Michael Behrisch
email: michael.behrisch@uni-konstanz.de.

Benjamin Bach

Michael Hund
email: michael.hund@uni-konstanz.de.

Michael Delz
email: michael.delz@uni-konstanz.de.

Laura Von R Üden

Jean-Daniel Fekete
email: jean-daniel.fekete@inria.fr.

Tobias Schreck
email: tobias.schreck@cgv.tugraz.at.

• M Behrisch

J.-D Fekete

Magnostics: Image-based Search of Interesting Matrix Views for Guided Network Exploration

Keywords: Matrix Visualization, Visual Quality Measures, Quality Metrics, Feature Detection/Selection, Relational Data 1 INTRODUCTION

In this work we address the problem of retrieving potentially interesting matrix views to support the exploration of networks. We introduce Matrix Diagnostics (or MAGNOSTICS), following in spirit related approaches for rating and ranking other visualization techniques, such as Scagnostics for scatter plots. Our approach ranks matrix views according to the appearance of specific visual patterns, such as blocks and lines, indicating the existence of topological motifs in the data, such as clusters, bi-graphs, or central nodes. MAGNOSTICS can be used to analyze, query, or search for visually similar matrices in large collections, or to assess the quality of matrix reordering algorithms. While many feature descriptors for image analyzes exist, there is no evidence how they perform for detecting patterns in matrices. In order to make an informed choice of feature descriptors for matrix diagnostics, we evaluate 30 feature descriptors-27 existing ones and three new descriptors that we designed specifically for MAGNOSTICS-with respect to four criteria: pattern response, pattern variability, pattern sensibility, and pattern discrimination. We conclude with an informed set of six descriptors as most appropriate for MAGNOSTICS and demonstrate their application in two scenarios; exploring a large collection of matrices and analyzing temporal networks.

quantification of distribution of points in scatter plots, called Scagnostics. Each measure describes a different characteristic of the data and helps, for example, to filter the views with different Scagnostics measures than the majority. The underlying scatter plots are likely to exhibit informative relations between the two data dimensions. Besides static ranking tasks, image-based data descriptions can also form a basis for dynamic training of classifiers to identify potentially relevant views [START_REF] Behrisch | Feedback-driven interactive exploration of large multidimensional data supported by visual classifier[END_REF]. This is particularly useful for cases in which a given (static) description and selection heuristic may not fit some user's requirements.

We propose a set of six FDs, called MAGNOSTICS features, which quantify the presence and salience of six common visual patterns in a matrix plot, which are the result of a particular matrix ordering (Fig. 2). Each pattern refers to a topological graph motif, such as clusters, central nodes, or bigraphs. MAGNOSTICS are similar to Scagnostics features describing e.g., the degree of stringyness, clumpiness and outlyingness as relevant patterns in Scatterplots.

Unlike statistical graph measures, which allow describing global graph characteristics, such as density and clustering coefficient, MAG-NOSTICS represent interpretable visual features for matrix displays. This is of great importance, because the order or rows and columns in the matrix influences which type of information is visible or hidden from the viewer [START_REF] Behrisch | Matrix Reordering Methods for Table and Network Visualization[END_REF], just like in a 2D layout for node-link representations. Quantifying for one given ordering how well the information is represented in terms of visual patterns helps to assess the visual quality.

MAGNOSTICS can be used for a large variety of tasks, such as finding good orderings for visual exploration, finding matrices with specific patterns in a large network data set, analyzing a collection of varied networks, or series of stages in an evolving network (e.g., brain functional connectivity data).

While many FDs for image analysis exist, there is no evidence how they perform for detecting patterns in matrices. In order to make an informed choice of FDs for MAGNOSTICS, we evaluate 30 FDs, including three new descriptors that we specifically designed for detecting matrix patterns. Using a set of 5,570 generated matrix images, we evaluated each FD with respect to four criteria: pattern response, pattern variability, pattern sensibility, and pattern discrimination. For each of the FDs that are part of MAGNOSTICS, we provide a more detailed description, showcasing its performance on real-world data sets. We demonstrate MAGNOSTICS on two application scenarios (Sect. 7). Firstly, querying a large database by example (query-by-example) and via a sketch interface (query-by-sketch). The second scenario analyses a network evolving over time based on time-series of MAGNOSTICS.

Fig. 1: Different matrix orderings for the same matrix data.

RELATED WORK

Finding Relevant Views in Large Data Spaces

Visual data analysis methods need to be able to handle increasingly large data sets. However, not only the data size grows, but also the possible visualization space for this data. This problem gets even worse when the number of view parameters is taken into consideration. In the case of the analysis of an n-dimensional data set with scatter plots, (n × (n -1))/2 two dimensional projections can be produced [START_REF] Tatu | Automated analytical methods to support visual exploration of high-dimensional data[END_REF]. If the same data set is visualized with a Parallel Coordinates Plot even n! possible column orderings exist [START_REF] Dasgupta | Pargnostics: Screen-space metrics for parallel coordinates[END_REF]. Similar problems arise in visualization of adjacency matrices, which comprise (n! ×n! ) valid row/column orderings. However, all of these visualization approaches have in common that only few view configurations lead to relevant or non-redundant information. Hence, intelligent methods for compressing and filtering data for potential patterns of interest are researched.

General approaches to support the identification of relevant views in large view spaces include clutter reduction [START_REF] Ellis | A taxonomy of clutter reduction for information visualisation[END_REF][START_REF] Peng | Clutter reduction in multidimensional data visualization using dimension reordering[END_REF] and dimensionality reduction [START_REF] Ingram | Dimstiller: Workflows for dimensional analysis and reduction[END_REF][START_REF] Tatu | Subspace search and visualization to make sense of alternative clusterings in high-dimensional data[END_REF]. Besides fully-automated approaches, others explore interactivity, empowering the user. For example, in [START_REF] Behrisch | Feedback-driven interactive exploration of large multidimensional data supported by visual classifier[END_REF] an interactive scatter plot exploration approach using a classifier to learn the notion of interestingness from user feedback is proposed. A visual query interface for multivariate data using regressional features is presented in [START_REF] Scherer | Retrieval and exploratory search in multivariate research data repositories using regressional features[END_REF]. Alternatively, sketching can be used to express patterns of interest in a large scatter plot space [START_REF] Shao | Guided Sketching for Visual Search and Exploration in Large Scatter Plot Spaces[END_REF]. MAGNOSTICS is meant to be used in similar interactive interfaces, while focusing on quantifying the view relevancy.

Methods Based on View Quality

Quantifying the interestingness of visualizations typically requires heuristic feature-based approaches that respond to the (potentially) interesting structural characteristics of a visualization. These methods try to mimic human perception in that they distinguish one or more visual patterns from noise. Several previous works exist, tailored towards specific patterns for certain visualization techniques.

For scatter plots, Wilkinson et al. [START_REF] Wilkinson | Graph-theoretic scagnostics[END_REF] introduce Scagnostics (scatter plot diagnostics), using graph-theoretic measures to describe point distributions. Their feature vector consists of nine interpretable characteristics which are important in the analysis of scatter plots. By using one of these measures, an analyst could make assumptions about inherent information of the described scatter plot. Scagnostics features are global features, describing a whole scatter plot at once. Recently, Shao et al. [START_REF] Shao | Guiding the exploration of scatter plot data using motif-based interest measures[END_REF] proposed usage of local features to rank scatter plots. The approach first applies a density-based segmentation of local scatter plot patterns, and then identifies relevant views by an interest measure defined over local patterns.

Similarly, Dasgupta et al. [START_REF] Dasgupta | Pargnostics: Screen-space metrics for parallel coordinates[END_REF] propose Pargnostics for Parallel Coordinate Plots with the goal to optimize the axis layout so that user's preferences are met. Pargnostics introduces several statistical and image-space measures to quantify e.g., the number of line crossings, crossing angles, convergence, or overplotting measures, all being candidates to rank relevant or informative views. For dense pixel displays, Schneidewind et al. proposed Pixnostics [START_REF] Schneidewind | Pixnostics: Towards measuring the value of visualization[END_REF], a set of statistical measures in pixel-oriented visualizations. The entropy of an image is measured and shows to be useful to distinguish structured views from noisy ones, reducing the interactive search time for pattern retrieval tasks. In line of this work, Albuquerque et al. present the Noise-Dissimilarity measure for Jigsaw Maps [START_REF] Albuquerque | Improving the visual analysis of high-dimensional datasets using quality measures[END_REF], which we also adapted and tested for our matrix pattern analysis scenario. For high-dimensional data analysis, Bertini et al. [START_REF] Bertini | Quality Metrics in High-Dimensional Data Visualization: An Overview and Systematization[END_REF] proposed a conceptual model for assessing the quality in image spaces and to integrate view quality into the visual exploration process. Finally, Seo et al.'s [START_REF] Seo | A rank-by-feature framework for unsupervised multidimensional data exploration using low dimensional projections[END_REF] rank-by-feature framework makes use of correlation and entropy measures to find an appropriate order within histograms, boxplots and scatter plot views.

MAGNOSTICS follows a line of previous works applying view quality selection based on visual view properties. We extend this methodology to matrix visualizations and their visual patterns. Our approach is based on image features extracted for ordered matrices, which are used as a selection or ranking measure to identify relevant views.

