Gaël Obein

est destinée au dépôt

Introduction

For metrologists, the measurement of appearance is a particular activity because, unlike other metrological fields, the measurand is located in the observer's head and is not directly accessible by the instrument. The technique involves developing two parallel scales. A physical scale, which characterizes the optical properties of surfaces using mainly spectrophotometric techniques. A visual scale, which characterizes the perceptual properties of the object using psychophysical techniques. Once these two scales are established, correlations are sought that allow for proposing numerical indices that are acquired by spectrophotometric means and that correlate with visual sensation. The best example of achievement in this field is the adoption in 1924 by the CIE of V(λ), the spectral sensitivity curve of the standard observer, which links radiometric measurements (optical measurement based on the watt) to photometry (perception measurement based on the lumen) [START_REF] Ohno | Principles governing photometry (2nd edition)[END_REF]. Another great example is that of "traditional" colorimetry, which extracts a numerical triplet from the spectral reflectance factor, that identifies a given colour in people's perceptual colour space [START_REF]International Organization for Standardization[END_REF]. Thanks to this approach and these tools, it became possible to finely control the colour of manufactured objects using colorimeters. Some famous brands have even gone up to appropriating certain colours, making them a signature. Think about Coca Cola's "red," Pepsi's "blue," or Veuve Clicquot's "orange-yellow," for example. This makes life easier when it comes to finding the desired bottle among all the others.

The story could have ended there, but that was without counting on the inventiveness of our engineers.

These engineers realized that adding highly reflective mica particles to painting subtract generates tiny bright spots that shine on the surface of the object under the direct light of the sun, like stars in the sky. The paint becomes almost alive… Visual fascination and romance mixed? The public loves it. The sparkle effect was born (fig. 1a). It now covers more than 80% of new vehicles produced worldwide. Adding sub-micrometre streaks to these flakes causes them to diffract light, and the stars become individually coloured. Sublime! Let's now change the light and move from the sun to a cloudy sky. The shiny dots disappear and the appearance of the coating changes. Now it looks more like the visual appearance of a granitic stone that has been sculpted by thousands of years. It is the graininess effect.

It is also possible to play with the transparency of multilayer coatings, inspired by certain butterflies or beetles. Then, the colour changes with the direction of illumination and observation. If the change is rapid and describes the entire visible spectrum, it is called iridescence (fig. 1b); if the change is slow and limited to a few colours, it is called goniochromatism. In any case, these effects allow the edges of objects to be emphasized and the shapes to be sublimated.

In the 2000s, laptops became democratized. We know their complexity, which underlies the feeling of fragility. But we take them everywhere! The user is reassured if the outer shell of his laptop appears solid, like the good old machine tools of yesteryear. Sandblasted aluminium or brushed steel finish appeared (fig. 1c). The effect is anisotropic and metallic. It conveys a feeling of robustness. Its success is such that it has quickly invaded the household appliance and furniture market.

In the 2010s, perhaps it is the awareness of the human footprint on our planet that drives us to return to surfaces that appear more natural, more biological. Gloss, which was a symbol of luxury in the 20th century, becomes "bling-bling." We prefer the satin of the patina of old wooden furniture or the matte of cork or stone. Matte or satin finishes are emerging (fig. 1d).

Radiometric quantities

All of these new effects are directional. To grasp their subtlety, the surface must be illuminated from multiple directions, and for each of these directions, the light they reflect must be measured in multiple directions. The appropriate radiometric quantity is the Bidirectional Reflectance Distribution Function.

CIE defines this quantity as "function describing the change with direction of irradiation i and direction of observation o of the quotient of the element of radiance of the surface element in the given direction of view at the given wavelength dLo , by the corresponding element of irradiance incident on the medium from the given direction of irradiation at the given wavelength, dEi" [3] (fig. 2, left).

Unit is inverse steradian [sr -1 ]. It is a radiometric quantity. It has six degrees of freedom.

The BRDF characterizes the reflection of light on the surface of a material. It contains the information exploited by observers to analyse the different visual attributes of appearance.

Colour comes from the light that has been through the interface, has interacted with pigments or multiple layers, and has been re-emitted in the hemisphere in a random direction. To access it, an accurate control and a tied sampling of the wavelength is requested. But it doesn't need to get it for a lot of angular configurations. After all, a uniform surface roughly has the same colour in all directions and a goniochromatic surface, whether it is interferometric or diffractive, presents "soft" angular variations, manifesting themselves to the order of a degree or even a dozen degrees [START_REF] Strothkämper | How to Efficiently Characterize Special Effect Coatings[END_REF] [START_REF] Ferrero | Color characterization of coatings with diffraction pigments[END_REF].

For gloss, it's a bit the opposite. Gloss comes from the light reflected by the surface. It is localized around the mirror direction, in what is called the "specular peak". The sharper the peak, the glossier the material is. To access gloss, it is necessary to measure the BRDF with very fine angular resolution and with very high dynamic range, to be able to analyse this sharp peak [START_REF] Rabal | What is the true width and height of the specular peak according to the level of gloss ?[END_REF] [START_REF] Obein | Metrological issues related to BRDF measurements around the specular direction in the particular case of glossy surfaces[END_REF]. But what's the point of covering the entire hemisphere? And why acquire spectral information? We know that gloss is confined in the specular and is not spectral.

For sparkle, we have seen that it consists of tiny luminous dots, that shine like stars. In the BRDF, very thin luminance peaks will appear in different directions, like a hedgehog. Here again, a very fine angular resolution is required, but this time covering a much larger part of the hemisphere. Quantifying sparkle effect is still under works today [START_REF] Ferrero | The measurement of Sparkle[END_REF]. The problem is well broken down. Indicators correlating with the visual sensation are proportional to the density and to the intensity of these peaks [START_REF] Gómez | Visual and instrumental correlation of sparkle by the magnitude estimation method[END_REF]. The recent addition of colour in this effect further complicates the task because now we must be spectral. For this type of measurement, the use of an imaging system becomes mandatory. This type of device must be calibrated, which requires meticulous work [START_REF]Calibration, Characterization and Use of Array Spectroradiometers[END_REF].

Texture comes from the variation of the BRDF as a function of the displacement of the measurement surface A (fig. 2 left). We then speak of acquiring the SVBRDF, the Spatially variable BRDF. This is the favourite quantity of the computer graphics community. It is a eight degrees of freedom quantity, easier to model than to measure [START_REF] Schwartz | Design and implementation of practical bidirectional texture function measurement devices focusing on the developments at the university of bonn[END_REF].

Transparency is located in the other hemisphere. To characterize it, we do not make "reflectance" measurements but "transmittance" measurements. We then speak of measuring the BTDF (Bidirectional Transmittance Distribution Function) (fig. 2 right). This quantity is similar to the BRDF but in transmission. Recent work has made it possible to define it clearly [START_REF] Fu | Preliminary Results of Angle-Resolved BTDF Characterization of Optical Transmissive Diffusers[END_REF]. Metrology laboratories have developed instruments to measure it.

The measurement of translucency must be approached with an even more complex quantity. Indeed, the sensation of translucency appears when the object has the property of letting the incident light travel into its body and re-emits a part of it in a given direction in space. The quantity that characterizes this type of behaviour is the BSSRDF, for Bidirectional Surface Scattering Distribution Function (fig. 2 right). It is probably the ultimate quantity to characterize the optical properties of materials. The BSSRDF is the ratio of the luminance at a point on the surface, in a direction given by the incident flux, when the surface is illuminated by a collimated and punctual beam, at a wavelength λ and according to a polarization ρ. It is expressed in [sr -1 •m -2 ] [13] [START_REF] Ferrero | Fundamental scattering quantities for the determination of reflectance and transmittance[END_REF]. As for SVBRDF, we reach 8 degrees of freedom. Many recent works have been carried out on the measurement of the BSSRDF [START_REF] Santafé-Gabarda | Primary facility for traceable measurement of the BSSRDF[END_REF] [START_REF]Definitions for bidirectional scattering surface reflectance distribution function (BSSRDF)[END_REF].

To conclude this inventory of the quantities involved in the measurement of appearance, we can finally attempt to acquire information on fluorescence. This requires illuminating the sample at a given wavelength and measuring the BRDF for another wavelength. It must be repeated, combining all the visible wavelengths, as well as UV for the incident beam. This must be done for different illumination and observation directions, as researchers have realized that fluorescence is not completely Lambertian. We are talking about measuring the bi-spectral and bidirectional reflectance distribution. This may seem insurmountable, but metrologists have carried out this type of measurement in recent years [17][18].

