Aurélie Dessier

Paco Bustamante

Tiphaine Chouvelon

Martin Huret

Marc Pagano

Elise Marquis

Frederic Rousseaux

Cécilia Pignon-Mussaud

Françoise Mornet

Christine Dupuy
email: christine.dupuy@univ-lr.fr

Frédéric Rousseaux

Martine Bréret

The spring mesozooplankton variability and its relationship with hydrobiological

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Introduction

Mesozooplankton (200-2,000 µm) play a pivotal role in marine ecosystems by transferring energy from primary producers to the upper trophic levels. They are very sensitive to hydroclimatic features, so climate-mediated changes in zooplankton abundance and composition may affect upper trophic levels and fisheries [START_REF] Beaugrand | Plankton effect on cod recruitment in the North Sea[END_REF]. Zooplankton monitoring therefore represents a powerful tool to detect, understand, and anticipate how global changes induce modifications in pelagic ecosystems [START_REF] Beaugrand | Plankton effect on cod recruitment in the North Sea[END_REF]Beaugrand, 2004;[START_REF] Perry | Identifying global synchronies in marine zooplankton populations: Issues and opportunities[END_REF][START_REF] Richardson | In hot water: zooplankton and climate change[END_REF][START_REF] Hinder | Multi-decadal range changes vs. thermal adaptation for north east Atlantic oceanic copepods in the face of climate change[END_REF]. Although extensive and long-term zooplankton surveys have been undertaken (ICES Working Group on Zooplankton Ecology Zooplankton Status Report: http://wgze.net/zooplankton-status-report; O' Brien et al., 2013), they still are in relatively short supply compared to fish time-series from commercial catches [START_REF] Batchelder | Spatial-temporal scales of synchrony in marine zooplankton biomass and abundance patterns: A world-wide comparison[END_REF].

In this study, we investigated the assemblage structure of mesozooplankton (at the level of the species, genus, or family) in the Bay of Biscay, an important Northeast Atlantic fisheries area and a relatively stable ecosystem that primarily is structured around bottom-up forces (e.g., [START_REF] Lassalle | An assessment of the trophic structure of the Bay of Biscay continental shelf food web: Comparing estimates derived from an ecosystem model and isotopic data[END_REF]. Our investigation covers a large spatio-temporal scale: from the Spanish coast at 46°N to the French coast at 3°35'W, from the spring of 2003 through the spring of 2013. Previous mesozooplankton studies in the Bay of Biscay have been conducted in the spring as well because it is the key period for plankton blooms and the reproductive period for anchovies and sardines (Huret et al., this issue). Although some of these studies considered large spatial and/or temporal scales, they had more limited scopes; some relied on the LOPC (Laser Optical Plankton Counter) technique and were limited to size-structure analyses [START_REF] Sourisseau | Spatial distribution of zooplankton size spectra on the French continental shelf of the Bay of Biscay during spring 2000 and 2001[END_REF], while others used the CPR (Continuous Plankton Recorder) method and were restricted to the "ultra subsurface" (0-7 m) (Beaugrand et al. 2000a(Beaugrand et al. , 2000b)). Studies with high taxonomic resolution focused on a single field survey [START_REF] Albaina | Fine scale zooplankton distribution in the Bay of Biscay in spring 2004[END_REF]Irigoien et al., 2011) or were conducted on limited spatial scales despite their large temporal scales [START_REF] Albaina | Fine scale zooplankton distribution in the Bay of Biscay in spring 2004[END_REF][START_REF] Stenseth | Seasonal plankton dynamics along a cross-shelf gradient[END_REF][START_REF] Valdés | Time-series analysis of copepod diversity and species richness in the southern Bay of Biscay off Santander, Spain, in relation to environmental conditions[END_REF][START_REF] Valdés | A decade of sampling in the Bay of Biscay: What are the zooplankton time series telling us?[END_REF]Gonzalez-Gil et al., 2015;[START_REF] Cabal | Mesozooplankton species distribution in the NW and N Iberian shelf during spring 2004: Relationship with frontal structures[END_REF][START_REF] Bode | Comparing copepod time-series in the north of Spain: Spatial autocorrelation of community composition[END_REF]2013). Other studies focused on one or two species on a high spatio-temporal scale, such as [START_REF] Bonnet | An overview of Calanus helgolandicus ecology in European waters[END_REF] on Calanus helgolandicus and [START_REF] Lindley | Variations in the distributions of Centropages chierchiae and Temora stylifera (Copepoda: Calanoida) in the north-eastern Atlantic Ocean and western European shelf waters[END_REF] on Temora stylifera and Centropages chierchiae. Finally, only two studies were quite similar to ours, conducting large spatio-temporal surveys of the Bay of Biscay, albeit with a lower taxonomic resolution (groups were defined by image analysis) [START_REF] Irigoien | Spring zooplankton distribution in the Bay of Biscay from 1998 to 2006 in relation with anchovy recruitment[END_REF][START_REF] Vandromme | Springtime zooplankton size structure over the continental shelf of the Bay of Biscay[END_REF]. [START_REF] Irigoien | Spring zooplankton distribution in the Bay of Biscay from 1998 to 2006 in relation with anchovy recruitment[END_REF] identified permanent features in the spatial distribution of spring zooplankton between 1998 and 2006, with a higher abundance of large organisms over the shelf break and offshore areas. [START_REF] Vandromme | Springtime zooplankton size structure over the continental shelf of the Bay of Biscay[END_REF] used a combination of LOPC data and WP2 sampling processed with the Zooscan and employed it over the same network of stations used in our study between 2005 and 2012. They found a negative relationship between the zooplankton biomass and normalized biomass size spectra slopes, thus suggesting a clear association between zooplankton size distribution, productivity, and transfer efficiency.

The novelty of the present study lies in the temporal and spatial coverage of the mesozooplankton community structure, with a focus on the main mesozooplankton groups and the key genera or species of copepods. These aspects have not been investigated previously in the Bay of Biscay. From a large data set of annual spring PELGAS ('PELagique GAScogne') surveys (Doray et al., this issue), our study aimed to elucidate which drivers control the spring mesozooplankton community and whether any spatial and/or temporal changes in this community occurred between 2003 and 2013. We had three objectives: 1) to summarize the habitat variabilities in terms of temperature, salinity, and chlorophyll a data; 2) to analyze the temporal patterns of the mesozooplankton and copepod spring communities over the studied decade; and 3) to elucidate which local hydrological and trophic variables may account for the variability of mesozooplankton communities over space and time.

Materials and Methods

Sampling area

The Bay of Biscay is characterized by a morphostructural dissymmetry opposing the large northeastern edge of a narrow meridional shelf (Fig. 1). Our study focused on the southern part of the Armorican shelves, which are largely under the influence of the Gironde and the Adour river plumes.

Data collection

Samples were collected during the annual PELGAS surveys (Doray et al., this volume-b), which have been conducted every spring since 2000 over the whole continental shelf of the Bay of Biscay. In this study, we selected a subset of data with a homogenous mesozooplankton sampling protocol, i.e. data related to the southern part of the Bay of Biscay from 2000-2013 (Fig. 1). PELGAS surveys routinely collect several parameters for all system components, including hydrobiology, pelagic fish abundance and distribution, marine mammals, and seabird observations. We used data that had been collected at night from a total of 118 visited stations (Table 1). Each station was separated from the next by approximately 44 km in the along-shore direction and 10-25 km in the cross-shelf direction. PELGAS surveys were not carried out on exactly the same calendar dates over the series (especially at the beginning of the studied decade), although they always did take place during springtime over the course of about 15 days (Table 1).

Hydrology and phytoplankton biomass

Our station network for hydrology data consisted of 26 to 34 stations per year (Table 1, Fig. 1). At each station, the salinity and temperature were measured over the water column with a CTD (Seabird 19+v2) probe. Two water column integrated indices were calculated: the equivalent freshwater depth (m) and the deficit of potential energy or DEP (kg.m -1 .s -2 ). As detailed in [START_REF] Huret | A multidecadal hindcast of a physical-biogeochemical model and derived oceanographic indices in the Bay of Biscay[END_REF], the equivalent freshwater depth represents the local depth of freshwater in the absence of mixing. As such, equivalent freshwater depth is a good indicator of the plume influence in a given year and location. The DEP is an index of stratification that is calculated from the vertical distribution of density values.

