Jérôme Boéro

Franck Schoefs
email: franck.schoefs@univ-nantes.fr

Jérôme Boero

Bruno Capra

Effect on Risk Based Inspection of spatio-temporal dependence of ROC curves: Study of the corrosion of steel harbour structures

Keywords: Decision process, detection theory, probabilistic modeling of inspection, Maintenance plans, Non-Destructive Testing (NDT) tools

come

Effect on Risk Based Inspection of spatio-temporal dependence of ROC curves: Study of the corrosion of steel harbour structures

Introduction

Reassessment of existing structures generates a need for up-dated materials properties. Non Destructive Testing (NDT) tools are often required for the inspection of coastal and marine structures where conditions of inspection are harsh. In these fields, the cost of inspection can be prohibitive and an accurate description of the on-site performance of NDT tools must be provided. Inspection of existing structures by a NDT tool is not perfect and it has become a common practice to model their reliability in terms of probability of detection (PoD), probability of false alarms (PFA) and Receiver Operating Characteristic (ROC) curves [START_REF] Rouhan | Probabilistic modelling of inspections results for offshore structures[END_REF]. These quantities are generally the main inputs needed by owners of structures in view to achieve Inspection, Maintenance and Repair plans (IMR) [START_REF] Sheils | Development of a two stage inspection process for the assessment of deteriorating bridge structures[END_REF] through Risk Based Inspections methods (RBI). The assessment of PoD and PFA is even deduced from inter-calibration of NDT tools or from the modeling of the noise and the signal [START_REF] Rudlin | The ICON database. Assisting underwater inspections[END_REF]. In this last case when the noise and the signal depend of the time and the location on the structure PoD and PFA are spatio-temporally dependent.

This aspect is highlighted for a steel sheet pile seawall submitted to uniform corrosion. In a first part, the probabilistic modeling of residual thickness measurements obtained by Non-Destructive Testing (NDT) tool is illustrated based on detection theory. Second part is devoted to the introduction of inspection results in decision process. Finally, results of cost analysis are compared with results obtained by the αδ method.

Corrosion of steel sheet pile seawalls in marine environment

Corrosion of steel structures is classically assessed by ultrasonic non destructive testing. In France, a protocol is given by the CETMEF (French Center for Maritime and Fluvial Technical Studies). This protocol consists in performing residual thickness measurements for several depths of the structure. By using this technique and considering the harsh conditions for marine inspections, the noise on the measurements at a given point on the structure cannot be neglected. Error comes both from the physical measurement (around 0.1 mm) and from the protocol (grinding, link diver-operator, etc.). Thus three measurements are performed on a given location: every 120° in a circle, with diameter of about 5 cm. The average of these three readings is considered as the "true" measurement of residual thickness. We assume that the variance between each of the three readings and their average corresponds to the noise.

In this paper, we use results given by two campaigns of corrosion measurements realised by ultrasonic non destructive testing at two times (T1 = 22 and T2 = 38 years) during the life of a wharf. Corrosion measurements are studied at two different depths (D1, D2). D1 is located in the zone of low seawater level and D2 in the immersion zone near the mud zone. In each case, characteristics of noise η and loss of thickness d ˆ (signal+noise) are illustrated on Fig. 1 and Fig. Loss of thickness due to corrosion increases logically in the time and is the most important in the zone of low seawater level (D1). Furthermore, loss of thickness decreases with depth. We also notice that the standard deviation of loss of thickness increases in the time, but decreases with depth.

Due to its definition, noise is represented by a mean equal to 0 and a standard deviation which seems to be constant for the two depths studied at a given time. We highlight the fact that standard deviation of noise is more important at time T1 that at time T2 (0.4 versus 0.3). At first, we explain this difference by an improvement of the quality of protocol in the time. However, this hypothesis must be validated through the analysis of the other corrosion measurements available within the framework of the project GEROM (Risk Management of maritime and river structures in harbours).

Probabilistic modeling of inspection based on detection theory

Probability of detection and probability of false alarm

Assessment of Probability of Detection (PoD) and Probability of False Alarm (PFA) from the knowledge of detection threshold can be directly deduced from inter-calibration of NDT tools [START_REF] Rudlin | The ICON database. Assisting underwater inspections[END_REF]. Generally these projects are expensive, and consequently, sometimes it is necessary to choose another approach. This article takes place in this context where inter-calibration is not available. So calculation of PFA and PoD results from probabilistic modeling of the noise and signal+noise pdf [START_REF] Rouhan | Probabilistic modelling of inspections results for offshore structures[END_REF].

Fig. 1 and Fig. 2 illustrate the probability density functions to be computed for the evaluation of PoD and PFA in the case where signal+noise and noise are represented by discrete and continuous distributions. The choice of the theoretical distributions and then the parameters to fit the data were be found by computing the maximum likelihood estimate. In most of time, loss of thickness is fitted by Gumbel distribution and noise by normal distribution.

Receiver Operating Characteristic (ROC) curve

ROC curve links the Probability of Detection and the Probability of False Alarm. For a given detection threshold a d , the couple (PFA, PoD) allows defining NDT performance. This couple can be considered as coordinates of a point in R 2 with axis PFA and PoD. Let us consider that a d takes values in the range ]-∞;+∞[, these points belong to a curve called Receiver Operating Characteristic (ROC).

ROC curves plotted on Fig. 3 and Fig. 4 are computed with the pdf presented on Fig. 1 and Fig. 2. ROC curves indicated " ROC " corresponding to discrete distributions and respectively " ROC' " to continuous distributions. Looking for the best detection performances, the probability of detection should always take larger values than the probability of false alarm (low noise sensibility). We have then PoD ≥ PFA.

The probability of detection is an increasing function of the defect size. This aspect is highlighted for example by ROC (T1-D1) and ROC (T2-D1).

ROC curve is a fundamental characteristic of the NDT tool performance for a given defect size. Perfect tool is represented by a ROC curve reduced to a single point whose coordinates are: (PFA, PoD) = [0, 1]. The worst curve is the one with the lowest signal / noise ratio (ROC (T1-D2)), meaning that some noise can be easily detected, even if nothing is to be detected and finally leading to a high number of false alarms. Overall performances are poor. At the opposite, the best plotted ROC curve is the one with a high signal / noise ratio (ROC (T2-D1)). Differences with the previous curve are considerable. The probability of detection reaches very quickly values near 1, with small probabilities of false alarms for high values of PoD. Overall performances are very good.

Introduction of inspections results in decision process

To introduce inspections results in a RBI scheme, conditional probabilities P i have to be defined. Then a bayesian modeling is suitable and decision theory offers the theoretical basis [START_REF] Rouhan | Probabilistic modelling of inspections results for offshore structures[END_REF]. Note that an inspection result can be entirely characterized by a set (PoD, PFA). So, in view to perform a cost analysis, points of ROC curves can be considered for the computation of P where characterizes the scenario in the decision tree [START_REF] Rouhan | Probabilistic modelling of inspections results for offshore structures[END_REF]. If the detection threshold is unknown, the performance of the technique is given by the whole ROC curve. Then, computation of P leads to project ROC curves on P surfaces. I i i∈ [1:4] i i n this case, P i are replaced in cost analysis by the following performance indicator (e.g. Eq. 1):

∫ = ROC ROC i ROC ROC i dl P L 1 ) ) P (( µ (1)
where is the curvilinear abscissa along the projected ROC curve on P ROC l i surface, ROC i P value of P i at this abscissa and the length of ROC curve in (PFA, PoD) plane.

This indicator can be interpreted as the ratio of the area under the projected ROC and the length of this curve in (PFA, PoD) plane.

ROC L

Optimization of the inspection plans lies generally on a minimization of a cost function. In case of inspections, two cost functions are considered. They are related to the cases of detection or no detection. For simplicity, we consider here the policy: a 'detection' leads to a repair; a 'no detection' leads to a failure in case of defect presence and to another inspection in case of defect absence.

In the following, we focus only on the cost overrun in case of no detection which is denoted nd ) C ( E (e.g. Eq. 2).

) ) P (( C ) C ( E ROC 3 3 nd µ = ( 2
)
where: is the extra cost associated to the event "defects knowing that there are no detected defects":

3 C failure inspection 3 C C C + = Extra cost expectation in case of no detection nd ) C ( E
is presented on Fig. 5 for values of γ equal to 0.1 and 0.9. γ corresponds to the probability of defect presence used in calculation of the conditional probabilities P i [START_REF] Rouhan | Probabilistic modelling of inspections results for offshore structures[END_REF]. Influence of γ on extra cost in case of no detection nd ) C ( E is more important for high probabilities of defects presence (0.5 to 0.9). Extra costs are minimum for corrosion measurements realized in the zone of low seawater level (D1) where loss of thickness is the most important. Consequently, due to the spatial dependence of corrosion process, extra costs increase with depth, i.e. in immersion zone (D2). The worst performance detection corresponding to corrosion measurements realized at the depth D2 where the signal+noise / noise ratio is the lowest. In this case, some noise can be easily detected, even if nothing is to be detected and finally leading to a high number of false alarms.

Performance detection increases between the two times of inspection (T1, T2) due to the temporal dependence of corrosion process which leads to an increase of signal+noise / noise ratio. These results lead to say that from a point of view of the detection, it's better to wait as long as possible before realizing corrosion measurements. However, to define the optimal inspection interval for structures, the probability of failure must be also introduced into the cost analysis [START_REF] Sheils | Development of a two stage inspection process for the assessment of deteriorating bridge structures[END_REF].

Finally, differences between extra costs obtained with discrete and continuous distributions are observed.

5 The αδ method: Effect of the shape of ROC curves on the decision process

Aim and principle

The αδ method lies on the characterization of ROC curves by the Polar coordinates of the Best Performance Point of the NDT tool (NDT-BPP). This point corresponds on the ROC curve to the minimal distance between the curve and the best performance point BPP of coordinates (PFA = 0, PoD = 1) [START_REF] Schoefs | Spatial dependence of Receiver Operating Characteristic curves for Risk Based Inspection of corroded structures: application to on-pile wharf[END_REF] NDT-BPP is defined by:

• the radius δ NDT equal to the performance index (NDT-PI) (distance between the best performance point and the ROC curve).

• the angle α NDT between axis (PFA = 0) and the line (BPP, NDT-BPP).

Objective of the αδ method is to perform parametric studies lying on two parameters to analyze the effect of the shape of ROC curves on the decision process: inspection, maintenance and repair. To achieve this goal, the influence of the performance of ROC curves, represented by δ NDT and α NDT , is appreciated through the expectation of the extra cost in case of detection

2

 2 Fig. 1 and Fig.2.

  Fig. 1 and Fig.2.

