Anne Joulain

Valérie Audurier

Pascal Gadaud

Joël Bonneville

Clio Azina

Yongfeng Lu

Jean-François Silvain

Correlation of the mechanical properties of Cu/C composite materials with the chemistry of Cu-C interfacial zone

Keywords: metal matrix composite, microstructure, mechanical properties, carbon fiber, copper matrix

In the frame of thermal management applications, copper metal matrix reinforced by carbon fibers (CF) are undoubtedly one of the most promising composites for heat sinks. In this work, two types of composite materials were produced: Cu(Cu-Ti)x/CF composites fabricated with a mixture of Cu and Cu-Ti powders by a solid-liquid co-existent phase process and Cu/CF composites fabricated without the Cu-Ti powder. The mechanical properties and postdeformation microstructures of both composite materials have been investigated. Compression tests were performed at room temperature under constant strain-rate deformation condition. Elastic properties were examined using a dynamic resonant method over the temperature range 20°C -250 °C. The results show that the addition of Ti and the resulting formation of the TiC interphase at the Cu-CF interfaces are able to create strong interfacial bonding evidenced by a deformation without pull-out. When the volume fraction of CFs reaches 40%, crack percolation occurs in the Cu(CuTi)/CF composite leading to the sample ruin in case of strong interfaces. In the case of Cu/CF, fiber pull-out allows for deformation.

Introduction

High-power electronic devices, such as supercomputers, generate considerable amount of heat.

If the heat is not dissipated away from the internal circuitry of the devices, the circuits would be overheated, leading to a significantly reduced lifetime. Thermal management materials, featured by tailored thermal properties, are used to dissipate heat away from the device circuitry to minimize device degradation during service cycles.

Heat sinks are a component or assembly in electronic packaging systems wherein the heat produced in electronic chips (usually made of silicon (Si) or silicon carbide (SiC)) is dissipated externally to fluids or air both in the normal and tangential directions [START_REF] Mathias | Architectural optimization for microelectronic packaging[END_REF], [START_REF] Luedtke | Thermal Management Materials for High-Performance Applications[END_REF][START_REF] Zweben | Advances in composite materials for thermal management in electronic packaging[END_REF][START_REF] Geffroy | Structural and Thermal Properties of Hot Pressed Cu/C Matrix Composites Materials Used for the Thermal Management of High Power Electronic Devices[END_REF]. To avoid thermally induced stresses in the chips, the coefficient of thermal expansion (CTE) of the heat sinks should closely match that of the chips while they should have a thermal conductivity (TC) as high as possible for effective heat dissipation.

In general, metal matrix composites (MMCs) show several improvements in comparison with the currently used materials in electronic packaging, including: i) lower and tailorable CTEs (the higher the volume fraction of reinforcement is used, the lower the CTE would be); ii) high heat dissipation capability; iii) light-weight, suitable for space applications; and iv) high stiffness at elevated temperatures (for dimensional stabilities).

Cu-based materials are the most promising ones among MMCs [START_REF] Zweben | Advances in composite materials for thermal management in electronic packaging[END_REF][START_REF] Schubert | Interfacial characterization of Cu/diamond composites prepared by powder metallurgy for heat sink applications[END_REF][START_REF] Weber | On the influence of active element content on the thermal conductivity and thermal expansion of Cu-X (X=Cr, B) diamond composites[END_REF][START_REF] Chu | Thermal conductivity of SPS consolidated Cu/diamond composites with Cr-coated diamond particles[END_REF]. Most composites based on this matrix are reinforced by ceramics (particles, short fibers, and long fibers) in order to reduce their extremely high CTEs (e.g., Cu: 16.8×10 -6 /K) in an effort to match with those of the semiconductors (e.g., Si: 4×10 -6 /K) or other ceramic substrates (e.g., Al2O3: 8×10 -6 /K).

Since carbon fibers (CFs) have high thermal conductivity (100 to 1000 W/m.K) along the axial direction, MMCs reinforced with CFs show excellent thermal conductivity along the fiber axial directions.

For a thermally conductive assembly, the interfaces should allow proper heat transfer between the two materials and efficient transfer of thermomechanical load during thermal cycling. In nonreactive systems such as Cu-C, the absence of chemical bonding compromises the thermal and mechanical transfers [START_REF] Silvain | The role of controlled interfaces in the thermal management of copper-carbon composites[END_REF]. Several approaches have proposed to solve the lack of wettability (chemical recation) in Cu-C system. First, carbide-forming elements (Ti, Cr, W) [START_REF] Li | Microstructure and thermal conductivity of Cu/diamond composites with Ti-coated diamond particles produced by gas pressure infiltration[END_REF][START_REF] Kang | Preparation of copperdiamond composites with chromium carbide coatings on diamond particles for heat sink applications[END_REF][START_REF] Che | Spark plasma sintering of titanium-coated diamond and copper-titanium powder to enhance thermal conductivity of diamond/copper composites[END_REF][START_REF] Abyzov | High thermal conductivity composite of diamond particles with tungsten coating in a copper matrix for heat sink application[END_REF] or directly carbide (TiC, BC) [START_REF] Zhang | Improvement in Mechanical and Thermal Properties of Graphite Flake/Cu Composites by Introducing TiC Coating on Graphite Flake Surface[END_REF][START_REF] Bai | Thermal conductivity and mechanical properties of flake graphite/copper composite with a boron carbide-boron nano-layer on graphite surface[END_REF] are used as surface coating for the reinforcements prior to sintering. A second approach consist in addition of the metal alloying elements in the metallic powders, the layer nucleating during the sintering process [START_REF] Schubert | Interfacial characterization of Cu/diamond composites prepared by powder metallurgy for heat sink applications[END_REF][START_REF] Sinha | Influence of interfacial carbide layer characteristics on thermal properties of copper-diamond composites[END_REF][START_REF] Chung | Effect of Titanium Addition on the Thermal Properties of Diamond/Cu-Ti Composites Fabricated by Pressureless Liquid-Phase Sintering Technique[END_REF][START_REF] Che | The influence of minor titanium addition on thermal properties of diamond/copper composites via in situ reactive sintering[END_REF][START_REF] Veillère | Relationship between interphase chemistry and mechanical properties at the scale of micron in Cu-Cr/CF composite[END_REF]. An alternative consist in using graphene as effective interlayer between carbon reinforcement and Cu matrix [START_REF] Cao | Graphene interlayer for enhanced interface thermal conductance in metal matrix composites: An approach beyond surface metallization and matrix alloying[END_REF][START_REF] Cao | Wide and fine alignment control and interface modification for high-performance thermally conductive graphite/copper composite[END_REF]. If the thermal and thermomechanical properties of MMC composite materials have been widely investigated, the mechanical properties and their correlation with the chemistry of the interfacial zones are less studied. The authors generally report improvement of the composites strength and hardness that however depend on the alloying element [START_REF] Bai | Thermal conductivity and mechanical properties of flake graphite/copper composite with a boron carbide-boron nano-layer on graphite surface[END_REF][START_REF] Wan | Effects of fiber volume fraction, hot pressing parameters and alloying elements on tensile strength of carbon fiber reinforced copper matrix composite prepared by continuous three-step electrodeposition[END_REF][START_REF] Ureña | Characterization of interfacial mechanical properties in carbon fiber/aluminium matrix composites by the nanoindentation technique[END_REF][START_REF] Tang | Interface characteristics and mechanical properties of short carbon fibers/Al composites with different coatings[END_REF][START_REF] Jun | Tensile and Friction Properties of Tin Bronze Matrix Composites Reinforced by Carbon Fibers[END_REF][START_REF] Wang | Improvement of interfacial interaction and mechanical properties in copper matrix composites reinforced with copper coated carbon nanotubes[END_REF]. Few is reported on ductility and plastic behavior.

In solid-liquid co-existent phase process, well known in Al-based composites [START_REF] Schubert | Interfacial characterization of Cu/diamond composites prepared by powder metallurgy for heat sink applications[END_REF][START_REF] Beffort | Interface formation in infiltrated Al(Si)/diamond composites[END_REF], the presence of a liquid phase has been shown to enhance the reactivity between the carbideforming elements and the carbon reinforcement as well as the density of the materials. In the case of Cu-based composites, it is shown that the addition of such carbide interface enhances the thermal properties of the Cu/CF and Cu/diamond composite materials [START_REF] Azina | Effect of titanium and zirconium carbide interphases on the thermal conductivity and interfacial heat transfers in copper/diamond composite materials[END_REF][START_REF] Azina | Solidliquid co-existent phase process: Towards fully dense and thermally efficient Cu/C composite materials[END_REF].

Therefore, In this work, the mechanical properties and post-deformation microstructures of the Cu/CF and Cu(CuTi)/CF composite materials have been investigated; the Cu(CuTi)/CF composites being obtain using the solid-liquid co-existent phase process. Compression tests have been performed at room temperature with a constant strain rate. Elastic properties have been studied by means of dynamic resonant method (DRM) at room temperature and at temperatures up to 250 °C. Mechanical properties of the fabricated composite materials have been correlated with the chemistry of the interfacial zones.

Experimental

Synthesis and microstructural characterization of composite materials

Composite materials studied in the work have been fabricated using conventional powder metallurgy process. Pure Cu powders and a mixture of Cu and Cu-Ti powders have been used as matrix whereas CFs have been used as the reinforcement. Cu powders have dendritic shape (ECKA ® Granules Germany GmbH) with a mass median particle size a d50 value close to 35 m, and Cu-Ti alloyed powders have spherical shape with a d50 value close to 16.7 m. The Cu-Ti alloy was produced by atomization with a composition of 27 at.% of Ti (NANOVAL GmbH & Co. KG). CFs (K223HM, CTN DIALEAD™/BOBBINS, Sumitomo Corporation Europe Limited) have an average length of 250 μm and an average diameter of 10 m (aspect ratio = 25). Cu powders (+ Cu-Ti powders) and CFs are cautiously introduced together inside a Siemens 3D mixing device and mixed at 20 RPM for 90 min.