MATRICES AND VISUAL PATTERNS IN MATRICES

An adjacency matrix M = (n × n) is a two-dimensional vector with n = |N| with N being the nodes in an undirected network. A matrix cell c i j ; 0 ≤ i, j < n denotes the existence of a link between node i and j. In the most simple case c i j = 1 if i and j are connected, otherwise c i j = 0. Depending on the type of data, c i j can carry particular attributes, such as a strength (e.g., degree of friendship in a social network), or relation type (e.g., friend vs. college) resulting in a weighted adjacency matrix. Here, we focus on symmetric binary matrices.

A visualization of a matrix is an n × n plot with each cell representing the underlying value in the matrix using shades, color, or glyphs. Crucial in using matrix visualization and to extract meaningful information is a good ordering of rows and columns, indicating the presence of topological structure in the data. Fig. 1 shows the same data (matrix), using different orderings for rows and columns.

Matrix Ordering

The problem of finding a good matrix ordering is similar to the problem of finding a layout in node-link diagrams that makes, e.g., clusters and outliers visible pre-attentively. In matrices, visual patterns emerge by re-ordering rows and columns, so that neighboring rows and columns are visually similar. Matrix reordering surveys have been presented by Liiv [START_REF] Liiv | Seriation and matrix reordering methods: An historical overview[END_REF] and more recently, by Behrisch et al. [START_REF] Behrisch | Matrix Reordering Methods for Table and Network Visualization[END_REF].

For a single data set, multiple orderings can be created, but not all ordering algorithms may be equally well suited to make certain structures in the data visible. Little research has been conducted to understand, which algorithm is best suited to reveal certain data characteristics. Hence, it appears useful to generate several matrix orderings and chose the ordering with the most suited results, for the task at hand.

Visual Patterns in Matrices

A visual pattern is visual structure in the matrix that reveals information about the underlying graph topology. Some work has been conducted [START_REF] Behrisch | Matrix Reordering Methods for Table and Network Visualization[END_REF][START_REF] Mueller | Interpreting large visual similarity matrices[END_REF][START_REF] Wilkinson | The Grammar of Graphics (Statistics and Computing)[END_REF] to collect the main visual patterns in matrix plots, along with their graph-theoretic interpretations. While there is an infinite amount of visual patterns, for MAGNOSTICS we refer to the selection detailed in [START_REF] Behrisch | Matrix Reordering Methods for Table and Network Visualization[END_REF] (Blocks, Off-Diag. Blocks, Star/Lines, Band), where the used visual patterns are also related to user tasks.

Visual patterns are of importance, for example, to biologists searching for cycles in biological process networks, or to sociologists studying social interactions and how people form and connect to groups.

Fig. 2 summarizes the patterns we want to retrieve in matrices. For each of these patterns as shown in Fig. 2, we assume an optimal ordering of matrix rows and columns; permuting rows and columns in these examples can make the pattern less evident, though the topological information in the network, i.e. the motif, is still there.

• Block-Diagonal Pattern: A Block-diagonal pattern consists of a block (at least 2 × 2 cells) on the diagonal of the matrix. A diagonal block refers to a densely connected clique in a graph where every node is connected to every other node. Clique motifs can be found in social networks representing groups of mutual friends. A slightly weaker version of a clique, i.e., not every node is connected to every other node, is called a cluster and appears as a block with holes or less sharp boundaries. • Off-Diagonal Block Pattern: An off-diagonal block is visually similar to a diagonal block, but placed at the corners of the matrix not touching the main diagonal (top-left/bottom right in our definition).

Off-diagonal blocks refer to bi-cliques in the networks that consist of two sets of nodes where each node from the one set is connected to each node of the second set. Bi-cliques can be found in 2-mode networks, e.g. persons related to cities they have visited. • Star Pattern: Star patterns in matrices consist of one horizontal and one vertical closed line. However, a line does not have to span the entire matrix. A star pattern corresponds to the star graph motif, i.e., a highly connected node in the network, such as an important airport in a traffic network, or a famous person in a friendship network. • Band Pattern: A band pattern consists of lines parallel to the matrix diagonal, but not being placed on the diagonal. A band indicates a path in the network, i.e., a sequence of links from one to another node. Paths can represent a possible way of information transmission in a social network or a sequence of reactions in a biological networks.

While patterns indicate motifs and hence information in the network, we are also interested in patterns conveying algorithm artifacts. Detecting artifacts can help to assess the appropriateness of matrix ordering algorithms and to explicitly hide matrices from the user.

• Bandwidth Anti-pattern: The bandwidth pattern is a typical artifact of graph-based matrix reordering algorithms, such as the Cuthill-McKee algorithm. While these algorithms are generally fast, their visual performance greatly depends on the existing/salient ordering within the formed envelope. See [START_REF] Behrisch | Matrix Reordering Methods for Table and Network Visualization[END_REF] for more information. • Noise Anti-pattern: By noise we refer to a random distribution of black cells in the matrix. The more noise a matrix contains, the less information it shows. Throughout the paper we use noise matrices as base-line patterns to assess the quality of a feature descriptor.

FEATURE DESCRIPTOR ANALYSIS METHODOLOGY

After the conceptual analysis of relevant structures in matrix views, we next detail on our FD analysis methodology, as depicted in Fig. 3.

Selecting an Initial Set of Feature Descriptors

The literature on image analysis provides an abundance of image FDs, including such based on color, texture, shape, structure, among other properties. These FDs are traditionally developed and used for processing of real-world images. Our goal is to make an informed selection of candidate FDs appropriate for responding to patterns in matrix visualizations shown in Fig. 2. To that end, we started with an initial set of 27 existing, well-known image measures described in the literature.

The main selection criteria are the suitability to respond to our set of visual patterns in matrices, availability, and stability of the respective implementations. We also made sure to include two to five FDs from every different image analysis subdomain [START_REF] Rui | Image retrieval: Current techniques, promising directions, and open issues[END_REF][START_REF] Smeulders | Contentbased image retrieval at the end of the early years[END_REF]: texture descriptors, (localized) color-, edge-and line descriptors, shape-, structure-and contour descriptors, interest point descriptors, and noise descriptors.

We include three additional FDs that we designed specifically to respond to patterns in matrix views which by their nature show different

v v v v v v v v v v v v v v v v v v v v 4 C1 C2 C3 C4
Analysis and result tables Fig. 3: FD evaluation methodology and main concepts: After a selection of candidate FDs and the generation of a pattern retrieval benchmark dataset for matrices, we evaluated all FDs with respect to four distinct evaluation criteria (C1-C4).

properties than real-world images. For example, our BLOCKS FD not only responds to blocks, but is able to return their number and density (Fig. 2a). NOISE STATISTICAL SLIDINGWINDOW quantifies the (local) amount of noise in a matrix (Fig. 2f), while the PROFILE FD is designed to respond to matrices with many lines (Fig. 2c). Table 1 summarizes the full list of FDs we considered for our analysis. [1] GRADIENT [START_REF] Von Rüden | Visual analytics of parallel-performance data: Automatic identification of relevant and similar data subsets[END_REF] Table 1: Overview over all tested feature descriptors (FDs). FD names are hyperlinks to access an interactive FD profile page with e.g., a distance-to-noise and a distance-to-base ranking.

Creating a Matrix Pattern Benchmark Data Set

We tested each FD against the same data set, i.e., visual matrices. An appropriate data set must contain patterns and variations thereof, and different degrees of pattern quality. Moreover, we need multiple samples for the same pattern and its variations in order to account for the variability in the individual data samples. We decided to create an artificial controlled benchmark data set to control for the presence, variation, and quality of patterns, as well as to create as many data samples as necessary. Fig. 4 shows example matrices from the data set. The complete benchmark data set is available online.

Patterns and Variations

For each of the five patterns in Fig. 2, we generated prototypes of 30 × 30 matrices and variations thereof (Fig. 4 first line). A prototype is an image with only the pattern in an otherwise empty matrix. Any purposeful FD must respond to this pattern. A variation of a prototype is a variation of the general characteristics of the pattern, mainly number, size, and position. For example, a variation of the block pattern varies the number of blocks; a variation of the line patterns changes the line width or the amount of lines, and so forth. The goal is to assess which type of variations a FD is able to differentiate.

Gradual Pattern Degeneration

To measure a FD's ability to respond to unclear and noisy patterns, we generated a gradual degeneration schema for each pattern and its variation, i.e., we gradually decreased the quality of the pattern by introducing "noise" into the matrix. We generated matrices with the following degeneration functions, making sure that the last steps of every degradation resulted in a completely random matrix. a) Point-Swap-A first type of noise function introduces structural noise into the graph, by randomly swapping cells in the matrix (Fig. 4b)). Any cell-swap randomly exchanges one black and one white cell in the matrix (symmetry is preserved by a second corresponding cell-swap in each degeneration step). We can consider the number of cell-swaps as a quality measure how salient a pattern is expressed in the data. For example, a complete block without holes represents a clique in the graph, while the presence of holes indicates a less dense cluster. For our data set, we generated pattern degenerations with the following numbers of cell-swaps: 0, 1, 2, 4, 8, 16, 32 percent of the data, with the last step (32%) showing no evidence of any pattern.

b) Index-Swap-With a second noise function, we iteratively swap rows and columns in the matrix (Fig. 4c)). An index swap preserves the topology of the graph, by randomly exchanging two rows (and columns). Degrading a pattern with an index-swap is similar to using a matrix reordering algorithm that fails to show a topological structure, even though it is present in the data. For our data set, we generated data samples from 0 to 10 index-swaps. We can use the number of index-swaps as quality measure of the respective pattern.

c) Masking-Lastly, we gradually add additional black points (noise) to the matrix to mask the pattern (Fig. 4d)). Thereby, we simulate situations in which the visual pattern is overlapping and intervenes with other patterns, e.g., overlapping clusters, closely connected nodes. The applied noise is exponentially increasing (0% to 16%).