Chlorophyll a-based biomass (chla, see Introduction of [START_REF] Boyer | Phytoplankton bloom status: Chlorophyll a biomass as an indicator of water quality condition in the southern estuaries of Florida[END_REF]) was used as a proxy of autotrophic biomass (mostly phytoplankton). Water samples (200-500 mL) were collected with Niskin bottles at the subsurface. Once on board, the samples were passed through successive filtrations on three membranes with different porosities (Whatman GF/F with pore sizes of 0.7, 3, and 20 µm and a diameter of 25 mm) to fractionate the samples into three size classes: pico-(< 3 µm), nano-(3-20 µm), and microphytoplankton (>20 µm) including large taxa such as diatoms. Each sample was stored at -20°C for subsequent analysis. Laboratory extraction was performed with a Turner TD-700 fluorometer according to the protocols of [START_REF] Aminot | Hydrologie des écosystèmes marins. Paramètres et analyses[END_REF] and of [START_REF] Lorenzen | Determination of chlorophyll and pheopigments: spectrophotometric equations[END_REF]. The chla-based biomass was expressed in µg.L -1 . An index of water-column integrated chla biomass (µg.m -²) was calculated using the fluorescence data from the vertical profiles (WETStar fluorometer, WET Labs, USA) and corrected by chla-based biomass data.

Mesozooplankton

The mesozooplankton samples were collected by vertical trawls using WP2 nets (0.25 m 2 opening, 200 µm mesh size), from a depth of 100 m (or the bottom depth for inshore stations). For each annual survey, ten or 12 stations were selected from four transects; this sampling included coastal, continental shelf, and slope stations (Fig. 1B). After collection, the net samples were preserved in 4% formaldehyde. The organisms were identified by species, genus, family, or more general categories/forms (Table 2; identification protocol of [START_REF] Rose | Faune de France -Copépodes Pélagiques[END_REF] and [START_REF] Tregoubof | Le manuel de planctonologie méditerranéenne[END_REF]), and were enumerated using a Leica M3Z stereo microscope (65× to 100× magnification). The abundance was expressed in individuals m -3 (ind.m -3 ).

Data analysis

Ordinary kriging

To describe the spatio-temporal patterns of the different studied compartments, an ordinary kriging procedure (ArcMap 10.2 using the Geostatistical Analyst toolbox) was applied to the data for the subsurface temperature, salinity, and size-fractionated chla-based biomass. For each parameter, annual data were compiled from 2003-2013 and interpolated to provide an overview of the spring spatial patterns over the time series. For each parameter, annual kriged maps are presented in Supplemental Figures 1234. To identify significant temporal variations (i.e., across years) for each parameter (temperature, salinity, and pico-, nano-, and microphytoplankton biomasses), a non-parametric multiple pairwise comparison (Statistica®, Tulsa, OK, USA) of mean ranks was applied to all years from 2003-2013; pvalues < 0.05 were considered significant. All other statistical analyses were performed with the R-Cran project free software [START_REF] Core | R: A language and environment for statistical computing[END_REF]. Furthermore, to consider these five water mass variables together throughout the decade, confidence ellipses (surrounding the barycentre of coordinate stations) were determined on a station factor map produced by a principal component analysis (PCA, 'FactoMineR' package [START_REF] Husson | Factors determining the distribution and betadiversity of mesozooplankton species in shelf and coastal waters of the Bay of Biscay[END_REF]).

Mesozooplankton community analysis

The time-variability of the mesozooplankton community was analyzed by considering the mean yearly relative abundance of classical characteristic groups of mesozooplankton (meroplankton, gelatinous plankton, copepods, and other holoplankton). The abundance and taxonomic composition of the dominant group (copepods) was analyzed according to the variability in space and over time. As done in previous studies, a temporal analysis was conducted via a multiple comparison of the mean ranks for all years based on copepod abundance. The spatio-temporal variation in the composition of the adult copepod community was also described with a non-metric multi-dimensional scaling (NMDS), performed using Primer 6 (Plymouth Routines In Multivariate Ecological Research) software. A matrix of sampling points (n=118 samples; see Table 1) was created for the abundance data of copepods species or genera (n= 23). In this matrix, the columns corresponded to the copepod taxa abundances, and the lines to the sampling points. The data were transformed with log x + 1 before the Bray-Curtis metric was applied to estimate the similarity between stations. The similarity matrix was then ordinated by NMDS. A SIMPER (SIMilarity PERcentage) analysis was performed to identify the genera or species contributing most to similarity (or dissimilarity) within (or between) three groups of sampling years defined from the time series analysis.

Finally, to quantify the relative influences of the food-resource (chla) and abiotic parameters (temperature, salinity) that underlie the patterns observed in the copepod community structure, a variation partitioning analysis (using "vegan" and "ade4" packages in the R-Cran project free software) was applied [START_REF] Volis | Variation partitioning in canonical ordination reveals no effect of soil but an effect of co-occurring species on translocation success in Iris atrofusca[END_REF]. .We considered biotic variables (subsurface and integrated water column values of chla for pico-, nano-, and microphytoplankton fractions) and abiotic variables (subsurface values of temperature and salinity, and three water column integrated indices; the DEP, the equivalent fresh water, and the mixed-layer depth). First the variables to include in the analysis (ie variables that influenced the most the copepod distribution) were selected through forward selection (pack for package). After the forward selection, two matrices (H matrix for abiotic parameter and C matrix for biotic parameters) were buit using only the most influential variables. Finally, using these two matrices, the variation partitioning was performed aiming at identifying the part of technology copepod distribution variation explained by each variable. By this way, our aim is to evaluate if copepod distribution is better explained by hydrological parameters than by food resources. Indeed, in ecological matrices each variable has a pure variation and a part of variation linked to the other variables. This covariation between variables can be evaluated through the variation partitioning.

Variation partitioning evaluates diverse components of variation: 1) the pure effect of each individual matrix, 2) the redundancy of the two explicative matrices, and 3) the residual effects that are unexplained by the chosen variables. Redundancy analysis (RDA), partial redundancy analysis (pRDA), and Monte Carlo permutation (999 permutations) tests were used to test the significance of the canonical axis.

Results

Subsurface salinity and temperature

The absence of a spatial pattern in the decadal average map (Fig. 2) means that no spring-time mesoscale process had a strong recurrent impact on the surface temperature in the southern Bay of Biscay. However, a coast-to-offshore positive gradient can be observed in certain years (e.g., in 2006, 2010, and 2013; see The spatial pattern of salinity was driven by the plumes of the Gironde and the Adour rivers (Fig. 2). Despite some interannual variability in the extension of the plumes (maxima in 2007, 2009, and 2013; minima in 2011 and 2012), the interannual variability of the subsurface salinity was not significantly different between years (multiple pairwise comparison, p=0.05) (see Fig. S2). Subsurface salinities varied from 26.07 psu to 36.4 psu (see Fig. S2).

Chlorophyll a-based biomasses

The average picture of the chla biomasses (Fig. 2) revealed a homogeneous concentration over the shelf, with lower values off-shelf, for the two smallest size classes (< 3 µm and 3-20 µm). For the largest size class (> 20 µm), the highest values were found over a coastal strip only. Generally, biomasses were higher in the area influenced by the Gironde plume as compared to the most other southern locations.

Substantial differences appeared when analyzing the annual maps of chla biomasses (see Figs. S3, S4, andS5). For the smallest size class (Fig. S3), significant interannual differences allowed the years to be divided into five groups: 2003 exhibited the lowest values (0.20 ± 0.38 µg.L -1 ) and 2009-2010 exhibited the highest (0.66 ± 0.41 µg.L -1 ). For the 3-20 µm size class, the interannual variability revealed four groups of years, with mean biomasses ranging from 0.17 ± 0.26 µg.L -1 to 0.45 ± 0.37 µg.L -1 . For the > 20 µm size class, no significant interannual differences were found between years.

The non-parametric multiple pairwise comparison of the five environmental variables (subsurface salinity and temperature, subsurface pico-, nano-, and microphytoplankton biomasses) over the decade could not extract significant differences between years.

The average contribution of each size class over the studied decade (Fig. 3) was 44% for picophytoplankton (< 3 µm), 23% for nanophytoplankton (3-20 µm), and 33% for microphytoplankton (> 20 µm) (Fig. 3). The relative contributions varied from 23% ( 2003

Mesozooplankton

Total abundance and the contribution of the main groups

The mean spring abundance of mesozooplanktonic organisms over the study period varied from 1,321 ± 391 ind.m -3 (2008) to 4,986 ± 355 ind.m -3 (2005) (Fig. 4A). Between 2003 and 2006, abundances were higher (4,454, 3,233, 4,985, and 4,191 ind.m -3 for each year, respectively) than the mean decadal value (2,995 ± 1,195 ind.m -3 ), while the mean abundances were lower than the mean decadal value between 2007 and 2013, with the exceptions of 2010 and 2012 (with 3,349 and 3,061 ind.m -3 , respectively). The spring abundance of mesozooplanktonic organisms revealed three temporal phases: from [2003][2004][2005][2006] (higher than the mean decadal value), from 2007-2009 (lower than the mean decadal value), and from 2010-2013 (close to the mean decadal value, except 2011, which was below the mean decadal value). The lowest contribution of copepods was registered in 2006 (Fig. 4B).

