Je´re´my Jabiol

Brendan G Mckie

Andreas Bruder

Caroline Bernadet

Mark O Gessner

Eric Chauvet

Trophic complexity enhances ecosystem functioning in an aquatic detritus-based model system

Keywords: aquatic hyphomycetes, biodiversity and ecosystem functioning, detritivores, fungi, litter decomposition, shredders, stream, trophic cascade

Understanding the functional significance of species interactions in ecosystems has become a major challenge as biodiversity declines rapidly worldwide. Ecosystem consequences arising from the loss of diversity either within trophic levels (horizontal diversity) or across trophic levels (vertical diversity) are well documented. However, simultaneous losses of species at different trophic levels may also result in interactive effects, with potentially complex outcomes for ecosystem functioning. 2. Because of logistical constraints, the outcomes of such interactions have been difficult to assess in experiments involving large metazoan species. Here, we take advantage of a detritus-based model system to experimentally assess the consequences of biodiversity change within both horizontal and vertical food-web components on leaf-litter decomposition, a fundamental process in a wide range of ecosystems. 3. Our concurrent manipulation of fungal decomposer diversity (0, 1 or 5 species), detritivore diversity (0, 1 or 3 species), and the presence of predatory fish scent showed that trophic complexity is key to eliciting diversity effects on ecosystem functioning. Specifically, although fungi and detritivores tended to promote decomposition individually, rates were highest in the most complete community where all trophic levels were represented at the highest possible species richness. In part, the effects were trait-mediated, reflected in the contrasting foraging responses of the detritivore species to predator scent. 4. Our results thus highlight the importance of interactive effects of simultaneous species loss within multiple trophic levels on ecosystem functioning. If a common phenomenon, this outcome suggests that functional ecosystem impairment resulting from widespread biodiversity loss could be more severe than inferred from previous experiments confined to varying diversity within single trophic levels.

Introduction

What 'species do in ecosystems' [START_REF] Lawton | What do species do in ecosystems?[END_REF] has become a leading theme of ecological inquiry. Central to this development have been investigations into ecosystem consequences arising from species interactions within trophic levels [START_REF] Hooper | A global synthesis reveals biodiversity loss as a major driver of ecosystem change[END_REF]). This research is generally conducted under the label of biodiversity effects on ecosystem functioning [START_REF] Hillebrand | Biodiversity in a complex world: consolidation and progress in functional biodiversity research[END_REF][START_REF] Reiss | Emerging horizons in biodiversity and ecosystem functioning research[END_REF][START_REF] Loreau | Linking biodiversity and ecosystems: towards a unifying ecological theory[END_REF][START_REF] Cardinale | Biodiversity loss and its impact on humanity[END_REF], motivated in part by the current rapid species loss worldwide [START_REF] Dudgeon | Freshwater biodiversity: importance, threats, status and conservation challenges[END_REF][START_REF] Naeem | The functions of biological diversity in an age of extinction[END_REF] and its repercussions for the human benefits afforded by *Correspondence author. E-mail: jeremy.jabiol@gmail.com doi: 10.1111/1365-2656.12079 ecosystems with diverse communities [START_REF] Cardinale | Biodiversity loss and its impact on humanity[END_REF]. Although initially focused on terrestrial plant diversity and primary productivity (e.g. [START_REF] Isbell | High plant diversity is needed to maintain ecosystem services[END_REF], such relationships have now been documented for a wide range of ecosystem properties and community types [START_REF] Stachowicz | Understanding the effects of marine biodiversity on communities and ecosystems[END_REF][START_REF] Scherber | BottomÀup effects of plant diversity on multitrophic interactions in a biodiversity experiment[END_REF][START_REF] Cardinale | The functional role of producer diversity in ecosystems[END_REF], including aquatic and terrestrial detritus-based systems in which leaf litter decomposition is a central process [START_REF] Srivastava | Reducing horizontal and vertical diversity in a foodweb triggers extinctions and impacts functions[END_REF][START_REF] Gessner | Diversity meets decomposition[END_REF][START_REF] Cardinale | Biodiversity loss and its impact on humanity[END_REF].

Similar attention has been given to the concept of trophic cascades [START_REF] Baum | Cascading topÀdown effects of changing oceanic predator abundances[END_REF][START_REF] Terborgh | Trophic Cascades À Predators, Prey, and the Changing Dynamics of Nature[END_REF] and their repercussions for ecosystem functioning. Trophic cascades refer to the phenomenon that toppredators suppress the biomass of intermediate consumers, which in turn releases consumers at the next lower trophic level from predation pressure, with this alternate suppression-and-release effect propagating down to the producer level. As originally formulated, trophic cascades operate over entire trophic levels [START_REF] Hairston | Community structure, population control and competition[END_REF], but this stringent condition was later relaxed as it became clear that the concept is also useful to describe trophic relationships between individuals or clusters of species interacting across trophic levels in a cascading fashion [START_REF] Knight | Trophic cascades across ecosystems[END_REF][START_REF] Mooney | Interactions among predators and the cascading effects of vertebrate insectivores on arthropod communities and plants[END_REF][START_REF] Terborgh | Trophic Cascades À Predators, Prey, and the Changing Dynamics of Nature[END_REF]. In addition, the concept has been expanded to encompass behaviourally mediated cascades [START_REF] Schmitz | Effects of predator hunting mode on grassland ecosystem function[END_REF]) and ecosystem-level effects other than biomass suppression at alternate trophic levels [START_REF] Croll | Introduced predators transform subarctic islands from grasslands to tundra[END_REF][START_REF] Rasher | Chemically rich seaweeds poison corals when not controlled by herbivores[END_REF]. This has led to a rich conceptual framework (K efi et al. 2012), and compelling evidence for the existence of trophic cascades in a wide variety of biological communities and ecosystems [START_REF] Sommer | Trophic cascades in marine and freshwater plankton[END_REF][START_REF] Baum | Cascading topÀdown effects of changing oceanic predator abundances[END_REF][START_REF] Terborgh | Trophic Cascades À Predators, Prey, and the Changing Dynamics of Nature[END_REF].

Investigations into trophic cascades and biodiversity effects on ecosystem functioning share the goal of gaining insight into the significance of species interactions for ecosystem properties. This notwithstanding, the two lines of research have proceeded largely independently, although there have been repeated calls to incorporate the vertical component of biodiversity across trophic levels into assessments of effects on ecosystem functioning arising from horizontal, or within-trophic level, biodiversity change [START_REF] Petchey | Species loss and the structure and functioning of multitrophic aquatic systems[END_REF][START_REF] Duffy | The functional role of biodiversity in ecosystems: incorporating trophic complexity[END_REF][START_REF] Hillebrand | Biodiversity in a complex world: consolidation and progress in functional biodiversity research[END_REF][START_REF] Reiss | Emerging horizons in biodiversity and ecosystem functioning research[END_REF][START_REF] Gessner | Diversity meets decomposition[END_REF][START_REF] Cardinale | Biodiversity loss and its impact on humanity[END_REF].

When trophic complexity has been addressed in previous biodiversity-ecosystem functioning experiments involving metazoans, it has been limited to either concomitant variation of both species richness within a single trophic level and food chain length (e.g. [START_REF] Wojdak | Relative strength of top-down, bottom-up, and consumer species richness effects on pond ecosystems[END_REF], or to species richness across two trophic levels (e.g. [START_REF] Gamfeldt | Species richness changes across two trophic levels simultaneously affect prey and consumer biomass[END_REF]. Results of the few published experiments show that resource diversity, as well as consumer presence and diversity, can change species interactions within-trophic levels and thereby modify biodiversity effects on ecosystem processes, depending on consumer food selectivity or responses to predation [START_REF] Duffy | The functional role of biodiversity in ecosystems: incorporating trophic complexity[END_REF]). However, consequences of biodiversity loss in more complex food webs involving metazoans have been poorly explored so far, owing to the logistic constraints associated with manipulating the large number of required experimental units.

Here we capitalize on a tractable, well characterized detritus based food web from forest streams to assess the extent to which interactions between horizontal and vertical components of biodiversity affect leaf litter decomposition. Detritus-based food webs in streams are amenable to diversity manipulations at all trophic levels, including basal resources (leaf litter), microbial decomposers (primarily aquatic hyphomycete fungi), detritivorous primary consumers (litter consuming arthropods) and predators. Using a realistic food-web configuration (Fig. 1a), in which species richness decreases with increasing trophic level [START_REF] Petchey | Species loss and the structure and functioning of multitrophic aquatic systems[END_REF], we simultaneously manipulated the species richness of both fungal decomposers and invertebrate detritivores, together with the presence or absence of predatory fish scent. We then used a statistical model to partition the effects arising from the presence of each trophic level, from richness within two of the three levels, and from the interaction of these factors. Our central hypothesis was that biodiversity effects on ecosystem functioning emerge, or grow stronger, when communities comprise multiple species at multiple trophic levels, because increasingly complex food webs increase the scope for species interactions and hence biodiversity effects to occur. Specifically, we hypothesized that (i) horizontal diversity effects depend on trophic structure, including the presence and/or diversity of higher and/or lower trophic levels, and (ii) these relationships are driven by the performance of detritivores, which can reach very high densities on decomposing leaf litter, and can greatly contribute to litter decomposition in streams (e.g. [START_REF] Hieber | Contribution of stream detrivores, fungi, and bacteria to leaf breakdown based on biomass estimates[END_REF]. We expected that detrivore performance will be affected by both the presence of predators (reflecting reduced feeding activity to minimize the risk of detection; Malmqvist 1993) and the presence and diversity of aquatic hyphomycete fungi (resulting in complementary selective feeding on a mosaic of patches on leaves colonized by distinct fungal species; Suberkropp 1992).

