Roger
email: fruget@aralep.com

Keywords: freshwater macroinvertebrates, Rhône River, climate change, long-term survey, biological traits, alien species

    Long-term effects of global and local changes on benthic macroinvertebrate communities in multi-stressed large rivers: The example of the Rhône River during the last 30 years

The study of biological traits have enhanced the understanding of the changes in the macroinvertebrate communities of the Rhône River during the last thirty years, as well as the potential effects of hydroclimatic factors and thermal discharges on the structure and the functioning of these communities at the regional scale. If every section of the Rhône had specific features, we observed over time a trend towards a higher uniformisation of invertebrate communities, especially in the Lower section. The strong impacts of the alien species and the water warming subsequent to the 2003 heat wave have been detected in the Lower Rhône and the Middle Rhône: the communities of the Middle Rhône gradually exhibit profiles closer to those of the communities of the Lower Rhône. The Upper Rhône was less colonized by alien species but was impaired by the global warming: its communities exhibited biological profiles closer to those of communities of further-downstream zones. In this site, the thermal discharges have led to a lower diversity of the communities and a higher occurrence of eurythermic species. Hence the benthic macrofauna of the Rhône River seems to have reacted quickly and strongly to environmental changes and to the arrival of invasive species. However numerous trait adaptations being common to Mediterranean and alien species, it seems complex to evaluate the respective weight of each of these potential sources of impairment. Predicting trends in invertebrate community composition is a complex objective because of the competition between native and/or invasive species in addition to man-induced environmental variation (flow, temperature). However, if biological invasion does not occur continuously but only based on specific events (especially hydroclimatology), we can legitimately believe that this drift will continue with the arrival of new Ponto-Caspian species via the Danube-Main Canal, their usual way to western and southern Europe. The common feature of these different species is that they are essentially predators or filterers, thermophilic and euryecic, and efficient functional competitors. Finally, this study once again emphasizes the importance of long-term monitoring in the study of biological communities in the context of global warming. En complément de l'aspect systématique, l'étude des traits biologiques a permis de mieux comprendre l'évolution des peuplements de macroinvertébrés du Rhône au cours des trente dernières années, ainsi que les effets potentiels des facteurs hydroclimatiques et thermiques sur la structure et le fonctionnement des peuplements à une échelle régionale. Si chaque tronçon du Rhône possède ses propres particularités, on observe au cours du temps une tendance vers une uniformisation des peuplements à l'échelle du fleuve. Cette tendance s'accentue à mesure qu'on descend le cours d'eau. Le peuplement du Rhône Moyen se rapproche au cours du temps du profil bioécologique du Bas Rhône. Tous deux subissent l'influence des espèces invasives et du réchauffement des eaux suite à la canicule de 2003. Le Haut Rhône subit moins fortement l'influence des espèces invasives mais subit celle du réchauffement climatique. L'effet de l'évolution thermique se traduit par une moindre variété du peuplement, tant du point de vue systématique que fonctionnel, et par une plus grande présence des espèces eurythermes. La macrofaune benthique semble ainsi réagir assez rapidement et fortement à l'évolution du milieu et à l'arrivée d'espèces invasives. Prédire l'évolution de la composition des peuplements est un objectif complexe car la compétition entre les espèces natives et/ou invasives s'ajoute aux effets des modifications environnementales liées aux activités anthropiques (débit, température). Toutefois, si le flux d'invasion n'apparaît pas continu mais fonction d'événements précis (en particulier hydroclimatiques), on peut légitimement penser que cette dérive va se poursuivre avec

INTRODUCTION

The effects of climate change on the functioning of freshwater ecosystems have become more and more apparent over the past three decades and they are now evident (IPCC, 2013). However, long-term global-change studies are scarce, especially those on the effects of global change in large rivers. This scarcity is due to the scarcity of available long-term data sets (Daufresne and Boet, 2007). Studies and models of the effects of global change on freshwater systems currently predict an increasing seasonality in discharge regime (i.e. more frequent floods and drought events) and decreasing mean annual discharge [START_REF] Hendricks | Impact hydrologique d'un changement climatique sur le bassin du Rhône[END_REF][START_REF] Dai | Changes in continental freshwater discharge from 1948-2004[END_REF][START_REF] Stahl | Streamflow trends in Europe: evidence from a dataset of near-natiral catchments[END_REF][START_REF] Giuntoli | Évolutions observées dans les dénits des rivières en France. Sélection d'un réseau de référence et analyse de l'évolution temporelle des régimes des 40 dernières années. Collection « Comprendre pour agir[END_REF]. These thermal and hydrological changes have important ecological consequences. Water temperature has a fundamental role in the behaviour, growth and metabolism of aquatic organisms, but also in primary production, for example [START_REF] Stenseth | Ecological effects of climate fluctuations[END_REF]. This leads to significant changes in community structure and composition, especially among macroinvertebrate communities (Daufresne et al., 2004(Daufresne et al., , 2007;;Durance andOrmerod, 2007, 2009;[START_REF] Floury | Global climate change in large European rivers : long-term effects on macroinvertebrate communities and potential local confounding factors[END_REF]. For several decades many large rivers around the world have been subject to numerous global and local stressors (climate change, river channelization, dams, urban and industrial inputs, land use of their catchment, etc.) (Petts et al., 1989;[START_REF] Dynesius | Fragmentation and flow regulation of river systems in the northern third of the world[END_REF][START_REF] Tockner | Multiple stressors in coupled river-floodplain ecosystems[END_REF]. Despite the wide range of studies published within the field of climate change, the complex interactions of global changes with local changes in this multiple-stressor context have rarely been studied.

The aim of this study was to fill this gap using long-time series from a large river affected by simultaneous stressors and the effects of climate change. The French Rhône River is subject to multiple disturbances (Figure 1) such as hydropower dams, warmed water discharges of nuclear power plants (NPP), urban and industrial inputs from large cities, etc. [START_REF] Fruget | Ecology of the Lower Rhône following 200 years of human influence: a review[END_REF][START_REF] Fruget | Changements environnementaux, dérives écologiques et perspectives de restauration du Rhône Français: bilan de 200 ans d'influences anthropiques[END_REF]. A survey of the thermal discharges of NPP over more than 30 years has allowed us to study the thermal changes in the Rhône River and their long-term global and local effects on the aquatic fauna and flora, especially on the benthic macroinvertebrate communities. Previous studies on the Rhône River macroinvertebrate communities [START_REF] Bady | Étude thermique globale du Rhône. Phase 3. Influence de la variabilité hydroclimatique 1985-2004 sur les peuplements de macroinvertébrés[END_REF]Daufresne et al., 2007) have shown (i) a longitudinal gradient with clear differences between the Upper and the Middle and Lower Rhône communities (i.e. upstream vs. downstream from Lyon and the Saône/Rhône confluence), (ii) a gradual shift from psychrophilic (coldwater) and rheophilic (fast-water) species towards thermophilic (warm-water) and limnophilic (slow-water) species, and (iii) no significant differences between sites located upstream vs. downstream from warmed water discharges. The main driver of theses changes appeared to be climate change. [START_REF] Khalanski | Etude thermique globale du Rhône -Impacts hydrobiologiques des échauffements cumulés[END_REF] showed an increase of the river temperature by 1.6 • C in the Upper Rhône (Bugey) and by 3.0 • C in the Lower Rhône (Aramon) during the 1977-2004 period. These authors considered that the part due to the thermal discharges of nuclear power plants was 0.6 • C downstream from Lyon and 1.4 • C upstream from Aramon. Three NPP and a cold-water tributary (the Isère River) are located between these two points. Previous studies have shown that the Middle and Lower Rhône macroinvertebrate communities significantly changed after the flood of november 2002, the heat wave of summer 2003, and the arrival of alien species (which occasionally became invasive). Meanwhile the Upper Rhône community became more similar to the characteristic communities of the watercourse downstream parts. These changes were gradual and mainly related to specific hydroclimatic events. The Rhône River reacted primarily to environmental conditions (flow and temperature; Figure 2). At the local scale, the effect of thermal discharges was detected through a higher proportion of eurythermic species and a homogenization of bio/ecological attributes in communities, suggesting the settlement of a macroinvertebrate assemblage more homogeneous and more tolerant to environmental changes. So far, most studies on large rivers have primarily focused on the taxonomic structure of invertebrate assemblages. However, several recent studies examined the trait responses of communities to various types of multiple [START_REF] Statzner | Can biological invertebrate traits resolve effects of multiple stressors on running water ecosystems?[END_REF] or single pressures, e.g. global warming [START_REF] Bonada | Taxonomic and biological trait differences of stream macroinvertebrate communities between Mediterranean and temperate regions: implications for future climatic scenarios[END_REF], exotic species proliferation [START_REF] Statzner | Biological attributes discriminating invasive from native European stream macroinvertebrates[END_REF], eutrophication [START_REF] Lecerf | Assessing functional integrity of eutrophicated streams using direct and indirect approaches: litter breakdown versus macrobenthic assemblage taxonomic and trait structure[END_REF], salinity [START_REF] Piscart | Biodiversity patterns along a salinity gradient: the case of net-spinning caddisflies[END_REF][START_REF] Piscart | The role of salinity in the selection of biological traits of freshwater invertebrates[END_REF], sediment toxicity [START_REF] Ducrot | Using aquatic macroinvertebrate species traits to build test batteries for sediment toxicity assessment: accounting for the diversity of potential biological responses to toxicants[END_REF], or river dynamics loss [START_REF] Statzner | Invertebrate traits for the biomonitoring of large European rivers: an initial assessment of trait patterns in least impacted river reaches[END_REF].

