluating Local Community Methods in Networks[END_REF]. It increased the realism level even more by generating networks with power-law distributed degree. Among these newer models, we selected the LFR model, which seems to be the more realistic and was previously used as a benchmark to compare community detection algorithms [START_REF] Lancichinetti | Benchmark Graphs for Testing Community Detection Algorithms[END_REF][START_REF] Orman | A Comparison of Community Detection Algorithms on Artificial Networks[END_REF][START_REF] Lancichinetti | Community Detection Algorithms: A Comparative Analysis[END_REF]].

The LFR model was proposed by Lancichinetti et al. [START_REF] Lancichinetti | Benchmark Graphs for Testing Community Detection Algorithms[END_REF] to randomly generate undirected and unweighted networks with mutually exclusive communities. The model was subsequently extended to generate weighted and/or directed networks, with possibly overlapping communities [START_REF] Lancichinetti | Community Detection Algorithms: A Comparative Analysis[END_REF]. However, in this article, we focus on undirected unweighted networks with non-overlapping communities, because the community structure-related properties we want to study have been defined and/or used only for this type of networks. The model allows to control directly the following parameters: number of nodes , desired average and maximum degrees, exponent for the degree distribution, exponent for the community size distribution, and mixing coefficient . The latter represents the desired average proportion of links between a node and nodes located outside its community, called inter-community links. Consequently, the proportion of intra-community links is -. A node of degree has therefore an external degree of and an internal degree of .

The generative process first uses the configuration model (CM) [START_REF] Molloy | A Critical Point for Random Graphs with a Given Degree Sequence[END_REF] to generate a network with average degree , maximum degree and power-law degree distribution with exponent . Second, virtual communities are defined so that their sizes follow a power-law distribution with exponent . Each node is randomly affected to a community, provided the community size is greater or equal to the node internal degree. Third, an iterative process takes place to rewire certain links, in order to approximate , while preserving the degree distribution. For each node, the total degree is not modified, but the ratio of internal and external links is changed so that the resulting proportion gets close to .

By construction, the LFR method guaranties to obtain values considered as realistic [START_REF] Da Fontura Costa | Analyzing and Modeling Real-World Phenomena with Complex Networks: A Survey of Applications[END_REF][START_REF] Newman | The Structure and Function of Complex Networks[END_REF] for several properties: size of the network, power law distributed degrees and community sizes. Other properties are not directly controlled, but were studied empirically [START_REF] Orman | A Comparison of Community Detection Algorithms on Artificial Networks[END_REF]. It turns out LFR generates small-world networks, with relatively high transitivity and degree correlation. This is realistic [START_REF] Newman | The Structure and Function of Complex Networks[END_REF], but holds only under certain conditions. In particular, transitivity and degree correlation are dramatically affected by changes in , and become clearly unrealistic when it gets different from . An adjustment was proposed to solve this issue, consisting in using a different generative model during the first step [START_REF] Orman | The Effect of Network Realism on Community Detection Algorithms[END_REF]. By applying Barabási & Albert's preferential attachment model (BA) [START_REF] Barabási | Emergence of Scaling in Random Networks[END_REF] instead of the CM, the degree correlation and transitivity become more stable relatively to changes in .

It is rather clear the mixing coefficient is complementary to the embeddedness presented in section 2 (eq. 1):

. Yet, it was mentioned in the same section the embeddedness varies much from one node to the other in real-world networks, exhibiting bimodal and flat distributions. From this point of view, the LFR model is not realistic, since it produces networks whose nodes have all roughly the same mixing coefficient. To solve this problem, we implemented a small adjustment allowing to specify the complete distribution of in place of a single objective value.

Community Detection

Because of their number and great diversity, it is difficult to categorize community detection algorithms. Here, we chose to characterize them not by considering the process they implement, as it is usually done, but rather the definition of the community concept they rely upon. We selected a representative set of algorithms, favoring fast ones because of the size of the analyzed networks. We give very partial descriptions in this section, so the reader might want to consult the review by Fortunato [START_REF] Fortunato | Community Detection in Graphs[END_REF] to find more information concerning community detection. A very widespread informal definition of the community concept considers it as a group of nodes densely interconnected compared to the other nodes [START_REF] Fortunato | Community Detection in Graphs[END_REF][START_REF] Newman | Detecting Community Structure in Networks[END_REF][START_REF] Danon | Community Structure Identification. Large Scale Structure and Dynamics of Complex Networks: From Information Technology to Finance and Natural Science[END_REF]. In other terms, a community is a cohesive subset clearly separated from the rest of the network. Formal definitions differ in the way they translate and combine both these aspects of cohesion and separation.

A direct translation of the informal definition given above consists in first specifying two distinct measures to assess separately cohesion and separation, and then processing an overall measure by considering their difference or ratio. This approach led to many variants, differing on how the measures are defined and combined. The most widespread one is certainly the modularity, a chance-corrected measure which assesses cohesion and separation through the number of intra-and inter-community links, respectively. We selected two modularity optimization algorithms, which differ in the way they perform this optimization. Fast Greedy applies a basic greedy approach [START_REF] Newman | Finding and Evaluating Community Structure in Networks[END_REF], and Louvain includes a community aggregation step to improve processing on large networks [START_REF] Blondel | Fast Unfolding of Communities in Large Networks[END_REF].

Another family of approaches is based on node similarity measures. Such a measure allows translating the topological notions of cohesion and separation in terms of intra-community similarity and inter-community dissimilarity. In other terms: a community is viewed as a group of nodes which are similar to each other, but dissimilar from the rest of the network. Once all node-to-node similarities are known, detecting a community structure can be performed by applying a similarity-based classic cluster analysis algorithm [START_REF] Gan | Data Clustering: Theory, Algorithms, and Applications[END_REF]. We selected the Walktrap algorithm, which uses a similarity based on random walks and applies a hierarchical agglomerative clustering approach [START_REF] Pons | Computing Communities in Large Networks Using Random Walks[END_REF].

Some approaches based on data compression do not use the cohesion and separation concepts like the previous definitions. They consider the community structure as a set of regularities in the network topology, which can be used to represent the whole network in a more compact way. The best community structure is supposed to be the one maximizing compactness while minimizing information loss. The quality of the representation is assessed through measures derived from mutual information. Algorithms essentially differ in the way they represent the community structure and how they assess the quality of this representation. We selected the InfoMap algorithm [START_REF] Rosvall | Maps of Random Walks on Complex Networks Reveal Community Structure[END_REF], whose representation is based on coded ids affected to nodes.

The definition of the community concept is not always explicit: procedural approaches exist, in which the notion of community is implicitly defined as the result of the processing. To illustrate this, we selected the MarkovCluster algorithm, which simulates a diffusion process in the network to detect communities [START_REF] Van Dongen | Graph Clustering Via a Discrete Uncoupling Process[END_REF]. This approach relies on the transfer matrix of the network, which describes the transition probabilities for a random walker evolving in this network. Two transformations are iteratively applied on this matrix until convergence. The resulting matrix can be interpreted as the adjacency matrix of a network with disconnected components, which correspond to communities in the original network.

We have to mention another family of algorithms based on link centrality. They iteratively remove the most central links until disconnected components are obtained, which are interpreted as the network communities. The community structure largely depends on the selected centrality measure, e.g. edge-betweenness [START_REF] Girvan | Community Structure in Social and Biological Networks[END_REF]. However, the computational cost of such algorithms is very high and we were not able to apply them to our data.

4

Results and Discussion

Properties of the Generated Communities

Using our review of the literature, we selected realistic values for the parameters the LFR model lets us control. We used three different network sizes: , constant average and maximal degrees , , and exponent for the degree power-law distribution. The exponent was for the community size distribution, whose bounds were and . The mixing coefficient was distributed uniformly over its definition domain . We generated instances of network for each combination of parameter values, in order to check for consistency.

Among the community-related properties we described in section 2, two are directly controlled by the LFR model: the community size and embeddedness distributions. Our measurements confirm on all networks that the community sizes follow a power-law distribution as expected (cf. Fig. 1). Note the range of these sizes varies much from one real-world network to the other, and it is therefore difficult to describe a typical set of values. However, we can say the communities we generated are very similar in size to those from real-world networks of comparable size. For instance, we have communities containing between and nodes for , which is compliant with what was observed in networks of this size [START_REF] Lancichinetti | Characterizing the Community Structure of Complex Networks[END_REF]. For the embeddedness, we obtained a uniform distribution, as expected. It is close enough to what can be observed in social and information networks. The main difference is we do not have as many nodes with very high embeddedness as in those real-world networks. This could be easily corrected though, by specifying a more appropriate distribution when applying the modified LFR model.