Two sets of composite materials were sintered: 1) Cu/CF composites fabricated without Cu-Ti powders and 2) Cu(Cu-Ti)x/CF composites fabricated with a mixture of Cu and Cu-Ti powders.

The sintering of the composite materials was carried out using a Thermolab ® press. The powders were cold pressed in a carbon mold of 20 mm in diameter and then pressed/heated using an induction system. Powders for both sets were hot pressed at 950 °C under 40 MPa for 30 min. A reference Cu sample without reinforcement has been produced at 600 °C. A thermocouple inserted into the graphite mold close to the powder mixture was used to control the temperature. Primary vacuum (10 -2 mbar range) was used to prevent oxidation during both heating and cooling steps of the composite materials. Composite materials with 10 and 40 vol.% of CFs were densified. The amount of liquid Cu-Ti phase was set to 4 vol.%. The three composite materials were designed by the following notation: Cu60/CF40, Cu86(Cu-Ti)4/CF10, and Cu56(Cu-Ti)4/CF40.

The microstructures of the Cu/CF composites were characterized using scanning electron microscopy ((SEM, VEGA II SBH, TESCAN ® and field emission gun SEM (FESEM, Jeol ® 7001FTTLS) before and after the deformation. Transmission electron microscopy (TEM) was performed on JEOL 2100 microscope operating at 200 kV.

Mechanical characterization

For all mechanical characterizations, the samples were cut with a loading axis perpendicular to the compaction direction of the sintering process, so that no preloading was applied along the compression axis before mechanical testing.

Elasticity

The Young's modulus E was determined using the resonant frequency technique in bending mode on the beam samples [START_REF] Mazot | Mesure des constantes d'élasticité et du frottement intérieur des solides par méthode de résonance entre 20 et 1200°C[END_REF]. It allows the experiments performed at 2 K/min under secondary vacuum (10 -6 mbar) from -150 up to 1100 °C without any harmful contact. Steel wires located at the vibration nodes were used to maintain the samples horizontally. An electrostatic device (capacitance created between the sample and a unique electrode) insures excitation and detection.

Compression tests

The samples were extracted from the as-fabricated small cylinders using a resinoid cut-off wheel type C PRESI ® specially well adapted for soft materials such as Cu. Sample surfaces were then mechanically polished using abrasive SiC grinding papers sheets of successive finer grades up to 3 μm followed by a final polishing with silica suspension for removing eventual hardening damages that may arise during the cutting stage. Special care was given in the final polishing to obtain the best possible parallelism of the sample heads. The final polishing also allows microstructure analysis by SEM after the deformation. The final sample sizes were 3 mm x 3 mm in the cross-section with a 7 mm gauge length. At least two samples were deformed for each composite material.

The compression tests were performed at room temperature (RT) on an Instron ® 1114 type testing machine using an inverted compression device described elsewhere [START_REF] Bonneville | Deformation Regimes in the Intermetallic Alloy, Ni3Al[END_REF]. In this configuration, the decrease in sample lengths was obtained from the differential signal of two displacement transducers, each of them being equipped with a ceramic rod allowing displacement measurement close to the sample heads. All deformation tests were carried out at a constant crosshead displacement of 50 m/min, which corresponds to a nominal strain rate of around 1.2×10 -4 s -1 .

Results and discussions

Anisotropic distribution of CFs after hot densification

Figure 1 shows typical microstructures of Cu(CuTi)x/CF composite material where CFs are randomly distributed in the plane perpendicular to the compaction axis of the sintering process (Fig. 1a). Figure 1b reports chemical cartographies obtained on a surface parallel to the compaction direction. As expected, the interfacial zone between Cu matrix and CF is Ti rich.

High resolution TEM micrograph (Figure 1c -left) shows typical nanocrystalline structure of the interphase. The electron diffraction pattern (Figure 1c -right) shows rings of discrete spots characteristic of the nanocrystalline structure and the rings diameter correspond to the TiC structure. These observation are similar to the ones of Azina et al. [START_REF] Azina | Solidliquid co-existent phase process: Towards fully dense and thermally efficient Cu/C composite materials[END_REF] The higher magnification SEM micrograph shows a typical CF-Cu interfacial zone (insert in Fig. 1a). As expected, during the densification process, Ti atoms diffuse and react with the CFs to form continuous TiC coating around each CF. Thickness of the TiC interface can be monitored with the amount of Cu-Ti powders which are added to the Cu+CF mixture before the hot densification process [START_REF] Azina | Solidliquid co-existent phase process: Towards fully dense and thermally efficient Cu/C composite materials[END_REF].

INSERT FIGURE 1 HERE

Elasticity measurements

Young modulus at RT

Young modulus evolution with temperature

The Young modulus of Cu56(CuTi)4/CF40 (Fig. 2) was measured during the heating from RT to 250 °C (green points). The sample was then annealed for 15 h at 250 °C and the Young modulus was measured during the cooling process from 250 °C to RT (black points). We observed a slight decrease in the Young modulus with the increase in the annealing temperature.

Comparison between the Young modulus values before and after annealing shows no significant difference.

Similar experiments were performed on Cu60/CF40 samples: red points during heating and blue points during cooling in Fig. 2. In this case, we found a decrease in the Young modulus at RT of about 5 GPa after the heat treatment: 104 to 99 GPa. In this figure, the proof stresses 0.2% defined at 0.2% plastic strain are directly shown in Fig. 3 at the crossing of the stress strain curves and the dotted line parallel to the stress axis (the values are reported in Table 2). It is clearly seen, by comparing the results for the Cu86(CuTi)4/CF10 and Cu56(CuTi)4/CF40 composites, that the increase in the CF content induces a decrease in the 0.2% values. Also, for a similar CF content (40 vol.%), the composite material without TiC interphase presents a lower 0.2% than the one with TiC interfaces. The Cu86(CuTi)4/CF10 and Cu60/CF40 stress-strain curves have a similar shape, and both present a large ductility domain.

INSERT FIGURE 2 HERE

Note that for both composites the tests have been interrupted at = 8% without any breaking of the sample. On the contrary, Cu56(CuTi)4/CF40 exhibits very limited ductility (nearly 1.5%).

The ductile composites show a slight difference in their flow stress. Both composites behave quite similarly at the onset of the plastic deformation, but a higher flow stress is achieved for the Cu86(CuTi)4/CF10 composite which has the lowest CF content.

INSERT TABLE 2 HERE

Characterization of the composite microstructures after the compression tests

The microstructures of the Cu56(CuTi)4/CF40 and Cu60/CF40 composites, after the compression tests, have been analysed by SEM. As shown in Fig. 4a, the Cu56(CuTi)4/CF40 sample presents a heterogeneous deformation characterized by a barrel-shape at one head only. A large crack propagating along a direction at about 35° of the compression axis crosses the surface of this part. The crack propagates in the sample following a path along the Cu-CF interfaces through interface delamination. In rare cases, the crack propagates through the interface into the CF (see insert in Fig. 4b). As observed, when delamination takes place, TiC interphase adheres to the Cu matrix rather than to the CFs. In Fig. 4c, obtained in an area from the large crack, radial crack initiations are observed at the Cu-CF interface. The deformed Cu60/CF40 composite presents a quite homogeneous deformation as shown in Fig. 5a; no macroscopic crack propagates through the surface of the sample. In Fig. 5b obtained at a higher magnification, some cracks are visible but they do not propagate over long distances across the sample. Actually, the main observation is linked with the presence of pull-out CFs on the surface of the sample after the compression test (cf. Fig. 5c). As observed in Fig. 5c, no radial crack initiates at the matrix-CF interface.

INSERT FIGURE 4 HERE

INSERT FIGURE 5 HERE

Figure 5: SEM micrographs of the Cu60/CF40 composite materials after the compression test

Discussion

Elasticity

To understand the effect of CF addition on the Young's modulus value of the composite, we analyzed the complex elasticity of the Cu/CF composite that consists of a planar and homogeneous distribution of highly anisotropic CFs in a polycrystalline Cu matrix. The first step was to describe the elasticity of the CFs. From the CFs elastic data (E, G and ) provided by the supplier, the CF Sij compliances have been calculated. E, G, , and calculated Sij are listed in Table 3. We can note that the modulus ratio between the longitudinal and transverse directions is about 80, confirming the high elastic anisotropy of the CFs. It is worth noting that ratio of 30-40 can be found in literature for long CFs but it may increase for shorter CFs, as calculated in this work. Sij compliances allow to calculate the Young modulus E at any fiber angle with the loading direction. To take into account the random in-plane distribution of CFs (Fig. 1), we may consider a 2D statistical distribution of CF orientations. Different methods can be used to estimate the average Young modulus. As the anisotropy is very high, it is justified to use a self-consistent approach applied to transverse anisotropic elasticity [START_REF] Berryman | Bounds and self-consistent estimates for elastic constants of random polycrystals with hexagonal, trigonal, and tetragonal symmetries[END_REF]. With this approach, we obtained an average value of 57 GPa. This value is close to the modulus of the transverse direction due to the high anisotropy of the CF properties. The last step is to calculate the Young modulus of the two-phase composite using the Cu Young modulus and the average CF one calculated. As the modulus of the two components is in the same order of magnitude, the upper and lower limits of the composite elastic coefficients can be calculated using the Voigt (equal strain) and Reuss (equal stress) models. Table 4 lists the experimental values and the calculated ones (the scatter for Voigt and Reuss models is strictly the same as for experimental data). We can note that the experimental values are slightly higher than the limits calculated that is certainly due to the uncertainty on CF data and their complex distribution. It means that the average Young modulus of the CFs calculated is underestimated.

