Mathieu Floury
email: mathieu.floury@irstea.fr

Yves Souchon

K Van Looy

Kris Van

Looy M Floury

Climatic and

Climatic and trophic processes drive long-term changes in functional diversity of freshwater invertebrate communities

Introduction

One of the main purposes in ecology is to understand the drivers of biodiversity gradients [START_REF] Willig | Latitudinal gradients of biodiversity: pattern, process, scale, and synthesis[END_REF][START_REF] Field | Spatial species-richness gradients across scales: a meta-analysis[END_REF]. A multitude of biogeographic hypotheses have been proposed to explain diversity patterns that are now widely merged into three broad mechanisms: spatial heterogeneity, climate/productivity and history [START_REF] Oberdorff | Global and regional patterns in riverine fish species richness: a review[END_REF][START_REF] Tisseuil | Global diversity patterns and cross-taxa convergence in freshwater systems[END_REF][START_REF] Eme | Multi-causality and spatial non-stationarity in the determinants of groundwater crustacean diversity in Europe[END_REF]. Figuring out the underlying drivers of diversity as well as the forms of their relationships can still be controversial [START_REF] Currie | Predictions and tests of climate-based hypotheses of broad-scale variation in taxonomic richness[END_REF][START_REF] Field | Spatial species-richness gradients across scales: a meta-analysis[END_REF][START_REF] Whittaker | Meta-analyses and mega-mistakes: calling time on meta-analysis of the species richness-productivity relationship[END_REF]. Nonetheless, climatic and productivity-related factors are frequently identified as the strongest correlates of species-richness gradients [START_REF] Chase | Spatial scale dictates the productivity-biodiversity relationship[END_REF][START_REF] Field | Spatial species-richness gradients across scales: a meta-analysis[END_REF][START_REF] Chase | Stochastic community assembly causes higher biodiversity in more productive environments[END_REF][START_REF] Langenheder | Temporal variation of beta-diversity and assembly mechanisms in a bacterial metacommunity[END_REF]. According to the climate/productivity hypothesis, these variables describe the action of climate on species, either directly by influencing physiological processes, or indirectly by controlling resource productivity or biomass [START_REF] Hawkins | Energy, water, and broad-scale geographic patterns of species richness[END_REF][START_REF] Brown | Toward a metabolic theory of ecology[END_REF][START_REF] Currie | Predictions and tests of climate-based hypotheses of broad-scale variation in taxonomic richness[END_REF][START_REF] Field | Spatial species-richness gradients across scales: a meta-analysis[END_REF][START_REF] Eme | Multi-causality and spatial non-stationarity in the determinants of groundwater crustacean diversity in Europe[END_REF]. On the one hand, direct effects of climatic warming can involve fatal alterations of biological processes like growth, reproduction, foraging, immune competence, behaviour and competitiveness [START_REF] Pörtner | Physiology and climate change[END_REF]. These impacts on individuals then have repercussions on higher levels of organisation thereby contributing to the global loss in biodiversity [START_REF] Parmesan | A globally coherent fingerprint of climate change impacts across natural systems[END_REF]Yohe 2003, Walther 2010). On the other hand, a less-investigated indirect effect of warming is the trophic amplification process by which a significant increase in biological diversity arises from a productivity enhancement [START_REF] Kirby | Trophic amplification of climate warming[END_REF].

Streams and rivers are among the most vulnerable ecosystems to climate change [START_REF] Sala | Global biodiversity scenarios for the year 2100[END_REF]. As such, they are likely to experience the different types of climate-induced effects. For instance, deleterious effects of climate warming on stream communities have already been reported for a decade [START_REF] Durance | Climate change effects on upland stream macroinvertebrates over a 25-year period[END_REF]Ormerod 2007, Buisson et al. 2008). Conversely, recent studies in freshwaters have also highlighted a trophic amplification mechanism responding to temperature increase in phytoplankton [START_REF] Yvon-Durocher | Five years of experimental warming increases the biodiversity and productivity of phytoplankton[END_REF] and invertebrate [START_REF] Van Looy | Long-term changes in temperate stream invertebrate communities reveal a synchronous trophic amplification at the turn of the millennium[END_REF] communities. In both cases, observations suggest that the first consequence of climate change would be an increase in diversity because 1) most cool-water and warm-water species are promoted by newly suitable (i.e. warmer) conditions while cold-water species decrease but represent a very small minority [START_REF] Buisson | Climate change hastens the turnover of stream fish assemblages[END_REF]) and/or 2) the bottom-up propagation of the amplification signal through the food web raises an intensification and a multiplication of its trophic pathways [START_REF] Van Looy | Long-term changes in temperate stream invertebrate communities reveal a synchronous trophic amplification at the turn of the millennium[END_REF].

Usually, climate-and productivity-related variables have been combined under the climate/productivity hypothesis because both types have often been modelled using climatic proxies [START_REF] Hawkins | Energy, water, and broad-scale geographic patterns of species richness[END_REF][START_REF] Field | Spatial species-richness gradients across scales: a meta-analysis[END_REF]). Moreover, taxonomy-based indices can be inefficient to unambiguously disentangle such processes with functional relevance to the understanding of community dynamics [START_REF] Webb | A structured and dynamic framework to advance traits-based theory and prediction in ecology[END_REF]). The present study aimed at distinguishing the relative influence of the two mechanisms on functional diversity (FD) of invertebrate communities over two decades in French streams and rivers. To this end, we used two trait-based indices to represent distinctly the two climate-driven mechanisms: climate vulnerability (CV) and feeding specialisation (FS). First, we tested for their relevance as proxies using a set of multi-scale predictors expected to have significant effects on these processes. Second, we performed geographically weighted regression (GWR) models 1) to assess the relative contributions of the two proxies, along with the regional species-pool (i.e. g-diversity), to long-term changes in functional diversity of invertebrate communities and 2) to search for geographic non-stationarity in the contribution of the three components.

