Xiao Yi Zhou

Franziska Schmidt

Bernard Jacob

François Toutlemonde

Accurate and up-to-date evaluation of extreme load effects for bridge assessment

Keywords: Bridge, Extreme effects, Extrapolation, Assessment of structures

In the 1990"s, during the background works of Eurocode 1991-2 (Traffic loads on bridges), extreme loads and extreme load effects have been evaluated by using WIM data recorded at various European locations. The most used WIM data file is a WIM data record, 2-week long, recorded at Auxerre on a French heavy trafficked motorway in 1986. Today, WIM records are longer and much more accurate, thanks to the fast progresses of the WIM technology. Thus they give a better account of the traffic variations along time. After the action COST323, self-calibration of WIM system has been generalized and the sensor and software technologies were improved. Therefore, uncertainties in the calculation of traffic effects on bridges are lesser than 25 years ago. To up-date the maximum load effects calculated in the late 1980"s and used for the calibration of the load model LM1 of the Eurocode 1991-2, using the most recent WIM data, but also advanced extrapolation methods, extrapolations are made using various methods (Gaussian fitting, Gumbel fitting, Rice formula, Generalized Extreme Value, ..). Confidence intervals on the extremes that are found are derived. Among the several extrapolations methods found in the literature, a choice was made according to the objectives and the chosen methods were applied to traffic loads and traffic load effects. Results are discussed with respect to the method robustness vs the traffic data, the period of extrapolation and the load effect considered, as well of the likelihood of the final results.

Résumé

Dans les années 1990, durant les travaux préparatoires à l"Eurocode 1991-2 (Charges de trafic sur les ouvrages d"art), les charges extrêmes et les effets extrêmes des charges ont été évalués en utilisant des données de trafic enregistrées sur divers sites européens. L"enregistrement de trafic le plus utilisé correspond à deux semaines de données, enregistrées sur l"autoroute A6 à Auxerre en 1986, avec un trafic lourd intense. Aujourd"hui, les fichiers de trafic dont nous disposons sont de durées plus longues et de précision supérieure, grâce aux améliorations apportées à la technologie du pesage en marche. Ainsi ils donnent une meilleure vision des variations de trafic au cours du temps. Après l"action COST323, l"étalonnage automatique des stations de pesage en marche a été généralisé et les technologies des capteurs et de traitements ont été améliorées. Tout ceci a réduit les incertitudes des mesures de trafic, aujourd"hui très inférieures à celles d"il y a 25 ans. Afin d"actualiser les charges extrêmes du trafic calculées à la fin des années 1980 et utilisées pour le calage du modèle de charge LM1 de l"Eurocode 1991-2, des enregistrements récents de trafic et des méthodes d"extrapolation différentes ont été utilisées. Des intervalles de confiance ont pu être déterminés. Parmi les différentes méthodes trouvées dans la littérature, un choix a été réalisé qui a été appliqué aux charges de trafic et effets des charges de trafic. Les résultats sont discutés en fonction de la robustesse de la méthode par rapport aux données et l"effet considérés.

Mots-clé: Pont ; Effets extrêmes ; Extrapolation ; Evaluation de structures.

Introduction

A bridge structure should have the capacity to withstand the load expected with a given probability over the design life: it is stated in Eurocode 1 [START_REF] Afnor | NF EN 1991-1-2, Eurocode 1 : Actions sur les structures[END_REF] that the structures should be able to resist to the characteristic values for 1000-year return period, which means events with a probability of crossing of 5% in 50 years.

But it is impossible to collect enough data to determine the characteristic value of load effect expected over lifetime of loading. Even getting sufficient data for short return periods would require several samples of short period data in order to assess the corresponding probability, which is not currently available. Therefore, some extrapolation should be performed.

To develop the live load model of AASHTO, Nowak [START_REF] Nowak | Bridge live-load models[END_REF] proposed a method that uses normal probability paper. This method had and still has great influence on other American researchers, for example [START_REF] Kozikowski | WIM based live load model for bridge reliability[END_REF], [START_REF] Sivakumar | Protocols for collecting and using traffic data in bridge design[END_REF]. Straight lines are fitted to the tails of the load effect distributions plotted on normal probability paper. The extreme value of load effect can be easily determined by the inversed normal distribution, and the cumulative distribution of maximum load effect is calculated by raising the fitted distribution to a certain power according to the extreme value theory. Although the method is extensively used, the choice of the tail fraction is empirical and subjective: Nowak [START_REF] Nowak | Live load model for highway bridges[END_REF] does not state how he selects the beginning of the tail and Sivakumar uses the upper 5%, see [START_REF] Sivakumar | Protocols for collecting and using traffic data in bridge design[END_REF].

In the background studies for developing the traffic load model of Eurocode 1, five methods have been proposed to predict extreme traffic load or traffic load effect [START_REF] Jacob | Probabilistic Traffic Load Models and Extreme Loads on a Bridge[END_REF], [START_REF] Flint | Extreme traffic loads on road bridges and target values of their effects for code calibration[END_REF]. These are:

 a half-normal curve fitted to the end of the histogram,  a Gumbel distribution fitted to the tail of the histogram,  the asymptotic extreme distribution obtained with extreme value theory,  Rice"s formula for stationary Gaussian processes,  Monte-Carlo simulation of artificial traffic and Gumbel extrapolation.

Among these methods, Rice"s formula is different from the others as it uses the full history of the load effect. It has been proved that if the process is Gaussian and stationary, the up-crossing intensity can be expressed by Rice"s formula [START_REF] Rice | Mathematical analysis of random noise[END_REF]. In practice, the load effect is a mixed Gaussian process, therefore the level crossing rate has a Gaussian tail. Cremona [START_REF] Cremona | Optimal extrapolation of traffic load effects[END_REF] proposed an automatic method to select the optimal threshold from which the tail can be expressed by Rice formula. But the mathematical assumption of Gaussian stationary process is a strong requirement, as the required length of the influence line of interest is large compared to the length occupied by the single vehicles [START_REF] Ditlevsen | Traffic loads on large bridges modeled as white-noise fields[END_REF]. The approach may be not suitable to common load effect of short-to medium-span bridge as it has sharply varying nonzero influence area.

In recent years, the extreme value theory has been used for modelling traffic load effect. Many authors approach the problem by identifying the maxima load effect recorded during a loading event or in a reference period such as a day or a week, and then fit these maxima to an extreme value distribution. [START_REF] Bailey | Site specific probability distribution of extreme traffic action effects[END_REF] determined that the Weibull distribution is the most appropriate to model the extreme traffic load effect. Caprani et al. [START_REF] Caprani | Characteristic traffic load effects from a mixture of loading events on short to medium span bridges[END_REF] classified the loading events by the number of trucks involved in the maximal load effect, and then the maxima of each loading event are modelled by GEV distribution. This block maxima approach is wasteful of data as only one data point in each block is taken. The second highest value in one block may be larger than the highest of another block and this is generally not accounted for.

A peaks-over-threshold (POT) approach exists that avoids this drawback, by using the Generalized Pareto Distribution (GPD). Indeed, due to the advances in extreme value theory, the GPD emerged as a natural family for modelling crossings over a high threshold. The POT approach has shown its importance and success in a number of statistical analysis problems relating to finance, insurance, hydrology, geographical phenomena, and other domains [START_REF] Holmes | Application of the generalized Pareto distribution to extreme value analysis in wind engineering[END_REF]. However, despite the sound theoretical basis and wide applicability, fitting of this distribution in practice is not a trivial exercise. Two main factors, the choice of threshold and the choice of the parameter estimator, affect the accuracy of the the return values estimations. An extensive discussion of the various parameter estimation methods has been given by Zea Bermudez and Kotz [de Zea

Bermudez & Kotz, 2010a], [de Zea Bermudez & Kotz, 2010b]. Scarrott and MacDonald [START_REF] Scarrott | A review of extreme value threshold estimation and uncertainty quantification[END_REF] reviewed the threshold estimation methods. While each methodology has its advantages and disadvantages, traditional parameter estimator such as maximum likelihood is undefined in some regions of the parameter space. Due to these difficulties, the POT approach has not gotten much attention for modelling extreme bridge load effects [START_REF] James | Analysis of Traffic Load Effects on Railway Bridges[END_REF].