INSERT TABLE 3 HERE EL (GPa) ET (GPa) GL (GPa)L GT (GPa

For instance, a simulation using an average modulus of 80-90 GPa yields Voigt and Reuss limits that include the experimental values. Our approach reproduces the overall trends observed on the different composites, in particular, the composite modulus is lower than that of the Cu matrix. The main result is the different behaviors of the two composites with temperature: the composite with TiC interphase does not show significant Young modulus change while a significant decrease was observed for the Cu/CF composite materials without TiC interphase.

INSERT TABLE 4 HERE CF vol.% E (GPa) -Voigt E (GPa) -Reuss E (GPa

The stability, during the heat treatment, of the Young modulus of Cu56(CuTi)4/CF40 composite suggests that the composite microstructures do not change during the experiment. On the contrary, the decrease observed for Cu60/CF40 suggests microstructural changes of the composite. The main difference between both composites is the interface nature, with or without TiC interphase. Microstructural evolution in Cu60/CF40, during elasticity measurement under heat treatment, can be attributed to the Cu-CF interface debonding. After the compression tests, SEM analyses have also shown that the interfaces behave differently under stress with delamination at the Cu-C interfaces in Cu60/CF40 (Fig. 6c). During Young modulus measurement, when the specimen was heated, the difference between the CTE of C and Cu created this damage similar to what would occur during thermal fatigue. The presence of these discontinuities lowers the rigidity of the composite as commonly recognized and already studied with our experimental technique using electrolytic micro-cracked Cr [START_REF] Berryman | Bounds and self-consistent estimates for elastic constants of random polycrystals with hexagonal, trigonal, and tetragonal symmetries[END_REF][START_REF] Gadaud | Application of the dynamical flexural resonance technique to industrial materials characterization[END_REF].

A 2D mechanical calculation allows estimation of the interface transverse thermal stress during the heating from RT to 250 °C:

σ F = -αΔTE M E CF (1-𝑓) (1-ν F )((1-f)E M +fE CF ) (5)
σ M = αΔTE M E CF 𝑓 (1-ν M )((1-f)E M +fE CF ) (6)
where α is the CTE of Cu (we have neglected the fiber CTE which is much lower than that of Cu), ΔT is the temperature gap, f is the CF volume fraction, EM and ECF are respectively the matrix modulus and the transverse CF modulus respectively, νM and νCF are the respective Poisson's ratios.

Numerically we obtained σF = -54MPa and σM = +40 MPa. The transverse interface decohesive stress is about 94 MPa that is in the same order of the yield stress σ0.2% (99 MPa) observed.

Therefore, this approach is consistent with a local interface delamination. Actually Wan et al.

showed clearly such debonded interfaces in C/Cu the composites fabricated by hot pressing [START_REF] Wan | Effects of fiber volume fraction, hot pressing parameters and alloying elements on tensile strength of carbon fiber reinforced copper matrix composite prepared by continuous three-step electrodeposition[END_REF].

Compression tests

Considering the 0.2% of the different composite materials, our results show that increasing the amount of CFs decreases the strengthening. 0.2% which is the maximum for 10 vol.% of CFs (125 MPa for Cu86(CuTi)4/CF10) and then decreases to 114 MPa for 40 vol.% of CFs with TiC interphase(Cu56(CuTi)4/CF40) and to 99 MPa without TiC interphase (Cu60/CF40). Actually, the calculation, based on the 2D statistical distribution of CF orientations, leads to an estimation of an average CF Young modulus between 50 and 90 GPa -see above -that is inferior to that of the Cu (124 GPa). In this case ,CFs do not act as direct "reinforcing" elements of the Cu matrix and addition of CFs in the Cu matrix leads to a decrease in 0.2%. From a simple rule of mixture calculation, the decrease of 0.2% is close to 10 MPa when volume fraction increases from 10 vol.% to 40 vol.% of CFs that is in accordance with the experimental decrease from 125 MPa for Cu86(CuTi)4/CF10 to 114 MPa for Cu56(CuTi)4/CF40. Considering these two composites, microstructure and morphology of the interface are identical and therefore should not contribute to the observed 0.2% difference.

With the same volume fraction of CFs, Cu56(CuTi)4/CF40 presents a higher 0.2% than Cu60/CF40. This difference must be correlated with the different Cu-CF interfaces analysed in both composites; carbide interphase being present in Cu56(CuTi)4/CF40 composite. Interfacial reaction can play an important role on strengthening properties: chemical reaction ensure intimate interfacial contact and hence raise the bond strength. It may improve load transfer (direct strengthening) and/or change the strain state and then influence the indirect strengthening. In our case, CFs do not participate to direct strengthning. Therefore, improving load transfer has to be ruled out in the explanation of difference between 0.2% of Cu56(CuTi)4/CF40 and Cu60/CF40. This difference may be attributed to enhanced indirect strengthening in the case of strong interface. On the other hand, SEM analyses show that these interfaces (with or without carbide interphase) behave differently under stress: interface decohesion takes place, after compresion tests, for the Cu60/CF40 composite. Then, at least in the case of Cu60/CF40, 0.2% may be controlled by decohesion at the interfaces. This result is consistent with the results by Wan et al., attributed the decreased strength in the C/Cu composite to the interfacial debonding [START_REF] Wan | Effects of fiber volume fraction, hot pressing parameters and alloying elements on tensile strength of carbon fiber reinforced copper matrix composite prepared by continuous three-step electrodeposition[END_REF].

A reference Cu sample was deformed under the same conditions as the Cu/CF composite materials and 0.2%-Cu were measured. The 0.2%-Cu value measured, 70 MPa, is smaller than the composite value measured for any CF volume fraction. Therefore, despite the addition of CFs with lower average Young modulus, the composites present higher 0.2% than the Cu matrix. This strengthening of the composites observed can be correlated to the indirect strengthening due to the microstructural evolution of the Cu matrix.

The stress-strain curves of the composites exhibit very different shapes than the unreinforced Cu matrix. It is recognized that deformation Cu at room temperature is characterized by a large strengthening characteristic of work-hardening by dislocation forests [START_REF] Basinski | Plastic deformation and work hardening[END_REF]. The composite curves only show either a small strengthening or even a softening in the case of 40 vol.% of CFs without the TiC interphase. These curves indicate that forest hardening is not the only involved mechanisms of hardening. Indeed, SEM analysis shows crack initiation at Cu-CF interfaces, suggesting that microstructural damages, crack initiation, and cavitation at interfaces result from elastic stress relaxations in the composites. Such elastic stress relaxation by microstructural damages was also observed during strain-controlled thermal cycling like in Albased matrix reinforced by Al2O3 fibers [START_REF] Kwei | Thermal-mechanical fatigue behaviour of alumina fibre/aluminium-lithium composite[END_REF]. Compression tests also provide evidence of the lack of ductility of Cu56(CuTi)4/CF40 compared to Cu60/CF40. A strong interfacial bond will allow an incoming crack to go through the interface [START_REF] Chawla | Metal Matrix Composites[END_REF]. SEM analysis (Fig. 4) shows that in the case of Cu56(CuTi)4/CF40 cracks propagate across the whole sample, leading to its ruin. This propagation is possible when the volume fraction of the reinforcement is sufficiently large to reach percolation of cracks initated at the interfaces. Cu86(CuTi)4/CF10 composites reach around 8% of ductility due to the fact that cracks do not percolate. In the case of Cu60/CF40, weak interfaces lead to fibers debonding followed by crack deflection and finally by fiber pull-out. This phenomena leads to enhanced fracture toughness. In our case, the sample reach 8% strain without catastrophic failure (see figure 5a).

Conclusion

Data availability

The raw/processed data required to reproduce these findings cannot be shared at this time due to the General Information Security Policy (PGSI) of our institution (CNRS).

Figure 1 :

 1 Figure 1: Typical Cu/CF(TiC) composite materials microstructure. a-Observation plane parallel (left) and perpendicular (right) to the compaction direction. b-Chemical cartographies obtained by EDS. Titanium carbide interphase is observed. c-TEM analysis of Cu-Cu interphase and corresponding electron diffraction pattern.

Figure 2 : 3 . 3 Figure 3 :

 2333 Figure 2: Changes in the Young's modulus during heat treatments: Cu56(CuTi)4/CF40 and Cu60/CF40 were heated from RT to 250°C, annealed for 15h and then cooled from 250 °C to RT

Figure 4 :

 4 Figure 4: SEM micrographs of the Cu56(CuTi)4/CF40 composite materials after the compression test.

Table 4 :

 4 Comparison between the calculated and experimental values of the Young modulus of Cu/CF composite materials

  Mechanical properties and post-deformation microstructures of the Cu/CF and Cu(CuTi)/CF composite materials have been investigated. The results show that:  The addition of Ti and the resulting formation of the TiC interphase at the Cu-CF interfaces are able to create strong interfacial bonding evidenced by a deformation without pull-out.  Microstructural damages relax elastic stresses: crack initiation at interfaces and propagation in the case of Cu(CuTi)/CF or pull out in the case of Cu/CF.  When the volume fraction of CFs reaches 40%, crack percolation occurs in the Cu(CuTi)/CF composite leading to the sample ruin in case of strong interfaces. In the case of Cu/CF, fiber pull-out allows for deformation.