More specifically, we tested six hypotheses: 1) CV should follow a general decrease over the past two decades due to the expansion of thermo-tolerant taxa [START_REF] Durance | Climate change effects on upland stream macroinvertebrates over a 25-year period[END_REF]Ormerod 2007, Floury et al. 2013), 2) meanwhile, FS should exhibit a general increase related to trophic amplification as specialist taxa are believed to benefit from higher resource availability [START_REF] Vázquez | Ecological specialization and susceptibility to disturbance: conjectures and refutations[END_REF]Simberloff 2002, Mondy and[START_REF] Mondy | Using fuzzy-coded traits to elucidate the non-random role of anthropogenic stress in the functional homogenisation of invertebrate assemblages[END_REF], 3) consequently, both biotic trends should have significantly contributed to a general long-term rise in functional diversity of invertebrate communities, 4) geographically, we expected an increasing contribution of CV along a northsouth gradient according to the predicted northwards colonisation/migration by Mediterranean species [START_REF] Bonada | Taxonomic and biological trait differences of stream macroinvertebrate communities between mediterranean and temperate regions: implications for future climatic scenarios[END_REF], 5) likewise, we predicted a greater influence of FS in headwaters than in large rivers since more complex trophic networks of downstream reaches are less likely to be further densified [START_REF] Woodward | The effects of climatic fluctuations and extreme events on running water ecosystems[END_REF], and 6) the regional species-pool should have also influenced long-term changes in functional diversity of local communities, either jointly with the climate/productivity changes via species sorting processes, or separately via dispersal-driven mechanisms [START_REF] Leibold | The metacommunity concept: a framework for multi-scale community ecology[END_REF].

Material and methods

Functional trait-based indices

We compiled long-term data series from 305 sites located on French streams and rivers. In average, sites were sampled fifteen to sixteen times over twenty years within the period 1992-2013 for benthic macroinvertebrates following a common normalised protocol (multi-habitat sampling; norm XP T90-333 in AFNOR 2009). We focused on Ephemeroptera, Plecoptera, Trichoptera, Coleoptera and Odonata (EPTCO) orders for which we gathered presence-absence data on 278 taxa collected among 4734 samples (mostly genera, but 50 taxa were tribes, sub-families or families). Each taxon was characterised using 13 autecological traits and 70 categories (Supplementary material Appendix 1 Box A1, Table A1) from [START_REF] Tachet | Invertébrés d'eau douce: systématique, biologie, écologie[END_REF]. These traits were selected to define two functional indices measuring the climate vulnerability [START_REF] Hering | Potential impact of climate change on aquatic insects: a sensitivity analysis of European caddisflies (Trichoptera) based on distribution patterns and ecological preferences[END_REF][START_REF] Conti | A trait-based approach to assess the vulnerability of European aquatic insects to climate change[END_REF] and the degree of feeding specialisation [START_REF] Mondy | Using fuzzy-coded traits to elucidate the non-random role of anthropogenic stress in the functional homogenisation of invertebrate assemblages[END_REF] of each taxon (Supplementary material Appendix 1 Box A2, Fig. A1,A2). Community weighted means of the two indices were then calculated for each of the 4734 site-by-date samples by averaging the individual scores of occurring taxa. In addition, the overall functional diversity of each of the 4374 communities (i.e. site-by-date samples) was estimated as the dispersion (i.e. spread) of their taxa in the multi-dimensional space defined by the 70 trait categories. To this end, we first computed a taxon-by-taxon distance matrix from the 13 species traits and then measured the functional dispersion in each community as described by [START_REF] Laliberté | A distance-based framework for measuring functional diversity from multiple traits[END_REF].

Finally, we estimated the long-term changes in the three functional indices at each sampling site as areas between smoothed time series and initial index values averaged over the first ten years (i.e. 1992-2001; Supplementary material Appendix 1 Box A3, Fig. A3). Hereafter, 'CV', 'FS' and 'FD' refer to these values of long-term changes in climate vulnerability, feeding specialisation and functional diversity, respectively (Fig. 1). To account for the contribution of regional species-pools to diversity changes, functional indices were complemented by an estimator of the initial g-diversity (hereafter 'g 0 '; Fig. 1) at each site defined as the overall taxonomic richness of the site and its five nearest neighbours over the first ten years (i.e. 1992-2001).

Environmental predictors

We collected environmental data from predictors expected to drive patterns of CV, FS and g 0 either due to their longterm changes or their geographical differentiation. A first set of 5 'temporal' predictors was compiled to assess long-term changes in climate and water quality. Daily values of air temperature and precipitations were extracted from the Safran meteorological system at 8  8 km spatial resolution [START_REF] Vidal | A 50-year high-resolution atmospheric reanalysis over France with the Safran system[END_REF]. For each sampling site, temperature was extracted from the cell encompassing the site while precipitations were cumulated over the cells intersecting the upstream catchment of the site. Preliminary analyses highlighted strong correlations between annual and seasonal means for both variables, thus we focused on summer values since they were expected to be the most limiting for organisms. In addition to climate variables, monthly concentrations of dissolved oxygen, nitrates and phosphates were extracted at each sampling site from < www.data.eaufrance.fr >. First, we calculated the mean annual summer temperature and cumulated precipitations and the mean annual concentrations of oxygen, nitrates and phosphates for the 305 sites along their respective sampled periods. Then, we estimated the long-term trends in the five parameters (Fig. 1) using the slopes of the linear regressions onto years (i.e. their mean rates of change over the entire period).