Materials and methods

We conducted this multitrophic biodiversity-decomposition experiment at the Moulis Experimental Ecological Station located in the Pyrenees, southwestern France. We simultaneously manipulated the species richness and composition of both fungal decomposers (all species of a pool of six in isolation, plus all six possible five-species combinations) and invertebrate detritivores (all of four species in isolation, plus all possible three-species combinations) (Fig. 1b). In addition, we crossed all fungal and detritivore combinations with a predator treatment where consumption was precluded (presence or absence of fish scent). Control treatments without fungi, detritivores or fish were also included. There were three replicates for each treatment combination, resulting in a total of 702 experimental units. We used aquatic microcosms consisting of plastic containers (11 9 8 9 4 cm) filled with 160 mL of decanted ( ! 24 h), constantly aerated water from a nearby forest stream (R emillass e stream). The microcosms were placed in a temperature-controlled room at 10 °C. Three pebbles of similar size (1Á40 AE 0Á43 cm 3 SD) were added to each microcosm to allow detritivores to seek shelter from predation risk.

Fungi and detritivores used in the experiment were collected from local populations. Recent single-spore isolates of six com-mon species of aquatic hyphomycete (Articulospora tetracladia Ingold, Clavariopsis aquatica de Wildeman, Flagellospora curvula Ingold, Heliscus lugdunensis Saccardo et Th erry, Tetrachaetum elegans Ingold, and Tetracladium marchalianum de Wildeman), which co-occur on decomposing leaves in the region [START_REF] Gessner | Stable successional patterns of aquatic hyphomycetes on leaves decaying in a summer cool stream[END_REF], were obtained from freshly formed foam in stream riffles and maintained on 1% malt agar. Spores of these species were generated by submerging agar plugs from the leading edge of colonies in 40 mL of constantly aerated water. The resulting spore suspension was used to inoculate autoclaved oak (Quercus robur L.) leaf discs (10 mm diameter) submerged in 800 mL of constantly aerated and periodically renewed mineral nutrient solution (per liter 0Á01 g KNO 3 , 0Á55 mg K 2 HPO 4 , 0Á1 g CaCl 2 , 0Á01 g MgSO 4 . 7H 2 O, pH adjusted to 7). A total of approximately 90 000 fungal spores was added, corresponding to %18 000 spores of each of the five species in mixed communities or %90 000 spores of a single fungal species. Fungi were allowed to colonize the leaf disks for 35 days at 15 °C before batches of 6 discs from each fungal treatment were distributed to the microcosms. Spores of aquatic hyphomycetes produced during the colonization period were counted on 3 occasions, including after 35 days, to verify that all species developed in the experimental communities and no cross-contamination occurred. Forty mL of the spore suspensions were sampled for each species combination. Aliquots were filtered on membrane filters (SMWP, 5 lm pore size; Millipore, Bedford, MA, USA) and stained with 0Á05% Trypan blue. The spores trapped on the filters were identified and counted under the microscope at 9 200 [START_REF] Gessner | Qualitative and quantitative analyses of aquatic hyphomycetes in streams[END_REF]. All fungal treatments were successful, as indicated by sporulation of all inoculated species in all treatments and a complete lack of cross-contamination (Table S1).

Specimens of four species of detritivores (Sericostoma personatum Kirby and Spence, Nemoura flexuosa-marginata group Zwick, Protonemura meyeri Pictet and Gammarus fossarum Koch) were collected from three streams near the Ecological Station, kept in aquaria at 10 °C, and fed on naturally decomposing leaf litter collected in one of the above streams (R emillass e). We placed six individuals of a single species (for each of the four detritivore species in single-species treatments) or two individuals each of three different species (for each of four detritivore species mixtures) in the microcosms. Throughout the experiment, any of the few dead or emerged individuals were replaced daily with similar-sized conspecifics.

Brown trout (Salmo trutta fario L.) of a local population were obtained from a nearby fish hatchery. Three individuals, one 2-yr-old and two yearlings, were placed in each of three 40-L aquaria (one per experimental block). Water in the aquaria was renewed daily to ensure similar water quality throughout the experiment (i.e. similar kairomone and nutrient concentrations; Table 1). Decanted stream water from the aquaria with fish was added to half of the microcosms at the beginning of the experiment to simulate the presence of predators while preventing Table 1. Ion concentrations (mg L À1 ) in water from aquaria with or without fish. Water was analysed by ion chromatography (Dionex DX-120; Dionex Corp., Sunnyvale, CA, USA) after 5 fold dilution (see Materials and methods) and after 24 h of fish exposure. Concentrations of PO 4 3À and NO 2 À were below 10 and 5 lg L À1 , respectively. Mean AE SD, N = 6 to 8

Treatment N-NO 3 À N-NH 4 + S-SO 4 2À Cl À Ca 2+ Mg 2+ K + Na + Fish 0Á57 AE 0Á004 0Á56 AE 0Á27 0Á87 AE 0Á03 1Á85 AE 0Á19 3Á99 AE 0Á21 1Á54 AE 0Á03 0Á86 AE 0Á16 3Á10 AE 0Á23 Control 0Á58 AE 0Á04 0Á03 AE 0Á02 0Á86 AE 0Á10 1Á79 AE 0Á22 4Á06 AE 0Á07 1Á51 AE 0Á03 0Á69 AE 0Á10 2Á91 AE 0Á07
actual predation on the detritivores. During the experiment, half of the water volume of the microcosms was renewed daily using water with or without fish scent in the fish presence and absence treatments, respectively. Water exposed to fish was diluted fivefold for this purpose. To avoid strong fluctuations in the composition of fish kairomones, which can vary with diet (e.g. [START_REF] Crowl | Predator-induced life-history shifts in a freshwater snail[END_REF][START_REF] Chivers | Damsefly larvae learn to recognize predators from chemical cues in the predator's diet[END_REF], fish were starved both during and 48 h before the experiment (i.e. for 178 h in total). The experiment was stopped after 130 h when leaf mass loss approached 100% in the treatment experiencing the most rapid decomposition. Leaf discs and detritivores were collected, dried, and weighed to the nearest 0Á01 mg. Leaf mass loss was determined as the difference between the average initial dry mass of batches of six leaf discs (29Á7 AE 2Á3 mg, mean AE SD; N = 30) and the final dry mass at the end of the experiment. Detritivore biomass was determined for each species in each microcosm, with average individual biomass subsequently calculated by dividing the total biomass of each species by the number of individuals for that species in each microcosm.

To assess variation in the responses of the detritivore species relative to their metabolic potential, we also calculated an index of detritivore performance that standardizes for differences in body mass [START_REF] Mckie | Ecosystem functioning in stream assemblages from different regions: contrasting responses to variation in detritivore richness, evenness and density[END_REF]). The index relates the observed leaf mass loss attributed to detritivores to their estimated metabolic capacity. It is based on the observation that large animals consume more food per capita than small ones but that the relationship between feeding rate and body size is not directly proportional. Metabolic capacity of the detritivores was calculated by assuming a power relationship between the body mass and feeding rate of the detritivores according to the metabolic theory of ecology [START_REF] Brown | Toward a metabolic theory of ecology[END_REF]). Thus, for a given microcosm, the metabolic capacity of the detritivores was determined as the sum, across all individuals and species, of the average individual body mass raised to the three-quarter power [START_REF] Brown | Toward a metabolic theory of ecology[END_REF]). Mortality during the experiment was accounted for by using the mean individual biomass, weighted according to the length of time an individual was most likely to have laid dead before replacement (i.e. 12 h). Finally, we calculated the ratio of the leaf mass loss attributed to detritivores to the metabolic capacity in each microcosm, where the leaf mass loss attributed to detritivores was calculated as the difference between the final leaf dry mass in microcosms with and without detritivores (for the same combination of fungal communities and predator presence or absence). The resulting index of detritivore performance is a standardized measure of whether and to what extent detritivore feeding was stimulated or inhibited (rates higher or lower than expected from the detritivore biomass and corresponding metabolic capacity) in microcosms differing in fungal diversity and predator presence or absence.