The gelatinous organisms encountered in 2006 were mainly cnidaria and siphonophora as well as major meroplankton organisms (Bivalvia larvae and Cirripedia). On average, more than 80% of the spring mesozooplankton community comprised copepods, 8% meroplankton, 8% gelatinous plankton, and 4% other holoplanktonic organisms (Fig. 4B). Depending on the year, the relative abundance of copepods varied from 42% (2006) to 87% (both 2011 and 2009), those of meroplankton from 1% (2009) to 22% (2006), those of gelatinous organisms from 3% (2011) to 24% (2006), and those of the other holoplanktonic organisms from 2% (2009) to 11% (2010). Meroplanktonic organisms were found mostly along the coast, gelatinous organisms were scattered, and the other holoplanktonic organisms were widespread among the sampling stations (data not shown). Based on these observations, the following results focus on the main group: the copepods.

Copepod patterns

Over the 11 springtime surveys, copepodites (16% of the total copepod abundance) and nauplii (1.4%) of miscellaneous copepod species were recorded.

Twenty-five adult copepod taxa (at the family, genus, or species level) were recorded; orders included Harpacticoida, Poecilostomatoida, Cyclopoida, and Calanoida, as well as copepodites and copepod nauplii (Table 2). The spatial distribution of these 25 taxa is shown in Fig. 5. Irrespective of the year, the copepod abundance followed a longitudinal gradient: coastal waters had the highest values (2,848 ± 2,507 ind.m -3 ), shelf waters had intermediate values (2,335 ± 3,787 ind.m -3 ), and the continental slope had the lowest values (1,304 ± 1,546 ind.m -3 ), except for in 2010 (1,467 ind.m -3 ). One outlier of copepod abundance (21,127 ind.m - 3 ) was recorded in 2005 at a single station on the northern coast. From a temporal viewpoint and based on the annual abundances at each station, only 2009 could be distinguished from the other years (Fig. S6). Moreover, eight of these 25 adult taxa (Oithona spp., Acartia spp., Temora longicornis, Oncaea spp., Calanidae, Calanus helgolandicus, Paracalanidae, and Euterpina acutifrons) alone represented more than 1.5% of the copepod abundance (Table 2).

Their spring spatial abundances in the Bay of Biscay are plotted in Fig. 5. Oithona spp. was present preferentially from the continental shelf to the slope; Acartia spp., Oncaea spp., and Temora longicornis were most common at the coastal stations; and the genera Acartia, Oithona, Temora, and Oncaea were the most abundant within the copepod community (66% between 2003 and 2013; see details in Table 2).

Spatio-temporal variations of adult copepods

The NMDS ordination of the adult copepod abundance data (stress value of 0.23, indicating a good ordination) discriminated the temporal variations better than the spatial variations. The plots of the three time-sampling groups previously discerned by the temporal analysis of abundance (see above) showed that the adult copepod community in the 2003-2006 period was clearly distinct from the 2007-2009 period (Fig. 6). The last period (2010-2013) was intermediate, suggesting a return toward the initial situation (2003)(2004)(2005)(2006) (Fig. 6).

The SIMPER analysis (Tables 3 and4) confirmed this trend, with the same four taxa (Oithona spp., Oncaea spp., Acartia spp., and Temora longicornis) explaining > 65% of the similarity within the 2003-2006 and 2010-2013 periods, whereas in 2007-2009, Paracalanidae (15% contribution for this group) replaced Temora longicornis (7.8%) in these top-four taxa.

Overall, the within-group similarity was higher for the 2003-2006 (67.0%) and the 2010-2013 (59.9%) periods than for the 2007-2009 period (52.3%). The level of dissimilarity between the groups was highest between 2003-2006 and 2007-2009 (52.0%), and lowest between 2003-2006 and 2010-2013 (45.5%).

Hydrological versus trophic control on the spring copepod community

The forward selection identified four significant variables that significantly drive the copepod distribution:: microphytoplankton (> 20 µm) biomass at the subsurface, equivalent freshwater height, DEP, and subsurface temperature (Table 5). The variation partitioning highlighted that 49.2% of the variation was explained by both matrices H and C with the most variance (24.3%) attributable to chla-based microphytoplankton biomass and the next-most variance (13.7%) attributable to hydrological parameters (Figure 7, Supplemental table 1). The part of the variation due by the interaction between the 2 matrices (ie. between hydrological parameters and subsurface microphytoplankton) was 11.2 %. Partial RDA (without interaction between variables) concurred that the distribution of the copepod community was influenced significantly by the microphytoplankton subsurface biomass, equivalent freshwater height, and DEP (Supplemental table 1). The contribution of the subsurface temperature was not significant in the variation partitioning analysis.

Discussion

Hydrological and biological features of the mesozooplankton habitat

Throughout the 2003-2013 decade, surface water warming occurred continually in the Bay of Biscay, from the south to the north and from the coast to the open sea. The water mass circulation in the Bay of Biscay is drived by a combination of large-scale and local forces (Le [START_REF] Boyer | Circulation on the shelf and the upper slope of the Bay of Biscay[END_REF]; the warming of water masses in spring is modulated by slope currents, shelf residual circulation, and the Iberian Poleward Current from Galicia to the Bay of Biscay on a larger scale, and wind and irradiance conditions on a local scale [START_REF] Koutsikopoulos | Physical processes and hydrological structures related to the Bay of Biscay anchovy[END_REF][START_REF] Puillat | Hydrographical variability on the French continental shelf in the Bay of Biscay, during the 1990s[END_REF][START_REF] Rubio | Seasonal to tidal variability of currents and temperature in waters of the continental slope, southeastern Bay of Biscay[END_REF]. From our study, the spatial pattern of variability in the south of the Bay appeared to be independent of the interannual variability of the hydrobiological parameters (e.g., the subsurface temperature). From 2003-2013, the survey observed a mix of warm (in 2003, 2007, and 2011), intermediate, and cold years. This variation in temperature regimes is consistent with results previously reported in this area (e.g., [START_REF] Huret | A multidecadal hindcast of a physical-biogeochemical model and derived oceanographic indices in the Bay of Biscay[END_REF].

The size structure of the phytoplankton community contribute to the structure of pelagic food webs, so our study considered three size classes (pico-, nano-, and microphytoplankton). Indeed, mesozooplanktonic organisms are major grazers of nano-and microphytoplankton [START_REF] Marquis | Inverse analysis of the planktonic food web dynamics related to phytoplankton bloom development on the continental shelf of the Bay of Biscay, French coast[END_REF]. [START_REF] Calvo-Díaz | Seasonality of picophytoplankton chlorophyll a and biomass in the central Cantabrian Sea, southern Bay of Biscay[END_REF] recorded the monthly contributions (in Iberian Peninsula waters from [2003][2004][2005][2006] of each size fraction of phytoplankton, and showed that the spring (i.e., April) contribution of picophytoplankton was about 20%, corresponding to the minimum recorded over an annual cycle. By contrast, the contributions of nanophytoplankton and microphytoplankton were around 50% and 30%, respectively. In our study, the mean balance between pico-and nanophytoplankton varied widely, most likely because our spatial coverage involved more oceanic features beyond 200 m of bathymetry. It is important to note that the survey dates were not exactly the same throughout the decade and hence added further variability. For example, compared to the later surveys, the 2003 survey captured significantly different hydrology, plankton concentration, and size structure.

To summarize, taking into account both the hydrological and the phytoplanktonic components of the mesozooplankton habitat, the Bay of Biscay appeared to support a consistent spatial structure across years, due mainly to the continental supply of freshwater and nutrients, although a degree of interannual variability occurred in the range of the observed values.

The spring mesozooplankton community

Among the prominent groups of the mesozooplankton community, meroplanktonic organisms were restricted to the coastal area in our study, as previously reported by [START_REF] Ayata | Meroplankton distribution and its relationship to coastal mesoscale hydrological structure in the northern Bay of Biscay (NE Atlantic)[END_REF]. By contrast, gelatinous organisms were dispersed throughout the Bay of Biscay.

No clear spatio-temporal development of gelatinous plankton was observed, although this group (mainly cnidaria and siphonophora) was particularly abundant in 2006. Their proliferation may be linked to climate change, eutrophication, and/or habitat modifications (e.g., [START_REF] Lo | Enhancement of jellyfish (Aurelia aurita) populations by extensive aquaculture rafts in a coastal lagoon in Taiwan[END_REF]. However, the WP2 net used in the study probably was not the most suitable device for monitoring gelatinous plankton.