A second set of 11 'spatial' predictors was compiled to represent the landscape and habitat heterogeneity of the 305 sites at different spatial scales (Fig. 1; Table 1). Altitude and carbonates were considered as regional descriptors while catchment and reach scales were described by different geographical (area), hydrological (river network density), land-cover (e.g. riparian forest) and hydromorphological (e.g. straightening) variables (Table 1). We verified that variables were weakly correlated (|r|  0.32) within each spatial scale.

Finally, we performed an eigenfunction spatial analysis based on Moran's eigenvector maps (MEMs) to account for spatial structures among the sampling sites not captured by the different predictor sets (Dray et al. 2006, Griffith and[START_REF] Griffith | Spatial modeling in ecology: the flexibility of eigenfunction spatial analyses[END_REF]. The MEM variables (i.e. eigenfunctions) were obtained from a spectral decomposition of the truncated distance matrix based on Euclidean distances among the 305 sites. Only MEMs with significant positive eigenvalues were retained in further analyses [START_REF] Borcard | All-scale spatial analysis of ecological data by means of principal coordinates of neighbour matrices[END_REF]. These variables can be used as environmental predictors of spatial variation in biological indices since spatial patterns may be a consequence of environmental autocorrelation, dispersal limitation or historical effects on community composition [START_REF] Dray | Community ecology in the age of multivariate multiscale spatial analysis[END_REF][START_REF] Peres-Neto | Assessing the effects of spatial contingency and environmental filtering on metacommunity phylogenetics[END_REF].

Statistical analyses

First, we arcsin(√x)-transformed percentage and proportion data and we log10(x)-or log10(x  1)-transformed the other variables when needed to satisfy the normality assumption. All variables were then standardised.

In a first step (upper box in Fig. 1), we aimed at 1) assessing the effects of long-term trends in climate and water quality drivers (i.e. 'temporal' predictors) on CV and FS, 2) taking into account whether these temporal effects could have been mediated by multi-scale spatial drivers arranged along a 'topdown' hierarchical organization (i.e. 'spatial' predictors), and 3) accounting for spatial autocorrelation and/or additional drivers potentially not addressed in our dataset (i.e. using MEMs). For this purpose, we first assessed the effect of the temporal predictors on CV and FS by testing all the possible combinations of variables in generalised additive models (GAMs). For each combination, covariates were modelled with regression splines to account for non-linear relationships and we retained the model that maximised the adjusted R² as the best model. Then, we defined similarly the best GAMs using successively regional-scale, catchment-scale, reach-scale and MEMs variables as explanatory variables and residuals of the 'previous' model as response variable. Finally, we merged the five successive best models in a final additive model. The same approach was used for g 0 using the regional-scale model as the first model.

In a second step, we investigated the relative effects of CV, FS and g 0 on FD using geographically weighted regression (GWR) models (lower box in Fig. 1). GWR enabled to account for potential non-stationarity in the contribution spatial patterns of the three components by estimating independent regression parameters (i.e. coefficients and R² values) for each sampling site [START_REF] Eme | Multi-causality and spatial non-stationarity in the determinants of groundwater crustacean diversity in Europe[END_REF]. This approach relies 3 these data were extracted from the BD TOPO ® GIS layer. 4 where r is the water density, g is the gravitational acceleration, Q 99 is the 99th percentile of daily discharges and S v is the valley slope.

on the attribution of decreasing weights (using a Gaussian function) to the neighbouring sites within a given bandwidth according to their growing geographical distance to the focal site [START_REF] Brunsdon | Geographically weighted regression: a method for exploring spatial nonstationarity[END_REF]. The number of neighbours was optimised by searching between 7 and 30% of all sites with the Golden Section Search [START_REF] Svenning | Plio-Pleistocene climate change and geographic heterogeneity in plant diversity-environment relationships[END_REF]). Finally, variance partitioning based on partial GWR models was performed to assess the relative contribution of the three indices [START_REF] Eme | Multi-causality and spatial non-stationarity in the determinants of groundwater crustacean diversity in Europe[END_REF]. Residuals of the global GWR model were adjusted against the MEMs variables to check for a potential influence of spatial autocorrelation and/or additional drivers.

All analyses except GWR models were run in R statistical software (R Core Team). FCA, GAMs, integral calculation and MEMs were computed using respectively the ade4 [START_REF] Dray | The ade4 package: implementing the duality diagram for ecologists[END_REF], mgcv [START_REF] Wood | Generalized additive models: an introduction with R[END_REF], tis [START_REF] Hallman | tis: time indexes and time indexed series[END_REF] and PCNM [START_REF] Legendre | PCNM: MEM spatial eigenfunction and principal coordinate analyses[END_REF]) R packages. GWR and partial GWR models were performed using GWR4 software [START_REF] Nakaya | Semiparametric geographically weighted generalised linear modelling in GWR 4.0[END_REF].

Results

Functional trait-based index responses to environmental predictors

Overall, the average long-term change in climate vulnerability (CV) of invertebrate communities was slightly greater than zero (mean  0.1  0.4). However, CV was highly variable across France with 171 sites exhibiting positive values, mainly in the north-western and eastern regions, and 134 sites exhibiting negative values, mainly in the middle and the south-eastern regions (Fig. 2a). Longterm changes in feeding specialisation (FS) were more homogeneous in direction with 214 sites exhibiting positive values (mean  0.3  0.5), but were also spatially variable with the strongest values observed in the central region (Fig. 2b). Similarly, the initial g-diversity (g 0 ) showed various spatial patterns with regional species-pools ranging from 214 25 -roughly in the south-eastern quarter -to 135 taxa -in the southwestern region (Fig. 2c).

