Alexandre Duplan
email: alexandre.duplan@inrae.fr

Mamadou Régis Fichot

Dia Sow

Alain Delaunay

Isabelle Le Jan

Christian Daviaud

Odile Rogier

Patrick Poursat

Harold Duruflé
email: harold.durufle@inrae.fr

Leopoldo Sanchez
email: leopoldo.sanchez-rodriguez@inrae.fr

Régis Fichot¹

Mamadou Dia Sow

Alain Delaunay¹

Isabelle Le Jan¹

Yu-Qi Feng

Hervé Cochard

Isabel Allona

Vincent Segura

Jörg Tost

Stéphane Maury¹
email: stephane.maury@univ-orleans.fr

What epigenetics can bring to (plant) physiologists and ecologists in a climate change context

Keywords: Potri.018G047500, Potri.005G182100, Potri.001G210200

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

In this context, it's urgent to better understand the mechanisms underlying adaptation and plasticity of trees to better optimize genetic resources management. The study of the genetic bases of tree adaptation has mainly focused on the contribution of standing structural variation (genetic) to local adaptation. Epigenetic mechanisms remain largely unstudied while they can be extremely important for long-lived organisms as they allow rapid phenotypic modifications in reaction to changing environmental conditions ('priming effect'). Our objective (ANR EPITREE 2018-2023) Here the goal is to study short-term somatic memory and to identify a potential epigenetic control using Whole Genome Bisulfite Sequencing (WGBS). One year later, the trees were subjected to a second drought-watering cycle. The aim was to study inter-annual somatic memory and the corresponding epigenetic control.

Here, the goal is to test how epigenetic data can improve phenotypic predictive models trained by other omics data [5].

  is to characterize the importance of epigenetics in adaptation [1], plasticity [2][3] and memory-priming [4] of trees and to evaluate the use of epigenetic data in predictive models. with feature selection) Distribution area of the 241 black poplar genotypes covering 11 metapopulations Results of WGBS analysis showing DNA methylation variations associated to short-term (year 1) and inter-annual (Year 2) somatic memories in the DRA38 genotype. These modifications are associated to variations in gene expression involved in epigenetic and chromatin organization and signaling. The ability of these somatic memories to induce priming effects (better response during a second challenge) is under evaluation (Duplan et al, in prep). We have analyzed 241 black poplars originating from 11 natural populations in Europe and installed in a common garden (Orléans). We have obtained multi-omics data: epigenetic, genomic, transcriptomic and phenomic. Our goal is to identify signatures of potential local adaptation at the epigenetic level. A preliminary study by our consortium (ANR EPITREE) on 20 genotypes have already unravel epigenetic adaptative signature on disease resistant genes [1]. ≠ epigenome (modified DNA methylation via RNAi) How to use epigenetic data associated to phenotype for predictive models? Local adaptation signatures in the epigenome? Ecological epigenetic memory in trees? Experimental setup for drought rewatering experiments. Variations of the relative extractable water (REW) content over weeks for drought treatment on poplar in greenhouse. Black poplar (P. nigra) is present in a large geographic range in Eurasia and is considered as an indicator of the decades, widespread forest die-off due to drought and/or heat constraints has been observed around the world for all forest biomes and is predicted to increase with ongoing climate change. , allele, methylation [...] that can play a role in phenotypic prediction Height Diameter Wood composition Natural and methylation-mutant poplar plants were placed in a greenhouse under drought conditions (WD = Water deficit; WW = Well-Watered) for 5 weeks, then re-watered (ReW= Re-Watering) for one week and sampled after recovery (memory?).

Bibliography : [ 1 ]

 1 Sow et al. 2023; [2] Lafon-Placette et al. 2018, Journal of Experimental Botany; [3] Sow et al. 2021, New Phytologist; [4] Le Gac et al. 2018, Journal of Experimental Botany; [5] Wade et al. 2022, BMC Genomics


Egoi Ortego Sampedro
email: egoi.ortego@minesparis.psl.eu

About the effect of two-phase flow formulations on shock waves in flash metastable expansions Egoï

Keywords: flash boiling, expansion nozzles, non-homokinetic, interfacial transfer

Two-phase expanders are promising conversion machines that could help in increasing the energy efficiency of several systems such as heat-to-power plants, liquefaction processes or chillers. Expansion of two-phase flows is complex to model since the dynamics of the liquid-gas interactions depend on several factors. This work gives a preliminary insight on the effect of various formulations for liquid-gas interaction terms on the shock waves that may appear in over-expanded flash nozzles simulations. The case study is a water thrust nozzle from literature designed for geothermal energy conversion at inlet temperatures close to 150°C. The compared formulations differ mainly on the homogeneity assumptions regarding momentum and on the interface mass transfer term. The simulations results suggest that these assumptions have a fundamental effect on the flow behavior close to the outlet of the nozzle and in particular on the presence or not of the shock waves. This has meaningful consequences on the velocity profile in the nozzle.

INTRODUCTION

The renewed interest in two-phase turbines in the last years can be explained by several factors. Some of them are the need for diversification of electricity production sources (by the use of waste-heat driven Organic Rankin Cycles for example), the reduction of electricity consumption of cold power production systems (especially in the context of natural refrigerants deployment), or the increase of computational capabilities for the design of two-phase components in the last 5 to 7 years that helps for the design of such machines.

However, flashing flows are highly driven by non-ideal phenomena and there is still no consensus on simulation methodology and assumptions that would lead to satisfactory results for the two-phase expanding flows modeling. This is in particular the case of the phase velocities homogeneity assumption. For example, considering the case of hot water flash expansion, Downar-Zapolski et al. (P.Downar-Zapolski, Z.Bilicki, L.Bolle, & J. Franco, 1996) considered no velocity difference between liquid and vapor whereas [START_REF] Liao | 3D CFD simulation of flashing flows in a converging-diverging nozzle[END_REF] considered it because according to them it has great importance on the interfacial mass and heat transfer mechanisms. Besides, the velocities homogeneity assumption is very usual in the domain of two-phase expanding ejectors [START_REF] Bodys | Experimental and numerical study on the R744 ejector with a suction nozzle bypass[END_REF]. However, knowing that vapor has a lower density than liquid, for a given pressure gradient, the acceleration observed by the vapor is higher. This results in higher velocities for vapor than for liquid during the expansion. This was observed by various studies [START_REF] Elliott | Theory and Tests of Two-Phase Turbines[END_REF]) [START_REF] Sampedro | Two-phase nozzles performances CFD modeling for low-grade heat to power generation: Mass transfer models assessment and a novel transitional formulation[END_REF]. So velocities homogeneity assumption is likely to be incorrect. Nevertheless, the consequences of homogeneous and non-homogeneous assumptions need to be quantified.