We performed an analysis of variance (ANOVA) on leaf mass loss with predator presence (P P ), detritivore community composition (D C ) and aquatic hyphomycete community composition (H C ) as factors, as well as species richness terms. For the latter, a priori contrasts were defined to distinguish between the effects of aquatic hyphomycete presence (H P ) and detritivore presence (D P ; by comparing the 0 vs. 1 species treatments), and aquatic hyphomycete species richness (H R ; comparing the 1 vs. 5 species treatments) and detritivore species richness (D R ; comparing the 1 vs. 3 species treatments). All richness effects were tested relative to variation among species combinations, which represent the true replicates for the richness treatments, rather than among microcosms, by nesting the aquatic hyphomycete and detritivore species composition terms within fungal and detritivore richness, respectively [START_REF] Schmid | The design and analysis of biodiversity experiments[END_REF].

Our detritivore performance index was also analysed using a series of ANOVAs, to assess overall responses across detritivore treatments, and the responses of each detritivore single species treatment separately. As a first step, the effects of detritivore and aquatic hyphomycete richness, predator presence, and their interactions, were tested using the same ANOVA models as previously: Predator presence (P P ) was crossed with aquatic hyphomycete presence (H P ) as well as aquatic hyphomycete and detritivore richness (H R and D R ), with aquatic hyphomycete composition (H C ) and detritivore composition (D C ) nested in the respective richness terms.

Additionally, four further analyses were performed focusing specifically on the detritivore single-species treatments, to evaluate the responses of each individual detritivore species (taken separately) to aquatic hyphomycete diversity and predator presence. This latter analysis thus included predator presence (P P ) crossed with aquatic hyphomycete presence (H P ) and richness (H R ), and aquatic hyphomycete composition (H C ) nested in richness. The presence/absence contrast in detritivore combinations (D P ) was not included in the latter analyses. We used Type I sums of squares in all ANOVAs, with response variables square root-or log-transformed to satisfy assumptions of normality and homoscedasticity. All statistics were performed using R version 2.12 (R Development Core Team 2011).

Results

leaf mass loss

Average leaf mass loss ranged from 0Á71% to 93Á6% with a mean of 29Á9% AE 0Á71 SE (Fig. 2). Community composition of detritivores and aquatic hyphomycetes (P < 0Á001), but not species richness (P = 0Á74 and 0Á11, respectively), explained a considerable portion of the overall variability (SS of main effects = 13Á3 and 18Á6%, respectively; Table 2), suggesting that decomposition rates were more strongly influenced by consumer community composition than by species richness. Among all main effects relating to presence-absence or species diversity, only aquatic hyphomycete (P = 0Á007) and predator presence (P = 0Á004) were significant, with higher leaf mass loss occurring when either group was present (+23Á6% and +2Á6%, respectively; Fig. 2). Although detritivore presence accounted for an average of 16Á4% of total leaf mass loss, the effect was not significant (P = 0Á099). Multiple interactions involving both presence-absence and richness within trophic levels were apparent. In particular, there were several significant second-order interactions involving predator presence and both the presence and richness of aquatic hyphomycetes (Table 2). Further significant third-order interactions emerged (i) between aquatic hyphomycete diversity and the presence of predators and detritivores (P = 0Á009), and (ii) between detritivore diversity and predator and aquatic hyphomycete presence (P = 0Á002; Table 2). All these interactions increased decomposition rate with an increasing number of trophic levels (i.e. the presence-absence terms) and/or within-trophic level species richness. Most strikingly, the highest decomposition rate (average mass loss of 43Á9%) was observed when all trophic levels were present at the highest possible richness levels (Fig. 2).

detritivore performance

Detritivore performance (i.e. detritivore-mediated leaf decomposition in relation to the estimated metabolic capacity of the detritivore community [MC]; see Materials and methods) varied between 0 and 2Á54 mg MC À1 (mean AE SE = 0Á39 AE 0Á01 mg MC À1 ; Fig. 3). Species composition of detritivores and aquatic hyphomycetes explained a significant part of the observed variability (P < 0Á001; SS of main effects = 1Á9 and 17Á6%, respectively; Table 3), as did the interaction between aquatic hyphomycete and detritivore species composition (P = 0Á005, 7Á9% of the total SS). Furthermore, the interaction between aquatic hyphomycete diversity and predator presence was highly significant (P < 0Á001; Table 3), suggesting that detritivore performance was contingent on both resource diversity and the presence of predators. The latter interaction resulted in a negative effect of fish presence (decrease of 0Á13 mg MC À1 ) on detritivore performance for the single-species aquatic hyphomycete treatments, while it became positive (increase of 0Á10 mg MC À1 ) for diverse aquatic hyphomycete communities (Fig. 3).

Among the single-species detritivore treatments, the performance of Gammarus was lower (0Á29 AE 0Á03 mg MC À1 ) than that of the three insect species (0Á44 AE 0Á04, 0Á45 AE 0Á06 and 0Á42 AE 0Á03 mg MC À1 for Nemoura, Protonemura and Sericostoma, respectively). Detritivore responses to predator presence and aquatic hyphomycete communities varied among species (Table 4; Fig. 4), with Table 2. ANOVA results of square-root transformed data on leaf mass loss, testing for the effects of community composition and species richness at each of three trophic levels. Each richness (treatment) term is tested against the following composition (error) term, and error terms are tested against the residuals. E/F column indicates whether the factor is included as a factor (F) or error term (E) interactions apparent for Protonemura (H R 9 P P : P = 0Á011; Table 4), Sericostoma (H R 9 P P : P = 0Á015; Table 4) and Nemoura (H R x P P : P = 0Á045; Table 4). Specifically, Protonemura and Nemoura performance decreased in the presence of predators in the singlespecies treatments but not when five aquatic hyphomycetespecies were present. In contrast, Sericostoma performance was unaffected by predator presence in the single-species aquatic hyphomycete treatments, and increased when five aquatic hyphomycete species were present (Fig. 4). The performance of all detritivore species also varied with aquatic hyphomycete community composition (Table 4).

H P 9 D P F 1 2 Á3 0Á216 H P 9 D R F 1 <0Á1 0Á909 H R 9 D P F 1 5 Á8 0Á052 H R 9 D R F 1 3 Á6 0Á124 H C 9 D C E 92 136Á8 0Á002 Predator presence (P P ) F 1 7 Á5 0Á004 H P 9 P P F 1 3 Á9 0Á038 H R 9 P P F 1 4 Á4 0Á027 D P 9 P P F 1 0 Á6 0Á399 D R 9 P P F 1 <0Á1 0Á946 H P 9 D P 9 P P F 1 0 Á6 0Á428 H P 9 D R 9 P P F 1 9 Á0 0Á002 H R 9 D P 9 P P F 1 6 Á3 0Á009 H R 9 D R 9 P P F 1 1 Á6 0Á181 H C 9 D C 9 P P E 108 94Á7 0Á690 Residuals E 468 444Á9 (

Discussion

The chief discovery emerging from our manipulation of a model detritus-based system is that the ecosystem process we targetedlitter decompositionwas most efficient when both horizontal (within-trophic level) and vertical (across trophic-level) diversity components were present. Diversity effects on decomposition rate did not primarily arise because of species interactions within a given trophic level, but reflected complex interactions between the presence and species richness of microbial decomposers, detritivorous invertebrates, and the non-trophic influence of a predator. This experimental result supports outcomes of theoretical models suggesting that multitrophic interactions complicate assessments of the functional consequences of biodiversity change (Th ebault [START_REF] Th Ebault | FoodÀweb constraints on biodiver-sityÀecosystem functioning relationships[END_REF][START_REF] Th Ebault | The relationship between biodiversity and ecosystem functioning in food webs[END_REF], demonstrating that even relatively modest effects of change within single trophic levels can ramify and amplify through ecological networks to influence ecosystem functioning.