In total we used 23 pattern variations (4 + 4 + 6 + 5 + 4 ) and 24 degeneration types (7 point-swap + 11 index-swaps + 6 maskings). For each condition, we created ten samples, resulting in a set of 5,520 benchmark matrix images with patterns. On top of that, we added 50 pure random noise images with a varying noise density between 1% and 16%, leaving us with a total number of 5,570 MAGNOSTICS benchmark matrix images. The full data set can be downloaded from our website: http://magnostics.dbvis.de/#/benchmark.

Generating Experiment Conditions

For each one of our 5,570 matrix images m i we run each of our 30 FDs. This resulted in 167,100 trials FD j (m i ), each one returning an n-dimensional feature vector v = FD j (m i ). For most FD (except, BLOCKS, TAMURA and some others), vector dimensions may not have a specific human interpretation. In order to analyze and compare all feature vectors we have to rely on distances between individual feature vectors d(v i , v j ). Our distance function is the Euclidean distance between n-dimensional vectors.

Two FDs (ADAPTIVEGRIDRESOLUTION and HOUGH) had to be excluded from the analysis process, since their implementations did not reliably return comparable feature vectors.

MAGNOSTICS Evaluation Criteria

To inform a selection of FDs, we evaluate each FD according to four criteria. Generally, our criteria selection is inspired by the requirements imposed on information/image retrieval-and computer vision systems [START_REF] Gonzalez | Digital Image Processing[END_REF]. However, some criteria (esp. C2 and C4) have to be considered as initial research approaches selected specifically to tackle a visual pattern retrieval in matrix data. The individual results are reported in Sect. 5: C1: Pattern Response-To which specific matrix pattern(s) does the FD respond? An appropriate FD must distinguish patterns from noise, i.e., a matrix with random distribution of black and white cells. For every pattern in Fig. 2, we can generate a set of prototype patterns and measure the performance by precision and recall for every FD on our entire benchmark data set. C2: Pattern Variability-How much variation in the pattern can the FD detect? Patterns in matrices vary, mainly in size or number; for example, there can be one or more blocks, and each of the blocks can have a different size. To measure variability, we can generate variations for every pattern in Fig. 2 and calculate how much the FD response varies/discriminates, using Euclidean distance.

C3: Pattern Sensitivity-How sensitive is the FD to pattern degeneration, e.g., noise? Patterns are rarely encountered in a prototypical form. For example, blocks may show holes (less dense clusters), or less sharp boundaries (e.g., overlapping clusters). For every pattern in Fig. 2 and its variations, we gradually degrade the pattern until eventually returning a noise matrix (randomly distributed black cells). We develop and derive a pattern sensitivity measure to quantify how well a FD is able to cope with the degeneration of a pattern.

C4: Pattern Discrimination-How discriminatory can the FD differentiate between distinct patterns? An effective FD should yield discriminative results for different patterns. Otherwise, it does not allow to correctly interpret the FD's response. We measure the pattern discrimination for the FDs by analyzing the differences between vectors returned by the FD.

For MAGNOSTICS, we consider C1 a decisive criterion, meaning that we do not want to include FDs into MAGNOSTICS if they do not respond properly to any patterns. Results for C2 and C3 are descriptive in that depending on the final use case, a more variable (C2) and/or sensitive (C3) FD may be preferred. Both C1, C4 are considered decisive criteria as we want FDs to discriminate different patterns. In the following, we describe which initial FDs are included in our analysis, how we generated the benchmark data, and how we analyze the returned feature values for each defined experiment.

ANALYSIS PROCESS AND QUALITY METRICS

Each criteria (C1-C4) requires an individual analysis of the feature vectors. We report on each criteria individually.

Pattern Response (C1)

Our pattern response criteria refers to a FD's ability to respond to a specific pattern in the data. As a measure of effectiveness, we use precision and recall measures [START_REF] Baeza-Yates | Modern Information Retrieval -the concepts and technology behind search[END_REF]. High precision reflects a FD's ability to rank a larger number of correct answers at the early ranking positions. High recall means that the FD is able to retrieve a large fraction of all correct answers (matrices) from the target data set. The weighted harmonic mean is an aggregate that combines both measures, but prefers recall over precision (F 2 score, with β = 2 ). It is given in Equation 1 and will be used to assess the capability of the FDs to identify the sought matrices.

F β = (1 + β 2 ) • precision • recall (β 2 • precision) + recall (1)
Separate precision, recall and F 1 tables can be accessed online 1 .

Our experiment setup looks as follows and is repeated for all 30 feature descriptors: First, we derive an appropriate classifier training data set, which consists of all slightly degenerated pattern images (≤ 4% for point-swap and noise and ≤ 6 index swaps). Second, we conduct a 10-fold cross validation, where each repetition involves the random partitioning of the data into complementary subsets: the training set (70% of the data), which is used to train a classifier, and the validation set (30% of the data) to derive our performance measures. The validation results are averaged over the rounds to reduce the variability. To mitigate the impact of the classifier algorithm we run all experiments with three distinct classifiers (Random Forest, Naïve Bayes, Support Vector Machine). Since the results are comparable we decided to just report on the Random Forest Classifier 2 .

We present the results of our pattern response experiments in Fig. 8(a). The F 2 scores are ranging from 0 (low; white) to 1 (high; saturated). As shown in the table, most of the FDs perform with an F 2 score of 0.9 or higher, meaning that these FD are able to differentiate patterns from noise. Generally, texture descriptors yield the highest overall F-scores. None of the patterns were specifically a problem for any of our selected FDs, which means that altogether, our preselected set of FDs is able to respond to each of our six base patterns. Some measures yield higher scores for certain patterns while scoring less for others. For example, MPEG7 EDGE HISTOGRAM yields lower scores for both block patterns. These results confirm the purpose of an algorithm designed to respond to edges in images. In contrast, BLOCKS performs well for block patterns, but worse for lines.

We will report on the choice of each feature descriptor for each pattern separately in Sect. 6.

Pattern Variability (C2)

Pattern variability corresponds to how sensitive a FD is with respect to variations in the pattern. Therefore, we decided to take only prototypical patterns without any additional degeneration (e.g., noise) into consideration for these experiments. Since no scalar measure exists to describe the pattern variability, i.e., there is so far no vector dimension on the number of blocks or lines, we need to look at pair-wise distances between feature vectors and analyze if they allow us to discriminate the pattern variations.

Fig. 5 illustrates all pairwise distances of the test patterns between two selected feature vectors in a distance matrix (Descriptor Distance Matrix, DDM). One row and column represents each pattern variation. The last row contains the noise matrix as point of reference for a distance normalization. Black values mean low distances, red represents medium distances, and white reflects high distances. The example in Fig. 5 shows a desired distribution of distances for the selected FDs (THUMBNAIL and COMPACTNESS), i.e., pairwise distances become gradually higher for more variation of the pattern. Hence, we consider these FDs as good candidates to measure gradually the variability of matrix patterns by distance. For better quantification and comparison, we also report on the standard deviation of the normalized distance scores, as shown below.

σ FD i (PV) = 1 |PV| ∑ 1≤i, j≤|PV| ndist(PV i , PV j ) -x 2 (2)
Where, PV i corresponds to the i th pattern variation from a base pattern variation set (e.g., Block1-4), ndist() represents a normalized Euclidean distance and x corresponds to the average of all distance 2 All other experiment result tables can be found in the Appendix. combinations. We excluded the reference noise column from this calculation, since it has only illustration purposes.

Other than for precision and recall, poor performance on variability is not a sufficient reason to exclude a FD from the selection. A FD with low variability supports application cases where any expression of a pattern is of importance, e.g., finding matrices with block patterns. A FD with high variability supports applications where more detail is necessary, such as finding matrices most similar to a given one.

We report the results of our pattern variability experiments in Fig. 8(b). The standard deviation scores are ranging from 0 (low = white) to 0.5 (high = dark red). From the table we see that the only FD with no variability at all is HARALICK. Other FDs score consistently high for our variability measure meaning that they are able to discriminate between the pattern variations. We also found that variations for the off-diagonal and block pattern are lower for most FDs, which might be due to the fact these coherent rectangles are not recognized independently of their location in the matrix plot (c.f., translation invariance). Line patterns seem to yield generally high variability, suggesting that our FDs are sensitive to changes in the expression of lines.

Pattern Sensitivity (C3)

Pattern sensitivity refers to how sensitive a FD is to pattern degenerations (e.g., noise), implying a visually less salient pattern. High sensitivity means that only visually salient patterns can be detected, while a low sensitivity allows even less salient patterns to be detected.

Our analysis approach here is similar to the one for C2; we analyze the Euclidean distances between feature vectors of different degeneration levels (Sect. 4.2). The assumption is that with an increase in degeneration, the distances between feature vectors and the feature vectors for the non-degenerated base pattern follow a monotonic increase.

Fig. 5(b) shows a DDM for a variation of the Block-Diagonal Pattern (4 blocks) and examples of increasing degeneration with the PointSwap modification function. The matrix shows a monotonic increase in distances from the proto-pattern to the degenerated matrix. For our analysis of sensitivity, we only report a one pattern variation for every base pattern. Tests with the other pattern variations showed only small difference. Eventually, we obtained 150 DDMs, one for every combination of the five base patterns and the 30 FDs. In analyzing the monotony we (1) assess if there is any monotonic increase or not. If the increase in not monotonic the respective FD is very sensitive to any degeneration, i.e., the FD cannot accurately rank matrices according to their amount of noise. ( 2) For monotonic plots, we can then quantify the sensitivity of the FD: highly sensitive (fast increase of distances) or tolerant (slow increase of distances).