We now focus our attention on the uncontrolled properties. The results are very similar independently from the size of the network. The only difference seems to be that values measured on larger networks exhibit slightly smaller dispersion. For this reason we present only results for networks with size . The scaled density increases from to along with the community size. This means the smallest communities are clique-like ( ), and no tree-like communities are generated (

). These features cannot be considered as realistic: as mentioned before, in real-world networks the small communities are treelike and the large ones are either tree-like too, or much more clique-like. In other words: real-world networks exhibit two different behaviors, but the generated networks can be compared to none of them. It seems the links are distributed too homogeneously over the generated networks, making small communities too dense and large ones too sparse.

As shown in Fig. 1, the average distance increases regularly from to along with the community size. The main difference with real-world networks is these have a much lower average distance for smallest communities, reaching values slightly greater than . Consequently, we do not observe for the generated networks the fast increase of average distance which was characteristic of the real-world networks. For the rest of the communities, the observed distribution is comparable with communication networks though, with a stable average distance for medium and large communities. Moreover, the values measured for these communities are also realistic in terms of magnitude. Hub dominance is very high for the smallest communities, with values close to . For large communities, there is no general trend in networks: the property varies much over the networks we generated. This dispersion decreases when the network size increases though, and networks show a hub dominance decrease with community size increase, reaching values close to . This behavior is compatible with most classes of real-world networks, which exhibit hubs dominance mainly for small communities. Moreover, the same dispersion was also observed on real-world networks [START_REF] Lancichinetti | Characterizing the Community Structure of Complex Networks[END_REF]. This measure completely relies on the way high degree nodes are distributed over communities, since it directly depends on the maximal internal degree found in communities. The fact there are much less large communities, due to their power law-distributed sizes, can explain this dispersion. A possible solution would be to consider a measure based on the highest internal degrees of the community instead of a single one.

To summarize our observations: the generated communities exhibit some, but not all, of the properties observed on real-world networks. Their sizes are realistic, but the distribution of links is not always appropriate. The small communities are too dense and clique-like, when they should be sparser and tree-like, with a smaller average distance. In other terms, they should be star-shaped. They possess the high hub dominance characteristic of such structures though, but this is certainly due to their clique-like configuration. The fact their average distance is much higher than in comparable real-world communities is a surprise. Indeed, one would expect such dense, hub-dominated communities to have a lower average distance. It turns out they are constituted of a clique core and a few very low degree nodes connected to this 10 0 Frequency core: the latter explain the relatively high average distance. The larger communities, on the contrary, should be substantially denser and more clique-like. In some cases, their hub dominance is relatively low despite their small average distance and low density, which seems to indicate they do not contain a main central hub, but several interconnected medium ones. By definition, this feature is not reflected by the hub dominance measure, which only considers the maximal degree in the community.

Another issue is the fact generated networks do not comply with a specific class of real-world networks, but rather have similarities with different classes depending on the considered property. Their average distance have common points with communication networks, whereas this is not the case at all for their embeddedness and hub dominance distributions, which look like social and biological networks. Despites these limitations, the model produces what we think to be the most realistic networks to date, which is why the generated networks constitute an appropriate benchmark to analyze community detection algorithms.

Comparison of the Estimated Communities

We applied the selected community detection algorithms on the generated networks: Louvain (LV), Fast Greedy (FG), MarkovCluster (MC), InfoMap (IM) and Walktrap (WT). For time matters, it was possible to process networks with sizes and , but not . We however generated denser networks, with (instead of ), in order to study the effect of density. Table 1 displays the performance of each algorithm expressed in terms of Normalized Mutual Information (NMI), which is a measure assessing the similarity of two partitions (in our case: the reference and estimated community structures). It is considered to be a good performance measure for community detection, and was used in several studies [START_REF] Lancichinetti | Benchmark Graphs for Testing Community Detection Algorithms[END_REF][START_REF] Danon | The Effect of Size Heterogeneity on Community Identification in Complex Networks[END_REF][START_REF] Orman | A Comparison of Community Detection Algorithms on Artificial Networks[END_REF]. According to the NMI, IM clearly finds the closest community structure to the reference, followed by MC, LV, and WT, while FG is far behind. This type of quantitative analysis is characteristic of existing works dealing with algorithms comparison. In the rest of this section, we complete it with a qualitative analysis based on the previously presented community properties.

We first focus on the results obtained on networks. As we can see on Fig. 2, most algorithms have found communities whose sizes distribution is reminiscent of the power-law used during network generation. However, important differences exist between them. First, MC visibly finds many very small communities ( ), and the other sizes are consequently strongly under-represented. A more thorough verification showed most of these communities are even single nodes, which is particularly problematic since community identification consists in grouping them. It is important to remark this does not appear on the NMI values, since MC has the second best score. This raises a question regarding the appropriateness of this measure to assess community detection performance. IM also finds some small communities, but much less than MC, and the rest of the distribution is more similar to the reference. Compared to the reference and the other algorithms, communities detected by FG and LV have sizes distributed rather uniformly. Interestingly, these two algorithms have very different performances in terms of NMI, so despite the relatively similar sizes of their communities, their community structures are probably very different too. For WT, the size distribution is very close to the reference. Again, this fact alone is not equivalent to a high NMI value, since its performance is substantially lower to IM. For the embeddedness, MC and WT are clearly different from the reference, displaying a distribution with very few extreme embeddedness values. The small numbers of highly embedded nodes and the fact almost half the nodes have very low embeddedness with MC seems to be linked to the community size distribution. Many of the smallest communities identified by MC are certainly grouped together in the reference, leading to a smaller number of intercommunity links. Compared to the reference, WT does not contain nodes with low embeddedness, whereas it has more nodes with medium embeddedness. In this case, it cannot be related to the community sizes though, since they are comparable to those of the reference. Maybe the lack of low embeddedness nodes can be interpreted as a failure to classify interface nodes, located at the limit of their community and largely connected with other communities. The embeddedness distributions observed for FG and LV are again very similar. They also lack low embeddedness nodes, but not as much as WT. Finally, IM presents the values the most similar to the reference.

When considering the scaled density (Fig. 2), IM, MC and WT are very close to the reference, except IM and MC present very low values for their smallest communities (meaning these are tree-like). For FG and LV, the scaled density is relatively stable, and does not present the slow increase which is characteristic of the reference. This can be interpreted as the fact the communities detected by these algorithms all present the same structure, independently from their size.

The average distances measured on the FG and LV communities are much dispersed and do not follow the evolution observed for the reference. FG, in particular, has a much higher average distance than the reference and the other algorithms. This property is a good indicator of cohesion, so it seems this quality is absent from the communities identified by FG. The remaining algorithms (IM, MC, WT) are very close to the reference. IM displays two outliers though: the average distance is surprisingly high for its smallest and largest communities.

For hub dominance, IM, MC and WT seem to follow the reference, with a positive bias. The fact these algorithms have slightly higher scaled-density and lower hub dominance, relatively to the reference, is consistent with their slightly lower average distance. The inverse observation is valid for the smallest and largest communities detected by IM: sparse and non-centralized communities lead to high average distance. FG and LV once again display similar behaviors, with hub dominance values clearly bellow the reference. When also considering their stable scaled density, this can explain their increasing average distance. Fig. 2. Properties of the detected communities. Each shape/color corresponds to a different algorithm, whereas the reference is represented by a solid line. Points are averages over logarithmic bins of the community size. The dotted lines in the scaled density plot represent the limits of this property, as in Fig. 1.

The topological analysis of the estimated community structures gives a new perspective to the quantitative performance measures. The communities detected by IM, the best algorithm in terms of NMI, are unsurprisingly very close to the reference ones. However, MC, the second algorithm and not far from IM, presents a very different community structure, characterized by much more very small communities. On the contrary, most of the properties of the communities identified by WT are very similar to the reference. It only differs clearly in terms of embeddedness distribution, which is apparently sufficient to rank it only fourth in terms of NMI, relatively far from IM. It thus seems there is no equivalence between a high NMI value and a community structure with properties close to the reference. We conclude both approaches are complementary to perform a relevant analysis of community detection results. It is worth noticing LV and FG, both based on modularity optimization,

and (right). Shapes/colors meaning is the same as in Fig. 2, and points are also averages over logarithmic bins of the community size.