Unsurprisingly, the sheer presence of fungal decomposers strongly increased ecosystem process rates, reflecting their key role in leaf litter decomposition in streams and other ecosystems [START_REF] Gessner | Diversity meets decomposition[END_REF]. However, further increases in decomposition rate with increased fungal richness, although consistent (Fig. 2), were too small to be statistically significant unless predatory fish were present. This finding is in line with outcomes of previous biodiversity-decomposition experiments in the absence of detritivores where fungal diversity effects were weak or non-existent [START_REF] Dang | Magnitude and variability of process rates in fungal diversityÀlitter decomposition relationships[END_REF][START_REF] Duarte | Aquatic hyphomycete diversity and identity affect leaf litter decomposition in microcosms[END_REF]. Increased detritivore richness Table 3. ANOVA results of log-transformed data on detritivore performance (see Materials and methods for calculation), testing for the effects of community composition and species richness at two trophic levels as well as predator presence. Each richness (treatment) term is tested against the following composition (error) term, and error terms are tested against the residuals. E/F column indicates whether the factor is included as a factor (F) or error term (E) Source of variation E/F d.f. SS P Aquatic hyphomycete presence (H P )

F 1 1 Á92 0Á114 Aquatic hyphomycete species richness (H R ) F 1 1 Á71 0Á135 Aquatic hyphomycete community composition (H C ) E 10 6Á44 <0Á001 Detritivore species richness (D R ) F 1 0Á07 0Á501 Detritivore community composition (D C ) E 6 0 Á79 <0Á001
H P 9 D R F 1 <0Á01 0Á736 H R 9 D R F 1 0 Á11 0Á116 H C 9 D C E 82 3Á63 0Á005 Predator presence (P P ) E 1 0 Á04 0Á241 H P 9 P P F 1 <0Á01 0Á785 H R 9 P P F 1 1 Á10 <0Á001 D R 9 P P F 1 0 Á04 0Á317 H P 9 D R 9 P P F 1 0 Á15 0Á047 H R 9 D R 9 P P F 1 0 Á03 0Á410 H C 9 D C 9 P P E 98 3Á76 0Á039 Residuals E 416 12Á22
Table 4. ANOVA results of log-transformed data on detritivore performance (see Materials and methods for calculation), testing for the effects of aquatic hyphomycete community composition and diversity as well as predator presence in single-species detritivore treatments (Gammarus, Nemoura, Protonemura and Sericostoma). Each richness (treatment) term is tested against the following composition (error) term, and error terms are tested against the residuals. E/F column indicates whether the factor is included as a factor (F) or error term (E)

Source of variation E/F d.f.

Gammarus

Nemoura Protonemura Sericostoma

SS P SS P SS P SS P Aquatic hyphomycete presence (H P ) F 1 0 Á11 0Á228 0Á40 0Á184 0Á24 0Á238 0Á17 0Á232 Aquatic hyphomycete species richness (H R ) F 1 0 Á04 0Á451 0Á35 0Á206 <0Á01 0Á936 0Á30 0Á121 Aquatic hyphomycete community composition (H C ) E 10 0Á66 0Á005 1Á95 <0Á001 1Á55 0Á031 1Á03 <0Á001 Predator presence (P P ) F 1 0 Á02 0Á331 0Á21 0Á011 0Á02 0Á555 0Á04 0Á026 H P 9 P P F 1 0 Á01 0Á498 0Á06 0Á197 0Á09 0Á252 <0Á01 0Á823 H R 9 P P F 1 <0Á01 0Á731 0Á15 0Á045 0Á46 0Á011 0Á05 0Á015 H C 9 P P E 10 0Á23 0Á439 0Á70 0Á024 0Á56 0Á629 0Á12 0Á134 Residuals E 52 1Á17 1Á58 3Á64 0Á39
has more often yielded positive effects on decomposition in previous studies [START_REF] Mckie | Ecosystem functioning in stream assemblages from different regions: contrasting responses to variation in detritivore richness, evenness and density[END_REF]Srivastava et al. 2009), though neutral or negative detritivore diversity effects have also been observed [START_REF] Gessner | Diversity meets decomposition[END_REF]. Differences in microbial diversity, which previous experiments with detritivores did not control for, could be an important factor accounting for the variable outcomes of other studies, given that detritivore diversity effects in our experiment were only apparent when microbial diversity was high (and fish were present). Two previous experiments have addressed the effects of varying fungal diversity in the presence and absence of detritivores, but neither was designed to test for interactive effects of fungal and detritivore diversity [START_REF] Lecerf | Riparian plant species loss alters trophic dynamics in detritusÀbased stream ecosystems[END_REF][START_REF] Reiss | Assessing the contribution of microÀorganisms and macrofauna to biodiversity-ecosystem functioning relationships in freshwater microcosms[END_REF]. Nevertheless, in line with our results, both found generally stronger diversity effects (either positive or negative) when both trophic levels were present. This reinforces the conclusion suggested by our multitrophic experiment that reducing community complexity curtails biodiversity effects on ecosystem processes. Detritivores feeding on leaf litter are key intermediate consumers linking microbial decomposers and top predators in detritus-based systems (Srivastava et al. 2009;[START_REF] Gessner | Diversity meets decomposition[END_REF]. Accordingly, detritivore feeding could be influenced by both bottom-up (i.e. presence and diversity of microbial decomposers) and top-down forces (i.e. presence of predators). The bottom-up effect, termed conditioning, relates to the enhancement of leaf palatability, particularly by fungal biomass accumulation and changes in the properties of leaves resulting from partial enzymatic degradation [START_REF] Suberkropp | Interactions with invertebrates[END_REF]. As palatability of different fungal species varies among detritivores [START_REF] Suberkropp | Interactions with invertebrates[END_REF], there is scope for complementary resource use when multiple detritivore species encounter diverse fungal communities. Positive fungal diversity 9 detritivore diversity effects on decomposition can thus arise, driven by distinct feeding preferences. This hypothesis is supported by our finding that diverse aquatic hyphomycete communities enhanced consumer performance in the multi-species detritivore treatment (Fig. 3). However, this effect was only significant when fish were present, revealing that bottom-up and top-down forces acted together to produce a detritivore diversity effect on decomposition. This again highlights the significance of complex interactions in communities composed of multiple species within the same and at different trophic levels.

The observed cascading top-down effect from predators to detritivores and decomposition was clearly due to changes in detritivore feeding rates arising from nontrophic mechanisms, as fish scent rather than live trout was varied in our experiment. This finding demonstrates that non-consumptive (i.e. trait-mediated) responses (K efi et al. 2012) of primary consumers can elicit biodiversity effects on ecosystem processes in complex communities, similar to effects propagating in trophic cascades [START_REF] Mooney | Interactions among predators and the cascading effects of vertebrate insectivores on arthropod communities and plants[END_REF][START_REF] Strong | Human involvement in food webs[END_REF][START_REF] Terborgh | Trophic Cascades À Predators, Prey, and the Changing Dynamics of Nature[END_REF]. Clearly, trait-mediated species interactions not only can change trophic structure, but also rates of key ecosystem processes.

Fish can affect detritivore behaviour and consequent effects on ecosystems in at least two opposing ways. First, positive responses to simulated fish presence could arise through cascading bottom-up effects elicited by the release of nutrients from fish waste products. Nutrients released by fish (e.g. [START_REF] Mcintyre | Fish extinctions alter nutrient recycling in tropical freshwaters[END_REF], including NH 4 + (Table 1), can stimulate microbial litter decomposers [START_REF] Gulis | Leaf litter decomposition and microbial activity in nutrientÀenriched and unaltered reaches of a headwater stream[END_REF], detritivores [START_REF] Robinson | Nutrient addition accelerates leaf breakdown in an alpine springbrook[END_REF], or detritivore-microbe interactions, and thus enhance decomposition rates. However, it is not clear whether a fish-mediated nutrient effect was important in the present study, because concentrations of dissolved P, the limiting nutrient in microcosms as inferred from high N : P ratios, were not measurably influenced by the presence of fish.

Alternatively, fish release specific chemical cues (kairomones) that restrain the activity of prey who seek to limit their vulnerability to predators [START_REF] Chivers | Chemical alarm signaling in aquatic predatorÀprey systems: a review and prospectus[END_REF][START_REF] Br€ Onmark | Chemical Ecology in Aquatic Systems[END_REF]. In accordance with this second mechanism, the two stonefly species in our experiment reduced feeding in the presence of fish when fungal diversity was low. However, at the high fungal diversity level, the stoneflies maintained their feeding rates even when fish were present (Fig. 4). One possible explanation is that higher fungal diversity is associated with greater small-scale resource heterogeneity, which would allow stoneflies to maintain their feeding activity in their immediate surroundings, even if the presence of fish constrains active foraging over a larger area. In contrast to the stoneflies, Sericostoma personatum, a large caddisfly larva armoured by a case of coarse sand grains, increased its feeding rate in the presence of fish (Fig. 4). Protection by a sturdy case reduces vulnerability to predation, consistent with the observation that various cased caddisfly taxa, including Sericostoma, are insensitive to fish chemical cues [START_REF] Pestana | Fear and loathing in the benthos: responses of aquatic insect larvae to the pesticide imidacloprid in the presence of chemical signals of predation risk[END_REF]. Thus, our data on detritivore feeding performance indicate that their lower vulnerability could allow cased caddisflies to take advantage of reduced competition from other detritivore species that reduce feeding activity in the presence of vertebrate predators.