Figure 1 .

 1 Figure 1. Pdf of loss of thickness and noiseat time T1 for depths D1, D2.

Figure 2 .

 2 Figure 2. Pdf of loss of thickness and noiseat time T2 for depths D1, D2.

Figure 3 .

 3 Figure 3. ROC curves obtained at timeT1 for depths D1, D2.

Figure 4 .

 4 Figure 4. ROC curves obtained at time T2 for depths D1, D2.

NDTCE' 09 ,Figure 5 .

 095 Figure 5. Extra cost expectation in case of no detection nd ) C ( E .

Figure 6 .

 6 Figure 6. Mapping of extra cost in case of no detection nd ) C ( E in Polar plane for γ=0.9.

  extra cost in case of non detection nd ) C ( E .

NDTCE'09, Non-Destructive Testing in Civil Engineering

Nantes, France, June 30th -July 3rd, 2009

Influence of NDT-BPP Polar coordinates on extra costs and comparison with results obtained by cost analysis

The parameters of the αδ method (Polar coordinates of NDT-BPP) for the ROC curves plotted in Fig. 2 and Fig. 3 are indicated on mapping of extra cost in case of no detection (Fig. 6). Then a comparison between results given by mapping and cost analysis is made.

Variances exist between extra costs obtained with each of both methods when discrete distributions are used. We highlight the fact that due to the sensibility of extra costs to the Polar coordinates of NDT-BPP in the αδ method, the lack of precision on the value of α NDT when discrete distributions are used, can lead to a bad exploitation of the mapping.

On the contrary, the extra costs in case of no detection obtained with αδ method and cost analysis are coherent when continuous distributions of signal+noise and noise are used.

So, to increase the reliability during the exploitation of the previous mapping, we propose to use the projection on polynomial chaos to characterize the noise and signal+noise [START_REF] Schoefs | Inspection of Steel structures in Coastal Area with NDT tools: use of polynomial chaos decomposition for building Receiver Operating Curves[END_REF][START_REF] Schoefs | Assessment of spatially dependent ROC curves for inspection of random fields of defects[END_REF].

Conclusions

Concepts of ROC curves coming from detection theory are very useful in order to quantify the performance of Non-Destructive-Techniques. This paper reminds the main topics coming from detection theory and probabilistic modeling of inspections results in view to provide inputs in the computation of mathematical expectation of RBI cost models. These aspects are treated by an illustration of the process for the RBI of steel harbour structures submitted to uniform corrosion.

Effect of the shape of ROC curves on the extra costs is analyzed through the αδ method. The objective of these method is to assess the influence of the performance of NDT tools,


Pascal Casari

Pierre Ladevèze

Tsu-Wei Chou

DAMAGE MODELING AND CHARACTERIZATION OF A THREE-DIMENSIONAL WOVEN COMPOSITE

Keywords: damage, 3D, woven composites, mechanical properties, mesoscale

The characterization and modeling of the inplane damage behavior of a threedimensional woven composite are conducted with the use of the Mesoscale Composite Damage Theory, developed by Ladevèze. A first analysis of the composite fabric provides the main geometrical properties that can affect the mechanical behavior. A model previously established for aeronautical carbon/epoxy laminates is applied in a simplified version. It assumes an elastic and brittle behavior in the directions of the fibers, and degradation mechanisms like matrix micro-cracking and fiber debonding under a shear stress state. The model utilizes two experimental laws to be identified for the description of damage and inelastic strains. Then, the experimental procedure is presented by means of tensile tests on two relevant kinds of samples. The identification of the elastic, failure, damage and inelastic properties is performed. The comparison between complementary experiments and simulation shows a good fitting for small strains.

INTRODUCTION

This study deals with the characterization and modeling of damage in a 3D woven composite. A significant non-linear behavior can be observed through the mechanical response of this composite under inplane loading, except in the directions of the fibers. Then, a non-linear model, based upon the damage theory of Ladevèze [START_REF] Ladevèze | Sur la mécanique de l'endommagement des composites[END_REF], is applied in order to simulate the behavior of the composite. This study relies on a modeling and an associated experimental methodology of long-fiber reinforced cross-ply composites, which have been presented in [START_REF] Ladevèze | Damage modeling of the elementary ply for laminated composites[END_REF] and also in [START_REF] Herakovich | Mechanics of fibrous composites[END_REF] for aeronautical composite laminates made of unidirectional reinforcement. The analysis of the constitution of the material allows the use of this model for the modeling of the inplane behavior of the 3D composite. This methodology must also take the step of the identification into account, in order to make the characterization of damage and inelastic behaviors possible. As elastic, brittle failure, damage and inelastic properties must be measured, two tests at [0°] and [45°] from the warp direction have been chosen for their good sensitivity to these parameters. These classical uniaxial tension tests have been improved by measuring transverse strain and practicing loading-unloading cycles. Once the model has been identified, simulations of the behavior of cut-outs with orientations of [22.5°], [67.5°] and [90°] from 3D carbon plates have been performed. The comparison between tests response and simulation allow to predict the beginning of the stress/strain curves.

DESCRIPTION OF THE MATERIAL

The composite is manufactured under the shape of a plate made of a carbon woven preform and an epoxy resin. The orthogonal interlock fabric (Fig. 1) is made of T300 carbon fibers by Fiber Materials Inc. in one-run process. After manufacturing, some defects have been observed under a microscope (Fig. 1):

• Many voids appear in the resin-rich parts of the composite. Indeed, the interlock yarns are generating some paths in the fabric, which allow the resin to go through during injection, and the voids to stay there.

• The weft tows are curved by the pressure of the through-the-thickness tows. This predicts a reduction of stiffness compared to the behavior in the warp direction,

• The warp tows remain straight.

These remarks will help for the analysis of the stress-strain curves.

MODELING OF THE COMPOSITE

The mechanical behavior of the composite is modeled by means of damage mechanics. The goals of damage mechanics are to simulate the non-linear response of a material in the presence of damage and to predict the conditions for failure. The damage theory that serves as the foundation for this model was proposed by Ladevèze in 1986. It has been demonstrated in [START_REF] Guénon | Toughness properties of a threedimensional carbon-epoxy composite[END_REF] that, compared to the properties of a 2D laminate, the interlaminar fracture toughness of this composite is enhanced by adding through-the-thickness reinforcement. Our goal is not to analyze delamination in the composite, but to characterize the inplane behavior and then to evaluate the influence of the weaving on the inplane properties of the 3D composite

Mesoscale composite damage theory

In our configuration, the theory is called the mesoscale composite damage theory. It considers that damage is uniform through the thickness of individual layers of the composite. Mesoscale indicates that the scale of the analysis is between micro-mechanics (i.e., the level of the fiber and the matrix) and laminate analysis. Then the composite becomes a laminated structure made of two elementary constituents : layers (or plies) of composite and interfaces that separate the composite layers. The interface is considered to be a mechanical surface connecting two adjacent composite layers. Here delamination is not of interest, so the model is just an assemblage of composite layers. The main assumption is that the response of a damaged layer, at any load state, can be expressed in terms of elastic moduli degradation and inelastic strains due to damage and/or matrix plasticity, as depicted in Fig. 1. Degradation of the elastic moduli is expressed in terms of damage parameters that are functions of the associated thermodynamic forces which serve as damage evolution parameters. The modulus degradation parameters are internal variables, and the thermodynamic forces are the corresponding associated variables. The micro-level damage mechanisms taken into account are matrix micro-cracking, fiber debonding and fiber fracture. They are not identified explicitly in the mesoscale damage model ; damage evolution is identified on the stress-strain curves of tests on samples. Indeed, as damage occurs, the material loses stiffness and exhibits nonlinear, inelastic response with permanent strains after unloading.

E 0 E 0 (1-d) ε p ε σ σ y ε e

Fig. 1: Theoretical inelastic stress/strain response of damaged composite

The damage theory is explained below in a simplified case for this particular material because only two tests have been taken into account for characterization, which doesn't allow the full identification of a more complete model that would take damage in the transverse direction into account.

Modeling of the elementary ply

The laminate, made of a stacking sequence of 13 plies in the warp direction and 14 plies in the weft direction, is considered to be in a plane stress state. The elementary ply is here any of the warp or weft layers, considered to have the same behavior. In what follows, subscripts 1 and 2 designate, respectively, the fiber direction and the transverse direction of the elementary ply.

The developments of the model are based upon the classical laminate theory in a plane stress state. The initial values of moduli (Fig. 1) are indicated E 0 . In the direction of the fibers, the behavior is linear and brittle. In shear, a progressive damage is generating a non-linear behavior.

Effective Stress and response

The effective stresses are the stresses acting over the damaged area that effectively resists the forces. In a general case, any stress component σ i can be affected by a damage parameter d i ranging from 0 (undamaged state) to 1 (macroscopic damage or failure). Here only the shear stress is affected by the damage variable d as shown: In the usual applications of damage theory [START_REF] Ladevèze | Damage modeling of the elementary ply for laminated composites[END_REF], a damage variable also affects the transverse stress. Here, in order to show a simple application, this variable has not been taken into account:

11 11 ~σ = σ , 22 22 ~σ = σ , ( ) d 1 ~12 12 - σ = σ (1)
Now the principle of strain equivalence states that "any deformation behavior of a damaged material is represented by the constitutive laws of the virgin material in which the usual stress is replaced by the effective stress". Thus, the elastic constitutive equations for the damaged material in plane stress can be written as follows:

22 0 1 0 12 0 1 11 e 11 E E σ ν - σ = ε , 11 0 1 0 12 0 2 22 e 22 E E σ ν - σ = ε , ( ) d 1 G 2 0 12 12 e 12 - σ = ε (2)
From Eqn (2), we see that the damage parameter d is the internal variable representing the reduction of the shear modulus:

( )

d 1 G G 0 12 12 - = (3)

Thermodynamic force and progressive damage evolution law

The strain energy density E D is defined by:

( )       - σ + σ σ ν - σ + σ = d 1 G E 2 E E 2 1 E 0 12 2 12 22 11 0 1 0 12 0 2 2 22 0 1 2 11 D (4)
The thermodynamic force, Y d , associated to the internal damage variable d can be related to the mean value of the strain energy density E D by the partial derivative and then in term of stress component and damage variable:

cnst D d d E Y = σ ∂ ∂ = ( ) 2 0 12 2 12 d d 1 G 2 Y - σ = (5)
Now, in order to express the evolution of damage, a relation between d and Y d is required.