On size networks, FG and LV find communities much larger than the reference ones, as shown in Fig. 3. For these algorithms, roughly ranges from to , when it goes from to in the reference. Both are based on modularity optimization, so this might be due to the resolution limit characteristic of this measure [START_REF] Fortunato | Resolution Limit in Community Detection[END_REF], which prevents them from finding smaller communities. IM is relatively close to the reference, but not as much as it is on networks. WT is also very similar to the reference, but it departs from it by finding a very large community (

). MC results are relatively similar to those obtained on the networks, i.e. it finds many very small communities. In order to separate the effects of network size and density on the algorithms, we generated additional networks with the same size, but maximal degree (instead of ). This reduces slightly the overestimation of FG and LV community sizes, whereas MC has roughly the same results. On the contrary, IM and WT properties are excellent, they follow almost perfectly the reference values.

Conclusion

In this study, we took advantage of recent advances relative to the characterization of community structures in complex networks to tackle two questions: 1) Do artificial networks used as benchmark exhibit real-world community properties? 2) How do community detection algorithms compare in qualitative terms, by opposition to the usual quantitative measurement of their performances. We first applied a variant of the LFR model [START_REF] Lancichinetti | Benchmark Graphs for Testing Community Detection Algorithms[END_REF] to generate a set of artificial networks with realistic parameters retrieved from the literature. We studied their properties and concluded some of them are realistic (community sizes, hub dominance), some are only partly realistic (embeddedness, average distance), and others are not realistic at all (scaled density).

We then applied on these networks a representative set of five fast community detection algorithms: Fast Greedy, InfoMap, Louvain, MarkovCluster and Walktrap.

Frequency Community Size

It turns out the performance assessed quantitatively through the widely used Normalized Mutual Information (NMI) measure does not necessarily agree with a qualitative analysis of the identified communities. On the one hand, MarkovCluster, ranked second in terms of NMI, actually found an extremely large number of very small communities and almost no large community. On the other hand, the properties of the community structure estimated by Walktrap are very close from the reference ones, but the algorithm comes fourth in terms of NMI, with a score relatively far from MarkovCluster's one. It therefore seems both approaches should be applied to perform a relevant comparison of the algorithms. Our contributions are as follow. First, we introduced a slight modification to the LFR model, in order to make the embeddedness distribution more realistic in the generated networks. Second, we studied these generated networks in terms of community-centered properties. This complements some previous analyses focusing on network-centered properties such as transitivity or degree correlation [START_REF] Lancichinetti | Benchmark Graphs for Testing Community Detection Algorithms[END_REF][START_REF] Orman | A Comparison of Community Detection Algorithms on Artificial Networks[END_REF][START_REF] Orman | The Effect of Network Realism on Community Detection Algorithms[END_REF]. Third, we applied several community detection algorithms on these networks and characterized their results relatively to the same community-centered properties. Previous studies adopted a quantitative approach based on some performance measure [START_REF] Lancichinetti | Benchmark Graphs for Testing Community Detection Algorithms[END_REF][START_REF] Danon | The Effect of Size Heterogeneity on Community Identification in Complex Networks[END_REF][START_REF] Orman | A Comparison of Community Detection Algorithms on Artificial Networks[END_REF][START_REF] Orman | The Effect of Network Realism on Community Detection Algorithms[END_REF][START_REF] Bagrow | Evaluating Local Community Methods in Networks[END_REF].

Our work can be extended in various ways. First, it seems necessary to either increase the realism of the LFR model or to define a completely new approach able to generate more realistic networks. Second, by lack of time, we could test only a few algorithms, on a few relatively large networks. A more thorough analysis would consist in using much larger networks, with more repetitions to improve statistical significance. Moreover, applying several algorithms relying on the same definition of the community concept would allow to compare their properties and maybe associate a certain type of community structure to a certain family of algorithms. It could additionally be interesting to use other performance measures than the NMI to assess their relevance with the studied topological properties. Third, it would noticeably be interesting to apply classic network-wise measures to communities (transitivity, degree correlation, centrality, etc.), and to consider additional community specific measures, such as those designed in [START_REF] Guimerà | Functional Cartography of Complex Metabolic Networks[END_REF], which seem complementary to the embeddedness, and the concept of community profile [START_REF] Leskovec | Statistical Properties of Community Structure in Large Social and Information Networks[END_REF], although this one looks particularly costly from a computational point of view.

Fig. 1 .

 1 Fig.1. Properties of the generated communities. Each network instance is represented with a different shape/color. Points are averages over logarithmic bins of the community size. The dotted lines in the scaled density plot represents its limits ( and , cf. section 2).

  the reference, which confirms the importance of considering the community definition which characterizes an algorithm.

Fig. 3 .

 3 Fig.3. Community size distributions for size networks, with (left) and (right). Shapes/colors meaning is the same as in Fig.2, and points are also averages over logarithmic bins of the community size.

Table 1 .

 1 Algorithms performances, as measured with the Normalized Mutual Information.

	Algorithm	,	,
	Louvain
	Fast Greedy
	MarkovCluster
	InfoMap
	Walktrap

Acknowledgments. This project is supported by the Galatasaray University Research Fund.


M Mével

E Bodio

S Grosjean

Gilles F Montavon

J.-C Meslin

K Julienne

D Deniaud
email: david.deniaud@univ-nantes.fr

A rapid

Keywords: Astatine, radioimmunotherapy, pyrimidinone, triazinone, chelating agent

come   L'archive ouverte pluridisciplinaire

Radioimmunotherapy (RIT) is a developing and promising technique for the treatment of small tumors. [1][2][3] It consists of injecting patients with a radiopharmaceutical able to target and selectively destroy tumour cells. The radionuclides usually used are ぼ or ぽ -emitters with a short half-life, attached to a vector (antibody or hapten) through a bifunctional chelating agent. [4][5][6] In order to minimize irradiation of healthy tissue whilst delivering radionuclides to tumors, the metal complex between chelating agent and radionuclide has to be stable in human serum.

Among the potential radionuclides, 211 At has attracted interest as a prospective candidate for αradioimmunotherapy applications due to its adequate physicochemical characteristics: α-emitter with a halflife of 7.2 h, the emission of high energy α particles (6.8 MeV), and ability to deposit large amounts of energy in a microvolume. 7 Astatine is also an x-ray emitter allowing external imaging of the radiopharmaceutical distribution. Nevertheless, the chemistry of astatine remains in its infancy due to the absence of a stable isotope. The current approach for labelling biomolecules with 211 At rests on covalent attachment to a carbon atom. 8 Unfortunately, a significant number of studies have shown that astatinated radiopharmaceuticals can be stable to in vitro conditions, but generally more unstable in vivo. 9,11 Nevertheless, clinical studies are in progress in United State and in Sweden. 12,13 Although it is clear that much of the chemistry ascribed to halogens is applicable, the chemical similarity between astatine and its nearest halogen neighbour, iodine, is not always obvious. The general trend in the periodic system suggests that astatine is more metallic in character than iodine. Indeed, it has been reported that astatine presents a metal-like behaviour when existing under the oxidation states +I and +III as At + and AtO + species. 14,15 Different groups have reported the formation of coordination complexes between AtO + and N -or S -containing organic chelating agents. 16- 18 The stability of these complexes is however not sufficient to use this chelation approach in RIT.