Biodiversity experiments assessing the consequences of species loss on ecosystem processes have been criticized for their simplicity [START_REF] Duffy | Why biodiversity is important to the functioning of realÀworld ecosystems[END_REF], which limits extrapolation of results from such experiments to natural ecosystems. The study presented here overcomes one of the major limitations of those previous studies by explicitly testing for effects on litter decomposition that result from species interactions occurring simultaneously within and across trophic levels. Although still reflecting a simplified experimental setting, this design improves realism of the experimental food-web configurations. Densities of the detritivores in our experiment were high relative to the amount of food available. However, densities were not completely unrealistic (cf. [START_REF] Malmqvist | Dynamics of detritus in a small stream in southern Sweden and its influence on the distribution of the bottom animal communities[END_REF][START_REF] Hieber | Contribution of stream detrivores, fungi, and bacteria to leaf breakdown based on biomass estimates[END_REF], especially in view of the fact that leaf-shredding detritivores show strong aggregation behaviour on leaf litter patches in streams [START_REF] Ab Os | Aggregation among resource patches can promote coexistence in stream-living shredders[END_REF]) and that such patches become scarce following resource depletion as a result of litter decomposition or downstream transport during floods [START_REF] Argerich | Combined effects of leaf litter inputs and a flood on nutrient retention in a Mediterranean mountain stream during fall[END_REF]. Therefore, our results are most relevant for field situations in winter when litter resources have become scarce and consumer biomass is still high, although discrepancies between our experimental and natural field densities were within limits suggesting that our results could apply for situations even during leaf fall in autumn.

One could also argue that our experimental set-up might have exaggerated the effects of fish presence on detritivore performance, because even though addition of three pebbles provided some refuge in our microcosms, the caged detritivores were unable to move away from the fish scent imposed on them. However, such is the situation even in natural streams, where it is impossible for consumers to evade fish scent, which is ubiquitous along stream reaches with healthy fish populations and induces changes in the activity of stream consumers via traitmediated mechanisms, as has been demonstrated in a field experiment [START_REF] Peckarsky | Predator chemicals induce changes in mayfly life history traits: a whole-stream manipulation[END_REF]. Consequently, it is unlikely that fish scent in our microcosms triggered unnatural detritivore behaviour.

Ecosystems worldwide are suffering unprecedented rates of biodiversity loss at present [START_REF] Dudgeon | Freshwater biodiversity: importance, threats, status and conservation challenges[END_REF][START_REF] Butchart | Global biodiversity: indicators of recent declines[END_REF], with top predators often most vulnerable to extinction [START_REF] Duffy | Biodiversity loss, trophic skew and ecosystem functioning[END_REF]. It has long been understood that such extinctions can affect multiple ecosystem properties through trophic cascades [START_REF] Terborgh | Trophic Cascades À Predators, Prey, and the Changing Dynamics of Nature[END_REF]. Our results from a detritus-based model food web involving invertebrates and vertebrate consumers indicate that the situation is yet more complex in that top predator extinction is likely to interact with biodiversity declines at lower trophic levels to alter ecosystem functioning. Indeed, according to our results, it is the coupling between top predator loss and diversity declines at either the microbial or detritivore level that reduces decomposition rates most strongly.

In natural systems, predators alter food-web interactions not only through behavioural (i.e. trait-mediated) mechanisms [START_REF] Werner | A review of traitÀmediated indirect interactions in ecological communities[END_REF][START_REF] Mooney | Interactions among predators and the cascading effects of vertebrate insectivores on arthropod communities and plants[END_REF], as examined here, but also through direct consumption, and they can exert strong control on ecosystem processes, especially when primary consumers face multiple predator species [START_REF] Zhang | Detritus processing, ecosystem engineering and benthic diversity: a test of predator-omnivore interference[END_REF]. Thus, the range of possible interactions between vertical and horizontal diversity with repercussions on ecosystem process rates is likely to be even greater in nature than observed in our experiment. The implication of the results presented here is that mimicking scenarios of trophic complexity in experiments as realistically as possible is likely to strengthen rather than weaken evidence for the importance of biodiversity effects on the functioning of ecosystems.

Fig. 1 .

 1 Fig. 1. Schematic of trophic (solid lines) and non trophic (dashed lines) interactions in detritus-based stream food webs. (a) Relationships between leaf litter, fungal decomposers, detritivores and predators as reflected in the experimental design of this study. Indirect interactions include (1) fungal facilitation of detritivores through leaf conditioning, (2) trait mediated reduction of detritivore feeding by predators, and (3) fungal stimulation through nutrient excretion by vertebrate and invertebrate consumers. Direct and indirect predation effects on detritivores (grey lines) are not addressed in this study. (b) Two of 234 food web configurations realized in this study, including the most diverse community (left), and a reduced food web with a single detritivore and three trophic links to fungal species (right). H1-H5: hyphomycete species, D1-D3: detritivore species, P: predator.

Fig. 2 .

 2 Fig. 2. Leaf mass loss as a function of aquatic hyphomycete and detritivore species richness. Mean percentage (AE SE) of the initial dry mass in microcosms without aquatic hyphomycetes (s), with 1 aquatic hyphomycete species ( ) or 5 aquatic hyphomycete species (•) present, and with fish absent (a) or present (b).

Fig. 3 .

 3 Fig. 3. Detritivore performance as a function detritivore and aquatic hyphomycete species richness. Mean (AE SE; see Materials and methods for calculation of detritivore performance) in microcosms without aquatic hyphomycetes (s), with 1 aquatic hyphomycete species ( ) or 5 aquatic hyphomycete species (•) present, and with fish absent (a) or present (b).

Fig. 4 .

 4 Fig. 4. Detritivore performance for each single-species treatment as a function of aquatic hyphomycete species richness. Mean (AE SE; see Materials and methods for calculation of detritivore performance) in microcosm with fish present ( ) or absent (s).

Acknowledgements

We thank Jean Clobert for providing facilities at the Moulis Experimental Ecological Station of the CNRS, the pisciculture of Soueich for providing autochthonous brown trout, Sylvain Lamothe for technical assistance, Bernhard Schmid for statistical advice and several anonymous referees for their constructive comments. Project funding was provided by the French National Centre for Scientific Research (CNRS), the Swiss National Science Foundation (SNF) and the Swedish Research Council (VR) in support of the collaborative research project BioCycle of the European Science Foundation's (ESF) EuroCORES programme EuroDIVERSITY. BioCycle has been endorsed by DIVERSITAS as contributing toward its research priorities in biodiversity science.

Supporting Information

Additional Supporting Information may be found in the online version of this article.

Table S1. Contribution of each of 6 aquatic hyphomycete species used to assemble 12 experimental communities.


Avishek Maity

Rajesh Dutta

Oles Sendtskyi

Monica Ceretti

Angélique Lebranchu

Dmitry Chernyshov

Alexeï Bosak

Werner Paulus

Exploring Fast Room Temperature Oxygen Diffusion in Pr 2 NiO 4+δ Stand-Alone Single-Crystalline Electrodes

Keywords: Pr 2 NiO 4, transition metal oxides, non-stoichiometric oxides, in situ diffraction, synchrotron diffraction, oxygen ion conductors, single crystal electrode, domain ordering, electrochemistry