MATERIALS AND METHODS

> STUDY AREA

An environmental long-term survey of four nuclear power plants located on the French (i.e. below the Swiss border) Rhône River over the three geographic areas (i) Bugey, (ii) Saint-Alban, (iii) Cruas and Tricastin was performed since the beginning of the 80s. The Bugey site was located on the Upper Rhône (i.e. the portion of the river between the Swiss border and the confluence with the Saône River in Lyon), about 44 km upstream from the confluence; that of Saint-Alban on the Middle Rhône (i.e. the portion between the confluences of the Saône and Isère Rivers with the Rhône) 48 km downstream from Lyon; and those of Cruas and Tricastin on the Lower Rhône (i.e. the portion downstream from the Isère River to the delta), respectively 148 and 184 km downstream from Lyon (Figure 1). Three stations were sampled at each site: one upstream (0.5 km upstream at Cruas and Tricastin, 1.5 km at Saint-Alban but 5 km upstream at Bugey) called "upstream"; immediately downstream from the warmed water discharge (0.5 km downstream for all sites) and called "discharge"; far downstream from the discharge after mixing had begun (3 km downstream at Cruas, 6-7 km at Bugey and Tricastin, 13 km at Saint-Alban) called "downstream".

Figure 2

Synthesis of the changes in the macroinvertebrate communities of the Rhône River between 1985 and 2004 [START_REF] Bady | Étude thermique globale du Rhône. Phase 3. Influence de la variabilité hydroclimatique 1985-2004 sur les peuplements de macroinvertébrés[END_REF].

> DATA COLLECTION

The study was based on invertebrate samples collected with artificial substrates during a period of 32 years . The sampling design included over 1500 samples collected four times per year (i.e. one campaign per season) and per station. This method consisted in introducing an "empty" habitat into the environment for it to be be colonized by the local invertebrate fauna (see [START_REF] Khalaf | Colonization of artificial substrata by macroinvertebrates in a stream and variations accordind to stone size[END_REF]. The composition of the artificial substrates had to be as close as possible to the substrate types naturally present in the sampled environment. If the method did not allow a direct evaluation of macroinvertebrate densities per surface unit (the artificial substrate itself represented the "catch per unit effort", CPUE), its robustness was ensured by both the high reproducibility of the results and the high number of samples performed during the study period. Two types of artificial substrates were used during this study: (i) CTGREF-type substrates composed of a stack of parallel cement disks with synthetic brushes (Bugey, Cruas and Tricastin) and (ii) IBGA-type substrates originally developed for the monitoring of the site of Saint-Alban, and now used for the whole monitoring network of the French large and deep rivers by Water Agencies, and composed of sisal string and stones. These data have been archived in a database with Access software. Parallel to biological data, water quality was evaluated each year in four seasonal sampling campaigns, in particular the parameters describing organic matter (O 2 content and BOD 5 ) and nutrients (nitrogen and phosphorus).

Water temperature and Rhône discharge were also evaluated at each site. Water temperature was recorded hourly by automatic recording stations upstream from the NPP. Discharge was expressed by the hydraulicity coefficient, i.e. the ratio of the mean annual value to the mean inter-annual value. The discharge values were those of the gauging stations of Lagnieu, Ternay and Viviers, located immediately upstream from the nuclear plants of Bugey, Saint-Alban and Tricastin, respectively. Their mean inter-annual discharges were respectively 457, 1023 and 1477 m 3 /s over the 1920-2011 period.

> DATA ANALYSIS

Time periods

The preliminary analysis [START_REF] Bady | Étude thermique globale du Rhône. Phase 3. Influence de la variabilité hydroclimatique 1985-2004 sur les peuplements de macroinvertébrés[END_REF]Daufresne et al., 2007)

Taxonomy-based approach

Taxa with only one occurrence or less than five individuals over the whole sampling design were removed from the analysis to avoid giving excessive weight to rare taxa. As a result, only 222 taxa were included in the analyses. Individuals were identified at the species level whenever it was possible. Only the genus level was identified for several invertebrate samples from Cruas and Tricastin. The Diptera were identified only at the family or subfamily level. Abundances of taxa were log-transformed (x i replaced by log (x i + 1), with x i being the abundance of taxon "i") so as to reduce differences in the weight of abundant vs. rare taxa.

A Correspondence analysis (CA) was applied to (i) the whole data array, and (ii) the array including the mean composition of station assemblages per year. Because the same temporal trends were observed in both analyses, only the second strategy will be described for better readability.

The first axis of these analyses (not shown here) opposed the Upper Rhône and Middle Rhône, while both sites of the Lower Rhône, Cruas and Tricastin, superposed in an intermediate position and described the second axis (periods 1 and 2 on the positive side and period 3 on the negative one). This indicated that these two sites had the same community basis and the same temporal variations, hence they will be grouped under the name of "Lower Rhône" for further analyses and discussions.

Trait-based approach

Based on the River Habitat Templet [START_REF] Southwood | Habitat, the templet for ecological strategies?[END_REF][START_REF] Townsend | Species traits in relation to a habitat templet for rivers systems[END_REF], the trait-based approach examines how habitat filters, including anthropogenic pressure, select combinations of morphological, physiological and behavioural traits or ecological preferences in local invertebrate communities [START_REF] Tachet | Invertébrés d'eau douce, Systématique, biologie, écologie[END_REF][START_REF] Usseglio-Polatera | Long-term effects of global and local changes on benthic macroinvertebrate communities in multistressed large rivers: the example of the Rhône River during the last 30 years[END_REF]. A fuzzy coding method based on scores (from 0 to 3) allocated to each taxon for the different categories of a trait (see Chevenet et al., 1994;[START_REF] Tachet | Invertébrés d'eau douce, Systématique, biologie, écologie[END_REF] was applied to describe the biological and ecological trait profiles of the taxa.

Matching taxonomy with bio-ecological information

Co-inertia analysis [START_REF] Dolédec | Co-inertia analysis: an alternative method for studying speciesenvironment relationships[END_REF] was applied to examine the relationships between the spatio-temporal distribution of invertebrates in the Rhône River and their biological or ecological traits. All analyses were performed with R software using ade4 package.

RESULTS

> ENVIRONMENTAL TRENDS

Despite inter-annual variations, mean annual discharges showed a decreasing trend along the study period (Figure 3). The regression coefficients R 2 are respectively 0.155 for Bugey, 0.085 for Saint-Alban and 0.129 for Tricastin. An inverse trend is noted for temperature (Figure 3). The regression coefficients R 2 are respectively for each sector 0.281, 0.035 and 0.461. However, it appears lower in Saint-Alban, partly due to the post-2004 years (R 2 = 0.093 over the period [1985][1986][1987][1988][1989][1990][1991][1992][1993][1994][1995][1996][1997][1998][1999][2000][2001][2002][2003][2004]. These low linear regressions give rather trends than certainties. However, the number of dots used remains low; these are derived from average values, resulting in a smoothing of the data.

Taxonomic approach

The eigenvalues of the global CA (Figure 4) show that the first two axes explain 10.7% and 9.2%, respectively, of the total inertia of the data table. Only the most contributing taxa (invasive and/or indigeneous taxa of the river macrofauna according to our expertise) are represented on the factorial map.