Measurement devices

In this context, manufacturers of spectrophotometers are developing a new generation of instruments, able to access the light reflected by objects in several pre-established angular configurations, we talk then of "multi-angle spectrophotometer", or able to make the light source and the detector rotate around the object, we talk then of "goniospectrophotometer". Some of them integrate a spectral and/or high dynamic camera to collect millions of measurement points in few seconds [START_REF] Sole | Evaluating an image-based bidirectional reflectance distribution function measurement setup[END_REF]. Others take advantage of the recent progress in LEDs to provide compact devices [START_REF] Leloup | Development of an image-based gloss measurement instrument[END_REF] or to develop huge light domes [START_REF] Schwartz | DOME II : a parallelized BTF acquisition system[END_REF]. This approach, combined with image processing tools is promising. This market is definitively dynamic, innovating and exiting.

Nevertheless, all these instruments work usually in relative mode. They compare, in a given angular and spectral configuration, the signal emitted by the test sample with the one emitted by the calibrated artefact. In order to ensure the onpurpose calibration service for this new generation of spectrophotometers and to ensure that traceability to national standards is available, National Metrological Institutes (NMI) are developing on their side so called "primary goniospectrophotometers", that allow the realisation of absolute BRDF, BTDF and BSSRDF measurements [START_REF]BxDiff, New quantities for the measurement of appearance[END_REF].

The challenge here is to realize a mise en pratique of BRDF/BTDF/BSSRDF quantities that can satisfy the diversity of industrial needs. Some of them need a high angular resolution device devoted to gloss, others a high spectral resolution for gonioschromatism. Sometimes a few angular configurations are enough to characterize quasi-lambertian standard, sometimes its several millions that are mandatory to establish the traceability of sparkle measurement devices. In front of this situation, NMI have no other option than developing versatile goniospectrophotometers that can adapt to the demand [START_REF] Höpe | ARGon3: "3D appearance robot-based gonioreflectometer" at PTB[END_REF][29] [START_REF] Patrick | The NIST Robotic Optical Scatter Instrument (ROSI) and its Application to BRDF Measurements of Diffuse Reflectance Standards for Remote Sensing[END_REF]. But unfortunately, versatility works against uncertainty. Since 2012, European NMIs have adopted a coordinated approach in the frame of EMRP and EMPIR funded programs [START_REF]European Metrology Programme for Innovation and Research[END_REF]. The facilities developed in each country have been built to cover the diversity of measurement needs with complementarity while keeping an overlapping area to allow comparisons of national scales [START_REF] Höpe | Multidimensional Reflectometry for Industry[END_REF]. Therefore, each NMI can develop its specificity and push the uncertainty at its limit for one given application like fluorescence [START_REF] Bernad | Upgrade of goniospectrophtometer GEFE for near-field scattering and fluorescence radiance measurements[END_REF], gloss [START_REF] Ouarets | A new gonioreflectometer for the measurement of the bidirectional reflectance distribution function (brdf) at LNE-CNAM[END_REF], iridescence [START_REF] Höpe | ARGon3: "3D appearance robot-based gonioreflectometer" at PTB[END_REF][29] [START_REF] Patrick | The NIST Robotic Optical Scatter Instrument (ROSI) and its Application to BRDF Measurements of Diffuse Reflectance Standards for Remote Sensing[END_REF] or µBRDF [START_REF] Saha | Development of a µBRDF goniospectrophotometer for BRDF measurement on tiny surfaces[END_REF]. Often, more than one device is requested. It is the case when a new quantity or a new index is proposed. For sparkle for instance, an index has been proposed. Once it's accepted, at least 2 NMIs must realize the measurement based on the definition of this index, in order to check that they get compatible results [START_REF] Ferrero | An insight into the present capabilities of national metrology institutes for measuring sparkle[END_REF]. If yes, the index is validated. If not, it means that the definition is not robust enough and a new proposal have to be done [START_REF] Ferrero | Preliminary measurement scales for sparkle and graininess[END_REF]. This is the way of development of new measurements.

In 2016, 8 NMIs have compared their BRDF scales at one given angular configuration in the plane of incidence. Agreement between scale was at around 2% within the visible [START_REF] Strothkämper | Multilateral Spectral Radiance Factor Scale Comparison[END_REF]. This comparison pointed out the sensitivity of primary goniospectrophotometers to polarization and to misalignment. Both phenomenon have been studied and ameliorations have been implemented [START_REF] Quast | Polarization properties and microfacet-basedmodelling of white, grey and coloured matte diffuse reflection standards[END_REF] [START_REF] Molloy | Effects of rotation errors on goniometric measurements[END_REF]. In 2021, a new BRDF comparison has been carried out between 6 NMIs. This time, the agreement was at around 1% [START_REF] Basic | Intercomparison of bidirectional reflectance distribution function measurements at in-and out-of-plane geometries[END_REF]. Uncertainty on the BRDF scale has been reduced by a factor 2 in 5 years at the highest level. Now NMIs are moving on the development of primary scales for BTDF and BSSRDF and on multiscale traceability for BRDF.

New facilities have been built. Work is still in progress, but soon, absolute scales of these quantities will be ready, allowing the development of a traceable metrology that will go to the end user. On those stable foundations, commercial advanced spectrophotometers, new rendering models, new 3D printer checker protocols, news numerical index correlating with visual attributes will grow up.

All put together, progresses in the field of the measurement of optical properties that are linked to the appearance of surfaces are there. Today we are almost capable to measure reflected light from a surface with the same angular, spectral and spatial acuity than the human eye !

Figure 2 .

 2 Figure 2. Left : BRDF is the ratio of the radiance in a given direction o of a surface A by the irradiance of this surface coming from a given direction i, at a given wavelength and a given polarization. Angular resolution is limited by max(o ; i). (middle) The visual system exploits the information at different locations of the BRDF in order to extract visual attributes of appearance. (right) BRDF for colour, gloss & sparkle, BTDF for transparency, BSSRDF for translucency. (Right) BRDF, BTDF, BSSRDF are the bidirectional radiometric quantities linked to appearance

Acknowledgments

This study has been done in the frame of the project 19SIB03 BxDiff, that has received funding from the EMPIR programme co-financed by the Participating States and from the European Union's Horizon 2020 research and innovation programme.

I would like to thank Lou Gevaux for proofreading and providing valuable corrections..


Simon Pouil

Florence Phocas

Joël Aubin

M2 Priam

Deriving breeding goals and expected selection responses for a breeding program that limits the environmental impacts of rainbow trout farming

Keywords: Breeding objective, Fish farming, Life-Cycle Assessment, Optimal index selection, Salmonid, Sustainability

With the growing societal concerns about the sustainability of the food production systems, there is an increasing interest at considering not only economic gains but also environmental impacts in the selection of farmed species. In this study, we compared predicted selection responses for alternative breeding programs aiming to limit environmental impact of the production of rainbow trout, one of the most important fish species in European aquaculture. The environmental consequences of genetic improvement based on an optimal index selection were instigated in a theoretical rainbow trout fry production farm under a constant annual production volume. The tested breeding goals included three different traits: the body weight at 110 days post hatching (BW), the feed efficiency (FE) measured through the feed conversion ratio and the survival rate (SR) while we tested several correlations scenarios between the traits. A cradle-to-farm-gate life-cycle assessment was performed to evaluate the environmental value of each trait that have been used in the breeding goals defined in order to maximize selection responses while minimize environmental impacts. We explored different impact categories, such as acidification, climate change, cumulative energy demand, eutrophication, land occupation and water dependence. Annual genetic gains using optimal selection indexes were ranging from 0.9 to 1.4% for the different impact categories while the annual genetic gains were ranged from 0.4 to 4.6 % for BW, 0.0 to 2.8 % for FE and -11.0 to 0.9 % for SR. We demonstrated the interest of using ENV in breeding goals to minimize environmental impacts at the farm level while maintaining high genetic improvements in growth and feed efficiency related traits. Nevertheless, another selection strategy should be considered to avoid negative consequences on SR when considering possible negative correlations between traits. Although our results are promising, their interpretations have to be qualified by the lack of considerations for the economic repercussions of such selection strategy.

Introduction

Rainbow trout (Oncorhynchus mykiss) is the main fish species farmed in France and one of the major salmonid species farmed worldwide (960,000 t in 2020; FAO, 2022). Production is historically performed in flow-through systems, in which inlet water is diverted from a river, passed once through the rearing tanks and then returned to the river. In trout production systems, all nutrients are provided by exogenous formulated feed containing fish meal, fish oil and plantbased ingredients in various proportions. The entire production cycle is not necessarily ensured on the same site. Thus, the farms producing from a few to several hundred tons annually have different production objectives responding to different markets. For instance, some farms produce fry, pan-sized trout and/or large trout for fillets (fresh or smoked), while others produce fish for restocking rivers or ponds for angling [START_REF] Chen | Environmental assessment of trout farming in France by life cycle assessment: using bootstrapped principal component analysis to better define system classificatio[END_REF]. These different production strategies imply different practices (e.g., feed type, feeding management, oxygen supply, rearing densities, and water treatment) and also drive breeding programs. Rainbow trout breeding programs are currently mainly focused on the increase of productivity (growth, disease resistance, processing yield), but also on answering consumer demands (fish morphology, product quality; [START_REF] Chavanne | A comprehensive survey on selective breeding programs and seed market in the European aquaculture fish industry[END_REF].