INTRODUCTION

Mixed ionic-electronic conductors are an important class of materials for a variety of technological applications such as energy conversion and storage devices, fuel-cells, supercapacitors, oxygen separation, catalysts and electrocatalyst. [1][START_REF] Huang | Double Perovskites as Anode Materials for Solid-Oxide Fuel Cells[END_REF][START_REF] Sunarso | Mixed ionic-electronic conducting (MIEC) ceramic-based membranes for oxygen separation[END_REF][START_REF] Lacorre | Designing fast oxide-ion conductors based on La 2 Mo 2 O 9[END_REF] Different strategies have been used to enhance oxygen ion conductivity at already moderate temperatures, but the role of pure bulk and interface oxygen diffusion is still not fully explored. The modification and engineering of grain boundaries in terms of stoichiometry, dislocations and specific microstructures has been recently investigated on thin films, indicating fast oxygen diffusion pathways around 500°C at the interface, which to a certain extent can be decoupled from the bulk diffusion. [START_REF] Garbayo | Thin film oxideion conducting electrolyte for near room temperature applications[END_REF][START_REF] Chroneos | Oxygen diffusion in solid oxide fuel cell cathode and electrolyte materials: mechanistic insights from atomistic simulations[END_REF][START_REF] Chiabrera | Engineering Transport in Manganites by Tuning Local Nonstoichiometry in Grain Boundaries[END_REF][START_REF] Saranya | Unveiling the Outstanding Oxygen Mass Transport Properties of Mn-Rich Perovskites in Grain Boundary-Dominated La 0.8 Sr 0[END_REF][START_REF] Navickas | Fast oxygen exchange and diffusion kinetics of grain boundaries in Sr-doped LaMnO 3 thin films[END_REF] Thereby the increase of the oxygen mobility can attain several orders of magnitude, while the diffusion mechanism itself is far from being understood. On the other hand, low-T oxygen diffusion mechanisms have been reported to be phonon assisted and related to structural instabilities, supported by DFT simulations down to ambient temperature for several non-stoichiometric Ruddlesden-Popper type oxides. [START_REF] Ceretti | Low temperature oxygen diffusion mechanisms in Nd 2 NiO 4+δ and Pr 2 NiO 4+δ via large anharmonic displacements, explored by single crystal neutron diffraction[END_REF][START_REF] Paulus | Lattice Dynamics To Trigger Low Temperature Oxygen Mobility in Solid Oxide Ion Conductors[END_REF][START_REF] Perrichon | Lattice Dynamics Modified by Excess Oxygen in Nd 2 NiO 4+δ[END_REF][13][14][15][16] Pr 2 NiO 4+d presents one of the most promising oxygen membranes already at moderate temperatures, for which oxygen diffusion pathways have been visualized from neutron scattering density maps for Pr 2 NiO 4+d single crystals, evidencing an almost continuous dynamically activated overlap between apical and interstitial lattice sites at 400°C. [START_REF] Chroneos | Oxygen diffusion in solid oxide fuel cell cathode and electrolyte materials: mechanistic insights from atomistic simulations[END_REF][START_REF] Ceretti | Low temperature oxygen diffusion mechanisms in Nd 2 NiO 4+δ and Pr 2 NiO 4+δ via large anharmonic displacements, explored by single crystal neutron diffraction[END_REF][17][18][START_REF] Yashima | Role of Ga 3+ and Cu 2+ in the High Interstitial Oxide-Ion Diffusivity of Pr 2 NiO 4 -Based Oxides: Design Concept of Interstitial Ion Conductors through the Higher-Valence d 10 Dopant and Jahn-Teller Effect[END_REF][START_REF] Yashima | Structural Disorder and Diffusional Pathway of Oxide Ions in a Doped Pr 2 NiO 4 -Based Mixed Conductor[END_REF] Further on electrochemical oxidation/reduction of polycrystalline Pr 2 NiO 4+d electrodes, carried out at room temperature (RT) in an aqueous alkaline solution, showed that oxygen ions can be intercalated reversibly, revealing a rich phase diagram. [START_REF] Ceretti | Nd/Pr) 2 NiO 4+δ : Reaction Intermediates and Redox Behavior Explored by in Situ Neutron Powder Diffraction during Electrochemical Oxygen Intercalation[END_REF] Moreover, spontaneous topotactic oxygen diffusion in Pr 2 NiO 4+d even at ambient temperature has been recently shown to be linked to sub-mesoscale oxygen ordering. Thereby, translational periodicities of more than 100 Å were uncovered, thus contradicting the paradigm that performant ionic conductivity is intrinsically related to structural disorder. [START_REF] Dutta | Long-range oxygen ordering linked to topotactic oxygen release in Pr 2 NiO 4+δ fuel cell cathode material[END_REF] In this work we were interested to deepen the structural insights of the oxygen diffusion mechanism or Pr 2 NiO 4+d by re-investigating the oxygen intercalation reaction by in situ single crystal synchrotron diffraction.

3D reciprocal lattice scanning allows to obtain valuable information as diffuse scattering, low intensity superstructure reflections, but also quantitative values of the volume fraction of twin domains and related microstructural changes during a chemical reaction, impossible to access with powder diffraction methods. We show in the following the necessity to use single crystalline electrodes to access all these details simultaneously by in situ diffraction studies under applied electrochemical potential.

On the other hand, we could evidence for the first time, anti-phase domain ordering with a periodicity of 7 nm, together with a significantly faster oxygen diffusion kinetics in single crystalline electrodes, related to the major absence of grain boundaries. It underlines together with sub-mesoscopic oxygen ordering, the importance competitive, weak interactions may play, to trigger long-range ordering phenomena for diffusion processes at ambient conditions, and which are largely unexplored so far.

EXPERIMENTAL

Single crystal growth. Single crystals of Pr 2 NiO 4.25 have been successfully grown by the floating zone method at ICGM as described in ref [START_REF] Ceretti | Growth and characterization of large high quality brownmillerite CaFeO 2.5 single crystals[END_REF] , resulting in a diameter of about 6 mm while reaching lengths of more than 10 cm. [START_REF] Wahyudi | Growth of high quality single crystals of strontium doped (Nd,Pr)-nickelates, Nd 2-x Sr x NiO 4+d and Pr 2-x Sr x NiO 4+d Crystengcomm[END_REF] Synchrotron and X-ray diffraction experiments. Diffraction experiments have been carried out on BM01, SNBL@ESRF at l = 0.6630 Å, using the 2M Pilatus detector. The electrochemical reduction of Pr 2 NiO 4.225 was followed up by in situ single crystal synchrotron diffraction on a 60 ´ 60 ´ 1000 µm 3 shaped crystal in a specifically adapted electrochemical setup (see Fig S1). Size and shape of the crystal were chosen to optimize the reaction kinetics, and consequently to minimize any inhomogeneous phase formation during the discharge reaction. In this regard, the [001] longitudinal direction of the needle shaped crystal allows a maximized oxygen diffusion along the [110] direction inside the Pr 2 O 2 rock salt layer, here presenting the shortest crystal dimension. The crystals was transferred into the electrochemical cell, consisting of two Debye-Scherrer quartz capillaries as described in ref [START_REF] Maity | Solid-state reactivity exploredin situby synchrotron radiation on single crystals: from SrFeO 2.5 to SrFeO 3 via electrochemical oxygen intercalation[END_REF] . In order to minimize absorption and extinction problems, the crystal was turned around its long axis (200° in steps of 0.1°/image), the exposure time being 0.5 s/frame, resulting in a collection time of about 17 min per dataset. The whole reaction was finished in 20 hours, thus yielding 72 complete data collections corresponding to a variation of Dd = 0.003 oxygen/f.u. per data set. With a linear absorption coefficient of 231cm -1 , the transmission for a 60 µm thick crystal amounts to at minima to 25%, which is still a very satisfying value, guaranteeing to obtain a volume information throughout the crystal. The electrochemical reaction required to apply a permanent current of 10 µA, to overcome problems related to parasitic currents as outlined in the text below. The applied reaction conditions consequently involve a continuous production of hydrogen bubbles at the crystal site inside the capillary, which perturbs the data analysis as it changes the total absorption behavior and changes locally the current density of the setup. This problem could be overcome by constantly pumping fresh 1N-KOH electrolyte through the inner capillary at a velocity of 5ml/min, and which evacuated all additionally generated hydrogen instantly.

Data Analysis. Single crystal data analysis has been performed using the SNBL Tool Box 26 , the Crysalis pro (Rigaku) and ALBULA software package (Dectris) as well as the X-Area software package (STOE Darmstadt).

RESULTS AND DISCUSSION

The structure of Pr 2 NiO 4+d is generally schematized as a layer structure consisting of corner shared NiO 6 octahedra where in between are inserted Pr atoms as spacers (Figure 1a). Oxygen diffusion has been shown to be highly anisotropic, 16,18,[START_REF] Yashima | Structural Disorder and Diffusional Pathway of Oxide Ions in a Doped Pr 2 NiO 4 -Based Mixed Conductor[END_REF][START_REF] Bassat | Anisotropic Oxygen Diffusion Properties in Pr 2 NiO 4+δ and Nd 2 NiO 4+δ Single Crystals[END_REF] For the electrochemically obtained phase diagram of Pr 2 NiO 4+d, in situ neutron powder diffraction studies revealed three distinct phases. [START_REF] Ceretti | Nd/Pr) 2 NiO 4+δ : Reaction Intermediates and Redox Behavior Explored by in Situ Neutron Powder Diffraction during Electrochemical Oxygen Intercalation[END_REF] Two of them were identified as stoichiometric line phases with orthorhombic symmetry, Pr 2 NiO 4.225 and Pr 2 NiO 4.00 , the additional intermediate non-stoichiometric phase Pr 2 NiO 4.08±0.02 is tetragonal. The symmetry changes during the course of reduction pass from orthorhombic to tetragonal to become again orthorhombic for the fully reduced phase. The sequence of three phases may be considered as a "re-entrant" transition in the sense that the same translational symmetry reappears in the structure for the end members but differs from that for the intermediate phase.

Recently, the structure of Pr 2 NiO 4+d has been revealed to be of unprecedented complexity. [START_REF] Dutta | Long-range oxygen ordering linked to topotactic oxygen release in Pr 2 NiO 4+δ fuel cell cathode material[END_REF] For the freshly prepared oxide in air, an extra oxygen stoichiometry of d = 0.25 is obtained, adopting a monoclinic symmetry. Subsequent storing under ambient conditions for several months, yields a topotactic oxygen release towards Pr 2 NiO 4.225 . Being the ground state for The intensity repartition for all four twin domains shows a clear inversion of the respective intensity ratio between the starting and final phases. The initially weak twin domains D1 and D3 strongly increase in reflection intensity, finally exceeding the initially strong domains D2 and D4.

For Pr 2 NiO 4.0 , the volume fractions for the twin domains D1-D4 yield a final intensity ratio of 32:14:38:16 respectively (Fig. 4). The evolution of all twin domains vs. time is given in the Smedia file.