In the present study, copepods represented the most dominant holoplankton taxa of the mesozooplankton community, as highlighted by various studies in the same area (e.g., [START_REF] Albaina | Fine scale zooplankton distribution in the Bay of Biscay in spring 2004[END_REF][START_REF] Irigoien | Spring zooplankton distribution in the Bay of Biscay from 1998 to 2006 in relation with anchovy recruitment[END_REF][START_REF] Valdés | A decade of sampling in the Bay of Biscay: What are the zooplankton time series telling us?[END_REF][START_REF] Villate | Mesoscale structure of microplankton and mesoplankton assemblages under contrasting oceanographic conditions in the Catalan Sea (NW Mediterranean)[END_REF][START_REF] Villate | Mesozooplankton community indicates climate changes in a shelf area of the inner Bay of Biscay throughout 1988 to 1990[END_REF]. Previous observations of the spatial distribution of the spring size structure of mesozooplankton have reported a negative coastal-to-offshore gradient (e.g., [START_REF] Vandromme | Springtime zooplankton size structure over the continental shelf of the Bay of Biscay[END_REF], as also observed in the present study for copepod taxa. Here, the sample represented three dominant genera and one dominant species (> 10% of the copepod abundance) Acartia spp., Oncaea spp., Oithona spp., and Temora longicornis-consistent with previous investigations (e.g., [START_REF] Albaina | Fine scale zooplankton distribution in the Bay of Biscay in spring 2004[END_REF]Irigoien et al., 2011).

According to the literature regarding the copepod community in the Bay of Biscay, Temora longicornis and Pseudocalanus elongatus are dominant neritic species that occur preferentially on the continental shelf, whereas Acartia spp. dominates stations under coastal influence, and Calanus helgolandicus and Eucalanidae dominate under oceanic influence.

More specifically, C. helgolandicus is found in the southern part of the Bay of Biscay and in the surface layers in the north during the spring [START_REF] Bonnet | An overview of Calanus helgolandicus ecology in European waters[END_REF].

Temporal trends in the mesozooplankton and copepod communities

Climatic indicators increasingly are being explored to identify major changes affecting plankton (e.g., [START_REF] Wouters | Evidencing a regime shift in the North Sea using early-warning signals as indicators of critical transitions[END_REF] and fish communities [START_REF] Guénette | Shifting baselines in European fisheries: The case of the Celtic Sea and Bay of Biscay[END_REF]. On a similar spatial scale as in the present study, previous research detected oscillations mainly in the vicinity of the Gironde river plume, which represents a major source of nutrient inputs into the Bay of Biscay for both plankton (David et al., 2005) and fish [START_REF] Pasquaud | Increase of marine juvenile fish abundances in the middle Gironde estuary related to warmer and more saline waters, due to global changes[END_REF].

Overall temperatures in the Gironde estuary increased significantly around 1987 and again around 2001 [START_REF] Chaalali | Climate-Caused Abrupt Shifts in a European Macrotidal Estuary[END_REF].

During the decade studied here, the year 2005 brought additional abrupt changes in mesozooplankton abundance and diversity in the Gironde estuary-a relatively closed system-and in the Arcachon basin (Chaalali, personal communication). It is possible that this abrupt change also occurred in the Bay of Biscay, albeit with a time lag that is linked to the Bay's resilience properties. As described above, three temporal phases of adult copepod dominance were observed in the present study : 2003-2006, 2007-2009, and 2010-2013, with abundance values that were higher, lower, and higher, respectively, than the spring mean decadal abundance (including 2003-2013). This temporal oscillation also correlated with taxonomic composition changes (see Tables 3 and4). However, we observed that 2010-2013 witnessed a reversal to the initial situation (2003)(2004)(2005)(2006) with regard to both the abundance and taxonomic composition of the adult copepod community. The only anomaly detected was the high percentage of gelatinous organisms in the spring of 2006, which correlated with the low percentage of copepods observed that year. These gelatinous organisms comprised cnidaria and siphonophora primarily. It is reasonable to consider predation as a possible cause, as this would result in top-down control on copepods and spatial occupation of a very close ecological niche between carnivorous copepods, cnidarian, and siphonophora organisms.

Factors controlling the spring copepod community

The structure and functioning of planktonic food webs depend largely on the hydrodynamics of the water column. Our study found that four variables of the pelagic habitat (subsurface temperature, stratification with the deficit of potential energy, equivalent freshwater height, and subsurface microphytoplankton biomass) accounted for more than 49% of the variability in the main mesozooplanktonic community. [START_REF] Zarauz | Modelling the influence of abiotic and biotic factors on plankton distribution in the Bay of Biscay, during three consecutive years (2004-06)[END_REF] suggested that the mesozooplankton biomass is driven mainly by hydrogeographic data (e.g., latitude, longitude, surface temperature, salinity, stratification index, and water depth), and to a lesser extent by potential trophic resources (e.g., the nano-microplankton biomass). By contrast, the present study showed that for the same study site (same scale and season), the spring copepod community (described taxonomically) was influenced more by trophic variables (e.g., microphytoplankton biomass; 24.3% of the total variability) than by hydrographic variables (13.7% of the total variability) over the 11-year time period. These differences can be explained by the fact that [START_REF] Zarauz | Modelling the influence of abiotic and biotic factors on plankton distribution in the Bay of Biscay, during three consecutive years (2004-06)[END_REF] studied mesozooplankton at the biomass level only, whereas our study took into account the abundance of taxa (species, gender, or family) to describe the community. These methods do not provide the same ecological information.

Moreover, the temporal dataset was not exactly the same: Zarauz et al. ( 2008) studied three spring seasons (2004)(2005)(2006) while the present study included eleven spring seasons (2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013). Finally, the two studies used different trophic variables for the statistical analysis: nano-microplankton biomass in [START_REF] Zarauz | Modelling the influence of abiotic and biotic factors on plankton distribution in the Bay of Biscay, during three consecutive years (2004-06)[END_REF] vs. phytoplankton biomasses by size classes in the present study.

At the scale and with the spring timing of our study, the trophic link (i.e., the subsurface microphytoplankton biomass) appeared to be the major driver of the copepod community, while hydrographic variables appeared to play less important roles. There are two potential reasons for this: i) the trophic dimension probably represents a time integration of hydrological conditions (i.e., more integrated than the temperature and salinity variables in the present context), and ii) the planktonic food web probably has an ecological succession of physical and geographical parameters that control the initial phytoplanktonic blooms in late winter. Nutrients then become limited in spring, ultimately influencing the production and life cycle of mesozooplankton, which thus are maintained by trophic control during the PELGAS spring surveys. However, copepods have other potential trophic sources, such as ciliates and heterotrophic flagellates, that can influence the mesozooplankton distribution but were not considered in our study.

According to the present observations, both the thermal stratification and equivalent freshwater height significantly affected the copepod community, whereas subsurface salinity did not. This probably is because thermal stratification and equivalent freshwater height are more integrated spatially and temporally. However, it is surprising the water column integrated chla index did not have a prominent effect in the non-parametric multiple pairwise comparison of mean ranks. Thus, an approach using functional traits appears to be more efficient for understanding the springtime copepod community, as copepods are major predators of microphytoplankton [START_REF] Marquis | Inverse analysis of the planktonic food web dynamics related to phytoplankton bloom development on the continental shelf of the Bay of Biscay, French coast[END_REF]. Moreover, although fewer stations were sampled in our study than in Irigoien et al. (2011), we explained a greater percentage of the community's variability, probably because our data set spanned a longer period of time and therefore captured more variability. However, half of the variation in the copepod community over the studied decade remained unexplained. We concur with Irigoien et al. (2011) that other biological functional traits of the present community-including the effect of copepod density on feeding activities-merit consideration.

Concluding remarks

This study of annual springtime PELGAS survey data is the only analysis of the southern Bay of Biscay's mesozooplankton community between 2003 and 2013. We claim the following contributions: The external square represents the whole variation of the copepod community. Each circle represents the explanatory tables and values are the part of the variation explained by each explanatory table. The fraction "Int" is the intersection of the amount of variation explained by both types of explanatory variables. Statistically significant pure fraction of variation of copepod community is given in supplemental table 1.