Damage will grow as Y d increases, but no more damage will occur for any value of Y d beneath a previous maximum value already reached. This is expressed by the definition of the maximum value Y d of the thermodynamic force Y d attained throughout the load history:

( ) { } τ = ≤ τ ≤ d t 0 d Y max Y ( 6 )
In the damage theory, the damage evolution law is material dependent.

A convenient law, already established for carbon and glass laminates, can be written in the form:

C 0 d Y Y Y d + - = (7)
where Y 0 and Y C are damage evolution parameters determined from experimental results. This law is depicted in Fig. 3 with the experimental data.

Inelastic strains coupled with damage and evolution law

As depicted in Fig. 1, the type of composite studied here exhibits non-linear response when stressed beyond some elastic limit stress, σ y . When the material is completely unloaded from a stress in excess of this limit, there are inelastic (permanent) strains ε p . As carbon fibers exhibit linear, elastic response, plasticity effects are associated with the matrix, and mostly under shear stress state. The formalism for the inelastic strains is that of classical plasticity, with an elastic domain function depending on the current effective stress 12 σ , and the accumulated effective inelastic strain p ~, based upon the use of the effective inelastic shear strain rate p 12 ε ! :

p 12 2 p ~ε = ! ! with ) d 1 ( ~p 12 p 12 - ε = ε ! ! (8)
p ~ can also be expressed in the form:

p 12 0 p 12 ) d 1 ( 2 p ~ε - = ∫ ε d (9)
For no (or neglected) inelastic strains in the fiber direction and in the transverse direction, the elasticity domain function is defined by:

( ) ( ) 0 R p R R , f 0 12 ≤ - - σ = σ (10)
where ( ) p R is a function of p ~ and R 0 is the initial threshold value for R. A typical result for carbon/epoxy is expressed as follows, where α and β are material parameters:

( ) α β = p p R ( 11
)

Failure prediction

In the mesoscale damage theory, failure may occur by one of three mechanisms, depending on the multi-axial stress level: fiber brittle failure, transverse tensile failure or instability condition defined as a zero slope on the stress/strain curve. Then the brittle failure is predicted by means of the failure stresses

TESTING AND CHARACTERIZATION

The testing procedure is based on tensile tests on which the longitudinal strain ε L , the transverse strain ε T and the stress σ L are measured, and load-unload cycles are practiced in order to characterize damage and inelastic parameters. The samples chosen for the tests must be sensitive to the properties of the elementary ply to be measured. Usually, for laminates based on unidirectional plies, tensile tests on specially fabricated laminates of [0], [±45] and [±67,5] are performed. The [±67,5] test is necessary for the characterization of damage in the transverse direction, and also for the measure of coupling of damages in shear and transverse tension. In the present case, this degree of freedom is not allowed because no specific fabrication can be made, and the influence of the transverse behavior never seems to be significant.

Analysis of the test results

The tests are performed on samples cut in a three-dimensional composite plate at [0°] and [45°] from the warp direction (Fig. 2). This selection of tests already allows the identification of most of elastic, damage and failure properties of the ply. The elastic properties of the laminates, like elastic moduli and Poisson's ratios, and the brittle failure behavior have been characterized by the initial slope and the maximum stress point of the stress/strain curves (Fig. 2 and Table 2). linear relation between the longitudinal strain ε L , the transverse strain ε T and the macroscopic stress σ L (Eqn 12).

2 L 12 σ = σ 2 T L 12 ε - ε = ε 12 12 12 . G . 2 ε = σ (12)
The failure strain of this sample is 8% (Fig. 5-b). This value is not due to the material's behavior, but due to an effect of the heterogeneity occurring during the test. Thus, some cycles have been practiced only in the strain range from 0 to 2%. For each load cycle "i", a set of the following quantities is measured:

• The damage variable i d characterized on the stress-strain curve by a reduction of the elastic modulus.

• The thermodynamic force Y di evaluated with Eqn (5) and the measure of the stress i σ .

• The permanent strain P i ε measured at the zero stress points after unloading. • The threshold value (R+R 0 ) (Eqn 10) obtained from the measurement of the shear stress These four data points are reported on the damage master curve (Fig. 4). The construction of the plastic master curve expressed by Eqn (11) from p 12 ε and R requires a complex processing.

The expressions of the plastic threshold and the cumulate plastic strain have been established in Eqn [START_REF] Allix | Damage Mechanics of Interfacial Media : Basic aspects, identification and application to delamination[END_REF]. The variable p is obtained from Eqn (9) and evaluated by the gray area on Fig. 3. Furthermore, the values of p are calculated and marked on the plastic master curve (Fig. 3).

Cycle

COMPARISON BETWEEN EXPERIMENTS AND SIMULATION

The parameters identified above are directly used for the simulations. The non-linear simulations are performed with Damlam. At first, the simulations fit the experimental responses until failure for brittle samples like [0°] and [90°] with a little higher predicted stiffness for [90°]. This is due to the waviness of the weft yarns which affects the elastic modulus of the plies oriented in this direction (Fig. 2, Fig. 5-a). The response of the [45°] tension test is well simulated until 1.5% of strain (Fig. 5-b), but for higher strains, it seems that the yarns undergo frictional sliding under the load, whereas they are probably debonded but still constrained by the interlock yarns. Thus, the damage mechanism changes and the modeling of this behavior would require an extension of the damage master curve for high damage values and also for damage in transverse tension. A simulation is performed on two other samples cut at [22.5°] and [67.5°] from the warp direction of the composite (Fig. 5-c Fig. 5-d). The [22.5°] and [67.5°] results are well fitted until a stress around 100 MPa, but the same yield behavior with frictional sliding and inelastic strains seems to occur and allows the composite to deform to a higher stress level. The difference of "knee point" and failure stress between these two tests is probably due to a higher stiffness of the plies in the warp direction than in the weft direction. However, the first part of the non-linear behavior is always predicted until a strain around 1.5 %, which is already higher than the failure strain in the [0°] and [90°] directions.

ε T (%) a) ε L (%) ε T (%) b) ε L (%) ε T (%) c) ε L (%) ε T (%) d) ε L (%) σ L (MPa) σ L (MPa) σ L (MPa) σ L (

CONCLUSIONS

The inplane mechanical behavior of the three-dimensional woven composite has been modeled as a laminate of two-dimensional damageable elementary plies. Moreover, an associated experimental procedure has been performed in order to identify the properties of the ply. The application of this approach led to the following conclusions:

• The model requires only two extra behavior laws, which are represented by the damage and the plastic master curves, to describe the non-linear behavior of the composite, and to quantify damage evolution.

• The experiments based on the standard tests for loading-unloading cycles enable a better understanding of the behavior of the composites.

• This simple approach already increases significantly the representation of the mechanical behavior of the composite up to failure. Then, the damage theory is used as a tool for the analysis and the characterization of the threedimensional composite. The results indicate that:

• The comparison of the [0°] and [90°] test responses seem to show that the waviness of the weft yarns affect the stiffness of the composite and enhance the strength in the weft direction.

• The damage behavior, observed on [45°] specimen, is enhanced by the through-thethickness yarns that constrain the warp and weft yarns and cancel delamination.

• The validations performed on [22.5°] and [67.5°] specimens are successful if we consider the stress-strain curves up to the knee around 100 Mpa. The first goal of this study was to present the damage theory through the use of a very simple model and its direct characterization. This model is extremely simple compared to the potential of damage theory. The presentation of the model under this simple version allowed a direct characterization, otherwise a numerical fitting is necessary. The full modeling of the behavior of the composite requires a second damage variable in order to describe damage evolution in transverse tension. This work will then be extended in this way.

Fig. 1 :

 1 Fig. 1: Cross-sections of the composite in the warp and weft directions

σ

  of the ply. The non-linear simulation software called Damlam, which has been developed by Ladevèze and co-workers, is used to simulate the mechanical response of the composite until final failure by any of these criteria.

Fig. 2 :

 2 Fig. 2: Stress/strain curves of a) [0°] and b) [45°] tension tests used for characterization.

Fig. 3 :YFig. 4 :

 34 Fig. 3: Integration for calculating the cumulated plastic strains

Fig. 5 :

 5 Fig. 5: Comparison between experimental and theoretical responses of tension tests: a) [90°], b) [45°], c) [22.5°], d) [67.5°],

Table

Table 1 :

 1 Geometrical characteristics of the composite.

		Warp direction	Weft direction	Through-the-thickness
	# of plies	13	14
	Fiber volume fraction	22 %	22 %	1 %
	Thickness	Total: 5.2 mm	Ply: 0.19 mm

Table 2 :

 2 Elastic and failure properties of the laminates.

	Test Elastic modulus (GPa) Poisson's ratio Failure stress (MPa) Failure mode
	[0°]	44.2	0.02	361	Brittle
	[45°]	9.9	0.83	120	Instability
				12 ,ε σ	12	(Fig. 2) was built from the

Damage variables and inelastic strains have been measured on the [45°] test by means of loading-unloading cycles. The stress-strain curve in shear ( )

Table 3 :

 3 Data measured from the shear stress-strain curve

	Cycle	d	d Y (MPa)	p 12 ε	R+R 0 (MPa)
	1	0,12	0,37	0.00065	27
	2	0,17	0,48	0.0011	35
	3	0,35	0,71	0.0022	52
	4	0,40	0,88	0.006	64

ACKNOLEDGEMENTS

Tsu-Wei Chou thanks the partial support of the U.S. Air Force Office of Scientific Research Grant No. F49620-98-0384, Program Manager Major Brian Sanders.


Samuel Westrelin
email: samuel.westrelin@irstea.fr

Romain Roy

Laurence Tissot-Rey

Laurent Bergès

Christine Argillier

) Irstea

Habitat use and preference of adult perch (Perca fluviatilis L.) in a deep reservoir: variations with seasons, water levels and individuals

Keywords: acoustic telemetry, littoral zone, depth, seasonal migrations

Perch Perca fluviatilis is a widespread predator in European reservoirs, frequent in open waters but also known to spend a lot of time in the littoral zones. To get insight into how adult perch used and selected their habitat in an environment subject to water level fluctuations, 21 perch were continuously tracked using acoustic telemetry over 2 years in the Bariousses reservoir (France). The different available habitats were characterized by depth classes and substrate types, presence of emerging trees, and presence of tree stumps in the littoral zone. We showed that perch habitat preferences were strongly dependent on the season, except for substrate type, and in line with their habitat use. Surprisingly we did not find any influence of the water level which however reduced the structural complexity of the littoral zone when lowering. In spring and summer, whatever the water level, we observed a strong preference for the littoral zone and complex habitats. In autumn and winter, perch migrated into deeper waters. However, the individual variability of the habitat preferences was quite high. This type of research helps to understand the spatial ecology of fish and provides useful guidance to hydromorphological restoration for fish populations.