This paper aims to analyze the effects of the velocities homogeneity assumption on the flow modeling results. In particular, the pressure and velocity profiles and the presence or not of a shock wave in simulations are analyzed. This is done on the case study of a hot water thrust nozzle tested by Ohta et al. [START_REF] Ohta | Performance and flow characteristics of nozzles for initially subcooled hot water (influence of turbulence and decompression rate)[END_REF]. The analysis of two-phase expansion nozzles presents the interest of being a relatively simple case of study that can also be considered as a real-life component used in particular as a stator in a low degree of reaction turbines. The experimental pressure profile data by [START_REF] Ohta | Performance and flow characteristics of nozzles for initially subcooled hot water (influence of turbulence and decompression rate)[END_REF] are used as a reference.

The computational fluid mechanics (CFD) model used in this paper is based on the general Euler-Euler description for two-phase flows. The interfacial mass transfer is modeled using two approaches to test the sensitivity of the simulation results to this aspect. Regarding the interface momentum coupling assumptions, two extreme situations were analyzed: the homogeneous and the non-homogeneous. The last was modeled using an interface friction formulation based on an interface drag coefficient from the literature. In addition, three supplementary values of the drag coefficient were tested to virtually observe the implications of this term in the flow behavior.

Then, the validity of the models is discussed based on the pressure profiles analysis. Besides, the paper gives a special insight into the literature models for sound velocity estimation. These models are used to analyze the CFD simulation results.

METHODS AND EQUATIONS

Models and definitions

The general formulation of conservation equations for a two-phase flow requires a phase-per-phase description i.e. an Euler-Euler formulation. In the literature dealing with flash nozzle flows, the general multiphase description is often reduced to simpler formulations. For further insight into these aspects, the reader is invited to read the very useful review maide by [START_REF] Yixiang | Computational modeling of flash boiling flows, a literature survey[END_REF] or the models' benchmark previously made by the author [START_REF] Sampedro | Two-phase nozzles performances CFD modeling for low-grade heat to power generation: Mass transfer models assessment and a novel transitional formulation[END_REF]. In this paper, the general Euler-Euler formulation is adopted using the commercial software Ansys CFX. The detail of the equations is presented in a previous paper by the author [START_REF] Sampedro | Two-phase nozzles performances CFD modeling for low-grade heat to power generation: Mass transfer models assessment and a novel transitional formulation[END_REF]. The CFX solver can handle, in an Euler-Euler formulation, all the assumptions to be tested on the coupling terms between phases. This is valid also for velocities homogeneity and non-homogeneity.

As a general remark for the rest of the article, since the term homogeneous is not specific enough from a semantic point of view, for clarity reasons regarding each assumption done on the coupling terms between the phases, the following definitions are adopted:

 Homokinetic: assumption of velocities equality between phases  Homothermal: assumption of temperatures equality between phases Regarding the mass transfer models, a substantial diversity in the interfacial transfer models exists as can be read in [START_REF] Yixiang | Computational modeling of flash boiling flows, a literature survey[END_REF]. In the present, paper a thermal phase change model explored by the author (TABD model [START_REF] Sampedro | Two-phase nozzles performances CFD modeling for low-grade heat to power generation: Mass transfer models assessment and a novel transitional formulation[END_REF]) and the so-called Homogeneous Relaxation Model (HRM (P.Downar-Zapolski, Z.Bilicki, L.Bolle, & J.Franco, 1996)) are used. The motivation for using two mass transfer models is to separate the effects of mass and momentum interfacial transfer terms on the results.

For both models, heat transfer was assumed to occur between phases. Since the test case is the same that in the present paper, the reader is invited to read the complete configuration and calibration parameters for both models used by the author in previous work [START_REF] Sampedro | Two-phase nozzles performances CFD modeling for low-grade heat to power generation: Mass transfer models assessment and a novel transitional formulation[END_REF].

Regarding the momentum transfer, the liquid/vapor interfacial drag force is included for the general case. The standard drag coefficient has a value of 𝐶𝑑 = 0.44. The homokinetic case is assumed to represent an extreme case where the interfacial forces would be enough high to avoid any difference in liquid and vapor velocities in any situation. To show the effect of the interfacial force on the phasic velocities, three additional values for Cd were tested (5, 50, and 500). A homokinetic case was also tested. The HRM mass transfer based cases associated with the non-homokinetic assumption were modeled using the same interfacial area density and characteristic length as TABD.

Regarding the properties of the fluids, the liquid properties (𝜌, 𝐶 𝑝 , 𝜇) were computed as a function of the temperature computed from the enthalpy resulting from the energy balance. This means that the liquid's meta-stable condition was computed by considering it in a temperature based saturation state and not in a pressure based saturation state. The vapor was supposed to be in pressure based saturated conditions i.e. its properties were a function of the static pressure. The liquid and vapor properties of water were computed from standard IAPWS IF97 tables available in Ansys CFX. The kwSST closure was used as turbulence model.

CFD simulation configuration

The control volume used for the simulations is presented in Figure 1. It represents the nozzle and an open volume at its outlet. This is a 3D domain maide by a partial revolution of 3 degrees. The inlet conditions are static pressure, static temperature, and liquid and vapor volume fractions. The outlet is defined as an opening with static pressure, and backflow temperature and volume fractions. The dimensions and boundary conditions values are given in section 3. The mesh was built by the same method and with the same characteristic sizes presented previously by the author [START_REF] Sampedro | Two-phase nozzles performances CFD modeling for low-grade heat to power generation: Mass transfer models assessment and a novel transitional formulation[END_REF]. The mesh number per unit volume was similar in the nozzle than in the outlet volume. A mesh sensitivity was also presented in the cited work. The grid used here has 22500 elements. The commercial CFD code Ansys CFX 16.0 was used for CFD simulations. The CFX solver is a coupled solver using a pseudo-transient formulation; the coupled option was selected for volume fraction as well. A bounded second-order upwind scheme was selected for advection. Please refer to Ansys CFX (CFX, 2020) documentation for details on numerical resolution. A steady-state simulation was done. The physical time step was set to 1.10 -5 s. This parameter acts like a relaxation coefficient. The simulation was supposed to be converged when the mass and energy imbalance was lower than 0.5%, the inlet mass flow rate was steady and the outlet velocity was steady; all residuals were in this situation lower than 1.10-5. The total energy formulation of the energy conservation equation was selected. The flow field was initialized at 0 vapor volume fraction, at inlet temperature and pressure, and at 0m/s velocity.

Speed of sound

The speed of sound is a parameter that helps in analyzing the flow. The two-phase flow speed of sound is not obvious to estimate since the wave propagation in a two-phase media is affected by several parameters. Among these, the following can be mentioned: interfacial mass transfer, heat and momentum transfers, and sound wave frequency [START_REF] Staedtke | Gasdynamic Aspects of Two-Phase Flow[END_REF]. Depending on the intensity of the interfacial coupling terms, the effective speed of sound will differ from the ideal homokinetic homothermal case.

The following lines aim to give a summary of the approaches and concepts nowadays available to handle this question.