Fig. 6 shows examples of monotonic increases of distances. The x-axis shows the degeneration level, the y-axis shows the distance to the average of one base-pattern vector. Each point in the plot represents the distance of a sample. The red points and line represent average distances. Fig. 6 (a) shows low sensitivity, (b) high sensitivity, (c) medium sensitivity but with a high variation in the distances, and (d) non-monotonically increasing distances.

To quantify monotony of the 150 DDMs and to better inform our final choice, we calculated a quality metric for the monotony of a feature descriptor FD i and a base pattern P j as follows

monotony(FD i , P j ) =      1, (mean l+1 -mean l + 0.05) > 0;
∀l ∈ noise levels. 0, otherwise where mean l indicates the average of feature vectors retrieved for the noise level k. For monotonic increases, we then calculated the sensitivity as the signed difference between the averaged vector for each degeneration level, and the normalized equality function x = y. sensitivity(FD i , P j ) is high for sensitivity > 0 (fast increase), and low (slow increase) for sensitivity < 0.

sensitivity(FD i , P j ) = |noise levels|-1 ∑ l=0 (mean k -( l |noise levels| )
We show the results of our pattern sensitivity analysis for the pointswap modification function in Fig. 8(c). Cross signs mean that the respective FD did not yield a monotonic increase of distances. The entire overview of our results for all degeneration functions and base patterns, as well as every distance distribution, can be explored on our interactive website 3 .

In summary, most feature vectors show low sensitivity (i.e., are tolerant) to our masking function. However, for structural degeneration (point-swap and index-swap), there are significant differences in the sensitivity of all FDs. In most cases, a FD is tolerant for all or for none base pattern. In our analysis, we found that MPEG7 COLOR LAYOUT and GABOR performed best across all modification functions.

Pattern Discrimination (C4)

Our last criteria focuses on how much an individual FD is able to discriminate different patterns, i.e., blocks, lines, etc. High discrimination means that an FD allows distinguishing between patterns. The respective DDM must show overall high values.

To measure discrimination for a given FD, we investigate pairwise distances between all feature vectors v for every FD, across all patterns. In order to obtain a single measure for all the pairwise differences per FD, we report on the median values of distances (we cannot assume distances to be normally distributed), as well as their scatter. High median distances indicate high distances among feature vectors for different patterns, suggesting a high ability to discriminate patterns. High scatter means that this FD can discriminate only a few patterns. Fig. 7 shows box plots with 25% and 75% quartiles for all FDs. A median distance of 0.0 would mean that FDs, across patterns, look all the same and hence this particular FD cannot represent the difference between patterns. A value of 0.5 means that FDs for different patterns are different by 50%. Our results suggest that most measures are capable of producing different vectors for different patterns. High discrimination is achieved with BLOCKS, EDGEHIST, and LOCAL BINARY PATTERN. Small spreads are found for BLOCKS, THUMBNAIL and MPEG7 EDGE HISTOGRAM. FDs with smaller discrimination and high spread (e.g. FAST or GABOR) may still show differences between individual patterns.

FEATURE DESCRIPTORS FOR MATRIX PATTERNS

From our experiments, summarized across all criteria in Fig. 9, we can now choose a purposeful subset of FDs that allows us to describe our matrix pattern selection. The exact choice of FDs required for a specific application may vary, but starting with our set of selected FDs -the MAGNOSTICS set-is expected to be a suitable fit. We disregarded FDs, which did not perform well with respect to our criteria C1-C4 or were outperformed by another FD for the same pattern.

We generally found that some patterns, e.g., blocks or off-diagonal blocks, appear to be easier to detect for our FDs than others, e.g., bands and bandwidths. This may be due to the fact that these patterns are (mostly) positioned around the diagonal/counter-diagonal. Especially, for lines our FDs allowed for little translational invariance (shifts in the x-/y-positions). For our selection we also found that we should incorporate trade-off considerations between pattern response (C1) and the pattern variability (C2), since for some patterns more variations can be expected then for others.

In summary, we selected six FDs for MAGNOSTICS that we found most purposeful according to our experimental comparison in the preceding section. For each FD we briefly describe its name, functionality, which patterns it detects, and report on variability (C2), stability (C3), discrimination (C4).

Block Descriptor

We designed the BLOCKS descriptor as a heuristic to measure the blockiness of matrix plots along the diagonal, thus allowing us to retrieve matrices with a Diagonal-Block matrix form . The BLOCKS FD, shows to be good in all the experiments (C1-4) with a F 2 score of 0.98, a high variability of 0.48 and a good sensitivity score of 0.68 for all degeneration functions. In a sliding window approach, the descriptor linearly scans for rectangles of a minimum size (width/height) and density (black to white ratio). Found blocks are iteratively enlarged if either the horizontal, vertical and diagonal direction leads to a block density increase. In a post-processing step we remove all blocks, which are fully covered by other blocks. In contrast to the minimum density factor, we also calculate a factor describing the separatedness/distinctiveness of a block

Local Binary Pattern Descriptor

The LOCAL BINARY PATTERN (LBP) texture descriptor [START_REF] Heikkl | A texture-based method for modeling the background and detecting moving objects[END_REF] is classically used for background-foreground detection in videos. In our experiments the descriptor showed to be responding to the off-diagonal block patterns . In comparison to our BLOCKS FD, which is designed for blocks along the matrix diagonal, LBP adds an additional off-diagonal component to the MAGNOSTICS feature vector. It performs well for the C1 and C2 experiments, with F2 score of 0.9 and a high variability of 0.46, but appears to be sensitive to index swaps. An alternative choice for Off-Diagonal Blocks can be the TAMURA textual FD, which is significantly more sensitive to noise.

In a sliding window approach the FD constructs histograms of pixel intensities, called local binary patterns (LBP) for a central pixel to N neighboring pixels.

Low Distance High Distance

Distance-to-Noise (higher better)

Distance-to-Base-Pattern (lower better)

Profile Descriptor

We designed the PROFILE descriptor with the aim to describe lininess characteristics (many/few short/long lines) in matrix plots. In our experiments the FD responds with a perfect F 2 score of 1.0, and distinguishes clearly between the base pattern variations, thus leading to a quite low variability score of 0.28. As all other FDs it reacts moderately to noise. However, C1 and C2 make this FD especially suited for query-by-example search tasks. The PROFILE FD computes two axis-aligned histograms of the plot, where every matrix row, respectively column, represents one histogram bin and the bin's value corresponds the number of black pixels within the respective row. In order to achieve translation invariance (i.e., an otherwise empty matrix with just one row/column line should be equally scored independent of the line's location) we are computing a standard deviation from the profile histogram with the intuition that matrix plots with many lines will show high values, while nearly empty matrices or highly blocky matrices will show low values (few jumps).

Low Distance High Distance

Distance-to-Noise (higher better)

Distance-to-Base-Pattern (lower better)

MPEG7 Edge Histogram

The MPEG7 Edge Histogram FD [START_REF] Park | Efficient use of local edge histogram descriptor[END_REF] can be used to retrieve lines along the diagonal . It responds most often to the band pattern (F 2 score of 0.92) and allows for some variability (0.42). As all other FDs, MPEG7 EDGE HISTOGRAM FD has problems to deal with pattern degenerations, which might be due to the high specificity of the pattern. The FD subdivides an image into 4 × 4 sub-images. From each sub-image an edge histogram (5 bins with vertical, horizontal, 45degree diagonal, 135-degree diagonal and non-directional edge types) is extracted [START_REF] Won | Proceedings, Part III, chap. Feature Extraction and Evaluation Using Edge Histogram Descriptor in MPEG-7[END_REF].

Low Distance High Distance

Distance-to-Noise (higher better)

Distance-to-Base-Pattern (lower better)

Color and Edge Directivity Descriptor (CEDD)

The CEDD descriptor [START_REF] Chatzichristofis | Cedd: color and edge directivity descriptor: a compact descriptor for image indexing and retrieval[END_REF] showed a good response to the bandwidth pattern. It incorporates color and texture information in a histogram form. While the texture information uses the same MPEG7 EHD implementation as described above, the color histogram is constructed from an adaptive binning of the HSV color space.

Low Distance High Distance

Distance-to-Noise (higher better)

Distance-to-Base-Pattern (lower better)

Although, CEDD does not have the best scores in our MAGNOSTICS evaluation (F 2 of 0.81, Variability of 0.48), we decided to include the CEDD FD. Similar to the closely related FCTH, CEDD outperforms the other FDs in terms of variability, which is an important factor for bandwidth patterns ( ). These patterns are often the result of graphbased reordering methods (e.g., the Cuthill-McKee matrix reordering), which enumerate row-/column permutations in a breath-first search leaving an envelope shape behind.

Haralick Texture Descriptor

The HARALICK FD [START_REF] Haralick | Textural features for image classification[END_REF] is one of the classical texture descriptors for images. It responds quite reliably to the noise anti-pattern . For Fig. 10: Query-By-Sketch interface for exploring large collections of matrix plots. The user can sketch in the canvas (1) an approximated matrix pattern and retrieve a ranked result list (2) according to a selected MAGNOSTICS FD [START_REF] Bay | Speeded-up robust features (surf)[END_REF].

this pattern we conducted only the C1 experiments, since C2-C4 are not meaningful. We decided to include Haralick even though its F 2 score is only 0.83, which is less accurate than three other color intensity approaches (GLOBAL COLOR HISTOGRAM, FUZZY HISTOGRAM, COMPACTNESS). However, Haralick is generally more expressive and reliable allowing to quantify a greater variety of noise levels.