The first axis (X-axis) discriminates the three sites spatially,indicating a fundamentally different community along the Rhône while the second axis (Y-axis) shows a temporal evolution towards a more or less pronounced unified community in each site. The Upper Rhône appears as the site with the highest taxonomic diversity 1 9 8 2 1 9 8 4 1 9 8 6 1 9 8 8 1 9 9 0 1 9 9 2 1 9 9 4 1 9 9 6 1 9 9 8 2 0 0 0 2 0 0 2 2 0 0 4 2 0 0 6 2 0 0 8 2 0 1 0 2 0 1 1 9 8 2 1 9 8 4 1 9 8 6 1 9 8 8 1 9 9 0 1 9 9 2 1 9 9 4 1 9 9 6 1 9 9 8 2 0 0 0 2 0 0 2 2 0 0 4 2 0 0 6 2 0 0 8 2 0 1 0 2 0 1 2

Hydraulicity Rhône Tricastin

y = -0,0073x + 1,1125 R 2 = 0,1285 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4
1 9 8 2 1 9 8 4 1 9 8 6 1 9 8 8 1 9 9 0 1 9 9 2 1 9 9 4 1 9 9 6 1 9 9 8 2 0 0 0 2 0 0 2 2 0 0 4 2 0 0 6 2 0 0 8 2 0 1 0 2 0 1 2 9 8 2 1 9 8 4 1 9 8 6 1 9 8 8 1 9 9 0 1 9 9 2 1 9 9 4 1 9 9 6 1 9 9 8 2 0 0 0 2 0 0 2 2 0 0 4 2 0 0 6 2 0 0 1 9 8 2 1 9 8 4 1 9 8 6 1 9 8 8 1 9 9 0 1 9 9 2 1 9 9 4 1 9 9 6 1 9 9 8 2 0 0 0 2 0 0 2 2 0 0 4 2 0 0 6 2 0 0 8 0 0 2 0 1 2

Temperature

Figure 3

Changes in the hydro-climatic variables of the different sections vs. time, expressed as mean annual values. Data from EDF nuclear power plant environmental survey programmes for temperature ( • C) and from CNR gauging stations for discharge, expressed as hydraulicity coefficients (www.rdbrmc.com/ hydroreel2).

linear changes, a real break appeared in the Lower Rhône after 2002. The Upper Rhône also followed this trend although the changes were much less marked. This seems to have lead to a greater uniformity of communities along the river after 2003.

A more detailed analysis of taxon distribution showed the strong influence of recent alien species such as the crustaceans Jaera istri (Jaeist), Chelicorophium curvispinum (Checur) and Limnomysis benedeni (Limben, even in lower numbers), or the polychaete Hypania invalida (Hypinv), in the benthic assemblages of the Middle and Lower Rhône.

> TRAIT-BASED APPROACH

When the bio-ecological average profiles per stations of the Rhône River were established, four main traits showed a temporal effect in the Middle and Lower Rhône: the number of generations (i.e. number of reproductive cycles per year), the mode of reproduction, the respiration and the longitudinal distribution (corresponding to biological traits "number of reproductive cycles per year", "reproduction" and "respiration" and ecological one "longitudinal distribution" in Tachet et al.'s classification -see Appendices 2 and 3). In contrast, the Upper Rhône showed a high temporal stability of its bio-ecological profiles.

A demonstrative example is given with the biological trait "number of reproductive cycles per year" (Figure 5). This trait is stable in the Upper Rhône with a slight dominance of monovoltine species, especially during periods 2 and 3. This temporal change in the two downstream sectors was confirmed by a Kruskal-Wallis test on each of the pairs sector x category of biological trait "number of reproductive cycles per year". Except for the category ">1 cycle : 1979-1987 "1", 1988-2002 "2", 2003-2010 "3" (see Appendix 1 for species codes).

per year" in the Upper Rhône, this test is statistically significant for all pairs considered, very often with the critical value p = 0.01 (Table I). In the Middle and Lower Rhône after the November 2002 flood and the 2003 heatwave it changed from a trait structure based on monovoltine species to a configuration in which the polyvoltine species dominated (a modality presumably influenced by the fact that warmer waters are favourable to alien species).

All the traits analysed show a true change of the community in the Middle and Lower Rhône after the November 2002 flood and the summer 2003 heatwave. Alien and Mediterranean species (and their specific characteristics) became dominant at the expense of more specialized native species. On the other hand, the Upper Rhône was characterized by the relative stability of traits over time.

The eigenvalues of the first two factorial axes in co-inertia analysis (Figure 6) provided 35% and 25% of the total variance in the biological traits, respectively. The first axis opposed the Middle and Lower Rhône vs. the Upper Rhône, while the second axis rather reflected the temporal changes of the first two sectors. The Upper Rhône remained fairly stable over time with a community mainly composed of individuals with short life cycles (<1 year), aquatic larvae and/or pupae, reproducing by terrestrial clutches or cemented eggs, aerial dispersal and eggs as a resistance stage. Both downstream sectors are rather closely located on the first factorial plane during the first two periods (Figure 6). The corresponding communities comprised organisms with tegument

Number of reproductive cycles per year

Figure 5

Functional approach: bio-ecological profiles. Example of average profiles of the biological trait "Potential number of reproductive cycles per year " per site.

Table I

Results of the Kruskall-Wallis test on the pairs sectors x categories of biological trait "number of reproductive cycles per year". * : H critical value for p (0.1%) = 13.815 -** : H critical value for p (1%) = 9.21 -*** : H critical value for p (5%) = 6.0, NS : no significant value. The eigenvalues of the co-inertia analysis (i.e. species abundances x species ecological trait profiles) performed on the ecological traits (Figure 7) show that the first factorial axis represents 71% of the variance and the second one 10%. The first axis opposes the Upper Rhône vs. the Middle and Lower Rhône, while the second axis rather reflects a different temporal drift in the three sectors over the period 2003-2010.

Categorie

In the first two periods, the Upper Rhône invertebrate community was characterized by psychrophilic organisms, living in oligo-and mesotrophic freshwaters, preferentially in the piedmont section (altitude < 1000 m) of rivers, on coarse mineral substrate, with moderate to fast current. The Lower and Middle Rhône communities included eurythermic species from

Figure 6

Co-inertia analysis of the biological traits. The numbers represent traits to which the different modalities belong (see Appendix 2 for trait and modality numbers).

downstream river sections with slow current (i.e. lowland rivers), ponds, marshes, and fine sediments or macrophytes as major bottom substrates. The longitudinal Rhône River community gradient was underlined by clearly different attributes for the traits "altitude" (alpine vs. piedmont and lowlands), "saprobity" (xeno-and oligo-vs. mesosaprobic), "salinity" (freshwater vs. brackish water), "temperature" (psychrophilic vs. eurythermic), "trophic status" (oligo-and mesotrophic vs. eutrophic), "longitudinal distribution" (epi-and hypo-rhithron vs. metapotamon) and "transversal distribution" (river channel vs. side channel). After 2003, the benthic communities of the three sectors became more ordinary with another set of bio/ecological attributes. The characteristics of the Upper and Middle Rhône communities became closer to those of the Lower Rhône as they had been before the 2003 heatwave, while the Lower Rhône community shifted to another type of community composed of thermophilic species of river downstream sections (e.g. metapotamon, and estuary).

DISCUSSION

> TEMPORAL TAXONOMIC AND TRAIT-BASED SHIFT OF THE COMMUNITIES

The gradual shift towards the homogenization of macroinvertebrate communities along the Rhône River noted in 2004 [START_REF] Bady | Étude thermique globale du Rhône. Phase 3. Influence de la variabilité hydroclimatique 1985-2004 sur les peuplements de macroinvertébrés[END_REF] has increased during the more recent years. This trend was especially illustrated by the gradual change from a macrofauna of running and cold headwaters ( e.g. the stoneflies Chloroperla and Protonemura) in the Upper Rhône, to slow-flowing water and thermophilic species assemblages closer to those of downstream areas ( e.g. the caddisflies Hydroptilidae, the stoneflies Leuctridae in the Upper Rhône), with rather limnophilic taxa such as Hydrobiidae and Planorbidae molluscs (all sectors) and the appearance of various alien taxa (such as Corbicula, Dikerogammarus, Hypania in the three sectors and Jaera downstream from Lyon). These results have confirmed the observations made in previous studies on the Upper Rhône: mainly psychrophilic individuals were observed during the first two periods [START_REF] Daufresne | Long-term changes within the invertebrate and fish communities of the Upper Rhône River: effects of climatic factors[END_REF][START_REF] Souchon | Rhône amont. CNPE Bugey. Tendances temporelles de l'hydrologie, de la température et des communautés biologiques de macroinvertébrés et de poisons au cours des trente dernières années[END_REF]. [START_REF] Floury | Global climate change in large European rivers : long-term effects on macroinvertebrate communities and potential local confounding factors[END_REF] found the same trend in the Middle Loire River with a decrease in rheophilic and psychrophilic taxa (e.g. Chloroperlidae) and an increase in limnophilic and thermophilic ones, which were also often invasive species (e.g. Mollusca Corbiculidae) during the last three decades. Downstream from Lyon, the biological characteristics of invasive species and the affinity of invertebrate assemblages for Mediterranean environments increased following the floods of the early 2000s and the heatwave in the summer of 2003. This influence is reflected in the dominant trait categories in invertebrate assemblages during the period 2000-2007, e.g. polyvoltine and ovoviviparous species with gill respiration. It indicates an increase in the thermal effect after 2003 and a water warming. This confirms the observation made by [START_REF] Khalanski | Etude thermique globale du Rhône -Impacts hydrobiologiques des échauffements cumulés[END_REF] of a gradual increase in the average annual temperature along the Rhône River, with a greater shift in its downstream part. Some traits reacted more specifically along the entire river and could thus serve as indicators (i.e. "metrics") of changing environmental conditions. These are:

-the duration of life cycles (less or more than one year) and the number of generations per year (mono-or polyvoltine species) ; -the trophic status; -temperature (psychrophily vs eurythermy), the longitudinal position on the river continuum and preferendum for substrate (coarse vs soft).

