Vero ´nica Ferreira

Eric Chauvet

V Ferreira

Future increase in temperature more than decrease in litter quality can affect microbial litter decomposition in streams

Keywords: Aquatic hyphomycetes, Atmospheric CO 2, Ecosystem functioning, Global change, Interactive effects

The predicted increase in atmospheric CO 2 concentration for this century is expected to lead to increases in temperature and changes in litter quality that can affect small woodland streams, where water temperature is usually low and allochthonous organic matter constitutes the basis of the food web. We have assessed the individual and interactive effect of water temperature (5 and 10°C) and alder litter quality produced under ambient CO 2 levels (ambient litter) or under CO 2 concentrations predicted for 2050 (elevated litter) on litter decomposition and on fungal activity and assemblage structure. Litter decomposition rates and fungal respiration rates were significantly faster at 10 than at 5°C, but they were not affected by litter quality. Litter quality affected mycelial biomass accrual at 5 but not at 10°C, while increases in temperature stimulated biomass accrual on ambient but not on elevated litter. A similar pattern was observed for conidial production. All variables were stimulated on elevated litter at 10°C (future scenario) compared with ambient litter at 5°C (present scenario), but interactions between temperature and litter quality were additive. Temperature was the factor that most strongly affected the structure of aquatic hyphomycete assemblages. Our results indicate that if future increases in atmospheric CO 2 lead to only slight modifications in litter quality, the litter decomposition and fungal activities and community structure will be strongly controlled by increased water temperature. This may have serious consequences for aquatic systems as faster litter decomposition may lead to food depletion for higher trophic levels.

Introduction

In temperate regions, small woodland streams constitute more than 80% of the length of hydrological networks [START_REF] Alan | Stream ecology. Structure and function of running waters[END_REF]. These are usually cold water, light-limited streams in which allochthonous organic matter constitutes the major source of energy and carbon (C) [START_REF] Vannote | The river continuum concept[END_REF]). As a consequence, aquatic communities in these streams are highly sensitive to changes in water temperature [START_REF] Poff | Aquatic ecosystems and global climate change. Potential impacts on inland freshwater and coastal wetland ecosystems in the United States[END_REF], litter seasonality, and the quantity and quality of litter inputs, which constitute the basal resource of aquatic food webs [START_REF] Cummins | Feeding ecology of stream invertebrates[END_REF].

The predicted doubling of atmospheric carbon dioxide (CO 2 ) concentration up to the end of this century will result in a 1.1-6.4°C increase in global air temperature [START_REF] Solomon | IPCC (Intergovernmental Panel on Climate Change) (2007) Climate change 2007: the physical science basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change[END_REF]. This increase will be paralleled by similar increases in stream water temperature [START_REF] Eaton | Effects of climate warming on fish thermal habitat in streams on the United States[END_REF], with consequences on biological processes and ecosystem functions [START_REF] Brown | Toward a metabolic theory of ecology[END_REF]. Litter decomposition may be particularly affected, since increased water temperature stimulates litter mass loss directly by promoting leaching [START_REF] Chergui | The influence of season on the breakdown of submerged leaves[END_REF] and indirectly by enhancing litter consumption by shredding invertebrates [START_REF] Gonza ´lez | Conversion of leaf litter to secondary production by a shredding caddis-fly[END_REF]. Higher temperatures stimulate fungal production (mycelia and conidia) by some species of aquatic hyphomycetes cultivated individually [START_REF] Chauvet | Temperature and sporulation of aquatic hyphomycetes[END_REF][START_REF] Rajashekar | Effects of temperature and light on growth and sporulation of aquatic hyphomycetes[END_REF][START_REF] Dang | Temperature oscillation coupled with fungal community shifts can modulate warming effects on litter decomposition[END_REF], which can also enhance decomposition [START_REF] Ferreira | Synergistic effects of water temperature and dissolved nutrients on litter decomposition and associated fungi[END_REF]. However, since temperature tolerance ranges are species specific [START_REF] Rajashekar | Effects of temperature and light on growth and sporulation of aquatic hyphomycetes[END_REF], and the effect of water temperature changes on interspecific interactions is mostly unknown [START_REF] Webster | Growth and sporulation of Tricladium chaetocladium and Lunulospora curvula in relation to temperature[END_REF], it is difficult to anticipate the impact of global warming scenarios on decomposition processes.

To complicate the matter further, increased atmospheric CO 2 concentration might also lead to delayed litter fall, increased litter production, and decreased litter quality [START_REF] King | Correlation of foliage and litter of sugar maple, Acer saccharum, as affected by elevated CO 2 and varying N availability, and effects on decomposition[END_REF][START_REF] Stiling | How does elevated carbon dioxide (CO 2 ) affect plant-herbivore interaction? A field experiment and meta-analysis of CO 2 -mediated changes on plant chemistry and herbivore performance[END_REF][START_REF] Taylor | Future atmospheric CO 2 leads to delayed autumnal senescence[END_REF]. Most studies examining the effect of elevated CO 2 concentrations on tree leaf chemistry report a decrease in nutrient concentration [mostly nitrogen (N)] and an increase in structural and secondary compounds, resulting in an altered nutritional quality (higher C/N) of these leaves compared to leaves grown under ambient CO 2 concentration [START_REF] Cotrufo | Elevated CO 2 affects field decomposition rate and palatability of tree leaf litter: importance of changes in substrate quality[END_REF][START_REF] Norby | Elevated CO 2 , litter chemistry, and decomposition: a synthesis[END_REF][START_REF] Stiling | How does elevated carbon dioxide (CO 2 ) affect plant-herbivore interaction? A field experiment and meta-analysis of CO 2 -mediated changes on plant chemistry and herbivore performance[END_REF]. The lower nutritional quality of leaves grown under elevated CO 2 atmosphere should be reflected in leaf litter, since increased atmospheric CO 2 does not seem to affect the readsorption efficiency of nutrients during senescence [START_REF] Norby | Nitrogen resorption in senescing tree leaves in a warmer, CO 2 -enriched atmosphere[END_REF][START_REF] Norby | Elevated CO 2 , litter chemistry, and decomposition: a synthesis[END_REF][START_REF] King | Correlation of foliage and litter of sugar maple, Acer saccharum, as affected by elevated CO 2 and varying N availability, and effects on decomposition[END_REF]. These results imply that, under a climate change scenario, higher amounts of lower quality litter might enter streams later in the year.

Decreased leaf litter quality might negatively affect aquatic communities, as these are known to colonize highquality litter faster than low-quality litter, and to be more active on the former [START_REF] Gessner | Importance of stream microfungi in controlling breakdown rates of leaf litter[END_REF]. Although most comparisons have been done among litter species differing in nutritional quality, this should also hold true between genotypes within the same species [START_REF] Leroy | Within-species variation in foliar chemistry influences leaf-litter decomposition in a Utah river[END_REF] or trees from the same species grown under different environmental conditions [START_REF] Cotrufo | Decomposition of birch leaf litter with varying C-to-N ratios[END_REF][START_REF] Lecerf | Intraspecific variability in leaf traits strongly affects alder leaf decomposition in a stream[END_REF]. A CO 2 -induced decrease in litter quality might therefore affect its use by aquatic decomposers and, thereby affect litter decomposition. However, to date, only a few studies have addressed this question [START_REF] Tuchman | Elevated atmospheric CO 2 lowers leaf litter nutritional quality for stream ecosystem food webs[END_REF](Tuchman et al. , 2003b;;[START_REF] Rier | Elevated-CO 2induced changes in the chemistry of quaking aspen (Populus tremuloides Michaux) leaf litter: subsequent mass loss and microbial responses in a stream ecosystem[END_REF][START_REF] Rier | Chemical changes to leaf litter grown under elevated CO 2 and the implications for microbial utilization in a stream ecosystem[END_REF][START_REF] Kelly | Growth of trees under elevated atmospheric CO 2 alters microbial communities colonizing leaf litter in a temperate woodland stream[END_REF], and in all of these studies CO 2induced changes in litter quality were considered irrespective of variations in temperature, despite the fact these two factors vary simultaneously.