Introduction

Whatever their origin, lake littoral zones are transitional areas between terrestrial and aquatic habitats that generally host a high biodiversity [START_REF] Schmieder | European lake shores in danger -concepts for a sustainable development[END_REF]. They provide resources available nowhere else in the lacustrine ecosystem [START_REF] Zohary | The littoral zone Lake Kinneret[END_REF] and most lake fishes use them during their life cycle [START_REF] Winfield | Fish in the littoral zone: ecology, threats and management[END_REF]. Littoral habitats can also be composed of complex structures (e.g. rocks, woody debris, vegetation) that provide both spawning grounds and refuges to a diverse assemblage of microorganisms, algae, invertebrates [START_REF] Gasith | The importance of physical structure in lakes: the case study of Lake Kinneret and general implications[END_REF] as well as fish larvae and juveniles [START_REF] Diehl | Effects of habitat structure on resource availability, diet and growth of benthivorous perch, Perca fluviatilis[END_REF][START_REF] Stoll | Effects of water depth and hydrodynamics on the growth and distribution of juvenile cyprinids in the littoral zone of a large pre-alpine lake[END_REF].

Littoral habitats are highly influenced by water level fluctuations (WLF) which can be particularly pervasive in lentic systems exploited by humans for water use and hydropower. Habitat complexity changes with water level (WL), particularly in the littoral zone [START_REF] Zohary | Ecological impacts of excessive water level fluctuations in stratified freshwater lakes[END_REF]. For instance, high WLF (frequent and wide) may engender coarser littoral substrate with less macrophyte coverage in the shallow zones of lakes [START_REF] Evtimova | Water-level fluctuations regulate the structure and functioning of natural lakes[END_REF], which in turn reduce the productivity and biodiversity of these areas [START_REF] Wetzel | Reservoir ecosystems: conclusions and speculations[END_REF][START_REF] Evtimova | Quantifying ecological responses to amplified water level fluctuations in standing waters: an experimental approach[END_REF]. More specifically, studies have shown that WLF can affect various ecological aspects of fish species such as their growth, distribution and behaviour (e.g. [START_REF] Gaboury | Influence of water level drawdown on the fish populations of Cross Lake, Manitoba[END_REF][START_REF] Rogers | Effects of a Fall Drawdown on Movement of Adult Northern Pike and Largemouth Bass[END_REF][START_REF] Fischer | Effects of water-level fluctuations on the littoral benthic fish community in lakes: a mesocosm experiment[END_REF][START_REF] Sutela | Effects of water-level regulation on the nearshore fish community in boreal lakes[END_REF][START_REF] Logez | Effects of water-level fluctuations on the environmental characteristics and fish-environment relationships in the littoral zone of a reservoir[END_REF]. Indeed, WLF can lead to loss of potential prey [START_REF] Winfield | Fish in the littoral zone: ecology, threats and management[END_REF], loss of refuge areas [START_REF] Kaczka | Size of age-0 crappies (Pomoxis spp.) relative to reservoir habitats and water levels[END_REF] and loss of spawning habitats [START_REF] Hudon | Historical changes in herbaceous wetland distribution induced by hydrological conditions in Lake Saint-Pierre[END_REF] for fish fauna. Finally, WLF may also decrease fish recruitment if WL drops after spawning [START_REF] Kahl | The impact of water level fluctuations on the year class strength of roach: Implications for fish stock management[END_REF] and fish eggs desiccate [START_REF] Michaletz | Factors affecting abundance, growth, and survival of age-0 gizzard shad[END_REF][START_REF] Winfield | Fish in the littoral zone: ecology, threats and management[END_REF]. Therefore, [START_REF] Coops | The role of water-level fluctuations in shallow lake ecosystems -workshop conclusions[END_REF] and more recently [START_REF] Tao | Productive capacity of fish habitats: a review of research development and future directions[END_REF] highlighted the urgency of collecting ecological data on fish-habitat relationship. Fish habitat use is a key driver of population dynamics [START_REF] Hayes | Linking fish population dynamics to habitat conditions: insights from the application of a process-oriented approach to several Great Lakes species[END_REF] and an essential knowledge for predicting how populations will respond to management interventions [START_REF] Koster | Movement and habitat use of the freshwater catfish (Tandanus tandanus) in a remnant floodplain wetland[END_REF][START_REF] Cooke | A moving target-incorporating knowledge of the spatial ecology of fish into the assessment and management of freshwater fish populations[END_REF]. In particular, the identification of crucial habitats is important for efficient aquatic conservation in areas with strong human influence [START_REF] Halpern | Habitat size, recruitment, and longevity as factors limiting population size in stage-structured species[END_REF][START_REF] Sale | Critical science gaps impede use of no-take fishery reserves[END_REF].

A thorough in situ study of WLF effects on the behaviour of a species has rarely been conducted and can contribute to valuable knowledge on management decisions, as [START_REF] Gardner | Seasonal water level manipulation for flood risk management influences home-range size of common bream Abramis brama l. in a lowland river[END_REF] recently showed on the common bream (Abramis brama L.) which altered their home range size according to the WL while keeping the same activity level. In the present work we propose to study habitat-use patterns of the Eurasian perch (Perca fluviatilis L.), a species present in most lowland reservoirs [START_REF] Irz | Comparison between the fish communities of lakes, reservoirs and rivers: can natural systems help define the ecological potential of reservoirs?[END_REF] and widespread in Europe [START_REF] Kottelat | Handbook of European Freshwater Fishes[END_REF] but on which the effects of WLF have never been investigated. Although frequent in open waters, their dependence on the littoral zone is high [START_REF] Zamora | Quantifying the activity and movement of perch in a temperate lake by integrating acoustic telemetry and a geographic information system[END_REF][START_REF] Jacobsen | Behavioural strategy of large perch Perca fluviatilis varies between a mesotrophic and a hypereutrophic lake[END_REF]. At night, they rest in the littoral zone on the bottom [START_REF] Imbrock | Diel and seasonal distribution of perch in Lake Constance: a hydroacoustic study and in situ observations[END_REF]. They are highly selective in their choice of spawning habitat, generally preferring shallow and sheltered areas with rigid and structurally complex substrates [START_REF] Probst | Spawning site selection by Eurasian perch (Perca fluviatilis L.) in relation to temperature and wave exposure[END_REF][START_REF] Snickars | Habitat selectivity of substrate-spawning fish: modelling requirements for the Eurasian perch Perca fluviatilis[END_REF]Čech et al., 2012a) but can spawn in deeper waters depending on the environmental conditions (Čech et al., 2012a; Čech et al., 2012b). Perch spawning usually takes place when water temperatures reach about 5°C [START_REF] Souchon | Synthesis of thermal tolerances of the common freshwater fish species in large Western Europe rivers[END_REF].

Given that the littoral zone is a critical habitat for the perch, we designed the present study to evaluate whether and how WLF affect its habitat preferences, here defined as the higher likelihood that an individual chooses a habitat type if offered on an equal basis to others [START_REF] Johnson | The comparison of usage and availability measurements for evaluating resource preference[END_REF]. As WLF can modify the availability of the different littoral habitat types [START_REF] Zohary | Ecological impacts of excessive water level fluctuations in stratified freshwater lakes[END_REF][START_REF] Evtimova | Water-level fluctuations regulate the structure and functioning of natural lakes[END_REF], we expected a shift of perch habitat preferences with WL. For example, when an habitat becomes very scarce, if perch keeps on frequently using it, then its preference will automatically raise; on the contrary, if perch switches to another habitat, its preference will decline for this scarce habitat and raise for the other. In particular, we could expect this to happen during the spawning season, in spring in our case, when the habitat choice appears crucial. To answer this question, we set up a high spatial and temporal resolution study over a French reservoir, subject to human induced WLF ranging from days to seasons. More specifically, we tracked 21 large perch by acoustic telemetry over a 2 year period. We first evaluated how WLF affected the relative availability of the littoral and pelagic areas in the reservoir. Then, we assessed the effects of WLF and seasons on individual habitat preference. Lastly, perch habitat use and preferences were analyzed in detail.

Materials and methods

Study site

The study was conducted in the Bariousses hydropower reservoir (45.33°N, 1.49°E) in the west central part of France (Figure 1). The reservoir is located in a rural and natural environment, in a forest land cover dominated catchment with low anthropogenic activities [START_REF] Logez | Effects of water-level fluctuations on the environmental characteristics and fish-environment relationships in the littoral zone of a reservoir[END_REF]. This reservoir, with a 229 km 2 watershed, is an impoundment of the Vezere River. It is the second dam on this river and it is located 42 km downstream the source; the average flow is 4.37 m 3 /s at Bugeat, 20 km upstream from the dam. The main inflow to Bariousses lake comes from deep waters of the first dam located 12 km upstream. As these waters are colder than those of the lake, especially in spring and summer, they probably flow at the bottom of the lake along the original river track. At the mean WL, altitude of 511.5 m, its area covers 86.6 ha, mean depth is 7.1 m and maximum depth reaches 19.4 m. The bathymetry of the reservoir was measured with a multibeam sounder (EDF, personal source), giving a 2×2-m resolution GIS map. The reservoir mean renewal time is 12 days.

The thermal regime of the reservoir is monomictic with four distinct temperature regimes. In spring (April to June), the water temperatures raise rapidly and the stratification is taking place; in summer (July to September), waters are warmer and stratified and the thermocline about 4.5m deep; the autumn (October to December) corresponds to a rapid decrease of water temperatures when the mixing is taking place and destratification is in progress and, in winter (January to March), the waters are homogeneously cold over the whole water column (Table 1). The summer thermocline is associated with an oxycline that separates saturated surface waters from deep waters; the deep layer has an oxygen saturation rate of 40%. These regimes can be linked with perch ecology. The broad range of optimum temperatures for perch spawning lies between 5°C and 19°C, depending on the region, and the limited one between 8°C and 15°C [START_REF] Souchon | Synthesis of thermal tolerances of the common freshwater fish species in large Western Europe rivers[END_REF]. Rising temperatures appeared to be the major factor inducing spawning [START_REF] Hokanson | Temperature Requirements of Some Percids and Adaptations to the Seasonal Temperature Cycle[END_REF][START_REF] Thorpe | Morphology, physiology, behavior, and ecology of Perca fluviatilis L. and P. flavescens Mitchill[END_REF][START_REF] Craig | Percid fishes: systematics, ecology and exploitation[END_REF] which suites well with spring. In addition, in the Bariousses reservoir, we observed some perch eggs laying on the shore in April and perch egg ribbons were also usually seen by regular anglers in early May in very shallow zones dewatered by the WLF. Perch activity was shown to raise with temperature [START_REF] Craig | Seasonal changes in day and night activity of adult perch, Perca fluviatilis L[END_REF] and to peak concomitantly with high summer temperatures [START_REF] Jacobsen | Activity and food choice of piscivorous perch (Perca fluviatilis) in a eutrophic shallow lake: a radio-telemetry study[END_REF].