The purpose of this paper is to introduce the use of the extrapolation methods on recent WIM data and the data used in the 1980"s during the background works of Eurocode 1991-2 in order to assess the effect of changing traffic on bridges. The rest of the article is organized as follows: section 2 provides some comparison between traffic of the 1980"s as recorded in Auxerre in 1986 and recent WIM data. Section 3 applies various extrapolation methods to these two WIM data files and summarizes the results. Discussions are carried out and conclusions are drawn in Section 4. More information on the extrapolation methods used in this article can be found in [START_REF] Zhou | Statistical analysis of traffic loads and traffic load effects on bridges[END_REF].

WIM data files

The first WIM data used in this study have been collected in 1986 at a WIM station, in Auxerre on the heavy trafficked A6 motorway. In addition, recent traffic data, recorded by a piezo-ceramic weigh-in-motion (WIM) system on the A9 motorway near Saint Jean de Vedas, in South-Eastern France, was used. The traffic of these two locations can be compared, to assess that they represent the national traffic. The data of 1986, recorded in Auxerre, have been used in the 1990"s to calibrate the Eurocode 1, part 2, on traffic loads on bridges. As shown in Thus the mean flow significantly increased since 1986, and the hour by hour daily flows are also rather different between the two traffic records (Figure 2). Both patterns are not only affected by the traffic increase along the time, but by the differences of location and type of traffic. In Auxerre 1986, a country side location with only long distance transport, the hourly flow rate varied between 80 and 220 vehicles/hour with two peaks in the morning and in the evening. In St Jean de Vedas in 2010, with a combined local and long distance traffic in a peri-urban area, the hourly flow is low at night and much higher along the day, with two peaks in the middle of the morning and afternoon.

Because of all these differences in the traffic patterns, but also in the load patterns, the extreme load effects experienced by the bridge have to be re-assessed.

The gross vehicle weight histograms of both traffic records are presented in Figure 3. As usually, there are two main modes, centred around 15 and 40 t. The first mode contains the smaller trucks (2 and 3-axle) and not fully loaded large trucks, while the second mode close or just above the legal limit contains fully loaded 5-axle and more trucks. The second mode is much more concentrated because it contains a homogeneous population of trucks. It is highlighted that the maximum allowed GVW was 36 t in 1986, and 40 t in 2010. The overload rate was much higher in 1986, as well as some measurements errors due to the early WIM systems, which induced a more scattered weight distribution. In addition a first class just above the 3.5 t lower limit of heavy commercial vehicle is highly populated with overloaded vans. But these vehicles do not influence the extreme load effects on bridges.

Finally the GVWs were modelled by a bi-modal Gaussian distribution. The traffic composition (Figure 4) shows that 5-axle trucks are the most frequent trucks, with a proportion which increased since 1986. The proportion of articulated trucks (4 and 5-axle) remained very stable, with a switch from 4 to 5-axle (2 to 3-axle semi-trailer). The characteristics of the trucks affect the load effect on bridges (the tridem is the most important element to take into account).

All these elements prove that it is important to re-assess the existing bridges, built according to Eurocodes calibrated with the traffic of 1986, by using recent traffic data files.

Extrapolated values for the considered WIM data

The results of the calculations done, both with the traffic data of 1986 and of 2010, are reported here for various extrapolation methods.

The first extrapolation method is fitting the level-crossing histogram to Rice formula, to assess the load effect level being exceeded with a given probability, which is called the characteristic values.

The second method is the Generalized Pareto Distribution (GPD) using the mathematical property that crossings of a given threshold follow a statistical distribution called Pareto distribution. That allows assessing the characteristic values.

The third method is named Generalized Extreme Value (GEV). The maximum values of the load effects on bridges are distributed as one of the generalized extreme value function, i.e. Gumbel, Fréchet and Weibull.

These methods give different results shown in Table 2, provided by [START_REF] Zhou | Statistical analysis of traffic loads and traffic load effects on bridges[END_REF]. Variations between the extrapolated effects with these various methods can be observed. This is a fact that has also been observed in other domains, as hydrology or fiancé. But it has been shown [START_REF] Zhou | Statistical analysis of traffic loads and traffic load effects on bridges[END_REF] that these different results are quite similar when the traffic data is accurate and long (several months). But it also highlights the fact that choosing the extrapolation methods is still an issue.

St Jean de Vedas, A9, 2010

Rice formula 10229

GPD 9631

GEV 9455

Table 2: Extrapolated effect values on a given bridge, for the various extrapolation methods and WIM data (1986 and 2010).

When comparing the effect of these two traffic files with the effect of the load model 1 of Eurocode 1, two cases can be found: spans under 30 meters and spans over 30 meters. For spans smaller than 30 meters the effect of actual traffic is higher than the effect of the traffic recorded in 1986. For spans longer than 30 meters, in which the governing case is the congested traffic, the extrapolated value of 1986 is higher than the extrapolated effect of the actual traffic. This is due to higher scattering of the "old" traffic data.

Conclusion

In all cases, it may be found that the effect induced by the load model 1 of Eurocode 1 is higher than the effect of the measured traffic. The safety margin seems to be reduced. But one issue remains to be solved: which dynamic amplification factor should be applied? Indeed, there is already some dynamic amplification included in the WIM data, but it should be assessed. And which remaining amplification factor should be taken into account when assessing a bridge?

Conclusion

Bridges have been built according to existing regulations, while the traffic is evolving in volume and frequency along the time. Extreme load effects and fatigue effects need to be assessed when reassessing bridges designed by a code or a past traffic, against the effects induced by the current traffic.

This article relates some works done on the issue of extreme load effects. Two WIM data files have been used, one recorded in 1986 which has been used to calibrate the Eurocodes, and another measured in 2010, while regulations on weights and dimensions had changed. Several extrapolation methods have then been used and compared to the load model of the Eurocode 1.

The safety margin seems to have been reduced, but the issue of the dynamic amplification remains.

Figure 1 :

 1 Figure 1: Location and length of WIM data files used in this study.

Figure 2 :

 2 Figure 2: Hourly flow rates comparison Auxerre 1986/St Jean de Vedas 2010.

Figure 3 :

 3 Figure 3: GVW (Gross Vehicle Weights) histograms in Auxere 1986 and St Jean de Vedas 2010.

Figure 4 :

 4 Figure 4: Traffic composition in 1986 (Auxerre, left) and in 2010 (St Jean de Vedas, right).

Figure 5 :

 5 Figure 5: Extreme mid-span bending moment for simply supported bridges of various span lengths, according to various methods.

Table 1

 1

		Auxerre, A6, 1986	Saint Jean de Védas, A9, 2010
	Number of days	7	138
	Number of trucks	46049	83546
	Mean flow (veh/hour)	107	259
	Mean flow (veh/day)	2558	6217

, significant changes occurred in weights and dimensions of trucks from 1986 till 2010. In 2010, 835468 trucks have been recorded; after cleaning, 581011 trucks over 86 days are drawn from the original data by excluding obvious false recordings, week-ends and system inactivity days. Nowadays, long and reliable data files may be recorded (e.g., a 138-day long traffic data in 2010). Moreover, as shown Table

1

, the mean flow has been more than doubled since 1986.

Table 1 :

 1 Comparison of the WIM data from 1986 and 2010.

Acknowledgements

The authors greatly acknowledge the financial support provided by the Marie Curie Initial Training Network TEAM (Training in European Asset Management) project.


J F Ponge

L Deharveng

Linking species, traits and habitat characteristics of Collembola at European scale

Keywords: Collembola, environmental filtering, habitats, broad scale distribution, species traits, species assemblages, sensory organs

) document to what extent environmental variables and species trait assemblages are related and which trends could be found in trait/environment relationships. The impact of vertical stratification, habitat closure, humus form, soil acidity, soil moisture, temperature, and to a lesser extent rainfall and altitude on species distribution, firstly revealed by indirect gradient analysis (correspondence analysis, CA), was further shown to be significant by direct gradient analysis (canonical correspondence analysis, CCA). RLQ analyses were performed to find linear combination of variables of table R (environmental variables) and linear combinations of the variables of table Q (species traits) of maximum covariance weighted by species occurrence data contained in table L. RLQ followed by permutation tests showed that all tested environmental variables apparently contributed significantly to the assemblages of the twelve species traits studied. A convergence was observed between traits related to vertical stratification and those related to habitat closure/aperture. Well-developed locomotory organs (furcula, legs), presence of sensorial organs sensitive to air movements and light (e.g. trichobothria and eye spots), spherical body, large body size, pigmentation (UV protection and signalling) and sexual reproduction largely occur in epigeic and open habitats, while most of woodland and edaphic habitats are characterized by short locomotory appendages, small body size, high number of defense organs (pseudocelli), presence of post-antennal organs and parthenogenesis. Climate and especially temperature exert an effect on the assemblage of traits that are mostly present above-ground and in open habitats. The contribution of combinations of some environmental variables to the occurrence of each species trait was tested by linear, logistic or multinomial regression (Generalized Linear Models). Vertical stratification, followed by temperature, played a dominant role in the variation of the twelve studied traits. Relationships between traits and environment tested here shows that it is possible to use some traits as proxies to identify potential ecological preferences or tolerances of invertebrate species. However, a significant part of species distribution remained unexplained, probably partly because some traits, like ecophysiological ones, or traits involved in biotic interactions (e.g. competition) were unavailable. The present work is thus a first step towards the creation of models predicting changes in collembolan communities.