Since a CO 2 -induced increase in water temperature and decrease in litter quality might have contradictory effects on decomposers and litter decomposition, the extent to which they interact with each other is unknown. This lack of knowledge makes responses of ecosystem processes rates under future climate change scenarios difficult to predict unless the combined effects of global change factors on communities and processes are examined. In the study reported here, we assessed the individual and interactive effect of CO 2 -induced changes in water temperature (two levels) and alder litter quality (two types) on litter decomposition and the associated aquatic hyphomycetes activity and assemblage structure in microcosms. Based on the effects of each factor individually, we predicted (1) lower fungal performance on, and slower decomposition of alder litter produced under elevated CO 2 than under ambient atmosphere because of the predicted decrease in litter quality under elevated CO 2 , and (2) higher fungal performance and faster decomposition at higher water temperature due to the predicted increase in metabolic activities with increased temperature. Also, (3) if quality markedly differs between the two litter types (ambient vs. elevated), then higher differences in fungal performance and litter decomposition would be expected between litter types at higher versus lower temperature, since metabolic activity might become nutrient limited at higher temperature [START_REF] Ferreira | Synergistic effects of water temperature and dissolved nutrients on litter decomposition and associated fungi[END_REF]. Finally, (4) the extent to which the stimulatory effect of increased temperature on fungal performance and litter decomposition would be compensated by decreases in litter quality depends on the differences between litters and on the interaction between litter quality and temperature.

Materials and methods

Fungal species assemblage

An assemblage of six species of aquatic hyphomycetes was used, as representative of fungal diversity found on a single leaf decomposing in natural streams (Ba ¨rlocher 1992): Articulospora tetracladia Ingold, Clavariopsis aquatica de Wildeman, Heliscus lugdunensis Saccardo and The ´rry, Lemonniera terrestris Tubaki, Tetracladium marchalianum Ingold, and Tetrachaetum elegans Ingold. Strains were isolated from single conidia trapped in naturally occurring foam collected from streams in southern France. Growing colonies were kept at room temperature in 9-cm-diameter petri dishes containing approximately 10 mL of growth medium (2% malt and 2% agar) until they were used to induce conidial production. Conidial inoculations (\1 day old) were produced at 15°C by agitation of agar plugs taken from the leading edge of growing colonies, in 25 mL of distilled water or nutrient solution [100 mg CaCl 2 Á2H 2 O, 10 mg MgSO 4 Á7H 2 O, 0.5 g 3-morpholinopropanesulfonic acid (MOPS), 5.5 mg K 2 HPO 4 , and 100 mg KNO 3 per liter of sterile distilled water], on an orbital shaker (100 rpm). An aliquot of each specific conidial suspension, based on conidial numbers, was used to make a combined conidial suspension to inoculate each experimental microcosm.

Leaf litter, microcosms, and experimental set-up Alder (Alnus glutinosa (L.) Gaertner) litter produced under ambient and elevated CO 2 atmosphere were provided by the Bangor FACE project (Bangor, UK). In this project, trees were planted in March 2004 and grown under either ambient atmosphere (present CO 2 level: 380 ppm; hereafter called ''ambient'' litter) or elevated CO 2 atmosphere (predicted CO 2 level by 2050: 580 ppm; hereafter called ''elevated'' litter), from April 2005 until August 2008; within each CO 2 level, trees were planted in four different areas to account for location variability. Both litters were collected after abscission in autumn 2007, air dried at room temperature, and stored in paper bags until experimental use.

Leaf litter was moistened with distilled water and left to rehydrate for 0.5-1 h. Litter discs were obtained using a 12-mm-diameter cork borer and oven dried ([3 days at 105°C). Sterile litter discs were used in this experiment to prevent microbial contamination (as litter is expected to carry its own biological community) from confounding the possible effects of the factors under study. However, any sterilization method (e.g., autoclave, UV-C radiation) can potentially alter the litter quality, which would be of minor importance if litter quality was not one of the factors of interest. Thus, several tests were performed, followed by determination of the phosphorus (P), N, and C concentrations in litter discs, to select the best sterilization method, so that the relative difference in chemical quality would be maintained between litters. Twelve batches of 20 oven-dry litter discs from each area (n = 4) within each CO 2 level were split into groups of three and (1) used to determine the initial chemical quality of the litter discs, (2) incubated in glass tubes with 10 mL of distilled water for 1 day at 10°C, (3) placed in glass tubes with 10 mL of distilled water and autoclaved (20 min at 121°C), and (4) irradiated with UV-C light in a sterile laminar flow cabinet for 1 day (being turned over several times so that both sides of the litter discs would be irradiated), and then incubated in glass tubes with 10 mL of distilled water for 3 h at 10°C. After treatments (1)(2)(3)(4), litter discs were oven-dried (24 h at 105°C), grinded using a mortar and pestle, and the powder weighed (±0.1 mg) and analyzed for P (APHA 1998), N and C (NA 2100 Protein, CE Instruments; ThermoQuest, Milan, Italy). The results were expressed as % litter dry mass (DM).

Specific leaf area (SLA), as a measure of thickness given by the area-to-mass ratio, was determined on batches of 20 individual, oven-dried litter discs (diameter 12 mm). Determinations were performed for each area within each CO 2 level, and the results were expressed as millimeter squared per milligram.

Forty-eight batches of 20 oven-dry litter discs were weighed (±0.1 mg) to determine the initial DM, placed inside glass tubes with 10 mL distilled water, and autoclaved (20 min at 121°C; see above). Twenty-four batches of 20 litter discs were subjected to the same treatment and were used to calculate the correction factor for mass loss due to leaching during sterilization.

Alder litter discs were incubated in laboratory microcosms designed to simulate stream conditions [START_REF] Suberkropp | Relationships between growth and sporulation of aquatic hyphomycetes on decomposing litter[END_REF]. Each microcosm consisted of a 50-mL glass chamber aerated from the bottom by a continuous air flow (80-100 mL min -1 ), which created turbulence and kept the litter discs in permanent agitation. A tap at the bottom allowed for the aseptic drainage of the chamber and recovery of the conidial suspension without removing litter discs. Fresh nutrient solution was added to microcosms through the open top, which was otherwise covered with a glass cap.

Incubations took place at 5°C to simulate the actual water temperature in temperate mountain streams in winter, and at 10°C to simulate predicted stream water temperature under a future climate warming scenario. The 5°C increase in water temperature is within that predicted for streams in the USA under a warming scenario [START_REF] Eaton | Effects of climate warming on fish thermal habitat in streams on the United States[END_REF]. In some areas of the world, air temperature is predicted to increase up to 7°C (e.g., Portugal; [START_REF] Miranda | 20th century Portuguese climate and climate scenarios[END_REF]; consequently a 5°C increase in water temperature in temperate streams is realistic. Forty-eight sterilized (30 min at 121°C) microcosms were distributed into two temperature-controlled chambers, the corresponding sterile litter discs were added, and the microcosms were then filled with 40 mL of a nutrient solution (100 mg CaCl 2 Á2H 2 O, 10 mg MgSO 4 Á7H 2 O, 0.5 g MOPS, 0.055 mg K 2 HPO 4 and 1 mg KNO 3 per liter of sterile distilled water) and aerated. After 24 h, the solution was changed and the microcosms inoculated with a total of 5,000 conidia equally partitioned among all species of the aquatic hyphomycete assemblage. For the first 2 h, the microcosms were aerated for periods of 20 min interspaced with periods of 20 min in which the conidia were allowed to settle. The microcosms were then aerated continuously until the end of the experiment. The nutrient solution was replaced after 24 h and then every 3 days for the duration of the experiment (73 days). All manipulations of microcosms took place in a sterile laminar flow cabinet.

Fungal sporulation

Four microcosms (one for each area of litter origin) from each temperature 9 litter quality treatment were sacrificed after 19, 43, and 73 days. The conidial suspensions were poured into 50-mL Falcon tubes; the volume was adjusted to 42 mL with distilled water and 3 mL of 37% formalin was added as a preservative. In preparation for conidia counting and identification, Triton X-100 (0.5%) was added to the suspensions, followed by mixing to ensure a uniform distribution of conidia; an aliquot of the suspensions was then filtered (SMWP, pore size 5 lm; Millipore, Bedford, MA). Filters were stained with 0.05% trypan blue in 60% lactic acid, and spores were identified and counted under a compound microscope at a magnification of 3209 (Ba ¨rlocher 2005). Sporulation rates were expressed as milligram conidial C per gram litter C per day. Conidial DM was calculated by multiplying the number of conidia from each species by the average mass of individual conidia (based on data reported in the literature; [START_REF] Chauvet | Temperature and sporulation of aquatic hyphomycetes[END_REF] or calculated from biovolume data assuming 70% water content (Ba ¨rlocher and Schweizer 1983). Conidial and litter C mass was calculated assuming a 50% C content of conidia and litter DM, respectively [START_REF] Gulis | Interactions between fungi and bacteria associated with decomposing leaf litter at different levels of nutrient availability[END_REF]. In addition, for the 16 microcosms that were sacrificed by day 73, the conidial suspensions were sampled each time the nutrient solution was changed (every 3 days), collected into 1-L jars, and preserved with 37% formalin. Preparation for conidia counting and identification were as described above, and the results were expressed as the total number of conidia produced per microcosm.