Depending both on human energy needs and hydrology, WLF are very variable in the Bariousses reservoir (Figure 2). Over the study period (June 2012 to March 2014), the hourly WL, measured by Electricité de France (EDF), ranged from 507.1 m to 513.5 m. The tertiles of the hourly WL distribution over the study period were used to split WL into low, mean and high WL. The mean lake area is 78.1, 86.6 and 90.5 ha respectively at low, mean and high WL. Typically, WL can shift from one class to a neighbouring class in a few days. Though, main annual features emerge. In spring, the high WL is from far the most frequent whereas the low one is in autumn because, at the beginning of this season, the WL is usually lowered in anticipation of rains [START_REF] Logez | Effects of water-level fluctuations on the environmental characteristics and fish-environment relationships in the littoral zone of a reservoir[END_REF].

In winter the occurrence of the three WL classes is more evenly distributed. In summer the WL is kept stable around its mean value 95% of the time to sustain recreational activities which are concentrated close to a sandy beach located on the west shore in front of the island (Figure 1), motorboats being forbidden.

The water conductivity is low over the whole water column all over the year. The Secchi transparency depth lies between 1.3 and 2.5 m. The characterisation of the phytoplankton community qualifies the reservoir as oligotrophic. Based on diversity, abundance and sensitivity to pollutants of invertebrates sampled in shallow waters, the reservoir appears in good condition (unpublished data).The fish fauna of the reservoir was determined with a standardized procedure [START_REF] Cen | Water quality -Sampling of fish with multi-mesh gillnets EN 14757[END_REF] in 2010 and comprises 15 species. It is dominated by Cyprinids and Percids, characteristic of a lowland reservoir [START_REF] Irz | Influence of site characteristics on fish community patterns in French reservoirs[END_REF]. The most dominant species, in terms of catch per unit effort, are roach (Rutilus rutilus), ruffe (Gymnocephalus cernua), Eurasian perch (Perca fluviatilis), pikeperch (Sander lucioperca) and common bream (Abramis brama). Beside Eurasian perch and pikeperch, another dominant predator, pike (Esox Lucius), is present. This community has been very little manipulated since a lake drainage in 1997. Fishing is allowed all along the year and only outside of spawning periods for pike and pikeperch.

Fish tagging

Following the suggestions of [START_REF] Thiem | Trends in the reporting of tagging procedures for fish telemetry studies that have used surgical implantation of transmitters: a call for more complete reporting[END_REF], below is detailed the followed surgical procedure. A total of 29 adult perch were caught with gillnets set at dawn, day and dusk for maximally 2 hours over four sampling campaigns: 16 in spring 2012, 1 in summer 2012, 7 in autumn 2012 and 5 in spring 2013. Once captured, to check their condition, they spent 3-6 hours in an aerated tank of lake water prior tagging, after a half an hour trip on the boat in another aerated tank to join the tagging site located in a building on the lake shore. Fishes were individually anesthetized, which took 8-10 min, by immersion in a 20 l tank filled with an aerated solution composed of 90% diluted clove oil (0.03-0.05% in lake water) and 10% ethanol. Once the fish had lost its balance (ventral side up), did not respond to stimuli anymore and had a very slow and steady operculum rate with large amplitude, it was weighted, measured and placed ventral side up on a V-shaped surgical table. The same anesthetic solution but less concentrated in clove oil (0.003%) was used to irrigate the gills during surgery.

A 10 to 15 mm long incision was made posterior to the pelvic girdle to insert an acoustic transmitter, previously sterilized in surgical spirit, in the peritoneal cavity. We used Vemco V9P-2L (47 mm long, 6.3 g in the air, 90 s mean burst interval, mean battery life 385 days) or V8-4L (20.5 mm long, 2 g in the air, 90 s mean burst interval, mean battery life 163 days) acoustic transmitters. The transmitter weight in the air did not exceed 2% of the fish body weight [START_REF] Winter | Underwater biotelemetry[END_REF]. The incision was closed using 2 to 3 simple surgical sutures (3-0 Polydioxanone Ethicon monofilament Ltd.) placed 5 mm apart. An antiseptic and antibiotic cream (Fucidine 2%) was applied on the incision wound to help healing and limit the risk of infection. The surgical procedure took 5 to 6 min. The same person always carried out the surgery. Fishes were then put in an aerated recovery tank, where they were continually observed until the opercular activity, swimming ability, balance and behavioural reponse to stimuli became normal again, usually after 10 min. Then, in a couple of minutes, they were transferred to a net set in the lake where they spent 6 to 12 hours. Lastly, they were transported by boat within half an hour in an aerated tank back to their capture site to be released.

Fish tracking

An array of 40 underwater VR2W 69kHz omnidirectional acoustic receivers (Vemco) with their associated synchronization tag (V13-1L) was anchored at the bottom throughout the reservoir from January 2012 until March 2014 (Figure 1). Eight additional synchronization tags were settled in the reservoir to detect anomalies in the tracking system. On average, neighboring receivers were positioned 150 m from each other (range, 72-223 m), 6 m deep (range, 2-15 m) [START_REF] Roy | Testing the VEMCO Positioning System: spatial distribution of the probability of location and the positioning error in a reservoir[END_REF]. Roughly every 6 months, receivers were removed from the lake to download fish detections. Fish positions were calculated by Vemco with their Vemco Positioning System (VPS) algorithm [START_REF] Smith | Understanding HPE in the VPS Telemetry System[END_REF]. The horizontal position error, a dimensionless parameter calculated by the VPS for each position that gives information on the quality of the position estimate, was used to filter the data set [START_REF] Espinoza | Habitat use, movements and site fidelity of the gray smoothhound shark (Mustelus californicus Gill 1863) in a newly restored southern California estuary[END_REF]. In this study, we followed the recommendations of [START_REF] Roy | Testing the VEMCO Positioning System: spatial distribution of the probability of location and the positioning error in a reservoir[END_REF] for the same system and only positions with horizontal position error not exceeding 15 were retained; this limit represented a good compromise between the mean position error (3.3 m throughout the reservoir) and the percentage of positions kept (79%) (see [START_REF] Roy | Testing the VEMCO Positioning System: spatial distribution of the probability of location and the positioning error in a reservoir[END_REF] for detailed calculations of these error and percentage). Moreover, the probability of location map, estimated by [START_REF] Roy | Testing the VEMCO Positioning System: spatial distribution of the probability of location and the positioning error in a reservoir[END_REF], showed that some parts of the lake were not well sampled, all located at the ends of the lake or on the shore. In parallel, in some of these areas very few locations were recorded. Not to introduce biases, we then removed from our study areas where the probability of location was below 2.5%; this threshold appeared as a good compromise between the representativeness of the sampling and the number of removed positions. So as not to include positions affected by behavioural modification following the surgery, only the positions recorded at least 2 days after release were included in the analyses [START_REF] Bridger | The effects of biotelemetry transmitter presence and attachment procedures on fish physiology and behavior[END_REF][START_REF] Vehanen | Movements and habitat use by pikeperch (Stizostedion lucioperca (L.)) in a hydropeaking reservoir[END_REF]. Some fish were already tagged in March 2012 but a problem of receiver memory saturation only fixed on late June 2012 caused the loss of data; the same problem caused the loss of data from August to October 2012. The downloading of receivers led to an interruption of the tracking for a few days in May 2013. In early October 2013, due to a sharp lowering of the WL for dam inspection, receivers were again downloaded and the experiment interrupted as the shallowest receivers could be dewatered; the interruption lasted till late November as the receivers could not have been put back into water sooner because of extended unavailability of divers and staff.

In the end, among the 29 perch initially tagged, 2 stationary fish were supposed to be dead rapidly after release, and 6 other, sparsely located from a few days to a few weeks, were then never located. These 8 individuals were omitted from the analyses. Hence, 21 adult perch, 320 to 486 mm long (Table 1), corresponding to 12-18 individuals depending on the season, were followed. The time series of their positions used in this study are represented on Online Resource 1.

Data analysis

We first define several terms used in the following. The use of an habitat is the quantity that is utilized by perch; the availability of an habitat is the quantity accessible to the perch; the selection of an habitat is the process in which perch choose an habitat and preference is a reflection of the likelihood that perch choose an habitat if offered on an equal basis to others [START_REF] Johnson | The comparison of usage and availability measurements for evaluating resource preference[END_REF]. Habitat availability, use, selection and preference were evaluated at the reservoir scale as most of the individuals used the whole reservoir (Online Resource 2).

Habitat description and availability

Based on the Secchi transparency depth, ranging from 1.3 to 2.5 m, we defined the littoral area of the reservoir as the lake area connected to the bank with a depth lower than 2.5 m. The substrate types observed in the Bariousses were silt, sand, gravel, pebble, stone, boulder and rock; at high WL, lawn was also present thanks to flooded grasslands. Other available habitats were tree stumps, coming from tree felling at the time of the impounding, emerging trees i.e. living shrubs or trees with roots and trunk in the water at least in some periods, helophytes and undercut banks. The last two categories were very scarcely present and thus not used further in the study. Thus the different available habitats were characterized by four variables: depth (7 classes: [0; 2.5[, [2.5; 5[, [5; 7.5[, [7.5; 10[, [10; 12.5[, [12.5; 15[ and [15; 22[ m) and, in the littoral zone, main substrate, emerging trees and tree stumps.

All the habitats listed above were mapped on October 2013 by visual observation all around the lake when the WL was 507.5m. Dewatered habitats between 513.5m and 507.5m were described as well as those down to 506.5m thanks to the water transparency. For each habitat variable, homogeneous polygonal areas were delimited with a differential GPS (Leica 1200 ® ) and the habitat map was discretized in 10×10 m 2 squares. In each grid square, for each habitat variable the habitat type which was selected was the one that covered more than 50% of the square. The mean square depth was used for depth. All habitats were mapped with ArcGis 10.0.