We also experimented with our own STATISTICAL SLIDINGWIN-DOW noise descriptor, which regards the sliding window values as a time series of differences for subsequent regions in the image. On this time series we calculated average, variance, and standard deviation.

Low Distance High Distance

Distance-to-Noise (higher better)

APPLICATION SCENARIOS

In this section, we report on two use cases that apply the MAGNOS-TICS FDs to support exploration of large matrix view data, specifically searching in a database of networks and matrices, and analyzing network changes over time. In both cases, MAGNOSTICS helps to retrieve information (matrices, or changes in a series of matrices) relevant to the respective task.

Searching in Collections of Networks

Large collections of networks may occur in many applications. As an example, von Rüden reports in [START_REF] Von Rüden | Separating the wheat from the chaff: Identifying relevant and similar performance data with visual analytics[END_REF] about existing matrix collections from the high-performance computing domain with more than 290,000 matrix plots with the analysis goal to retrieve matrices with similar patterns. Another example of large matrix collections is the results of the cross-product between networks/tables and their matrix reordering algorithms as presented in [START_REF] Behrisch | Matrix Reordering Methods for Table and Network Visualization[END_REF].

For the retrieval of similar patterns we developed a prototypical query-by-sketch interface, depicted in Fig. 10, which can also be accessed online 4 . The query-by-sketch interface allows the user to describe intuitively the expected visual patterns by drawing a sketch of a sought matrix pattern (Fig. 10 (1), and receiving a ranked list of similar images (Fig. 10 (2)) according to one or multiple selected feature descriptors (Fig. 10 (3)). For each individually selected FD the feature vectors of the sketch image and the database images are compared (Euclidean distance) to retrieve a ranking score. The MAGNOSTICS FD set is also available: Here, a derived six-dimensional feature vector is constructed by calculating the Distance-to-Base-Pattern for every individual MAGNOSTICS FD. The query image feature vector is subsequently compared with the Euclidean distance to the image feature vectors in the database. Fig. 10 shows an example using the BLOCKS descriptor for the matrix reordering data set collection with 4,313 matrices [START_REF] Behrisch | Matrix Reordering Methods for Table and Network Visualization[END_REF]. Matrices show several blocks for the drawn sketch.

Dynamic Network Analysis

Another challenge in the realm of large data collections are networks changing over time; every time step represents the network at a different time instance. Fig. 11 shows 11 matrices from a dynamic brain connectivity network, usually comprising around 300 time points (individual matrices). Brain connectivity refers to the co-variance (connection) between activity in brain regions (regions of interest, ROI). Neuroscientists are specifically interested in clusters (Blocks) and their evolution, as well as in identifying noisy time periods. Here, a time point represents 2-seconds, and dark cells indicate high connectivity (binarized to obtain un-weighted network). Rows and columns in the matrices are ordered to optimize the visual patterns independently for each matrix.

To find time points with major changes with respect to noise and blocks, we first calculate a feature vector v i for every matrix (time point) t i with HARALICK (noise) and another one with BLOCKS. Then, we calculate the difference for each feature vector v i and the following time step v i+1 (separately for both HARALICK and BLOCKS). High distances indicate high changes between two consecutive time points, low distances indicate little change (with respect to noise). Fig. 11 shows both distances plotted (red=BLOCKS, blue=HARALICK).

For noise we can observe major differences between time points 11-14, while the type of blocks changes most between time points 6-8. Both changes are observable in the respective matrices. Further, we observe, between 9 and 15, a constant change (constant distances) for the BLOCKS FD (red), indicating a salient trend; a possible explanation could be the change from two separate blocks (clusters) to one larger block.

DISCUSSION AND EXTENSIONS

Quantifying patterns in visualizations is an active research field with varying approaches. While pattern measures can also be derived from the data space, in our case by graph analysis, MAGNOSTICS follows the idea to take advantage of screen-space measures. This has the advantage that a direct correspondence to the human perceptual system can be constructed.

With MAGNOSTICS we propose an initial set of feature descriptors which showed appropriate based on certain desirable criteria (see Sect. 4.4) and showed useful to support ranking, searching and clustering of matrices (see Sect. 7).

Defining and Retrieving Interesting Matrix Views

While we have focused on six specific patterns and their variations, we believe our criteria and methodology from Sect. 4 will allow for the selection of FDs for different patterns including directed and weighted networks, as well as application specific patterns. Also, higher-level visual characteristics of matrices, such as the degree of "clumpy-ness" could be investigated with our MAGNOSTICS evaluation approach.

Further criteria for an effective MAGNOSTICS FD could also be considered. For example, the human users' assessment of feature descriptor quality in light of matrix exploration tasks could influence the FD selection process in a user-centric fashion. For example, lines may still be visible to humans, though the algorithms may not detect them and vice versa. It may also be interesting to link MAGNOSTICS analysis with interactive matrix exploration techniques. For example, the NodeTrix approach [START_REF] Henry | NodeTrix: a hybrid visualization of social networks[END_REF] includes node-link views aside the matrices, hence we would also need to include FDs for node-link views to jointly rank interesting views.

A scenario we have not followed further, but which is described in Scagnostics [START_REF] Wilkinson | Graph-theoretic scagnostics[END_REF], is to present matrix views that are most different from the others, i.e., outlier views. Since MAGNOSTICS is based on the distances between feature vectors, it is straightforward to cluster matrix views based on the feature-vector distances and to report on more common views and outliers. Finally, MAGNOSTICS can be embedded in interactive approaches, in that FDs get weighted either explicitly by the user, or implicitly by a function analyzing an user's preferences while navigating the matrix space.

Given that FDs and their corresponding distance functions are the basis for many data analysis tasks, more application scenarios as the presented can be supported. In this work we considered ranking and searching tasks. Other potentially useful applications include the classification of matrix views according to expected classes, according to user interest or the clustering of matrix views.

Novel Image Measures for Matrix Diagnostics

Another open question remains the development of novel feature descriptors for matrices. As described in the previous section, there may be more visual patterns important to users of matrix analysis. While our FDs are global, a natural extension would be to consider local FDs, focussing on specific subnetworks. Furthermore, we considered adjacency (binary) matrices, but MAGNOSTICS could be extended with FDs also for continuous matrices (e.g., representing weighted networks).

Finally, we mention that the MAGNOSTICS framework can easily be applied to evaluate existing matrix reordering algorithms in terms of the visual patterns they produce. Our approach could even inform the design of new reordering algorithms which aim to optimize matrix views for certain user-dependent patterns of interest.

CONCLUSION

We introduced MAGNOSTICS, an experimentally validated set of view descriptors aiming to guide exploration of large network collections, represented as matrix views. Starting from a set of 30 feature descriptors, including three novel specifically designed FDs, we identified a set of six useful FDs for the analysis of visual patterns in matrices. The selection of descriptors was guided by a structured and explorative methodology, using a novel large matrix benchmark data set and based on four quantifiable criteria: (1) pattern response, (2) pattern similarity, (3) pattern sensitivity and (4) pattern discrimination. We demonstrated how MAGNOSTICS can be applied in an interactive ranking and searching tasks, and to analyze time series of networks. MAGNOSTICS complements the set of previous feature-based analysis frameworks in the context of Visual Analytics tools.

Fig. 2 :

 2 Fig. 2: A Selection of Patterns and Anti-patterns in Matrices.

Fig. 4 :

 4 Fig. 4: Examples of matrices as used in benchmark. Benchmark data set can be downloaded at our MAGNOSTICS website.

Fig. 5 :

 5 Fig. 5: Distances between two selected feature vectors (THUMBNAIL and COMPACTNESS) of different pattern variations.

Fig. 6 :

 6 Fig. 6: Relations between degeneration levels and mean distance (red) to base patterns.In analyzing the monotony we (1) assess if there is any monotonic increase or not. If the increase in not monotonic the respective FD is very sensitive to any degeneration, i.e., the FD cannot accurately rank matrices according to their amount of noise. (2) For monotonic plots, we can then quantify the sensitivity of the FD: highly sensitive (fast increase of distances) or tolerant (slow increase of distances).Fig.6shows examples of monotonic increases of distances. The x-axis shows the degeneration level, the y-axis shows the distance to the average of one base-pattern vector. Each point in the plot represents the distance of a sample. The red points and line represent average distances. Fig.6(a) shows low sensitivity, (b) high sensitivity, (c) medium sensitivity but with a high variation in the distances, and (d) non-monotonically increasing distances.To quantify monotony of the 150 DDMs and to better inform our final choice, we calculated a quality metric for the monotony of a feature descriptor FD i and a base pattern P j as follows

Fig. 7 :

 7 Fig. 7: Pattern Discrimination (C4): High mean values indicate high distances between feature vectors for the individual patterns (CI=95%).

Fig. 8 :

 8 Fig. 8: Analysis result overview for all FD and patterns: (a) C1: numbers present the F2-score; higher scores (darker) indicate better response to the pattern, (b) C2: high values (darker) indicate higher variability between patterns, (c) C3: low values (darker) indicate lower sensitivity.

Fig. 9 :

 9 Fig. 9: Result table showing all values. Colors correspond to criteria (blue=C1 (response), red=C2 (variability), brown=C3 (sensitivity)). Black dots in each colored rectangle indicate our subjective ranking; 3 dots represent high ranks, 0 dots indicate low ranks.