Staedtke presents the case of the homokinetic non-homothermal case where mass exchange between phases is considered. The resulting sound velocity is the following [START_REF] Staedtke | Gasdynamic Aspects of Two-Phase Flow[END_REF])(page 61):

𝑎 ℎ𝑘𝑒 2 = 1 𝛼 𝑔 𝜌 𝛼 𝑔 2 𝜌 𝑔 + 𝛼 𝑙 𝜌 𝛼 𝑙 2 𝜌 𝑙 (1)
This expression was also used by [START_REF] White | Investigating the validity of the fundamental derivative in the equilibrium and non-equilibrium twophase expansion of MM[END_REF] to describe the so-called ''frozen homogeneous'' situation. White explores as well the expression proposed by Brennen [START_REF] Brennen | Fundamentals of Multiphase Flows[END_REF] for homokinetic homothermal situation [START_REF] White | Investigating the validity of the fundamental derivative in the equilibrium and non-equilibrium twophase expansion of MM[END_REF]:

1 𝜌𝑎 𝐵𝑟𝑒𝑛 2 = 𝛼 𝑔 𝑔 𝑔 + 𝛼 𝑙 𝑔 𝑙 (2)
The terms 𝑔 𝑔 and 𝑔 𝑙 depend on liquid and vapor phases state functions partial derivatives. Please refer to (White, 2020) or [START_REF] Brennen | Fundamentals of Multiphase Flows[END_REF] for the details.

For the non-homokinetic case, Wallis [START_REF] Wallis | One-dimensional Two-phase Flow[END_REF] proposed an expression of sound velocity:

𝑎 𝑊𝑎𝑙𝑙𝑖𝑠 2 = 𝛼 𝑔 𝜌 𝑙 + 𝛼 𝑙 𝜌 𝑔 𝛼 𝑔 𝜌 𝑙 𝛼 𝑔 2 + 𝛼 𝑙 𝜌 𝑔 𝛼 𝑙 2 (3)
However, according to Staedtke [START_REF] Staedtke | Gasdynamic Aspects of Two-Phase Flow[END_REF], this expression leads to numerical instabilities in the computational codes using it. Staedtke presents the results of the work done by the Joint Research Center Ispra. He gives a particular insight into the virtual mass force that affects the speed of sound. This force represents the non-viscous interaction forces due to relative acceleration between phases and is associated with space and time derivatives of transfer terms. Brennen mentions them as the terms emerging from the averaging process in two-phase modeling [START_REF] Brennen | Fundamentals of Multiphase Flows[END_REF]. The formulation of this force is based on the ''virtual mass'' coefficient (k) in the work on Staedtke. The resulting sound velocity is the following [START_REF] Staedtke | Gasdynamic Aspects of Two-Phase Flow[END_REF]:

𝑎 2 =
Figure 2: Sound velocity in water/steam media as a function of the void fraction; saturated conditions at pressure p = 1 bar [START_REF] Staedtke | Gasdynamic Aspects of Two-Phase Flow[END_REF] Figure 3: Two-phase sound velocity as a function of 𝛼; effect of the "virtual mass" coefficient, saturated water/steam at pressure p = 1 bar, equal phase velocities. [START_REF] Staedtke | Gasdynamic Aspects of Two-Phase Flow[END_REF] The ''virtual mass'' coefficient of k=0 represents a case with spatially separated phases where the momentum coupling is reduced to friction. If the friction term is small (|𝑢 𝑔 -𝑢 𝑙 |/𝑢 < 0.1), then the expression of ''a'' is reduced to the one of Wallis (eq 3). If the ''virtual mass'' coefficient k  ∞ then the flow is driven towards homokinetic conditions and the expression of "𝑎" approaches "𝑎 ℎ𝑘𝑒 ".

The ''virtual mass'' coefficient (k) was used by Staedtke as a calibration parameter for the two-phase flow computational method he presents in his book to estimate the sound velocity of water/steam flows. Staedtke mentions that the case where 0.25 ≤ k ≤ 0.5 corresponds to dispersed droplets flows and fits well with experimental observations. Figure 2 presents an example where a coefficient of k=0.25 represents well the measurements. Figure 3 shows an extensive sensitivity analysis of the sound velocity in the entire range of void fraction (or vapor volume fraction) for the same media.

The sound velocity estimations will be used to analyze the simulation results presented below. In Ansys CFX, virtual mass modeling is not considered for two continuous phase's description (it can be for dispersed media). For that reason, the effect of parameter "k" will not be considered. Only reference cases will be used i.e. homokinetic non-homothermal (eq. 1), homokinetic homothermal (eq. 2), and non-homokinetic non-homothermal (eq. 3). Virtual mass effects are important to keep in mind from a theoretical point of view.

TEST CASE

In the early '90s, a Japanese team [START_REF] Ohta | Performance and flow characteristics of nozzles for initially subcooled hot water (influence of turbulence and decompression rate)[END_REF] worked on waste heat recovery by impulse turbines using phase change nozzles. Two nozzle geometries were tested. The first was called the B nozzle which is a fairly simple nozzle. It was extensively studied for a wide outlet pressure range. The authors measured mass flow rate, efficiency, and pressure profiles. The efficiency was obtained thanks to thrust measurements. The dimensions and the operating conditions are shown in Figure 4 and Table 1 respectively.

Note that the mass flow in Table 1 does not depend on the outlet pressure; that means that the nozzle operates in critical conditions. The static pressure taps diameter was 0.6mm. The uncertainty on the pressure measurement was +/-1%.

Figure 4 : Ohta B nozzle [START_REF] Ohta | Performance and flow characteristics of nozzles for initially subcooled hot water (influence of turbulence and decompression rate)[END_REF])

Pressure profiles

The pressure profiles will help in defining which assumption leads to the more reliable results. Pressure profiles obtained with TABD and HRM models are presented respectively in Figure 5 and Figure 6. Each line represents a different assumption on the interfacial momentum transfer term. The 0mm position corresponds to the throat position.

It appears that the main difference between TABD and HRM models occurs just after the throat. TABD gives pressures closer to experiments; however, the difference between models is not significant.

Regarding the assumptions on momentum transfer intensity, the difference between models appears in particular close to the nozzle outlet. The effect of this series of assumptions on the difference to experiments is also particularly visible close to the nozzle outlet. The homokinetic case presents a pressure profile characteristic of a shock wave i.e. a sudden static pressure increase. This is confirmed by velocity profiles as will be presented in section 4.2. However, for the lowest value of Cd, there is no shock wave and the pressure profile is very close to the measured one. The pressure tap located at 4mm before the outlet is of particular interest. At this location, the static pressure value obtained with the homokinetic assumption is lower than in reality. The absolute discrepancy to the experimental value is presented in Figure 7. The discrepancy increases with Cd. For the nominal Cd, the discrepancy is close to 0.01bar. For the homokinetic case, it is close to 0.3bar for TABD and 0.4bar for HRM.

Velocities

Figure 8 shows the liquid and vapor velocities obtained with the TABD model. The velocity difference between vapor and liquid reduces with increasing value of Cd as expected. However, getting the same velocity would require increasing a lot the value of Cd. Also, with the increasing value of Cd, the velocities of both phases get closer to the homokinetic case.