The modelling approach based on successive GAMs was quite efficient in capturing these variations with final additive models explaining around 50% of the variance in CV and FS and more than 80% of the variance in g 0 (Table 2). Temporal and catchment-scale predictors along with MEMs exhibited the greatest contributions ( 10%) to CV and FS variations (Table 2). For instance, CV showed significant responses to changes in temperature and catchment area (Fig. 3a), while FS showed significant responses to changes in both temperature and phosphate concentration (Fig. 3b). If MEMs were by far the strongest predictors of g 0 , regional-(e.g. altitude) and catchment-scale (e.g. urban land-cover) variables had also a significant influence (Fig. 3c; Table 2).

Index contributions to changes in functional diversity

The three indices significantly contributed to the general increase (mean  4.2  4.2) in functional diversity (FD) of invertebrate communities over France, as observed for 266 of the 305 sites. Overall, CV and FS exhibited similar contributions of about 24% to FD variations, while g 0 had a slightly lower influence of about 17% (Table 3). Subsequently, the final model integrating the residual effect of MEMs (ca 10%) explained almost 75% of the variance in FD (Fig. 2d-e). The cumulated contribution was quite homogeneous over France, except for Brittany, Paris Basin and Moselle valley (Fig. 2f). Moreover, the local regression parameters of GWR models enabled to verify the consistency of the overall relationships: FD was negatively related to CV and g 0 at about 99 and 92% of the 305 sites, respectively, whereas FD was positively related to FS at about 87% of the sites (Supplementary material Appendix 2 Table A2).

Locally, CV and FS provided spatially varying contributions to FD, ranging from 0 to 43% (Fig. 4a-b; Table 3). The spatial contribution pattern of CV was highly related to latitude (p-value  0.001) with contribution increasing from north to south (Fig. 4d). The FS contribution pattern was significantly structured across a river size gradient (p-value  0.001) with greater proportions of variance explained in small streams than in large rivers (Fig. 4e). Finally, g 0 exhibited a more homogeneous contribution pattern ranging from 1 to 24% (Fig. 4c; Table 3).

Discussion

Overall, we observed 1) a general long-term increase in functional diversity (FD) of invertebrate communities over France, 2) a significant contribution (ca 24%) of long-term changes in climate vulnerability (CV) to FD, and 3) a negative relationship between CV and FD. These results supported our third hypothesis stating that a decrease in climate vulnerability would have significantly contributed to a general long-term rise in functional diversity of invertebrate communities. Although they could be somewhat counterintuitive, such 'positive' effects of climate-induced changes have already been demonstrated for different species [START_REF] Araújo | Climate warming and the decline of amphibians and reptiles in Europe[END_REF]. In France, [START_REF] Buisson | Climate change hastens the turnover of stream fish assemblages[END_REF] suggested that the global positive impact of climate change on stream fish assemblages could be due to the prevalence of cool-and warm-water species in temperate systems, which are further promoted by newly suitable (i.e. warmer) conditions. Consistently, we highlighted a greater influence of CV in the south where the proportion of climate-sensitive taxa decreased the most, albeit not everywhere, as expected following our fourth hypothesis. These results supported the assumption of a colonisation and migration pattern by Mediterranean species sustaining the diversity increase in southern France, in agreement with the species range shifts predicted by several studies [START_REF] Bonada | Taxonomic and biological trait differences of stream macroinvertebrate communities between mediterranean and temperate regions: implications for future climatic scenarios[END_REF][START_REF] Domisch | Modelling distribution in European stream macroinvertebrates under future climates[END_REF][START_REF] Conti | A trait-based approach to assess the vulnerability of European aquatic insects to climate change[END_REF]. As regards to our first hypothesis, nonetheless, we did not observe a generalised decrease in the climate vulnerability of invertebrate communities. More than half of the studied sites exhibited the contrary trend, that is, an increasing proportion of climate-sensitive taxa over the past two decades. According to the first modelling step, these sites would have consistently been exempted or partially preserved from warming, which seemed to occur more likely in small catchments (Fig. 3a). By hosting taxa that are threatened by warming, such locations provide biological refuges whose identification and protection are of priority for species conservation under future climate change [START_REF] Keppel | Refugia: identifying and understanding safe havens for biodiversity under climate change[END_REF].

Consistently with our second hypothesis, the predicted increase in the feeding specialisation (FS) of communities was more generalised over France with more than 70% of the sites involved. Moreover, we highlighted negative and hump-shaped responses of FS across gradients of changes in phosphate concentration and temperature, respectively (Fig. 3b). As a result, low FS values corresponded to strong phosphate decreases, which were associated to changes from hypertrophic to eutrophic conditions, thus less prone to generate significant responses in specialisation of communities. Conversely, the highest increases in specialisation over the past twenty years occurred under weak changes in phosphates and moderate warmings. Such a response pattern would typically correspond to a trophic amplification process by which a moderate temperature increase enhances productivity and promotes specialists of different resource Furthermore, FS positively contributed to the increase in functional diversity of communities, in the same extent than CV (ca 24%), in agreement with our third hypothesis. More specifically, the spatial contribution pattern gave evidence for a greater influence of specialisation in small streams than in large rivers as predicted under our fifth hypothesis. These findings supported the assumption that trophic amplification and bottom-up regulation is more likely to occur in less-complex food webs, like those encountered in headwaters for instance [START_REF] Woodward | The effects of climatic fluctuations and extreme events on running water ecosystems[END_REF]). Higher habitat heterogeneity has been acknowledged to inflate species richness through increased specialisation [START_REF] Ohlemüller | The coincidence of climatic and species rarity: high risk to small-range species from climate change[END_REF][START_REF] Eme | Multi-causality and spatial non-stationarity in the determinants of groundwater crustacean diversity in Europe[END_REF]. Therefore, considering food resources as a component of habitat sensu lato, higher resource heterogeneity would be more likely to enhance the diversity in these communities.