Breeding objectives always involve consideration of multiple traits, even in situations where output of a single trait is dominant [START_REF] Sölkner | Breeding objectives and the relative importance of traits in plant and animal breeding: A comparative review[END_REF]. In the optimal selection index derived to maximize the expected selection response on the breeding objective [START_REF] Hazel | The genetic basis for constructing selection indixes[END_REF], the relative importance of each trait is scaled by its weight defined for the multi-trait breeding goal. When considering that the aim of the breeding program is to maximize farm profit, the weights used in the breeding objective are economic values derived using profit equations [START_REF] Brascamp | Derivation of economic weights from profit equations[END_REF][START_REF] Dekkers | Applying breeding objectives to dairy cattle improvement[END_REF][START_REF] Gunia | Economic values of body weight, reproduction and parasite resistance traits for a Creole goat breeding goal[END_REF]. The economic value (EV) of the trait is then derived as the marginal profit related to a change in trait expression of one physical unit [START_REF] Hazel | The Selection Index-Then, Now, and for the Future[END_REF].

Deriving the optimal selection index corresponds to calculate the index weights for all the traits included in the selection index based on EV as well as on the phenotypic and genetic correlations between all traits considered in the breeding program. Using this optimal selection index will lead the direction and magnitude of the expected responses in the considered traits to maximize the economic return of genetic improvement. However, EV might not be the best weights to use in a breeding objective oriented towards the improvement of the environmental sustainability of fish production [START_REF] Olesen | Definition of animal breeding goals for sustainable production systems[END_REF].

With the growing societal concerns about the sustainability of animal and plant production, there is an increasing interest at considering not only economic gains but also environmental impacts in the selection of farmed species. This aspect of selective breeding remained, nevertheless, an open field of research with only few studies on cattle (e.g., [START_REF] Cantalapiedra-Hijar | Efficience Alimentaire : comment mieux la comprendre et en faire un élément de durabilité de l'élevage[END_REF][START_REF] Van Middelaar | Methods to determine the relative value of genetic traits in dairy cows to reduce greenhouse gas emissions along the chain[END_REF], pigs (e.g., [START_REF] Ali | Effects of incorporating environmental cost and risk aversion on economic values of pig breeding goal traits[END_REF] and fish (e.g., [START_REF] Besson | The genetic correlation between feed conversion ratio and growth rate affects the design of a breeding program for more sustainable fish production[END_REF][START_REF] Besson | Environmental impacts of genetic improvement of growth rate and feed conversion ratio in fish farming under rearing density and nitrogen output limitations[END_REF]. Recently, [START_REF] Besson | The genetic correlation between feed conversion ratio and growth rate affects the design of a breeding program for more sustainable fish production[END_REF] compared the use of EV or environmental values (ENV) as weights in a breeding goal combining thermal growth coefficient (TGC) and feed conversion ratio (FCR) in European sea bass (Dicentrarchus labrax). Such ENV can be used as weights in the breeding goal to derive a selection index that maximizes the reduction of the environmental impacts of fish production. They found that using ENV in the breeding goal generated an annual reduction of, at least, 0.92% in eutrophication per ton of fish produced. Integrating ENV into a breeding goal requires properly assessing the environmental impacts at the farm level which can be achieved using a life-cycle assessment (LCA).

LCA is an international standardized holistic method (ISO, 2006) designed to evaluate the global impact of a product or a process on the environment. Such evaluation implies the assessment of all the different phases required for or caused by the product's existence; it includes raw material uses and energy production, manufacturing, transport, and emissions to the environment at each stage until the product's end of life.

For the two last decades, LCA has been regularly used to assess the environmental impacts of aquaculture production through different environmental impact categories including mainly acidification, climate change, energy demand, eutrophication, land competition and water dependence. These categories are usually chosen for relevance to the known principal impacts of aquaculture systems and to enable comparison with previous seafood LCA studies [START_REF] Bohnes | Life cycle assessments of aquaculture systems: A critical review of reported findings with recommendations for policy and system development[END_REF][START_REF] Henriksson | Life cycle assessment of aquaculture systems-A review of methodologies[END_REF][START_REF] Pelletier | Impact categories for life cycle assessment research of seafood production systems: Review and prospectus[END_REF]. Salmonid production has been extensively studied through LCA with some investigations focused on rainbow trout production (e.g., [START_REF] Aubin | Assessment of the environmental impact of carnivorous finfish production systems using life cycle assessment[END_REF]d'Orbcastel et al., 2009;[START_REF] Dekamin | Life cycle assessment for rainbow trout (Oncorhynchus mykiss) production systems: A case study for Iran[END_REF][START_REF] Samuel-Fitwi | Comparative life cycle assessment (LCA) of raising rainbow trout (Oncorhynchus mykiss) in different production systems[END_REF].

The aims of our study were: i) to define various breeding goals based on ENV derived from different LCA impact categories and ii) to predict the expected selection responses for all those breeding objectives as well as for the three main traits (growth rate, feed conversion ratio and fry survival) of interest in a rainbow trout farm producing fry.

Materials and Methods

Farm design and operations

All the data (i.e. zootechnical performances, farm management, infrastructures and equipment inventory, nature and quantities of inputs…) were derived from four interviews of fish farmers and visits to production sites in Brittany, the leading region for trout production in France, performed in February 2022. A theoretical commercial French fish farm producing rainbow trout fry in a flow-through system was considered in this study (see Table 1 for details). In trout farming, production volume in a given site is under strict regulations, so the production was constrained to a quota of 12 tons of fry sold annually.

Three cohorts of trout were reared on the site throughout the year. The first two cohorts, each consisting of 400,000 eyed eggs from a French breeder, entered the site in December (cohort 1) and March (cohort 2). They will be sold at a commercial size of 10 g. The last cohort (cohort 3) consisted of 200,000 eyed eggs that entered the site in August and will be reared up to size of 40 g. We defined a production cycle as the duration from the entrance of the eggs of cohort 1 on the farm to the exit of the fish of cohort 3.

The flow-through production system was divided into a 200-m 2 indoor facility where trout are reared from eggs to 1-2 g and outdoor rearing structures where fish were then reared up to the commercial sizes. In addition, two other buildings (30 and 50 m 2 ) were used for equipment and feed storage).

Table 1. Production data and inputs used for the rainbow trout fry production in a theoretical commercial French fish. In the indoor facility, rearing structures consisted of thirty-six 0.38-m 3 fibre-glass tanks under artificial light. The water supply was by gravity from a surrounding stream, and the average monthly temperature varied from 7 to 19 °C throughout the year, while the water flow ranged from 10 to 110 m 3 h -1 . During low water periods (in April and August), a 4-kWh pump was used for water recirculation, and a 1-kWh blower supplied air. When the density of fish became limiting in the indoor system (i.e. 30 kg m -3 ) without air or oxygen supply, fish were sorted and transferred in outdoor rearing facilities consisting of four 32-m 2 raceways and two 85-m 2 raceways. Fish first transferred into two 32-m 2 raceways were sorted and distributed into the other raceways once the stocking density reaches 30 kg m -3 . Up to eight 0.75-kWh aerators were used during this rearing phase during low water periods. Another river provided the water supply throughout the outdoor rearing to reach the commercial size. Over the production cycle (i.e. 3-6 months), fish were fed using four different diets, and their rationing was adjusted according to fish size and water temperature.

Daily growth of the fish was modelled using a model developed by [START_REF] Muller-Feuga | Modélisation De La Croissance Des Poissons En Elevage[END_REF], considering the fluctuating temperatures occurring during the rearing phase:

𝑑𝐵𝑊 𝑑𝑡 = Г 𝑓 1 (𝐵𝑊) 𝑓 2 (θ)
Expression dBW/dt is the body weight increase, f1(BW) is the weight function, and f2(θ) is the thermal function. Parameter Γ is exogenous and incorporates all other factors influencing growth.

The weight function is assumed to be log-linear [START_REF] Ricker | Growth Rates and Models[END_REF]. Thus, an increase in weight is positively related to fish weight (BW), but with a smaller percentage as the size rises. That is:

𝑓 1 (𝐵𝑊) = 𝐶 𝐵𝑊 𝑚
Where C is the log-linear regression parameter. The parameter m has been estimated for hot blood vertebrates, obtaining a value of 0.7 [START_REF] Brett | Physiological Energetics[END_REF].