> DRIVING FACTORS

Temperature is not the only driving factor which has influenced the French Rhône macrobenthic communities in the past 30 years. Even if they are more difficult to quantify, other driving forces must be considered: (i) the improvement of the physico-chemical quality (nutrients and dissolved oxygen) during the 1980s and early 1990s due to more efficient treatments and efforts to reduce urban wastes [START_REF] Carrel | Caractérisation physico-chimique des eaux du Rhône. Évolution des paramètres classiques au cours de la période 1985 -2004[END_REF], (ii) changes in river dynamics and sediment transport of the Upper Rhône with the gradual commissioning of all the CNR dams during the 1980s, and (iii) the water management of the Upper Rhône and associated energy hydropeakings with their consequences on the regime of the river. Nevertheless the thermal changes seem to be the main drinving factor, with hydrology (during the whole period) and main flood events (more specifically). These were in fact the most common causes of the spread of new taxa while temperature promoted their sustainable settlement [START_REF] Fruget | Changements environnementaux, dérives écologiques et perspectives de restauration du Rhône Français: bilan de 200 ans d'influences anthropiques[END_REF]. These parallel and similar changes in communities subjected to different environmental conditions (e.g. free-flowing Rhône at Bugey vs artificial diversion canal at Tricastin) emphasize the dominant influence of climate change. These observations are in accordance with those made by [START_REF] Daufresne | Impacts des changements climatiques et non climatiques sur les communautés piscicoles de grands fleuves français[END_REF] and [START_REF] Daufresne | Climate change impacts on structure and diversity of fish communities in rivers[END_REF] on the fish communities of various French large rivers (Seine, Loire, Rhône) and their significantly changing composition during the last decades.

Finally, this study once again emphasizes the importance of long-term monitoring for the study of biological communities on one hand, in the global warming context on the other hand.

> PERSPECTIVES

Ecological perspectives are difficult to establish. In a multiple stressor context, competition between native species and/or invasive ones acts in addition to anthropogenic effects (mostly on discharge and temperature). However, if the flow of invaders does not appear continuous but based on specific events (especially hydro-climatic events), one can legitimately believe that this drift will continue in the future.

( 1 )

 1 ARALEP, Campus LyonTech-La Doua, 66 Bld Niels Bohr, CS 52132, 69603 Villeurbanne Cedex, France (2) Present adress: UMR 7208 BOREA -IRD 207, MNHN, 43 rue Cuvier, 75231 Paris Cedex, France (3) IRSTEA Aix-en-Provence, 3275 Route de Cézanne, CS 40061, 13182 Aix-en-Provence Cedex 5, France (4) IRSTEA Lyon, 5 rue de la Doua, CS 70077, 69626 Villeurbanne Cedex, France RÉSUMÉ Effets à long-terme des changements globaux et locaux sur les communautés de macroinvertébrés benthiques des grands fleuves anthropisés : exemple du Rhône au cours des

  Figure 1Location of the sampled sites and hydroelectric impoundments of the French Rhône River from Geneva to the Mediterranean sea.

  potamo-lentic species cold water and potamo-lotic species

  distinguished three time periods: -1979-1987: commissioning of the hydroelectric and nuclear plants; -1988-2002: improving water quality, high flood successions and increasing water temperature; -2003-2010: post-2003 heat wave with confirmation of the trend of rising temperatures and the arrival of new alien species.

  . The flood of November 2002 and the heat wave of summer 2003 seem to have marked a turn in the invertebrate communities of the Lower and Middle Rhône. If the latter underwent rather

  Figure 4Changes in the macroinvertebrate communities of the Rhône River between 1985 and 2010, and projection of the most contributing species. Three sectors : Upper Rhône (Bugey) "UpperR", Middle Rhône (Saint-Alban) "MiddleR", Lower Rhône (Cruas-Tricastin) "LowerR".Three periods : 1979Three periods : -1987Three periods : "1", 1988Three periods : - 2002Three periods : "2", 2003Three periods : -2010 " "3" (see Appendix 1 for species codes).

  Indeed, since the arrivals of Atyaephyra desmarestii and Gammarus roeseli in the mid-19th century,[START_REF] Bollache | Patterns of biological invasions in French freshwater systems by non-indigenous macroinvertebrates[END_REF] identified a total of 43 non-native species of invertebrates in French water courses. Thus, Bij de[START_REF] Bij De Vaate | Geographical patterns in range extension of Ponto-caspian macroinvertebrate species in Europe[END_REF] identified fifteen Ponto-Caspian species which have penetrated the Rhine Basin. Ten of these are present in the Rhône Basin. This suggests that among species not yet present in the Rhône River, some of them will arrive during the next years, such as crustaceans Dikerogammarus bispinosus and Dikerogammarus haemobaphes, Echinogammarus ischnus and Echinogammarus trichiatus. The common feature of these different species is that they are mainly predators or filter-feeders, thermophilic and euryecic species, i.e. functional competitors according to the environmental changes of river characteristics. The planarian Dendrocoelum romanodanubiale which is very common in the Moselle River, the bivalves Dreissena bugensis and Sinanodonta woodiana (already present in the Rhône basin according[START_REF] Mouthon | Découverte de Sinanodonta woodiana (Lea, 1834) (Bivalvia: Unionacea) dans un réservoir eutrophe: le Grand Large en amont de Lyon (Rhône, France)[END_REF] and the Asian tiger mosquito, Aedes albopictus (already present in southern France and now migrating up the Rhône valley) could also colonize the Rhône River in the coming years (J.N. Beisel, pers. comm.).

STABILITY UPPER RHONE INCREASE OF THE NUMBER OF REPRODUCTIVE CYCLES

	Upper Rhone	Middle Rhone	Lower Rhone
	Period 1:
	1979-1987
	Period 2:
	1988-2002
	Period 3:
	2003-2010

  , asexual reproduction or cemented clutches, active aquatic dissemination, potential cells against desiccation or a diapause during their development. A shift in trait combinations appeared after 2003 in the Middle and especially the Lower Rhône communities, which were composed of polyvoltine, ovoviviparous species with gill respiration. All these attributes are frequently observed simultaneously in alien and/or Mediterranean species.

		Sector	Upper Rhône	Middle Rhône	Lower Rhône
	<1 cycle/year	observed value H probability P	50.206 <0.0001 * <0.0001 * 0.0472 *** 23.722 6.106
	=1 cycle/year	observed value H probability P	16.014 0.0003 *	40.470 <0.0001 * <0.0001 * 84.178
	>1 cycle/year	observed value H probability P	5.695 0.0580 NS <0.0001 * <0.0001 * 39.164 85.144

respiration

ACKNOWLEDGEMENTS

This work was supported by Electricité de France (EDF) in the framework of the research programme called "Étude Thermique Rhône Phase 4" (ETRP4). Financial support was also provided by the French Water Agency Rhône Méditerrannée & Corse and the Council of Europe. Data were taken from monitoring programmes carried out each year in the vicinity of EDF nuclear plants located along the Rhône River. Many thanks to two anonymous reviewers whose comments and suggestions have greatly improved the early version of the draft, and to Professor Eric Pattee for english corrections.

Theodoxus fluviatilis Mollusc

In italic alien species.

Appendix 2. List of biological traits and modalities of the aquatic macroinvertebrates used in this study (numbers from [START_REF] Tachet | Invertébrés d'eau douce, Systématique, biologie, écologie[END_REF]. Numbers were used as labels in Figure 6.

No.

Traits

No. [START_REF] Tachet | Invertébrés d'eau douce, Systématique, biologie, écologie[END_REF]. Numbers were used as labels in Figure 7.