As such, trophic amplification processes could be involved in partial mitigation of the deleterious warming effects on biodiversity in headwaters, which are particularly sensitive to climate change [START_REF] Durance | Climate change effects on upland stream macroinvertebrates over a 25-year period[END_REF]Ormerod 2007, Buisson et al. 2008), especially at high elevations where cold-adapted species are already at the edge of their geographical distribution range [START_REF] Domisch | Modelling distribution in European stream macroinvertebrates under future climates[END_REF].

While the long-term changes in functional diversity were strongly driven by the climate/productivity mechanisms represented by CV and FS, they were also influenced by the regional species-pools, as emphasised by the significant contribution of g 0 (ca 17%), thus supporting our sixth hypothesis. Overall, the functional diversity increase was less pronounced in regions with higher initial richness. The spatial contribution pattern of g 0 revealed that this relationship was almost equally important over France. Basically, this result can be explained by the fact that the more diverse were the communities, the fewer were the available niches and, thus, the narrower was the margin for a potential functional diversity increase. More broadly, this response pattern can also be related to the spatial insurance hypothesis, which states that diversity acts as insurance for ecosystem functioning against environmental changes, especially at large spatial and temporal scales [START_REF] Loreau | Biodiversity as spatial insurance in heterogeneous landscapes[END_REF][START_REF] Shanafelt | Biodiversity, productivity, and the spatial insurance hypothesis revisited[END_REF]. These spatial insurance effects rely on spatial exchanges among local systems [START_REF] Loreau | Biodiversity as spatial insurance in heterogeneous landscapes[END_REF], thereby depending on dispersal processes that are essential to community persistence within heterogeneous landscapes [START_REF] Tonkin | Dispersal distance and the pool of taxa, but not barriers, determine the colonisation of restored river reaches by benthic invertebrates[END_REF]). As a result, more diverse assemblages are expected to be more stable since different species will have various responses to environmental fluctuations that compensate each other, hence stabilising community productivity in time [START_REF] Loreau | Biodiversity as spatial insurance in heterogeneous landscapes[END_REF]. Furthermore, it is worth noting that the lowest temporal variations in functional diversity of invertebrate communities were also related to weak changes in feeding specialisation. In other words, functional diversity was more stable at the sites where specialists did not significantly increase. This observation may have involved differential responses among communities depending on their dominant initial feeding strategy, since a greater insurance potential is expected for communities made up of generalists [START_REF] Matias | Ecological strategies shape the insurance potential of biodiversity[END_REF]. Thereby, invertebrate assemblages mainly composed of feeding generalists would have been already 'stable' by the end of the 1990s, making them (nearly) unchanged in response to climatic and trophic changes afterwards. Conversely, specialist assemblages would have reached (or will reach) this stable state several years later. Following this assumption, we could now expect equivalent insurance potentials given that 1) the diversity-productivity relationship is steeper for specialist communities [START_REF] Gravel | Experimental niche evolution alters the strength of the diversity-productivity relationship[END_REF]) and 2) generalist and specialist communities tend to be similarly productive at higher levels of diversity [START_REF] Matias | Ecological strategies shape the insurance potential of biodiversity[END_REF].

Nonetheless, -whatever the ecological strategies involved (e.g. specialists vs generalists) -the counterpart of the spatial insurance is a buffering effect of biotic interaction processes which can lead to a homogenisation of the regional ecosystems and its subsequent risks of biodiversity loss [START_REF] Olden | Ecological and evolutionary consequences of biotic homogenization[END_REF][START_REF] Shanafelt | Biodiversity, productivity, and the spatial insurance hypothesis revisited[END_REF][START_REF] Wang | Biodiversity and ecosystem stability across scales in metacommunities[END_REF]. Up to now, however, there is no evidence for a homogenisation pattern emerging at the scale of France thanks to the geographical differentiation of the functional processes involved in the maintenance of species diversity. Conversely, the largescale rise in diversity even provides a greater resilience capacity to invertebrate communities against disturbances [START_REF] Mori | Response diversity determines the resilience of ecosystems to environmental change[END_REF][START_REF] Isbell | Biodiversity increases the resistance of ecosystem productivity to climate extremes[END_REF]). Similarly, for example, the regional zooplankton biodiversity has been shown to partially dampen the effects of temperature warming on ecosystem productivity [START_REF] Thompson | Regional zooplankton biodiversity provides limited buffering of pond ecosystems against climate change[END_REF].