The homokinetic case shows a shock wave close to the nozzle outlet whereas the case with Cd=0.44 doesn't. The values computed for the sound velocity for the different models presented in section 2.3 are given in Figure 9. The figure gives also the values of the average mixture velocity before and after the nozzle outlet (respectively "av ex-4mm" and "av final"). The sound velocity models based on homokinetic assumption give low values of the speed of sound whereas the non-homokinetic model gives a high value (close to the vapor phase sound velocity).

For the homokinetic simulation, it appears that at some point, if the mixture velocity exceeds sound velocity, a shock wave may occur leading to a sudden increase in static pressure and a rapid drop of the velocity. It seems that the homokinetic assumption in the CFD simulation and its consequences on the sound velocity were modeled in coherence with literature models for homokinetic sound velocity i.e. 𝑎 𝐵𝑟𝑒𝑛𝑛𝑒𝑛 and 𝑎 ℎ𝑘𝑒 .

For the case with Cd=0.44, the mixture average velocity remains always below all the sound velocities computed. Besides, no shock wave was observed for this CFD simulation. To explain this, two hypotheses may be possible:

 The sound velocity in the non-homokinetic case is very high as suggested by the Wallis model. In this case, the momentum coupling between phases is weak and the CFD simulation represents it relatively well. This suggests that frictional and non-friction coupling terms are small and could be reduced to frictional only (at least close to the nozzle outlet in the given conditions). Please note that the Wallis model is close to the model presented by Staedtke in the case of dispersed flow (small value of "k") which corresponds to the high void fraction situation in the last third of the nozzle.  The non-homokinetic case creates so much friction that the total enthalpy of the flow is highly degraded leading to moderate maximal velocity. This velocity is thus never higher than any sound velocity. The last hypothesis seems to the author not probable since in the last part of the expansion, where the maximum velocities are reached, the average vapor volume fraction is very high (0.99) and the mixture density is very low (6kg/m 3 ). Furthermore, given the moderate length, such energy losses seem unlikely. However, this needs to be verified in the future.

CONCLUSIONS AND FUTURE WORKS

The simulation based on the homokinetic assumption produces a two-phase mixture shock wave close to the nozzle outlet. The presence of this shock is coherent with the sound velocity models from the so-assumed homokinetic mixture theory. The non-homokinetic case doesn't show any shock wave; that seems coherent with the non-homokinetic sound velocity models.

From the comparative analysis made on the static pressure profiles, it can be concluded that whatever the mass transfer model is, the homokinetic model provides unrealistic results at high velocity. The non-homokinetic model provides results in accordance with the measurements. It can be concluded that the homokinetic assumption implies very important interface momentum coupling that provides erroneous simulated flow velocities and pressures. This has particularly remarkable effects when the homokinetic mixture velocity attains homokinetic sound velocity. It would be useful to consolidate the results on pressure profiles by measuring a larger number of pressure points close to the nozzle outlet. Also, the interfacial momentum transfer modeling needs to make assumptions on the interfacial area density. For the present work, the parameters used to set it were defined using the TABD model. And no extended analysis of the correctness of the drag coefficient value was discussed. It would be useful to analyze it further.

Finally, according to the Wallis model, the sound velocity in the non-homokinetic case is very high, close to pure vapor sound velocity. This is coherent with the model by Staedtke. However, these are theoretical models, and experimental measurement of sound velocity in mixtures, in particular at vapor volume fractions higher than 0.7, would be extremely useful for phase-changing expansions study. Besides, it seems that the momentum coupling between phases was weak in reality as suggested by Staedtke for mist flows. For that reason, including the non-frictional momentum transfer terms was not problematic for the presented case. However, for mixtures with lower vapor/liquid density ratios, this may be no more valid and thus these terms could require further research.

Figure 1 :

 1 Figure 1: computational domain; black arrows : inlet; blue arrows : outletThe commercial CFD code Ansys CFX 16.0 was used for CFD simulations. The CFX solver is a coupled solver using a pseudo-transient formulation; the coupled option was selected for volume fraction as well. A bounded second-order upwind scheme was selected for advection. Please refer to Ansys CFX (CFX, 2020) documentation for details on numerical resolution. A steady-state simulation was done. The physical time step was set to 1.10 -5 s. This parameter acts like a relaxation coefficient. The simulation was supposed to be converged when the mass and energy imbalance was lower than 0.5%, the inlet mass flow rate was steady and the outlet velocity was steady; all residuals were in this situation lower than

Figure 5 :

 5 Figure 5: pressure profiles; simulation vs experiments ; TABD model

Figure 8 :

 8 Figure 8: vapour and liquid velocities for TABD

  𝛼 𝑔 𝛼 𝑙 𝜌 𝑔 𝜌 𝑙 (𝑢 𝑔 -𝑢 𝑙 ) 2 (𝜌 𝑙 + 𝑘𝜌)(𝜌 𝑔 + 𝑘𝜌) (𝜌 𝑔 𝜌 𝑙 + 𝑘𝜌 2 )

	𝛼 𝑔 𝜌 𝑙 + 𝛼 𝑙 𝜌 𝑔	1 + 𝑘	𝛼 𝑔 𝜌 𝑔 + 𝛼 𝑙 𝜌 𝑙 𝛼 𝑔 𝜌 𝑙 + 𝛼 𝑙 𝜌 𝑔
	𝛼 𝑔 𝜌 𝑙 𝛼 𝑔 2 +	𝛼 𝑙 𝜌 𝑔 𝛼 𝑙 2	1 + 𝑘	𝜌 𝑔 𝜌 𝑙 𝜌 2	2

-

Table 1 :

 1 Ohta B nozzle operating points[START_REF] Ohta | Performance and flow characteristics of nozzles for initially subcooled hot water (influence of turbulence and decompression rate)[END_REF]

	𝑇 𝑖𝑛 (°𝐶)	𝑃 𝑖𝑛 (𝑘𝑃𝑎)	𝑆𝐶(𝐾)	𝑃 𝑜𝑢𝑡 (𝑘𝑃𝑎)	𝑚̇(𝑔/𝑠)
	148	470	1,5	18/45/73/100	122
	137,5	470	12	16/43/70/100	156

NOMENCLATURE


Christophe Morin
email: ch.morin@u-pec.fr

Adèle Bressy

Melissa Saichi

Clément Leroyer

Yaël Guttmann

Régis Moilleron

Laure Garrigue-Antar
email: laure.garrigue-antar@u-pec.fr

Ecotoxicological impacts of cosmetic products preservatives in a zebrafish model

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.

Introduction

Parabens are ingredients of most personal care products (PCPs), as preservatives. From their massive use and their ubiquitous presence in the environment, these molecules have a potential negative effect on aquatic ecosystems as endocrine disruptors , thus representing a source of increasing concern. Parabens have been the subject of an alert following a 2004 publication, which reported a potential link between parabens and breast cancer. Growing consumer awareness led cosmetic industry to move away from parabens towards paraben-free or organic products and to use alternatives substances in their formulations, processes and packaging. Among the key unanswered questions, is the identification of the products used in the formulations that need to be substituted, and their replacement by other potentially harmful substances. Objectives (i) Determination of which chemicals replace parabens (ii) Evaluation of the toxicity of these molecules on the development and the behavior of zebrafish (Danio rerio) larvae.