Fungal respiration

A subset of five litter discs from each sacrificed microcosm was used to determine fungal oxygen consumption rates using a closed 6-channel dissolved oxygen measuring system (Strathkelvin 928 System; Strathkelvin Instruments, North Lanarkshire, Scotland) connected to a computer. The oxygen electrodes were calibrated against a fresh 4% sodium sulfite solution [0% oxygen (O 2 )], and a 100% O 2saturated nutrient solution at the target temperature. Litter discs were incubated in 3-mL chambers containing a 100% O 2 -saturated nutrient solution, with constant stirring, and kept at the target temperature of 5 or 10°C by the circulation of water originating from a temperature-controlled water bath. O 2 consumption rates were determined by the difference in the oxygen concentration in the sample and the control over a 20-min interval during which O 2 consumption over time was linear, corrected for the chamber's volume, time, and disc mass. After a 1-h incubation, the litter discs were enclosed in small sterile zip lock bags and promptly frozen at -20°C for storage until remaining DM determination and ergosterol extraction (see below). O 2 consumption rates were converted into C production rates considering a 50% C content of litter DM and a respiratory quotient of 1 [START_REF] Gulis | Interactions between fungi and bacteria associated with decomposing leaf litter at different levels of nutrient availability[END_REF][START_REF] Ferreira | Synergistic effects of water temperature and dissolved nutrients on litter decomposition and associated fungi[END_REF]. The results were expressed as milligram C per gram litter C per hour.

Litter mass loss and mycelial biomass

The remaining 15 litter discs from each microcosm were enclosed in small sterile zip lock bags and promptly frozen at -20°C. All 20 litter discs from each microcosm were combined, lyophilized, and weighed (±0.1 mg) to determine remaining DM and subsequently used for ergosterol extraction as a surrogate for mycelial biomass [START_REF] Gessner | Ergosterol-to-biomass conversion factors for aquatic hyphomycetes[END_REF][START_REF] Gessner | Ergosterol as a measure of fungal biomass[END_REF]. Ergosterol was extracted in 5 mL of KOH/methanol (8 g L -1 ) for 30 min at 80°C. The extract was then purified by solid phase extraction (Waters Oasis HLB 3 cc cartridges; Waters Corp, Milford, MA; Gessner 2005) and quantified with high-performance liquid chromatography (HPLC pump 422, HPLC detector 432, HPLC autosampler 360; Kontron Instruments, Neufahru, Germany) by measuring absorbance at 282 nm. The HPLC detector was equipped with a FLT 0.5-lm A-316 precolumn (Upchurch Scientific, Oak Harbour, WA) and a LispRP 18-5 250 9 4.6-mm column (Thermo-Hypersil Keystone, Bellefonte, PA) maintained at 33°C. The mobile phase was 100% methanol, and the flow rate was set to 1.4 mL min -1 . The relative contribution of each species to total ergosterol mass was estimated based on the specific contribution to total conidial mass production. Ergosterol mass was converted into mycelial biomass using either specific conversion factors for A. tetracladia (5.0 lg ergosterol mg -1 mycelial biomass), C. aquatica (8.0), L. terrestris (5.3), T. elegans (2.9), and T. marchalianum (2.6), or the overall conversion factor for H. lugdunensis (5.5 lg ergosterol mg -1 mycelial biomass; no specific conversion factor available) [START_REF] Gessner | Ergosterol-to-biomass conversion factors for aquatic hyphomycetes[END_REF]. The results were expressed as milligram mycelial C per gram litter C, considering a 50% C content of mycelial and litter DM.

Fungal C budget

Fungal C budgets were calculated assuming a 50% C content of litter, conidial and mycelial DM and a respiratory coefficient of 1 [START_REF] Gulis | Interactions between fungi and bacteria associated with decomposing leaf litter at different levels of nutrient availability[END_REF][START_REF] Ferreira | Synergistic effects of water temperature and dissolved nutrients on litter decomposition and associated fungi[END_REF]. The amount of initial litter C converted into conidia C by the end of the experiment was estimated by multiplying the specific number of conidia accumulated each 3 days over the experiment by the average mass of individual conidia obtained from the literature [START_REF] Chauvet | Temperature and sporulation of aquatic hyphomycetes[END_REF] or calculated from biovolume data (Ba ¨rlocher and Schweizer 1983). The amount of initial litter C converted into mycelial C was estimated for the date when maximum biomass was recorded (day 73). The amount of initial litter C converted into CO 2 -C was estimated by summing up values of daily CO 2 -C, assuming linearity between sampling dates. Fractions of initial litter C converted into conidia, mycelia or mineralized where calculated as C converted by a given fungal activity 9 100/total litter C loss. The difference between total litter C loss and the C loss due to overall fungal activities was attributed to the release of fine particulate organic matter (FPOM) and dissolved organic matter (DOM).

Data analysis

Phosphorus, N, and C concentrations of initial, leached, autoclaved, and irradiated alder discs, and the initial SLA were compared between ambient and elevated litter by t tests. The relationship between SLA and litter P, N, and C was assessed by linear regression.

Exponential decomposition rates (k) of alder discs were calculated by linear regression of ln-transformed fraction of remaining C mass over time, with the intercept fixed at 0. Slopes were compared among treatments by analysis of covariance (ANCOVA), with time as the continuous variable and temperature and litter quality as categorical variables [START_REF] Zar | Biostatistical analysis[END_REF].

Fungal respiration rate, biomass, and sporulation rate from sacrificed microcosms were compared among treatments by three-way analyses of variance (ANOVAs); time, temperature, and litter quality as categorical variables). Total and specific cumulated number of conidia per microcosm, and litter C fractions converted into mycelial C, conidial C, and CO 2 -C were compared among treatments by two-way ANOVAs (temperature and litter quality as categorical variables).

Aquatic hyphomycete assemblages associated with alder discs were compared among treatments by principal response curve (PRC) analysis, which is a constrained form of principal component analysis [START_REF] Ter Braak | CANOCO reference manual and user's guide to CANOCO for windows: software for canonical community ordination[END_REF]. The analysis output is a graph with time on the x axis and the principal responses, i.e., compositional differences of treatments (5°C, elevated; 10°C, ambient; 10°C, elevated) against the control (5°C, ambient), displayed on the y axis. Species scores reflect the contribution of each species to the overall community response as described by the PRCs (CANOCO for Windows 4.5; Microcomputer Power, Ithaca, NY; ter Braak and Smilauer 1998).

Data were log (x ? 1) transformed when necessary to achieved normality and homoscedasticity. Tukey's test was used for post hoc comparisons. All analyses were performed with STATISTICA v7 software (StatSoft, Tulsa, OK), unless otherwise indicated.

Results

Litter chemical quality and specific leaf area

Litter produced under elevated CO 2 atmosphere had 41% lower initial P concentration than litter produced under ambient atmosphere (t test, P = 0.001). Growth conditions did not affect litter initial N (t test, P = 0.922) or C concentration (P = 0.114; Table 1).

Litters lost 46-63% of their initial P concentration after leaching for 1 day or autoclaving; however, the relative difference in P concentration between litters was maintained (36 and 31% for leaching and autoclaving, respectively; t test, P \ 0.005; Table 1). Leaching led to a 40% decrease in initial N concentrations, while autoclaving resulted in a 6-8% increase; this did not affect the initial differences between litters (t test, P [ 0.672; Table 1). Leaching and autoclaving increased the initial C concentration by 0.7-2.8%, and differences between litters became significant (t test, P \ 0.022; Table 1).

Irradiating litter with UV-C light led to smaller decreases in initial P concentration compared with leaching or autoclaving, while the differences between litters remained significant (t test, P \ 0.004; Table 1). However, the relative difference in N (t test, P = 0.018) and C concentration (t test, P = 0.020; Table 1) was altered between litters.

Summarizing, autoclaving the litter led to changes in chemical composition that mimicked those due to leaching and maintained the relative differences in P and N between litters, while irradiation changed the relative differences in chemical composition between litters. Autoclaving was therefore chosen as the sterilization method.

Contrary to expected, SLA was higher for elevated than for ambient litter (14.1 vs. 17.3 mm 2 mg -1 ; t test, P \ 0.001). SLA and P concentration were negatively related (linear regression, P = 0.016, R 2 = 0.65, n = 8).