Beyond these present trends, one could also wonder how invertebrate communities will further respond to future changes. Even though the decrease in climate vulnerability has sustained a gain in diversity for now, the growing number of colonizing tolerant taxa could, in return, foster species losses by competitive exclusions [START_REF] Buisson | Climate change hastens the turnover of stream fish assemblages[END_REF]. Moreover, the most sensitive taxa still present up to now are expected to gradually disappear owing to distribution range contractions due to rising temperatures [START_REF] Domisch | Modelling distribution in European stream macroinvertebrates under future climates[END_REF]. Similarly, the positive effect of the trophic amplification on diversity -as being based on moderate warmings -could be drastically dampened or suppressed by even-warmer temperatures. Finally, the spatial insurance effects are also expected to be less effective in maintaining community diversity in the face of global changes like climate change due to increasing synchrony among ecosystems [START_REF] Shanafelt | Biodiversity, productivity, and the spatial insurance hypothesis revisited[END_REF].

Under these threats to biodiversity, we argue that the present study can provide insights for practical conservation. Overall, our findings provided a strong support to the relevance of the functional indices built for this study, which allowed explaining about 75% of the long-term changes in the functional diversity of invertebrate communities over the last two decades in France. As such, they reinforced the great interest of using species traits and/or trait-based composite metrics to investigate specific issues like large-scale, long-term drivers of functional diversity of communities. In addition, we emphasised the importance of taking into account the spatial non-stationarity of ecological processes and responses when carrying out such investigations. As a consequence, we were able to highlight both direct and indirect effects of climate change on running water ecosystem functioning and whether these processes differed spatially, offering wider perspectives in a better identification of 1) geographical areas and/or stream types that need a priority protection, and 2) potential mitigation options that could be considered.

Figure 1 .

 1 Figure 1. Overall workflow for statistical analyses. The upper dashed box depicts the relationships between the environmental variables (i.e. temporal and spatial predictors and MEMs) and the three indices [i.e. changes in climate vulnerability (CV), changes in feeding specialisation (FS) and initial g-diversity (g 0 )], assessed with GAM models. The lower dashed box depicts the relationships between the three indices (i.e. CV, FS and g 0 ) and the changes in functional diversity (FD), assessed with GWR models. See Material and methods for further details on variable definition and model computation.

Figure 2 .

 2 Figure 2. (a-d) Smoothed maps of observed patterns for the four indices over France (see Material and methods for details on index definitions): (a) changes in climate vulnerability (CV); (b) changes in feeding specialisation (FS); (c) initial g-diversity (g 0 ); (d) changes in functional diversity (FD). (e-f ) Smoothed maps of GWR results: (e) FD predicted by the final model; (f ) R² values. Points indicate the site locations.

Figure 3 .

 3 Figure 3. Examples of index responses to environmental predictors assessed with GAMs: (a) changes in climate vulnerability (CV) modelled across gradients of catchment area and changes in temperature; (b) changes in feeding specialisation (FS) modelled across gradients of changes in phosphate concentration and temperature; (c) initial g-diversity (g 0 ) modelled across gradients of urban land-cover and altitude.

Figure 4 .

 4 Figure 4. (a-c) Smoothed maps of contribution to changes in functional diversity (FD) assessed with GWR models: percentage of variance explained by (a) changes in climate vulnerability (CV); (b) changes in feeding specialisation (FS); (c) initial g-diversity (g 0 ). Points indicate the site locations. (d) Relationship between CV contribution and latitude (black dots). The grey area represents the 95%-confidence interval of a linear regression model. (e) Relationship between FS contribution and river size (small  1st-2nd Strahler order, medium  3rd-5th order, large  6th order and more). As the sites were unequally distributed across the river size gradient, the boxplots were computed by randomly sampling 50 sites (with replacement) of each size.

Table 1 .

 1 Details on the variables used to describe the different spatial scales.

	Spatial scale	Type of variable	Variable	Details
	Regional	Biogeochemical	Carbonates	Calcium concentration 1 averaged over 1992-2013
		Geographical	Altitude	Measured at the sampling site
	Catchment	Geographical	Area	Upstream catchment surface
		Hydrological	Hydrographic network density	Calculated over the upstream catchment
		Land-cover	Intensive agriculture	Proportion (%) of the upstream catchment 2
		Land-cover	Riparian forest	Mean proportion (%) of the upstream 30-m riparian buffer 3 ,
				i.e. averaged over the upstream stretches and tributaries
	Reach	Land-cover	Urban area	Proportion (%) of the 100-m riparian buffer 2
		Land-cover	Riparian forest	Proportion (%) of the 30-m riparian buffer 3
		Morphological	Channel straightening rate	Proportion of straight units over the stretch
		Morphological	Weir density	Number of weirs/stretch length
		Hydro-morphological	Potential stream power	rgQ 99 S v 4

1 these data were extracted at < www.data.eaufrance.fr >. 2 these data were extracted from the Corine Land Cover GIS layer (EEA 2007).

Table 2 .

 2 Summary results of the final additive models: percentage of variance in the three indices explained by the different sets of predictors (temporal, spatial and MEMs).

	Variance explained (%)
	Spatial predictors

types

[START_REF] Yvon-Durocher | Five years of experimental warming increases the biodiversity and productivity of phytoplankton[END_REF][START_REF] Van Looy | Long-term changes in temperate stream invertebrate communities reveal a synchronous trophic amplification at the turn of the millennium[END_REF]

).

Table 3 .

 3 Summary results of the GWR models. Global coefficients denote the percentage of variance in functional diversity (FD) explained by the three indices and MEMs. Local extremes ('min', 'max') and standard deviations ('SD') were calculated from the independent regression parameters estimated at the 305 sites.

				Variance explained (%)
	Coefficients	CV	FS	g 0	MEMs	Total
	Global Local	min	23.8 0 *	23.4 5.2	16.7 1.2	10.5 -	74.4 -
		max	42.7	40.9	23.5	-	-
		SD	9.9	8.2	4.9	-	-
	* negative values arising from the partial GWR approach were con-
	sidered as null.