Substitution of parabens in cosmetic products

Bibliography and industrial survey :

•Identification of parabens substitutes •Potentially hazardous effect of some substitutes on aquatic organisms : phenoxyethanol (PE), methylisothiazolinone (MIT), chlorphenesin (CPN)..

Substances:

-



  Methyl Parabene (MeP) -Chlorphenesin (CPN) -MethylIsoThiazolinone (MIT) -Phenoxyethanol (PE) This study is part of the Cosmet'eau project which is funded within the framework of a French call for project about "Micropollutants: innovation and changes of practices" launched in 2013 by the French Ministry of Environment, The French National Agency for Biodiversity (AFB) and a French water agency (Agence de l'Eau Seine-Normandie). Methodology Dose-response between 0 -75mg/L (MEP) + 2[MEP] (PE) -PE presence alters MeP ecotoxicity :  Increased survival rate  Apparitions of important abnormalities, unseen for MeP alone  MeP, MIT & CPN affect survival and development  No obvious effect for PE At high concentrations (5000x and over), the mix of molecules decreases larvae' response to tactile stimulus  No significant effect of single molecules or mix of molecules at low concentrations (<1000x)  No sensitivity of the test at environmental concentrations  Single molecules, but not mixes, produce a significant hypolocomotion during the light periods, except PE  Significant hyperactivity of the larvae with the mix CPN/PE during the light periods  No significant effect observed during the dark periods, except MIT/CPN  Unpredictable effect of combination of molecules  Sensitive test suitable for concentrations found in the environnement MIT + CPN CPN 1x: 0,1µg/L MIT 1x: 0,05µg/L Kimura et al,, Chemosphere (2014) 107, 393-99; Peng et al, 2016, Pharmacology, Biochemistry and Behavior 145 (2016) 55-65; Rafoth J, Chromatogr A 1164, (2007), 74-81 Yearly evolution of marketed cosmetics containing parabens (left) and substitutes (right) [Mintel database, 2015] post hoc Dunnett's test ***: p < 0.001 ; ** : p < 0.01 ; * : p < 0.05

Acknowledgements


Émile Brisson-Curadeau

Charles-André Bost

Yves Cherel

Kyle Elliot

King penguins adjust foraging effort rather than diet when faced with poor foraging condi�ons

Keywords: diet, Southern Ocean, specialist, isotope, foraging, seabird, king penguin

The links between foraging success, foraging effort and diet in a myctophid specialist seabird, the King Penguin Aptenodytes patagonicus, were inves�gated during seven breeding seasons using tracking and isotopic data. Despite the variable foraging condi�ons encountered by the birds, isotopic signature (a proxy for diet) were invariable throughout the study. On the other hand, penguins stayed longer at sea when the foraging success indices (i.e. prey capture atempts per day and mass gained per day) were low.

While King Penguins can compensate low prey capture rates by increasing foraging effort, their specialist diet during reproduc�on makes the species par�cularly sensi�ve to prey availability, with its conserva�on �ghtly linked to its main prey.

Intro

There are mul�ple strategies available to birds to cope with periods of low prey availability. For example, dietary-specialist species can increase foraging effort to compensate for low prey capture rates [START_REF] Abrams | Life history and the rela�onship between food availability and foraging effort[END_REF][START_REF] Cox | Rainy springs linked to poor nestling growth in a declining avian aerial insec�vore (Tachycineta bicolor)[END_REF][START_REF] Fromant | Impact of extreme environmental condi�ons: foraging behaviour and trophic ecology responses of a diving seabird, the common diving petrel[END_REF]. Alterna�vely, generalists can switch to feeding on other s�llavailable prey [START_REF] Scopel | Varied breeding responses of seabirds to a regime shi� in prey base in the Gulf of Maine[END_REF][START_REF] Milchev | Temporal and spa�al dietary shi�s of a generalist top predator: longterm study of an Eagle owl Bubo bubo popula�on[END_REF]. The strategy chosen is highly speciesdependant, with both specialist and generalist displaying variable flexibility in both foraging effort and diet.

In the marine environment, species composi�on is changing dras�cally, as environmental disturbances such as overfishing or recurrent marine heat waves might induce periods of low prey availability [START_REF] Jones | Massive mortality of a plank�vorous seabird in response to a marine heatwave[END_REF][START_REF] Osborne | Breeding seabirds increase foraging range in response to an extreme marine heatwave[END_REF][START_REF] Sydeman | Hemispheric asymmetry in ocean change and the produc�vity of ecosystem sen�nels[END_REF]. While generalist species that switch prey will likely beter tolerate these ecosystemic changes, specialists might be impacted as the foraging effort increases to compensate for poor condi�ons [START_REF] Gilman | A framework for community interac�ons under climate change[END_REF]. Such is the case for species including the Litle Auk Alle alle or the African Penguin Spheniscus demersus, two specialist species that increased �me spent foraging in response to reduced availability of their main prey [START_REF] Jakubas | Response of dovekie to changes in food availability[END_REF][START_REF] Pichegru | Industrial fishing, notake zones and endangered penguins[END_REF]).

Yet, even species regarded as specialists can some�mes shi� their diet in cri�cal periods, so that a certain level of flexibility might help these species cope with a changing environment (e.g. [START_REF] Ludynia | Surviving off junk: low-energy prey dominates the diet of African penguins Spheniscus demersus at Mercury Island, Namibia, between 1996 and 2009[END_REF][START_REF] Ancona | Effect of El Niño on the diet of a specialist seabird, Sula nebouxii, in the warm eastern tropical Pacific[END_REF].

Here, we inves�gate the links between foraging success, foraging effort, and diet in a specialist deep-diving seabird, the King Penguin Aptenodytes patagonicus. This species feeds mainly on small mesopelagic myctophids, o�en dominated by Krefftichthys anderssoni, for which the availability to the top predators may change across the polar region, mainly due to clima�c anomalies [START_REF] Bost | Feeding of diving predators and diel ver�cal migra�on of prey: King penguins¹ diet versus trawl sampling at Kerguelen Islands[END_REF][START_REF] Bost | Large-scale clima�c anomalies affect marine predator foraging behaviour and demography[END_REF][START_REF] Bohec | King penguin popula�on threatened by Southern Ocean warming[END_REF][START_REF] Péron | Projected poleward shi� of king penguins'(Aptenodytes patagonicus) foraging range at the Crozet Islands, southern Indian Ocean[END_REF]). Yet, King Penguins can also forage opportunis�cally on other prey such as squids and other myctophids (Adams & Klages 1997, Bost et al. 2002, Cherel et al. 2007).

Consequently, the species could theore�cally diversify its diet in periods of low prey availability.