Further studies are required to inform ecophysiological traits, in order to complete such models. Moreover the niche width of species will have to be determined.

Introduction

Identifying the main factors that drive the composition of communities and the distribution of species is a fundamental goal in community ecology and is of particular importance for predicting biodiversity responses to environmental changes [START_REF] Belyea | Assembly rules within a contingent ecology[END_REF]. Selection of species by habitat constraints (deterministic process) is one of the four classes of processes that influence patterns in the composition and diversity of species [START_REF] Vellend | Conceptual synthesis in community ecology[END_REF]. Functional traits, (named "traits" hereafter), are well-defined, measurable properties of organisms, used comparatively across species, and that strongly influence organismal performance [START_REF] Mcgill | Rebuilding community ecology from functional traits[END_REF]. Focusing on the selection of species functional traits rather than only on species identity, allows to (1) identify mechanisms implied in the distribution of species and in the dynamics of biodiversity, (2) understand the mechanisms that shape communities comprised of many species (3) identify general patterns and hence, help to predict potential changes in the composition of communities, and consecutive ecosystem functioning, following disturbance [START_REF] Mcgill | Rebuilding community ecology from functional traits[END_REF][START_REF] Vellend | Conceptual synthesis in community ecology[END_REF]. The use of functional traits of species allowed to understand species responses to varied disturbances such as fragmentation, land use change or agricultural practices [START_REF] Cole | Relationships between agricultural management and ecological groups of ground beetles (Coleoptera: Carabidae) on Scottish farmland[END_REF][START_REF] Barbaro | Linking bird, carabid beetle and butterfly life-history traits to habitat fragmentation in mosaic landscapes[END_REF][START_REF] Ozinga | Dispersal failure contributes to plant losses in NW Europe[END_REF][START_REF] Vandewalle | Functional traits as indicators of biodiversity response to land use changes across ecosystems and organisms[END_REF]. For example, [START_REF] Ozinga | Dispersal failure contributes to plant losses in NW Europe[END_REF] showed that differences between plant species in characteristics (traits) involved in dispersal processes contribute significantly to explaining losses in plant diversity in response to habitat degradation. Species traits of diverse communities (plants, carabids, butterflies, birds, spiders) also have been shown to vary with environmental factors such as habitat fragmentation [START_REF] Barbaro | Linking bird, carabid beetle and butterfly life-history traits to habitat fragmentation in mosaic landscapes[END_REF], presence of planted hedgerows in highway verges [START_REF] Viol | Plant and spider communities benefit differently from the presence of planted hedgerows in highway verges[END_REF], post-fire age [START_REF] Langlands | Predicting the postfire responses of animal assemblages: testing a trait-based approach using spiders[END_REF], salinity [START_REF] Pavoine | Linking patterns in phylogeny, traits, abiotic variables and space: a novel approach to linking environmental filtering and plant community assembly[END_REF], agricultural land use and urbanisation [START_REF] Vandewalle | Functional traits as indicators of biodiversity response to land use changes across ecosystems and organisms[END_REF]. Nevertheless, the role of habitat constraints and dispersal abilities as filters, allowing only species with similar traits to assemble, has never been demonstrated at broad spatial scales, due to lack of suitable data, especially in soil invertebrates [START_REF] Barbaro | Linking bird, carabid beetle and butterfly life-history traits to habitat fragmentation in mosaic landscapes[END_REF][START_REF] Decaëns | Niche overlap and species assemblage dynamics in an ageing pasture gradient in north-western France[END_REF][START_REF] Makkonen | Traits explain the responses of a sub-arctic Collembola community to climate manipulation[END_REF][START_REF] Pavoine | Linking patterns in phylogeny, traits, abiotic variables and space: a novel approach to linking environmental filtering and plant community assembly[END_REF]. This may bias to a great extent the relationships between habitat preferences and species traits. Because the overall species response to habitat constraints involves trade-offs [START_REF] Uriarte | Multidimensional trade-offs in species responses to disturbance: implications for diversity in a subtropical forest[END_REF] between responses to different environmental factors (e.g. bedrock and climate, habitat openness and humidity, or temperature, or soil pH), it is easy to correlate erroneously a trait to an environmental factor. For example, the collembolan species Heteromurus nitidus, thought to strictly depend on soil pH since it was never found in soils at pH <5 in North and West of France (Ponge, 1980(Ponge, , 1993)), was later found in soils at pH <4 in south-western mountains of France (Cassagne et al., 2003(Cassagne et al., , 2004)). One way of avoiding this error risk is to determine habitat preferences of species over a wide range of habitats, encompassing a variety of temperature and altitude levels, at a scale close to the geographic distribution range of the species.

Moreover, despite the abundance, high diversity and essential functional role of soil invertebrates [START_REF] Hopkin | Biology of the Springtails (Insecta: Collembola)[END_REF][START_REF] Coleman | Fundamentals of Soil Ecology[END_REF], trait-based approaches were not explicitly used to study species/environment patterns and processes in these animal groups [START_REF] Vandewalle | Functional traits as indicators of biodiversity response to land use changes across ecosystems and organisms[END_REF]. Only studies focusing either on a restricted number of traits (especially dispersal), or of habitats have been made to assess the effects of land-use disturbance or climate change on soil communities [START_REF] Ponge | Decreased biodiversity in soil springtail communities: the importance of dispersal and landuse history in heterogeneous landscapes[END_REF][START_REF] Vandewalle | Functional traits as indicators of biodiversity response to land use changes across ecosystems and organisms[END_REF][START_REF] Decaëns | Niche overlap and species assemblage dynamics in an ageing pasture gradient in north-western France[END_REF][START_REF] Makkonen | Traits explain the responses of a sub-arctic Collembola community to climate manipulation[END_REF][START_REF] Bokhorst | Extreme winter warming events more negatively impact small rather than large soil fauna: shift in community composition explained by traits not taxa[END_REF].

The taxonomic Class of Collembola is a good model to address such questions, because it comprises a high number of species, occupying highly diverse habitats over a broad biogeographic area [START_REF] Hopkin | Biology of the Springtails (Insecta: Collembola)[END_REF]. Moreover, some authors have hypothesized, from field observations, the existence of five or more "eco-morphological groups" based on conspicuous morphological differences among Collembola living in diverse habitats [START_REF] Gisin | Ökologie und Lebensgemeinschaften der Collembolen im schweizerischen Exkursionsgebiet Basels[END_REF][START_REF] Delamare-Deboutteville | Microfaune du sol des pays tempérés et tropicaux[END_REF][START_REF] Rusek | A new classification of Collembola and Protura life forms[END_REF]. They classified collembolan species according to the relationships between some morphological characteristics and different gradients of vertical stratification (edaphic, hemiedaphic, epigeic) and soil moisture (hydrophilic, xerophilic), but no attempt was made to rely statistically morphological characteristics (traits) to environmental variables. Europe, as a wide area including a high diversity of landscape and vegetation types, is a favourable terrain for exploring multivariate relationship between species trait values, assembly processes, and environmental factors.

In this study, we asked the following questions: (1) What is the pattern of relationships between species assemblages and environmental variables at broad geographic scale? (2) Which environmental variables are associated with trait variation in Europe and which environmental variables contribute to the assemblage of local communities?

To this end, we compiled a large volume of data about species traits and environmental characteristics of sites where species have been collected throughout Europe.

To enable this, we created "Coltrait", a database collating traits and occurrence data of European collembolan species across a wide range of habitats, mostly from Northwest Europe. Occurrence data and associated descriptions of samples and sampling sites were either provided by our own studies, or collected in the literature. For traits, we selected collembolan characteristics expected to explain the distribution of species and the subsequent composition of species communities through three processes that drive patterns of community composition, namely (1) Abiotic components of habitat, (i.e. environmental variables) adaptation/selection (e.g. sensorial organs, cuticle protection, reproduction type); (2) Dispersal ability (e.g. locomotory appendages); (3) Biotic components of habitat selection (predator defence, e.g. detection by sensory organs, excretion of repulsive substances).