Fig. 11 :

 11 Fig. 11: Detail from a dynamic network representing brain connectivity (300 time records).

  Manuscript received xx xxx. 201x; accepted xx xxx. 201x. Date of Publication xx xxx. 201x; date of current version xx xxx. 201x. For information on obtaining reprints of this article, please send e-mail to: reprints@ieee.org.

Digital Object Identifier: xx.xxxx/TVCG.201x.xxxxxxx

http://magnostics.dbvis.de/#/evaluation/patternresponse

http://magnostics.dbvis.de/#/sketch

ACKNOWLEDGMENTS

The authors wish to thank Nayeem Khan for the discussions that contributed to this work. We also thank Bianca Orita, Manuel Hotz and Raffael Wagner for the development of the block feature descriptor and the statistical noise descriptor. The authors thank the German Research Foundation (DFG) for financial support within project A03 "Quantification of Visual Analytics Transformations and Mappings" of SFB/Transregio 161.


Simon Pouil

Jean-Louis Teyssié

Claude Rouleau

Scott W Fowler

Dr Marc Metian
email: m.metian@iaea.org

Paco Bustamante

Michel W Warnau

Pacobustamante

Comparative study of trophic transfer of the essential metals Co and Zn in two tropical fish: a radiotracer approach

Keywords: Cobalt, Zinc, Assimilation, Kinetics, Tissue distribution, Interspeciesdifferences

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Essential metals are part of the functional groups of various enzymes, play a structural role in respiratory pigments and metalloenzymes,and can act as activating co-factors for various enzymes (see e.g. [START_REF] Simkiss | Metal ions in cells[END_REF][START_REF] Williams | The Bakerian lecture, 1981: Natural selection of the chemical elements[END_REF]. For example, Co is a key component of vitamin B12 (cyanocobalamin), which is a coenzyme in a number of cellular processes including the oxidation of fatty acids and the synthesis of DNA (e.g. [START_REF] Blust | Cobalt[END_REF]). Zn has structural and catalytic roles in many proteins and almost 10% of all genes in sequenced fish genomes carry the annotation of Zn binding (e.g. [START_REF] Hogstrand | Zinc[END_REF]). Healthy conditions of fish are optimal if these elements are present in sufficient amounts in their tissues: depletion in these elements can provoke pathological damages and/or physiological alterations and their excess can also lead totoxic effects (e.g. [START_REF] Rainbow | Trace metal concentrations in aquatic invertebrates: Why and so what?[END_REF]Förstner&Wittmann 2012).

In fish, foodappears increasingly as an important pathway for acquiring essential metals (e.g. [START_REF] Xu | Exposure and potential food chain transfer factor of Cd, Se and Zn in marine fish Lutjanusargentimaculatus[END_REF][START_REF] Mathews | Dominance of dietary intake of metals in marine elasmobranch and teleost fish[END_REF]. For example, the metal intake from the diet in the teleost Scophthalmus maximus was estimated to be responsible for more than 70% of the body burden of Co, Mn and Zn [START_REF] Mathews | Dominance of dietary intake of metals in marine elasmobranch and teleost fish[END_REF].Despite a growing dataset showing the major role that foodplays in essential and non-essential metal accumulation in fish (e.g. [START_REF] Spry | Relative contributions of dietary and waterborne zinc in the rainbow trout, Salmo gairdneri[END_REF][START_REF] Zhang | Effects of Zn pre-exposure on Cd and Zn bioaccumulation and metallothionein levels in two species of marine fish[END_REF], there is still limited understanding of the factors that influence metal assimilation at the interspecific level. Among these factors, feeding strategies have been reported to be crucial in the differential metal assimilation incoexisting species (e.g. [START_REF] Ni | Transfer of Cd, Cr and Zn from zooplankton prey to mudskipper Periophthalmuscantonensis and glassy Ambassisurotaenia fishes[END_REF].

A key parameter for understanding and modeling metal trophic transfer in fish is the assimilation efficiency (AE). This variablecan be easily determined under laboratory conditions,using radiotracer techniques (e.g. Mathews et al. 2008;[START_REF] Pouil | Trophic transfer of 110m Ag in the turbot Scophthalmus maximus through natural prey and compounded feed[END_REF]. A complementary approach is the determination of the dynamics of inter-organ metal transfer, based on the measurements of metal in the different organs and tissues at different time intervals during the depuration phase. Although of interest, this approach is not very commonly reported in the literature. It has however been applied fortoxicokineticstudies in fish (e.g. [START_REF] Hogstrand | Internal redistribution of radiolabelled silver among tissues of rainbow trout (Oncorhynchus mykiss) and European eel (Anguilla anguilla): The influence of silver speciation[END_REF] or with other aquatic aquatic active predatorslike cephalopods [START_REF] Bustamante | Biokinetics of zinc and cadmium accumulation and depuration at different stages in the life cycle of the cuttlefish Sepia officinalis[END_REF][START_REF] Bustamante | Uptake, transfer and distribution of silver and cobalt in tissues of the common cuttlefish Sepia officinalis at different stages of its life cycle[END_REF].

In this context, the present work investigated the trophic transfer of two essential elements (Co and Zn) in adults and juveniles of two tropicaleuryhalinefish species, the silvermoonyMonodactylus argenteus and the spotted scatScatophagusargus,using gammaemitting radiotracers( 57 Co and 65 Zn).Thisbiokinetic study has focused on obtaining transfer rate data for tropical fish species given the fact that the majority of availableinformation has to date come from studies carried out with temperate species. Recent reviews on the topic of trace element and radionuclide transfer in marine organisms have stressed the need for more data on tropical species in order to make valid comparisons on a global scale (see e.g. Fowler &Fisher 2005).

Two levels of biological organization were considered in this study, i.e. the whole organism and the different organs and tissues, in order to evaluate the biokinetic parameters of the metal depuration and to identify metal transfer dynamics among the body compartments during the depuration phase.

Materials and Methods

Acclimation of organisms

One hundred juveniles and 20 adults of each species (silvermoony M. argenteus and spotted scat S. argus)were shipped to the International Atomic Energy Agency-Environment Laboratories" premises in the Principality of Monaco. Fish were acclimated for 3 months to laboratory conditions, adjusted to replicate as closely as possible their natural tropical environment (2000-L tank for adults and 700-L aquarium for juveniles;open circuit: 200 L h -1 in each tank;0.45-µm filtered seawater; salinity: 35p.s.u.; temperature: 25 ± 0.3°C; pH: 8.1 ± 0.1; light/dark: 12h/12h). During the acclimation period for both species, the juvenile fish were fed 3 to 4 times per day with adult brine shrimp (Artemiasalina) at a daily ration of 130-290 mg wet weight (wwt)per individual. Adults were fed4 times per day with compounded pellets (JBL Mariperls ® ) at a daily ration of 1.6-2 g dry weight (dwt)per individual. Virtually no mortality was observed during the acclimationperiod. Since body size (age) is known to affect metal bioaccumulation in marine organisms [START_REF] Boyden | Trace element content and body size in molluscs[END_REF]Warnau et al. 1996a;[START_REF] Hédouin | Allometric relationships in the bioconcentration of heavy metals by the edible tropical clam Gafrariumtumidum[END_REF]), only individuals with homogeneous sizes were used in the experiments.

Experimental Procedure

Radiolabelling of brine shrimp

In order to investigate the trophic transfer of the two essential elements (Co and Zn) by M. argenteus and S. argus, adult brine shrimp (Artemiasalina) were used as prey. Preparation of the radiolabelled brine shrimp was carried out by exposing them for 18 h in aerated 20-L aquaria(approx. 300gwwt of adult brine shrimp per aquarium). At the end of the exposure period, brine shrimp were brieflyrinsed and stored at -20°C. Exposure was repeated using 6 batches of brine shrimp in order to obtain enough radiolabelled food for trophic transfer experiments (with both juvenile and adult fish). Radiotracers of high specific activity were purchased from CERCA, France ( 57 Co, [T 1/2 ] = 271.8 days) and Amersham, UK ( 65 Zn, [T 1/2 ] = 243.9 days). Stock solutions of radiotracers were prepared in 0.1 M HCl.

Seawater was spiked with the radiotracers (nominal activity of 3kBq L -1 for Co and 2 kBq L -1 for Zn). Small volumes (1 mL) of the diluted radiotracer solution were added to the aquaria (close circuit), and no change in pH and salinity was detectable after the tracer addition. At the end of the exposure period, average activities in the brine shrimp were 239 Bq g -1 wwt for 57 Co and 40 Bq g -1 wwt for 65 Zn.

Exposure of juvenile fish

One batch of 86juvenile silvermooniesandone of 96 juvenile spotted scats (8.4 ± 1.4gand 4.8 ± 1.4g wwt, respectively) were eachtransferred intoa 70-L aquarium (open circuit: 100 L h -1 ; aerated, 0.45-µm filtered seawater; salinity: 35p.s.u.; temperature: 25 ± 0.3°C; pH: 8.1 ± 0.1; light/dark: 12h/12h)prior tothe exposure to radiolabelled brine shrimp.