These considerations brought us to develop new N x polydentate ligands with variable size and number of coordination centres. At the same time as a fundamental, theoretical and pragmatic study around element astatine, we led here a purely empirical approach. This paper reports the synthesis of chelating agents L 1-8 containing heterocyclic rings (Figure 1). Our expertise in the synthesis of heterocycles led us to this choice of ligands. They present a semi-rigid scaffold due to partial conjugation between the linker and heterocycle. This characteristic is essential to preorganization, an important ligand property. 19,20 The degree of freedom is minimized, so that the structure of the chelate before complexation is similar to that in the complex. Preorganization provides high thermodynamic stability as well as increased kinetic inertness of the metal complex. Commercially available methylisothiocyanate was used as the starting reagent for the synthesis of chelating agents L 1-8 . The key step in this synthetic process was the preparation of the two corresponding hydrazinoheterocyclic rings 3 and 4 (Scheme 1). The intermediary pyrimidinone 1 and triazinone 2 were obtained in high yields according to our previously described methodology. 21,22 Nucleophilic displacement of the methylsulfanyl group of 1 and 2 with hydrazine was carried out using ethanol as solvent to afford 2-hydrazonopyrimidine 3 and 2-hydrazonotriazine 4. 23 The reaction was performed under microwave irradiation in order to minimize reaction time and secondary reactions. Indeed, with pyrimidinone 1, at room temperature and after 20 h, a by-product (20%) resulting from double attack of hydrazine onto two heterocycles, was observed. Finally, the heterocyclic rings 3 and 4 were converted to the new polydentate ligands L 1-8 with 4 to 6 coordination centres (N 4 , N 5 and N 6 ) by a double imination reaction with dialdehydes 5,8 or diketones 6,7. [START_REF]General procedure for ligands L 1-8 : to a 10 mL microwave reaction vessel was placed heterocyclic ring 3 or 4 (0.5 mmol) and dialdehyde 5 or 8 or diketone 6 or 7 (0.25 mmol) in methanol for L 1,2,7,8 (4 mL) or in acetic acid for L 3-6 (4 mL). The vial was heated (internal temperature measured by fibre-optic) in a microwave synthesizer (MultiSYNTH ® , Milestone S.r.l.) to 110°C (2 min (110 W) ramp + 15 min irradiation (80 W))[END_REF] These carbonyl compounds were commercially available except 5. This latter compound was prepared by initial reduction (using BH 3 .THF) of 5-tert-butylisophtalic acid to give the corresponding diol, which was subsequently oxidized (PCC/CH 2 Cl 2 ) into the dialdehyde. 25 To prepare N 4 tetradentate ligands L 1-4 , two equivalents of heterocyclic ring 3 or 4 were reacted with 1,3bis(formyl)-5-tert-butylbenzene 5 or butane-2,3-dione 6 (Scheme 2). The syntheses were performed under microwave irradiation at 110°C in ethanol for dialdehyde 5 and at 130°C in acetic acid for diketone 6 and afforded the N 4 ligands in high yields. [START_REF]General procedure for ligands L 1-8 : to a 10 mL microwave reaction vessel was placed heterocyclic ring 3 or 4 (0.5 mmol) and dialdehyde 5 or 8 or diketone 6 or 7 (0.25 mmol) in methanol for L 1,2,7,8 (4 mL) or in acetic acid for L 3-6 (4 mL). The vial was heated (internal temperature measured by fibre-optic) in a microwave synthesizer (MultiSYNTH ® , Milestone S.r.l.) to 110°C (2 min (110 W) ramp + 15 min irradiation (80 W))[END_REF] Microwave irradiation significantly improved yields and condensation reaction kinetics compared to conventional thermal protocol. All new ligands L 1-8 were isolated with a high degree of purity by simple filtration after microwave heating in glass vial. Their structure was determined unequivocally by complementary 1 H/ 13 C-2D NMR techniques (COSY, HMQC and HMBC). 26 In conclusion, the synthesis of N x polydentate ligands (N 4 , N 5 and N 6 ) was efficiently and simply performed by use of microwave-assisted technology. These chelators were prepared in 50-80% overall yield from methylisothiocyanate. The described way of synthesis will be easily adaptable to various starting heterocyclic structures. Study of the complexing ability of these new chelating agents toward astatine, suitable for αradioimmunotherapy, is under progress. According to the results of this study we envision the synthesis of various analogues of ligands L 1-8 in order to adjust their structure (size, nature, number of coordination centers and heterocyclic ring) to finally find out the ligand which would be best suited for astatine. A rapid microwave-assisted procedure for easy access to N x polydentate ligands for potential application in α-RIT.

N NH N N O CO 2 Me N HN N N O CO 2 Me N NH N N N O N HN N N N O Ligands L 1-4 Ligands L 5-8 (N) x (N) x x=0,1, 2

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Scheme 1

 1 Scheme 1 Synthetic route to heterocyles 3 and 4

Scheme 2

 2 Scheme 2 Tetradentate ligands L 1-4 with pyrimidinone and triazinone scaffolds.

N 5 6 (Scheme 3 8

 5638 Scheme 3 Pentadentate ligands L 5 and L 6 with pyrimidinone and triazinone scaffolds

LETTER

  Template for SYNLETT and SYNTHESIS © Thieme Stuttgart • New York 2011-06-27 page 6 of 6

assisted procedure for easy access to N x polydentate ligands for potential application in

  Mathieu Mével, a Ewen Bodio, a Sylvain Grosjean, a Gilles Montavon, b Jean-Claude Meslin, a Karine Julienne, a David Deniaud *a

Figure 1 Polydentate chelators prepared in the study A rapid microwaveα-RIT. LETTER Template for SYNLETT and SYNTHESIS © Thieme Stuttgart • New York 2011-06-27 page 2 of 6

Acknowledgment

The authors thank the French National Research Agency (ANR) (JCJC06_137852), the French Ministry of Education and CNRS for financial support.


Frank Dietz

Tero Rigét

Olle Harkonen

Aqqalu Karlsson

Florence Rosing-Asvid

Aurore Aubail
email: aaubail@yahoo.fr

Jonas Teilmann

Rune Dietz

Frank Rigét

Tero Harkonen

Olle Karlsson

Aqqalu Rosing-Asvid

Florence Caurant

Investigation of mercury concentrations in fur of phocid seals using stable isotopes as tracers of trophic levels and geographical regions

Keywords: Hg, nitrogen, carbon, hair, Arctic, Antarctica

HAL is

Introduction

Mercury (Hg) is a global contaminant released into the ecosystem from both natural and anthropogenic sources [START_REF] Pacyna | Global anthropogenic mercury emission inventory for 2000[END_REF]. The gaseous elemental form of this metal is very volatile, and once in the atmosphere, it can be transported from mid to high latitudes over long distances, and thereby reach the polar regions [START_REF] Brooks | Transport pathways and processes leading to environmental exposure[END_REF]. Although Hg is partly re-emitted to the air, it is accumulated in organisms and biomagnified in the trophic chain in polar ecosystems [START_REF] Atwell | Biomagnification and bioaccumulation of mercury in an arctic marine food web: insights from stable nitrogen isotope analysis[END_REF][START_REF] Bargagli | Biomagnification of mercury in an Antarctic marine coastal food web[END_REF]. Thus, organisms feeding on species at high trophic levels generally show greater Hg concentrations than those feeding on species at lower trophic levels.

Since marine mammals mainly are exposed to Hg through their diet [START_REF] Aguilar | Biological factors affecting variability of persistent pollutant levels in cetaceans[END_REF], differences in foraging strategies and feeding habits among species may lead to differences in exposure to Hg, resulting in interspecific disparities in concentrations of Hg.

Biological factors like age, sex or physiological status are known to influence the diet, and thereby, the exposure and accumulation of Hg in many species. However, differences in Hg concentrations can also result from geographical or temporal variations in the environmental levels of Hg. Whether differences in Hg concentrations among species result from differences in diet or environmental levels of Hg can be investigated by analysing naturally occurring variations in stable isotopes of nitrogen ( 15 N and 14 N) and carbon ( 13 C and 12 C) [START_REF] Hobson | Determination of Trophic Relationships Within A High Arctic Marine Food Web Using δ 13 C and δ 15 N Analysis[END_REF]. The underlying principle is that ratios of heavier vs lighter isotopes of nitrogen and carbon in tissues of predators can be traced to those of their prey as these two elements are assimilated through the diet.

Consumer tissues are stepwise enriched in 15 N relative to those of their prey, and consequently, δ 15 N measurements can be used to determine the trophic position of organisms [START_REF] Minagawa | Stepwise Enrichment of N-15 Along Food-Chains -Further Evidence and the Relation Between δ 15 N and Animal Age[END_REF]. In contrast, δ 13 C values vary little through the food chain (<1‰), and can thus help to determine the source of carbon used by primary consumers in a food web, and provide information on the foraging habitat of the studied organisms (Fry and Sherr 1984). Furthermore, turn over rates of stable isotopes in tissues vary with the metabolic rate of the tissue [START_REF] Tieszen | Fractionation and Turnover of Stable Carbon Isotopes in Animal-Tissues -Implications for δ 13 C Analysis of Diet[END_REF], and isotopic analyses can give information on feeding habits over the last days, weeks, months or years, depending on which tissue types are analysed.