Litter decomposition

Alder litter discs lost between 26 and 44% of their initial C mass after being incubated in microcosms for 73 days (Fig. 1a), which resulted in decomposition rates between 0.0043 and 0.0075 day -1 (Table 2). There was a tendency, although non-significant (Tukey's test, P [ 0.459), for elevated litter to decompose faster than ambient litter at both temperatures. The increase in water temperature by 5°C significantly stimulated decomposition of both litters (P \ 0.009). Elevated litter incubated at 10°C (future global change scenario) also decomposed faster than ambient litter incubated at 5°C (present scenario) (Tukey's test, P \ 0.001; Table 2).

Fungal respiration, biomass, and sporulation

Maximum values of fungal respiration (0.029-0.030 mg C g -1 C h -1 ; Fig. 1b), mycelial biomass (72-82 mg C g -1 C; Fig. 1c) and sporulation rates (0.08-0.11 mg C g -1 C day -1 ; Fig. 1d) were attained at 10°C. Litter quality did not affect respiration rates at any temperature (Tukey's test, P [ 0.299), while it affected mycelial biomass accrual and sporulation rates at 5°C only (P = 0.044 and P = 0.023, respectively; Table 3). The increase in water temperature by 5°C stimulated fungal respiration and sporulation rates on both litters (Tukey's test, P \ 0.037) and increased biomass accrual on ambient litter only (P \ 0.001; Table 3). Mycelial biomass and sporulation rates were also higher on elevated litter at 10°C (future global change scenario) than on ambient litter at 5°C (present scenario) (Tukey's test, P \ 0.001; Table 3).

Fungal C budget

Litter C loss due to conidial production, although low (\1.2%), was higher at 10°C than at 5°C on both litters (Tukey's test, P \ 0.009) and higher on elevated litter at 10°C than on ambient litter at 5°C (P = 0.034; Fig. 2; Table 4). C loss due to mycelial production was similar among treatments (15-22%; 2-way ANOVA, P [ 0.050), while C loss due to mineralization varied between 15 (5°C, elevated) and 29% (10°C, ambient) and was higher on ambient than on elevated litter at both temperatures (Tukey's test, P \ 0.041) and higher on elevated litter at 10°C than at 5°C (P = 0.004; Fig. 2;Table 4). C loss explained by overall fungal activities varied between 31 (5°C, elevated) and 52% (10°C, ambient) of total C loss and tended to be higher at higher temperature and for ambient litter, although significant differences were found only between elevated and ambient litter at 5°C (P = 0.043; Fig. 2; Table 4). C loss as fine particulate organic matter (FPOM) and dissolved organic matter (DOM) varied between 48 (10°C, ambient) and 69% (5°C, elevated).

Aquatic hyphomycete assemblages

Aquatic hyphomycete assemblages on both ambient and elevated litter at 10°C were most dissimilar from those on ambient litter at 5°C (control; Fig. 3a), indicating that temperature was more important than litter quality in structuring fungal assemblages. Temperature and litter quality treatments explained 49.3%, while time explained 22.3% of the variability among samples (Monte Carlo permutation, P = 0.002). C. aquatica was the species that was most related to the pattern shown by the PRCs, followed by T. elegans and L. terrestris, suggesting that these species were the ones most stimulated by increases in temperature (Fig. 3b,c).

The total number of conidia produced per microcosm during the incubation period varied between 91,200 (5°C, elevated) and 1,018,726 (10°C, ambient; Table 5). There was no effect of litter quality on total conidial production at either temperature (Tukey's test, P [ 0.276). Contrary, the number of conidia was six and ninefold higher at 10 than at 5°C on ambient and elevated litter, respectively (Tukey's test, P \ 0.002). There were species specific differences in conidial production among treatments. C. aquatica (101 fold; Tukey's test, P = 0.008), T. elegans (45; P = 0.008), T. marchalianum (22; P = 0.003) and L. terrestris (5; P = 0.011) had higher conidial production on elevated litter at 10 than at 5°C; the same discrepancies, although with different proportions, were also observed on ambient b Chosen sterilization method litter between 10 and 5°C (Table 5). Conversely, differences between species contribution among litter quality treatments were generally weak. These changes translated into shifts in the assemblages' structure with A. tetracladia and L. terrestris co-dominating at 5°C and C. aquatica and L. terrestris (together with T. marchalianum on ambient litter) dominating at 10°C (Fig. 3c).

Discussion

The future increase in water temperature and alterations in litter quality that are anticipated due to the predicted increase in atmospheric CO 2 levels are expected to affect small woodland streams, where the water temperature is usually low and food webs strongly depend on the terrestrial litter input [START_REF] Vannote | The river continuum concept[END_REF]. To the best of our knowledge, no study has yet assessed the combined effects of increased water temperature and changes in litter quality on aquatic microbial communities and processes. Here, we have attempted to fill this gap by assessing the performance of aquatic hyphomycetes, the most important group of microorganisms involved in litter decomposition in freshwaters [START_REF] Weyers | Fungal and bacterial production during the breakdown of yellow poplar leaves in 2 streams[END_REF], when submitted to changes in both water temperature and litter quality, as those expected in a future climate change scenario. In such a scenario (10°C, elevated litter), decomposition rates and all fungal variables increased, although not more than expected from the individual effects of temperature and litter quality, indicating additive effects. Increased water temperature was, however, the most important factor driving responses of fungal activities and decomposition rates. The possibility that the effect of decreased litter quality can to some degree compensate for the effect of increased water temperature on litter mass loss probably depends on the litter species and on the extent to which litter chemistry and toughness are modified by increased CO 2 . In this study, ambient and elevated litter apparently differed only in P concentration, which can be considered a small difference compared with the discrepancies in N and C often reported in the literature [START_REF] Cotrufo | Elevated CO 2 affects field decomposition rate and palatability of tree leaf litter: importance of changes in substrate quality[END_REF][START_REF] Norby | Elevated CO 2 , litter chemistry, and decomposition: a synthesis[END_REF][START_REF] Stiling | How does elevated carbon dioxide (CO 2 ) affect plant-herbivore interaction? A field experiment and meta-analysis of CO 2 -mediated changes on plant chemistry and herbivore performance[END_REF].