List of Figures

  Fig. S1), revealing the intermittent occurrence of an upwelling process along the southern French coast. The Gironde plume brought characteristically lower temperatures in 2005 and 2006, and a latitudinal gradient also appeared in some years (e.g., in 2010, 2012, and 2013), albeit without any consistent pattern across years. These anomalies may be explained by the changing meteorological conditions (e.g., wind, irradiance) during the 15-day survey conduction. During the studied decade (2003-2013), the subsurface temperature varied from 10.8°C to 19.8°C, highlighting the large interannual variability in the surface warming and the stratification process during this rapidly changing season. The non-parametric multiple pairwise comparison allowed for a separation of the years into three groups: 2003 was the warmest, 2007 and 2011 had intermediate temperatures, and the remaining years were the coldest (see Fig. S1).

  ) to 67% (2009) for the picophytoplankton, from 19% (2008) to 42% (2003) for the nanophytoplankton, and from 10% (2007) to 42% (2008) for the microphytoplankton (including larger taxa such as diatoms).

Figure 1 :

 1 Figure 1: Map of the Bay of Biscay showing the location of the sampling stations of A) sub-

Figure 2 :

 2 Figure 2: Results of the annual (2003-2013) spatial interpolation of sub-surface temperature

Figure 3 :

 3 Figure 3: Interannual variation of the mean relative biomass of surface size-fractionated

Figure 4 :

 4 Figure 4: Interannual variation of the mesozooplankton abundance between 2003 and 2013: A) mean decadal and annual abundances (ind.m -3 ±SD) of the entire mesozooplankton

Figure 5 :

 5 Figure 5: Annual spatial distribution of abundance (ind.m -3 ) for major families, genera or

Figure 6 :

 6 Figure 6: Non-metric Multi-Dimensional Scaling (NMDS) on adult's copepods dataset in two

Figure 7 :

 7 Figure 7: Venn diagram based on a variation partitioning presenting the explained variability

  Figure 1

  Figure 4 703

Table 1 :

 1 Number of stations used in kriging (N.Station.Kriging) and multivariate (N.Station.VarPart) analysis per year start and the end dates of the surveys.

	Year	First Station	Last Station	N.Station.Kriging	N.Station.VarPart
	2003	30 May	09 June	34	11
	2004	29 April	10 May	26	10
	2005	05 May	16 May	30	12
	2006	02 May	13 May	30	11
	2007	27 April	08 May	31	10
	2008	27 April	09 May	31	9
	2009	26 April	09 May	29	12
	2010	26 April	09 May	29	10
	2011	26 April	09 May	28	11
	2012	27 April	13 May	31	12
	2013	28 April	16 May	30	10

Table 2 :

 2 Representative list of taxa and species of mesozooplankton found in the Bay of Biscay with distinction between major groups: copepods, gelatinous organisms (G), other holoplankton (H) and meroplankton (M) organisms. For adult copepods, order affiliation is represented by Calanoida (Ca), Poecilostomatoida (P), Cyclopoida (Cy) and Harpaticoida (Ha) following by their relative percentage of abundance between 2003 and 2013 on copepods community.

	Copepods	Taxonomic level	Order(%)	Other taxonomic groups	Taxonomic level	Group
	Acartia spp.	Genus	Ca (19.3)	Appendicularia	Class	G
	Oithona spp.	Genus	Cy (18.5)	Siphonophorae	Order	G
	Temora longicornis	Species	Ca (17.4)	Indetermined Cnidaria	Phylum	G
	Copepodites	Development stage	-(16)	Chaetognata	Phylum	G
	Oncaea spp.	Genus	P (10.8)	Salpida	Order	G
	Calanidae	Family	Ca (4.5)	Doliolida	Order	G
	Calanus helgolandicus	Species	Ca (2.8)	Annelida larvae	Phylum	M
	Paracalanidae	Family	Ca (2.2)	Cirripedia	Infra-class	M
	Euterpina acutifrons	Genus	H (1.6)	Decapoda	Order	M
	Centropages spp.	Genus	Ca (1.5)	Scaphopoda	Class	M
	Copepods nauplii	Development stage	-(1.4)	Gastropoda larvae	Class	M

Table 2 :

 2 continued 742

	Copepods	Taxonomic level	Order(%)	Other taxonomic groups	Taxonomic level	Group
	Coryceidae	Family	P (1.3)	Bivalvia larvae	Class	M
	Eucalanidae	Family	Ca (1.3)	Enteropneusta	Class	M
	Metridia spp.	Genus	Ca (0.4)	Anthozoa larva	Class	M
	Pseudocalanus elongatus	Species	Ca (0.5)	Ectoprota	Phylum	M
	Microsetella spp.	Genus	H (0.1)	Cyphonauta larvae	Development stage	M
	Candacia spp.	Genus	Ca (0.1)	Bryozoa	Phylum	M
	Pleuromamma spp.	Genus	Ca (0.1)	Echinodermata larvae	Phylum	M
	Calocalanus spp.	Genus	Ca (0.1)	Hydrozoa	Class	M
	Clytemnestra spp.	Genus	H (<0.05)	Scyphozoa	Class	M
	Aegistus spp.	Genus	H (<0.05)	Ostracoda	Class	H
	Aetideus armatus	Species	Ca (<0.05)	Isopoda	Order	H
	Euchaetidae	Family	Ca (<0.01)	Mysida	Order	H
	Rhincalanidae	Family	Ca (<0.01)	Amphipoda	Order	H
	Anomalocera patersoni	Species	Ca (<0.01)	Euphausiacea	Order	H
				Cladocera	Infraorder	H
				Chordata	Phylum	H
				Cumacea	Order	H
				Foraminifera	Phylum	H

Table 3 :

 3 Results of the similarity percentage (SIMPER) analysis based on spring adult copepods matrix in the Bay of Biscay between 2003 and 2013.

	Group [2003-2006]	Group [2007-2009]		Group [2010-2013]
	Average similarity: 66.83	Average similarity: 52.32	Average similarity: 59.89
	Genus/Species/Family	Contrib%	Genus/Species/Family	Contrib% Genus/Species/Family	Contrib%
	Oithona spp.	22.4	Oithona spp.	24.37	Oithona spp.	24.02
	Oncaea spp.	17.8	Acartia spp.	17.96	Acartia spp.	19.21
	Acartia spp.	13.04	Oncaea spp.	17.1	Temora longicornis	13.24
	Temora longicornis	12.2	Paracalanidae	15.16	Oncaea spp.	10.96
	Eucalanidae	11.94	Temora longicornis	7.77	Calanus helgolandicus	7.95
	Calanidae	10.54	Coryceidae	3.76	Calanidae	6.97
	Centropages spp.	5.31	Calanus helgolandicus	3.04	Paracalanidae	4.84
			Calanidae	2.9	Euterpina acutifrons	4.11

Table 4 :

 4 Results of the dissimilarity percentage (SIMPER) analysis based on spring adult copepods matrix in in the Bay of Biscay between 2003 and 2013.

	Groups [2003-2006] and [2007-2009]	Groups [2003-2006] and [2010-2013]	Groups [2007-2009]and [2010-2013]
	Average dissimilarity: 52.01	Average dissimilarity: 45.51	Average dissimilarity: 46.88
	Genus/Species/Family	Contrib%	Genus/Species/Family	Contrib%	Genus/Species/Family	Contrib%
	Eucalanidae	11.04	Eucalanidae	11.29	Temora longicornis	10.09
	Paracalanidae	10.49	Calanus helgolandicus	9.44	Calanidae	9.78
	Temora longicornis	9.62	Calanidae	8.55	Calanus helgolandicus	9.05
	Calanidae	8.59	Temora longicornis	8.46	Paracalanidae	8.79
	Acartia spp.	8.2	Acartia spp.	7.85	Acartia spp.	8.39
	Oncaea spp.	7.2	Oncaea spp.	7.67	Euterpina acutifrons	7.48
	Centropages spp.	6.87	Paracalanidae	7.15	Oncaea spp.	7.38
	Coryceidae	6.29	Euterpina acutifrons	7.1	Oithon aspp.	6.31
	Oithona spp.	5.77	Centropages spp.	6.92	Centropages spp.	5.99
	Euterpina acutifrons	4.98	Coryceidae	6.49	Coryceidae	5.97
	Metridia spp.	4.54	Metridia spp.	4.79	Metridia spp.	4.71
	Calanus helgolandicus	4.4	Oithona spp.	3.74	Pseudocalanus elongatus	3.46
	Candacia armata	2.65	Microsetella spp.	3.06	Candacia armata	3.04

Table 5 :

 5 Selection of the most influential variables explaining the most the patterns of copepod community using a forward selection. The eigen values sums (a measure of explained variance, R²), "F" statistic and p-values were reported.