We firstly analyzed the impact of environmental variables on the distribution of species in Europe, and then we analyzed patterns of trait/environment relationships. Habitat characteristics and occurrences of collembolan species in these habitats were provided either by our own studies (Arpin et al., 1984(Arpin et al., , 1985(Arpin et al., , 1986;;Ponge, 1980Ponge, , 1993;;da Gama et al., 1994da Gama et al., , 1997;;Ponge, 2000;Loranger et al., 2001;Ponge et al., 2003;Gillet and Ponge, 2005) or were extracted from articles dealing with field studies on collembolan communities (e.g. Hågvar, 1982;Rusek, 1989Rusek, , 1990;;da Gama et al., 1994da Gama et al., , 1997;;Cassagne et al., 2003Cassagne et al., , 2004;;Dunger et al., 2004;Chauvat et al., 2007; see Appendix 1 for the complete list of references). We selected habitat characteristics (environmental variables) that were described for a large amount of samples, proved to be linked to the composition of communities at local scale in previous studies and/or were susceptible to "filter" species traits.

Materials and methods

We collected qualitative and quantitative data regarding site and sample descriptions (i.e. habitat characteristics) of 926 samples. Quantitative data (temperature and rainfall, altitude, soil pH and C/N) were directly incorporated in the data base (Table 1). We aggregated qualitative data into binary classes, assigning each sample to one of two classes for each modality of a given habitat: "1" if sampling occurred in the modality (e.g. close habitat, mull humus…), "0" if sampling did not occur in the modality and this for each field study. Modalities were (1) for habitat closure "close" (forest, wood), "open" (pasture, grassland, meadow, cultivated field) and "intermediate" (hedgerow, forest clearing, forest edge, heathland), (2) for soil characteristics "mull", "moder" and "mor" humus, "peat" and "cultivated" soil, "organic" and "organo-mineral" horizons and "hydromorphic" soils, (3) for vertical stratification "edaphic" (soil), "hemiedaphic" (litter), "epigeic-1" (ground surface and mosses), "epigeic-2" (herb layer, boulder), "epigeic-3" (tree trunk and canopy) (Table 1).

These data allowed us determining the occurrence of species and their traits along several environmental gradients: vertical stratification, habitat closure, soil acidity, decomposition rate (humus form and C/N), moisture, minimum annual air temperature (hereafter named "temperature"), minimum annual rainfall (hereafter named "rainfall") and altitude.

As sampling strategies varied between different studies and was not always precisely described regarding every sampling area, volume or depth of soil, we only compiled the presence/absence of species and not their abundance. We selected species that were recorded in at least 10 studies and 20 samples, providing a list of 58 most frequent collembolan species in Europe (Table 2). Habitat and species occurrence data covered the following countries:

Germany, United Kingdom, Austria, Belgium, Denmark, Spain, Finland, France, Italy, Norway, the Netherlands, Poland, Portugal, Czech Republic, Slovakia, Sweden, two thirds of samples being from France. Available data from Greece were discarded because the 58 selected species were generally present in the 17 above-cited countries while 33 species out of 58 were not recorded in Greece according to Fauna Europaea. Consequently, in our analysis, biogeographic segregation does not bias species distribution.

Species traits

We first listed traits that were most likely to influence community assembly either through habitat characteristics, dispersal abilities, or biotic interactions. We then eliminated traits for which detailed and complete information was not available for a high number of species. This selection step provided a set of 11 morphological traits and one life-history trait (reproduction mode). Physiological traits would have been highly relevant, however, as far as we are aware this information is only available for a few species reared in laboratory conditions. In the same way, life-history traits were poorly informed except for reproduction mode.

Traits were collected from a number of specified synopses and identification keys [START_REF] Gisin | Collembolenfauna Europas[END_REF][START_REF] Jordana | Fauna Iberica. Collembola, Poduromorpha[END_REF][START_REF] Fjellberg | The Collembola of Fennoscandia and Denmark. Part 1: Poduromorpha[END_REF][START_REF] Fjellberg | The Collembola of Fennoscandia and Denmark. Part II: Entomobryomorpha and Symphypleona[END_REF][START_REF] Bretfeld | Synopses on Palaearctic Collembola. Volume 2. Symphypleona[END_REF]Potapow, 2001;[START_REF] Thibaud | Synopses on Palaearctic Collembola Hypogastruridae[END_REF][START_REF] Chahartaghi | Sex ratio and mode of reproduction in Collembola of an oak-beech forest[END_REF][START_REF] Hopkin | A key to the Collembola (springtails) of Britain and Ireland[END_REF][START_REF] Chernova | Ecological significance of parthenogenesis in collembola[END_REF][START_REF] Dunger | Synopses on Palaearctic Collembola: Tullbergiidae[END_REF]. Visual and jumping apparatus and leg lengths are supposed to be related to dispersal abilities of species [START_REF] Ponge | Decreased biodiversity in soil springtail communities: the importance of dispersal and landuse history in heterogeneous landscapes[END_REF]. Antennal length, eye (ocelli) number, presence of trichobothria and presence and complexity of post-antennal organs play a role in sensory functions [START_REF] Hopkin | Biology of the Springtails (Insecta: Collembola)[END_REF] and are expected to vary between close versus open, and epigeic versus endogeic habitats. Body pigmentation and presence of scales are involved in UV protection, thermodynamic buffering and signalling [START_REF] Hopkin | Biology of the Springtails (Insecta: Collembola)[END_REF] and are also suspected to vary with habitat characteristics, as well as body shape and length and length of jumping apparatus. Pseudocelli are circular structures allowing Collembola to extrude repulsive fluids from specialized glands [START_REF] Hopkin | Biology of the Springtails (Insecta: Collembola)[END_REF][START_REF] Rusek | Morphology, ultrastructure and function of pseudocelli in Onychiurus armatus (Collembola, Onychiuridae)[END_REF] and thus play a role in protection against predation [START_REF] Rusek | Morphology, ultrastructure and function of pseudocelli in Onychiurus armatus (Collembola, Onychiuridae)[END_REF]. At last sexual/parthenogenetic reproduction is associated to survival or colonizing strategy [START_REF] Chernova | Ecological significance of parthenogenesis in collembola[END_REF][START_REF] Lavelle | Adaptive strategies of Pontoscolex corethrurus (Glossoscolecidae, Oligochaeta), a peregrine geophagous earthworm of the humid tropics[END_REF]. Most of these traits are species-or clade-(e.g.

pseudocelli) specific and we did not consider here intra-specific variability since data on morphometric variation over broad geographical areas are unavailable in Collembola. Data may be quantitative (e.g. body length), binary (e.g. presence/absence of scales), or semiquantitative (e.g. furcula length, see Table 3). We computed traits of the 58 selected collembolan species. All trait attributes (e.g. furcula length categories) were issued from precise definitions (Table 3) and not from expert appreciations. Some of these traits, currently in the Coltrait database, will be integrated in the BETSI database [START_REF] Hedde | BETSI, a complete framework for studying soil invertebrate functional traits[END_REF].

Statistical analyses

Correspondence analysis (CA) was used to analyze species-environment relationships without constraining species distribution (samples as observations, species as active variables, environmental variables as passive variables). As an explanatory step, CA allowed us to visualize patterns of species distribution with environmental variables superposed on the revealed gradients.

Canonical correspondence analysis (CCA) and Monte Carlo permutation tests were used to verify whether species distribution was significantly explained by environmental factors and to know the importance of each factor. The type of horizon (organo-mineral or organic) and the C/N ratio were discarded because they were not available for a high number of samples. As Spearman correlation tests revealed that some environmental variables or levels of environmental variables were correlated we discarded some of them and we tested only the effect of temperature and rainfall (for climate), soil pH, hydromorphy and only some modalities of habitat closure (Open), vertical stratification (Hemi, Epi-1, Epi-2,Epi-3), and humus forms (Mull, Moder). Missing values were estimated by the nearest neighbor method.

Seven partial CCAs were then performed to test the effect of above-mentioned variables while discarding the effect of one of them on species distribution.