Growing alder leaves under elevated CO 2 atmosphere resulted in a 41% decrease in litter P concentration. This was a surprising result since trees grown under elevated CO 2 tend to have faster growth rates than those grown under ambient CO 2 [START_REF] Curtis | A meta-analysis of elevated CO 2 effects on woody plant mass, form, and physiology[END_REF] and should therefore have higher P demands and sequestration. However, alder trees might have invested more in the growth of fine roots than in that of leaves, diverting P from the latter to the former [START_REF] Rey | Growth response of young birch trees (Betula pendula Roth.) after four and a half years of CO 2 exposure[END_REF]. Similar decreases in P concentration in leaf litter grown under elevated CO 2 levels have been reported for Quercus pubescens (60%, [START_REF] Cotrufo | Decomposition and nutrient dynamics of Quercus pubescens leaf litter in a naturally enriched CO 2 Mediterranean ecosystem[END_REF] and Betula pendula (30%, [START_REF] Ferreira | Effect of increased atmospheric CO 2 on the performance of an aquatic detritivore through changes in water temperature and litter quality[END_REF]. Additionally, elevated CO 2 is most often reported to lead to decreases in N concentration in leaves [START_REF] Cotrufo | Elevated CO 2 affects field decomposition rate and palatability of tree leaf litter: importance of changes in substrate quality[END_REF], although for N-fixers, the opposite trend might occur [START_REF] Vogel | Growth and nitrogen accretion of dinitrogen-fixing Alnus glutinosa (L.) Gaertn. under elevated carbon dioxide[END_REF]). Neither of these patterns was observed in our study as both litters presented similar N concentrations, which might be attributed to alder being an N-fixing species [START_REF] Cotrufo | Elevated CO 2 affects field decomposition rate and palatability of tree leaf litter: importance of changes in substrate quality[END_REF][START_REF] Temperton | Effects of elevated carbon dioxide concentration on growth and nitrogen fixation in Alnus glutinosa in a long-term field experiment[END_REF]. The small differences in litter quality between CO 2 levels in this study might also be partially explained by the conditions in which the alder trees grew. The elevated CO 2 concentration used in our study was intended to reproduce the concentration predicted by 2050, i.e., 580 ppm, which is lower than the concentrations that have been used in most studies performed to date (e.g., 600-1200 ppm; [START_REF] Cotrufo | Elevated CO 2 affects field decomposition rate and palatability of tree leaf litter: importance of changes in substrate quality[END_REF]. Also, the free air CO 2 enrichment technology used in our study has been reported to produce less strong effects on plant responses than those observed when plants are grown in enclosures (e.g., open top chambers, solar domes), indicating the potential for artifacts associated with enclosures [START_REF] Norby | Elevated CO 2 , litter chemistry, and decomposition: a synthesis[END_REF]. Even though the differences in quality between ambient and elevated litter were not those that had been anticipated, elevated litter was of poorer nutrient quality, given that P is frequently the limiting nutrient for microbial growth [START_REF] Francoeur | Meta-analysis of lotic nutrient amendment experiments: detecting and quantifying subtle responses[END_REF][START_REF] Rosemond | Landscape variation in phosphorus concentration and effects on detritus-based tropical streams[END_REF][START_REF] Elser | Global analysis of nitrogen and phosphorus limitation of primary producers in freshwater, marine and terrestrial ecosystems[END_REF]). Therefore, elevated litter was expected to have a lower fungal activity and decomposition rate than ambient litter [START_REF] Gessner | Importance of stream microfungi in controlling breakdown rates of leaf litter[END_REF]. However, contrary to the findings reported for most studies, namely, an increased leaf thickness when leaves are grown under elevated CO 2 [START_REF] Stiling | How does elevated carbon dioxide (CO 2 ) affect plant-herbivore interaction? A field experiment and meta-analysis of CO 2 -mediated changes on plant chemistry and herbivore performance[END_REF]; but see [START_REF] Heagle | Effects of carbon dioxide enrichment on leaf chemistry and reproduction by twospotted spider mites (Acari: Tetranychidae) on white clover[END_REF], we found that the SLA was higher on elevated litter than on ambient litter. This result, associated with the fact that SLA was negatively related to litter P concentration, might to some extent compensate for the negative effects expected from poorer nutrient quality on fungal performance and litter decomposition (see below). Aquatic organisms, however, are not usually exposed to the initial chemical composition of the litter since once in water litter starts to leach soluble compounds and its chemical composition changes [START_REF] Gessner | A perspective on leaf litter breakdown in streams[END_REF]. Changes in quality after leaching for 1 day were also observed in our litter. Since litter discs had to be sterilized, autoclaving was the chosen method because it simulated the leaching process, which would be intensive during the first 24-48 h of litter submersion, and it maintained the relative difference in quality between litters. Incubation of ambient and elevated leaf litter in streams is associated with changes in litter quality, with some studies reporting that the relative difference in initial chemical composition between litters disappeared [START_REF] Rier | Elevated-CO 2induced changes in the chemistry of quaking aspen (Populus tremuloides Michaux) leaf litter: subsequent mass loss and microbial responses in a stream ecosystem[END_REF][START_REF] Rier | Chemical changes to leaf litter grown under elevated CO 2 and the implications for microbial utilization in a stream ecosystem[END_REF][START_REF] Adams | Atmospheric CO 2 enrichment alters leaf detritus: impacts on foraging decisions of crayfish (Orconectes virilis)[END_REF]Tuchman et al. 2003b), was maintained [START_REF] Tuchman | Elevated atmospheric CO 2 lowers leaf litter nutritional quality for stream ecosystem food webs[END_REF](Tuchman et al. , 2003a;;[START_REF] Adams | Atmospheric CO 2 enrichment alters leaf detritus: impacts on foraging decisions of crayfish (Orconectes virilis)[END_REF][START_REF] Ferreira | Effect of increased atmospheric CO 2 on the performance of an aquatic detritivore through changes in water temperature and litter quality[END_REF], or was even amplified [START_REF] Rier | Chemical changes to leaf litter grown under elevated CO 2 and the implications for microbial utilization in a stream ecosystem[END_REF].

Litter decomposition rates increased by more than 30% with a 5°C increase in water temperature, but they were insensitive to litter quality. Faster litter decomposition rates at higher temperatures have been documented in aquatic and terrestrial systems [START_REF] Irons | Latitudinal patterns in leaf litter breakdown: is temperature really important?[END_REF][START_REF] Aerts | Table 5 Specific and total number of conidia on alder discs produced under ambient or elevated CO 2 concentrations and incubated in microcosms at 5 and 10°C over 73 days Temperature (°C) 5 10 Litter quality Ambient Elevated Ambient[END_REF][START_REF] Dang | Temperature oscillation coupled with fungal community shifts can modulate warming effects on litter decomposition[END_REF][START_REF] Ferreira | Synergistic effects of water temperature and dissolved nutrients on litter decomposition and associated fungi[END_REF] and can be explained by stimulated biological activity [START_REF] Fabre | Leaf breakdown along an altitudinal stream gradient[END_REF][START_REF] Dang | Temperature oscillation coupled with fungal community shifts can modulate warming effects on litter decomposition[END_REF][START_REF] Ferreira | Synergistic effects of water temperature and dissolved nutrients on litter decomposition and associated fungi[END_REF]; see below). The anticipated lower decomposition rates of elevated litter due to its lower P concentration were not observed and might be attributed to a trade-off between lower litter P concentration, which would reduce the nutritional quality of the litter, and lower litter toughness, which would facilitate mycelial colonization. Litter toughness has been shown to determine litter decomposition rates, sometimes even overcoming the importance of litter chemistry [START_REF] Quinn | Influences of leaf toughness and nitrogen content on in-stream processing and nutrient uptake by litter in a Waikato, New Zealand, pasture stream and streamside channels[END_REF][START_REF] Li | Effects of leaf toughness and nitrogen content on litter breakdown and macroinvertebrates in a tropical stream[END_REF]. The few studies addressing the effects of changes on litter quality induced by increases in atmospheric CO 2, on aquatic microbial communities and litter decomposition have shown that these effects are stronger at early stages of litter decomposition than at later stages, when secondary compounds have been leached; however, overall they remain weak and speciesdependent [START_REF] Rier | Elevated-CO 2induced changes in the chemistry of quaking aspen (Populus tremuloides Michaux) leaf litter: subsequent mass loss and microbial responses in a stream ecosystem[END_REF][START_REF] Rier | Chemical changes to leaf litter grown under elevated CO 2 and the implications for microbial utilization in a stream ecosystem[END_REF]Tuchman et al. 2003b;[START_REF] Kelly | Growth of trees under elevated atmospheric CO 2 alters microbial communities colonizing leaf litter in a temperate woodland stream[END_REF]. Evidence from terrestrial systems also indicates that the effects of elevated CO 2 on litter quality are species specific and not always translated into differences in litter decomposition rates [START_REF] Gorissen | Decomposition of leaf and root tissue of three perennial grass species grown at two levels of atmospheric CO 2 and N supply[END_REF][START_REF] King | Correlation of foliage and litter of sugar maple, Acer saccharum, as affected by elevated CO 2 and varying N availability, and effects on decomposition[END_REF][START_REF] Norby | Elevated CO 2 , litter chemistry, and decomposition: a synthesis[END_REF]).

Fungal respiration rates, a measure of overall activity, were stimulated at 10°C, as expected, since increases in temperature within a non-stressful range stimulate enzymatic activities [START_REF] Bekku | Effect of warming on the temperature dependence of soil respiration rate in arctic, temperate and tropical soils[END_REF]. To the contrary, the similarity in respiration rates between litters might indicate that differences in litter quality were not strong enough or that litter quality was not the most important factor driving microbial activities. Microbial activity has been reported to be higher on ambient litter than on elevated litter when there is a difference in quality [START_REF] Rier | Elevated-CO 2induced changes in the chemistry of quaking aspen (Populus tremuloides Michaux) leaf litter: subsequent mass loss and microbial responses in a stream ecosystem[END_REF]Tuchman et al. 2003b). This indicates that microbial activity sensitivity to temperature is not always dependent on litter quality. This result is in contrast with reports from terrestrial systems where differences in litter quality are high (Conant et al. 2008a, b). The increase in CO 2 release from litter with increased temperature might have consequences on the C cycle, leading to a positive feedback on global warming [START_REF] Knorr | Long-term sensitivity of soil carbon turnover to warming[END_REF]. The effect of elevated temperature on the decomposition of litter submerged in aquatic environments should therefore be taken into consideration when the effects of CO 2 release from decomposing litter are modeled on atmospheric CO 2 concentrations.