Table 1

 1 lists the density and Young's modulus of Cu86(CuTi)4/CF10, Cu56(CuTi)4/CF40 and Cu60/CF40 measured at RT. We first see that the modulus value have small fluctuation, consistent with a homogeneous distribution of CFs in all the sintered volume. A second point is that comparison between Cu56(CuTi)4/CF40 and Cu60/CF40 shows that the addition of Ti does not change the modulus value. Actually, a few amount of TiC is present in the composite (2-4%) and our results show that interfaces do not affect the Young modulus values. The Young's modulus value of composites with 10 vol.% of CFs (124 GPa) is larger than those with 40 vol.% of CFs (108 GPa). Then the addition of CFs reduces the composite modulus.

		INSERT TABLE 1 HERE
		Density	E (GPa)
	Cu86 (CuTi)4/CF10	8.13 ± 0.01	124 ± 2
	Cu56(CuTi)4/CF40	5.80 ± 0.01	107 ± 3
	Cu60/CF40	5.9 ± 0.1	108 ± 4

Table 1 :

 1 Young

's modulus values and fluctuation for three different composites determined at RT by the dynamic resonant method

Table 2 :

 2 The

	Composite compositions	0.2% values (MPa)
	Cu86 (CuTi)4/CF10	125 ± 2
	Cu56(CuTi)4/CF40	114 ± 7
	Cu60/CF40	99 ±2
	0.2% values for Cu60/CF40, Cu86(CuTi)4/CF10, and Cu56(CuTi)4/CF40.

Table 3 :

 3 Second line: CF elastic data provided by fiber suppliers (L corresponds to the longitudinal direction and T to the transverse one). Fourth line (in grey): Sij are the compliances calculated from the elastic data of E, G and  provided by the supplier.

	)	νL	νT


Alexandre Schickele
email: alexandre.schickele@univ-cotedazur.fr

Eric Goberville

Boris Leroy

Gregory Beaugrand

Tarek Hattab

Patrice Francour

Virginie Raybaud

| Gregory Beaugrand

European small pelagic fish distribution under global change scenarios

Keywords: climate change, ecological niche, exclusive economic zone, range shift, species distribution models, uncertainties

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

| INTRODUC TI ON

European Small Pelagic Fish (SPF) species have a key economic and ecological role [START_REF] Checkley | Climate change and small pelagic fish[END_REF][START_REF] Fréon | Sustainable exploitation of small pelagic fish stocks challenged by environmental and ecosystem changes: A review[END_REF]. SPFs are the main harvested fish group worldwide, representing between 20% and 30% of the global commercial landings, depending on yearly environmental fluctuations and fishing effort (FAO, 2011). These species accounted for 17% of the E.U. catches in 2015 (European Commission & DG-MARE, 2018) and up to 53% of the Mediterranean and Black Sea landings between 2000 and 2013, but most of them are significantly impacted by overfishing (FAO, 2016).

They are also the main prey of most piscivorous fishes, cetacean and seabirds [START_REF] Bachiller | Trophodynamics and diet overlap of small pelagic fish species in the Bay of Biscay[END_REF][START_REF] Cury | Global seabird response to forage fish depletion-one-third for the birds[END_REF], transferring organic matter from the base of the food web to upper trophic levels [START_REF] Cury | Small pelagics in upwelling systems: Patterns of interaction and structural changes in "wasp-waist" ecosystems[END_REF]. Abundantly found in upwelling ecosystems [START_REF] Cury | Small pelagics in upwelling systems: Patterns of interaction and structural changes in "wasp-waist" ecosystems[END_REF], SPFs cover a wide range of regions, therefore overlapping with a large range of environmental conditions [START_REF] Checkley | Climate change and small pelagic fish[END_REF]. European Seas, especially the Mediterranean Sea host a high diversity of SPFs, including both temperate-cold and temperatewarm water species [START_REF] Ben Rais Lasram | The Mediterranean Sea as a 'cul-de-sac' for endemic fishes facing climate change: A marine endemic hotspot under threat[END_REF][START_REF] Coll | The biodiversity of the Mediterranean Sea: Estimates, patterns, and threats[END_REF].

In the context of climate change, a potential range shift of SPFs may induce (a) major economic and social consequences-especially for countries that rely on fisheries for protein supply [START_REF] Tacon | Fishing for aquaculture: Non-food use of small pelagic forage fish-a global perspective[END_REF]-and (b) deep changes in ecosystem and food web functioning (e.g. [START_REF] Chaalali | From species distributions to ecosystem structure and function: A methodological perspective[END_REF]. Predicting climate-induced range shifts of these largely harvested species is therefore essential for sustainable resource management and food security [START_REF] Cheung | How to make progress in projecting climate change impacts[END_REF].

Contemporary fisheries management is mainly based on stock assessment models (e.g., [START_REF] Methot | Stock synthesis: A biological and statistical framework for fish stock assessment and fishery management[END_REF]) that estimate populational parameters (e.g., recruitment, abundance and sustainable harvesting rate) for a given fish stock. Over the last decade, several modelling procedures were developed to include environmental variability in fish stock assessment by focusing on the environment-recruitment relationship (e.g., [START_REF] Mackenzie | Incorporating environmental variability in stock assessment: Predicting recruitment, spawner biomass, and landings of sprat (Sprattus sprattus) in the Baltic Sea[END_REF][START_REF] Tommasi | Improved management of small pelagic fisheries through seasonal climate prediction[END_REF]. Considering environmental uncertainty in stock recruitment is a preliminary step towards a possible integration of global climate change impacts on stock dynamics, however [START_REF] Edgar | Weaknesses in stock assessment modelling and management practices affect fisheries sustainability[END_REF][START_REF] Lee | The benefits and risks of incorporating climate-driven growth variation into stock assessment models, with application to Splitnose Rockfish (Sebastes diploproa)[END_REF][START_REF] Punt | Fisheries management under climate and environmental uncertainty: Control rules and performance simulation[END_REF]. In the context of ecosystem-based fisheries management (EBFM), several modelling techniques have been developed to integrate trophic, environmental and societal factors (e.g., [START_REF] Romagnoni | The Ecospace model applied to the North Sea: Evaluating spatial predictions with fish biomass and fishing effort data[END_REF][START_REF] Smith | Using an Atlantis model of the southern Benguela to explore the response of ecosystem indicators for fisheries management[END_REF] in order to thoroughly evaluate the status of fish stocks [START_REF] Forrest | Do marine ecosystem models give consistent policy evaluations? A comparison of Atlantis and Ecosim[END_REF]. One caveat is that robust stock assessment or EBFM requires data-intensive models [START_REF] Hilborn | Future directions in ecosystem based fisheries management: A personal perspective[END_REF][START_REF] Pauly | Ecopath, Ecosim, and Ecospace as tools for evaluating ecosystem impact of fisheries[END_REF][START_REF] Wetzel | Performance of a fisheries catchat-age model (Stock Synthesis) in data-limited situations[END_REF], an approach not yet applicable to routine use at large-scale and long-term [START_REF] Edgar | Weaknesses in stock assessment modelling and management practices affect fisheries sustainability[END_REF]. There is therefore an urgent need for basin-scale longterm management plans that include the combined effects of fishing pressure and climate change, for effective conservation of SPFs and sustainable fisheries management [START_REF] Faillettaz | Atlantic Multidecadal Oscillations drive the basin-scale distribution of Atlantic bluefin tuna[END_REF].

Over the last decades, species distribution modelling has been intensively used to project the effects of past and future climate change on the distribution of suitable habitat for species of conservation concern. [START_REF] Beaugrand | Prediction of unprecedented biological shifts in the global ocean[END_REF][START_REF] Bellard | Will climate change promote future invasions?[END_REF][START_REF] Cheung | Projecting global marine biodiversity impacts under climate change scenarios[END_REF]. Species Distribution Models (SDMs), statistical tools based on the niche-biotope duality [START_REF] Colwell | Hutchinson's duality: The once and future niche[END_REF]sensu Hutchinson, 1978) to conceptualize and investigate biogeographical patterns in relation to environmental conditions, are a popular way to assess which species will be under most threat in a near future and/or which regions will be the most impacted by a reorganization of communities [START_REF] Sinclair | How useful are species distribution models for managing biodiversity under future climates[END_REF]. While stock assessments are based on parameters related to stock dynamics (e.g. spawning biomass, recruitment, growth, mortality), these techniques model the ecological niches of species using (a set of) environmental conditions where the species has been observed. The modelled niche can then be used to project potential distribution of species under different environmental conditions on a broad temporal and spatial scale [START_REF] Colwell | Hutchinson's duality: The once and future niche[END_REF], allowing the investigation of potential future range shifts. The capacity of SDMs to produce long-term, large-scale and comparable (i.e. between species, regions or management zones and periods) future projections is of major importance for species conservation and management [START_REF] Hollowed | Projected impacts of climate change on marine fish and fisheries[END_REF]. The main objective of SDM-based approaches is the production of robust scenarios of future species distribution for reliable management and conservation perspectives [START_REF] Cheung | Building confidence in projections of the responses of living marine resources to climate change[END_REF][START_REF] Goberville | Uncertainties in the projection of species distributions related to general circulation models[END_REF][START_REF] Stock | On the use of IPCC-class models to assess the impact of climate on Living Marine Resources[END_REF] and best practices recommend multimodel ensemble projections [START_REF] Buisson | Uncertainty in ensemble forecasting of species distribution[END_REF], that is the use of a large set of SDMs and climate models (e.g. General Circulation Model, GCM; [START_REF] Wilby | Robust adaptation to climate change[END_REF]. Most SDM applications on European SPFs did not include long-term distributional range projections at the regional or European scales [START_REF] Brown | Investigating the distribution of small pelagic fish in Spanish Mediterranean waters using environmental modelling and essential fish habitat mapping[END_REF][START_REF] Maynou | Future distribution of early life stages of small pelagic fishes in the northwestern Mediterranean[END_REF][START_REF] Sabatés | Sea warming and fish distribution: The case of the small pelagic fish, Sardinella aurita, in the western Mediterranean[END_REF][START_REF] Tsikliras | Climate-related geographic shift and sudden population increase of a small pelagic fish (Sardinella aurita ) in the eastern Mediterranean Sea[END_REF], however, and a few studies addressed this challenge at the European scale [START_REF] Lenoir | Modelled spatial distribution of marine fish and projected modifications in the North Atlantic Ocean[END_REF][START_REF] Raybaud | Forecasting climate-driven changes in the geographical range of the European anchovy (Engraulis encrasicolus)[END_REF] but only for a few SPFs.