RLQ analyses [START_REF] Dolédec | Matching species traits to environmental variables: a new three-table ordination method[END_REF] were performed to assess whether species traits distribution was significantly correlated with environmental variables, and to determine patterns observed when variables were constrained. RLQ analysis allows to perform a double inertia analysis of two arrays (R: environmental variables, and Q: species traits) with a link expressed by a contingency table (L: species occurrences). We discarded C/N, organo-mineral and organic horizons and soil pH, that were not sufficiently informed. As missing observations were deleted when variables (e.g. mull, moder) were not fully informed (Table 1), and as informed variables varied among studies (either humus form, or climate) we performed two RLQs to minimize the loss of data in each analysis. We transformed quantitative data (temperature, altitude and rainfall, leg and furcula lengths, ocelli and PAO vesicle numbers) into semi-quantitative data with three or two classes each. This transformation was performed by discretizing data over two classes when the trait might be absent and consequently it comprises a class "0" (e.g. ocelli, PAO vesicle numbers) in addition to the two classes created by the discretization. Discretization was performed over three classes for the other traits (e.g. lengths). To limit deleting observations we pulled together samples taken either in edaphic or in hemiedaphic levels (S.Soil), creating a vertical stratification category gathering samples taken either from the soil or from the litter. We also created another level of vertical stratification (S.Soil-Epi) that includes moss cushions or grass tufts with adhering humus or soil. Other variables were the same as those used in CA (Table 3). The first RLQ tested the interaction of traits with climate, vertical stratification, habitat closure, and soil moisture, while the second RLQ tested the interaction of traits with humus form, habitat closure, and soil moisture.

At last, traits were analyzed separately using statistical models to test the effect of environmental variables highlighted by RLQ. We first calculated the percent occurrence of each species for each level of binary environmental variables (e.g. edaphic level, hemidaphic level, mull humus, moder humus, etc…), and for continuous environmental variables (soil pH, altitude, temperature and rainfall) we selected minimum or maximum values for each species. We then implemented linear models on continuous trait values, binary logit models on binary traits, and a multinomial logit model on pigmentation which included three categories. We excluded variables with a variance inflation factor (VIF) higher than four to avoid multi-colinearity. We selected models with contributive variables that significantly explained the greatest part of trait variability (i.e. with highest adjusted R² and log-likelihood for linear and logit models, respectively). All variables bringing significant information to the model were included, even if their impact was not significant when evaluated separately (Type III analysis). In order to fulfill linear model assumptions, some variables had to be logtransformed. As pseudocelli number did not follow a normal distribution even after transformation, we analyzed their presence/absence with a binary logit model.

RLQ analysis was performed with the package "ade4" in R software (R Development Core Team, 2010). CA, CCA, general linear models (GLM) and other calculations (e.g. data normalization, discretization) were done using XLSTAT ® (Addinsoft ® , Paris, France).

Results

Species and environmental variables

The relationship between species, environmental variables and traits was first analyzed by CA using samples as observations, species as active variables and environmental variables as passive variables (Figs. 1a,1b). The first three components of CA extracted 17.4% of the total variance (6.3%, 5.9% and 5.2% for F1, F2 and F3, respectively). The projection of species and environmental variables along axes 1 and 2 (Fig. 1a) shows that species are spread along Opposed along axis 2 to these two groups of edaphic and hemi-edaphic species, we find epigeic species living on the soil surface (epigeic-1), herb layers and boulders (epigeic-2)

and trees (epigeic-3) ( discarding the effect of one or the other variable did not affect to the same extent the constrained inertia (12.5% for total CCA): 5.2%, 8.0%, 10.5%, 10.6%, 10.6%, 11.5%, and 11.6% of the total inertia were explained when discarding vertical stratification, humus form, rainfall, temperature, habitat closure, hydromorphy and pH effect, respectively.

Traits and environmental variables

A first RLQ analysis was applied to climate (temperature and rainfall), altitude, vertical stratification, habitat closure, soil moisture, and traits (Figs. 2a,2b). Axis 1 separates levels of rainfall, temperature, vertical stratification, soil hydromorphy, and to a lesser extent, Small body, leg and antennae length, with pseudocella and well developed PAO, but no pigmentation, scales and trichobothria, are observed in both mull and moder humus (negative side of axis1 and axis 2). Some traits varied along axis 2 in relation to the humus form, especially the increase in organic horizon thickness. From mull to moder the following changes are observed: mixed reproduction shifts towards parthenogenesis, absence of eye towards simple eye, absence of furcula towards mean-length furcula. In humus forms with thickest organic layers (Mor and Peat) particular traits are observed, e.g. stocky body, short furcula and variable pigmentation. This change of traits from mull with thin organic layers to humus forms with thicker organic layers (moder, then mor and peat) coincides with the passage from deep organo-mineral horizons with small interconnected pores (earthworm galleries, allowing Collembola to go deeper in the soil as in mull) to upper thick organic horizons that offer more space, allowing the movement of large bodies and the use of a medium-size or short furcula, while eyes are larger in relation to a little more light.

Monte-Carlo tests based on 1000 replicates were highly significant (p < 0.001) for the two RLQs, indicating a significant relationship between traits and environmental variables.

Linear and logistic models showed that environmental variables explained antenna, leg, body and furcula lengths, number of eyes and PAO vesicles, reproduction mode, spherical and cylindrical body shape, and presence of trichobothria, pseudocelli, scales and pigment to significant levels (Tables 5 and6). Only the stocky body shape (McFadden R² = 0.099; Chi² = 3.362; p-value = 0.067) was not significantly explained by environmental variables. Logistic and linear regressions corroborated that temperature plays a significant part in the explanation of most trait variation (Tables 5 and6). Antenna, furcula, leg, and body lengths, number of ocelli, sexual reproduction, spherical body shape, and presence of trichobothria were significantly and positively explained by minimum temperatures. Some of these traits tended to be (body length) or were (trichobothria) negatively explained by altitude.

Vertical stratification (mostly through epigeic and hemiedaphic levels) contributed to the explanation of all traits (except stocky body). Both the number of PAO vesicles and the presence of pseudocelli were significantly and negatively explained by minimum temperatures and epigeic-1 level, and were positively explained by soil pH. Humus form and habitat openness contributed to explain variations of only five and two traits, respectively, and this contribution was significant in two cases only (peat and mor explained trichobothria presence and antenna length, respectively).

Discussion

Species and environmental variables

We showed that the distribution of species is conditioned, first by vertical stratification, then by humus form, air temperature, rainfall, and habitat closure. Soil moisture and acidity were also shown to affect species distribution but more indirectly, probably through the effect of humus form [START_REF] Ponge | Humus index: an integrated tool for the assessment of forest floor and topsoil properties[END_REF]Cassagne et al., 2004), while the effect of altitude was correlated to air temperature and rainfall (and more probably to insolation). These results arise from an analysis performed at a broad scale, that covers most part of the biogeographic distribution area of species. The multiplicity of sites over such a broad geographical scale allows to overcome eventual interactions between spatial autocorrelation and environmental variables that could arise at lower scales, e.g. at the scale of habitat (e.g. a forest) or microhabitat (e.g. soil characteristics) [START_REF] Caruso | Relative role of deterministic and stochastic determinants of soil animal community: a spatially explicit analysis of oribatid mites[END_REF].

Our results show that these habitat constraints contributed in structuring collembolan communities to an extent of about 12%. Consequently, at least 12% collembolan species assemblies were explained in a deterministic way (Streit et al., 1985;[START_REF] Weiher | Assembly rules, null models, and trait dispersion: new questions from old patterns[END_REF] while about 88% species distribution remained unexplained. A part of this unexplained variation is probably due to the lack of data about biotic interactions like competition [START_REF] Mcgill | Rebuilding community ecology from functional traits[END_REF][START_REF] Comita | Abiotic and biotic drivers of seedling survival in a hurricane-impacted tropical forest[END_REF].

We characterized habitat preferences for many species (see section 3.1.). The three levels of epigeic species were well separated between soil surface (epige-1), herb layers and boulders (epige-2) and trees (epige-3) while hemiedaphic species were closely related to edaphic species. This could in part be due to the fact that some samples contained a mixture of litter and organo-mineral or even mineral soil (soil), leading to a connection of species living in one or the other level, but also to the vertical movement of animals through horizons [START_REF] Hassall | Vertical migration of Onychiurus subtenuis (Collembola) in relation to rainfall and microbial activity[END_REF]. The distribution of species in the three epigeic levels was related to habitat closure, above-ground species that live in forests being preferentially located either at the soil surface (epige-1) or on trees (epige-3), contrary to above-ground species living in open areas which are located preferentially in herb layers or on boulders (epige-2). Species segregation according to habitat closure thus especially occurs for epigeic species because they are living far from the protection ensured by soil/litter layers, and occupy different substrata, some of them being more frequent in forests (trees) or in open environments (herb layers). Edaphic species appear in both closed and open habitats while hemiedaphic species seem more linked to closed habitats (due to thicker litter layers). However, their central location on the F2-F3 biplot of CA makes hemiedaphic habitats more difficult to interpret in terms of relationships with habitat closure. Edaphic species were actually segregated according to humus form and acidity.