The experiment consisted of a single exposure to radiolabelled brine shrimp via ingestion (thawed prey, single feeding method also called pulse-chase feeding; see e.g. [START_REF] Metian | Metal and metalloid bioaccumulation in the Pacific blue shrimp Litopenaeusstylirostris (Stimpson) from New Caledonia: Laboratory and field studies[END_REF][START_REF] Pouil | Trophic transfer of 110m Ag in the turbot Scophthalmus maximus through natural prey and compounded feed[END_REF]. Juvenile fishwere fed ad libitum for 1.25 h in a closedcircuit system (247gwwt and 255g wwtof radiolabelled brine shrimp distributed to silver moony and spotted scat, respectively). Two hours after the beginning of ingestion, all fish were whole-body γcounted alive and each batch of fish was removed and divided into two groups. Twenty-one individuals were transferred into a 20-L aquarium containing clean, flowing seawater (parameters as previously described). The remainder of the fish were returned into the initial 70-L aquarium. No regurgitation of the ingested radiolabelled brine shrimp was observed.

The 21 individuals from the 20-L aquarium were weighed separately (for individual recognition) and γ-counted alive (see section 2.3)at different time intervals over 45d to follow the whole-body depuration kineticsof 57 Co and 65 Zn. The aquarium was cleaned during each counting period to avoid contamination from radiotracerscontained in the faeces.Fish from the 70-L aquarium were regularly sampled (n=3) using the same protocol, anesthetizedand dissected (see section 2.2.4) after γ-counting.

Exposure of adult fish

Eighteenadult silvermooniesand 13 adult spotted scats (81 ± 12g and 193 ± 35g wwt, respectively) were fed ad libitum in a 70-L aquariumduring 6 h with thawed radiolabelled brine shrimp (i.e. 11 feedings for 30min each time) in order to maximise the ingested activity in the fish (total distribution of 795g of radiolabelled brine shrimp for both species). Due to the size of adult individuals, γ-counting was not performed with livingwhole organisms;thus, 3 fish were randomly collected at different time intervals and dissected during the 45-d depuration period. For this purpose, fish were anesthetized, sacrificed and dissected into 15 body compartments (see details in section 2.2.4).

Body distribution of metals in fish

Juvenile fish maintained in the 70-L aquarium and all adults were regularly sampled, anesthetized usingeugenol,and dissected in order to compare the metal organotropism in the tissues of both species. At each sampling time, 3 individuals (for both juvenilesand adults) were dissected intothe followingbody compartments: (1) muscles with the skin, (2) stomach and pyloric caeca, (3) intestine, (4) liver, (5) gall bladder, (6) pancreas and spleen, (7) kidneys, (8) heart, (9) gills, (10) eyes, (11) brain, ( 12) skeleton ( 13) head, and in addition for adult fish (14) gonads and (15) red gland.All compartments were separated, weighed (wwt) and radio-analysed (see section 2.3) to determine the radiotracer distribution among the various tissues. During all the experiments, no mortality occurred.

Radiotracers and Counting

The radioactivity of the tracers was measured using a high-resolution γ-spectrometer system composed of 3 Germanium N type detectors (EGNC 33-195-R, Intertechnique ® ) connected to a multi-channel analyser and a computer equipped with spectra analysis software (Interwinner 4, Intertechnique ® ). The radioactivity in live organisms and tissue samples was determined by comparison with known standards of appropriate geometry (calibration and counting).

Measurements were corrected for background and physical radioactive decay. Liveorganisms were placed in polystyrene counting tubes (diameter: 80 mm, height: 50 mm), filled with clean seawaterduring the counting period. The volume of seawater was kept as low as possible to ensure atthe same time the welfare of the fish and a constant geometry during the counting period(i.e. reduced fish movement). The counting time was kept as short as possible and adjusted to obtain a propagated counting error less than 5% (e.g. Rodriguez y [START_REF] Rodriguez Y Baena | A single vs double spike approach to improve the accuracy of 234 Th measurements in smallvolume seawater samples[END_REF][START_REF] Metian | Delineation of Pb contamination pathways in two Pectinidae: The variegated scallop Chlamysvaria and the king scallop Pecten maximus[END_REF]). In the case of radioanalysis oflive fish, counting timesgenerally ranged between 15 and 55 min.Tests were performed prior to the experiments, where fish were placed in similar counting conditions in order to observe their behaviour,i.e. in a counting box for 1 hour in the dark. Dissolved O 2 concentration was monitored throughout these tests and was always > 3mg L -1 . No alteration in organism health or behaviourwasobserved.

Data treatment and statistical analyses

Whole-body depuration kinetics in juvenile fish

Depuration of radiotracers was expressed as the percentage of remaining radioactivity (radioactivity at time t divided by the initial radioactivity measured in the organism at the beginning of the depuration period * 100; Warnau et al. 1996b). The depuration kinetics of the radiotracers were best fitted using a two-component exponential model(Eq. 1), with a decision based on F test and ANOVA tables [START_REF] Hédouin | Influence of food on the assimilation of selected metals in tropical bivalves from the New Caledonia lagoon: Qualitative and quantitative aspects[END_REF]):

(1) 𝐴 𝑡 = 𝐴 0𝑠 . 𝑒 -𝑘 𝑒𝑠 𝑡 + 𝐴 0𝑙 . 𝑒 -𝑘 𝑒𝑙 𝑡 where A t and A 0 are the remaining activities (%) at time t (d) and 0, respectively; k e is the depuration rate constant (d -1 ); "s" and "l" are the subscripts for the "short-lived" and "longlived" components, respectively. The short-lived component represents the depuration kinetics of the radiotracer fraction that is weakly associated with the organisms and rapidly eliminated (e.g. fraction in faeces), whereas the long-lived component describes the depuration kinetics of the radiotracer fraction that is assimilated by and tightly bound tothe organism (Warnau et al. 1996b). The long-lived component allows assessing the assimilation efficiency (AE) of the radiotracer ingested with food (AE = A 0l ). For each exponential component (s and l), a biological half-life can be calculated (T b½s and T b½l ) from the corresponding depuration rate constants (k es and k el , respectively) according to the relation T b½ = ln2/k e . The model was fitted using non-linear routines and model constants were estimated by iterative adjustment of the model, using the Quasi-Newton method in the Statistica ® software 7.0.

Distribution among body compartments (juveniles and adults)

For juveniles and adults of the two fish species,distribution of Co and Zn among the body compartments was determined over time andcompared usingthenon-parametric Mann-Whitney U test [START_REF] Zar | Biostatistical analysis: Third edition[END_REF]. Furthermore, in order to quantify the transfer of each element over time among the internal body compartments, the ratio of the concentration of Co and Zn in each organ and/or tissue (Bq g -1 wwt) over the whole-body (Bq g -1 wwt) was calculated (sicconcentration index, I c , as defined by [START_REF] Rouleau | Accumulation of silver from the diet in two marine benthic predators: The snow crab (Chionoecetesopilio) and American plaice (Hippoglossoidesplatessoides)[END_REF].Values of I c > 1 indicate that a tissue is enriched in Co or Zn compared to the average whole-body metal concentration.This indexcomplements the information provided by metal body distribution andis useful forquantifying and comparing the storage capacitiesof the different body compartments in fish whose weight and ingested activity were variable. Comparisons of I c values amongbody compartments werecarried out using theKruskall-Wallis non-parametric test,followed by a multiple-comparison test of Siegel and Castellan [START_REF] Zar | Biostatistical analysis: Third edition[END_REF].

The level of significance for all statistical analyses was always set at α = 0.05. All the statistical analyses were performed using either the Statistica ® software 7.0 or R freeware 3.0.1 (R Development Core Team 2014).

Results

Depuration kinetics and assimilation efficiencies of 57 Co and 65 Zn in juveniles

The whole-body depuration kinetics of 57 Co and 65 Zn following the ingestion ofradiolabeled A. salinasby thejuveniles of bothfish species were best described bya twocomponentexponential model (Table 1 and Fig. 1). Assimilation efficiency (AE) and retention capacities are metal-and species-dependent. Both species assimilated poorly 57 Co (AE <6%), whereasspotted scat assimilated 65 Zn more efficientlythan silver moony (AE = 24.2 ± 1.0%vs.14.7 ± 0.9%, respectively; p<0.05). Assimilated 57 Co and 65 Zn were slowly eliminated, with biological half-life (T b½l ) values ranging from 33 to 55 d for 57 Co and from 67 to 83 d for 65 Zn (Table 1).

Body distribution and body dynamic of metals

During the 45-d depuration phase, dissections were carried outregularly in order to determine the metal distribution among selected body compartments (see section 2.2.4). Figures 2,3 and 4 describe the distribution of Co and Zn,respectively, in the 4 main body compartments (i.e. stomach, intestine, liver, and muscles with skin representing 50-98% and 40-99%of total activity for Co and Zn, respectively) and in the remaining parts (i.e. the sum of the remaining body compartments) during the depuration phase in juveniles and adults of both species. The detailed distributions in each body compartment are provided in the supplementary material for this article. Considering elementdistribution, the depuration may be divided into three phases. The first phase (days 0-1), very rapid, corresponds to the passage of the food into the stomach which containsup to 80% of the radioactivity body burden at the end of the feeding period (85 min). The second phase (days1-4) is characterized by the occurrence of the digestive processes. During phases 1 and 2 (i.e. the first 4d of depuration), almost all the activity was distributed in the stomach and the intestine (up to 95% of the total body burden).

Then, after4 days a third phase can be depicted and corresponds to elementtranslocations among the main compartmentswhen whole-body activities are stable (i.e. whenthe absorbed fractionhas stabilized; Fig. 1). Gradually, the liver and the muscles with skin becomethen the predominant compartments in terms of trace element burden.Distributions arehoweverrelatively stable after day 10 except for Co inS. argus. Indeed, the percentage of 57 Co body burden in the liver tended to decrease between days 10 and 45 in both juvenile and adult fish,whereas a concomitant increase was observed in the muscleswith skin(Fig. 2 and Fig. 4).Distribution patterns over time were similar between the species, juveniles or adults, for 65 Zn (Fig. 3 and Fig. 4), but not for 57 Coin whichcase the distribution in the liver was significantly higher in S. argus than in M. argenteus (Fig.2 and Fig. 4;p<0.05).