The relative availability of habitat type i, π i , was defined as the ratio of the number of grid squares with habitat type i on the total number C of 10x10m 2 grid squares in the study area (the whole lake if the considered habitat is depth, the littoral area for other habitat variables) at the considered WL. The different available habitats of the lake were quantified at low, mean and high WL. For each hourly WL of the study period and each habitat variable, the relative availability of each habitat type was estimated. Mean and standard deviation of these relative availabilities were calculated in grouping the data by the three WL classes.

Environmental variables impacting habitat preference

For each fish position, the used habitat corresponded to the habitat of the grid square in which the fish was. The number of positions in a grid square was corrected with the probability of location in this grid square, estimated by [START_REF] Roy | Testing the VEMCO Positioning System: spatial distribution of the probability of location and the positioning error in a reservoir[END_REF], to minimize the spatial variability of the sampling inherent to a telemetry system. The proportion of each type was calculated for each habitat variable.

The corrected number of positions of fish j in habitat type i is then given by:

u ij = ∑ n ij c p c C c=1
where n ij c is the number of positions of fish j in the grid square c containing the habitat type i and p c the probability for a tagged fish present in the grid square c to be located (see Roy et al 2014 for more details).

The corrected number of positions of fish j in all classes of habitat type i (1,…, I) is :

u +j = ∑ u ij I i=1
where I is the number of types in the considered habitat variable (for example, the "main substrate" habitat variable contains 8 types).

The relative use of habitat type i by fish j is the ratio of u ij on u +j .

The selection ratios were then used to quantify the habitat preference [START_REF] Manly | Resource selection by animals : statistical design and analysis for field studies[END_REF]. For individual j and habitat type i, the selection ratio is as follows:

w ̂ij = u ij u +j ⁄ 𝜋 i
For each habitat variable, the effects of habitat type, season, WL and two-way interactions on perch individual selection ratios were explored using generalized additive mixed-effects models (GAMM) [START_REF] Zuur | New York, NY: Spring Science and Business Media. Tables Table 1 Extent of the study period characterized by the mean, minimum and maximum temperatures (T, °C)[END_REF]. The fish identity was considered as a random effect to explicitly account for individual heterogeneity. To take into account the skewed distribution of individual selection ratios towards zero, a Tweedie family function with a log-link was used [START_REF] Gilman | Hawaii longline tuna fishery temporal trends in standardized catch rates and length distributions and effects on pelagic and seamount ecosystems[END_REF]. As water temperature regimes were very similar over the 2-year study period (Table 1), data from the same seasons of different years were merged.

For one habitat variable, the full model could be written as follows:

log(SR ind ) = α + HAB + SEASON + WL + HAB:SEASON + HAB:WL + WL:SEASON + s(ind) + ε where SR ind is the expected mean individual selection ratio, strictly positive; α is the overall intercept; HAB is the habitat variable (depth, main substrate, emerging trees, tree stumps) split into different types corresponding to the variable classes; SEASON is the season (four classes, Table 1); WL is the water level (three classes, Figure 2); s(ind) is a smoothing function modeling the individual effects [START_REF] Wood | Fast stable direct fitting and smoothness selection for generalized additive models[END_REF] having the advantage to get a significance test of these effects and an evaluation of the explained deviance of the model; and ε is the error term following a normal distribution with zero mean.

For each habitat variable, the most parsimonious simple model was selected by running a forward stepwisebased procedure [START_REF] Venables | Random and mixed effects Modern Applied Statistics with S[END_REF] and applying the recommendations of [START_REF] Richards | Dealing with overdispersed count data in applied ecology[END_REF]: all models having an AIC value within a range of 6 from the lowest AIC value were initially selected and, among them, the more complex models that did not have an AIC value lower than all the simpler models within which they were nested were removed.

The model fitting was assessed with regards to the homogeneity and normality of the residuals [START_REF] Zuur | New York, NY: Spring Science and Business Media. Tables Table 1 Extent of the study period characterized by the mean, minimum and maximum temperatures (T, °C)[END_REF] and to the percentage of explained deviance [START_REF] Hastie | Generalized additive models[END_REF].

Habitat use and preference

For each of the habitat variables, habitat use and preference were explored according to those of the environmental variables that had significant effects in the GAMM.

The compositional analysis as proposed by [START_REF] Aebischer | Compositional analysis of habitat use from animal radio-tracking data[END_REF] was applied on each habitat variable to test for habitat selection and to investigate habitat use. For each habitat variable, this analysis tests with a Wilk's lambda if the different habitat types are used more or less than expected from their availability and ranks the habitat types in order of use by comparing them two by two. For each habitat variable, the compositional analysis was also used to test for the significance of the use of each habitat type compared to all other combined.

Although the aforementioned analysis [START_REF] Aebischer | Compositional analysis of habitat use from animal radio-tracking data[END_REF] allows testing the significance of the relative habitat use and the occurrence of habitat selection, no absolute preference per habitat type is calculated [START_REF] Pauwels | Habitat use and preference of adult pike (Esox lucius L.) in an anthropogenically impacted lowland river[END_REF]. Therefore, we calculated selection ratios for the pool of individuals, hereafter called mean selection ratios, and their associated Bonferroni-adjusted 95% confidence intervals as proposed by [START_REF] Manly | Resource selection by animals : statistical design and analysis for field studies[END_REF].

The mean selection ratio is given by:

w ̂i = u i+ u ++ ⁄ 𝜋 i
where u i+ is the corrected number of positions of all fish in habitat type i,

u i+ = ∑ u ij n j=1
with n the total number of fish, and u ++ is the corrected total number of positions

u ++ = ∑ u i+ I i=1
The variance of w ̂i is estimated as:

var(w ̂i)= 1 u ++ 2 n n-1 ∑ ( u ij π i -w ̂iu +j ) 2 n j=1
Simultaneous Bonferroni confidence intervals for mean selection ratios can then be constructed with an overall confidence level of 100(1-α)%, so that the probability of all the intervals containing the true value is 1-α. These intervals are of the form w ̂i ± z ∝/2I √var(w ̂i) where z ∝/2I is the value exceeded with probability ∝/2I by a standard normal random variable.

The mean selection ratio pools observations from all fish in the sample, but the confidence interval takes the variation in resource selection from individual to individual into account [START_REF] Manly | Resource selection by animals : statistical design and analysis for field studies[END_REF].When a selection ratio and accompanying confidence interval is higher than 1.0, habitat preference is considered significant [START_REF] Manly | Resource selection by animals : statistical design and analysis for field studies[END_REF][START_REF] Rogers | Analysis of Movement and Habitat Use from Telemetry Data[END_REF].

Compositional analysis and selection ratios were generated in R 3.0.1 (R Core Team, 2013) using adehabitatHS package [START_REF] Calenge | The package "adehabitat" for the R software: A tool for the analysis of space and habitat use by animals[END_REF]. GAMM were implemented using the mgcv package [START_REF] Wood | Generalized additive models: an introduction with R[END_REF].

Methodological considerations

We can mention that the pool of individuals was not strictly the same from one season to another but we took this into account both in the GAMM, by modelling individual effects, and in the confidence interval of mean selection ratios. By construction, the habitat use analysis also considers this.

We also paid great attention to the crucial step of telemetry experiment design [START_REF] Kessel | A review of detection range testing in aquatic passive acoustic telemetry studies[END_REF][START_REF] Steel | Performance of an ultrasonic telemetry positioning system under varied environmental conditions[END_REF] and evaluated its performance [START_REF] Roy | Testing the VEMCO Positioning System: spatial distribution of the probability of location and the positioning error in a reservoir[END_REF] as recommended by [START_REF] Biesinger | Testing an autonomous acoustic telemetry positioning system for fine-scale space use in marine animals[END_REF]. The spatial variability of the performance was assessed in a prior study [START_REF] Roy | Testing the VEMCO Positioning System: spatial distribution of the probability of location and the positioning error in a reservoir[END_REF]: the performance (positioning error and probability to get a position) was lower in the littoral zone than in the pelagic one. At least two reasons can explain this: firstly, the littoral zone is a structurally complex zone what has been shown to affect the system performance in terms of detection and error [START_REF] Baktoft | Performance Assessment of Two Whole-Lake Acoustic Positional Telemetry Systems -Is Reality Mining of Free-Ranging Aquatic Animals Technologically Possible[END_REF]; secondly, by construction of the receiver network, the littoral zone is mainly outside this network whereas the pelagic one is inside and the VPS theory tells that the performance of the system is lower outside the network [START_REF] Smith | Understanding HPE in the VPS Telemetry System[END_REF]. Hence, we brought a correction to smooth this artificial spatial variability by using the probabilities of positioning calculated by [START_REF] Roy | Testing the VEMCO Positioning System: spatial distribution of the probability of location and the positioning error in a reservoir[END_REF] in winter when the mixing of water was complete. In addition, the performance of a system can vary in time due to the modifications of the thermocline gradient and thermocline depth [START_REF] Huveneers | The influence of environmental parameters on the performance and detection range of acoustic receivers[END_REF].

We checked this over the 40 synchronizing tags and eight reference tags and no strong seasonal pattern of detection was found in this reservoir making our positioning adequate to study seasonal variability of habitat preferences.

Results

WL influence on habitat availability

When the WL rose, the relative availability of the littoral area ([0, 2.5[m) dropped from 19.5% at low level to 13.3% at high level (Figure 3a). These proportions, applied to the mean lake area at the different WL, also showed that the surface of the littoral area diminished when the WL rose. In the littoral zone, the relative availabilities of stone and boulder/rock were quite low (less than 10%) and little influenced by WL (Figure 3b).

Similarly, the relative availability of tree stumps was not strongly impacted by WL and remained stable around 20% (Figure 3d). On the contrary, the WL influenced the relative availability of finer substrates and lawn (Figure 3b). The relative availability of silt prevailed at the lowest WL and dropped rapidly when the WL rose; conversely, the relative availability of gravel/pebble and lawn (class almost not present at low WL) increased with increasing WL to reach 19.5 and 27.6% respectively, whereas the relative availability of sand peaked at the mean WL (Figure 3b). The relative availability of emerging trees increased with increasing WL, roughly from 18.9% at low WL to 59.6% at high WL (Figure 3c).

Which variables influence perch habitat preference ?