Our study aims to address this gap in knowledge by examining (a)

long-term and (b) large-scale distributional range projections under different climate change scenarios (IPCC Representative Concentration Pathways; RCP) for a set of seven largely harvested European Small Pelagic Fish (SPF) species of major ecological and economic importance [START_REF] Checkley | Climate change and small pelagic fish[END_REF][START_REF] Fréon | Sustainable exploitation of small pelagic fish stocks challenged by environmental and ecosystem changes: A review[END_REF] and using a multi-SDM, multi-GCM and multi-RCP approach, we investigated future potential range shifts of these largely harvested species at the European scale. To evaluate expected changes at a manageable level [START_REF] Zeller | Still catching attention: Sea around us reconstructed global catch data, their spatial expression and public accessibility[END_REF], we then aggregated our results per Exclusive Economic Zones (Flanders Marine Institute, 2019; EEZ; U.N. General Assembly, 1982eneral Assembly, 1982) and discussed possible economic consequences of climate change on the allocation of fishing effort.

| MATERIAL AND ME THODS

| Description of the modelling framework

We used the future Environmental Suitability Index (ESI; i.e. spatialized index ranging from 0 to 1, based on suitability estimated from contemporary 1990-2017 conditions) of the seven SPFs, retrieved from [START_REF] Schickele | Modelling European small pelagic fish distribution: Methodological insights[END_REF]. This recently developed modelling framework includes (a) a spatial and environmental sampling bias reduction, (b) the use of the convex hull method to generate pseudo-absence, (c) a numerical and ecological evaluation of model outputs and (d) the quantification of uncertainties associated to the selection of SDMs. Environmental parameters used to assess contemporary species distribution (Table 1), the calibration procedure and how we selected the most accurate models (Table 2) are therefore only briefly discussed in this section. Contemporary (1990Contemporary ( -2017) ) distributions of SPFs were obtained using an ensemble forecasting framework that select-among eight different statistical algorithms-the models that best reproduce the observed spatial distribution of each species [START_REF] Araújo | Ensemble forecasting of species distributions[END_REF][START_REF] Buisson | Uncertainty in ensemble forecasting of species distribution[END_REF][START_REF] Pearson | Model-based uncertainty in species range prediction[END_REF]. To account for the source of uncertainty related to the choice of a given species distribution model, we considered seven algorithms computed from the Biomod2 package [START_REF] Thuiller | Ensemble platform for species distribution modelling. R-Forge Repository[END_REF][START_REF] Thuiller | Ensemble platform for species distribution modelling. R-Forge Repository[END_REF] To model each of the seven contemporary distribution, we first constructed an ecologically and statistically meaningful set of environmental parameters by calculating their respective explicative power using a bootstrap method [START_REF] Leroy | Forecasted climate and land use changes, and protected areas: The contrasting case of spiders[END_REF]. Log_PP: log-transformed sea surface primary production IPSL [START_REF] Dufresne | Climate change projections using the IPSL-CM5 Earth System Model: From CMIP3 to CMIP5[END_REF][START_REF] Hourdin | Impact of the LMDZ atmospheric grid configuration on the climate and sensitivity of the IPSL-CM5A coupled model[END_REF], MPI [START_REF] Giorgetta | Climate and carbon cycle changes from 1850 to 2100 in MPI-ESM simulations for the Coupled Model Intercomparison Project phase 5: Climate Changes in MPI-ESM[END_REF][START_REF] Stevens | Atmospheric component of the MPI-M Earth System Model: ECHAM6[END_REF], CNRM [START_REF] Voldoire | The CNRM-CM5.1 global climate model: Description and basic evaluation[END_REF], HadGEM [START_REF] Jones | The HadGEM2-ES implementation of CMIP5 centennial simulations[END_REF] and GISS [START_REF] Schmidt | Configuration and assessment of the GISS ModelE2 contributions to the CMIP5 archive: GISS MODEL-E2 CMIP5 SIMULATIONS[END_REF] models.

SST: mean annual sea surface temperature (°C)

AVHRR Very High Resolution Radiometer [START_REF] Casey | The past, present, and future of the AVHRR Pathfinder SST program[END_REF] IPSL [START_REF] Dufresne | Climate change projections using the IPSL-CM5 Earth System Model: From CMIP3 to CMIP5[END_REF][START_REF] Hourdin | Impact of the LMDZ atmospheric grid configuration on the climate and sensitivity of the IPSL-CM5A coupled model[END_REF], MPI [START_REF] Giorgetta | Climate and carbon cycle changes from 1850 to 2100 in MPI-ESM simulations for the Coupled Model Intercomparison Project phase 5: Climate Changes in MPI-ESM[END_REF][START_REF] Stevens | Atmospheric component of the MPI-M Earth System Model: ECHAM6[END_REF], CNRM [START_REF] Voldoire | The CNRM-CM5.1 global climate model: Description and basic evaluation[END_REF], HadGEM (C. D. [START_REF] Jones | The HadGEM2-ES implementation of CMIP5 centennial simulations[END_REF] and GISS [START_REF] Schmidt | Configuration and assessment of the GISS ModelE2 contributions to the CMIP5 archive: GISS MODEL-E2 CMIP5 SIMULATIONS[END_REF] models.

SSTr: mean annual sea surface temperature range (°C)

SSTvar: mean monthly sea surface temperature variance (°C)

Note: Empty cells stands for parameters that we considered as constant over time in our simulations.

Salinity (SSS), (f) bathymetry and (g) distance to coast. To reduce model over-parametrization, bathymetry and distance to coast were included by means of a hierarchical filtering approach [START_REF] Hattab | Towards a better understanding of potential impacts of climate change on marine species distribution: A multiscale modelling approach[END_REF]. Because SPFs are strictly planktonophagous species and depend on coastal ecosystems for their early lifestages, they are distributed in the epipelagic zone (i.e., bathymetrical area where photosynthesis takes place) and neritic areas only [START_REF] Checkley | Climate change and small pelagic fish[END_REF]. Geographical cells were therefore considered as suitable for SPF only if suitable environmental conditions were found in neritic areas (i.e., >50 km from the coast, independently of depth) or in low-bathymetric (i.e., between 0 and 300 m depth) oceanic regions [START_REF] Schickele | Modelling European small pelagic fish distribution: Methodological insights[END_REF]. To prevent from multicollinearity and unnecessary model complexity [START_REF] Dormann | Methods to account for spatial autocorrelation in the analysis of species distributional data: A review[END_REF], only one parameter from clusters of correlated parameters (Pearson's r correlation >0.7) was retained [START_REF] Leroy | Virtualspecies, an R package to generate virtual species distributions[END_REF].

For each species and combination of environmental parameters, the calibration data set was then filtered in an environmental space to reduce sampling bias as much as possible [START_REF] Varela | Environmental filters reduce the effects of sampling bias and improve predictions of ecological niche models[END_REF].

Pseudo-absences were then generated in the same filtered environmental space outside the corresponding convex hull of observation (i.e. considered as a proxy of environmental suitable conditions; [START_REF] Cornwell | A Trait-Based Test for Habitat Filtering: Convex Hull Volume[END_REF][START_REF] Getz | A local nearest-neighbor convex-hull construction of home ranges and utilization distributions[END_REF], excluding the 2.5 and 97.5 percentiles. Finally, we used the Continuous Boyce Index (CBI; [START_REF] Hirzel | Evaluating the ability of habitat suitability models to predict species presences[END_REF]-the appropriate evaluation metric for a presence/ pseudo-absence calibration data set-to evaluate the robustness of model outputs (see discussion in [START_REF] Leroy | Without quality presence-absence data, discrimination metrics such as TSS can be misleading measures of model performance[END_REF]: each model with a CBI value over 0.5 was retained (e.g., [START_REF] Faillettaz | Atlantic Multidecadal Oscillations drive the basin-scale distribution of Atlantic bluefin tuna[END_REF]. Finally, we calculated the response curve of each environmental parameters by keeping other parameters at their mean values for modelled species, using the evaluation strip method [START_REF] Elith | The evaluation strip: A new and robust method for plotting predicted responses from species distribution models[END_REF]. The ecological realism and relevance of the models were then corroborated by an expert-based inspection/validation of each response curve in order to discard spurious responses to environmental factors (e.g. bimodal response to temperature).

| Future scenarios and General Circulation Models (GCMs)