Phocid seals are long-lived marine mammals at the top of food chains in polar ecosystems. Using stable isotopes of nitrogen and carbon as tracers of the trophic level and habitat use respectively, we investigated if concentrations of Hg in seal species from different geographical areas could be used to determine the trophic levels they prey upon. We studied a Ross seal (Ommatophoca rossii), Weddell seals (Leptonychotes weddellii) and crabeater seals (Lobodon carcinophaga) from Antarctic regions, harbour seals (Phoca vitulina) and grey seals (Halichoerus grypus) found throughout coastal regions of the Northern hemisphere, and ringed seals (Phoca hispida) and a bearded seal (Erignathus barbatus), which both show Northern circumpolar distributions [START_REF] Reeves | The Sierra Club Handbook of Seals and Sirenians[END_REF].

While the Ross seal has a varied diet based on squid, fish and krill, and the Weddell seal mainly feeds on fish, but also on various cephalopods and crustaceans, the crabeater seal is specialised on feeding almost exclusively on Antarctic krill [START_REF] Bowen | Pinniped ecology[END_REF]. In the Northern hemisphere, harbour and grey seals feed on a wide range of organisms, pelagic and benthic fish, cephalopods and crustaceans [START_REF] Reeves | The Sierra Club Handbook of Seals and Sirenians[END_REF]. Finally, ringed seals are believed to feed mainly on a variety of fish and invertebrates such as amphipods, euphausiids and cephalopods, while the bearded seal consumes mainly benthic invertebrates, i.e. clams, crustaceans, cephalopods as well as some fish [START_REF] Reeves | The Sierra Club Handbook of Seals and Sirenians[END_REF]. [START_REF] Pauly | Diet composition and trophic levels of marine mammals[END_REF] estimated the trophic levels of several marine mammals mainly by stomach content analysis. Values for trophic levels ranged from 3.3 for the crabeater seal to 4.1 for the Ross seal. Estimated values were 3.4 for bearded seals, 3.8 for ringed seals, harbour seals and grey seals, whereas it was estimated at 4.0 for Weddell seals.

Soft tissues are commonly used for analysis of metals and stable isotopes. However, fur provides a non-invasive way to investigate metals and stable isotopes of seals. Fur is keratin-based containing records of metallic and isotopic elements which are deposited there during the annual moult.

Mercury is one of the trace elements transported to the fur follicles via the blood supply [START_REF] Ikemoto | Comparison of trace element accumulation in Baikal seals (Pusa sibirica), Caspian seals (Pusa caspica) and northern fur seals (Callorhinus ursinus)[END_REF], and subsequently incorporated into the hair during periods of growth [START_REF] Brookens | Trace element concentrations in the Pacific harbor seal (Phoca vitulina richardii) in central and northern California[END_REF]. Hair is widely used as an indicator of blood Hg levels for mammals, and particularly for humans, and has been used as an indicator of exposure to the environmental pollution also in pinnipeds [START_REF] Brookens | Trace element concentrations in the Pacific harbor seal (Phoca vitulina richardii) in central and northern California[END_REF][START_REF] Gray | Trace element analysis in the serum and hair of Antarctic leopard seal, Hydrurga leptonyx, and Weddell seal, Leptonychotes weddellii[END_REF][START_REF] Ikemoto | Comparison of trace element accumulation in Baikal seals (Pusa sibirica), Caspian seals (Pusa caspica) and northern fur seals (Callorhinus ursinus)[END_REF][START_REF] Medvedev | Levels of heavy metals in seals of Lake Ladoga and the White Sea[END_REF][START_REF] Watanabe | Trace element accumulation in Baikal seal (Phoca sibirica) from the Lake Baikal[END_REF][START_REF] Wenzel | Trace-Metal Accumulation in Hair and Skin of the Harbor Seal, Phoca-Vitulina[END_REF][START_REF] Yamamoto | Tissue Distribution of Heavy-Metals in Weddell Seals (Leptonychotes weddellii)[END_REF].

The purpose of this study was to determine Hg concentrations in the fur of seven species of phocid seals from different geographical areas, and to evaluate the influence of biological factors in the bioaccumulation process. Stable isotope analyses were used to evaluate differences or similarities in the diet or in the foraging habitat among species that could explain variations in Hg concentrations.

We also evaluated if fur can be used for monitoring of Hg in phocid seals in the future.

Materials and methods

Sampling procedure and preparation

Hair samples of 85 seals were obtained from seven phocid seal species, i.e. Ross seal, Weddell seal, crabeater seal, harbour seal, grey seal, ringed seal, and bearded seal. The samples were collected from three distinct geographical areas, Ross Sea, Antarctica (Ant), Denmark (Dk), and Greenland (Gr) (cf. Fig. 1). Samples were taken in the period 1996 -2009. Length and weight of the animals were recorded, and age was estimated visually based on size and fur colour, according to three classes (yearling, juvenile and adult). Number of individuals, estimated age and gender are summarised for each species in Table 1.

Samples were stored in polyethylene plastic bags and kept at -20°C. Prior to analysis, fur samples were washed in a diluted standard detergent (RBS 35; Bie & Berntsen A/S, Denmark).

Subsequently, the hair samples were rinsed in several ultra-pure Milli-Q water baths, and dried for 24 hours at room temperature.

Analytical procedures, instrumentation and quality assurance for Hg measurements

The Hg measurements were performed at the laboratory of the National Environmental Research Institute in Roskilde, Denmark, using a solid sample atomic absorption spectrometer AMA-254 (Advanced Mercury Analyser-254 from LECO, Sweden). A homogenised subsample of 5 to 10 mg of fur was analysed from each individual. The use of this apparatus does not require chemical pretreatment, which reduces risks for contamination or loss of Hg. The analytical process consists of a drying period at 120°C prior to a combustion phase at 750°C, which leads to desorption of Hg from the samples. The Hg vapour produced is subsequently carried by an oxygen flow to a gold amalgamator, and trapped on its surface. The collected Hg is thereafter released from the amalgamator by a short heat-up to 900°C, and carried in a pulse through a spectrophotometer, where Hg is measured by UV absorption. The operating times used for this study, i.e. drying, decomposition, and waiting time, were 30, 150, and 45 s, respectively. The instrument is described in detail elsewhere [START_REF] Hall | Evaluation of a direct solid sampling atomic absorption spectrometer for the trace determination of mercury geological samples[END_REF].

The accuracy and reproducibility of the method were tested by including human hair (IAEA-086) reference material at the beginning and at the end of the analysis cycle, and by running it every 10 samples. Results of quality controls showed a good precision with a relative standard deviation of 3.9%. The accuracy was 96% of the assigned concentration (n = 9). The National Environmental Research Institute participates in the international inter-laboratory comparison exercises conducted by the EEC (QUASIMEME), and showed satisfactory results in the latest test in 2007 for the AMA-254 (0 < z < 0.5). All data are presented on a dry weight basis (dw) and the detection limit is 0.1 ng.g -1 dw.

Analytical procedures and instrumentation for stable isotope measurements

A homogenised aliquot of approximately 0.5 mg of hair from each individual was weighted and loaded into tin capsules.

Relative abundances of stable isotopes of carbon (δ 13 C) and nitrogen (δ 15 N) were determined using an elemental analyser (Flash EA 1112 fitted with a "No Blank" option, Thermo Scientific, Milan, Italy) coupled to an isotope ratio mass spectrometer (Delta V Advantage with a Conflo IV interface, Thermo Scientific, Bremen, Germany). Stable isotope results are expressed in delta notation (δ), defined as the part per thousand (‰) deviation from a standard material:

δ 13 C or δ 15 N = [(Rsample / Rstandard) -1] × 10 3 ,
where Rsample and Rstandard are the fractions of heavy to light isotopes in the sample and standard, respectively. The international standards are the Pee Dee Belemnite (PDB) marine fossil limestone formation from South Carolina for δ 13 C, and atmospheric nitrogen for δ 15 N.

The analytical precision of the measurements was < 0.06‰ for carbon and < 0.1‰ for nitrogen, based on replicate measurements of acetanilide as internal laboratory reference material.

Statistical analysis

Prior to the statistical analyses, the Hg data were log-transformed (base e) to reduce skewness and fit parametric requirements. Shapiro-Wilk and Bartlett test were applied to test the assumptions of parametric tests, such as analysis of variance (ANOVA) and linear regression analysis. In few cases, the assumptions were not fulfilled because of a couple of high Hg concentration values.

However, ANOVA tests are robust to small deviations of the data from the normal distribution [START_REF] Zar | Biostatistical analysis: International edition[END_REF].