The twin domain structure and formation, related to the ortho/tetra/ortho symmetry sequence also allows to analyze straightforwardly the evolution of the respective volume fractions, and thus, to access to the evolution of the microstructure. From the established volume fractions discussed above, the formation of nano-domains can be ruled out as it would imply an even distribution for the volume fractions of 25% each. Instead, the twin-domain structure encountered here, is very specific. This is also evidenced by the diffuse scattering illustrated in Fig. 3 domain ordering. [START_REF] Zubko | X-Ray Diffraction Studies of 180° Ferroelectric Domains in PbTiO 3 /SrTiO 3 Superlattices under an Applied Electric Field[END_REF][START_REF] Zubko | Electrostatic Coupling and Local Structural Distortions at Interfaces in Ferroelectric/Paraelectric Superlattices[END_REF][START_REF] Sarott | In situ monitoring of epitaxial ferroelectric thin-film growth[END_REF] In the absence of ferroelectricity for Pr 2 NiO 4.0 , the most reasonable explanation for domain ordering would be the formation of anti-phase domains involving different octahedra tilting (see Fig S7).

These findings are the first indication for a domain organization, emerging during an electrochemical reaction at RT. Thereby a length scale of translational periodicities corresponding to more than 12 times the unit cell parameters, significantly differs from an averaged domain distribution. From this perspective, the diffusion process, normally considered as a local process, can be seen at larger scale as an anisotropic "field" that optimizes structural features at the macroscopic level of the domain structure. The long-range oxygen-ordering phenomena found for Pr 2 NiO 4+d , [START_REF] Dutta | Long-range oxygen ordering linked to topotactic oxygen release in Pr 2 NiO 4+δ fuel cell cathode material[END_REF] deliver, together with the ordering processes of the domains, a clear evidence for the existence of mesoscopic interactions at both, structural and domain level, thus giving a first meaningful descriptor to better understand to what is generally discussed as domain engineering.

Due to the fast reaction kinetics, one may assume that the high current applied throughout the reaction, will induce the formation of a phase gradient and/or inhomogeneities from the crystal surface to its inner part for kinetical reasons. A very homogeneously discharge of the entire crystal is instead observed throughout the whole reaction. It implies that the phase formation and stability during oxygen release is strongly aligned with the applied potential, which is supposed to be uniform all over the crystal related to the high metallic conductivity of Pr 2 NiO 4+d .

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - h (r.l.u.)
k (r.l.u.) . This value appears to be remarkably high although not directly comparable to the standard chemical diffusion coefficient, as it is obtained under applied electrochemical potential. Nevertheless, it roughly reflects the corresponding effective oxygen transport which is, however, similar to oxygen diffusion coefficients in solid oxides usually encountered above 600-800°C. Only a very few cases have been reported with unusually high oxygen diffusion coefficients at ambient, i.e. polycrystalline Nd 1-x Sr x CoO 3 , La 2 CoO 4+d and La 2 CuO 4+d . [START_REF] Girgsdies | Spontaneous topotactic oxidation of La 2 CoO 4 at room temperature[END_REF][START_REF] Kudo | Electrochemical Behavior of the Perovskite-Type Nd 1 -x Sr x CoO 3 in an Aqueous Alkaline Solution[END_REF][START_REF] Grenier | The Role of The Additional Oxygen Atoms on the Superconducting Properties of La 2 CuO 4 -Related Compounds[END_REF] Oxygen diffusion coefficients as high as 2*10 -8 cm 2 s -1 were reported by the 18 O/ 16 O tracer diffusion method for La 2 Ni 1-x Co x O 4+d and Pr 2 NiO 4+d at 500°C. [START_REF] Bassat | Anisotropic Oxygen Diffusion Properties in Pr 2 NiO 4+δ and Nd 2 NiO 4+δ Single Crystals[END_REF][START_REF] Munnings | Oxygen transport in the La 2 Ni 1-x Co x O 4+δ system[END_REF] For Pr 2 NiO 4+d the T-dependence of D* obtained by the isotope tracer diffusion method 27 can be extrapolated to D* » 10 -15 cm 2 s -1 at ambient temperature (see Fig S6). The effective oxygen mass transport obtained here under applied electrochemical potential at RT, importantly reveals a diffusion coefficient of more than 4 orders of magnitude higher, clearly evidencing the potential of single crystalline electrodes for oxygen diffusion at ambient conditions.

Only a few examples of oxygen diffusion investigated using single crystals or epitaxial thin films by in situ diffraction methods. Thermally induced oxygen uptake/release reactions have also been studied on epitaxially grown non-stoichiometric SrCoO 3-x thin films with a thickness of 30-60 nm. [START_REF] Jeen | Reversible redox reactions in an epitaxially stabilized SrCoO x oxygen sponge[END_REF] The revealed oxygen diffusion at 300°C, as indicated by the reversible switching of Brownmillerite-type SrCoO 2.5 towards the cubic SrCoO 3-x perovskite framework, has been reported to proceed quantitatively in about one minute. Given the diffusion pathway of 30 nm, these diffusion values correspond exactly to what is obtained for the electrochemical reduction of single crystalline Pr 2 NiO 4+d electrodes with 30µm crystal radius and a reduction time of 20 h. The difference is that the electrochemical reaction on Pr 2 NiO 4+d is performing at ambient conditions, while the thickness of the used crystal is clearly indicating the oxygen diffusion to be a true bulk property.

We also note that the reaction time obtained on Pr 2 NiO 4+d single crystalline electrodes is about 5 times faster compared to polycrystalline electrodes when running under equilibrium conditions. [START_REF] Ceretti | Nd/Pr) 2 NiO 4+δ : Reaction Intermediates and Redox Behavior Explored by in Situ Neutron Powder Diffraction during Electrochemical Oxygen Intercalation[END_REF] The same also holds for the electrochemical oxidation of polycrystalline electrodes of SrFeO 2.5 and SrCoO 2.5 . [START_REF] Le Toquin | Time-Resolved in Situ Studies of Oxygen Intercalation into SrCoO 2.5 , Performed by Neutron Diffraction and X-ray Absorption Spectroscopy[END_REF][START_REF] Piovano | Time Resolved in Situ XAFS Study of the Electrochemical Oxygen Intercalation in SrFeO 2.5 Brownmillerite Structure: Comparison with the Homologous SrCoO 2.5 System[END_REF]

CONCLUSIONS

Using single crystalline Pr 2 NiO 4.225 electrodes, we observed an impressively fast reaction kinetics during the reduction towards stoichiometric Pr 2 NiO 4.0 . Our results suggest that the reduced amount of grain boundaries in single crystalline material presents a tremendous advantage to reach high diffusion rates. A complex microstructure was evidenced with the appearance of satellite reflections, indicating long-range periodicities of 7 nm along [110], related to anti phase domains along the oxygen diffusion pathway. We thus observed a hierarchy of large-scale oxygen and domain periodicities, associated with twinning or structural modulations linked to stoichiometry, on the scale of tens of nano-meters and larger. This observation, together with a control of the large-scale periodicity via stoichiometry, shows that these materials, in a certain range of compositions, may be seen as periodic multi-layer dielectric stacks -photonic crystals, and therefore be of interest for application in the field of photonic devices that can modulate and process light signals [START_REF] John | Photonic Crystals: Molding the Flow of Light[END_REF] . In this context it is interesting to note that pure stoichiometric Pr 2 NiO 4.0 crystals, as we could obtain recently for the first time, are fully transparent.

Our results clearly underline that oxygen diffusion mechanisms performing at ambient temperature are obviously more complex and far from being seen as a single particle hopping process. Phenomenologically, these results present a promising approach for stand-alone single crystalline electrodes to be used for oxygen membranes/electrolytes or oxygen sensor material, also related to their stronger mechanical performance compared to sintered electrodes.

Finally, we want to underline the importance of high resolution in-situ single crystal diffraction carried out at performant single crystal diffractometers using low noise 2D area detectors, which is decisive to obtain high-resolution maps of the reciprocal space, thus accessing information, that goes beyond to what classical powder diffraction methods can provide.

Supporting Information. The following files are available free of charge:

Additional experimental details, structural characterizations, and oxygen diffusion data, including a scheme and a photo of the experimental setup.