Acknowledgements -We thank the Regional Environment Directorates (DREALs) for their collaboration in harmonising the long-term invertebrate data series used in this study, and more particularly the macroinvertebrate biologists for the quality and the continuity of the sampling network. We are very grateful to Marta Prieto-Montes and Martial Ferréol for their considerable work in collecting, compiling and cleaning the data used in this study, and to the editor for constructive comments on the manuscript. Funding -This work received a financial support from EDF R&D.


Prou -F. Vernier -R. Mongruel -C. Bacher -P. Bordenave -J. Candau - F. Delmas -H J Levrel -

J Perez

-P Raux

- A Rivaud

-K Petit

SSA n°10 -PERTUIS CHARENTAIS FRESHWATER MANAGEMENT ON THE CHARENTE RIVER BASIN AND ITS COASTAL ZONE Partners of Study Site n°10 -Pertuis Charentais

HYDROLOGICAL SYSTEM

AGRICULTURE SHELLFISH FARMING

The SSA10 formulation approach BIODIVERSITY Biodiversity issue "species" Input : Water volume Output : Abundance of eels, salmon, shad and lamprey. Surface of wetlands.

Processes : If the volume of water is under a certain threshold, abundance of species decrease.

Biodiversity issue "wetlands"

Input : Water volume Output : Regulation services (buffering and filtering) Processes : If the volume of water is under a certain threshold, regulation services decrease.

Summer restrictions on water pumping for irrigation

Farmers are allowed to pump a maximum annual volume (VTW y) of freshwater for irrigation. At the beginning of summer (16th June), a yearly bylaw authorizes farmers to pump a maximum volume (VTW yt -For year y and ten days period t) reduced by the prior pumping from 1st April to 15th June (V cons ).

VTW yt = VTW y -V cons At each ten days period t, measured flow rates of each tributary is compared to thresholds defined by law each year. Restriction are applied on pumping allowance if flow rate are under threshold.

Restrictions are calculated as a decreasing percentage (α t, β t, μ t ) applied to the maximum authorized volume (VTW yt ). α t, β t, μ t are given each year by law and depends on the period (decreasing from 15th June to 1 st September).

GOVERNANCE SYSTEM

α t VTW yt (1 -α t ) DOE DI VTW yt (1 -α t ) β [VTW yt (1 -α t )](1 -β t ) DC [VTW yt (1 -α t )](1 -β t ) μ t =

Aim:

  preserving balanced water uses at the scale of the Charente hydrosystem first for the good natural functioning of aquatic ecosystems and the supply in drinkable water, then for other domestic uses, industries and crops irrigation Inputs: Climatic forcing variables (precipitations, sun irradiance, PET) Soil occupation (urban areas, agriculture,...) Necessary data: Stock of water in dams, daily dam management data Uptakes (drinkable water, irrigation,…) Outputs: Groundwater daily levels at sub-basin key-points Daily mean flow of Charente at the downstream key-point (Beillant) Indicators: annual duration of low-flow under the threshold, annual duration of pumping interdiction … Processes: the catchment water stocks increase during winter due to precipitation. Some of the water stocks in soils, wetlands and underground aquifers and a part of the flow is stored in dams. Some water demands occur all along the year (drinking water, other domestic uses, industrial water, minimum needs for natural functioning of aquatic ecosystems) other ones are more seasonal during low-flow periods (irrigation=80% of the uptakes in summer). Two kinds of regulation have been set-up : a inter-annual participatory negotiation leading to the allocation of quotas to the different uses A day-to-day monitoring during low-flows by respect to thresholds ("crisis" management) : crisis regulations are gradually set-up if flow > low-flow threshold then pumping allowed (limit = uptake authorization) If flow < low-flow threshold then pumping interdiction for secondary uses (crop irrigation, other domestic uses…) Scenarios: Increasing the minimum freshwater discharge (DOE) Increasing the substitution storage volumes Aim This economic activity is concerned by the water management by the fact that water represents an economic production factor for the oyster cultures (spat and adults). Basic segmentation of companies : -Companies specialised on spat collection (collect and sell spat) -Other companies (produce and/or sell oysters at collect a part of their spat needs) Inputs: water availability, coastal water salinity, temperature, shellfish farming policy Necessary data : Shellfish farming practices/ growth and spat collection functions Outputs : Binomial decision in terms of water demand If 1 = demand If 0 = no demand Pressure indicators (spatialised or aggregated) Technical and economical results/year (depend on the satisfaction of the water demand) Processes -Water and ecosystem factors determine spat collection and growth of oyster functions -Spat collection function determines the spat production of all companies -For companies specialised on spat collection: if revenue issue from spat production lower of a fixed level, then insatisfaction and then fresh water claim -In case of water lack then a) direct impacts in real time for spat collection if penury in summer (in July-August) b) Shifted impacts on oyster growth if lack in summer (because no growth in reproductive period) -For the other companies : 2 possibilities a) If expected spat production is lower than observed then fresh water claim (same period) b) If the oyster growth rate is lower than a fixed level, then insatisfaction. A cumulative situations of insatisfaction drive toward a fresh water claim. If cumulative effects in several years then possibility to anticipate water claims Scenarios : Changes in water availability (climatic changes, farming practices, etc.) Changes in spat collection strategies Changes in oyster growth rates

Table of restrictions on Volumes during summer

	Flow rates Thresholds	VTW yt before exceeding thresholds	decreasing percentage	VTW yt when exceeding thresholds
	DSA	VTW yt

Agriculture

Aim: Because of an important increase of irrigated areas since the 70s, Charente river basin face important imbalance between the available water resources and uses. The relationships between agricultural activities and the water resources (water demand for crops, diffuse pollution pressure) must be characterized upstream (main irrigated area) and downstream.