Standard parametric tests such linear regression analysis and analysis of variance, were applied to test for the influence of factors (i.e. age category, sex, species and region of sampling) on the logtransformed Hg concentrations or δ 13 C and δ 15 N values. If the first runs of ANOVA test showed no significance of the interaction between two factors, the interaction factor was removed and the test re-run. Tukey HSD (Honestly Significant Difference) test was used as a posterior ANOVA test to determine which means were significantly different from one another. Wilcoxon tests were used to test for differences in log-transformed Hg concentrations or stable isotope ratios between two species from the same region or among individuals from the same species originating from two regions. Non-parametric test Spearman rank correlation were used to test the relationships between Hg concentrations, δ 13 C and δ 15 N values.

The number of individuals was low for some of the species, and only crabeater seals, Weddell seals and ringed seals were represented by more than 10 individuals (Table 1). All species (7 species, 85 individuals) are shown on the graphs, but the bearded seal (n = 1) and the Ross seal (n = 1) are excluded from statistical analyses due to low sample size.

The significance level was set to p = 0.05.

The statistical analyses were performed using the free software R, version 2.1.1 (R Development Core Team 2008).

Results

Hg concentrations and stable isotope ratios

Mercury concentrations in the hair ranged from 0.07 µg.g -1 dw for the crabeater seal to 30.6 µg.g -1 dw for the harbour seal, and mean concentrations increased in the sequence: crabeater seals < Ross seal < bearded seal < Weddell seals < ringed seals < harbour seals (Dk) < grey seals < harbour seals (Gr) (Table 2). Nitrogen stable isotopic ratios in hair of the different seal species varied from 6.02‰ for the crabeater seals to 19.33‰ for the ringed seals (crabeater seals < Ross seal < Weddell seals < bearded seal < harbour seals = grey seals < ringed seals, for mean values), while δ 13 C values ranged from -25.11‰ for the crabeater seals to -15.06‰ for the harbour seals (crabeater seals < Weddell seals < Ross seal < grey seals < ringed seals < harbour seals (Dk) < bearded seal < harbour seals (Gr), for mean values) (Table 2).

Influence of sex and age classes

Only adult individuals were selected to test the factor sex. However, the three categories of age (yearling, juvenile and adult) were not all well represented for each species (Table 1). Thus, the influence of sex on Hg concentrations was tested only on the crabeater seals, while the influence of age classes was tested on crabeater seals, Weddell seals and ringed seals.

No difference in Hg concentrations between genders was recorded among the crabeater seals (Oneway ANOVA, F = 0.26; p = 0.62). Figure 2 shows Hg levels for the different age classes for crabeater seals, Weddell seals and ringed seals. Log-transformed Hg concentrations increased significantly with age for crabeater seals (One-way ANOVA, F = 221.1, p < 0.001), where adults showed a higher mean Hg concentration (0.61 µg.g -1 dw) compared with juveniles (0.11 µg.g -1 dw).

However, no significant differences among age classes were found for Weddell seals (F = 1.71, p = 0.23) or ringed seals (F = 2.7, p = 0.09).

The δ 15 N and δ 13 C values also differed significantly among age groups for the crabeater seals (Oneway ANOVA, F = 9.53, p = 0.004 and F = 113.3, p < 0.001, respectively), with the adults of this species showing lower mean δ 15 N and δ 13 C values ± standard errors (7.26 ± 0.27‰, -23.38 ± 0.16‰, respectively, n = 10) than the juvenile individuals (7.89 ± 0.07‰, -24.67 ± 0.04‰, respectively, n = 23) (Fig. 3). However, this difference in δ 15 N and δ 13 C values between age groups was not significant for the Weddell seals (F = 0.65, p = 0.55 and F = 4.20, p = 0.051, respectively) and the ringed seals (F = 0.31, p = 0.73 and F = 1.30, p = 0.29, respectively). Age specific differences were not tested for in ringed seals due to small sample sizes in age groups yearlings and juveniles.

Influence of the species and the geographical area

The average Hg concentration increased in the sequence: crabeater seals (Ant), Ross seal (Ant), bearded seal (Gr), Weddell seals (Ant), ringed seals (Gr), harbour seals (Dk), grey seals (Dk), harbour seals (Gr) (Table 2). Highly significant differences between species were found for logtransformed Hg concentrations (One-way ANOVA, F = 84.73, p < 0.001) and δ 15 N and δ 13 C values (F = 648.8, p < 0.001 and F = 537, p < 0.001, respectively), with the crabeater seal showing the lowest Hg, δ 15 N and δ 13 C values of all species (Fig. 4A/B). Tukey HSB tests showed that crabeater seals had significantly lower Hg concentrations compared with the other species, and that Hg concentrations in hair of harbour seals were significantly greater than in Weddell seals and ringed seals (Table 2, Fig. 4A). Moreover, the δ 15 N values differed among the species, except for between harbour seals and grey seals (Table 2, Fig. 4A) while δ 13 C values also varied among the species except for between ringed seals and grey seals (Table 2, Fig. 4B).

No significant difference was found for Hg (Wilcoxon, W = 6, p = 0.7), δ 15 N (W = 6, p = 0.7) and δ 13 C (W = 6, p = 0.7) contents in hairs between harbour seals from Denmark and Greenland; however, it is worth noticing that the number of individuals was low and age groups were not comparable. Significant differences were found for Hg, δ 15 N and δ 13 C values in hair from seals collected in the three regions. Subsequent Tukey tests revealed that Antarctic seals had lower values of Hg, δ 15 N and δ 13 C while there were no significant differences between Greenland and Denmark (Table 2, Fig. 4). Significant correlations were also found between log-transformed Hg

Discussion

Influence of sex and age groups on Hg concentrations in fur

The influence of gender on Hg concentrations varies among studies and species. Thus, a study carried out on fur from Baikal seals Phoca sibirica showed no difference in Hg concentrations between genders [START_REF] Watanabe | Trace element accumulation in Baikal seal (Phoca sibirica) from the Lake Baikal[END_REF], whereas [START_REF] Wenzel | Trace-Metal Accumulation in Hair and Skin of the Harbor Seal, Phoca-Vitulina[END_REF] observed higher levels and a greater variability in Hg concentrations in fur from female compared to male harbour seals. In the same way, greater concentrations of Hg were found in fur from adult male Pacific harbour seals Phoca vitulina richardii and leopard seals Hydrurga leptonyx as compared with females in both species [START_REF] Brookens | Trace element concentrations in the Pacific harbor seal (Phoca vitulina richardii) in central and northern California[END_REF][START_REF] Gray | Trace element analysis in the serum and hair of Antarctic leopard seal, Hydrurga leptonyx, and Weddell seal, Leptonychotes weddellii[END_REF]. Gender specific differences in Hg concentrations could be the result of sexual dimorphism or dissimilarities in dietary intake or dietary preferences between male and female seals. This could be partially linked to the different energy requirement for gestation and lactation. Crabeater seals do not show any marked sexual dimorphism [START_REF] Shirihai | Seals. In: Kirwan GM (ed) A Complete Guide to Antarctic Wildlife -The Birds and Marine Mammals of the Antarctic Continent and the Southern Ocean, 2nd edn. A & C Black[END_REF], and no significant differences for Hg concentrations between male and female crabeater seals were found, which would be consistent with comparable exposure for both genders in this species.

Concentrations of Hg increased significantly with age in crabeater seals, but not for the Weddell seals or the ringed seals (Fig 2). Such age related differences have been previously reported for harbour seals [START_REF] Brookens | Trace element concentrations in the Pacific harbor seal (Phoca vitulina richardii) in central and northern California[END_REF][START_REF] Wenzel | Trace-Metal Accumulation in Hair and Skin of the Harbor Seal, Phoca-Vitulina[END_REF]) and ringed seals [START_REF] Medvedev | Levels of heavy metals in seals of Lake Ladoga and the White Sea[END_REF]).