𝑓 2 (θ) = 𝐷(𝑒 𝛼(𝜃 𝑀 -𝜃) -𝑒 𝛽(𝜃 𝑀 -𝜃) )

Function f2(θ) is based on exponential form, and it includes maximum and minimum water temperature limits beyond which growth is impossible. D is a temperature adjusting parameter, while α and β are the first and the second temperature function parameters, respectively [START_REF] Muller-Feuga | Modélisation De La Croissance Des Poissons En Elevage[END_REF]. The variable θ = θ(t) represents water temperature in time t. Parameter θM is the maximum temperature for possible growth under culture conditions.

On this farm, the mortality rate was estimated at 7% for the indoor rearing (Min), the most sensitive phase and 3% over the outdoor rearing (Mout). Thus, the number of eggs or fish for a given day (Nbn) can be calculated as follows:

𝑁𝑏 𝑛 = 𝑁𝑏 𝑛-1 -((𝑁𝑏 𝑛-1 𝑀 𝑖𝑛 𝑜𝑟 𝑜𝑢𝑡 )/𝑑)
Were Nbn-1 is the number of eggs or fish the day before and d is the duration of the rearing phase (i.e. indoor or outdoor) in days.

Rearing density (RD) was calculated as the product of the individual weight (BW) and the number of eggs or fish (Nb) divided by the volume of the rearing structure (V):

𝑅𝐷 (𝑘𝑔 𝑚 -3 ) = 𝐵𝑊 (𝑘𝑔) 𝑁𝑏 𝑉 (𝑚 3 )
Feed conversion ratio (FCR) was calculated as the ratio between the feed distributed per production cycle and the fish production (i.e. the biomass of fry at the exit of the farm minus the biomass of eggs at the entrance):

𝐹𝐶𝑅 (𝑘𝑔 𝑘𝑔 -1 ) = 𝐹𝑒𝑒𝑑 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑒𝑑 (𝑘𝑔) 𝐹𝑟𝑦 𝑜𝑢𝑡 (𝑘𝑔) -𝑒𝑔𝑔𝑠 𝑖𝑛 (𝑘𝑔)
All combined, this information allowed us to model each rearing step on a daily basis using Excel® version 2019 software. The outputs of this model were used to generate inventory data for the LCA. Two limiting factors were considered in this step: (1) the annual production should stay constant, and (2) without providing O2 addition, the rearing density should not exceed 30 kg m -3 .

Life cycle assessment

Goal and scope

An LCA was conducted according to the steps described in Figure 1 and general requirements of the methodology proposed by ILCD standards (Joint Research Centre, 2010). The methodology was adapted to the characteristics of fish farming. The goal and scope of this study is the environmental assessment of trout farming in a theoretical farm producing rainbow trout fry. Effects of changes in performances of several traits (see Section 2.4) on the environmental impacts have been investigated. The system was defined from cradle-to-farm-gate and included five distinct sub-systems (Figure 2): (1) production of purchased feed, including cultivation of ingredients, processing, and transportation; (2) production of energy expended at farm level (electricity and diesel); (3) production of farming facilities and equipment used; (4) fish farming, including nutrients emission from the biological transformation of feed after onsite treatment of wastewater. The functional unit, basis for the environmental calculation, was one ton of fry produced at the farm gate.

Life cycle inventory

Life cycle inventory (LCI) was conducted on the basis of the data collected on production farms and using Agribalyse® version 3.0 and EcoInvent® version 3.8 databases.

(1) Production of purchased feed -Crop-derived ingredients used in fish feed mainly originated from Brazil and France (e.g. soybean meal from Brazil and wheat bran from France). In contrast, fish-derived ingredients originated from the Peruvian and the Norwegian fish milling industry (e.g. fish meal from Peru and fish meal from fish trimming from Norway).

The exact composition of the different feeds used and their nutritional values were given by the feed manufacturers. The transport of feed ingredients to feed manufacturers in France was by trans-oceanic ship and by lorry (>32 t), whereas the transport of feed from France to the fish farm in Brittany was by lorry (>32 t). Transport distances and other data required to compute the environmental impact of feed ingredients were based on the literature [START_REF] Boissy | Environmental impacts of plant-based salmonid diets at feed and farm scales[END_REF][START_REF] Pelletier | Not all salmon are created equal: Life cycle assessment (LCA) of global salmon farming systems[END_REF]. (2) Production of energy expended on the farm -Most of the water circulation in the farm is done by gravity flow. So, the farm's electricity consumption was estimated at 20,500 kWh over one production cycle, while diesel and gasoline consumption were limited to 200 L. The electricity used by the farm was coming from the French energy mix proposed by the Ecoinvent version 3.8 [START_REF] Wernet | The ecoinvent database version 3 (part I): overview and methodology[END_REF]. ( 3) Production of farming facilities and equipment used -We considered the construction of three different buildings of 30, 50 and 200 m 2 with a life span of 30 years. The production of equipment used (i.e. pump, tanks) was calculated using data from INRAE. The use of building and equipment was adjusted to consider the period of the year and the size of the fish. The surface of the rearing structures has been adjusted to the optimal to include possible effects of changes in performances of several traits (see Section 2.4) in rearing structures' occupancy. (4) Farm operation -The farm operation sub-system included the use of energy, facilities and equipment and the emission of pollutants from the biological transformation of the feed distributed to the fish. The amount of nitrogen (N), phosphorus (P) and chemical oxygen demand (COD) of the dissolved organic matter excreted by the fish in effluent water were calculated through mass balance considering the onsite treatment capacity of the sludge settling pond. Sludge produced by the farm was used for neighbourhood agricultural purposes and was not included in the analysis.

Life cycle impact assessment

Each flow observed in the system was assigned to different impact categories relatively to its potential environmental effects. The six environmental categories investigated were: acidification, climate change, cumulative energy demand, eutrophication, land competition, water dependency (CML2 Baseline 2000 version 2.04) [START_REF] Guinée | Handbook on Life Cycle Assessment Operational Guide to the ISO Standards[END_REF] and cumulative energy demand [START_REF] Frischknecht | Cumulative energy demand in LCA: The energy harvested approach[END_REF]. These six impact categories were chosen because they represent the main environmental impacts aquaculture contributes [START_REF] Bohnes | Life cycle assessments of aquaculture systems: A critical review of reported findings with recommendations for policy and system development[END_REF][START_REF] Henriksson | Life cycle assessment of aquaculture systems-A review of methodologies[END_REF][START_REF] Pelletier | Impact categories for life cycle assessment research of seafood production systems: Review and prospectus[END_REF]. Acidification refers to the negative effects of acidifying pollutants, such as SO2, NOx, HCL and NH3, on the environment and is expressed in kg SO2-equivalents. Climate change is the potential impact of gaseous emissions, such as CO2 and CH4, on the heat radiation absorption in the atmosphere. Climate change was calculated according to the GWP100 factors (potential effect at a 100-year time horizon) and expressed in kg CO2-equivalents. Cumulative energy demand (CED) expresses the depletion of energy resources, expressed in GJ. Eutrophication is mainly the consequence of nitrogen (N) and phosphorus (P) emissions to the air, water and soil and is expressed in kg PO4 3--equivalents. Land competition (m 2 yr -1 ) corresponds to the ground surface used directly (land occupied by ponds) and indirectly (land used to grow feed) by the production system, while water dependency (m 3 ) corresponds to the water flowing into the production system. The environmental impacts were calculated using Simapro® version 8.0 software.

Simulated breeding program

We simulated a simple breeding program using R freeware version 4.0.3 (R Development Core Team, 2020) derived from current breeding schemes in rainbow trout in France that can be described in four different steps (see Figure 3):

(1) Families are created by artificial fertilization according to a partial factorial mating design of sires and dams: 10 independent full factorial designs of 10 sires and 10 dams are thus considered to produce about 400,000 eyed eggs from which 50,000 are randomly chosen to be reared. Therefore, 1,000 full sibs' families are produced, corresponding to 100 paternal and 100 maternal families. The age at reproduction is two years for males and three for females.

(2) Mass selection is then performed on the candidates (n = 2000) randomly chosen among the 50,000 descendants. (3) Assignment of the kinship of the candidates and indexing on lethal characteristics (such as disease resistance) measured on collaterals (n = 1200) randomly chosen for a derived batch in parallel to the choice of the batch of selection candidates. (4) In a last step, selection of brooders (n = 200) is normally performed.

Breeding goals

The breeding goal (H) combined three traits covering key aspects of trout production. In trout farming, the market is segmented with products sold mainly at constant weight while regulations limit the production of farms. So, growth rate plays an important role in trout rearing by reducing the duration of production cycles. For this reason, the first trait included in the breeding objective was the body weight at 110 days post hatching (BW).