Processes:

Several temporal scales need to be addressed: -An inter-annual management: which type of crops in which area (risk assessment)? Depending on the climate of previous years, the market, the previous results of the farmer (satisfaction of the water demand for crops, yield, profit


Adrien Contesse

Chloé Thomas

Claudia S Bianchini

Claire Danet

Patrick Doan

Morgane Rébulard

Jean-François Dauphin

Léa Chèvrefils

Mathieu Réguer

Dominique Boutet

Toward a typeface for the transcription of facial actions in sign languages

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

Each qualifier from the graphematic formula has its own symbolic "generic" glyph. These glyphs enable the transcription of any facial action using only a few glyphs which greatly reduces the amount of time needed to transcribe facial actions corpora.

An 18m 20s long facial action corpus of two deaf signers has been recorded using two different cameras. The first one, RGB HQ, is used to capture a high quality image and the second, infrared Kinect, is used to captured the depth. The latter was linked with Brekel Proface 2 ( Leong et al. 2015 ), a 3D animation software that enables automatic recognition of facial actions. This corpus has been fully annotated using Typannot's generic glyphs. These annotations were then compared to the automatic recognition results given by Breckel Proface 2.

Typannot graphematic formula is based on a 3 dimensional grid. Indeed all the different configurations of facial actions can be described by its X, Y, Z axis positions. As a result, all facial actions be described and encoded using a restricted list of 39 qualifiers. This methodical decomposition of all facial components enables a precise and accurate transcription of a complex facial.

Typannot is an interdisciplinary project led by linguists, designers, and developers, which aims to set up a complete transcription system for SL that includes every SL parameter : handshape, localisation, movement, facial actions.

All facial actions can be transcribed using only six active facial parts. Indeed some facial parts like the lips and nose are physicaly linked so that positions of the former induce positions of the latter.


Alejandro Gronskis

Dominique Heitz

Etienne Mémin

Control of unsteady wake flows using local oscillation of body surface: a data assimilation study

Variational data assimilation (DA) can expand active flow control techniques to design wall actuators such as synthetic jets or plasma discharges which are difficult to model computationally due to ambiguous boundary conditions at the wall. Here, the control vector for the DA problem is formed by the initial flow and the solid boundary conditions for the body, that means its tangential speed at all times where no particular form is prescribed to the body motion. The control domain takes into account the modeled body surface by means of a direct forcing immersed boundary method (IBM). We consider a configuration of reference flow past a rotationally oscillating cylinder given by Mons & Sagaut, 2017, J. Fluid Mech.. The proposed methodology is applied to the reconstruction of a reference flow generated by a partial control restricted to an upstream part of the cylinder surface as given by Bergmann & Cordier, 2006, Phys. Fluids. DA is also employed to build wall conditions for a direct numerical simulation (DNS) of flow around an airfoil with local oscillation, from synthetic observations of the wake flow downstream the body.

Data assimilation for flow spatio-temporal reconstruction

Goal Provide a DA technique integrating experimental data and DNS to reconstruct the flow dynamics around complex stationary or moving geometries

∂ t X (x, t) + M(X (x, t), η(t)) = 0 X (x, t 0 ) = X 0 (x) + (x) Dynamical model ∇ • u = 0 ∂u ∂t = -∇p - 1 2 [∇(u ⊗ u) + (u • ∇)u] + ν∆u + f

Data Assimilation -Cost Functional

Minimization problem constraint ⇒ state dynamics ⇒ dependence of the system's state variable X on the control variable γ X ≡ u(γ), γ = { (x), η(t)} ≡ {u(x, t 0 ), u(x S B , t)} Objective lowest discrepancy between observations and state variable

J(γ) = t N t 1 Ω A ω(x, t) -ω obs (x, t) 2 R d x ∆ t * dt + ν(x) Ω C u(x, t 0 ) - u k=0 (x, t 0 ) 2 d x
w c (θ g , t) = Γ(θ g ) A sin (2πft)

Local control on the airfoil upper surface

Flow configuration non-uniform tangential speed of the NACA0012 at Re=1000 and α=10 • :

v t (x g , t) = Γ(x g ) A sin (2πft)

Controlled airfoil by arrays of actuators

Flow configuration non-uniform tangential speed of the NACA0012 at Re=1000:

upper wall: v t u (x g u , t) = Γ(x g u ) A u sin (2πf u t)
lower wall: v t l (x g l , t) = Γ(x g l ) A l sin (2πf l t)

Conclusion and Outlook

A new method for reconstructing the flow field from limited measurements where no velocity information is available in a neighborhood of the solid boundary has been introduced. Though being restricted to reasonable mesh resolution at the body surface, present technique allows for an accurate pressure reconstruction in a region close to the solid boundary.

The addition of a penalization term for the wall condition in the cost function will allows us to prevent drastic changes in the temporal solution during the optimization process.

Introducing a moving boundary cond. as a control parameter will extend VDA to FSI.

1 aleg@fi.uba.ar 2 dominique.heitz@irstea.fr

  F k ) ∆x ∆y IBM for simulating flows with moving rigid boundaries Gronskis et al., 2016, Comput. Fluids

  Control on the Initial and Wall ConditionFlow configuration rotational speed of the cylinder at Re=100: w c (t) = A sin (2πft) Partial control on the cylinder surface Flow configuration non-uniform rotational speed at Re=200 and θ c =120 • :