As expected, mycelial biomass accrual and fungal sporulation rates were stimulated by an increase in temperature [START_REF] Chauvet | Temperature and sporulation of aquatic hyphomycetes[END_REF][START_REF] Rajashekar | Effects of temperature and light on growth and sporulation of aquatic hyphomycetes[END_REF][START_REF] Dang | Temperature oscillation coupled with fungal community shifts can modulate warming effects on litter decomposition[END_REF][START_REF] Ferreira | Synergistic effects of water temperature and dissolved nutrients on litter decomposition and associated fungi[END_REF]. At 5°C, fungal biomass accrual and sporulation were higher on ambient litter than on elevated litter, which might indicate that on elevated litter, both variables were more sensitive to decreased P concentration than to decreased toughness. This result is probably due to the increasing needs of P for nucleic acid production, which is necessary to sustain higher mycelial and conidial production. However, contrary to our expectations, differences in biomass accrual and sporulation were greater between litters at 5°C than between those at 10°C. Since higher water temperature resulted in stimulated fungal production, the P demand for nucleic acid production should have been higher to sustain higher mycelial and conidial production. Given that P concentration was lower on elevated litter, this should have translated into differences between litters at 10°C. At the lower water temperature, this P demand would be low on both litters because growth was lower, and elevated litter would therefore be able to support the P demand for fungal production. The fact that the difference between litters occurred only at 5°C might be attributed to the structure of the assemblages and the species-specific P needs at 5 and 10°C. Because a species such as T. elegans, which dominates assemblages at 5°C, but not 10°C, apparently behaves differently from other species in terms of N and P use and requirements, as judged from preliminary experiments (M Danger and E Chauvet, results not shown), this may have resulted in the observed contrast in response to litter quality at the two temperatures.

Fungal-induced mass loss was higher from ambient litter than from elevated litter, likely due to differences in overall fungal respiration, which was higher on the ambient litter. In contrast, mass loss through FPOM and DOM release was higher on elevated litter than on ambient litter, resulting in similar amounts of mass being lost from the system (mineralization, FPOM, and DOM) for both litters. In a stream situation, this would mean, on one hand, that the local invertebrate detritivores might not be strongly affected by small changes in litter quality as the ones reported here (but see [START_REF] Ferreira | Effect of increased atmospheric CO 2 on the performance of an aquatic detritivore through changes in water temperature and litter quality[END_REF]) while, on the other hand, downstream communities in which collectors become the dominant functional feeding group of invertebrates [START_REF] Vannote | The river continuum concept[END_REF]) might be favored since the release of FPOM from elevated litter might increase. The higher levels of DOM leached from elevated litter might also affect periphytic algal accrual and further affect grazing invertebrates [START_REF] Kominoski | Elevated CO 2 alters leaf-litter-derived dissolved organic carbon: effects on stream periphyton and crayfish feeding preferences[END_REF]).

Litter quality did not affect the absolute or relative specific conidial contribution to total conidial production, probably because the differences between litters were small. A recent study also found that fungal communities were not affected by litter quality changes induced by increased atmospheric CO 2 [START_REF] Kelly | Growth of trees under elevated atmospheric CO 2 alters microbial communities colonizing leaf litter in a temperate woodland stream[END_REF]). However, when differences in litter quality are greater, for example, between litter species, aquatic hyphomycete community structure can be affected [START_REF] Gulis | Are there any substrate preferences in aquatic hyphomycetes?[END_REF][START_REF] Ferreira | Whole-stream nitrate addition affects litter decomposition and associated fungi but not invertebrates[END_REF]. In contrast, increased water temperature affected the assemblage structure, as expected [START_REF] Ba ¨rlocher | Raised water temperature lowers diversity of hyporheic aquatic hyphomycetes[END_REF][START_REF] Dang | Temperature oscillation coupled with fungal community shifts can modulate warming effects on litter decomposition[END_REF][START_REF] Ferreira | Synergistic effects of water temperature and dissolved nutrients on litter decomposition and associated fungi[END_REF]; this change was due to species having temperature preferences (e.g., T. elegans and T. marchalianum were stimulated at higher temperatures, [START_REF] Chauvet | Temperature and sporulation of aquatic hyphomycetes[END_REF]. These effects of water temperature on the structure of assemblages help in explaining the higher litter decomposition at 10°C since different species might differ in degradative capabilities [START_REF] Suberkropp | Comparison of degradative ability, enzymatic activity, and palatability of aquatic hyphomycetes grown on leaf litter[END_REF]. In streams, temperature-induced changes in the structure of fungal assemblages might also indirectly affect litter decomposition through their effects on shredding invertebrates. Shredders exhibit preferences for certain species of aquatic hyphomycetes (Arsuffi and Suberkropp 1984) and derive a large amount of energy from fungal mycelium [START_REF] Chung | Contribution of fungal biomass to the growth of the shredder, Pycnopsyche gentilis (Trichopetra: Limnephilidade)[END_REF]. Therefore, litter bearing preferred species in higher amounts will be more palatable, resulting in higher invertebrate-induced mass loss [START_REF] Arsuffi | Selective feeding by shredders on leaf-colonizing stream fungi: comparison of macroinvertebrate taxa[END_REF].

In conclusion, our results indicate that if increased atmospheric CO 2 concentration affects litter quality only slightly, then litter decomposition and fungal activities and community structure will be strongly controlled by the future increase in water temperature. This may have serious consequences for aquatic systems, as faster litter decomposition will probably lead to food depletion at higher trophic levels [START_REF] Poff | Aquatic ecosystems and global climate change. Potential impacts on inland freshwater and coastal wetland ecosystems in the United States[END_REF]. The fast disappearance of litter from the streambed can, however, be mitigated if increases in atmospheric CO 2 result in higher litter production [START_REF] Finzi | Forest litter production, chemistry, and decomposition following two years of free-air CO 2 enrichment[END_REF][START_REF] Stiling | How does elevated carbon dioxide (CO 2 ) affect plant-herbivore interaction? A field experiment and meta-analysis of CO 2 -mediated changes on plant chemistry and herbivore performance[END_REF].

More studies on the effects of elevated CO 2 on litter quality and the decomposition rates of different litter species are necessary to allow a better understanding of the effects of this global change factor on aquatic communities and ecosystem functioning. Since an increased atmospheric CO 2 concentration can also change plant phenology and litter production, as well as co-vary with other environmental factors, such as dissolved nutrients, multi-factor experiments will likely provide a better picture of ecosystem functioning under a future climate change scenario.

Fig. 1

 1 Fig. 1 Remaining alder leaf litter mass (a), fungal respiration rate (b), mycelial biomass (c), sporulation rate (d) associated with alder discs produced under ambient (present CO 2 level: 380 ppm) or elevated (predicted CO 2 level by 2050: 580 ppm) CO 2 concentrations and incubated in microcosms at 5 and 10°C for 73 days. Data are presented as the mean ± 1 standard error (SE)

Fig. 2

 2 Fig.2Litter mass loss due to fungal activities of alder discs produced under ambient or elevated CO 2 concentrations and incubated in microcosms at 5 and 10°C over 73 days. Data are presented as the mean ± 1 standard error (SE)

Fig. 3 a

 3 Fig.3a Principal response curves for aquatic hyphomycetes assemblages associated with alder discs produced under ambient or elevated CO 2 concentrations and incubated in microcosms at 5 and 10°C for 73 days, b species scores (the higher the score, the more the species was stimulated by the treatments), c relative contribution of each species to the total conidial production. At Articulospora tetracladia Ingold, Ca Clavariopsis aquatica de Wildeman, H1 Heliscus lugdunensis Saccardo and The ´rry, Lt Lemonniera terrestris Tubaki, Te Tetrachaetum elegans Ingold, Tm Tricladium marchalianum Ingold

Table 1

 1 Phosphorus, nitrogen, and carbon concentrations of initial, leached, autoclaved and UV-C irradiated alder discs produced under ambient or elevated carbon dioxide concentrations Values are given as the mean concentration ± 1 standard error (SE). Values within the same treatments (column) and litter state (row) followed with the same letter are not significantly different (t test, P [ 0.05) P phosphorus, N nitrogen, C carbon, CO 2 , carbon dioxide, DM dry mass a Ambient, ambient atmosphere (present CO 2 level: 380 ppm); elevated, elevated CO 2 atmosphere (predicted CO 2 level by 2050: 580 ppm)

	Litter state	Litter quality a	P (% DM)	N (% DM)	C (% DM)
	Initial	Ambient	0.25 ± 0.02 a	3.37 ± 0.06 a	49.9 ± 0.1 a
		Elevated	0.15 ± 0.02 b	3.35 ± 0.11 a	49.5 ± 0.2 a
	Leached	Ambient	0.12 ± 0.01 a	2.03 ± 0.10 a	51.0 ± 0.2 a
		Elevated	0.08 ± 0.01 b	2.02 ± 0.19 a	49.9 ± 0.2 b
	Autoclaved b	Ambient	0.09 ± 0.01 a	3.58 ± 0.08 a	51.3 ± 0.1 a
		Elevated	0.07 ± 0.01 b	3.63 ± 0.11 a	50.7 ± 0.2 b
	UV-C irradiated	Ambient	0.23 ± 0.01 a	3.54 ± 0.09 a	50.6 ± 0.1 a
		Elevated	0.16 ± 0.02 b	3.21 ± 0.10 b	49.9 ± 0.3 b