To project the future ESI of each species, we considered five GCMs retrieved from the 5th phase of the Coupled Model Intercomparison Project (CMIP5; Table 1). Future SST and PP were averaged for three different periods to cover: (i) short-to-medium (2030-2039), (ii) midcentury (2050-2059) and (iii) late-century (2090-2099) range timescales. To cover the range of year-2100 radiative forcing values found in the literature, that is from 2.6 to 8.5 W/m 2 , we used three RCPs scenarios: (a) the optimistic peak and decline (RCP2.6), the intermediate "stabilization" (RCP4.5) and the "business as usual" (RCP8.5) scenarios [START_REF] Meinshausen | The RCP greenhouse gas concentrations and their extensions from 1765 to 2300[END_REF][START_REF] Van Vuuren | The representative concentration pathways: An overview[END_REF]. We considered SSS as constant over time because its temporal variance is negligible in comparison with its spatial variance [START_REF] Dickson | The "great salinity anomaly" in the Northern North Atlantic 1968-1982[END_REF][START_REF] Faillettaz | Atlantic Multidecadal Oscillations drive the basin-scale distribution of Atlantic bluefin tuna[END_REF][START_REF] Marchand | Climate change in the Bay of Biscay: Changes in spatial biodiversity patterns could be driven by the arrivals of southern species[END_REF]

| Pre-treatment of future temperature data

Because temperature-related parameters (Table 1) were retrieved from both observation-based (i.e. for the contemporary period) and GCMbased data (i.e. for the three future periods), our projections may be altered. To assess possible bias, we performed Taylor diagrams [START_REF] Taylor | Summarizing multiple aspects of model performance in a single diagram[END_REF]) using a common time period (i.e. 2006-2017) to estimate the consistency between current and future climate data (Supplementary Material 2): the correlation coefficient, the root-mean-square difference (RMSD) and the standard deviation (SD) difference were calculated for each temperature-related parameter (Table 1). For each GCMs, RCPs, and geographical cell, we therefore estimated the difference between the two datasets and corrected the model-based temperature data accordingly. This process, already applied by [START_REF] Péron | Projected poleward shift of king penguins' (Aptenodytes patagonicus) foraging range at the Crozet Islands, southern Indian Ocean[END_REF] and

| Projection of future environmental suitability

Projections of ESI values were carried out at spatial resolutions suitable for either ecological analyses, that is on a 0.1° × 0.1° spatial grid obtained from a linear spatial interpolation [START_REF] Goberville | Uncertainties in the projection of species distributions related to general circulation models[END_REF], or (c) commonly used in the literature to project the socioeconomics consequences of climate change on fisheries (Cheung, Jones, et al., 2016;[START_REF] Sumaila | Climate change impacts on the biophysics and economics of world fisheries[END_REF][START_REF] Sumaila | Winners and losers in a world where the high seas is closed to fishing[END_REF].

| Uncertainties related to future projections

The selection of a GCM may greatly influence the projected distributions of a species [START_REF] Goberville | Uncertainties in the projection of species distributions related to general circulation models[END_REF]: GCMs may diverge for technical or parameterization reasons, may simulate ocean-atmosphere processes in different ways or may vary due to their initial spatial resolution [START_REF] Beaumont | Why is the choice of future climate scenarios for species distribution modelling important?[END_REF][START_REF] Goberville | Uncertainties in the projection of species distributions related to general circulation models[END_REF][START_REF] Wiens | Niches, models, and climate change: Assessing the assumptions and uncertainties[END_REF].

Because of their wide variety and complexity, and because we cannot identify a model that performs better than another [START_REF] Martinez-Meyer | Climate change and biodiversity: Some considerations in forecasting shifts in species' potential distributions[END_REF], it is essential to consider a full range of GCMs to examine the full range of potential future species distributions (e.g. [START_REF] Friedlingstein | Uncertainties in CMIP5 Climate Projections due to Carbon Cycle Feedbacks[END_REF][START_REF] Shepherd | Atmospheric circulation as a source of uncertainty in climate change projections[END_REF]. In our study, we adapted the ensemble modelling for future projections: for each set of environmental parameters and each statistical algorithm, five GCMs and three RCP scenarios were considered to project future environmental suitability. For a given period and for each RCP, we performed 10 cross-validation runs, leading to the production of 50 simulations (5 GCM × 10 cross-validation runs) per statistical algorithm. We then computed the corresponding SD among SDMs (i.e. the variability related to the calculation of the ecological niche) and GCMs (i.e. the intrinsic variability linked to the climate system and expected climate conditions) to fully explore the uncertainty related to future environmental suitability projections [START_REF] Goberville | Uncertainties in the projection of species distributions related to general circulation models[END_REF].

| RE SULTS

| Future environmental suitability

Here, we present for each of the seven SPFs, the projected ESIs in the spatial domain ranging from 10 to 70°N and -30 to 45°E. Species distributional range under RCP8.5 conditions for the late 21st century (2090-2099) are detailed in Figure 1 while other RCPs and periods are provided in Supplementary Material 5.

| Temperate-cold water species

Strong northward shifts in the distribution of ESI are expected for "temperate-cold" water species (Figure 1

| Temperate-warm water species

Expected changes in ESI values for "temperate-warm" water species (Figure 1

| Uncertainties in expected environmental suitability

For all SPFs, our projections showed only weak variations, with mean SD ranging from 0.1 to 0.4 (Figure 1).

| Climatic range shifts between Exclusive Economic Zones

Here, we explored the consequences of potential distribution shifts at the scale of EEZs (Figure 2), manageable units commonly used for projecting the possible socioeconomic impacts of climate change on fish stocks (Cheung, Jones, et al., 2016). For each EEZ and SPF, we calculated the total value of landings for the period 1990-2017 (Figure 2, top-left panel) and confronted observed landings with potential changes in ESI by the end of the century for RCP2.6, RCP4.5 and RCP8.5 (Figure 2, bottom and right panels).

| Temperate-cold water species

The four temperate-cold water species are of major importance in European fisheries (FAO, 2020), especially along the Atlantic façade (c.a. 50,000 t/year per EEZ), except for European sprat that is largely harvested in the Baltic Sea (Figure 2). These species are currently mostly captured in regions where we found high ESI values over the period 1990-2017 (Figure 2; [START_REF] Schickele | Modelling European small pelagic fish distribution: Methodological insights[END_REF]. Our models projected a decrease in the ESI values in southern and western Europe (Figure 2). While the Mediterranean EEZs showed a decrease in mean ESI values from 0.48 (1990-2017) to 0.39 (RCP2.6) or 0.24 (RCP8.5), we projected an increase in the EEZs of the Baltic Sea from 0.43 (1990-2017) to 0.51 (RCP2.6) or 0.59 (RCP8.5; Figure 2). Our results highlight that a potential mismatch between current fisheries areas and changes in the species climatic range of temperatecold water species could occur by the end of the century; a major decrease in ESI values was for example expected in Morocco and Turkey (Figure 2), that is where species are currently abundantly captured. In contrast, we projected that ESI values may remain steadily constant over the current century in Denmark, the main fishing area for European sprat (Figure 2). At the European scale, the absolute variation of ESI values (i.e. relative to 1990-2017) was expected to range from 22% (RCP2.6) to 33% (RCP8.5), suggesting a potential reallocation of temperate-cold water species population in fisheries management zones.

| Temperate-warm species

In European seas, the three temperate-warm water species are less harvested than temperate-cold water species (FAO, 2020) (Figure 2, top-left panel). For all species except round sardinella, we projected

| D ISCUSS I ON

| Ecological impact of climate change on Small Pelagic Fishes

For all climate scenarios and all SPFs-except round sardinella-we projected substantial climate-induced northward distributional range shifts (Figure 1, Supplementary Material 5; [START_REF] Dulvy | Climate change and deepening of the North Sea fish assemblage: A biotic indicator of warming seas[END_REF][START_REF] Jorda | Ocean warming compresses the three-dimensional habitat of marine life[END_REF][START_REF] Perry | Climate change and distribution shifts in marine fishes[END_REF]. The narrow aerobic tolerance of species embryonic and reproduction lifestages-under direct influence of SST-is the main limiting factor of the physiological activity, growth, and survival of SPFs [START_REF] Dahlke | Thermal bottlenecks in the life cycle define climate vulnerability of fish[END_REF][START_REF] Peck | Life cycle ecophysiology of small pelagic fish and climate-driven changes in populations[END_REF].

The projected decrease in ESI value in the Mediterranean Sea, as a response of the expected increase in temperature, may be explained by a limitation of eco-physiological processes [START_REF] Dahlke | Thermal bottlenecks in the life cycle define climate vulnerability of fish[END_REF] that hinders the survival and/or development of SPFs [START_REF] Lehodey | Climate variability, fish, and fisheries[END_REF][START_REF] Perry | Climate change and distribution shifts in marine fishes[END_REF][START_REF] Torri | Planktonic stages of small pelagic fishes (Sardinella aurita and Engraulis encrasicolus) in the central Mediterranean Sea: The key role of physical forcings and implications for fisheries management[END_REF]. If warming continues in the Mediterranean Sea (Supplementary Material 3), SPFs may experience hypoxia during their reproduction stage [START_REF] Dahlke | Thermal bottlenecks in the life cycle define climate vulnerability of fish[END_REF], leading to lower egg production rates, with putative effects on recruitment, and a bottleneck effect towards northern regions of the Mediterranean Sea [START_REF] Ben Rais Lasram | The Mediterranean Sea as a 'cul-de-sac' for endemic fishes facing climate change: A marine endemic hotspot under threat[END_REF]. The combination of warmer annual and winter temperature in northern