	Variables order	Eigenvalues	F
		sums
	Sub-Surface Chla>20µm (Microphytoplankton)	0.35	65.28	**
	Based biomass
	Equivalent fresh water height	0.42	15.47	**
	Deficit of potential energy	0.45	7.50	*
	Sub-surface temperature	0.49	8.84	**

Codes:0 '***';0.001 '**';0.01 '*'

Acknowledgments

We thank the entire PELGAS teamresearchers, technicians, students, captains and crews of R/V "Thalassa"who have contributed to the collection of the PELGAS samples since 2003.

We would like to express our thanks to two teams' laboratory, LIENSs and EMH and especially, M. Jacques, P. Petitgas, M. Doray, and P. Bourriau. We are grateful to Proofreading and Dr. Sophie Domingues-Montanari for English corrections. We also grateful to Céline Lavergne for its statistical advices. The IUF (Institut Universitaire de France) is acknowledged for its support to PB as a Senior Member. This research was supported through a PhD grant for A. Dessier from the Conseil Régional de Poitou-Charentes and by the European project REPRODUCE (EraNet-Marifish, FP7). This work was supported by the "Plateau Microscopie" of the LIENSs laboratory.

 We demonstrated that the spatial structure found in the Bay of Biscay is attributable to continental outflow, although some interannual variability occurred in the range of the values observed.

 We generated interpolation maps that represent a valuable foundation for future studies in the Bay of Biscay. Supplemental figure 1: 10. 7 -11.3 11. 3 -11.7 11. 7 -12.3 12.3 -12.8 12.8 -13.3 13.3 -13.6 13.6 -13.8 13.8 -14.1 14.1 -14.3 14.3 -14.8 14.8 -15.3 15.3 -15.8 15.8 -16.3 16.3 -16.8 16.8 -17.3 17.3 -17.8 17.8 -18.3 18.3 -18.8 18.8 -19.3 19.3 -19.8 Temperature (°C)


Diadié Sow

Pierre Couturier

Abdelhak Imoussaten

Jacky Montmain

A qualitative evaluation of mechatronic concepts

Keywords: mechatronic design, evaluation, conceptual design, multi criteria decision support, qualitative possibility

How to make, early in the development cycle of a mechatronic product, the most promising design choices as regards the customers' requirements and being at the limit of what is technically feasible? To contribute to solve such a difficult problematic we propose an original qualitative evaluation method based on qualitative possibility theory. The method takes into account the uncertainty weighing on the designers' knowledge at this design stage. The method may help the decision makers to select the most satisfying design alternatives considering not only the preference of the stakeholders but also the feasibility of the alternatives.

I. INTRODUCTION

Mechatronics design is an interdisciplinary activity which aims at developing, at lowest costs, high quality and innovative products by integrating always more functionality while respecting severe geometrical constraints. In nowadays competitive marketplace, studying and finalizing several mechatronic concepts before selecting only the most satisfactory one is a too much expensive and time consuming way of working. So, the best design choices have to be made at the earliest during the product design stages [START_REF] Hehenberger | Hierarchical design models in the mechatronic product development process of synchronous machines[END_REF]. However, rating the merit factor of different alternative solutions, from the conceptual design stage, is generally subject to uncertainty and inaccuracy due to the incompleteness inherent at this stage, in both the product specification and the available product models. That is why the problem of assessing the consequences on the final product performance of early choices from among several design alternatives (DAs) has still not been resolved effectively [START_REF] Torry-Smith | Mechatronic design -still a considerable challenge[END_REF].

Moreover if setting ambitious targets when designing a product can be business profitable, such targets have to remain within the reach of the enterprise [START_REF] Hauser | The house of quality[END_REF]. So the problem to be solved by the industrials is how to make, early in the development cycle of a product, the most promising design choices as regards the customers' requirements and being at the limit of what is technically feasible as they are aware of their available enterprise-level skills.

In such a context, this paper addresses the effectiveness evaluation of mechatronic product at the conceptual phase of their design. At this aim an original qualitative evaluation approach is proposed that takes into account both the preferences of the stakeholders and the belief of the design teams in the feasibility of the DAs.

Section 2 presents some evaluation methods applicable when adopting systems engineering as a suitable framework for mechatronics design. Section 3, proposes a qualitative approach of DA evaluation in conceptual design and the steps to be followed to lead such qualitative evaluation. An illustrative example of mechatronic concepts evaluation is presented in section 4. Finally section 5 gives some conclusions and perspectives.

II. SE FRAMEWORK AND APPLICABLE EVALUATION METHODS

A. Systems engineering and mechatronics

Systems Engineering (SE) is an interdisciplinary and collaborative approach based on the standards ISO/IEC 15288 [START_REF]IEEE Standards 15288.2008, Systems engineering -System life cycle processes[END_REF], ANSI/EIA 632 and IEEE 1220, as well as on conceptual guidelines, e.g. SEBoK [START_REF]System Engineering Book of Knowledge[END_REF] and best practice guidelines, e.g. INCOSE handbook [START_REF]INCOSE, System Engineering (SE) Handbook Working Group, System Engineering Handbook, A Guide For System Life Cycle Processes And Activities, Version 3.2.1[END_REF] or Nasa handbook [START_REF][END_REF]. The interest of such a framework for mechatronics design is that it provides the multidisciplinary design team members with common and sharable concepts and vocabulary relative to the system level design, i.e. a level above the particular discipline points of view (Fig. 1). It is only when the system level concepts and architectures have been defined resulting from several design iterations and taking into account the mechatronic disciplines requirements and constraints (these primary loops should solve the coupling between mechatronic pillars as defined in [START_REF] Hehenberger | Hierarchical design models in the mechatronic product development process of synchronous machines[END_REF]) that the identified disciplinary parts can be specified and developed in parallel and then integrated in a final product as described by the V-model of the VDI2206 guideline [START_REF] Gausemeier | VDI 2206 -a new guideline for the design of mechatronic system[END_REF]. Fig. 1. Technical and support processes in SE [START_REF] Couturier | Tracking the consequences of design decisions in mechatronic systems engineering[END_REF] According to the SE framework five technical processes run in an iterative manner when engineering a system. These processes, identified in Fig1, are [START_REF]System Engineering Book of Knowledge[END_REF]: mission analysis, stakeholders' needs and requirements analysis, definition of system requirements, design of logical and physical architecture. They are supported by three services, namely: system verification, system validation, and system analysis. System analysis is an activity that evaluates one or more system artifacts created during the activities involved in synthesizing possible solutions [START_REF]System Engineering Book of Knowledge[END_REF]. System analysis allows ensuring that decisions are based on necessary relevant knowledge and are duly justified and traceable to stakeholders needs. In particular, criteria on which rely both architecture evaluation and value assessments should be derived from functional and non-functional requirements [START_REF] Couturier | Tracking the consequences of design decisions in mechatronic systems engineering[END_REF].

B. Evaluation approaches for mechatronics

An evaluation is requested each time engineering choices must be made or justified, e.g. choice of major operations and solution concepts, research and resolution of inconsistencies between requirements, choice of logical vs. physical architecture.

Though SE does not promote any evaluation approach or method it is generally assumed that the evaluation process includes the generic activities consisting of: defining the evaluation objectives ("why and what"), preparing the job ("how"), producing results and conducting sensibility analyses ("do and check"), and finally delivering outcomes ("conclude").

How activities' of the evaluation process specify the relevant decision-making model. Such a model takes into account core elements such as evaluation criteria, stakeholders' preferences, the scoring function used to assign desirability levels to system attributes, and the aggregation methods chosen to estimate the DA overall desirability levels used to classify or rank design solutions.

The 'why and what' activity is critical since it orientates the engineering effort that has to be turned towards stakeholders' needs. At this aim, Quality Function Development (QFD) [START_REF] Hauser | The house of quality[END_REF] fosters an enhanced consideration of the customer's voice. Four successive 'Houses of Quality' based on matrix formalism are built to cover the product development and production processes. Fig. 2. Technical and support processes in SE [START_REF] Hauser | The house of quality[END_REF] The first of them, shown in Fig. 2, helps to: structure and prioritize the customers' needs, evaluate competitors strengths and weak, translate the needs into engineering characteristics (technical requirements in SE language), identify the correlations between engineering characteristics, consider how strongly needs are influenced by the design characteristics, estimate the importance and difficulty of the engineering characteristics, estimate the target values for the engineering characteristics. The next house of Quality is built on the same model and aims at finding which parts (element of architecture) characteristics can achieve the engineering characteristics.

QFD helps to define the importance of engineering characteristics but does not consider any customers' preferential interactions. It does not suggest how to take into account the difficulty to achieve engineering characteristics. So, QFD is an interesting support for decision making in the early stage of designing a product but does not provide evaluation or assessment rules or methods.