Because commercial feeds are the most important inputs in fish farming and have both economic and environmental consequences, the feed efficiency (FE) measured through the feed conversion ratio was added to the breeding objective. The last trait we included in H is the survival rate (SR). The breeding goal can be expressed as follows:

𝐻 𝑋 = 𝐸𝑁𝑉 𝐵𝑊 𝑋 𝐴 𝐵𝑊 + 𝐸𝑁𝑉 𝐹𝐸 𝑋 𝐴 𝐹𝐸 + 𝐸𝑁𝑉 𝑆𝑅 𝑋 𝐴 𝑆𝑅
where Ai is the breeding value (or true additive genetic value) of the trait i; ENVi of trait i is calculated as the marginal impact in HX (impact variation per physical unit) and based on the difference in environmental impact values before and after changing the average performance of the trait by one genetic standard deviation, while maintaining the other traits at constant values.

We calculated the ENV in the same way for each of the impact category (X) from LCA (i.e. acidification, climate change, CED, eutrophication, land occupation and water dependency). In order to describe the importance of traits, we estimated the relative environmental weights (RWs) by multiplying trait's ENV by its genetic standard deviation (σg).

We obtained six different breeding goals, so-called Hacid, Hclimate, HCED, Heutro, Hland and Hwater, whose responses we seek to maximize by selecting on the corresponding optimal selection indexes.

Figure 3. Modelled rainbow trout breeding scheme. We assumed non-lethal measurements on candidates such as growth and efficiency related traits while survival rate from disease resistance was tested on collaterals.

Selection indexes and responses to selection

The response to selection under each scenario was assessed by means of an optimal selection index (I). The same traits were considered in the breeding goal (HX) and in the selection index (IX):

𝐼 𝑋 (𝑧) = 𝑏 𝐵𝑊 𝑋 𝑌 𝐵𝑊 (𝑧) + 𝑏 𝐹𝐸 𝑋 𝑏 𝐹𝐸 𝑌 𝐹𝐸 (𝑧) + 𝑏 𝑆𝑅 𝑋 𝑌 𝑆𝑅 (ℎ𝑠)

where Y indicated phenotype observed on candidates (z) or half-sibs (hs). Non-lethal measurements for BW and FE were performed on candidates. Here, we assumed that SR is mostly influenced by the occurrence of the cold-water disease and rainbow trout fry syndrome caused by the bacteria Flavobacterium psychrophilum. In France, these two diseases are reported as among the major bacteriosis affecting rainbow trout farming [START_REF] Siekoula-Nguedia | Genetic diversity of Flavobacterium psychrophilum isolated from rainbow trout in France: Predominance of a clonal complex[END_REF]. Here, we assumed SR was measured through challenges to F. psychrophilum infection performed on collaterals (Figure 3) while all candidates for selection have the same number of half-sibs in the challenge (hs = 23) so that we can estimate the performances on SR (YSR) for a candidate for selection as follows:

𝑌 𝑆𝑅 = 1 ℎ𝑠 ∑ 𝑆𝑅 𝑖 ℎ𝑠 𝑖=1
The vector of coefficients (bX) containing index weights for each trait of the optimal index is given by:

𝒃 𝑿 = 𝑷 -𝟏 𝑮 𝑬𝑵𝑽 𝑿
where 𝑬𝑵𝑽 𝑿 is the vector containing the ENV values of the three traits of interest included in HX; P is the matrix denoting the variances and covariances among the predictors Y in I and G is the matrix denoting the variances and covariances between the predictors Y in I and the true additive genetic values A in HX. Derivation of P and G is provided in Appendix A1.

We calculated the variance of the selection index I (σi 2 ) as:

𝜎 𝐼𝑥 2 = 𝒃 𝑿 ′ 𝑷𝒃 𝑿
and the genetic variance of the breeding objective (H) as:

𝜎 𝐻𝑥 2 = 𝑬𝑵𝑽 𝑿 ′ 𝑽 𝑯 𝑬𝑵𝑽 𝑿
where VH is the matrix denoting the genetic variances and covariances across traits in H with rg the genetic correlations between traits:

𝑉 𝐻 = ( 𝜎 𝑔1 2 ⋯ 𝑟 𝑔13 √𝜎 𝑔1 2 𝜎 𝑔3 2 ⋮ ⋱ ⋮ 𝑟 𝑔31 √𝜎 𝑔3 2 𝜎 𝑔1 2 ⋯ 𝜎 𝑔3 2 )
Accuracy of index selection (ρx) was calculated as:

𝜌 𝑥 = 𝜎 𝐼𝑥 𝜎 𝐻𝑥
The genetic gain (AGGHx) can be calculated as follows:

𝐴𝐺𝐺 𝐻𝑥 = 1 2 (𝑖 𝑓 + 𝑖 𝑚 )𝜌 𝑥 𝜎 𝐻𝑥 𝐿
where, for female (f) and male (m), if = im = i the selection intensity derived for the same selection rate (i.e. 10%) in male and female candidates for selection. L is the average generation interval of 2.5 years (3 years for females and 2 years for males).

Annual genetic gains for each trait have been calculated as follows:

𝑨𝑮𝑮 𝑿,𝒕𝒓𝒂𝒊𝒕 = 𝐴𝐺𝐺 𝐻𝑥 𝜎 𝐼𝑥 ² 𝑮′𝒃 𝑿
We estimated the selection accuracy (ρx) and annual genetic gains (AGGHx) for the breeding goals corresponding to the different impact categories: climate change (kg CO2 eq), cumulative energy demand (CED; GJ), land competition (m 2 yr -1 ) and water dependence (m 3 ).

In order to assess the consequences of a selection to maximize responses on a given breeding objective Hx on the responses for the other impact categories (Y ≠ X), we calculated:

𝛥𝑅 𝑌≠𝑋 = ∑𝐸𝑁𝑉 𝑡𝑟𝑎𝑖𝑡 𝑌 𝐴𝐺𝐺 𝑋,𝑡𝑟𝑎𝑖𝑡

Genetic parameters

The genetic parameters of the three traits are presented in Tables 2 and3. Heritability (h 2 ) values were extracted from literature in rainbow trout: 0.15-0.55 for body weight at different ages (e.g., [START_REF] Evenhuis | Rainbow trout (Oncorhynchus mykiss) resistance to columnaris disease is heritable and favorably correlated with bacterial cold water disease resistance[END_REF][START_REF] Haffray | Negative genetic correlations between production traits and head or bony tissues in large all-female rainbow trout (Oncorhynchus mykiss)[END_REF][START_REF] Kause | Genetic improvement of feed conversion ratio via indirect selection against lipid deposition in farmed rainbow trout (Oncorhynchus mykiss Walbaum)[END_REF], 0.10-0.23 for feed efficiency traits [START_REF] Grima | Genetic variability in residual feed intake in rainbow trout clones and testing of indirect selection criteria[END_REF]Kause et al., 2006a[START_REF] Kause | Genetic improvement of feed conversion ratio via indirect selection against lipid deposition in farmed rainbow trout (Oncorhynchus mykiss Walbaum)[END_REF][START_REF] Knap | Phenotyping for genetic improvement of feed efficiency in fish: Lessons from pig breeding[END_REF]) and 0.23-0.35 for resistance to F. psychrophilum [START_REF] Fraslin | Rainbow trout resistance to bacterial cold water disease: two new quantitative trait loci identified after a natural disease outbreak on a French farm[END_REF][START_REF] Vallejo | Similar genetic architecture with shared and unique quantitative trait loci for bacterial cold water disease resistance in two rainbow trout breeding populations[END_REF]. Genetic standard deviations (σg) were calculated as follows:

𝜎 𝑔 = √ℎ 2 𝜎 𝑝 2
where σp 2 is the phenotypic variance of each trait.

For BW and FE, σp 2 as calculated assuming a coefficient of variation of 0.20 and knowing the phenotypic mean of the traits (i.e. 10 g and 0.70 kg kg -1 for BW and FE, respectively, Table 1).

For SR, σp 2 = p (1-p) was estimated considering that p = 10% of mortality in the theoretical farm (Table 1). Based on the literature estimates, genetic correlations between BW and FE were assumed to be null, while phenotypic correlations remained uncertain, but probably negative in rainbow trout; thus, we tested values at -0.4, -0.2 and 0. For the same reason, we also tested genetic correlations of -0.3, -0.15 and 0 between BW and SR, while the phenotypic correlation was assumed to be null between these two traits. As no information was available in the literature, both genetic and phenotypic correlations were assumed to be null between FE and SR (Table 3).