Our results support studies done at a more local scale on the vertical distribution of species [START_REF] Delamare-Deboutteville | Microfaune du sol des pays tempérés et tropicaux[END_REF]Hale, 1966;[START_REF] Hågvar | Collembola in Norwegian coniferous forest soils. II. Vertical distribution[END_REF]Ponge, 2000), preferences

for humus forms and soil acidity levels [START_REF] Ponge | Les collemboles indicateurs du type d'humus en milieu forestier. Résultats obtenus au Sud de Paris[END_REF][START_REF] Hågvar | Collembola in Norwegian coniferous forest soils. III. Relations to soil chemistry[END_REF]Loranger et al., 2001), and comparisons between forests and open habitats (Ponge, 1993).

They reveal an impact of the minimum annual air temperature at which species have been found as well as the segregation of epigeic species among the three levels of epigeic habitats (see above). However, as our analysis encompasses a broad spatial area, and consequently more diverse levels of environmental factors, we found some contrasted results compared to more local studies. For example Mesaphorura macrochaeta, previously observed in more relative abundance in acidic soils in a more local study (Ponge, 1993), is here found not really responding to acidity level, and even tending to occur more often in subacidic or non-acidic soils. The collembolan H. nitidus, proved to prefer edaphic and hemiedaphic habitats in mull humus and calcareous or neutroacidocline soils (see 2.2 Results) on a broad scale, was able to live in acidic soil in some places (Cassagne et al., 2003(Cassagne et al., , 2004)). Such contrasted responses of species to varied environmental conditions show that the response (reaction norm) of species results from trade-offs between preferences for a variety of environmental factors and varies according to the value of each factor [START_REF] Fry | Detecting ecological trade-offs using selection experiments[END_REF][START_REF] Uriarte | Multidimensional trade-offs in species responses to disturbance: implications for diversity in a subtropical forest[END_REF]. They also highlight that in spite of marked habitat preferences, the studied collembolan species were able to live in extremely diverse conditions. Consequently, the niche width will remain to be defined for the present 58 species in order to determine precisely the habitat limits of each species and thus provide a tool that could be used for eventual predictions of changes in collembolan communities. Nevertheless, we have to keep in mind that some species appearing in our study as ubiquitous, such as Parisotoma notabilis or Isotomiella minor, might in fact be species complexes composed of two or more species with narrower niches as suggested by recent sequencing of a barcode DNA fragment (5" end of COI gene) [START_REF] Porco | Cryptic dversity in the ubiquist species Parisotoma notabilis (Collembola, Isotomidae): a long-used chimeric species?[END_REF].

Traits and environmental variables

RLQ and GLM analyses showed that all tested environmental variables contributed to the assemblage of species traits. Vertical stratification followed by annual air temperature play a dominant role in the explanation of variation of the 12 studied traits.

The relationship between traits and vertical distribution of species, which was previously hypothesized by Collembola specialists [START_REF] Gisin | Ökologie und Lebensgemeinschaften der Collembolen im schweizerischen Exkursionsgebiet Basels[END_REF][START_REF] Delamare-Deboutteville | Microfaune du sol des pays tempérés et tropicaux[END_REF][START_REF] Hågvar | Collembola in Norwegian coniferous forest soils. II. Vertical distribution[END_REF][START_REF] Rusek | A new classification of Collembola and Protura life forms[END_REF] on the basis of their observations, is now statistically tested over a wide range of ecosystems. The contribution of habitat closure/openness and humus form to traits assemblages is showed at broad scale for the first time. We also showed that traits of species living in open habitats (e.g. grassland) or above-ground are both adapted to surface life, i.e. to light, a potentially dry environment and a wide space: high mobility (long legs and furcula), big size often associated with spherical body, scales, pigments (protection against UV), sensorial organs sensitive to air and light (trichobothria, ocelli and antennal organs), and sexual reproduction. On the opposite side, traits that are dominant in woodland are quite similar to those observed in hemiedaphic and edaphic levels and are mostly associated with subterranean concealed life or at least with a stable microclimate (litter in forests): small size, small locomotory appendices, toxic excreta (pseudocelli), post-antennal organs as main sensorial organs, and parthenogenesis. Such variation of trait modalities between open habitats and forests probably explain the higher soil fauna diversity (γdiversity) observed in landscapes composed of a mixture of forests and open habitats in regard to homogeneous landscapes [START_REF] Vanbergen | Scale-specific correlations between habitat heterogeneity and soil fauna diversity along a landscape structure gradient[END_REF].

The convergence of traits observed along gradients of habitat closure and of vertical distribution is explained by a higher incidence of environmental stress (drought, UV and wind) in less protected open as well as aboveground habitats. Among species previously recorded as drought-sensitive (Lindberg and Bengtsson, 2005), many appears here as being edaphic and woodland species (Micraphorura absoloni, Willemia anophthalma, Micranurida pygmaea, Mesaphorura macrochaeta), while drought-tolerant species are found to be epigeic (Lepidocyrtus spp., Entomobrya nivalis).

The relatively large body size of epigeic species is a protection strategy against frost and desiccation [START_REF] Kaersgaard | The importance of cuticular permeability, osmolyte production and body size for the desiccation resistance of nine species of Collembola[END_REF][START_REF] Bokhorst | Extreme winter warming events more negatively impact small rather than large soil fauna: shift in community composition explained by traits not taxa[END_REF]. Moreover, open unstable and stressful environments like agricultural fields require higher motility (long legs and furcula) than shrubby fallows where litter begins to accumulate or woodland [START_REF] Mebes | A method for estimating the significance of surface dispersal for population fluctuations of Collembola in arable land[END_REF].

Escaping from predators aboveground also relies on jumping, ensured by long furcula acting as a spring [START_REF] Bauer | Habitat dependent differences in the flight behavior of Collembola[END_REF], as well as visual (ocelli) or tactile (trichobothria) sensorial organs to detect their presence [START_REF] Baatrup | Predation of the mite Hypoaspis aculeifer on the springtail Folsomia fimetaria and the influence of sex, size, starvation, and poisoning[END_REF]. In epigeic and open habitats longer antennae, bearing specialized tactile and chemosensory setae and vesicles, also allow detecting chemicals and air vibration at a higher distance [START_REF] Hopkin | Biology of the Springtails (Insecta: Collembola)[END_REF]. Increased ocelli number and furcula, antenna and body lengths were also used by [START_REF] Rusek | A new classification of Collembola and Protura life forms[END_REF] to propose two epigeic collembolan "life form groups", namely "Macrophytobionts" and "Microphytobionts", corresponding to epigeic levels 2 and 3, respectively, in our study. Conversely, reduced pigmentation, furcula length and number of ocelli fit generally well with the "Euedaphobiont life form group" [START_REF] Rusek | A new classification of Collembola and Protura life forms[END_REF]. Ocelli number, antenna and furcula lengths had also previously been shown to be correlated with change in the vertical distribution of species in response to tree plantation affecting litter quality and quantity [START_REF] Vandewalle | Functional traits as indicators of biodiversity response to land use changes across ecosystems and organisms[END_REF].

Pseudocelli, mostly present in edaphic species, probably compensate for the difficulty to escape predators through active movement in deep soil by excreting chemicals that repel predators [START_REF] Negri | Spatial distribution of Collembola in presence and absence of a predator[END_REF]. In the same way the presence of post-antennal organs (PAO) in edaphic and hemiedaphic species only, support the hypothesis raised by [START_REF] Salmon | Species traits and habitats in springtail communities: a regional scale study[END_REF] that these organs could compensate for the absence of other sensorial organs that are adapted to air (trichobothria), light (ocelli) and spacious environments (sensory organs on long antennae), PAO being supposed to be composed of thermo-, hygro-, or chemosensitive receptor cells [START_REF] Altner | The postantennal organ: a specialized unicellular sensory input to the protocerebrum in apterygotan insects (Collembola)[END_REF]. At last, the reproductive insurance hypothesis [START_REF] Jain | The evolution of inbreeding in plants[END_REF] predicts that parthenogenesis is favored in populations where mates are difficult to find. This hypothesis can explain the higher rate of parthenogenesis observed among euedaphic species, living in deep soil horizons and faced to deficit of space and need to explore narrow soil pore networks for mating [START_REF] Chahartaghi | Sex ratio and mode of reproduction in Collembola of an oak-beech forest[END_REF][START_REF] Chernova | Ecological significance of parthenogenesis in collembola[END_REF].