Among the evaluation methods of solution principles, the Pugh matrix [START_REF] Frey | The Pugh Controlled Convergence method: model-based evaluation and implications for design theory[END_REF] is a type of matrix diagram that allows for the comparison of several DAs at the conceptual stage of design: the columns of the Pugh matrix are labeled with design concepts, one of which acting as a baseline, the rows are labeled with criteria by which the DAs are compared to the baseline. The importance of criteria can be revealed by some ponderation. Each cell in the matrix is marked +, -or S whether a design concept is better than, worse than, or roughly the same as the baseline. After scoring (using for instance a weighted sum operator) the total of + and -gained by each candidate, different decisions can be made, for instance: eliminate certain weak concepts; further development of some concepts; merge some concepts. The Pugh matrix should be run iteratively as part of a convergence process. The method is questionable as the sum of positive or negative qualitative impacts generally does not represent the impact of a DA on the global satisfaction of the stakeholders. Moreover eventual preferential interactions cannot be taken into account and there is no consideration about the difficulty to realize the DAs.

The multiattribute utility theory (MAUT) remains the welldefined framework to assess alternatives described by several attributes. It provides axiomatics for rational decision making under multiple objectives [START_REF] Keeney | Decisions with Multiple Objectives: Preferences and Value Tradeoffs[END_REF]. In the framework of MAUT some works focuses on defining most important criteria to improve without actual feasibility considerations [START_REF] Labreuche | Determination of the criteria to be improved first in order to improve as much as possible the overall evaluation[END_REF], which may lead to define unachievable objectives. Reversely, some other works using goal model framework, focuses on the capacity to achieve specific goals while not taking into account the commitment to do it [START_REF] Giorgini | Reasoning with Goal Models, 21 st Int. Conf. on Conceptual Modeling (ER02)[END_REF][START_REF] Felix | Relationships between goals in multiple attribute decision making[END_REF], which may lead to focus on meaningless goals. Some attempts seem nevertheless to be aware of the necessity to deal with both aspects when improving and designing systems [START_REF] Montmain | Multi-criteria improvement of complex systems[END_REF][START_REF] Fleurey | Modeling and validating dynamic adaptation[END_REF].

In [START_REF] Sow | Between policy aspirations and capacity to act: how designing achievable goals[END_REF] we propose to identify the coalition of criteria to be improved first while being the least difficult to satisfy. The priority between criteria coalitions is founded upon an estimation of the expected gain as defined in [START_REF] Labreuche | Determination of the criteria to be improved first in order to improve as much as possible the overall evaluation[END_REF] by 'an index value'. The computation of the capacity to achieve a subset of criteria has been originally proposed in [START_REF] Montmain | Multi-criteria improvement of complex systems[END_REF]. The method in [START_REF] Montmain | Multi-criteria improvement of complex systems[END_REF] consists in merging the qualitative confidence in the impacts (eventually contradictory) of design parameters on each expected performance and in deducing the overall confidence in the impact a DA may have on a set of criteria. However, in [START_REF] Montmain | Multi-criteria improvement of complex systems[END_REF] only binary choice between improvement and deterioration is proposed, to each of them being associated a degree of belief. In this paper we investigate a qualitative evaluation approach taking into account the stakeholders' preference, several possible levels of satisfaction on criteria and the designers' confidence on the reachability of such satisfaction levels in relation with available means and resources.

III. A QUALITATIVE EVALUATION APPROACH

A. Problem characterization and definitions

In order to design a mechatronic product, the design parameters are the parameters whose values are chosen by the designers. For example, an autonomous robot can be characterized by several design parameters such as: type of rolling base, size of the body, engine type, embedded energy capacity… Each acceptable vector of values of these parameters is a configuration of the robot. Let us denote = {1,2, . . } the set of criteria that the system has to satisfy and , , . . the design parameters of the system. For instance, = ( , , . . , ) is an initial configuration of the system. Let us denote = { , , . . , } the set of actions applied on the initial configuration ( , , . . , ) : corresponds to the action of modifying the value of the j th parameter. Let us assume that to each criterion ∈ and each configuration is associated its current performance measure . The aim of the evaluation approach that we propose here is to synthesize qualitative and uncertain information about each configuration in order to find among a set of configurations the most satisfying ones taking into account the preference of the stakeholders and the feasibility of the configuration.

The synthetizing data processing is composed by two operations: (1) merging information concerning an alternative w.r.t to a criterion; (2) aggregation of the merged information on all the criteria.

The Qualitative Possibility Theory (QPT) offers an interesting representation framework for handling imprecise values pervaded with qualitative uncertainty [START_REF] Dubois | The use of the discrete Sugeno integral in decision-making: a survey[END_REF]. Let be an ordinal scale of levels of satisfaction, = {1,2, … , | |} where, for example, 1 corresponds to very bad…, and | | corresponds to very good. A possibility distribution is a mapping from to an ordinal scale = {0, , … ,1} where 0 corresponds to impossibility and 1 corresponds to total possibility. Imprecise scores (intervals, including single values) are modeled by a possibility distribution taking the value 1 in the interval and 0 outside. Blanks (absence of answers) are interpreted as a possibility distribution being 1 everywhere (modeling "unknown").

In a qualitative assessment approach, the Sugeno integral is an appropriate operator to aggregate performances related to criteria. Sugeno integrals are based on a capacity that allows taking into account the preferential interactions between criteria in the aggregated result [START_REF] Marichal | Aggregation operators for multicriteria decision aid[END_REF] [START_REF] Grabisch | A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid[END_REF]. Let us recall some notations concerning this integral. Let be an ordered qualitative scale with 1 its highest value and 0 its lowest value. A function : 2 → is called a fuzzy measure if it satisfies the following conditions:

1.

(∅) = 0 2.

( ) = 1 3.

is monotonic non decreasing for inclusion, i.e., for any , ⊆ ⊆ ⇒ ( ) ≤ ( ). The monotonicity of means that the weight of a subset of criteria cannot decrease when new criteria are added to it [START_REF] Dubois | The use of the discrete Sugeno integral in decision-making: a survey[END_REF]. Let = ( , , … , ) ∈ a vector of values in . The Sugeno integral of with respect to , denoted ( ) is given by:

( ) = max , (min( ( ) , ( ) ),
where is a permutation on such that ( ) ≤ ( ) ≤ ⋯ ≤ ( ) , with ( ) = { ( ), ( + 1), … ( )}.

B. Steps of the proposed qualitative evaluation

Let us select a configuration as a baseline to which all other configurations should be compared (as in the Pugh matrix) by one or a panel of experts. Some expertise is expected to provide, for each action and each criterion i: -A score, i.e. an estimation of the degree to which an action improves or distracts the i th criterion compared to the baseline. Any score value is chosen in an ordinal scale comprising discrete values between 0 and 1 L . The score 0 is applied in case of satisfaction equivalent to the one of the baseline (0 : satisfaction is equal to the baseline one). A case of 'no opinion' is mentioned '?'. A score may be imprecise and represented as an interval of values in L.

-The confidence level which corresponds to the confidence one may have on the impact of action on criterion i.

takes its values in an ordinal scale (0 corresponding to not confident at all, level 1 to very confident). This parameter models the capability of an action to act as expected given the available means and resources in the studied project.

Then, to compute the global score of a configuration tacking into account the confidence of actions, the proposed method relies on the QPT as presented in [START_REF] Dubois | Using the transferable belief model and a qualitative possibility theory approach on an illustrative example: The assessment of the value of a candidate[END_REF]. The main steps of the method are resumed hereafter.

1) Incertitude modeling After collecting for each configuration

, the score and the feasibility data, the uncertainty attached to each score value on scale is formalized by a qualitative possibility ∶ → ({0, , , … ,1}). Firstly, the score is given as an interval. The highest possibility value 1, is attributed to the values of in the interval given by the experts, the lowest 0 is attributed to the other score in . Secondly, due to the lack of available quantitative knowledge at the preliminary stage of the design, a fuzzification transformation is applied to : it is assumed that adjacent score values to the one chosen by the experts receive non null possibility values. In the case of no opinion ("?") all the scores values (positive and negative) take the possibility 1. We denote the qualitative possibility distribution for the criterion when choosing action : it is the fuzzy representation of the score (single or interval) of action relatively to the criterion i. More precisely, since actions may improve or distract performances, two fuzzy representations are distinguished:

(resp. ) when the improving (resp. distracting) action is applied. * ( ), where * stands for + or -and k takes its value in , is then the degree of possibility of the score value k relatively to the criterion when applying .