Results

Environmental impacts and contribution analysis

Among fry trout-production stages, feed (i.e., feed production, milling, and transport) was among the main contributors to the environmental impacts related to climate change (36% of 2381 kg CO2 eq), acidification (33% of 12.7 kg SO2 eq) and cumulative energy demand (CED; 25% of 65.3 GJ) (Figure 4). Farm functioning (i.e., farm operations and on-farm emissions) was the main contributor to eutrophication (65% of 50.5 kg PO4 3-eq) and water dependence (58% of 112,103 m 3 ) and influenced land competition (24% of 703 m 2 ). Eggs (i.e., production and transport of trout eggs) were highly contributing to water dependence (43%), eutrophication (28%) and CED (24%). Electricity consumption was the main contributor to the CED (28%), while buildings and rearing structures, depending on the impact category, accounted for 0-14% of the environmental impacts at the farm level. Chemicals (i.e., production and transport of medicines, cleaning products and other chemicals) had a negligible contribution (<3%) (Figure 4).

A summary of the environmental impacts of the visited rainbow trout farms is available in Appendix A2.

ENV determination

LCA was used to determine environmental values (ENV) used as weights in the three-trait breeding goals. ENV estimated from the different impact categories were provided in Table 4.

While for SR, the relative weight of the ENV remained low in all the breeding goals HX (i.e. from 0% in Hacid to 2.4% in Hwater) RW for BW and FE (i.e. RWBW and RWFE, respectively) were highly variable for the different HX. For instance, RWBW varied from 0.0 to 97.6% in Heutro and Hwater respectively. Nevertheless, in all HX excepted Hwater, the highest RWs were for FE with values ranging from 52.2% to 99.6% in HCED and Heutro respectively, while RWBW varied from 5.9% to 47.1%. The only situation where RW of these two traits tended to be equilibrated was in HCED with RWFE = 52.2% and RWBW = 47.1% (Table 4). Interestingly, Hwater was the only breeding goal whose RWs were distinctly different from others. Indeed, while for the others H, RWs were ranging according to the following ascending order: RWSR < RWBW < RWFE, in Hwater we estimated RWFE < RWSR << RWBW.

Given the similarities in weighing between Hacid and Hclimate, and then Heutro and Hland, we focused on four breeding goals only: Hclimate, HCED, Hland and Hwater (Table 4) for the subsequent analysis.

Genetic gain and changes in environmental impacts

In a three-trait breeding goal, the responses to selection results from a complex interaction between weights assigned to each trait and the genetic and phenotypic parameters between the three traits. Overall, the selection accuracy ranged from 0.39 to 0.62. The accuracy of index selection was the highest for the breeding goal HCED with values ranging from 0.50 to 0.63 while the lowest accuracy was found for Hland (0.39-0.45) (Table 5). Annual genetic gains expected for H (AGGH), expressed for one ton of fry produced at the farm level, ranged from 20.3 to 26.0 kg CO2 eq for Hclimate, 0.73 to 0.91 GJ for HCED, 7.0 to 8.9 m 2 yr -1 for Hland and 1264 to 1385 m 3 for Hwater.

To assess the phenotypic significance of such gains compared to the environmental impacts calculated in the hypothetical farm before selection, we calculated annual relative gains when considering the optimal selection indexes (Table 6). We found that relative gains were ranging from 0.9% to 1.4% for the different breeding goals. The highest relative gains were obtained for HCED (i.e. 1.2% to 1.4%) and, to a lesser extent, Hland (i.e. 1.0% to 1.3%), while breeding goals targeting limitations for climate change (Hclimate) or water dependence (Hwater) leaded to lower relative gains (i.e. 0.9-1.2%). Relative gains varied depending on correlations between traits, with the lowest relative gains obtained when considering a null phenotypic correlation between BW and FE and a negative genetic correlation between BW and SR (rp12 = 0 and rg13 = -0.3) while the highest relative gains were observed when rp12 = -0.4.

When looking at the genetic gains for each trait, AGGBW greatly differed among Hx with values ranging from 0.04 to 0.23 g/year in Hland while AGGBW reached 0.42-0.46 g/year in Hwater.

Overall, AGGBW increased when considering a negative phenotypic correlation between BW and FE (rp12) and a negative genetic correlation between BW and SR (rg13). For instance, in HCED, AGGBW increased from 0.34 g/year when rP12 and rG13 were null to 0.43 g/year with rp12 = -0.4 and rg13 = -0.3 (Table 5).

For FE, the annual gains were positive in Hclimate, HCED and Hland with AGGFE ranging from 0.01 to 0.02 kg kg -1 /year, the highest AGGFE being estimated in Hland. Nevertheless, when considering water dependence (Hwater), AGGFE was null when the phenotypic correlation between BW and FE was null (rp12 = 0) while the response became slightly favourable (AGGFE <0.01 kg kg -1 /year) when rp12 was negative. As for BW, AGGFE were particularly affected by the rp12 and rg13 values with the highest values estimated when rp12 = 0 and rg13 = 0 while AGGFE gradually decreased when both genetic and phenotypic correlations decreased (Table 5).

Whatever the breeding goal considered, AGGSR was null when rp12 and rg13 were null, but became negative when negative correlations were assumed. The most unfavourable response to selection was obtained at the stronger negative correlations tested (rp12 = -0.4 and rg13 = -0.3), and it was especially true for HCED and Hwater with respective expected annual survival rate decreasing by -0.8%/year (AGGSR = 0.008) and -1.0%/year (AGGSR = 0.010) (Table 5).

Figure 5 displayed the genetic gains for the four impact categories depending on which impact category was considered as the breeding goal (i.e., the impact used to define the optimal selection index). We focused on the comparison between two scenarios of correlations: (1) the reference scenario where both phenotypic and genetic correlations are nulls (rp12 = 0 and rg13 = 0) and (2) a scenario with moderate phenotypic and genetic correlations (rp12 = -0.2 and rg13 = -0.15) that we assumed being the most realistic scenario. Overall, as demonstrated earlier, adding negative phenotypic (rp12) and genetic correlation (rg13) tended to reduce the gains. The gains for a given impact category decreased when using a nonoptimal selection index for this category. Thus, a drastic ten-fold decrease in gains was observed for land competition and water dependence where gains dropped from 8.9 to 0.8 m 2 yr -1 and from 1264 to 120 m 3 in the reference scenario when considering the less-efficient selection index (i.e. based on ENVwater and ENVland, respectively). Interestingly, such decrease was less drastic in the realistic scenario considering the negative correlations. Altogether, results displayed in Figure 5 showed that selection based on optimizing response on Hwater tended to greatly differed from the others.

Discussion

To our knowledge, this study is the first investigating the efficiency of a breeding program that limits the environmental impacts of rainbow trout farming. We focused on rainbow trout fry production stage through a theoretica farm designed based on surveys from French fish farmers. Several breeding goals (H) linearly combining three traits of major interest (BW, FE and SR) weighted by their environmental values (ENV), which express the marginal changes in environmental impacts due to improvement in trait performances, have been evaluated. ENV have been derived from six LCA impact categories previously highlighted as the main environmental impacts in aquaculture production systems from past LCA studies [START_REF] Bohnes | Life cycle assessments of aquaculture systems: A critical review of reported findings with recommendations for policy and system development[END_REF][START_REF] Henriksson | Life cycle assessment of aquaculture systems-A review of methodologies[END_REF][START_REF] Pelletier | Impact categories for life cycle assessment research of seafood production systems: Review and prospectus[END_REF]. A cradle-to-farm-gate LCA was carried to avoid over estimation of ENV of traits decreasing environmental impacts at farm level, but increasing environmental impacts at sector level [START_REF] Van Middelaar | Methods to determine the relative value of genetic traits in dairy cows to reduce greenhouse gas emissions along the chain[END_REF].