Modalities

No


Smrati Gupta

E Veronica Belmega

M A Vázquez-Castro

Game Theoretical Analysis of the Tradeoff Between QoE and QoS Over Satellite Channels

In this work, a game-theoretic analysis of a video exchange application in which two users exchange their video streams over a satellite channel using Quality of Experience (QoE) driven rate adaptation is studied. In such an interaction, users aim at maximizing the Quality of Service (QoS) and QoE of their received video while minimizing their individual cost incurred by their video transmission, which is modeled as a repeated game. Given the payoff model of the users, it is shown that adaptive video exchange between selfish autonomous nodes for a deterministic time will not be sustained. However, if video is exchanged over an unlimited or indeterminate period, the nodes have an incentive to cooperate and exchange video streams with QoE-driven rate adaptation based on the trust they build among themselves. Our simulation results show that a tradeoff exists between the QoS and the QoE of the perceived video. Furthermore, it is shown that the expected interaction length has a high impact on such tradeoff.

I. INTRODUCTION

With the recent growth in demands of satellite services like video applications based services, there has been a lot of research to find mechanisms for efficient use of limited resources in satellite communications. Such mechanisms include the design of transmission rate adaptation schemes to utilize and adapt to the dynamic satellite environment [START_REF] Sun | Ka-band link optimization with rate adaptation for Mars and lunar communications[END_REF], [START_REF] Pimentel-Niño | Optimized ASMIRA Advanced QoE Video Streaming for Mobile Satellite Communications Systems 30[END_REF]. These rate adaptation schemes are designed on the basis of various factors like satisfaction of the end users' demands, optimization of resource utilization etc.. However, due to the limited and expensive resources in satellite communications, there is competition among the terrestrial user nodes over existing resources, and therefore an important factor influencing the performance of rate adaptation schemes is the competitive behavior among these nodes. It is needed to design the schemes with an in-depth analysis of such behavior.

Game theoretical framework allows us to capture this competitive behavior under the light of natural satellite environment limitations. The use of game theoretical framework to study the problems in satellite networks has been mostly focussed on resource allocation among the nodes (e.g.. [START_REF] Del Re | A Game Theory Approach for DVB-RCS Resource Allocation[END_REF], [START_REF] Vázquez-Castro | Rate allocation for satellite systems with correlated channels based on a Stackelberg game", Game Theory for Networks[END_REF]). However, the game theoretical analysis of interaction between two nodes employing complex rate adaptation strategies has been quite limited and focussed upon single shot games [START_REF] Ye | Priority-based rate adaptation using game theory in vehicular networks[END_REF], [START_REF] Trinh | A game-theoretic analysis of tcp vegas[END_REF]. Therefore, in this paper, we study a video exchange application over the satellite channels among two nodes using game theoretical tools, in particular, under the light of repeated games framework. Our contributions can be summarized as follows:

First, with the help of repeated games' framework, we identify the best performing QoE-driven rate adaptation strategies for adaptive video transmission in different satellite networks. We show that our framework is similar to the repeated prisoners dilemma [START_REF] Fudenberg | [END_REF] and that the adaptive video exchange between selfish autonomous nodes for a limited time will not be sustained. However, if video is exchanged over an unlimited period of time, the nodes have an incentive to cooperate and exchange video stream with QoE-driven rate adaptation based on the trust they build among themselves. The details of the proofs are omitted because of the lack of space. They follow in the similar lines as [START_REF] Belmega | Repeated games for privacyaware distributed state estimation in interconnected networks Network Games, Control and Optimization[END_REF] in which the authors studied the interaction among two agents engaged in a competitive privacy interaction in an information-theoretic distributed source coding scenario.

Second, with the help of numerical simulations, we illustrate that the speed of rate adaptation used by the nodes is influenced by two factors: the expected satellite channel conditions and the expected length of interaction between the terrestrial user nodes in the repeated game framework. Our simulations show that as the expected length of interaction increases, the speed of rate adaptation to the channel conditions increases thus providing better QoS. Good channel conditions require a smaller length of interaction to achieve faster adaptation rates as compared to bad channel conditions. It turns out that these two factors also imply a tradeoff between QoS and QoE. This tradeoff is analyzed in details via numerical results. This paper is organized as follows: in section II, we describe the system model and QoE-driven rate adaptation model. In section III, we describe the game theoretical approach applied to the adaptive video exchange between the users. The numerical simulations and analysis is presented in section IV, followed by the conclusions in section V.

II. SYSTEM MODEL AND QOE-DRIVEN RATE ADAPTATION

In this section, we describe the system model and the QoE-driven rate adaptation scheme used. We also define the performance metrics which will be considered in the analysis further.

A. System Model 1) Network Topology: Our focus is on a scenario in which two terrestrial nodes want to exchange their videos via a satellite relay. Such scenarios model situations like video streaming between two parties across geographically separated areas. The node A (or B) transmits the video packets to the satellite and the satellite forwards these packets to node B (or A) as shown in figure 1. The wireless channel between any two nodes has variable capacity to transmit packets across the nodes depending on various factors like environmental conditions (rain, cloud, etc.), congestion due to other users, etc. We model channel links between the nodes to have a certain throughput capacity which varies with time. The throughput capacity is the maximum number of packets that can be transmitted between any node k and node l at time t and is denoted by R kl (t). It is measured in packets per time slot (pps). As shown in figure 1, R AB = 0 for all t. Throughout this paper, for simplicity, at any time instant t, all links are assumed to have equal throughput capacities R c (t), that is, R kl (t) = R c (t), ∀kl ∈ {AR, BR, RA, RB}. Each time instant is described by t = n∆, where n ∈ Z + and ∆ is the time interval size, i.e., a precision parameter. We will therefore, refer to instantaneous quantities using the integer value n. We also assume that the satellite node simply forwards the packet without any on-board processing. Therefore, R c (n) is the instantaneous end to end throughput capacity of the satellite channel between A and B and vice versa.

2) Channel Model: We model the satellite channel using a 2-state Markov channel model as described in [START_REF] Lutz | A Markov Model for Correlated Land Mobile Satellite Channels[END_REF]. The two-state markov chain model is shown in figure 2. The 'good' channel state corresponds to the channel being in good conditions, like line of sight situations, clear weather s etc.. The 'bad' channel state refers to channel being in bad conditions for example in situations when there is obstruction to transmission across the channel like clouds, rains etc. The markov chain model in figure 2 shows the state diagram for transition from one state to another. The probability of the channel to move from good state to bad and vice versa is p GB and p BG respectively. Consequently, the probability to remain in good and bad state are p GG = 1 -p GB and p BB = 1 -p BG . From this model, the probability of the channel to be in bad state p B and probability of channel to be in good state p G is given by p

B = p GB p GB + p BG (1)
p G = p BG p GB + p BG (2)
We define that in good state the channel has a throughput capacity of R 1 whereas in bad state it has R 2 , such that R 1 >

R c (n) = R 1 good state R 2 bad state (3)
In this paper, we assume that the channel coherence time is given by T c = c∆ slots where c ∈ Z + . This means that given the channel is in a state, the channel state will not vary for at least c∆ slots. This assumption is reasonable as the satellite channel conditions, which are influenced by the environment, usually take time to vary. Another assumption is that each video stream exchange lasts for T = N ∆ slots and T T c . Note that for better accuracy of channel model, this analysis can also be extended for the three-state Markov channel model [START_REF] Vázquez-Castro | LMS Markov model and its use for power control error impact analysis on system capacity[END_REF].

3) Cross-layer Design Model: The video content is transmitted using UDP (User Datagram Protocol) over RTP (Real-Time Transport Protocol). The source node is equipped with a codec responsible for compression of the video content. The output rate of the codec can be reconfigured to deliver a target bit-rate. Therefore, at the source node, the output rate can be adjusted as desired. This output rate from any node k ∈ {A, B} at time t = n∆ is denoted by r k (n) and it is measured in packets per time slot. The packets are further passed down to the network layer maintaining coherence with standard protocol stack. The rate of transmission of video payload is adapted to the network conditions by optimization of the QoE perceived at the end-user. With the use of Real Time Control Protocol (RTCP) signaling, the source node collects the feedback information about the Round Trip Time (RTT) from the destination. The RTCP feedback signaling provides the source node with information to re-configure the codec rate to suit the target needs.