In terms of concentration index, I C , Tables 2 and3 provide a ranking ofthe I C for Co and Zn, respectively, in each body compartment during the depuration phase in juveniles and adults of both species. The resultsindicate that after 2days 57 Co was mainly concentrated in the liverfor S. argusjuveniles and adults(Table 2).In the case of M. argenteus, there was no significant difference between the calculated I c values of juveniles and adults for all the compartments, although the liver and the pancreas seem to play an important role in the storage of 57 Co during the depuration phase. For 65 Zn,regardlessofthe species and the life stage,the highest values of I c were always measured inthe stomach and the intestine during the first 24hthen, after this period, in the gall bladder, the pancreas and spleen (Table 3; p<0.05).

Discussion

The tropical silver moony,Monodactylus argenteus, and the spotted scat,Scatophagusargus, were selected to investigate theassimilation,retention and transfer among organs and tissues of Co and Zn ingested from radiolabeled food under controlled laboratory conditions.

Experimental approaches commonly used, based on whole-body kinetics (e.g. [START_REF] Zhao | Biomagnification of radiocesium in a marine piscivorous fish[END_REF][START_REF] Mathews | Dominance of dietary intake of metals in marine elasmobranch and teleost fish[END_REF][START_REF] Pouil | Trophic transfer of 110m Ag in the turbot Scophthalmus maximus through natural prey and compounded feed[END_REF], do not allow easily discerningthe dynamics of metal transfer among organs and tissues. This fact underscores the originality of the present study since it combines different approaches to provide new information regarding the mechanisms of assimilation and the subsequent dynamics of translocation of these trace metals among the tissues and organs of these euryhaline fish.

At the whole-body level, results show that AEs of Co are quite similarfor the two fish species whereas theydiffer for Zn. Indeed, ranges of AE for 57 Co and 65 Zn in silver moony and spotted scat were 5-6% and 15-24%, respectively. These AEs are in accordance with those reported in the literature for other species of marine fish,for whichAEs ranged from 2 to 44% for Co and 1 to 52% for Zn (Table 4).

Many factors could explain the variations of AEs. [START_REF] Wang | Comparison of metal uptake rate and absorption efficiency in marine bivalves[END_REF] proposed in his review a ranking of these factors classified in 3 different categories: (1) environmental quality (such as food quality and quantity), (2) metal geochemistry and (3) feeding physiology and biology (such asingestion rate and gut passage time). Although only bivalves were considered in that review, these factors are generally relevant for fishas well. In the present study, interspecific difference in Zn AE was observed. Indeed, results indicated a higher AE for S. argus.Exposureconditions (i.e. the use ofradiolabeled brine shrimp as unique food for trophic transfer in both species maintained under the same experimental conditions) did not allow addressing categories (1) and (2) mentioned by [START_REF] Wang | Comparison of metal uptake rate and absorption efficiency in marine bivalves[END_REF]. Although both species are omnivorous, as indicated by their identical Fishbasetrophic levels (3.0 for the both species;

Froese and Pauly 2015a, b), differences exist in their trophic ecology.Indeed, analyses of the stomach contents from field surveys indicated that detritus is the main diet of M. argenteus [START_REF] Blaber | Fish of the Trinity Inlet System of North Queensland with notes on the ecology of fish faunas of tropical Indo-Pacific estuaries[END_REF][START_REF] Rainboth | Fishes of the Cambodian Mekong FAO species identification field guide for fishery purposes.Food and Agriculture Organization of the United Nations[END_REF],whereas S. argus feedsmainly onzoobenthos such as worms and nekton such as finfish [START_REF] Mills | The Tetra encyclopedia of freshwater tropical aquarium fishes[END_REF][START_REF] Monkolprasit | Fish composition and food habits in mangrove forests at Phang-Nga Bay and Ban Don Bay, Thailand[END_REF]Jeyasselan 1998). These observations suggestthat spotted scat has a stronger predatory behavior than silver moony.Dietary habits are related to specific mixes of digestive enzymes or at least to variability of some enzymes"activity (e.g. [START_REF] Furne | Digestive enzyme activities in Adriatic sturgeon Acipensernaccarii and rainbow trout Oncorhynchus mykiss: A comparative study[END_REF]. For example, among 6 fish species, [START_REF] Hidalgo | Comparative study of digestive enzymes in fish with different nutritional habits: Proteolytic and amylase activities[END_REF] have demonstrated that amylase displayedhigher enzymatic activity in omnivorous species than in carnivorous predators.Thus, in the presentstudy, the higher Zn AE measured in S. argus could be due to a more efficient enzymatic system for the digestion of brine shrimp than in silver moony.In short, spotted scat might be better "equipped" to deal with digesting complex multicellular prey. This suggested interspecific variation in the fish digestive enzyme array cannot explain the trends observed for Co. For this element, AEs were very low and very similar between the two fish species. Differences,however, occurredin terms of body distribution and I C .The Regarding the potential effect of thelife-stage, juveniles and adults of both specieshad comparable patterns of distribution and concentrations (i.e. "concentrationindex") for Co and Zn,i.e.the major fraction of both elements was found in the same organs and the metal concentrations in the organs were similar between the two life-stages.These comparable patterns can result from asimilar metabolism in juveniles and adults(viz. similar digestive activity and AE) although there were differencesin size (adults of silver moony and spotted scat were respectively 10 and 40 times larger than juveniles). In addition, it is important to note that adults of both species were notsexually matureat the moment of the experiment.This would potentially affect the results due to the non-negligible allocation of some essential elements to reproductive organs, especially in mature females with oocyte production(e.g. [START_REF] Protasowicki | Sex effects on Cd, Pb, Cu and Zn contents in selected fish organs[END_REF]Rajkowska&Protasowicki 2013).

Conclusion

The biokinetic approach at two levels of biological organization, (1) the whole organism and Parameters of depuration kinetics and their statistics are given in Table 1. argenteus) and spotted scat (S. argus) after a single feeding with radiolabelled brine shrimp and then maintained for 45d in a clean flowing seawater. Depuration parameters: A 0s and A 0l : activity (%) lost according to the short-and the long-lived exponential component,respectively;the A 0l value is also the assimilation efficiency (AE; %),T b½ : Zhang & [START_REF] Zhang | Significance of subcellular metal distribution in prey in influencing the trophic transfer of metals in a marine fish[END_REF]

  results highlightthe major role played by the liver in Co storage in spotted scat.This organ is involved in the mechanisms of detoxification and storage of Co,as previously shown in the European plaicePleuronectesplatessa fedradiolabeled annelid worms Arenicola marina, where Amiard-Triquet&Amiard (1974) reported a low Co AE with almost all the activity found inliver and kidney.Thus, trophic ecology could lead to the occurrence of specific mechanisms of storage and detoxification. Further investigation is howeverneeded to obtain a betterunderstanding of the mechanisms of detoxification and storage of Co in the twospeciesexamined in this study.

( 2 )

 2 the different organs and tissues, has provided animproved understanding of the mechanisms responsible forthe difference in Co and Zn assimilation efficiency observed betweenM. argenteus and S. argus.Dissections carried out at different times during the depuration provided new information about the dynamics of metal translocation in the different organs and tissues. Thus, changes observed in the Co distribution between the liver and the muscles in S. argusare a good example of the contribution of this radiotracerbasedmethodology. Theseresults also demonstrated interspecific variations in the assimilation and tissue distribution of Co and Zn in tropicalmarine fish.

Figure 1 .

 1 Figure 1. Whole-body depuration of 57 Co and 65 Zn after a single-feeding with radiolabelled brine shrimp in juvenile silver moony (Monodactylus argenteus, n=21) and spotted scat (Scatophagusargus, n=21) expressed as percentage of remaining activities (means ± SD).

Figure 2 .

 2 Figure 2. 57 Co distribution among 4 body compartments (intestine, stomach, liver, and muscles with skin) of juvenile silver moony (M. argenteus) and spotted scat (S.argus) over the depuration phase after feeding with radiolabelled brine shrimp. At each time three fish were dissected. All the values are expressed as percentage of the whole-body activity (means + SD).

Figure 3 .

 3 Figure 3. 65 Zn distribution among 4 body compartments (intestine, stomach, liver, and muscles with skin) of juvenile silver moony (M. argenteus) and spotted scat (S.argus) over the depuration phase after feeding with radiolabelled brine shrimp. At each time three fish were dissected. All the values are expressed as percentage of the whole-body activity (means + SD).

Figure 4 .

 4 Figure 4. 57 Co and 65 Zn distribution among 4 body compartments (intestine, stomach, liver and muscles with skin) of adult silver moony (M. argenteus) and spotted scat (S.argus) over the depuration phase after feeding with radiolabelled brine shrimp. At each time three fish were dissected. All the values are expressed as percentage of the whole-body activity (means + SD).

  biological half-life (d).ASE: asymptotic standard error; R 2 Comparison of Co and Zn dietary assimilation efficiencies (AEs; means in %) in marineand brackish water fish species. * Data obtained from FishBase(Froese &Pauly, 2015c)

Table 1 .

 1 Estimated depuration kinetic parameters of 57 Co and 65 Zn insilver moony (M.