Increasing concentrations with age in our study likely result from a difference in foraging habits between juveniles and adults, which was confirmed by the significant difference in δ 15 N and δ 13 C values among age classes detected for the crabeater seals (Fig. 3). The greater variability of δ 15 N values for the adults compared to the juvenile crabeater seals suggests that older individuals feed on a wider range of prey than younger seals. In addition, the distinct δ 13 C values displayed by the juvenile individuals and the adults indicate that they have different feeding habitats. Since δ 13 C values are generally greater in benthic or sea-ice algae than in pelagic algae (Fry and Sherr 1984;[START_REF] Tamelander | Trophic relationships and pelagic-benthic coupling during summer in the Barents Sea Marginal Ice Zone revealed by stable carbon and nitrogen isotope measurements[END_REF], our results, with significantly lower δ 13 C values in the juveniles, suggest that juvenile individuals may forage mainly krill in the water column. Previous findings indicate that despite the high degree of specialisation of this species on a single prey resource, i.e. krill, crabeater seals have the behavioural plasticity to forage successfully under a wide range of environmental conditions, for example, at varying depths and duration of dives and selecting prey in a greater panel if necessary [START_REF] Burns | Winter habitat use and foraging behavior of crabeater seals along the Western Antarctic Peninsula[END_REF]). Similarly to our study, higher δ 13 C values have previously been observed in adult and subadult crabeater seals compared to juveniles and pups by Zhao et al. (2004), though no statistical difference between age classes was found in that study.

Differences in diving and foraging behaviour between adults and juveniles, and ontogenetic shifts in diet have previously been documented in several species of phocid seals [START_REF] Born | Habitat Use of Ringed Seals (Phoca hispida) in the North Water Area (North Baffin Bay)[END_REF][START_REF] Burns | The diet of Weddell seals in McMurdo Sound, Antarctica as determined from scat collections and stable isotope analysis[END_REF][START_REF] Holst | Diet of ringed seals (Phoca hispida) on the east and west sides of the North Water Polynya, northern Baffin Bay[END_REF][START_REF] Lowry | Variability in the Diet of Ringed Seals, Phoca hispida, in Alaska[END_REF][START_REF] Reeves | The Sierra Club Handbook of Seals and Sirenians[END_REF]. Generally, newly weaned pups forage less efficiently and have more limited diving capacity compared with older seals, leading to differences in diet [START_REF] Holst | Diet of ringed seals (Phoca hispida) on the east and west sides of the North Water Polynya, northern Baffin Bay[END_REF][START_REF] Reeves | The Sierra Club Handbook of Seals and Sirenians[END_REF]. Similarly to crabeater seals, distinct δ 13 C values were observed between juvenile and adult individuals of ringed seals and Weddell seals, suggesting that juvenile seals of those species tend to explore different foraging habitats than the adults. One such example is the dichotomy among Weddell seal yearlings, where some individuals predominantly feed on benthic species in shallow waters, whereas others mainly forage in the same deep-water pelagic zone as the adults do [START_REF] Burns | The diet of Weddell seals in McMurdo Sound, Antarctica as determined from scat collections and stable isotope analysis[END_REF].

Differences among geographical areas and species (feeding strategies)

Phocid seals renew their fur once a year over a relatively short period, the annual moult, which occurs at different times of year depending on species [START_REF] Berta | Pinnipedia, overview[END_REF]. The hair grows rapidly and discontinuously, and concentrations of Hg measured in the hair reflect the availability of Hg to the growing pile via blood during the annual moult [START_REF] Berlin | Mercury[END_REF]. Most seals moult within a twomonths period [START_REF] Stutz | Moult in Pacific Harbour Seal Phoca Vitulina Richardi[END_REF], and Hg concentrations in fur result from the diet composition during or prior to the moulting period. In addition, the moulting period occurs from late spring to late summer in both hemispheres. As a result, months during which it occurs differ, and species from the Northern hemisphere tend to moult between May and September, whereas species from the Southern hemisphere moult between December and February [START_REF] Reeves | The Sierra Club Handbook of Seals and Sirenians[END_REF][START_REF] Shirihai | Seals. In: Kirwan GM (ed) A Complete Guide to Antarctic Wildlife -The Birds and Marine Mammals of the Antarctic Continent and the Southern Ocean, 2nd edn. A & C Black[END_REF].

Thus, seasonal variations in the origin of Hg, its long-range atmospheric transport and its deposition -including Mercury Depletion Events or MDEs which have been shown to occur at the respective springtime in both Arctic [START_REF] Schroeder | Arctic springtime depletion of mercury[END_REF] and Antarctica [START_REF] Ebinghaus | Antarctic springtime depletion of atmospheric mercury[END_REF])-, may have a great influence on the Hg exposure and bioaccumulation in the seals. Levels of Hg concentrations in fur of species from Antarctica did not exceed 3.5 µg.g -1 dw which was relatively low compared to those from Greenland and Denmark, and earlier studies of Hg levels in hair from Antarctic pinnipeds have not reported concentrations exceeding 11 µg.g -1 dw [START_REF] Gray | Trace element analysis in the serum and hair of Antarctic leopard seal, Hydrurga leptonyx, and Weddell seal, Leptonychotes weddellii[END_REF][START_REF] Yamamoto | Tissue Distribution of Heavy-Metals in Weddell Seals (Leptonychotes weddellii)[END_REF]. Although this difference can be related to the fact that the various species have different feeding habits, the global distribution pattern of released Hg may also contribute to those differences in Hg concentrations observed in seals from the Northern and the Southern hemispheres. Indeed, the total deposition pattern of Hg (dry and wet deposition) in the 2000's shows that concentrations of Hg are much lower in the Southern hemisphere than in the Northern hemisphere (AMAP/UNEP 2008).

The variation in stable isotopic values between species from Northern and Southern polar ecosystems could likely reflect geographical differences in the δ 15 N and δ 13 C values at the base of food webs. Phocid seals from Northern ecosystems generally show greater δ 15 N values and significantly greater δ 13 C values than those from Southern waters (Fig. 4). However, δ 15 N values reported for producers do not differ between both hemispheres. [START_REF] Horton | Stable isotope food-web analysis and mercury biomagnification in polar bears (Ursus maritimus)[END_REF] determined a mean value of approximately 6.5‰ (range between 4 and 8‰) for phytoplankton and 6‰ for ice algae (range between 4 and 7‰) from different studies carried out in the Arctic. [START_REF] Mincks | Trophic structure on the West Antarctic Peninsula shelf: Detritivory and benthic inertia revealed by δ 13 C and δ 15 N analysis[END_REF] reported similar mean values in the West Antarctic Peninsula Shelf, ranging from 3.3 to 7.5‰ for phytoplankton and from 4.5 and 6‰ for ice algae. Thus, the δ 15 N values found in our study would imply a greater number of steps in the Arctic food web and thus higher trophic levels for seals. Earlier studies have shown that Hg concentrations in biota increase with the trophic levels (i.e. δ 15 N values), i.e. predators feeding on high trophic levels usually show higher Hg concentrations than those feeding on lower levels [START_REF] Atwell | Biomagnification and bioaccumulation of mercury in an arctic marine food web: insights from stable nitrogen isotope analysis[END_REF][START_REF] Campbell | Mercury and other trace elements in a pelagic Arctic marine food web (Northwater Polynya, Baffin Bay)[END_REF]. The biomagnification of Hg in the food web is also demonstrated in our study by the greater Hg concentrations as well as δ 15 N values exhibited by the Northern hemisphere species.

Concerning carbon stable isotopes ratios, [START_REF] Rau | Plankton C-13/C-12 Ratio Changes with Latitude -Differences Between Northern and Southern Oceans[END_REF] reported distinct latitudinal trends in plankton δ 13 C between the Northern and Southern oceans, with δ 13 C values of the Southern ocean decreasing more and faster toward the South Pole than toward the North Pole. The isotopic results of our study illustrate these latitudinal variations of δ 13 C values between Northern and Southern oceans, the phocid seal species from Antarctic waters showing lower δ 13 C values of approximately 4‰ relative to the Arctic species (Table 2). In addition, some of the variations in δ 13 C values could also be due to the influence of the different foraging habitats of the species, which imply various carbon sources, i.e. pelagic, sympagic or benthic. It seems indeed that the sympagic or iceassociated algae, which exhibits approximately mean δ 13 C values of -20 to -18‰ in both polar regions (see review in [START_REF] Horton | Stable isotope food-web analysis and mercury biomagnification in polar bears (Ursus maritimus)[END_REF][START_REF] Mincks | Trophic structure on the West Antarctic Peninsula shelf: Detritivory and benthic inertia revealed by δ 13 C and δ 15 N analysis[END_REF] would influence more the δ 13 C values of the Arctic seals (mean value of -16.95 ± 0.94‰ (sd)), and especially the ringed seals, than the Antarctic ones (-23.95 ± 0.81‰). Thus, it would indicate a greater participation of the Northern species in the sympagic food web than the Southern ones. As a result, according to the type of food web and prey species on which seals feed, the Hg exposure and bioaccumulation would be different.