Depth selection ratios were the best modelled with 44.4% of the deviance explained (Table 2). This model showed that perch preferences were different between depth classes and influenced by the season with individual variability. The WL did not impact significantly the depth preferences. The models selected for tree stumps and emerging trees selection ratios explained respectively 33.4% and 24.3% of the deviance (Table 2) without significant individual differences. Perch preference for tree stumps and emerging trees had a significant seasonal component but was not influenced by WL. Main substrate selection ratios were the most poorly modelled with only 11.2% of deviance explained by the selected model in which neither the season nor the WL had a significant effect. The individual variability was not significant.

Depth use and preference

The selection of depth occurred in the four seasons. Whatever the season, perch used the [2.5, 5[m zone the most, significantly in spring, summer and autumn (Table 3). In spring and summer, the littoral zone use ranked second and was significantly more used than other depths only in summer whereas in autumn and winter the [5, 7.5[m depth ranked second. In autumn and winter, the littoral zone use only ranked four.

In spring and summer, perch preferred littoral and [2.5, 5[m zones (Figure 4a), in good agreement with the high use of these depths (Table 3). In autumn, perch preferred the [2.5, 5[m zone and tended to prefer the [5, 7.5[m depth, again in line with the high use of these depths, whereas they tended to avoid the littoral zone and avoided all other depths. In winter the littoral zone was avoided and areas between 2.5 and 10 m deep tended to be preferred, and also more used. Over the four seasons, the areas deeper than 10 m were avoided or rarely explored by perch, except by some individuals in the winter.

Use and preference of littoral habitats

Perch selected the littoral substrate (Table 3). In the littoral zone, boulder/rock was significantly the most used substrate type, followed by stone and sand which were not significantly more used than other substrates (Table 3). In line with their high use, boulder/rock and stone tended to be preferred (Figure 4b), as lawn although ranked second last regarding its relative use (Table 3). Perch tended to avoid finer substrates (silt, sand, and gravel/pebble) (Figure 4b). However, no preference/avoidance was significant due to a high individual variability, highlighted by large confidence intervals, especially for stone and boulder/rock. Perch selected littoral zones with emerging trees in spring and summer; they were significantly more used than those without in these both seasons and also in winter (Table 3) but preferred only in spring and summer (Figure 4c). In autumn and winter, perch also tended to prefer them but the individual variability was high (Figure 4c).

The tree stumps were also selected in spring and summer and significantly more used (Table 3). Not completely in line with the habitat use analysis, they were preferred in spring and autumn and only tended to be in summer and winter, with a very high individual variability in spring and winter (Figure 4d).

Discussion

Variability of habitat availability with WL

Using a precise qualitative and quantitative description of the different habitats, we highlighted an influence of WL on the structure of the available littoral habitats of the Bariousses reservoir: they tended to become more homogeneous with a lowering structural complexity when the WL dropped. These results, based on the entire lake, are in agreement with other studies [START_REF] Gasith | Effects of water level fluctuation on the structure and function of the littoral zone Large lakes[END_REF][START_REF] Gasith | The importance of physical structure in lakes: the case study of Lake Kinneret and general implications[END_REF], and mean that lowering WL correspond to fewer refuge areas and probably fewer food resources for perch [START_REF] Zohary | Ecological impacts of excessive water level fluctuations in stratified freshwater lakes[END_REF][START_REF] Zohary | The littoral zone Lake Kinneret[END_REF]. They also confirmed the trends observed by [START_REF] Logez | Effects of water-level fluctuations on the environmental characteristics and fish-environment relationships in the littoral zone of a reservoir[END_REF] with a point sampling on the same lake, but brought additional information as the stable availability of littoral tree stumps with WL and the rise of the relative availability and surface of the littoral area when the WL dropped.

The highest diversity of habitats was observed in spring, which corresponds to the perch spawning period, while the lowest diversity was noted in autumn. It was intermediate almost throughout the summer when WLF were very limited around the mean WL, and very contrasted in winter when WL were quite evenly distributed between low, mean and high classes.

Influence of WL on habitat preference

WLF directly impacted the relative availability of the different littoral habitats; however we did not observe any significant effect of WL on the habitat preference of adult perch. This suggests that the preference of littoral habitats remained the same whatever their availability, in the ranges and timing encountered in this reservoir.

The scarcity of some preferred resources probably did not reach any critical threshold. Low WL were the most frequent in autumn and winter and corresponded to the highest relative availability of the littoral zone which was however much less used in these two seasons than in spring and summer.

In the same reservoir in summer and autumn, [START_REF] Logez | Effects of water-level fluctuations on the environmental characteristics and fish-environment relationships in the littoral zone of a reservoir[END_REF] observed that the littoral fish assemblages, composed of juveniles and adults, were dependent on the WL and tended to homogenize when the habitat complexity lowered, suggesting variations in habitat use when its availability changed, even if adults seemed to be the less affected. Considering the advantages of the littoral zone for fish fauna [START_REF] Schiemer | Land and inland water ecotones -intermediate habitats critical for conservation and management[END_REF][START_REF] Schmieder | European lake shores in danger -concepts for a sustainable development[END_REF][START_REF] Lewin | The influence of anthropogenic shoreline changes on the littoral abundance of fish species in German lowland lakes varying in depth as determined by boosted regression trees[END_REF] and the importance of the habitats impacted by WLF for perch [START_REF] Imbrock | Diel and seasonal distribution of perch in Lake Constance: a hydroacoustic study and in situ observations[END_REF][START_REF] Zamora | Quantifying the activity and movement of perch in a temperate lake by integrating acoustic telemetry and a geographic information system[END_REF][START_REF] Pekcan-Hekim | Diel changes in habitat preference and diet of perch (Perca fluviatilis), roach (Rutilus rutilus) and white bream (Abramis björkna)[END_REF][START_REF] Cech | Distribution of egg strands of perch (Perca fluviatilis L.) with respect to depth and spawning substrate[END_REF][START_REF] Muska | To migrate, or not to migrate: partial diel horizontal migration of fish in a temperate freshwater reservoir[END_REF], we expected some changes in the habitat preferences at different WL. As shown on some terrestrial species, variations in habitat availability can lead to changes in habitat preferences [START_REF] Godvik | Temporal scales, tradeoffs, and functional responses in red deer habitat selection[END_REF][START_REF] Hansen | Functional response in habitat selection and the tradeoffs between foraging niche components in a large herbivore[END_REF][START_REF] Pellerin | Habitat use by female western roe deer (Capreolus capreolus): influence of resource availability on habitat selection in two contrasting years[END_REF]. With the loss of some emerging trees and boulder/rock habitat types when the WL dropped, we could have expected a higher attractiveness of tree stumps, whose availability remained stable, for feeding and spawning. In the Bariousses reservoir, the temporal scales of WLF (days) mainly changed the habitat availability without imposing great physical stress on organisms living in the littoral zone as short term WLF would [START_REF] Hofmann | Temporal scales of water-level fluctuations in lakes and their ecological implications[END_REF]. Moreover, the relative availability and surface of the littoral area rose when the WL dropped, which could mitigate the effects of the WLF. Above all, the relative availability of the complex preferred habitats by adult perch was the highest in spring and summer, respectively the period of spawning [START_REF] Craig | Percid fishes: systematics, ecology and exploitation[END_REF] and of highest activity [START_REF] Jacobsen | Activity and food choice of piscivorous perch (Perca fluviatilis) in a eutrophic shallow lake: a radio-telemetry study[END_REF], when this type of habitat is the most required regarding perch ecology. In autumn and winter, when food requirements lessen because perch activity is reduced [START_REF] Jacobsen | Activity and food choice of piscivorous perch (Perca fluviatilis) in a eutrophic shallow lake: a radio-telemetry study[END_REF], perch could cope with a limited availability of complex habitats. Aside this uneven distribution of WL between seasons, the lack of a net effect of WL on adult perch habitat preferences can also be related to their plastic nature regarding the environment [START_REF] Craig | Percid fishes: systematics, ecology and exploitation[END_REF]. Besides, Čech et al. (2012b) have shown that, being able to spawn at various depths depending on the period and temperature, perch have evolved a mechanism to cope with a large spectrum of conditions.

Individual variability

Finally, even if the individual effect was globally significant only for depth selection, high individual variability, quantified by the confidence interval length of selection ratios, was observed on numerous habitat types. It is however important to emphasize that no link appeared between the individual variability and the number of individuals used in the sample. Regarding the substrates, the individual variability was very high especially for the most complex ones what could be linked to their relatively reduced availability in this reservoir.

Such variability is frequent among fish [START_REF] Magurran | Individual differences and alternative behaviours[END_REF]) and contributes to the population adaptation to rapid changes in the environment. This variability could reflect different strategies adopted by perch, possibly related to sex-specific responses to environmental changes [START_REF] Estlander | Sex-dependent responses of perch to changes in water clarity and temperature[END_REF] or to predation risk [START_REF] Estlander | Feeding under predation risk: potential sex-specific response of perch (Perca fluviatilis)[END_REF] that also exists even if limited on these large individuals, as well as to the existence of different fish personalities in the population, for example bold or shy individuals, which have been shown to forage or manage the predation risk differently [START_REF] Kekalainen | Individually assessed boldness predicts Perca fluviatilis behaviour in shoals, but is not associated with the capture order or angling method[END_REF][START_REF] Harkonen | Behavioural variation in Eurasian perch populations with respect to relative catchability[END_REF]. Unfortunately, despite the surgical operation, the gender of perch was seldom determined because the smallest possible incision was favored to provide the greatest chance of full healing.