4) Buffer and Delay Model: Each of the source nodes (A and B) maintains a transmission buffer of size B c packets. The number of packets stored in transmission buffer at time t = n∆ is given by B(n). The buffer is maintained using a First In First Out (FIFO) queue. Let the source node k transmit the packets at time t = n∆ at the rate r k (n). The source node is unaware of the channel link capacity R c (n). Assume that the buffer is initially empty. If r k (n) < R c (n), all the packets are transmitted through the channel with rate r k (n). If r k (n) > R c (n), then packets are transmitted with a rate of R c (n) through the channel link. From the remaining r k (n) -R c (n) packets per time slot, B(n) ≤ B c packets are stored in the empty space in the transmission buffer, while the remaining packets are lost. In the next time slot, the packets stored in the buffer are transmitted through the channel. These packets face a delay in reaching the destination. The same process as above is applied to rest of the new packets to be transmitted, but now the effective channel capacity is R c (n) -B(n -1).

Using the above system model, we will now describe the Quality of Experience-driven rate adaptation model which is used in the rest of the paper. Furthermore, we describe the pertinent performance metrics derived using [START_REF] Gupta | Joint Network Coded-Cross Layer Optimized Video Streaming Over Relay Satellite Channel[END_REF] which take into account the applicability of the system model.

B. QoE-driven Rate Adaptation and Performance Metrics

The cross layer rate adaptation model shows the framework to optimize the output codec rate of a source node with feedback from the network in the form of RTCP signals. We will focus on the rate adaptation based on optimizing Quality of Experience of the video obtained by the end-user. The QoE of the end user can be quantified using different metrics in spatial domain like SSIM (structural symmetry) and temporal domain like flow continuity. In this work, we focus on using flow continuity of the end-user video as a measure of the QoE in the time domain. This is done in order to ensure that the enduser is able to view the video without any freezing. The rate is adapted to the channel conditions as follows. The source begins the transmission at a certain initial rate. The rate is increased with time, as long as the source observes no delay. However, as soon as the source observes a delay, it reduces the rate to its initial value. The process is again repeated. This adaptation is shown in figure 3. Mathematically, any source k begins the transmission at rate r k (1) = β < R c (1), where β ∈ R + . With each RTCP received, the rate is updated by

r k (n, α k ) = β + δr k (n, α k ) if no delay observed β if delay observed (4)
where the increment in rate is

δr k (n, α k ) = [α k (n mod p(n))∆] 2 such that ∆ is the time interval size, α k ∈ (0, tan(π/2))
is the slope of the rate adaptation curve and p(n) is the time period of the waveform in figure 3 given by

p(n) = R c (n) -β α k ∆ + 1
Note that this rate adaptation is done at the source node k, and it is adapted according to the delay statistics observed at node l = k. Henceforth, we denote any node other than k as -k. Note that the increment in rate can be modeled using different functions like logarithmic function, linear function or exponential function etc. In this paper, we have assumed an squared function to model the rate increment having a slow start followed by a rapid growth. Such a function models rate adaptation in different protocols like TCP variants which are slow start [START_REF] Afanasyev | Host-to-Host Congestion Control for TCP[END_REF], [START_REF] Pimentel-Niño | Optimized ASMIRA Advanced QoE Video Streaming for Mobile Satellite Communications Systems 30[END_REF].

We now describe the performance metrics which will be used to analyze the performance of the scheme.

1) Quality of Service Metric:

The network utility is defined as the ratio of the network capacity utilized to transmit packets to a node and the total network capacity provided by the network. The number of packets obtained at node k depends on the rate of transmission at the other node r -k (n, α -k ). However, the packets obtained at the node k cannot exceed the instantaneous channel capacity. Therefore, the instantaneous network utility at time t = n∆ is given by

µ(R c , r -k , n, α -k ) = min(R c (n), r -k (n, α -k )) R c (n)
where R c (n) is given by ( 3) and r -k (n, α -k ) is given by ( 4). We define the averaged network utility from n = 0 to n = N in providing the video to node k as the Quality of Service at node k and it is given by

f QoS k (α -k ) = 1 N N n=0 µ(R c (n), r -k (n, α -k )) (5)
It can be seen that the QoS of node k depends on the rate adapted by the other node and consequently on α -k .

2) Quality of Experience Metric: The flow continuity is defined as the probability of the delay in the network not to exceed the threshold delay. The delay in the network leads to video packets arriving at the end user in more than expected time, leading to a visible freezing of the displayed video and degrading the quality of experience. In this paper, flow continuity is chosen as the QoE metric which is a simplified choice for the analysis. Assuming the threshold delay to be 0 (allowing no freezing of video), we notice in the buffer and delay model described in section II-A4 that the delay is observed at the node k when the rate r -k exceeds the channel capacity. Let us define a delay counter function ϕ(.) which determines if there is an instantaneous delay in the network or not. It takes the instantaneous rate and the channel capacity as the input and generates 0 if there is no delay or 1 if there is a delay in the network. It is defined as

ϕ(r(n, α), R) = max(0, sgn(r(n, α) -R)) where sgn(r(n, α) -R) =    -1, if r(n, α) < R 0, if r(n, α) = R 1, if r(n, α) > R
Therefore, we can write the total number of events when the delay occurs as

N n=0 ϕ((r -k (n, α -k ), R c (n))
We define the Quality of Experience metric as the average flow continuity of the network and it is given by

f QoE k (α -k ) = 1 - N n=0 ϕ(R c (n), r -k (n, α -k )) N (6)
We note that the flow continuity at k is a function of the rate adaptation gradient at the other node α -k .

3) Cost: In order to transmit packets, the sender node k incurs a cost of transmission due to the power usage, hardware requirements etc. This cost is dependent on not only the magnitude of resources used for transmission but also on the gradient of increment in the rate. This is because the higher the gradient in rate increment, the more is the difference between two consecutive instantaneous rates. This asserts a higher energy demand on the resources to make a sharper change in the rate leading to higher cost. In order to model this cost of transmission, for simplicity, we use a logarithmic function of the rate adaptation slope or α given by

f COST k (α k ) = log 2 (1 + arctan(α k )) (7)
Note here that the cost of transmission incurred at the node k is determined by the rate adaptation gradient used by the node k.

With these metrics, in the next section, we will define the utility function given by

w 1 f QoS k (α -k ) + w 2 f QoE k (α -k ) -w 3 f COST k (α k )
where w i ∈ Z and it will be optimized further in the gametheoretical analysis.

III. GAME THEORETICAL ANALYSIS FOR ADAPTIVE SATELLITE VIDEO TRANSMISSION

It can be seen from section II-A that the quality of the video obtained by a node, say A, depends on the rate of transmission of node B and vice versa. Additionally, in order to transmit the video packets to node A, node B incurs a cost and vice versa. Therefore, for two selfish nodes A and B, there is a conflict of interest as both nodes want to incur minimum cost (affecting the video quality of other user) and also obtain good quality of video themselves (affected by the rate of transmission by other user). Therefore, there is an interaction arising naturally among the two nodes which is modeled using game theory.

We assume that each of this interaction occurs for a video stream exchange lasting for T = N ∆ slots, which means that each video stream exchange session lasts for at least T slots. We will now study the model of the game when the two nodes exchange video stream only once (lasting for T slots). In the subsequent sections, we will consider how this interaction varies if the nodes exchange the video streams repeatedly where each exchange lasts for T slots.

A. One-Shot Game Analysis

We define a one-shot non-cooperative game by the following tuple:

G O ={P, {A k } k∈P , {u k } k∈P } (8)
where P refers to the set of players which selfishly maximize their own payoffs given by u k by choosing their actions from the action set A k for every k ∈ P . With the QoE-driven rate adaptation model to exchange video, we define the following component sets of the game tuple G O :

Players Set P: The set of players is given by P = {A, B} which are the two nodes A and B that exchange the video packets.

Action Set A k : The set of actions that can be taken by the player k, where k ∈ {A, B}, is given by A k = 0, λ π 2 and λ ∈ (0, 1). The action chosen by k-th player from A k is denoted by α k . Hence the player can choose the gradient of rate adaptation as its action in order to maximize its own benefits. The factor λ ensures that the gradient is always α < π 2 to prevent infinite increase in rate.