Europe and the Black Sea rather may allow SPFs to overcome thermal constraints during reproduction and development, with positive effects on egg quality [START_REF] Dahlke | Thermal bottlenecks in the life cycle define climate vulnerability of fish[END_REF]. While sea water salinity may influence the specific gravity of marine pelagic fish eggs, that is their vertical distribution in the water column, egg size of SPFsthat has a fundamental impact on the capacity of young larvae to be active, grow, and survive-is under direct influence of SST [START_REF] Huret | Size, permeability and buoyancy of anchovy (Engraulis Encrasicolus) and sardine (Sardina Pilchardus) eggs in relation to their physical environment in the Bay of Biscay[END_REF][START_REF] Peck | Life cycle ecophysiology of small pelagic fish and climate-driven changes in populations[END_REF][START_REF] Torri | Planktonic stages of small pelagic fishes (Sardinella aurita and Engraulis encrasicolus) in the central Mediterranean Sea: The key role of physical forcings and implications for fisheries management[END_REF]. SPFs are planktonic feeders [START_REF] Bachiller | Trophodynamics and diet overlap of small pelagic fish species in the Bay of Biscay[END_REF] which depend on high productive areas such as the gulf of Gabès or the eastern North Sea during early development [START_REF] Rijnsdorp | Resolving the effect of climate change on fish populations[END_REF]. Despite the projected warming in the Mediterranean Sea, temporal changes in primary production may remain negligible in comparison with its spatial variance: using a multimodel approach, [START_REF] Macias | Productivity changes in the Mediterranean Sea for the twenty-first century in response to changes in the regional atmospheric forcing[END_REF] report a slight increase in primary production of about 9.5 mmol N/m 2 over the period 2015-2095. This supports why primary production did not greatly influence our projections. At an ecosystem scale, SPFs have a pivotal role [START_REF] Chaalali | From species distributions to ecosystem structure and function: A methodological perspective[END_REF] in marine food webs, contributing to carbon fluxes from lower trophic level to top predators [START_REF] Cury | Small pelagics in upwelling systems: Patterns of interaction and structural changes in "wasp-waist" ecosystems[END_REF].

Projected distributional range shifts-and potential ensuing changes in abundance patterns [START_REF] Helaouet | Physiology, ecological niches and species distribution[END_REF][START_REF] Kulhanek | Using ecological niche models to predict the abundance and impact of invasive species: Application to the common carp[END_REF][START_REF] Vanderwal | Selecting pseudo-absence data for presence-only distribution modeling: How far should you stray from what you know?[END_REF]-may deeply modify the Mediterranean or Baltic seas ecosystems through trophic cascading effects on the upper trophic levels which feed on these species, including negative effects on their fisheries [START_REF] Maynou | Clues from the recent past to assess recruitment of Mediterranean small pelagic fishes under sea warming scenarios[END_REF]. This climatic resilience-related issue may be assessed through the development and adaptation of ecosystem management and protection strategies [START_REF] Giakoumi | Ecological effects of full and partial protection in the crowded Mediterranean Sea: A regional meta-analysis[END_REF]e.g. McLeod et al., 2009), in regions or for species (e.g. SPFs) identified as sensitive to climate-induced changes (e.g. the Mediterranean Sea; Figure 2).

| Management and economic implications

While fishing has expanded into the high seas over the last decades as a result of an increasing demand for fish and the overexploitation of coastal waters [START_REF] Sumaila | Winners and losers in a world where the high seas is closed to fishing[END_REF], quantifying changes in the allocation of fisheries catches by maritime country and within EEZ waters allows to focus on a spatial scale that is politically and economically viable (Cheung, Jones, et al., 2016;[START_REF] Zeller | Still catching attention: Sea around us reconstructed global catch data, their spatial expression and public accessibility[END_REF].

Depending on the EEZ, SPFs may experience high fishing mortalities, especially in the Mediterranean Sea (i.e. twice the maximum sustainable yield; FAO, 2016), with putative negative impacts on species growth, reproduction and stock production [START_REF] Brander | Global fish production and climate change[END_REF][START_REF] Fréon | Sustainable exploitation of small pelagic fish stocks challenged by environmental and ecosystem changes: A review[END_REF][START_REF] Lehodey | Climate variability, fish, and fisheries[END_REF]. In our study area, 65% of the SPFs were captured in 2014 by fishing fleets originating from the same EEZ (Supplementary Material 4), mostly low to medium size and coastal fishing vessels (FAO, 2016;[START_REF] Saup | Sea around us[END_REF]. In comparison, European EEZs may experience a variation of suitable environmental conditions for SPFs up to 51% (Figure 2). These potential upcoming changes in fishing ground location and the magnitude of impacted vessels may lead to (a) a redefinition of the European distribution of SPF stocks, (b) allocate fishing effort (i.e. licenses, number of boats) in a way that explicitly incorporate the influence of climate change on SPF stocks and (c) design new international fishing agreements in order to allow fishing fleets to operate in areas outside their EEZs [START_REF] Gaines | Improved fisheries management could offset many negative effects of climate change[END_REF][START_REF] Link | Guidelines for incorporating fish distribution shifts into a fisheries management context[END_REF]; e.g. based on historical fisheries; [START_REF] Perry | Sensitivity of marine systems to climate and fishing: Concepts, issues and management responses[END_REF]. We argue that basing fisheries management strategies-such as a progressive and precautious adaptation of fishing fleet (e.g. gear, target or quotas; Grafton 2010)-on an ensemble of long-term ecological scenarios that take into account projections of climate change effects at the scale of manageable units (i.e. EEZ), is a valuable information to mitigate the unsustainability of marine fisheries [START_REF] Lotze | Global ensemble projections reveal trophic amplification of ocean biomass declines with climate change[END_REF]. The vulnerability of marine countries depends on the state of their fishery [START_REF] Barange | Impacts of climate change on marine ecosystem production in societies dependent on fisheries[END_REF][START_REF] Sumaila | Climate change impacts on the biophysics and economics of world fisheries[END_REF]: local fisheries (e.g. Morocco, Turkey) may be less resilient than long-range fisheries (e.g. Denmark; Supplementary Material 4) to a climate-induced range shift on their primary target (i.e. SPFs). Our projections at the scale of EEZs may therefore serve as a support for future socioeconomic research (e.g. [START_REF] Fe R E N C E S Allison | Vulnerability of national economies to the impacts of climate change on fisheries[END_REF][START_REF] Badjeck | The vulnerability of fishing-dependent economies to disasters[END_REF].

| Perspectives on modelling small pelagic fisheries

Despite their popularity, SDMs have inherent limitations-depending on their application context-such as the assumption of niche conservatism [START_REF] Peterson | Species distribution modeling and ecological niche modeling: Getting the concepts right[END_REF] and the failure to integrate species interactions or dispersal processes [START_REF] Araújo | Five (or so) challenges for species distribution modelling[END_REF]. While recent advances in species distribution modelling proposed to overcome such shortcomings (e.g. dispersal constrained SDM; [START_REF] Boulangeat | Accounting for dispersal and biotic interactions to disentangle the drivers of species distributions and their abundances[END_REF]e.g. joint-SDMs;[START_REF] Harris | Generating realistic assemblages with a joint species distribution model[END_REF], most of these ecological processes are mainly associated with local changes [START_REF] Beaugrand | How do marine pelagic species respond to climate change? Theories and observations[END_REF]. These perspectives are at the cost of the amount of data needed to calibrate the models which can impede their broad scale-applicability, one of the main strength of SDM [START_REF] Marmion | Evaluation of consensus methods in predictive species distribution modelling[END_REF]. Based on our multi-GCM, multi-SDM and multi-RCP approach that integrated climate uncertainty [START_REF] Friedlingstein | Uncertainties in CMIP5 Climate Projections due to Carbon Cycle Feedbacks[END_REF][START_REF] Goberville | Uncertainties in the projection of species distributions related to general circulation models[END_REF][START_REF] Shepherd | Atmospheric circulation as a source of uncertainty in climate change projections[END_REF] and to contribute to increase the probability of success in fishery management strategies [START_REF] Jones | Harnessing nature to help people adapt to climate change[END_REF], we encourage further research in the regions that we have identified as the most vulnerable, such as the Mediterranean Sea. The whole Mediterranean Sea ecosystem, including highly impacted regions [START_REF] Bănaru | Trophic structure in the Gulf of Lions marine ecosystem (north-western Mediterranean Sea) and fishing impacts[END_REF][START_REF] Hattab | An ecosystem model of an exploited southern Mediterranean shelf region (Gulf of Gabes, Tunisia) and a comparison with other Mediterranean ecosystem model properties[END_REF][START_REF] Piroddi | Modelling the Mediterranean marine ecosystem as a whole: Addressing the challenge of complexity[END_REF], has been extensively studied over the last decades, and it is now well documented that changes in small pelagic populations-due to fishing or natural drivers-will strongly alter ecosystem structure and functioning [START_REF] Palomera | Small pelagic fish in the NW Mediterranean Sea: An ecological review[END_REF]. Considering results from SDMs in combination with ecosystem models for fisheries management will help to better anticipate the consequences of climate-induced distributional shifts in small pelagic fish on the whole ecosystem [START_REF] Chaalali | From species distributions to ecosystem structure and function: A methodological perspective[END_REF]. The need is urgent as many countries in the Mediterranean Sea are directly or indirectly dependant on activities that involve exploitation of marine fish resources [START_REF] Selig | Mapping global human dependence on marine ecosystems[END_REF].

ACK N OWLED G EM ENTS

This paper is dedicated to the memory of Pr. Patrice Francour who passed away on 13 October 2019. He dedicated his life to the protection and understanding of Mediterranean ecosystems, initiated and co-supervised this work. We acknowledge the Ocean Biogeographic

Information System (OBIS), the Global Biodiversity Information Facility (GBIF) and FishBase for providing species occurrence data.

Finally, we thank the IPCC Coupled Model Intercomparison Project (CMIP) and the climate modelling groups for making available their model output.