2) Merging actions scores on a criterion

To get the global score (deterioration or improvement) of the envisaged configuration (a configuration corresponds to a set of actions that are parameters' changes relatively to the baseline) with respect to each criterion, we process the fusion of the elementary scores * , taking into account the level of confidence in their achievability. and are processed in parallel (improving and degrading actions are separately processed). This merging operation may be performed by a disjunctive or conjunctive operator, depending on whether or not, the scores are conflicting. The conflict is yet computed as proposed in [START_REF] Dubois | Using the transferable belief model and a qualitative possibility theory approach on an illustrative example: The assessment of the value of a candidate[END_REF]:

( ) = max ∈ ( min ( * ( ))
When ( ) = 0 then a disjunctive operator is used else a conjunctive one is preferred. Conjunctive fusion is applied only if there is no conflict in the above sense.

For instance, given a configuration and a criterion i, in the case of a disjunctive operator the qualitative possibility distribution * is computed as follows:

∀ ∈ , * ( ) = max ( ( * ( ), ))

We assume here that = .

So any value of L having high possibility degree and resulting from an action with a high degree of confidence is favored. Moreover, in case of low confidence or low possibility degree ( ) then the minimum of the two values has little chance to be the result.

In case of no conflict at all, the qualitative possibility distribution * should be computed by a conjunctive operator as follows:

∀ ∈ , * ( ) = min ( ( * ( ), ( )))

where ( ) denotes the value corresponding to the reversal scale of S (e.g., the equivalent of 1in the scale [0,1]). * has finally to be normalized before applying the extension principle in the next aggregation step.

3) Aggregation of scores on several criteria

At the issue of step 2), to each configuration and for each criterion i is associated two normalized qualitative possibility distributions (merging improvement values) and (merging deterioration values). Let ∶ → be a fuzzy measure defined on the set of criteria . For ⊆ , ( ) represents the importance of the expected improvement of criteria in I according to the preference of the stakeholders. This fuzzy measure is then used to build the aggregation operator, i.e. the Sugeno integral in our qualitative assessment framework.

The global score of the configuration with respect to all the criteria can be computed: the criteria distributions (resp.

) are merged into two possibility distributions and over L using the extension principle of Zadeh:

∀ ∈ , * ( ) = max * ( ,.., ) ∈ ( ( * ( ), * ( ), … , * ( )))

where the computations of and are inspired from [START_REF] Grabisch | The Symmetric Sugeno Integral[END_REF]: -for the improvement scores (better than those of the baseline), for any in {0 , … ,

, where is a permutation on such that ( ) ≤ ( ) ≤ ⋯ ≤ ( ) , with ( ) = { ( ), ( + 1), … ( )}.

-for the deterioration scores (worse than those of the baseline), for any in {0 , … ,

, where is a permutation on such that -

( ) ≤ -( ) ≤ ⋯ ≤ -( ) , with ( ) = { (1), (2), … ( )}.

4) Exploitation of the results

In conclusion, to each configuration are associated two qualitative possibility distributions and . expresses the possibility to obtain improvement levels in L w.r.t the baseline and expresses the possibility to obtain deterioration levels. The most promising configurations are those with the highest possibility values (the highest feasibility confidence levels) on the highest improvement score values.

The configurations with a possibility of deterioration w.r.t. the baseline higher than the possibilities of improvement should be rejected. To this end, the following decision rule is introduced: max ( ) > max ( ) then the configuration is rejected ( = 0) otherwise the expected possibility of improvement is modeled by = max ( ).

Other more sophisticated strategies may be envisaged for the comparison of any two possibility distributions. The interested readers may refer to [START_REF] Imoussaten | A multicriteria decision support system using a possibility representation for managing inconsistent assessments of experts involved in emergency situations[END_REF].

Let us now illustrate below the proposed approach on an example.

IV. APPLICATION

A. Presentation of the example

The robotic challenge RobAFIS is organized annually by the French association of Systems Engineering AFIS to promote Systems Engineering practice in engineers' schools 1 . The scope of the challenge is for instance (Robafis_2013) to build an autonomous mobile robot able to compete with other robots and using some provided and imposed materials. Each robot is limited to a 0.3m square cube and has to achieve the following mission as quickly as possible: to grasp and transport some various colored spheres between several stock devices spread over a plan playground. Some dark lines are drawn on the ground to guide the robot between stock devices. The autonomous robot was broken down into four subsystems: a gripper device, sensors equipment, a rolling base, a control device. The programmable control device type is also imposed to the competitors. The physical alternatives (the possible robot configurations) depend on the design options and on the skills of each competitor. The preference model depends on the strategy followed by each competitor. The solution principles are resumed in Table 1. There are three principles for designing the gripper device, three for the rolling base and two for the sensors equipment. Four criteria are considered to decide between configurations: the sparsity of used components (Cr1), the robot speed capacity (Cr2), the reliability of the robot (Cr3), and the maintainability of the robot (Cr4).

B. Data of the example

Let us choose configuration (G3, R3, S2) as the baseline configuration. The experts provide the scores of the design parameters on scale ∶ 0 1 (+ for improvement, -for degradation) and the confidence level of their reachability values on scale = 0 1 as given in Tables 2 and3.

TABLE 2. SCORE VALUES

For instance, the experts are very confident in the fact that designers will succeed to build a robot that will move faster than the baseline robot if they choose the 'two wheels and a third free wheel' rolling base. They are not so sure that, with 1 robafis.fr such a rolling base they will succeed in achieving a better maintainability than the baseline. For instance, according to Table4, it is more important to have a fast and reliable robot than to have a fast and maintainable robot (it is a tactic choice). It is not so important to achieve simultaneously reliability and maintainability to win the competition.

C. Application of the method

Let us consider, for instance, the configuration = ( 1, 1, 1). Taking into account the expertise, the possibility values associated to the deterioration, equivalence and amelioration cases are ranked from left to right in vectors in Table 5. The possibility 1 is attributed to each score value provided by the experts (Table 2). For instance the possibility 1 at intersection of the S 1 line and Cr 1 column is affected to the score valuesand 0 . After a fuzzification we obtain the possibility values of Table 6. In Table 6 the possibility of scores adjacent to those proposed by the experts is here judged to be rather low (u value on the scale S). Then, because of conflictual scores, the fusion of score on each i th criterion is computed in Table 7 by: = max ( min( ( ), ))

Before the aggregation, the data have to be normalized as shown in Table 8 (possibility values are translated until the maximum possibility value is 1). 2 and of reachability values in Table 3. No guarantee can be given upon the real performance of the robot since it depends on the pertinence of the data provided by the experts in Table 2 and3. V. CONCLUSION In this paper is proposed a qualitative method for the evaluation of concepts in the preliminary design stage of complex products such as mechatronics products. The method is based on qualitative possibility and explicitly takes into account the uncertainty of the designers' knowledge at this design stage. Moreover the method may help the decision makers to select the most satisfying design alternatives considering not only the importance of sets of objectives (described through criteria) but also the confidence of the designers in their reachability. Although an illustration example has been provided, more concrete cases have to be treated for deeper validation of the method. Further research work is engaged firstly to consider aggregation of positive and negative scores and secondly to extend the method in a fuzzy logic framework.

  wheel drive and one third free wheel S2: one color sensor for following the dark line, one color sensor for recognizing the

Configuration (G 1 ,

 1 R 1 , S 1 ) should be rejected since its possibility of degradation is higher than the possibility of amelioration. 'u' possibility values for the baseline configuration (G 3 , R 3 ,S 3 ) are due to the 'fuzzification'. Other two configurations should be retained. Configuration (G2, R2, S1) should be preferred since max ( 2, 2, 1)( ) = 1 > (max ( 2, 1, 2)( ) = ). The validity of the proposed approach is analyzed by verifying that the final result values change accordingly to the changes of the scores values in Table

TABLE 1 .

 1 SOLUTION PRINCIPLES

	Gripper device	Rolling base	Sensors equipment
	G1: Fork (taking	R1:	Four	S1: two color sensors for following
	the sphere from	wheels rolling	the dark lines, one light sensor for
	below)	base		recognizing the sphere color

TABLE 3 .

 3 REACHABILITY VALUES

Table 4

 4 provides an example of competitors' preferences between the criteria as a qualitative capacity function defined on the set of all the possible criteria combinations, given the qualitative scale .

TABLE 4 .

 4 EXAMPLE OF COMPETITORS' PREFERENCE

TABLE 5 .

 5 POSSIBILITY VALUES FOR ap=(G1,R1,S1)

TABLE 6 .

 6 POSSIBILITY VALUES AFTER FUZZYFICATION

TABLE 7 .

 7 DATA FUSION FOR EACH CRITERION

TABLE 8 .

 8 NORMALISATIONFinally the result of the aggregation is given in table9for 4 examples of the 18 configurations.

TABLE 9 .

 9 FINAL SCORE & FEASIBILITY