We test whether King Penguins would become more opportunis�c when foraging success is low by comparing isotopic values (a proxy of diet) of foraging breeding adults over seven years. We predicted that, if penguins compensated for low prey availability by switching diet, we would find different isotopic values in individuals experiencing dissimilar foraging success. On the other hand, if penguins did not seek different prey despite low prey availability, we expected a compensa�ng increased foraging effort (e.g. longer foraging trips, deeper dives) as foraging success decreases, while isotopic values would remain constant.

Methods

All data were collected in February on chick-rearing King Penguins at Ratmanoff's colony (around 85 000 pairs, [START_REF] Barbraud | Popula�on trends of penguins in the French Southern Territories[END_REF] in the Kerguelen archipelago (-49° 14ʹ 33ʺ, 70° 33ʹ 40ʺ) situated in the southern Indian Ocean. Data were obtained during the chick-rearing period in all years from 2015 to 2022 except 2019 (i.e. seven years total). The ethics commitee of the Ins�tut polaire français Paul-Émile Victor approved all field procedures. King penguins of this colony feed mostly on a small myctophid, Krefftichthys anderssoni, and opportunis�cally (up to 25% of their diet) on other prey such as other fish species and squids [START_REF] Bost | Feeding of diving predators and diel ver�cal migra�on of prey: King penguins¹ diet versus trawl sampling at Kerguelen Islands[END_REF][START_REF] Cherel | Isotopic niches and trophic levels of myctophid fishes and their predators in the Southern Ocean[END_REF][START_REF] Cherel | Top predators and stable isotopes document the cephalopod fauna and its trophic rela�onships in Kerguelen waters. The Kerguelen Plateau: marine ecosystem and fisheries[END_REF]. During the chick-rearing period, parents make trips at sea las�ng about 4 to 10 days. While prey availability es�mates are not known during the study period, the years 2015 and 2016 were possibly less favorable for King Penguins at Kerguelen (Brisson-Curadeau et al.

2023).

Isotopic analysis

Stable isotopes of nitrogen (δ15N) are considered to be indica�ve to the trophic posi�on of consumers, thus reflec�ng its diet, while δ13C is a proxy of the consumers' foraging habitat [START_REF] Hobson | Using stable isotopes to determine seabird trophic rela�onships[END_REF][START_REF] Quillfeldt | Diet and foraging areas of Southern Ocean seabirds and their prey inferred from stable isotopes: review and case study of Wilson's storm-petrel[END_REF], Cherel & Hobson 2007). The resul�ng isotopic niche described by these two isotopes can be thus used as a proxy of the consumers' trophic niche.

Since 2015, 83 chick-rearing penguins were blood sampled (2 ml) a�er their return from a single foraging trip. Birds were captured using a long wooden perch. The blood was freeze-dried and about 0.7mg was weighed into �n capsules. The capsules were shipped for bulk stable isotopes ra�o of nitrogen ( 15 N/ 14 N) and carbon ( 13 C/ 12 C) at the Ján Veizer Stable Isotope Laboratory (Otawa, Ontario, Canada). Isotopic composi�on was measured by combus�on on an Elementar VarioEL Cube Elemental Analyser followed by "trap and purge" separa�on and on-line analysis by con�nuous-flow with a DeltaPlus Advantage isotope ra�o mass spectrometer coupled with a ConFlo III interface. The isotope concentra�on determina�on used the following conven�onal equa�on: δ = ([Rsample/Rstandard]-1) *1000

where Rsample and Rstandard are the corresponding ra�os of heavy to light isotope in the sample and standard, respec�vely. The standards used were air for nitrogen, Pee Dee Belemnite for carbon. Replicate measurements of internal laboratory standards indicate measurement errors of 0.35‰ and <0.1‰ for δ 13 C and δ 15 N, respec�vely.

All alternate prey types of King Penguins have a higher δ 15 N value than K. anderssoni [START_REF] Bost | Feeding of diving predators and diel ver�cal migra�on of prey: King penguins¹ diet versus trawl sampling at Kerguelen Islands[END_REF][START_REF] Cherel | Isotopic niches and trophic levels of myctophid fishes and their predators in the Southern Ocean[END_REF]. We therefore expected individuals with a more diverse diet to have a higher δ 15 N value.

To full list of poten�al prey and their respec�ve δ 15 N value around Kerguelen can be found in Table S1.

Foraging effort

Foraging effort during the foraging trip was determined using biologgers from various brands recording GPS loca�on and/or depth. Some of these loggers also recorded 3D accelera�on (star�ng in 2020) as well as water temperature. Over the seven years, 52 birds were equipped with one or two of these devices (see Table S2-S3 for exact sample size by year). Loggers were retrieved a�er a single foraging trip. Penguins were weighed before and a�er each foraging trip. The weigh of the loggers varied with models, but never exceeded 2% of the bird's mass.

For analysis, only dives >50m were considered, as shallower dives are not associated with foraging ac�vity [START_REF] Charrassin | Penguins as oceanographers unravel hidden mechanisms of marine produc�vity[END_REF]. Depth was used to compute two foraging effort metrics for each individual: mean diving depth and total ver�cal distance travelled during a foraging trip, calculated as the sum of the maximum depths of all dives [START_REF] Charrassin | Penguins as oceanographers unravel hidden mechanisms of marine produc�vity[END_REF]. Using loca�on data, we computed the mean distance to the colony of all foraging dives, as well as the mean la�tude and longitude for correla�on with isotopic variables. A final metric of foraging effort was calculated as the total number of days spent at sea during the foraging trip.

Due to logis�cal reasons, not all blood sampled penguins were assessed for foraging effort. Reasons explaining this mismatch include logger failures and logger detachment.

Conditions encountered and foraging success

King Penguins target the depth just below the thermocline to capture prey [START_REF] Charrassin | U�lisa�on of the oceanic habitat by king penguins over the annual cycle[END_REF][START_REF] Scheffer | Combined influence of meso-scale circula�on and bathymetry on the foraging behaviour of a diving predator, the king penguin (Aptenodytes patagonicus)[END_REF]. Consequently, shallower thermoclines are more accessible and therefore provide beter condi�ons for foraging penguins. To assess the condi�ons encountered, we therefore combined depth data and temperature data to calculate the depth of the thermocline for each dive. We defined the thermocline as the depth where the change in temperature was the greatest (see [START_REF] Charrassin | U�lisa�on of the oceanic habitat by king penguins over the annual cycle[END_REF].

We then calculate the average thermocline depth among all dives for each individuals.

We computed two metrics of foraging success. First, we calculated the mass gained per day of foraging at sea. A second metric was computed using the accelerometry data: the number of Prey Capture Atempts (PCAs) in each dive was es�mated with the algorithm from Brisson-Curadeau et al. ( 2021) using the number of accelera�on peaks in the dive. We then used the number of PCAs per day as a measure of foraging success.