Utility u k : The utility, or payoff function of the k-th user is defined as follows

u k (α k , α -k ) = w 1 f QoS k (α -k ) + w 2 f QoE k (α -k ) -w 3 f COST k (α k ) (9)
The utility of the k-th player is a function of the action α k taken by the node k and the action α -k taken by the other node. The components of utility function are as follows: the utility is a joint measure of the quality of video experienced by the node k and the cost incurred in the transmission of video to the other node. The video quality at node k is affected by the throughput and the flow-continuity given by f QOS k (α -k ) and f QOE k (α -k ) , using ( 5) and ( 6) respectively, which are both determined by the action of the other node α -k . Since the node k wants to maximize its quality of video perceived, the utility is directly proportional to both throughput and flow continuity. However, the node k incurs a cost f COST k (α k ), given by [START_REF] Fudenberg | [END_REF], to transmit video to the other node, which is inversely proportional to its utility. Finally the weight w i ∈ (0, 1) assigns the appropriate dimensions to different factors such that

3 i=1 w i = 1.
Consider the scenario when the two players interact only once for T slots to exchange the video streams. This leads to the one shot game G O in [START_REF] Belmega | Repeated games for privacyaware distributed state estimation in interconnected networks Network Games, Control and Optimization[END_REF]. Before the players begin to exchange, they decide their actions, i.e. at which gradient they will transmit during the next T slots. The Nash Equilibrium (NE) of a non-cooperative game G is defined as a set of actions of the players (α * k , α * -k ), from which no player has an incentive to deviate unilaterally. Hence, the selfish rational players are expected to play the action at NE irrespective of the other players action.

In the one-shot game, when the players cannot build trust with each other, they selfishly choose the action to maximize their utility. Node k can maximize its utility by minimizing the cost given by ( 7) at α k = 0. The node k has no control over the action taken by the other user, therefore, the part of its utility affected by the other user's action, i.e., its QoS and QoE, cannot be controlled. Given that the strictly dominant strategy for each user is not to cooperate, the following result follows [START_REF] Fudenberg | [END_REF]: Lemma 1. The unique Nash Equilibrium of oneshot QoE-driven adaptive video exchange game

G O ={P, {A k } k∈P , {u k } k∈P } is given by (α * 1 , α * 2 ) = (0, 0).
The intuition is that no selfish end user would be willing to incur a cost to send the video when there is no guarantee of receiving any video in return.

B. Repeated Game Analysis

We will now present how the results of the interaction between the two players vary when the video exchange (of T slots each) takes place repeatedly. A repeated game, in which the game G O defined in ( 8) is played repeatedly, is defined using the following tuple:

G R = {P, {S k } k∈P , {v k } k∈P , T R } (10)
The set P refers to the set of players, given by the set of nodes {A, B}.

The set S k is the strategy set of user k. The strategy set is different from the action set in (8) because it describes the actions taken by the player k based on the history of the play and on the actions at each instant. More precisely, let the actions taken by the players in the τ -th stage be a (τ ) = (a

(τ ) 1 , a (τ )
2 ). Then the history of the game at the end of stage t ≥ 1 is given by h (t+1) = (a (1) a (2) . . . a (t) ). The set of all possible histories up to t is given by H (t) = {A k × A -k } t where A k is the action set in [START_REF] Belmega | Repeated games for privacyaware distributed state estimation in interconnected networks Network Games, Control and Optimization[END_REF] given by [0, λ π 2 ]. The strategy of a player k is s k = (s

(1) k , s (2)
k ..., s (T ) k ) ∈ S k and maps each possible history to an action, as s

(t) k : H (t) → A k such that s (t) k (h (t) ) = a (t) k .
The long term utility for the repeated game is a discounted utility function v k such that for a strategy profile s = (s 1 , s 2 ), is the weighted sum of the stage utilities obtained by user k following the strategy s, such that the user discounts the future payoffs by a discount factor δ. It is given by

v k (s) = (1 -δ) (1 -δ T ) T t=1 δ t-1 u k (a (t) ) (11)
where a (t) is the action profile at stage t induced by strategy s (i.e. s

(t) k (h (t) ) = a (t)
k ∀ k), discount factor δ ∈ (0, 1) and u k is the one-stage payoff function defined in [START_REF] Lutz | A Markov Model for Correlated Land Mobile Satellite Channels[END_REF]. The parameter T R > 1, refers to the number of times the interaction takes place.

Before we discuss the outcome of the repeated game G R , we briefly describe the concept of sub-game perfect equilibrium for repeated games [START_REF] Aumann | Handbook of Game Theory with Economic Applications[END_REF]. In coherence with the NE of one-shot game, the NE of repeated game is a strategy profile from which no player gains by unilaterally deviating. However, there are some strategy profiles, which are not expected to occur due to rational behavior of the players. Hence the NE region can be narrowed down to define a subgame perfect Equilibrium region, as a subset of NE. A subgame is a game from stage t onwards having a history h (t) , and is denoted by G R (h (t) ). The strategies and payoffs used for the sub-game are the functions of possible histories that are consistent with h (t) . A subgame perfect equilibrium (SPE) is defined as a strategy profile s * = (s 1 , s 2 ) such that for all h (t) ∈ H (t) , the strategy s * | h (t) is a NE for any subgame G R (h (t) ).

Consider the scenario when the two players begin their video exchange. Both players are aware of the fact that the transmission is going to be repeated for T R > 1 and hence they play the game G R in [START_REF] Vázquez-Castro | LMS Markov model and its use for power control error impact analysis on system capacity[END_REF]. Before the players begin the transmission, they decide their strategy i.e., at what gradient they both should adapt their rates. This decision depends on the perception of the players of whether T R is finite or infinite.

1) Finite Horizon Repeated Game: In this case, the two players exchange the video streams with each other (each exchange lasting for T slots) repeatedly but a finite number of times given by T R < ∞. In such a case, the players are aware that the they will interact only for a limited time. Similarly to the repeated prisonners' dilemma, let us consider the last stage of the game, when it is played T R -th time. The players are aware that they interact for the last time. They have no incentive to transmit the video for the other player while incurring a cost themselves, when there is no guarantee that the other player will transmit the video or not. Hence, their optimal strategy is s (T R ), * k = 0. Now, when the players play the game at time T R -1, given that in stage T R they will not transmit, there is no incentive to transmit at stage T R -1. Therefore, s (T R -1), * k = 0. Using this principle, the following lemma can be deduced: Lemma 2. The unique sub-game perfect equilibrium of the video exchange game between two nodes, defined by G R = {P, {S k } k∈P , {v k } k∈P , T }, where T < ∞ and is known to both nodes is given by s (t), * k = 0, ∀k ∈ P, ∀t ∈ {1, 2 . . . T } Given that the players are aware of the number of times the video exchange will occur, they act selfishly at each stage of the game in order to maximize their payoffs. There is no incentive in building trust in this case.

2) Infinite Horizon Repeated Game: In this case, the players will interact and exchange the video streams (lasting for T slots), but such interaction lasts for an infinite time T R . In other words, the players are not aware of how many times they will exchange the video with the other user. The reason why cooperation (i.e., any strategy apart from (0, 0)) is not sustainable in finite horizon games is that the players know precisely when the interaction ends. However, in infinite horizon repeated games, the players in the game G R do not know precisely when the game will end, or equivalently, T R → +∞. We will now describe some of the achievable SPE for such games. Note that the overall achievable SPE region for the infinite horizon repeated games is an open problem and not known in general [START_REF] Fudenberg | [END_REF], [START_REF] Aumann | Handbook of Game Theory with Economic Applications[END_REF]. We will consider two of such achievable SPE.

In an infinite horizon repeated game, when the players begin to interact, they decide their strategy based on the information that the interaction will last for an infinite amount of time. One possible SPE for such games is given by the noncooperative strategy at each stage of the game (give by (0, 0)). We will focus here on more interesting SPE in which nontrivial cooperation can be achieved. The intuition for existence of other SPE is similar to the infinite time horizon prisoner's dilemma [START_REF] Fudenberg | [END_REF]. At any stage of the game, the pay-off in (9) has two components: (i) the component controlled by the opposite player's action which increases the utility, but the player k has no control over it (ii) the component influenced by the player's own action which decreases the utility. The player has no control over the first component, but in long term, it can build trust with the other player to influence the other player's decision and thereby both players can obtain a long term sustainable utility which is higher than utility achieved by the (0, 0). We focus on such an action profile to evaluate the long term sustainability of the action profile whose utility is better than the one-shot NE for both players and are given by

u 1 (α * 1 , α * 2 ) > u 1 (0, 0) u 2 (α * 1 , α * 2 ) > u 2 (0, 0) (12)
In the following lemma, we identify the SPE which can achieve non-trivial outcomes due to the trust built among the players.

Lemma 3. In an infinite-horizon repeated game G R = {P, {S k } k∈P , {v k } k∈P , +∞}, and with an agreement profile (α * 1 , α * 2 ) satisfying ( 12), if the discount factor is bounded by

1 > δ > δ min (α * 1 , α * 2 ) (13)
where δ min (α * 1 , α * 2 ) is given by ( 14) on the next page, then the following strategy is an SPE: "A node k transmits with gradient α * k at the first stage and continues to adapt the rate with this gradient as long as the other player adapts its rate at least by α * -k . If any player has ever defected, then the players transmit at α = 0 for the rest of the interaction."