CO N FLI C T O F I NTE R E S T

The authors have no conflict of interest to declare.

AUTH O R CO NTR I B UTI O N

VR and PF conceived and supervised the study. AS, VR and EG collected the data. BL provided the initial modelling framework. AS performed the numerical analysis. GB, BL, TH, EG and VR helped in the modelling process. AS wrote the first draft. All authors made substantial contributions to the successive versions of the manuscript.

  The following environmental parameters were tested: (a) mean annual Sea Surface Temperature (SST), (b) annual SST range, (c) monthly SST variance, (d) Primary Production (PP), (e) mean annual Sea Surface TA B L E 1 Description of the environmental parameters considered in the ensemble model procedure and corresponding referencesEnvironmental parameter Contemporary Future Bathymetry: spatial seafloor depth (m) Global seafloor topography (Smith & Sandwell, 1997) Distance to coast: distance to the nearest coast (km) NASA Goddard Space Flight Center (2009) (https:// ocean color.gsfc.nasa.gov/docs/distf romco ast/) SSS: sea surface salinity Levitus' climatology (Levitus, 2011) completed with ICES data (http://www.ices.dk/)

  [START_REF] Cristofari | Climate-driven range shifts of the king penguin in a fragmented ecosystem[END_REF], ensured (a) a perfect correlation (Pearson coefficient r = 1), (b) no RMSD and (c) the same SD between the two data sets for a common period. Results from the correction procedure and corresponding anomalies are shown in Supplementary Material 3.

F I G U R E 1

 1 Left panels: maps showing the differences in Environmental Suitability Index(ESI) values between 2090-2099 under scenario RCP8.5 (Representative Concentration Pathway) and 1990-2017. Middle panels: modelled ESI of the seven small pelagic fish species for the period 2090-2099 under scenario RCP8.5. Right panels: standard deviation based on 50 simulations per algorithm (i.e., 10 cross-validation runs × 5 general circulation models per algorithm). Note that the figure appears in colour in the online version only [Colour figure can be viewed at wileyonlinelibrary.com] that is in each Exclusive Economic Zone[START_REF] Zeller | Still catching attention: Sea around us reconstructed global catch data, their spatial expression and public accessibility[END_REF]. Among the existing fishery zones, we chose to focus on EEZsarea stretching from the coastline out to 200 nautical miles over which a country has special rights regarding the use of marine resources-as they are (a) basic units for fisheries management (e.g. attribution of maximum allowed catches by EEZs) and conservation perspectives[START_REF] Fe R E N C E S Allison | Vulnerability of national economies to the impacts of climate change on fisheries[END_REF] Cheung, Jones, et al., 2016;[START_REF] Zeller | Still catching attention: Sea around us reconstructed global catch data, their spatial expression and public accessibility[END_REF], (b) at a spatial resolution well-adapted for biogeographic research[START_REF] Claus | Marine Regions: Towards a global standard for georeferenced marine names and boundaries[END_REF]

  ; i.e. Atlantic horse mackerel, European pilchard, European sprat and European anchovy). While ESI values increased along the Norwegian and Baltic seas between +0.2 and +0.6-especially for European anchovy (+0.6)-we forecasted a decrease in ESI values that ranged from -0.2 to -0.6 along the Mediterranean Sea, the Bay of Biscay and the English Channel, but to a lesser extent, except for European anchovy. We projected a potential local extinction (ESI values <0.05) in the southwestern Mediterranean Sea for all temperate-cold water species, in particular for European sprat that may face unsuitable environmental conditions in the whole Mediterranean Sea. With ESI values above 0.4, the distributional centre of the four temperate-cold species may range from the North Sea to the southern Norwegian Sea by the end of the century. For all temperate-cold species, we projected the amplitude of the changes in ESI values to increase through time and when the intensity of the radiative forcing increases (Supplementary Material 5). The decrease in ESI value (maximum value of -0.6) in the Mediterranean Sea, that may potentially lead to local extinctions by the end of the century under RCP8.5 conditions, may be limited under scenario RCP2.6 with a reduction between -0.1 (2030-2039) and -0.4 (2090-2099). The potential range expansion of temperatecold species in the Baltic and Norwegian seas is expected to increase by +0.4 for all RCPs and periods. The geographical expansion may decrease for scenario RCP2.6, however.

F I G U R E 2

 2 Changes in the Environmental Suitability Index (ESI) per Exclusive Economic Zone (EEZ) and species in comparison to their fish landings. From top to bottom and left to right: the averaged (1990-2017) landings per species and EEZ, the ESI values per EEZ for the decade 2090-2099 for Representative Concentration Pathways (RCPs) 2.6, 4.5 and 8.5. Bar plots for ESI are scaled from 0 to 1, the dashed lines correspond to an ESI value of 0.5 and the full line spectre corresponds to the ESI values per EEZ for the period 1990-2017. Countries with catches under 20,000 metric tons are not shown. Note that the figure appears in colour in the online version only [Colour figure can be viewed at wileyonlinelibrary.com] between -0.3 (2030-2039) and -0.4 (2090-2099) for Mediterranean horse mackerel in the Mediterranean Sea. By limiting global warming to +2°C (i.e. RCP2.6), an expansion of Mediterranean horse mackerel and bogue may be negatively affected, despite a maximum increase in ESI value of about +0.4 for all RCPs and periods.

  important late-century changes in the ESI values at the EEZs scale.While we forecasted a moderate decrease in ESI values-from 0.62 to 0.54 (RCP2.6) and 0.53 (RCP 8.5)-in the EEZs of the Mediterranean Sea (RCP8.5; Figure2), our simulations revealed a moderate to high increase in EEZs of the Atlantic façade, the Black Sea and the Baltic Sea. The Baltic Sea EEZs are likely to undergo an important expansion of temperate-warm species, with changes in ESI values from 0 (1990-2017) to 0.03 (RCP2.6) or 0.22 (RCP8.5), and so a major extension of the northern boundary of temperatewarm species (Figure2). In contrast, we expect lower ESI values throughout their distributional ranges, especially for Mediterranean horse mackerel. At the European scale, the absolute variation in ESI (i.e. relative to 1990-2017) is predicted to range from 30% (RCP2.6) to 51% (RCP8.5). Our simulations therefore suggest a possible major reallocation of the suitable environment for temperate-warm species along European EEZs.

  . While the spatial variance of SSS allowed us to discriminate marine from brackish waters (e.g., from 35 to 15 between the west and the east of the Danish strait), its temporal var-

iance is negligible: for the period 2016-2065,

[START_REF] Lavoie | Projections of future trends in biogeochemical conditions in the Northwest Atlantic Using CMIP5 Earth System Models[END_REF]

report expected salinity trends of +0.063 per decade at the maximum, a value comparable to the rise of SSS observed since 1950

[START_REF] Durack | Ocean salinities reveal strong global water cycle intensification during 1950 to 2000[END_REF]

.

  Environmental parameters used to model each SPF species. Parameters are ranked according to their explanatory power.

		Environmental
	Species	parameters
	Mediterranean horse mackerel	SST, SSTvar, log_PP
	Atlantic horse mackerel	SST, SSTvar, log_PP
	European pilchard	SST, SSTr, SSS
	Round sardinella	SST, SSTr, log_PP
	European sprat	SST, SSTr, log_PP
	European anchovy	SST, SSTvar, SSS
	Bogue	SST, SSTr

TA B L E 2

  The stock assessment areas considered for SPFs (http://www.ices.dk/) overlap with the EEZs of the European Seas (Flanders Marine Institute, 2019) as the European Atlantic façade and enclosed seas do not include high sea areas (i.e. outside EEZs). In 2014, 35% of the SPFs were captured by fishing fleet operating outside the EEZ of their respective countries (e.g. Denmark, Poland, Spain, Sweden; Supplementary Material 4), indicating the importance of international fishing agreements within the European Union (i.e. the latest available data; SAUP, 2020). Here, the mean ESI value was calculated by aggregating, within each EEZ, the 0.1° × 0.1° geographical cells retained after application of the hierarchical filtering approach (see 2.1.).

  ; i.e. Mediterranean horse mackerel, round sardinella and bogue) were variable with species-specific patterns. No major changes in ESI values were expected for round sardinella but we showed a potential increase in the Black Sea (between +0.4 to +0.6).

	For Mediterranean horse mackerel and bogue, we projected an im-
	portant increase in ESI values (between +0.2 and +0.6) in northern
	regions (e.g. in the North Sea) and a moderate to high decrease in
	ESI values in the Mediterranean Sea for both species (ranging from
	-0.2 to -0.6 for the Mediterranean horse mackerel and about -0.2
	for the bogue). We expect a range expansion towards the Norwegian

Sea for both species. With ESI values ranging from 0.6 to 0.8, our models also projected a distributional shift of Mediterranean horse mackerel towards the Bay of Biscay. For all temperate-warm species, projected changes in ESI values may increase in amplitude over time, when the magnitude of the warming increases (Supplementary Material 5). If global warming is small (RCP2.6), the decrease in ESI

Acknowledgements 221

Data Availability Statement 221

FUNDING INFORMATION

This work was supported by the Prince Albert II of Monaco Foundation through the project CLIM-ECO 2 . AS's PhD is funded by the Provence-Alpes-Côte-d'Azur (PACA) Region in partnership with the Comité Régional des Pêches Maritimes et des Elevages Marins (CRPMEM) de PACA.

DATA AVA I L A B I L I T Y S TAT E M E N T

These data were derived from the following resources available in the public domain: the Ocean Biogeographic Information

S U PP O RTI N G I N FO R M ATI O N

Additional supporting information may be found online in the Supporting Information section.

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