Statistics

We tested how blood δ 15 N and δ 13 C values were influenced by the following variables: mean diving depth, total ver�cal distance travelled, mean thermocline depth, mean distance from the colony, mean la�tude, mean longitude, trip dura�on, mass gained per day and PCAs per day. We also tested the influence of the foraging effort variables (mean diving depth, total ver�cal distance travelled, trip dura�on, mean distance from colony) on the two foraging success metrics. All these tests were conducted by crea�ng several linear models with mixed effects, each with one of these variables and "year" as a random effect. Only one fixed effect was used per model to avoid overfi�ng and correla�on between explanatory variables.

Because most of these variables had a different number of observa�ons, and because models with different number of observa�ons are not directly comparable, we created a corresponding null model (with only the random effect) for each model using only the observa�ons available. We then scored the models using the Akaike Informa�on Criterion (AIC) and compared the score with its associated null model.

Only models that had a Δ2 with their corresponding null model were considered.

We also tested if there were differences among years for all variables (isotopes, foraging effort, and foraging success) using ANOVAs. In such a case, we did Tukey's tests to iden�fy the pairs of years that differed.

All analysis were conducted in R version 4.1. Package lme4 was used to build the mixed-effect models [START_REF] Bates | Fi�ng Linear Mixed-Effects Models Using lme4[END_REF]. Valida�on of assump�ons were conducted on all models (see also table S4). We tested for heteroskedas�city of residuals using the Breusch Pagan test on the lmtest package [START_REF] Breusch | Tes�ng for Autocorrela�on in Dynamic Linear Models[END_REF], Zeleis & Horton 2002). Pearson correla�on test were conducted between residuals and the independent variables, while the autocorrela�on in the residuals was assessed by extrac�ng the autocorrela�on coefficient [START_REF] Venables | Modern Applied Sta�s�cs with S. Fourth Edi�on[END_REF].

Results

Foraging behavior

Most foraging effort indices varied greatly among individuals (Fig. 1), as shown by the standard devia�on (σ) and mean (μ) of total ver�cal distance travelled (μ = 123 km, σ = 62 km, n = 48), trip dura�on (μ = 8.5 days, σ = 3.1 days, n = 53) and mean distance from the colony (μ = 251 km, σ = 102 km, n = 36). To a lesser degree, mean diving depth also differed among individuals (μ = 141m, σ = 16 m, n = 48). Two foraging success variables, mass gained per day (μ = 0.28 kg/day, σ = 0.15 kg/day, n = 31) and PCAs per day (μ = 406 PCAs/day, σ = 185 PCAs/day, n = 52) also varied greatly from one individual to another. When tes�ng for among-year differences, only mean depth and total ver�cal distance showed significance (Fig. 1, Table S5).

Stable isotopes

Model selec�ons showed that blood δ 13 C (-22.0 ± 0.4‰, n = 83) varied with mean longitude, as the model containing this variable was the only model which scored higher than its associated null model (Table 1).

There was a strong tendency for δ 13 C to decrease as penguins foraged farther east, off the Kerguelen shelf (Fig. 2). Furthermore, δ 13 C varied significantly among years as shown by ANOVA analysis (Fig. 3, Table S4).

Similarly, blood δ 15 N (10.1 ± 0.2 ‰, n = 83) varied among years (Fig. 3, Table S4). However, the inter-year varia�on in δ 15 N was less pronounced than with δ 13 C and only two years (2016 and 2021) were significantly different from each other according to the Tukey's tests (p value = 0.02). Overall, there was litle varia�on in δ 15 N among individuals (δ 15 N range: 9.6 -10.6 ‰). As for the models predic�ng δ 15 N using foraging effort and success variables, none scored higher than their corresponding null model, despite high variability detected in all these explanatory variables (Table 1).

Foraging success

When considering mass gained per day as a response variable, only the model with foraging trip dura�on as a fixed effect scored beter than its respec�ve null model. Similarly, when PCAs per day was considered as a response variable, foraging trip dura�on again was the fixed effect in the only model scoring beter than its respec�ve null model (Table 1).

Discussion

The seabird species include both species labelled as diet generalists and specialists. Yet, almost all seabird species can display a certain level of flexibility, as even specialist species can feed opportunis�cally on prey outside of their main diet (e.g. [START_REF] Ancona | Effect of El Niño on the diet of a specialist seabird, Sula nebouxii, in the warm eastern tropical Pacific[END_REF]. This flexibility might be of par�cular u�lity when certain prey types become temporarily scarce. Yet, we found that the King Penguin, a myctophid specialist, does not greatly vary its diet in terms of trophic posi�on (δ 15 N), even when encountering highly variable foraging condi�ons. Instead, the species relies more on increasing foraging effort to compensate for low prey capture rates. Our research emphasizes the �ght link exis�ng between some marine predators and their prey, with the conserva�on of the former being strongly dependant on the later.

Isotopic landscape

A first observa�on that can be made from our results is that there is a strong longitudinal gradient of δ 13 C in the environment near Kerguelen. In the Southern Ocean, most reported gradients for this isotope is usually la�tudinal, not longitudinal (Cherel & Hobson 2007[START_REF] Espinasse | La�tudinal gradient consistency in carbon and nitrogen stable isotopes of par�culate organic mater in the Southern Ocean[END_REF]. However, the North-South gradient is evident at a larger scale, while at a smaller scale δ 13 C is influenced by habitat, with 13 C depleted in offshore habitats rela�ve to coastal habitats (Cherel & Hobson 2007). As the Kerguelen Plateau extends south of the island to Heard Island (Fig. 2), penguins foraging south will remain in the same shelf habitat. On the other hand, penguins foraging east will quickly encounter deeper bathymetry, likely explaining the gradient in δ 13 C as habitat changes with longitude.

Diet specialisation

The use of δ 15 N as a proxy of diet has been controversial when used at a large scale, as spa�al gradients of the isotope exist regardless of trophic posi�on due to varia�on in baseline δ 15 N [START_REF] Seminoff | Stable isotope tracking of endangered sea turtles: valida�on with satellite telemetry and δ15N analysis of amino acids[END_REF]). However, we did not detect spa�al gradients influencing δ 15 N at a local scale near Kerguelen. It is therefore a fair assump�on that δ 15 N could be used in this study to assess trophic posi�on of King Penguins, as in similar studies conducted in the Southern Ocean (Cherel & Hobson 2007[START_REF] Cherel | Isotopic niches and trophic levels of myctophid fishes and their predators in the Southern Ocean[END_REF][START_REF] Polito | Contras�ng specialist and generalist paterns facilitate foraging niche par��oning in sympatric popula�ons of Pygoscelis penguins[END_REF]. Consequently, we expected δ 15 N to vary with foraging success in our study. Indeed, low food availability some�mes causes even specialist species to become more opportunis�c in their diet (e.g. [START_REF] Ancona | Effect of El Niño on the diet of a specialist seabird, Sula nebouxii, in the warm eastern tropical Pacific[END_REF][START_REF] Buren | Linking predator diet and prey availability: common murres and capelin in the Northwest Atlan�c[END_REF]. As all alterna�ve prey of King Penguins on Kerguelen islands have a higher δ 15 N value than their main prey Krefftichthys anderssoni, we expected δ 15 N value of King Penguin to be higher in low foraging success individuals [START_REF] Bost | Feeding of diving predators and diel ver�cal migra�on of prey: King penguins¹ diet versus trawl sampling at Kerguelen Islands[END_REF][START_REF] Cherel | Isotopic niches and trophic levels of myctophid fishes and their predators in the Southern Ocean[END_REF]. Items some�mes consumed by King Penguins at Kerguelen that have a higher δ 15 N value include the squid Gonatus antarcticus and almost all alternate myctophids prey (see Table S1). Yet, blood δ 15 N value of foraging penguins did not increase (or decrease) significantly with the substan�ally different foraging effort, foraging success and marine condi�ons encountered by the penguins. In fact, the δ 15 N range of Kerguelen's King Penguins was very narrow across individuals and across years -even when compared to other seabirds regarded as specialists -sugges�ng litle varia�on in the diet (see Table 2).