Table 2

 2 Exponential decomposition rates of alder discs produced under ambient or elevated CO 2 concentrations and incubated in microcosms at 5 and 10°C for 73 days, standard error and coefficient of determination of the regression Temperature (°C) Litter quality k (day -1 ) Standard error R 2

	5	Ambient	0.0043 a	0.0003	0.72
		Elevated	0.0052 a,b 0.0003	0.81
	10	Ambient	0.0067 b,c 0.0005	0.76
		Elevated	0.0075 c	0.0004	0.84
	Values (treatments) followed by the same letter are not significantly
	different (Tukey's test, P [ 0.05)
	k exponential decomposition rate

Table 3

 3 Summary table for three-way ANOVAs performed on microbial variables associated with alder discs produced under ambient or elevated CO 2 concentrations and incubated in microcosms at 5 and 10°C for 73 days

	Analysis	Fungal respiration rate	Mycelial biomass		Sporulation rate
		df	F	P	df	F	P	df	F	P
	Three-way ANOVA
	Intercept	1	244.7	\0.001	1	5,492.0	\0.001	1	1,575.5	\0.001
	Temperature	1	25.7	\0.001	1	34.7	\0.001	1	112.9	\0.001
	Litter quality	1	2.9	0.095	1	2.8	0.103	1	4.1	0.051
	Time	2	2.7	0.085	2	40.5	\0.001	2	39.2	\0.001
	Temperature 9 litter quality	1	0.2	0.636	1	4.7	0.037	1	5.1	0.031
	Temperature 9 time	2	5.6	0.008	2	3.0	0.061	2	3.0	0.064
	Litter quality 9 time	2	2.1	0.132	2	3.3	0.047	2	3.9	0.029
	Temperature 9 litter quality 9 time	2	0.7	0.495	2	2.8	0.076	2	10.9	\0.001
	Error	34			35			36
	Tukey's test a

Table 4

 4 Summary table for two-way ANOVAs performed on the fraction of litter C lost due to fungal activities on alder discs produced under ambient or elevated CO 2 concentrations and incubated in microcosms at 5 and 10°C for 73 days

	Analysis	Litter C loss due to	Litter C loss due to	Litter C loss due to	Litter C loss due to overall
		conidial production	mycelial production	mineralization		fungal activities
		df	F	P	df	F	P	df	F	P	df	F	P
	Two-way ANOVA
	Intercept	1	72.6	\0.001	1	222.5	\0.001	1 1,335.2 \0.001	1	660.7	\0.001
	Temperature	1	56.8	\0.001	1	0.2	0.681	1	23.9 \0.001	1	6.1	0.029
	Litter quality	1	6.0	0.033	1	4.7	0.050	1	33.2 \0.001	1	15.5	0.002
	Temperature 9 litter quality 1	1.4	0.259	1	0.0	0.881	1	2.0	0.187	1	0.2	0.705
	Error	11			12			12			12
	Tukey's test a
	5°C, ambient			a			a			ab			a
	5°C, elevated			a			a			c			b
	10°C, ambient			b			a			b			a
	10°C, elevated			b			a			a			ab

a Tukey's test results are presented, with treatments with the same letter not being significantly different (P [ 0.05)

Acknowledgments Alder litter was kindly provided by Prof. Douglas Godbold (School of Agricultural and Forest Sciences, University of Wales, Bangor, UK) and was a product of the Bangor FACE project. We thank Franck Gilbert for laboratory equipment, Julien Cornut and Michael Danger for the isolation of aquatic hyphomycete species, and Marion Bottollier, Sylvain Lamothe, and Didier Lambrigot for providing technical help. The comments provided by Dr. Elena Litchman and two anonymous reviewers were most welcome. Financial support granted by the Portuguese Foundation for Science and Technology (FCT, Reference SFRH/BPD/ 34368/2006) to VF and by the National Center for Scientific Research (CNRS) to EC, as well as the Pessoa exchange program between Portugal and France (PHC 22808 TB) from the French Ministry of Foreign and European Affairs, are gratefully acknowledged.


Sara Zermani
email: sara.zermani@univ-brest.fr

Catherine Dezan

Reinhardt Euler

Jean-Philippe Diguet

Online Inference for Adaptive Diagnosis via Arithmetic Circuit Compilation of Bayesian Networks

I. INTRODUCTION AND CONTEXT

Considering technology and complexity evolution the design of fully reliable embedded systems will be prohibitively complex and costly. Onboard diagnosis is a first solution that can be achieved by means of Bayesian networks [START_REF] Mengshoel | Sensor validation using Bayesian networks[END_REF], [START_REF] Ricks | The diagnostic challenge competition: Probabilistic techniques for fault diagnosis in electrical power systems[END_REF]. An efficient compilation of Bayesian inference is proposed in [START_REF] Darwiche | A differential approach to inference in bayesian networks[END_REF] using Arithmetic Circuits (AC). ACs can be efficiently implemented in hardware to get very fast response time. This approach has been recently experimented in Software Health Management of aircrafts or UAVs [START_REF] Schumann | Towards real-time, on-board, hardware-supported sensor and software health management for unmanned aerial systems[END_REF]. However, there are two kinds of obstacles that must be addressed. First, the tree complexity can lead to intractable solutions and second, an offline static analysis cannot capture the dynamic behaviour of a system that can have multiple configurations and applications.

In this paper, we present our direction to solve these issues. Our approach relies on an adaptive version of the diagnosis computation for different kinds of applications/missions of UAVs. In particular, we consider an incremental generation of the AC structure. This adaptive diagnosis can be implemented using dynamic reconfiguration of FPGA circuits.

II. COMPILATION OF A BAYESIAN NETWORK AND INFERENCE COMPUTATION

Our work makes use of [START_REF] Darwiche | A differential approach to inference in bayesian networks[END_REF] and [START_REF] Darwiche | A differential approach to inference in bayesian networks[END_REF] as follows: each Bayesian network [START_REF] Cowell | Probabilistic networks and expert systems: Exact computational methods for Bayesian networks[END_REF] can be represented as a multi-linear function (MLF). This MLF is transformed into an arithmetic circuit (AC) and the probabilities are computed using this AC. The construction of the AC is done offline but the implementation is different and all conditional probabilities can be computed online as soon as the evidences (indicator values) are given.

A. Bayesian Networks as MLFs

For each Bayesian network we can define a unique MLF over two types of variables:

• Evidence indicators (λ x ): representing the members of a set of evidences (binary values). • Network parameters (θ x|u ): representing the parameters concerning the probability values associated with the variables X and U .

f = x xu∼x λ x θ x|u (1)
The Bayesian network of Fig. 1.a) relies on two variables A and B which have two states, a and a for A, b and b for B. Consequently, the MLF of this network is as follows:

f = λ a θ a λ b θ b|a + λ a θ a λ b θ b|a + λ a θ a λ b θ b|a + λ a θ a λ b θ b|a
To compute the margin probability at evidence e (P(e)=f(e)), each evidence indicator λ x is replaced in f by 1 if x is consistent with e, and by 0 otherwise. For example, if the evidence e is b, f(e) is computed by setting λ b =1, λ b =0, λ a =1 and λ a =1. Then From Bayes' theorem, we have P(x|e)= P (x,e) P (e) . We can see that P(x,e)= f(e,λ x =1, λ b = 0) or P(x,e)= ∂f ∂λx (e) (x not included in e).

BA  a b  a  a a A  A = 0.3 = 0.7 a b  a b  ) ( ) ( a b b a b b a a a b b a b b a a λ λ λ λ λ λ f           A B = 0.1 = 0.9 = 0.2 = 0.8 (a) (b)
Computing probabilities by means of MLFs explodes when the number of variables becomes large. For this reason, it is proposed to compile the network into an AC in order to reduce time and space.

B. Compilation into an AC

An arithmetic circuit is a compact graphical representation of a function f over variables (see Fig. 1

.b) ).

There are different ways to compile an MLF into an AC [START_REF] Lian | Real time diagnosis with compiling bayesian networks[END_REF], [START_REF] Chavira | Compiling bayesian networks using variable elimination[END_REF]. We have chosen the classical one based on factorisation and the jointree method. We present a hierarchical method of the AC construction.