Regarding the environmental impacts estimated at the farm level, the results are relatively different from previous LCA studies conducted on rainbow trout production. Among the observed differences, we highlighted a higher relative contribution of eggs/fish inputs in the eutrophication and water dependence of the theoretical farm compared to other studies while relative contribution of feeds is lesser for the others impact categories. These differences are mainly due to the fact that the theoretical farm considered only the fry production phase, whereas LCA studies were generally conducted using data from farms performing grow-out period or the rearing cycle from eggs to very large trout (e.g., [START_REF] Chen | Environmental assessment of trout farming in France by life cycle assessment: using bootstrapped principal component analysis to better define system classificatio[END_REF][START_REF] Samuel-Fitwi | Comparative life cycle assessment (LCA) of raising rainbow trout (Oncorhynchus mykiss) in different production systems[END_REF]. Thus, the comparison with literature must be made cautiously because the fry production phase is less dependent on some inputs known to strongly affect the environmental impacts of fish farming. This is particularly true for feeds with FCR generally >1 kg kg -1 during grow-out period while, for fry production, FCR are usually ~0.7 kg kg -1 as highlighted by the surveys we performed. The logic is the same for oxygen supply, that is generally not used during the fry production phase. The environmental balance sheet available in Appendix A2 shows great differences in environmental impacts between the farms performing the grow-out period and the farm producing fry. Overall, the consistency of the results obtained by our impact assessment method, also used to generate the environmental balance of the four existing farms (Appendix A2), with the existing literature validated the impact estimation approach carried out at the scale of the theoretical farm and, consequently, the estimation of the ENV. In this study, we considered three major traits of interest for farmers, highlighted from surveys, i.e. growth rate, expressed as the body weight at 110 days post-hatching, feed efficiency, expressed as FCR and survival rate. These traits were also identified as key traits in breeding in a previous investigation aiming to study breeding trait preferences among rainbow trout farmers [START_REF] Sae-Lim | Defining desired genetic gains for rainbow trout breeding objective using analytic hierarchy process[END_REF]. The relative weight of ENVs for different traits in breeding goals is highly variable depending on the impact category for which selection response is being maximized. Nevertheless, it appears that feed efficiency weighs heavily in the majority of environmental breeding goals, and this is particularly true for limiting eutrophication and land competition. Conversely, when selection is performed to reduce water dependence, the ENVFE was null and the breeding goal was then mainly weighted by ENVBW. Overall, we estimated very low ENVSR in the different breeding goals (HX) considered.

In order to understand the relative weights of the ENVs, it is necessary to analyse the consequences of a change of one genetic standard deviation in the performances observed for the three traits under the constraint of a constant annual production at the farm scale. Indeed, an improvement in survival, at constant annual production, mainly allows a reduction in the number of eggs at the entrance and the environmental impacts at this level will be reduced. Nevertheless, this reduction remains small since in the scenario considered, the reduction in the number of eggs at entry is less than 1%. The logic is the same for FE, where again, a better feed efficiency mainly results in a reduction of feed inputs while the environmental impacts of other items remain fixed. However, as feed is a major source of environmental impacts in aquaculture [START_REF] Bohnes | Life cycle assessments of aquaculture systems: A critical review of reported findings with recommendations for policy and system development[END_REF], the ENVFE was very high compared to the other traits. These results are consistent with other studies conducted in African catfish Clarias gariepinus and European sea bass [START_REF] Besson | The genetic correlation between feed conversion ratio and growth rate affects the design of a breeding program for more sustainable fish production[END_REF][START_REF] Besson | Effect of production quotas on economic and environmental values of growth rate and feed efficiency in sea cage fish farming[END_REF][START_REF] Besson | Environmental impacts of genetic improvement of growth rate and feed conversion ratio in fish farming under rearing density and nitrogen output limitations[END_REF]. The effects of a gain in growth rate on the environmental impacts of the farm are more complex to understand. Indeed, an improvement in growth rate, at constant production, will lead to a reduction in rearing times and, consequently, to changes in the use of rearing infrastructures and different equipment. However, the consequences of these changes rely on temperature and water availability. Indeed, the increase in early growth rate, leading to a faster exit of fry from the rearing indoor facility, will affect the use of equipment related to water recirculation or air supply. Nevertheless, this reduction in equipment use will be seasonally dependent. While in low water periods the effects will be marked (cohort 3), this will be less true in winter periods (cohort 1) where water abundance and low temperatures do not require water recirculation and air supply. Overall, it is not surprising to find that the relative weight ENVBW is intermediate in a majority of the H's but becomes much larger when selection is aimed at reducing water and electricity dependence (Hwater and Hland, respectively). There are very few studies that have quantified the ENV of growth-related traits by considering CED. To our knowledge, only [START_REF] Besson | Economic values of growth and feed efficiency for fish farming in recirculating aquaculture system with density and nitrogen output limitations: A case study with African catfish (Clarias gariepinus)[END_REF] found that for the thermal growth coefficient (TGC), the highest ENVs (expressed as %/ton of production) observed were for CED among four impact categories considered. Nevertheless, any comparison with the literature must be qualified by the fact that the production systems studied are very different and do not operate under the same constraints. Here, we have chosen a scenario with constant annual production (production quotas). Thus, the environmental impacts are not diluted by an increase in annual production.

Given the similarities observed in the ENVs of some HX, we decided to focus on the H aiming at impact reduction by considering four impact categories among the six initially assessed: climate change, CED, land and water. This arbitrary choice between Hacid vs. Hclimate and Heutro vs. Hland was made considering that there was no need to prioritize certain impact categories over others, the proximity of the Hs being such that it is possible to transpose the responses to the selection on one or the other impact category. Overall, we have demonstrated that the selection aimed at reducing environmental impacts is effective. The different HX tested allow an improvement of growth but in variable proportions. After one generation of selection, the growth gains expected for HCED and Hwater (between 7 and 9% of the mean before selection) are comparable with genetic gains achieved on the same species in production in Chile and Norway with breeding goals weighted by EV on the traits (7-13% per generation; [START_REF] Lhorente | Advances in genetic improvement for salmon and trout aquaculture: The Chilean situation and prospects[END_REF]. The gains are, however, lower for Hclimate and Hland. The same is true for feed efficiency where the gains are low in Hwater but quite comparable for the other H (7-9% per generation) to the values predicted by Kause et al. (2006b). The annual environmental gains ranging from 0.9% to 1.4% are comparable to the reduction of 0.9% per year of eutrophication observed by [START_REF] Besson | The genetic correlation between feed conversion ratio and growth rate affects the design of a breeding program for more sustainable fish production[END_REF] in European sea bass in a breeding goal with TGC and FCR weighted by ENV.

The responses to selection on HX were conditioned by the phenotypic and genetic correlations between the traits considered in the selection indexes. In rainbow trout, and more generally in fishes, although there are more and more studies on this subject, there is still a lot of uncertainty about the amplitude of the correlations between certain traits, the majority of studies being focused on growth and yield traits (e.g., [START_REF] Blay | Genetic parameters and genome-wide association studies of quality traits characterised using imaging technologies in rainbow trout, Oncorhynchus mykiss[END_REF][START_REF] Haffray | Negative genetic correlations between production traits and head or bony tissues in large all-female rainbow trout (Oncorhynchus mykiss)[END_REF]. Faced with some discrepancies in previous studies or in the absence of data, we explored different scenarios, by varying phenotypic correlations between BW and FE between -0.4 and 0 and genetic correlations between BW and SR between -0.3 and 0. We have shown that the responses to selection differ greatly according to the intensity of correlations between traits, and the same is true for the precision of selection indices. So far, in fish, there are strong indications that the genetic correlation between growth and feed efficiency is weak (between 0 and -0.4; e.g. [START_REF] Kause | Genetic improvement of feed conversion ratio via indirect selection against lipid deposition in farmed rainbow trout (Oncorhynchus mykiss Walbaum)[END_REF]. Hence, growth and feed-related traits should be included in the breeding goal and in the index to maximize the environmental responses [START_REF] Besson | The genetic correlation between feed conversion ratio and growth rate affects the design of a breeding program for more sustainable fish production[END_REF]. Nevertheless, it is interesting to note that environmental gains tend to decrease for Hland and Hclimate when negative phenotypic correlations were considered between BW and FE. Such a correlation implies that the largest individuals are also those with the highest FCR. The results are therefore consistent given the importance of feed in these impact categories. Considering a negative genetic correlation between BW and SR results in a marked reduction in environmental gains for Hclimate and Hland in particular. Here, we considered identical heritability between these two traits (h 2 = 0.30). Selection through optimal index where these two traits are included tended to decrease their respective responses leading to a negative response to selection for SR. In addition to a logical reduction of environmental gains, such a situation raises questions about the relevance of an optimal index based on all these traits. In this respect, if the genetic correlation between BW and SR is proven, it would seem wiser to adopt a threshold-based approach to ensure that selection on growth does not deteriorate the survival rate.

By considering a scenario of correlations that seemed the most realistic, we were able to estimate genetic gains for the four impact categories depending on which impact category was considered as the breeding goal. This approach allowed us to study the indirect effects of a selection strategy on the other impact categories evaluated in LCA. Logically, for a given impact category, the gains decrease when the optimal index is not used. Nevertheless, it is important to note that this reduction in gains never leads to an extreme situation where the environmental impacts after one year would be higher than those observed at generation 0 of selection. Overall, it is the selection for a reduction in water dependency that appears to be the least relevant for targeting the other impact categories as well, and this is particularly true for climate change and land competition. This point may help in making a choice among the tested breeding goals.