We confirmed that King Penguins are very restric�ve in their foraging strategy and targeted prey. Whatever the oceanic area used, they likely seek myctophid schools near frontal currents and have litle flexibility in their foraging tac�cs [START_REF] Bost | Importance of Southern Ocean fronts for seabird and marine mammals)[END_REF]. During the breeding season, marginal prey items such as squid might only be opportunis�cally captured by the King Penguins when preying on mesopelagic schools of K. anderssoni, rather than being the result of a switch in strategy as in some generalist seabirds (e.g. [START_REF] Brisson-Curadeau | Prey capture and selec�on throughout the breeding season in a deep-diving generalist seabird, the thick-billed murre[END_REF]. Consequently, unsuccessful individuals prolonged their stay at sea to compensate for low prey availability rather than changing their foraging strategy and diet. Indeed, both foraging success indices were nega�vely correlated to trip dura�on, sugges�ng that individuals encountering few prey stayed longer at sea.

In conclusion, our study shows an example of a strict specialists that seldom adjusts its diet despite the different condi�ons encountered, but rather stayed at sea for a longer period to compensate for lower foraging success. We highly suspect popula�on parameters of such species to be �ghtly linked to the availability of its main prey. Indeed, foraging effort cannot increase indefinitely to compensate for low prey availability, meaning strict specialists might face breeding failures and/or at-sea mortality if prey composi�on started shi�ing in the future, especially in the growing context of clima�c changes (e.g. [START_REF] Cury | Global seabird response to forage fish deple�onone-third for the birds[END_REF]. Ongoing popula�on monitoring efforts are par�cularly valuable for specialist species, as popula�on trends might be par�cularly sensi�ve to climate change. Long-term prey surveys are also important to detect such shi�s and predict future botom-up effects affec�ng seabirds.

atFigure 1 :

 1 Figure 1: Annual varia�on of foraging effort variables (middle and le� graphs) as well as foraging success

Figure 2 :

 2 Figure 2 : Mean diving posi�on of foraging King Penguins during breeding. Each point represents a

Figure 3 :

 3 Figure 3 : Annual varia�on of δ 13 C and δ 15 N for blood samples among King Penguins breeding at

  Figure 1

Table 1 :

 1 Best ranked models explaining δ 13 C, δ 15 N, mass gained per day and PCAs per day 230

	Best ranked models	Number of observations in the models	AIC	ΔAICc with null model	equation
		Blood δ 13 C as the response variable
	δ 13 C ~ Mean longitude of foraging dives (°)	n = 34	31.5	Δ -8.06	-0.33x + 2.61
		Blood δ 15 N as the response variable
	No models outranked the null model	-	-	-	-
		Mass

gained per day of foraging (kg/day) as the response variable

	Mass ~ Foraging trip dura�on (days)	n = 51	-55.5	Δ -8.39	-0.02x + 0.50
		PCAs per day as the response variable
	PCA ~ Foraging trip dura�on (days)	n =28	294.2	Δ -2.54	-7.72x + 419.6

Table 2 :

 2 Comparison of among-year and among-individuals varia�ons in δ 15 N between the King Penguin

Table S1 :

 S1 δ 15 N values of alternate prey items of king penguins at Kerguelen, in comparison with the main prey, Krefftichthys anderssoni

	Prey item	δ 15 N (‰)	Source
	Krefftichthys anderssoni	7.6 ± 0.2	Cherel et al. 2010
	Protomyctophum bolini	9.2 ± 0.4	Cherel et al. 2010
	Electrona carlsbergi	9.5 ± 0.2	Cherel et al. 2010
	Protomyctophum tenisoni	8.1 ± 0.3	Cherel et al. 2010
	Protomyctophum andriashevi	8.7 ± 0.4	Cherel et al. 2010
	Electrona antarctica	8.9 ± 0.3	Cherel et al. 2010
	Martialia hyadesi	7.7 ± 0.6	Cherel et al. 2011, Hobson & Cherel (2006)
	Gonatus antarcticus	13.3 ± 0.5	Cherel et al. 2011, Hobson & Cherel (2006)

Table S2 :

 S2 Loggers used from 2015-2022

	Table S3: deployment by year
	Year			Deployment
	2015	3 birds equipped with both FastLoc and Mk9
	2016	2 birds equipped with both FastLoc and Mk9 2 bird equipped with FastLoc only
	2017	7 birds equipped with both FastLoc and Mk9
	2018	6 birds equipped with both FastLoc and Mk9
	2020	3 birds equipped with both PTT Kiwisat and Mk9 4 birds equipped with Axy-Trek
	2021	7 birds equipped with Axy-trek 3 birds equipped with MK9
	2022	8 birds equipped with Axy-trek 7 birds equipped with both Axy 4XS and MK9
				Information recorded by logger
	Model name	Company	Company loca�on	GPS	Depth	3D accelera�on	Temperature
	FastLoc	SirTrack Ltd	Havelock North, NZ	x
	PTT Kiwisat	SirTrack Ltd	Havelock North, NZ	x
	MK9	Wildlife Computer	Redmond, US		x		x
	Axy-Trek	Technosmart Colleverde, It	x	x	x	x
	Axy 4 XS	Technosmart Colleverde, It			x

Table S4 :

 S4 Test for linear model assump�ons for models reported in the study

			Pearson correla�on test	Autocorrela�on	Breush Pagan Test
	Model	Mean of residuals	between residuals and	coefficient of the	(Homoskedas�city of
			independent variable	residuals	residuals)

Table S5 :

 S5 ANOVA results to compare differences among years for isotopic signatures, foraging effort indices and foraging success indices

	Variable	Degrees of freedom	F value	p-value
	δ 13 C	6	7.375	<0.001
	δ 15 N	6	2.971	0.01
	Mean distance to colony	6	1.406	0.25
	Trip dura�on	6	3.294	0.009
	Mean depth	6	9.769	<0.001
	Total ver�cal distance	6	5.196	<0.001
	PCAs per day	2	2.088	0.15
	Mass gained per day	6	1.049	0.41