The effect of climate, and especially of temperature, on the distribution of traits is mostly observed in aboveground and open habitats, i.e. in least protected and more unstable environments. Moreover, as climate drives vegetation patterns and humus forms [START_REF] Ponge | Geology and climate conditions affect more humus forms than forest canopies at large scale in temperate forests[END_REF], the effect of climate seems tightly linked to that of humus forms.

In [START_REF] Siepel | Biodiversity of soil microarthropods: the filtering of species[END_REF]. This is supported by the positive correlation of the activity of epigeic Collembola with temperature in agricultural soils (Frampton et al., 2001). At last, the postantennal organ seems more complex (larger numbers of vesicles, in relation to the number of dendritic branches of neural systems; [START_REF] Altner | The postantennal organ: a specialized unicellular sensory input to the protocerebrum in apterygotan insects (Collembola)[END_REF] in most species of mull humus and edaphic levels than in moder humus and hemiedaphic levels. This suggests that complex post-antennal organs, supposed to be more sensitive to chemical features of the immediate environment [START_REF] Altner | The postantennal organ: a specialized unicellular sensory input to the protocerebrum in apterygotan insects (Collembola)[END_REF], could compensate for the complete absence of eyes and reduction of other sensory organs observed in euedaphic species, providing better adaptation to deeper soil layers. Nevertheless, although the presence of PAO was essentially observed in edaphic and hemiedaphic species, only a study of the variation of PAO complexity in relation to habitat depth of each species along one or several lineages will be able to state on the importance of PAO complexity for adaptation to subterranean life.

Our results support some of the relationships between traits and environmental factors observed in a previous study realized at a more local scale [START_REF] Salmon | Species traits and habitats in springtail communities: a regional scale study[END_REF].

Nevertheless, some differences have to be noted since the cited study did not allow discerning a clear correlation between traits and humus types associated to soil acidity. The larger dataset used here allowed us to demonstrate such relationships.

The present study, by showing the change of traits along environmental gradients supports the importance of niche-based environmental filtering in the assembly of Collembolan species [START_REF] Mcgill | Rebuilding community ecology from functional traits[END_REF][START_REF] Weiher | Advances, challenges and a developing synthesis of ecological community assembly theory[END_REF]. However, models showed that environmental variables explained 23% (cylindrical body) to 71% (pseudocelli; Table 6) of trait variation, meaning that a high part of trait and species assembly variation is explained by other factors.

Community phylogenetics will probably add an important contribution to the explanation of species distribution and assembly as this has been shown for plant communities [START_REF] Prinzing | Less lineages -more trait variation: phylogenetically clustered plant communities are functionally more diverse[END_REF][START_REF] Pavoine | Linking patterns in phylogeny, traits, abiotic variables and space: a novel approach to linking environmental filtering and plant community assembly[END_REF]. In addition, ecophysiological traits such as resistance to desiccation, enzymatic equipment for food digestion, colonization rate, etc., were missing in our analysis because they were only available for a few species [START_REF] Hopkin | Biology of the Springtails (Insecta: Collembola)[END_REF] and lengthy researches are needed to assess them in a meaningful number of species. At last, although pseudocelli and furcula development allow taking into account repulsion to and escape from predators, respectively, the effects of other biotic interactions such as competition, or commensalism, known to be important drivers of community structuration [START_REF] Mcgill | Rebuilding community ecology from functional traits[END_REF][START_REF] Comita | Abiotic and biotic drivers of seedling survival in a hurricane-impacted tropical forest[END_REF][START_REF] Vellend | Conceptual synthesis in community ecology[END_REF], were not taken into account because of the little amount of available data. Limits of models relating species range distributions to environmental variables have been underlined, in particular when using species-or traitenvironment relationships to track large-scale effects of global change [START_REF] Fridley | Drivers of secondary succession rates across temperate latitudes of the eastern USA: climate, soils, and species pools[END_REF][START_REF] Urban | Moving forward: dispersal and species interactions determine biotic responses to climate change[END_REF][START_REF] Zhu | Dual impacts of climate change: forest migration and turnover through life history[END_REF]. We showed that within the studied group climate effects concern mainly traits associated to aboveground habitats in open environments, and that soil properties are the main driver of changes in belowground communities. However, predictions about the response of collembolan trait/species distributions at local scale to climate warming will have to take into account other factors like biotic interactions [START_REF] Urban | Moving forward: dispersal and species interactions determine biotic responses to climate change[END_REF]) and ecophysiological traits.

Conclusions

Our study shows that collembolan species assembly at a broad scale is conditioned by a set of interacting parameters including vertical stratification, humus form, habitat closure, air temperature, soil moisture and acidity, and to a lesser extent rainfall and altitude. Our results

show that all these environmental factors significantly contributed to the assemblages of twelve studied species traits. Combinations of certain environmental factors, especially stratification level and air temperature, explain a large variety of species traits and are thereby thought responsible for a great part of collembolan "species sorting". A convergence was observed between traits related to stratification level and habitat closure/openness, that we interpreted as the effect of similar physiological and behavioral constraints. The action of humus form would impact indirectly trait distribution/assembly through the interaction between vertical stratification and habitat openness. Ecological preferences were identified for the 58 studied collembolan species relatively to this set of traits, their niche width and their degree of specialization remaining to be more precisely defined. Nevertheless, relationships between traits and environments provide interesting proxies to identify ecological preferences of Collembola, even when not identified to species level. Beyond Europe (where the invertebrate fauna is relatively well-characterized), this approach may offer new insight, for example with respect to tropical soil communities where most species are still unknown to science, and will likely remain so in the near future. 3 for abbreviations of species traits.

Figure captions

  axis 1 mainly according to humus form, soil hydromorphy and habitat opening/closure and to a lesser extent soil acidity, temperature and altitude. Along axis 2, species are distributed according to vertical stratification, and to a lesser extent habitat closure/opening, soil hydromorphy, organic matter, and temperature. In the upper left side of the biplot, we find edaphic and hemiedaphic species living in acid soils with a low rate of organic matter decomposition (peat, mor, moder): Micraphorura absoloni, Mesaphorura tenuisensillata, Willemia denisi, Willemia anophthalma, Mesaphorura yosii, Micranurida pygmaea, Folsomia quadrioculata, Protaphorura armata and Pogonognathellus flavescens. Opposed to this group along axis 1, we find edaphic and hemiedaphic species living in mull on calcareous or neutroacidocline soils: Stenaphorura denisi, Mesaphorura hylophila, Mesaphorura krausbaueri, Heteromurus nitidus, Mesaphorura italica, Paratullbergia callipygos, and Pseudosinella alba.

  altitude. Axis 2 separates modalities of the same factors than for axis 1 in addition to habitat opening/closure. Traits mostly represented in deep soil and closed habitats (on the positive side of axes 1 and 2) are the absence of pigmentation, furcula, ocelli, trichobothria and scales, the presence of a post-antennal organ (PAO) comprising a great number of vesicles, of pseudocelli (defense organs), short legs and antennae and small body length. These habitats also display a parthenogenetic dominant reproduction. On the soil surface, the number of ocelli and furcula length increased slightly. When habitats are less edaphic, more open and in less favorable climatic conditions (higher altitude, associated to low temperature levels positive side of axis 1 and negative side of axis 2) the following trait modalities are more frequent: stocky body, variable pigmentation, PAO present but less developed, and furcula, present but usually regressed and not fully functional. In epigeic habitats and more favorable climatic conditions (i.e. high and intermediate temperature levels and lower altitude, negative side of axis 1) most common traits are larger body size, elongated legs and antennas, spherical and pigmented body, well-developed eyes, presence of trichobothria and scales, and absence of PAO and pseudocella, with sexual reproduction dominant.A second RLQ tested the relationships between humus forms and soil types, habitat closure, soil moisture, and traits(Figs. 3a, 3b). Axis 1 separates closed and open habitats while axis 2 separates humus forms. Open habitats (positive side of axis 1) hosted species displaying traits previously mostly observed in epigeic and favorable climate conditions: increased body, leg and antennae length, spherical and pigmented body, with scales and trichobothria, well-developed eye spots, absence of pseudocelli, absence or reduction of PAO vesicles, and dominance of sexual reproduction. Furcula may be either very long or regressed. Near the positive end of axis 1, higher body length is found in well moistened soils. Closed (forest) and intermediate (heathland and scrub) habitats (negative side of axis 1) are separated along axis 2 according to humus form and thickness of organic horizon.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Correspondence analysis showing the distribution and assembly of species (active

Fig. 3 .