The question of choice among the tested HX is central, but the interpretation of our results should not hide the absence of economic considerations in our study. Indeed, currently, it is difficult to establish a direct relationship between breeding goals weighted by EV or ENV in fish. [START_REF] Besson | The genetic correlation between feed conversion ratio and growth rate affects the design of a breeding program for more sustainable fish production[END_REF] were able to demonstrate that only minimal differences were observed between two-trait breeding goals based on EV or ENV when the genetic correlation between the two traits (FCR and TGC) was strongly negative (< -0.5). Nevertheless, such conclusions remained not consistent at other correlation intensities. In a context where feed cost is the first production cost in fish farming, representing up to 70% of production costs, and given the preponderant contribution of feed in the environmental impacts of farms, it seems coherent to prioritize breeding goals maximizing the response of FE. However, such an approach would require more studies to be validated by combining an economic approach. A relevant approach could be the combination of EV and ENV in the same breeding goal to take into account both the environmental and the economic impacts in selection similarly to [START_REF] Kariuki | Deterministic simulations to determine the impacts of economic and non-economic breeding objectives on sustainable intensification of developing smallholder dairy farms[END_REF]. These authors developed breeding goals on dairy cattle weighted by both economic and nonmarket values of the traits. Furthermore, one of the limitations of our study is the consideration of a single flow-through production system from egg to fry that does not include grow-out, the longest and most input-dependent rearing phase. This choice is not necessarily reflecting the evolution of trout production in France with a gradual shift towards RAS production systems [START_REF] Martins | New developments in recirculating aquaculture systems in Europe: A perspective on environmental sustainability[END_REF]. It is therefore logical to question the relevance of the breeding goals we studied. However, the evaluation of the environmental impacts of very contrasted trout farms (see Appendix A2) confirmed the interest of maximizing the response on FE because the feed remains a major source of impacts in, at least, four of the six categories of impacts evaluated, whatever the production system considered.

Conclusion

This study demonstrated the efficiency of using ENV in breeding goals to minimize environmental impacts at the farm level while maintaining high genetic improvements in growth and feed efficiency related traits in rainbow trout production. Although our results have to be qualified by the lack of considerations for the economic repercussions of such selection strategy, the significant weight of feeds in both the economic and the environmental performances of rainbow trout farms suggests that there is a real interest in integrating weights based on ENVs to balance growth and feed efficiency traits in breeding goals. However, care should be taken to avoid any risk of degradation of survival rate. This approach opens the way to designing selection indexes, in animal breeding, to include, in addition to EVs, ENVs but also other weightings based on current societal considerations related to ethics and animal welfare.

Figure 1 .

 1 Figure 1. The general methodological framework for life cycle assessment (LCA).

Figure 2 .

 2 Figure 2. System boundaries and flows of rainbow trout Oncorhynchus mykiss fry production.

Figure 4 .

 4 Figure 4. Environmental impacts of the rainbow trout fry production at the level of the theoretical farm for (A) acidification, (B) climate change, (C) cumulative energy demand (CED), (D) eutrophication, (E) land competition and (F) water dependence. Results are expressed per ton of fish produced.

Figure 5 .

 5 Figure 5. Annual gains (in physical units) for the different impact categories according to two different scenarios of correlations: (1) a reference scenario where both phenotypic and genetic correlations are nulls (rp12 = 0 and rg13 = 0) and, (2) a realistic scenario with moderate negative phenotypic and genetic correlations (rp12 = -0.2 and rg13 = -0.15). Responses on Hx for the optimal selection index IX for each impact category are black dashed.

Table 2 .

 2 Genetic parameters of body weight at 110 days post-hatching (BW), feed efficiency (FE), and survival rate (SR) used to predict the responses to selection.

	Trait	Heritability	Genetic standard deviation
	BW	0.30	1.10
	FE	0.15	0.08
	SR	0.30	0.16

Table 3 .

 3 Genetic (above diagonal) and phenotypic (below diagonal) correlations between body weight at 110 days post hatching (BW), feed efficiency (FE) and survival rate (SR).

	Trait	BW	FE	SR
	BW		0.0	{-0.3, -0.15, 0.0}
	FE	{-0.4, -0.2, 0.0}		0.0
	SR	0.0	0.0

Table 4 .

 4 Environmental

	Impact category	Breeding goal name	ENV (physical units) ENVBW ENVFE ENVSR	RWBW	RW (%) RWFE	RWSR
	Acidification (kg SO2 eq)	Hacid	0.1	5.0	0.0	22.22	77.78	0.00
	Climate change (kg CO2 eq)	Hclimate	20	1250	5	18.48	80.83	0.69
	Cumulative energy demand (GJ)	HCED	1.5	23.75	0.15	47.10	52.20	0.71
	Eutrophication (kg PO4 3-eq)	Heutro	0.00	83.75	0.15	0.00	99.62	0.38
	Land competition (m 2 yr -1 )	Hland	2	450	1	5.94	93.61	0.45
	Water dependence (m 3 )	Hwater	3000	0	500	97.56	0.00	2.44

values (ENV) for the three traits: body size at 110 days post hatching (BW), feed efficiency (FE), and survival rate (SR) expressed in physical units (see Section 2.2.3) and relative weights of the ENV (RW, %) in the breeding goal (H) with traits standardized by their genetic standard deviation.

Acknowledgements

The author warmly thanks Joël Aubin and Florence Phocas for their supervision and their advice and help to perform the analysis and write this report. The author also thanks Jean Ruche of the Coopérative des Aquaculteurs Bretons, and all the fish farmers involved in this study for organizing the visits, open their doors, and taking time to answers all our questions and sharing their data and perceptions. This study would not have been possible without their involvement.

Table 5. Index accuracy (𝜌H), annual genetic gains (AGG) expressed in physical units for the different breeding goals (i.e. Hclimate, HCED, Hland and Hwater) and for the three traits under selection according to scenarios based on phenotypic (rp) and genotypic correlations (rg) between BW (1), FE (2) and SR [START_REF] Ali | Effects of incorporating environmental cost and risk aversion on economic values of pig breeding goal traits[END_REF]. Table 6. Overall annual relative gains when considering the optimal selection indexes expressed as % of the hypothetical farm for the different impact categories: climate change (kg CO2 eq), cumulative energy demand (CED; GJ), land competition (m 2 yr -1 ) and water dependence (m 3 ). We considered different scenarios based on phenotypic (rp) and genotypic correlations (rg) between BW (1), FE (2) and SR [START_REF] Ali | Effects of incorporating environmental cost and risk aversion on economic values of pig breeding goal traits[END_REF].

Impact category

Scenarios

Appendix 1. Derivation of P and G matrices.

For the P-matrix:

Information sources: 𝑌 1 = performances on candidates (z) for BW 𝑌 2 = performances on candidates (z) for FE 𝑌 ̅ 3 = mean performance from 23 half-sibs (hs) for SR

for the phenotypic variance of measurements of BW and FE on candidates

for the phenotypic variance of a mean of SR records from n = 23 half-sibs per candidate

where 𝑟 𝑝12 is the phenotypic correlation between BW and FE

where 𝑟 𝑎13 is the genetic correlation between BW and SR

where 𝑟 𝑎23 is the genetic correlation between FE and SR

For the G-matrix:

for the genetic variance of measurements of BW and FE on candidates

for the genetic variance of a mean of n records of SR from n = 23 half-sibs per candidate

where 𝑟 𝑎12 is the genetic correlation between BW and FE 𝐶𝑜𝑣(𝑌 1 , 𝐴 )

Appendix A2. Summary of the environmental impacts of four rainbow trout farms considering economic allocations of impacts.

• Farm 1: production of pan-size (250-300 g) and very large trout (> 3 kg) from eggs in flow-through and recirculating aquaculture system (RAS). • Farm 2: production of fry (10 g and 40 g) from eggs in flow-through system.

• Farm 3: production of pan-size (250-300 g) and large trout (1.5-2.0 kg) from eggs with fry production in RAS and growing in flow-through system. • Farm 4: production of large (1 kg) and very large trout (> 3 kg) from eggs in flowthrough system.


Thomas Kronland-Martinet

Léo Poughon

Marcel Pasquinelli

David Duché

Julien Serres

Stéphane Viollet

SkyPole -A bio-inspired method to locate the north celestial pole

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

SkyPole -A bio-inspired method to locate the north celestial pole

Animal Navigation

• Insects such as Cataglyphis desert ants use skylight polarization to navigate [1] • Skylight polarization can be described by its angle and degree of linear polarization (AoLP and DoLP), modeled from Rayleigh single scattering model [2]

Polarization vision

Celestial rotation

• Migratory birds such as homing pigeons use the celestial rotation as a reference for calibrating their magnetic compass [3] [4]

• Celestial rotation helps nding the north celestial pole, giving access to geographical north bearing and latitude [5] • Celestial rotation can be observed during night or daytime [6] Question

How

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