The proof of the above can be derived in a similar way as in [START_REF] Belmega | Repeated games for privacyaware distributed state estimation in interconnected networks Network Games, Control and Optimization[END_REF] using the one-step deviation principle. The discount factor can be seen as the perception of the players of the probability for the game not to end at every stage of the game. If the players perceive the probability of the game not to stop above certain limits, there can be a non-trivial SPE. In other words, if the probability of the game not to stop is large enough, the players would rather prefer to develop trust and obtain better payoffs than minimize their one-shot costs. We also note here, that only those points which satisfy [START_REF] Afanasyev | Host-to-Host Congestion Control for TCP[END_REF] are sustainable thereby ensuring that the players agree upon the points which offer them incentive over one-shot NE.

IV. NUMERICAL RESULTS AND ANALYSIS

We will now present simulation results to identify how the satellite channel conditions modify the outcome of the infinite horizon repeated game. We assume that if the channel is in good state then R 1 = 350 kbps and if the channel is in bad state, then R Fig. 4: Achievable region increases as channel conditions improve and there is a higher probability of channel to be in good conditions

A. Effect of Channel Conditions on Game Outcome

We consider the scenario where two nodes exchange video repeatedly for an undefined horizon of time. We identify the action profiles (rate gradients), apart from (0, 0), which the players agree to transmit at given in Lemma 3. Given our varying channel model, the probability of channel to be in good state (p g ) also affects the achievable agreement points. In figure 4, we plot the achievable agreement region based on varying channel conditions. We assume δ → 1 which implies the probability of game to stop approaches 0. When p g tends to 1, there is a high probability that channel is in a good condition. This leads to a higher probability that payoff obtained by the players at action profiles farther away from (0, 0) exceeds payoff obtained at (0, 0) and such action profiles are achievable based on channel conditions [START_REF] Afanasyev | Host-to-Host Congestion Control for TCP[END_REF]. However, when channel conditions are bad and p g tends to 0, the magnitude of payoff at action profiles farther away from (0, 0) is not high enough to exceed payoff at (0, 0). Hence, a smaller agreement region is achievable in bad channel conditions than in good channel conditions. This implies that the players will adapt to the channel conditions faster, with a higher gradient, when the conditions are good, thereby utilizing the available resources more efficiently. However, in bad channel conditions, the players will not agree to faster adaptation to the channel conditions. Hence, bad channel conditions force the players to be cautious and the available resources remain under-utilized. Also note, the curve has spikes periodically due to the non uniform variation of utility function. The utility function u k (α k , α -k ) varies uniformly with α k because du k (α k ,α -k ) dα k is monotonously decreasing for increasing α k . This implies that increasing the user's own gradient simply incurs more cost to the user and hence decreases its own payoff. However, the utility function does not vary monotonously with α -k . As α -k increases, the flow continuity decreases due to more instances of rate exceeding the channel capacity (explained in detail in next subsections). In addition, as α -k increases, the quality of service increases for smaller values of α -k , when there are not many instances of rate exceeding the channel However, when such instances increase at high values of α -k , the quality of service decreases with increasing α -k . Therefore, due to the culmination of these two effects, the agreement point region does not show monotonous behavior.

δ min (α * 1 , α * 2 ) = max k∈P w 3 [f COST k (α * k ) -f COST k (0)] w 1 [f QoS k (0) -f QoS k (α * -k )] + w 2 [f QoE k (0) -f QoE k (α * -k )] (14)
In fact, the derivative of utility function with action profile of other user is a complex trigonometric function which is periodic in nature leading to the shape of the curve being similar to periodic function.

B. Effect of Channel Conditions on Minimal Discount Factor

Now, we will show how the minimal discount factor necessary to achieve any point varies based on different channel conditions. More precisely, we show how high should be the probability for game to continue for the players to agree on a specific gradient in a given channel condition. In figure 5, we plot the minimal discount factors necessary to achieve different action profiles within the achievable region which is based on channel conditions. As the achievable region decreases from good channel in figure 5a to bad channel in figure 5c, the discount factor necessary to sustain an action profile also varies proportionally. This fact can be observed more closely in figure 6 in which we consider that the players agree on the symmetric action profiles (or equal gradients). It can be seen (in figure 6) that, as the channel conditions improve and p g varies from 0 to 1, a lower probability of game to continue is needed for any action profile to be achievable. This implies that even when the probability of game to continue is low, the players have a high incentive in transmitting at a higher gradient to achieve a high utility because the channel condition is good. It can also be observed that the players will transmit at a higher gradient of α = 0.7 only in good channel conditions. For players to agree on a lower gradient like α = 0.4, there should be a high probability of game to continue in bad channel conditions, but in good channel conditions, this gradient can be achieved even with low probability of game to continue. Therefore, the rate of adaptation to channel by the players depends on the channel conditions as well as their perception of the game to continue.

C. Achievable QoS and QoE Tradeoff in Satellite Channel

We will now show the variation in the observed QoS and QoE at the user level based on the satellite channel conditions Fig. 8: QoE variation with varying discount factor and channel conditions as well as the discount factor. Assuming that the players agree to only symmetric action profiles which are pareto optimal, in figure 7 and figure 8, we show the variation in QoS and QoE, observed when the game is played under varying channel conditions and minimal discount factor.

In figure 7, it can be seen that the overall QoS improves as the channel conditions improve. This is due to a higher number of packets transmitted when the channel has higher average throughput capacity. The channel conditions are not very crucial in obtaining the flow continuity or QoE, as seen in figure 8. This is because QoE depends on the probability of rate to exceed the channel capacity leading to delays. It is independent of the magnitude of the channel capacity.

Figure 7 also shows that as the discount factor increases, the QoS increases. However, in case of QoE, in figure 8, as the discount factor increases, the QoE decreases. As the discount factor increases, the probability of the game to continue also increases which allows the players to agree on higher rate adaptation gradients. This causes a higher number of packets to be transmitted per unit time which improves the overall QoS. However, at higher gradients, there is a higher chance of the rate to exceed the channel capacity, which leads to higher chances of delay and freezing of video resulting in lower QoE. Therefore, there exists a tradeoff between QoS and QoE depending on the length of the interaction between the players. We now observe the joint effect of the two factors on QoS and QoE. As we saw in previous results, for a good channel higher adaptation gradients are achievable. This leads to higher QoS and lower QoE that are the extreme points in figure 7 and figure 8. However, in bad channel conditions lower adaptation gradients are achieved. This leads to lower QoS due to low throughput but higher QoE due to low probability of delay. Hence, depending on the perception of the user of the channel conditions and the length of interaction, the QoS and QoE are achievable. Overall, such effect of such factors can be used to potentially refine the rate adaptation algorithms.

V. CONCLUSIONS

In this paper, we have analyzed a QoE-driven adaptive video exchange between two selfish users (nodes) across a satellite channel and analyzed it using game theoretical tools. With the use of these tools, not only the selfish and realistic behavior of the users has been modeled but the expected outcomes of such an interaction have been predicted. It has been shown that the speed at which the users adapt the transmission rate to the channel conditions is influenced by the two fold effect of expected length of interaction between the users and the expected channel conditions. Consequently, the best strategies are chosen by the users based on available parameters which affects the QoS and QoE of the video achieved. It turns out that a tradeoff exists between the achieved QoS and QoE based on the expected length of interaction among the users. This work can be further explored to exploit more complicated satellite systems under the framework of repeated games.

Fig. 1 :

 1 Fig. 1: Network Topology. The nodes A and B exchange information via R. The arrows indicate the links with positive channel capacity.

Fig. 2 :

 2 Fig. 2: Two State Markov Model for Satellite Channel

Fig. 3 :

 3 Fig. 3: Illustration of Rate adaptation curve. The red line indicates the rate r k (n). The blue line indicates the channel capacity. Angle α remains constant for all time n, whereas period p(n) depends on channel capacity. It is assumed that T >> T c .

  2 = 200 kbps. The channel coherence time is T c = 20s whereas the length of time for which each video exchange lasts is T = 20000s. The other variables are fixed as β = 150 kbps, ∆ = 1, w 1 = w 2 = 0.45 and w 3 = 0.1.

action of user 1 : α 1 ( 5 action of user 1 : α 1 (Fig. 5 :

 115115 Fig. 5: Variation in minimal discount factor within achievable region for various conditions

1Fig. 6 :Fig. 7 :

 67 Fig.6: Different minimal discount factor needed to achieve different symmetric action profiles for various channel conditions. The better is the channel, the lower is the discount factor needed to achieve profiles farther away from (0,0).