• Arithmetic circuit by factorisation [START_REF] Darwiche | A differential approach to inference in bayesian networks[END_REF] In the example of Fig. 1.a): f=λ a θ a λ b θ b|a + λ a θ a λ b θ b|a + λ a θ a λ b θ b|a + λ a θ a λ b θ b|a , and by factoring over A we obtain: f=

λ a θ a (λ b θ b|a + λ b θ b|a ) + λ a θ a (λ b θ b|a + λ b θ b|a ).
To have the AC of the factorised fonction, the leaves of the arithmetic circuits are λ, θ, and the nodes of the tree represent a multiplication (addition), respectively. The Bayesian network and its AC structure is given in Fig. 1. The factorization is simple to obtain but it takes an exponential space.

• Arithmetic circuit by jointree [START_REF] Darwiche | A differential approach to inference in bayesian networks[END_REF] The goal is to generate the smallest possible circuit from a given jointree. After the choice of a root cluster, the arithmetic circuit is generated from the jointree (set of clusters and separators) as follows:

one output addition node f; one addition node for each instantiation of a separator; one multiplication node for each instantiation of a cluster; one input node (λ x ) and (θ x|u ) (for all parents of x).

• Hierarchical building of the AC structure We observe that an Incremental building of AC through jointree structure can be realised. A simple illustration is given in Fig. 2.

+ * * a  a λ a λ a  BE(a, B) BE(a, B) BE(a, C) BE(a, C) + * * a  a λ a λ a  BE(a, B) BE(a, B) A B A B C => => Fig. 2

. Hierarchical building of the AC

We propose to take advantage of this technique that can be applied to kinds of Bayesian networks (or jointrees). This hierarchical building avoids to store all AC structures corresponding to the possible Bayesian networks built for the diagnoses of the different applications running on the embedded system. Considering the exponential growth of the system this point is crucial.

C. Computing probabilities using AC

To compute P(x|e), we first need to evaluate f(e) and then to compute the circuit derivatives to get f(x,e)= ∂f ∂λx .

• Evaluating an arithmetic circuit: in an upward-pass, the value of a node in the AC tree is computed after the computation of the values of its children.

∂p ∂v = ∂v( v ′ v ′ ) ∂v = v ′ v ′ (2)
∂p ∂v = ∂v + ( v ′ v ′ ) ∂v = 1 (3)
With these equations, we can recursively compute the partial derivatives of f with respect to any node v. Complexity: the upward-pass clearly is achieved in a time linear in the size of the circuit (number of edges in the circuit). The downward-pass takes linear time only when each multiplication node has a bounded number of children. The disadvantage of this approach is that all the computations done in the upward-pass must be saved in order to be used in the downward-pass.

In the next section, we propose a simpler method for the AC computation without any downward-pass for the diagnosis of an application. We also propose to use a reconfiguration of AC when the application and its diagnosis have to change in time.

III. THE ADAPTIVE DIAGNOSIS OF A UAV EMBEDDED SYSTEM THROUGH MISSIONS

We want to define an adaptive diagnosis for a set of different applications (or tasks) by modifying the AC associated with the diagnosis of one of them.

A. The Bayesian network corresponding to a task

Consider a UAV including an embedded system with a task that consists in taking photos upon receipt of a demand. The system can take a photo only if is has enough memory. The scenario is the following: if it can't take a photo and it has got enough memory, or if it can take a photo and it doesn't have enough memory, then the functionality is turned to bad. We assume that the space in the memory is computed with a logical sensor, which can produce state ok or bad.

A Bayesian network associated with this task can be defined as follows: The detailed Bayesian network of this example and its jointree is given in Fig. 3.

B. Computing

the Health probability P (Health|Sensor, Command)

The goal is to diagnose the current state of the system by evaluating the node H representing its health. This evaluation is done upon the knowledge of some evidences (the value c is the evidence associated with the command C and the value s the evidence associated to the sensor S) and it corresponds to the computation of P (h|s, c).

We know that:

P (h|s, c) = P (h, s, c) P (s, c) P (h, s, c) = ∂f ∂(h) (s, c) P (s, c) = f (s, c)
Considering node H as the root node of the AC, we obtain at the last step of the upward-pass:

f (s, c) = f (λ h = 1) + f (λ h = 1) and f (h, s, c) = f (λ h = 1) + f (λ h = 0) = f (λ h = 1)
We can see that if we take H as the root node of the AC, we don't need the downward-pass any more. We can apply this to the other node HS. In general, for a health node HX, we compute as indicated until reaching λ hx and λ hx and with λ hx =1, we get f (e, hx) and by adding f(e,λ hx =1) we get f (e). After this step, we continue by taking into account the two computations for each node.

C. Reconfiguration of an AC for adaptive diagnosis

Now, assume that our UAV has some missions related to different type of applications (or tasks). There are two types of task: the static one (executed from the beginning to the end of the mission, as for example path-planning) and the temporary one (executed at a certain time, as for example taking photos, then writing into a file the external and the internal temperature, and finally writing into the same file the altitude measures using both barometric and laser altimeter).

The goal is to monitor the health of the system at any time. The complete arithmetic circuit for static and temporary tasks of the whole system has to be computed in a static way before the mission. Nevertheless, some parts of the diagnosis (or AC structure) could be done more on-the-fly, especially the temporary tasks.

We propose to compile the arithmetic circuit of the static tasks offline. For each new temporary task, we reconfigure the AC by deleting the nodes of the previous task and adding the node of the current one in real time. We assume that the UAV should execute task 1 'take photos' presented in Fig. 3 for a specific time slot and in a context of other static tasks. For the temporary task 2, we look at the computation of the altitude using 3 sensors (laser sensor, barometer sensor and IMU). The Bayesian networks for the diagnosis of these two tasks and their jointrees are given in Fig. 3 and Fig. 4. Since we have a large common part within the two jointrees, we can use the AC of task 1 to obtain the complete AC of task 2. For this we use the hierarchical building as illustrated in Fig. 2.

• For the cluster (U, S-IMU), these steps are as follows:

1) go to all (*) of U;

2) add a (+) node for each (*) node and add an arc for BE(U|HC,S-IMU), where U |HC corresponds to any • For the cluster (U, H-Bar, S-Bar), these steps are as follows:

1) go to all (*) of U;

2) add a (+) node and two (*) nodes for each (*) node of U.

For the first (*) node, add an arc for λ H-Bar , θ H-Bar and BE(U|HC, S-Bar). For the second (*) node, add an arc for λ H-Bar , θ H-Bar and BE(U|HC, S-Bar) for the corresponding instantiation.

This method can be generalised to any Bayesian network by adding corresponding constraints.

IV. CONCLUSION AND PERSPECTIVES

In this paper, we have applied adaptive diagnosis to a number of independent tasks. The next step will consist in applying adaptive diagnosis to tasks with interactions (e.g., being executed in the same or different contexts or sharing specific ressources). We also study the efficient hardware implementation of such configurable diagnosis engines that can offer very short response times. FPGAs provide the kind of parallelism that fit with Bayesian networks but architectures with different performances/area tradeoff are possible. We explore this design space, with two different approaches. The first one is based on partial/dynamic reconfigurations of Xilinx FPGAs. The second one is an application specific processor to be also implemented as a soft core on a FPGA.

Fig. 1 .

 1 Fig. 1. a) A Bayesian network with the factored function. b) The corresponding arithmetic circuit

Fig. 3 .

 3 Fig.3. The Bayesian network of a camera application (task 1) and its jointree.

U 3 UFig. 4 .

 34 Fig. 4. The Bayesian network of an altitude application (task 2) and its jointree

•

  Computing the circuit derivatives: in a downward-pass, the derivative of a node is computed after the computation of the derivative of its parent. Let v be an arbitrary node in a circuit f, and assume that we are interested in the partial derivative of f with respect to node v, ∂f ∂λv . If v is the root node (circuit output), then

	∂f ∂λv =1. If v is not the root node and has parents p, then by the chain rule of differential calculus:
	∂f ∂v	=	p	∂f ∂p	∂p ∂v
	Suppose now that v

′ is another child of a parent p. If p is a multiplication node, then Equation (2) applies and if p is an addition node, then Equation (3).

  Health(H): representing the health of the system associated to the internal state U . It takes the value Ok or Bad.

	(notation (h or h)).
	Sensor(S): indicating whether the capacity of the memory
	is sufficient or not. It takes the value Y es or N o. (notation
	(s or s)).
	Health-Sensor:(HS) representing the health of the Sensor.

• Nodes: Command(C): representing the demand of taking a photo. It takes the values Y es or N o (notation (c or c)). State(U): indicating whether the photo is taken or not. It can have the values Y es or N o (notation (u or u)).. It takes the value Ok or Bad (notation (hs or hs)), depending on the reliability of the sensor S. • Edges: C, H → U : U depends on C and H. U is commanded by C and monitored by H. U , HS → S: S depends on H and U . U is observed by S which is monitored by HS.