 3 Fig. 3. RLQ testing the relationships between humus forms and soil types, habitat closure, soil

  Parisotoma notabilisshows no preferences for the studied factors, like the very common species Isotomiella minor, which tends nevertheless to be observed more frequently in non-acidic soils.CCA indicated that the bulk of tested environmental variables, i.e. humus form, habitat closure, vertical stratification, hydromorphy, temperature, rainfall and soil pH significantly impacted species distribution (Table4). The seven partial CCAs computed without either vertical stratification (Hemie, Eda, Epi1, Epi2, Epi3), or humus form (Mull, Moder), or habitat closure (Open), or hydromorphy, or rainfall, or temperature, or soil pH showed that remaining factors impacted significantly the distribution of species (all p < 0.0001) but with a decrease in the rate of constraint inertia. This indicates that all factors impacted the distribution of species directly and not only through interactions with other factors. However,

	elegans, B. parvula, L. cyaneus, E. multifasciata, S. schoetti, I. palustris), to epigeic species
	living either at the soil surface (epigeic-1) or on trees (epigeic-3) in forests (X. tullbergi, O.

Figs 1a, 1b): Orchesella cincta, Heteromurus major, Xenylla tullbergi Lepidocyrtus curvicollis, Xenylla grisea, Brachystomella parvula, Isotomurus palustris, Sminthurinus elegans, Sminthurides schoetti, Entomobrya multifasciata and Tomocerus minor. Species distribution according to soil characteristics (humus form, acidity) thus occurs mainly for endogeic and hemiedaphic species.

Epigeic species are separated along axis 1 by low temperature levels and hydromorphy gradients, O. cincta, H. major, X. tullbergi , X. grisea and L. curvicollis occurring more often in slightly drier and/or warmer habitats (Temp), while B. parvula, S. elegans, E. multifasciata, I. palustris and L. cyaneus prefer hydromorphic soils (Hydro). Forests (close) and open habitats are better separated by axis 3 (Fig.

1b

) that opposes epigeic species living preferentially in herb layers or exceptionally on boulders (epigeic-2) in open habitats (S. cincta, L. curvicollis, Entomobrya nivalis, X. grisea, Allacma fusca). Species segregation according to habitat closure thus mainly occurs for epigeic species.

  this way, less favorable climatic conditions (high altitude associated with low temperature levels), when they allow vegetation development, often generate mor humus and peat, i.e. humus with thick organic horizons made of undecayed plant fragments where collembolan species with stocky body can move more easily than in small soil pores, and are impeded to go deep in the soil by waterlogging. Such conditions favor traits that are intermediate between strictly edaphic and epigeic life (pigmentation variable, PAO present but less developed, and short or regressed furcula). Species traits observed under more favorable climate conditions (moderately high temperature and moisture and low altitude), are the same as those present in epigeic levels because such conditions are favorable to epigeic life and because species adapted to drought can live above-ground in open habitats (see above;

Table 1

 1 Modalities, abbreviations, information level, and data type of environmental variables.

	Environmental variables	Modalities	Abbreviations for CA graphics	Information level (% )	Data type (units)
	Habitat	Close habitat	Close		0/1
	closure	Open habitat	Open		0/1
		Intermediate habitat	Int		0/1
		Epigeic 1 (soil surface and mosses)	Epi-1		0/1
		Epigeic 2 (herb layers and boulders)	Epi-2		0/1
	Stratification	Epigeic 3 (trees)	Epi-3		0/1
		Soil (edaphic and/or hemiedaphic)	Soil		0/1
		Hemiedaphic (litter)	Hemi		0/1
		Edaphic (A, H, B, E
		and layers deeper than 3	Eda		0/1
		cm)
		Peat	Peat		0/1
		Mull	Mull		0/1
	Humus form	Moder	Mod		0/1
		Mor	Mor		0/1
		Cultivated soil	Cult		0/1
		Mean annual temperature	Temp		value (°C)
	Geoclimatic	Annual rainfall	Pre		value (mm/year)
	features	Altitude	Alt		value (m)
		Hydromorphy	Hydro		0/1
		Soil pH	pH		0/1
	Soil	Organic layer	Org		0/1
	chemistry	Organo-mineral layer	OM		0/1
		C/N ratio	C/N		value

Table Table 2

 Table Name, abbreviations for CA analysis, and number of observations of the 58 most commonly recorded collembolan species.

	Species name Abbreviation Allacma fusca (Linnaeus, 1858) Afu Brachystomella parvula (Schäffer, 1896) Bpa Ceratophysella armata (Nicolet, 1841) Car Ceratophysella denticulata (Bagnall, 1941) Cde Dicyrtoma fusca (Lubbock, 1873) Dfu Dicyrtomina minuta (O. Fabricius, 1783) Dmi Entomobrya multifasciata (Tullberg, 1871) Emu Entomobrya nivalis (Linnaeus, 1758) Eni Folsomia candida Willem, 1902 Fca Folsomia manolachei Bagnall, 1939 Fma Folsomia quadrioculata (Tullberg, 1871) Fqu Friesea mirabilis (Tullberg, 1871) Fmi Friesea truncata Cassagnau, 1958 Ftr Heteromurus major (Moniez, 1889) Hma Heteromurus nitidus (Templeton, 1835) Hni Isotomiella minor (Schäffer, 1896) Imi Isotomurus palustris (Müller, 1776) Ipa Isotoma viridis Bourlet, 1839 Ivir Lepidocyrtus curvicollis Bourlet, 1839 Lcu Lepidocyrtus cyaneus Tullberg, 1871 Lcy Lepidocyrtus lanuginosus (Gmelin, 1788) Lla Lepidocyrtus lignorum (Fabricius, 1793) Lli Lepidocyrtus violaceus (Geoffroy, 1762) Lvi Lipothrix lubbocki (Tullberg, 1872) Llu Megalothorax minimus Willem, 1900 Mmi Mesaphorura hylophila Rusek, 1982 Mhy Mesaphorura italica (Rusek, 1971) Mit Mesaphorura krausbaueri Börner, 1901 Mkr Pminu Table 2 (continued) Number of observations Species name Abbreviation 43 Mesaphorura tenuisensillata Rusek, 1974 Mte 66 Mesaphorura yosii (Rusek, 1967) Myo 57 Metaphorura affinis (Börner, 1902) Maf 88 Micraphorura absoloni (Börner, 1901) Mca 69 Micranurida pygmaea Börner, 1901 Mpy 53 Neanura muscorum (Templeton, 1835) Nmu 54 Oncopodura crassicornis Shoebotham, 1911 Ocr 75 Orchesella cincta (Linnaeus 1758) Oci 36 Paratullbergia callipygos (Börner, 1902) Pca 268 Parisotoma notabilis (Schäffer, 1896) Pno 310 Pogonognathellus flavescens (Tullberg, 1871) Pfl 103 Protaphorura armata (Tullberg 1869) Par 239 Proisotoma minima (Absolon 1901) Pmi 124 Proisotoma minuta (Tullberg 1871) 68 Pseudosinella alba (Packard, 1873) Pal 642 Pseudachorutes parvulus Börner, 1901 Ppa 73 Pseudisotoma sensibilis (Tullberg, 1876) Pse 92 Sminthurinus aureus (Lubbock, 1862) Sau 51 Sminthurinus elegans (Fitch, 1863) Sel 119 Sminthurides schoetti Axelson, 1903 Ssc 459 Sminthurinus signatus (Krausbauer, 1898) Ssi 207 Sphaeridia pumilis (Krausbauer, 1898) Spu 30 Stenaphorurella denisi (Bagnall,1935) Sde 69 Tomocerus minor (Lubbock, 1862) Tmi 453 Willemia anophthalma Börner, 1901 Wan 161 Willemia denisi Mills, 1932 Wde 76 Willemia intermedia Mills, 1934 Win 174 Xenylla grisea Axelson, 1900 Xgr Mesaphorura macrochaeta Rusek, 1976 Mma Börner, 1903 513 Xenylla tullbergi Xtu	Number of observations 97 106 20 87 255 147 35 111 363 598 77 161 66 222 208 152 221 197

Table 3

Modalities of traits, abbreviations for RLQ and models, type of data, number of species for each category of categorical and binary traits and mean* for discrete and continuous data.

Trait

Trait modalities