Seasonal pattern of habitat use and preference

The high use of and preference for the shallow zones of the reservoir ([0, 5[m in depth) in spring and summer shown with high-resolution individual tracking are in agreement with previous conclusions obtained with fishing data [START_REF] Craig | Seasonal changes in day and night activity of adult perch, Perca fluviatilis L[END_REF][START_REF] Muska | To migrate, or not to migrate: partial diel horizontal migration of fish in a temperate freshwater reservoir[END_REF]. They also confirm results obtained with a comparable approach implemented in another temperate lake [START_REF] Zamora | Quantifying the activity and movement of perch in a temperate lake by integrating acoustic telemetry and a geographic information system[END_REF]. However, even if these shallow zones were highly used and preferred, the individual variability was also significant. In stratified reservoirs, fish are usually distributed in the surface waters due to the attraction of warmer temperatures in spring and to avoid deoxygenated hypolimnion in summer [START_REF] Kubecka | Horizontal beaming as a crucial component of acoustic fish stock assessment in freshwater reservoirs[END_REF]. What is more, the preference for shallow depths by adult perch could be related to the numerous juveniles of different fish species that live in this sheltered area and that provide food [START_REF] Degiorgi | Relations entre la topographie aquatique et l'organisation spatiale de l'ichtyofaune lacustre : définition des modalités spatiales d'une stratégie de prélèvement reproductible[END_REF][START_REF] Stoll | Effects of water depth and hydrodynamics on the growth and distribution of juvenile cyprinids in the littoral zone of a large pre-alpine lake[END_REF] and, in spring, also to the search for spawning support [START_REF] Cech | Distribution of egg strands of perch (Perca fluviatilis L.) with respect to depth and spawning substrate[END_REF]. Emerging trees and tree stumps, which are rigid, structurally complex and strongly used and preferred in spring, correlate to the type of spawning substrate sought by perch [START_REF] Gillet | A survey of the spawning of perch (Perca fluviatilis), pike (Esox lucius), and roach (Rutilus rutilus), using artificial spawning substrates in lakes[END_REF][START_REF] Cech | Distribution of egg strands of perch (Perca fluviatilis L.) with respect to depth and spawning substrate[END_REF][START_REF] Snickars | Habitat selectivity of substrate-spawning fish: modelling requirements for the Eurasian perch Perca fluviatilis[END_REF]. This preference for complex habitats observed throughout the year for the substrate type and to a lesser extent in summer for emerging trees and tree stumps can probably be related to feeding given that they can shelter macro-invertebrates and fish [START_REF] Czarnecka | Is coarse woody debris in lakes a refuge or a trap for benthic invertebrates exposed to fish predation?[END_REF]. With the beginning of autumnal mixing the perch migrated into slightly deeper waters as already described [START_REF] Craig | Seasonal changes in day and night activity of adult perch, Perca fluviatilis L[END_REF][START_REF] Imbrock | Diel and seasonal distribution of perch in Lake Constance: a hydroacoustic study and in situ observations[END_REF]. We showed that, in the Bariousses reservoir, the most used and preferred depths shifted to [2.5, 7.5[m in autumn and winter. The low use of the littoral zone in these seasons was accompanied by a decrease of the attractiveness of emerging trees and tree stumps. Regarding the preferences, some exceptions could appear in winter, when littoral zones with emerging trees were still significantly more used than those without (Table 3) or in autumn, when the compositional analysis did not see any significant use or selection of tree stumps (Table 3) whereas the selection ratios showed a significant preference (Figure 4d). In this last case, the significance was however not very strong and a small variation in the sample could probably have led to a non significant result, especially as the availability of emerging trees was the lowest in autumn.

Such studies would be worth conducting on different species to improve knowledge of the impacts of human induced WLF in reservoirs. Even if we did not show any effect of WLF on adult perch habitat preference, they could act differently on other species such as pike, a more demanding species in terms of spawning substrate [START_REF] Craig | A short review of pike ecology[END_REF]. Very recently, [START_REF] Cooke | A moving target-incorporating knowledge of the spatial ecology of fish into the assessment and management of freshwater fish populations[END_REF] submitted that: "quantifying and describing the spatial ecology of fish and their habitat is an important component of freshwater fishery assessment and management". Fish habitat requirement is the basis for rehabilitation [START_REF] Müller | Fish habitat requirements as the basis for rehabilitation of eutrophic lakes by oxygenation[END_REF][START_REF] Cooke | A moving target-incorporating knowledge of the spatial ecology of fish into the assessment and management of freshwater fish populations[END_REF] and could help to adapt hydraulic management to efficiently preserve fish populations. Operational tools to quantify human influence (through hydraulic management, stocking, recreational use) and environmental drivers (temperature, water quality) on fish populations in reservoirs still remain scarce. In environments where the littoral zone is altered, hydromorphological rehabilitation programs are often implemented [START_REF] Gonzalez | Restoration of riparian vegetation: A global review of implementation and evaluation approaches in the international, peer-reviewed literature[END_REF]. Any study that could provide insight into the impact of a hydromorphological restoration on the fish population is valuable (e.g. [START_REF] Boromisza | Lakeshore-restoration-landscape ecology-land use: assessment of shore-sections, being suitable for restoration, by the example of lake Velence (Hungary)[END_REF][START_REF] Rose | Proposed best modeling practices for assessing the effects of ecosystem restoration on fish[END_REF], including species-habitat preference studies.

In conclusion, our study indicated that large perch selected zones at different depths in the reservoir mainly according to seasons without any effect of WL. In spring and summer, they highly used and preferred the littoral zone and the complex habitats it hosts, independently of the WL, even if the structural complexity of the littoral zone was reduced when the WL lowered. In autumn and winter they migrated to deeper zones. Our results also highlighted quite a high individual variability in the habitat preferences. This study contributes to the understanding of the spatial ecology of fish, which is essential to leading efficient management actions [START_REF] Cooke | A moving target-incorporating knowledge of the spatial ecology of fish into the assessment and management of freshwater fish populations[END_REF]. Based on these findings, even if WLF were shown not to impact perch habitat preferences, we can propose the following management actions to prevent eggs from being dewatered: in spring, to keep the WL stable at mean or high level or at least to avoid sharp lowering of WL from mid-April, the likely start of the spawning season, to mid-June when the majority of eggs have hatched; to add spawning substrates, woody structures for example, at mean and low WL to encourage perch to spawn deeper.

Table 3 Results of the compositional analysis [START_REF] Aebischer | Compositional analysis of habitat use from animal radio-tracking data[END_REF] for each habitat variable (depth, main substrate, emerging trees, tree stumps). The habitat types are ranked from more used (top) to less used (bottom) and bold text indicates significance of the use of one habitat type compared to all other combined. The Wilk's lambda statistics is given with its associated 95% p-value which is in bold type when the habitat selection is significant

Figure captions Fig. 1 Fig. 3 Fig. 4 1

 captions1341 Figure captions

Acknowledgements

We thank Tiphaine Peroux, Julien Dublon, Marie-Laure Acolas, Mario Lepage, Virginie Raymond, and Charlie Roqueplo for their assistance in the field, Yann Le Coarer for dGPS treatments, Nathalie Reynaud for GIS treatments and Hervé Capra, Nicolas Lamouroux, and Hervé Pella for useful discussions. We also thank numerous other people who occasionally helped in the field. Furthermore, we thank Electricité de France, which manages the Bariousses reservoir, for permission to use the lake and water level data.The authors would like to thank two anonymous reviewers, whose advice substantially improved the manuscript.


Caught in the abyssal giddiness caused by the question of traces, the 21 st century finds itself constantly at risk of straying from meaning. The CNRS Human Trace series 3 shows how the trace is cognized in different disciplines and why reductive interpretive processes impose a deconstruction of the processes at work in the human interpretation of the notion of trace.

With the social and cultural dimension playing a major role, a situated analysis was necessary beforehand to distinguish between western and eastern cultural traditions whereby the former envisions a disconnection between the thinking subject and the object, between the body and mind, between the outside and inside of the body of the thinking human.

With the Human-Trace paradigm, we put forward a radical challenge to this idea of Human. Human beings are conceived as being "constructed by the traces of their interaction with their environment, whatever the nature of this might be; the environment in return bearing the traces of human actions, both of them retroacting in a systemic dynamic" (Galinon-Mélénec, 2011). This anthropological conception is the condition of an episteme which is not restricted to the humanities. Hence the gradual opening of the series' works to researchers from all disciplines agreeing to position themselves in relation to the definition of a human condition of the Human-Trace conceived as a blurred structuring of the processes of knowledge of the Real and as an epistemological obstacle to identify in order to integrate it better in the history of the sciences.

The dynamic of this paradigm has led us to place it as the keystone of different scientific works and articles which, in uniting praxis and episteme, aim to provide a deep understanding of "the complexity of the notion of trace" (Jeanneret, 2011).

An attempt to identify the hidden life of the trace processes operating in the interpretation of the real is all the more difficult as their resultants appear only in the form of sign-trace, i.e. as signs which integrate the origin of the production and interpretation (Galinon-Mélénec, 2011). With this terminological transfer, we wish to show that the use of the terms trace and sign taken alone leave those who use them to think that they carry a set meaning whereas, as Derrida said, it is revealed to each in their difference (Derrida, 1967) 4 .

Volume IV of the Human-Trace series questions specifically the body traces of the Human-Trace. While recognizing the interest of the type of anthropology which allows -for example -the doctor to consider a patient's body as an object of analysis independent of her own body, the Human-Trace anthropology requires examination of the "interpreted-body" of the patient and the "interpreting-body" of the doctor, as a body in co-presence, living bodytraces crossed by flows resulting from the process of permanent interaction inside the body, from inside to outside and from outside to inside.

Considering the body as a "body-trace" invites one to study the processes which have participated in its formation, that they come out of the ecological multifactorial system with which it is in interaction as a living-body present in the world or as an heir to the generations that preceded it in history.

By bringing together the viewpoints of researchers from different disciplines, Volume IV's purpose is to bring to the reader's understanding points of reference to be known by all who question themselves about the implications of using techniques which, integrating the nonliving with the living and the living with the non-living, blur the frontiers of the body image that human beings have of themselves and their identity. This work is consistent with the series' volumes, one of whose objectives is to lay down the foundations of an interpretation of the real by a Human-Trace conceived as unconfined by the boundaries between body and mind, nature and culture, human and environment, present, past and future.

By lifting the veil on the system of values which underpin the new relationships between humans and their bodies, human beings, animals and robots, and, more generally, information and communications technologies, it is possible to make readers face the consequences of their choices, be they on themselves, contemporary society or on the evolution of the human condition.

  Béatrice "Le corps-trace: arguments", Préface de L'Homme-trace, tome IV, (Galinon-Mélénec B. dir), CNRS éditions, 2017, pp 9-11). Publié sur Hal avec l'autorisation de Béatrice Galinon-Mélénec et de CNRS éditions _____________________________________________________________ "The body-trace: arguments" 1 Béatrice Galinon-Mélénec 2

Translator : Isobel Hié (UK). Source: Galinon-Mélénec Béatrice "Le corps-trace: arguments", Préface de L'Homme-trace, tome IV, (Galinon-Mélénec B. dir), CNRS éditions,

2017, pp 9-11). 2 UMR IDEES 6266 Normandie Université-CNRS, Le Havre. 3 Béatrice Galinon-Mélénec (dir.).

In using the term differance with an "a" instead of an "e", as in the usual spelling of the term "difference", we wish to refer the reader to the texts of Derrida (Derrida J., Of Grammatology,Speech and Phenomena. Writing and Difference, 1967).