Thus, the sequence of Hg impregnation was harbour seal > grey seal > ringed seal > bearded seal > Weddell seal > Ross seal > crabeater seal, which may reflect the influence of differences in diet of these species. The crabeater seal showed the lowest Hg (0.26 ± 0.04 µg.g -1 dw) and δ 15 N values (7.70 ± 0.11‰) in fur of all investigated seals, which is the result of its very specific diet, almost entirely composed of krill [START_REF] Bowen | Pinniped ecology[END_REF]. Of the three species from the Southern Ocean, the Weddell seal exhibited the greatest Hg concentration (2.09 ± 0.21 µg.g -1 dw) and δ 15 N value (13.46 ± 0.21‰). These high values reflect its diet consisting of pelagic fish, which are believed to be the predominant prey items of the Weddell seal in McMurdo Sound, near our sampling area, although this species has also been reported feeding on cephalopods and crustaceans [START_REF] Burns | The diet of Weddell seals in McMurdo Sound, Antarctica as determined from scat collections and stable isotope analysis[END_REF]).

Among the phocid seal species from the Northern hemisphere, harbour seals had greater Hg levels than ringed seals, although a bit lower δ 15 N values were found in ringed seals (Table 2). Harbour seals and ringed seals are small pinnipeds, feeding on a large variety of organisms, including fish, cephalopods and various crustaceans [START_REF] Reeves | The Sierra Club Handbook of Seals and Sirenians[END_REF]. [START_REF] Pauly | Diet composition and trophic levels of marine mammals[END_REF] reported the harbour seal being on a slightly higher trophic level (TL = 4) than the ringed seal (TL = 3.8). Our sample of Greenlandic harbour seals consisted of adults whereas ringed seals from Greenlandic waters were mainly represented by yearlings. The elevated δ 15 N values showed by the ringed seals in our study (17.64 ± 0.18‰) may be caused by the fact that the diet of yearlings partly included milk, which would give this pattern, as also found for Steller sea lions (Eumetopias jubatus) [START_REF] Hobson | Stable isotope analyses of tooth annuli reveal temporal dietary records: An example using steller sea lions[END_REF]. This maternal input to ringed seal yearlings is supported by the greater δ 15 N values displayed by this age group compared to the adult one. Similarly, the greater Hg concentrations in adult harbour seals could result from that they feed on larger prey with greater burdens of Hg than ringed seal yearlings.

No significant difference in Hg concentrations, δ 15 N or δ 13 C values was found between harbour seals and grey seals from Danish waters, which is in concordance with results from [START_REF] Pauly | Diet composition and trophic levels of marine mammals[END_REF], who estimated both species to the same trophic level at 4. The grey seal feeds on schooling fish, squid, cephalopods and occasionally sea birds [START_REF] Barros | Diet[END_REF], and a great variability in both Hg concentrations and stable isotopic ratio values was observed for this species, reflecting a wide range of prey from various foraging areas, but likely also the low sample size.

Finally, no significant difference was found in Hg contents in hair among harbour seals from Greenlandic and Danish waters, but the sample size was small for this species, and samples from Greenland and Denmark were not comparable since the Greenlandic sample of harbour seals consisted of adults, whereas the Danish sample was composed of a yearling and juvenile animals.

However, whereas all individuals showed similar δ 15 N values, suggesting a more or less similar diet, greater δ 13 C values found in the Greenlandic harbour seals compared to Danish ones, may reflect either a difference in the foraging strategy, related to the age dissimilarity, or a difference in the isotopic carbon signature of the two geographical areas. Furthermore, this difference could also highlight the influence of the ice-associated producers on the Greenlandic seals δ 13 C values, as shown by the greater δ 13 C value of ice algae compared to the phytoplankton one [START_REF] Horton | Stable isotope food-web analysis and mercury biomagnification in polar bears (Ursus maritimus)[END_REF][START_REF] Tamelander | Trophic relationships and pelagic-benthic coupling during summer in the Barents Sea Marginal Ice Zone revealed by stable carbon and nitrogen isotope measurements[END_REF]. The greater δ 13 C values of the Greenlandic harbour seals compared to those from Danish waters may thus underline the role of the sympagic food web in the Arctic marine ecosystem.

Conclusion

This study showed consistent variations in Hg concentrations and δ 15 N and δ 13 C values among species and geographical regions. This demonstrates that fur is a good tissue for monitoring exposure to Hg in phocid seals and for reconstructing their exposure history through their diet, especially with the non-destructive and invasive sampling protocols relative to this tissue. The significant correlation between Hg concentrations and δ 15 N values highlighted the biomagnification of Hg in the food webs. The comparison of both hemispheres showed the greater Hg concentrations in the Northern one, which would be the result of a greater contamination and /or somewhat longer food chains in the Arctic. Our study confirmed the tight link between Hg exposure and feeding habits (as revealed by δ 15 N and δ 13 C values) of seals. Thus, measurements of Hg contents in organisms in an ecosystem can provide information on the trophic levels of species and age groups.

In the most optimal way, Hg analysis should be combined with isotopic tracers, although the

  concentrations and δ 15 N values (Spearman's correlation,  = 0.68, p < 0.001, Fig. 4A, y = 0.133x -1.673), log-transformed Hg and δ 13 C values ( = 0.83, p < 0.001, Fig. 4B, y = 0.168x + 3.514), and δ 15 N and δ 13 C values ( = 0.76, p < 0.001, Fig. 4C, y = 1.064x + 34.835) including all species.

Fig. 1

 1 Fig. 1 Map of the world showing the three geographical areas, Antarctica (Ant), Denmark (Dk), Greenland (Gr), of fur sampling of the phocid species

Fig. 3 Fig. 4

 34 Fig. 3 Relations between δ 15 N (‰) vs δ 13 C (‰) values for the three age classes (filled circle = yearling, open circle = juvenile, open triangle = adult) for the Weddell seals, crabeater seals and ringed seals

Table 2

 2 Mercury concentrations and stable isotopic ratios of nitrogen (δ 15 N) and carbon (δ 13 C) (mean values ± standard error SE and range) in fur samples of the various phocid species from the different geographical areas

	Area	Species	Hg (µg/g dw)	δ	15 N (‰)	δ	13 C (‰)
			Mean ± SE	Range	Mean ± SE	Range	Mean ± SE	Range
	Antarctica	Ross seal	0.48			10.38		-22.31
		Weddell seal	2.09 ± 0.21 0.63-3.22 13.46 ± 0.21 12.51-14.89	-23.2 ± 0.12	-23.86-(-22.24)
		Crabeater seal	0.26 ± 0.04 0.07-0.99	7.7 ± 0.11	6.02-8.84	-24.28 ± 0.12 -25.11-(-22.63)
	Denmark	Harbour seal	7.79 ± 1.99 5.63-11.77 15.75 ± 0.05 15.65-15.82	-16.87 ± 0.36 -17.46-(-16.21)
		Grey seal	10.11 ± 5.47 4.11-21.03 15.76 ± 1.20 13.92-18.03	-17.41 ± 0.68 -18.54-(-16.20)
	Greenland	Harbour seal	16.27 ± 2.86 1.49-30.60 15.69 ± 0.16 15.03-16.44	-15.86 ± 0.15 -16.37-(-15.06)
		Ringed seal	3.06 ± 0.49 0.87-10.28 17.64 ± 0.18 15.86-19.33	-17.33 ± 0.16 -19.18-(-15.72)
		Bearded seal	1.97			14.26		-16.71
	All		3.45 ± 0.61 0.07-30.60 12.75 ± 0.47 6.02-19.33	-20.76 ± 0.39	-25.11-(-15.06)

Acknowledgements

We would like to thank all the people who helped collecting the samples in the field, especially the crew of the Swedish icebreaker "Oden" who skilfully managed to find the seals and manoeuvre through the dense pack ice around Antarctica. Special acknowledgement to Carine Churlaud from the Centre Commun d'Analyses (La Rochelle, France) for her valuable input on the Hg analysis, and to Pierre Richard and Gaël Guillou from LIENSs (UMR 6250 CNRS-La Rochelle University, France) for their contribution and advice on the stable isotope analysis. This study was financed by The Dancea Programme, KVUG (Kommissionen for Videnskabelige Undersøgelser i Grønland), the Swedish Research Council, the Swedish Polar Institute, the Poitou-Charentes region and the M.L. Furnestin-Faure foundation. Finally, we also thank Travis Horton, Liying Zhao and a third anonymous reviewer for their contribution to this manuscript through their relevant comments.