In the mov file, a time resolved evolution of characteristic single crystal reflection profiles throughout the electrochemical reduction are provided. ) reflections, the c-axis being the monoclinic axis. The loss of the mirror plane in the (a,c)-or (b,c)-plane of the orthorhombic phase, is then at the origin of the creation of the common plane for the monoclinic twin individuals. The proximity of the monoclinic angle to 90° renders this type of twinning to be taken as merohedral. Since (h & kl ̅

) and (hk & l ̅ ) in a setting with a monoclinic c-axis are not equivalent by symmetry, both twin configurations finally deliver for this type of merohedry a different structure factor for overlapping reflections. In addition, it is difficult to determine the volume fraction of the respective two twin individuals. Both arguments taken separated or together, result in the important consequence to not allow to separate related superimposed intensities of the superstructure reflections, since there is always an almost perfect superposition of pairs of non-equivalent (hkl) and (h & kl ̅

) in case of (010)-twinning as well as (hkl) and (hk & l ̅ ) reflections for (100)-twinning, rendering difficult further structure analysis beyond an average structure model. The given twinning scheme yields for each orthorhombic twin domain a maximum of 4 monoclinic twin domains, which could then result, in the presence of 4 orthorhombic twin domains, to a total number of 16 monoclinic domains. In case of a non-centrosymmetric space group this number would get even increased to 32. A macroscopic consequence of the twinning is the "appearance" of a second orientation of each incommensurate diffraction vector, resulting from the common (a,c) and/or (b,c) twin-planes and which corresponds in its orientation as being "mirrored" at these respective planes.

  with a diffusion pathway involving a direct and dynamically activated exchange of oxygen atoms between apical and interstitial lattice sites inside the rock salt type Pr 2 O 2 layers, as outlined in Fig 1b. Interstitial lattice sites can accommodate extra oxygen atoms, which are coordinated by 4 Pr and 4 O ap atoms, both forming a tetrahedron. For Pr 2 NiO 4.25 only one eighth of all available tetrahedral sites are occupied, leaving most of these sites vacant, promoting oxygen diffusion via a kind of push-pull diffusion mechanism.

Figure 1 :

 1 Figure 1: (a) idealized structure scheme of Pr 2 NiO 4+d , one out of 8 possible interstitial oxygen sites

Pr 2 Pr 2

 22 NiO 4+d at ambient conditions, this line phase shows a 3D modulated structure, the modulation vector being Q n = ± 5 6 ⁄ a* + 1 2 ⁄ b*. Pr 2 NiO 4.225 was consequently used as the starting phase for the electrochemically performed reduction towards the stoichiometric Pr 2 NiO 4.0 outlined below. A more detailed crystallographic description of the modulation vectors is discussed in Fig. S3. The reconstructed (hk0)-plane of the Pr 2 NiO 4.225 starting phase is given in Fig. 2a, revealing 4 orthorhombic twin domains with different volume fractions. This can be unambiguously concluded from the specific splitting and intensity ratio of the basic reflections of the parent orthorhombic framework with Fmmm space group (see Fig. 2a-c). All satellite reflections can be indexed with the Q n = ± 5 6 ⁄ a* + 1 2 ⁄ b* modulation vector as further outlined in ref 22 . A closer inspection of the integrated, individual intensities of the basic reflections reveals the existence of two main and two minor twin domains with a ratio of the corresponding volume fractions of » 4:44:3:49 for D1-D4 respectively. The corresponding simulated pattern (Fig. 2b) considers the positions of basic and satellite reflections with respect to the orthorhombic and monoclinic twinning as outlined in Fig. S2. From the size of the crystal, its mass is determined to be 25.2 µg, which would require a current of 35.2 nA, involving a charge transfer of 0.45 e -/f, for a total reaction time of 24h following the reaction equation: NiO 4.225 + 0.45 e -« Pr 2 NiO 4.0 + 0.225 O 2- (eq.1), The formally generated O 2-ions will instantly decompose together with one water molecule into OH-, following O 2-+ H 2 O ® 2OH -. All attempts to control the reaction (given in (eq.1)) in a galvanostatic reaction mode failed, as a current in the nA region is required. Such low current conditions did not even lead to a partial reduction of Pr 2 NiO 4.225 , most probably due to uncontrollable parasitic reactions which are always present during electrochemical charge/discharge and increasingly dominate over the main electrochemical reaction. The complete reduction towards the stoichiometric Pr 2 NiO 4.0 phase could, however, easily been obtained imposing a current of 10 µA, within a time window of less than 20 h. Such a high reaction kinetics appears to be surprising and interesting as such, but also implies that the autobalanced reaction kinetics no longer allows to correlate the charge transfer with the oxygen stoichiometry. The required current density thereby amounts to about 15µA/cm 2 , which is remarkably high, considering oxygen ions as the diffusing species together with the single crystalline nature of the electrode material. Reconstructed (hk0)-diffraction planes obtained during the discharge reaction are given in Fig S4, while positional and intensity changes of the (600/060) reflection group are illustrated in Fig.3 a-o. From these reconstructed sections, the contributions of 4 different twin domains are evidenced, which are separated in w and q, following the orthorhombic twinning scheme further outlined in Fig. S2. The crystal twinning and respective reflection splitting presents here a decisive advantage, offering a direct access to a unique and quantitative information of changes in the orthorhombicity as well as the volume fractions of the individual twin domains during the electrochemical reaction. This becomes possible as the structure factor of (h00) and respective (0h0) reflections are almost similar for both orthorhombic phases, as the corresponding scattering differences are related to minor shifts of low-Z oxygen atoms, linked to the tilt of the NiO 6 octahedra around [100].

Figure

  Figure 2a-c. (a) Reconstructed (hk0)-plane of Pr 2 NiO 4.225 , indicating 4 orthorhombic twin

Figure 3 (

 3 Figure 3 (a-o). Evolution of the positions and intensities of the 4 twin domains, shown for the

  . The (600)-reflection of the tetragonal intermediate phase shows diffuse contributions along the [110]/[-110] directions over the whole non-stoichiometric region, relating the (600) and (060) reflections of all involved twin domains (see Fig.3j).

Figure 4 .

 4 Figure 4. Time dependent evolution of the integrated intensities of the (600/060)-reflections of

Further 2

 2 on, diffuse scattering becomes visible at the beginning of the transformation from the tetragonal intermediate towards the stoichiometric Pr 2 NiO 4.0 phase, relating both, the equivalent (600) reflections of twin domains D2 and D3 as well as (060) reflections of twin domains D1 and D4 respectively. No diffuse scattering is, however, observed between (600) and (060) reflections along the same longitudinal reciprocal lattice direction. Such a behavior is untypical, strongly suggesting that only domains of different twin individuals but same d-values, get averaged on a length scale within the correlation length of X-ray diffraction. It suggests the formation of strongly anisotropic twin domains, which are well defined within the (a,b)-layer but showing a strong stacking disorder of differently oriented domains along the c-axis. Equivalent (h00) as well as (0k0) reflections are nicely defined in the early stage of the formation of the orthorhombic Pr NiO 4.0 -phase (Fig3j) for all twin domains, but merge continuously upon further reduction (Fig 3k-o). The twin domain evolution of the (hk4)-plane, equally showing the corresponding reflection conditions of the reduced Pr 2 NiO 4.0 phase is given in Fig 5a-f. These observations are different to what is usually observed for the thermally induced twin domain formation related to the symmetry reduction, following a 2 nd order phase transition. The well-established twin-domains along the (a,b)-plane, i.e. parallel to the Pr 2 O 2 rock salt layer, indicate that rapid oxygen diffusion may be considered as a process that makes the formation of numerous domain borders along the principal diffusion pathway to be energetically unfavorable. Further on, additional satellite reflections emerge for several (hkl)-reflections along the [110]direction (see Fig. 6i-o) at the very first appearance of the stoichiometric Pr 2 NiO 4.0 . Their positions with respect to the respective basic reflections reveal a periodicity of about 7 nm, remaining invariant upon further reduction. The satellite reflections indicate a coherent domain scattering, similar to what has been reported for ordered nano-domains in ferroelectric superlattices with 180°

Figure 5 .

 5 Figure 5. Reflection conditions, formation, and splitting for a characteristic section of the (hk4)-

Figure 6 .

 6 Figure 6. Reconstructed (hhl)-planes for Pr 2 NiO 4+d phases during the electrochemical reduction,

Fig

  Fig S2 a-b:(100)-and (010)-twinning scheme for a monoclinic lattice, the small deviation from 90° is graphically exaggerated. In reality, an almost perfect overlap of (hkl) and (hk & l ̅ ) reflections is achieved in the upper case, while for the lower figure this is true for couples of (hkl) and (h & kl ̅) reflections, the c-axis being the monoclinic axis. The loss of the mirror plane in the (a,c)-or (b,c)-plane of the orthorhombic phase, is then at the origin of the creation of the common plane for the monoclinic twin individuals. The proximity of the monoclinic angle to 90° renders this type of twinning to be taken as merohedral. Since (h & kl ̅) and (hk & l ̅ ) in a setting with a monoclinic c-axis are not equivalent by symmetry, both twin configurations finally deliver for this type of merohedry a different structure factor for overlapping reflections. In addition, it is difficult to determine the volume fraction of the respective two twin individuals. Both arguments taken separated or together, result in the important consequence to not allow to separate related superimposed intensities of the superstructure reflections, since there is always an almost perfect superposition of pairs of non-equivalent (hkl) and (h & kl ̅) in case of

1

 1

c:Fig. S3 :

 S3 Fig. S3: Simulated diffraction pattern of Pr2NiO4.225 for the commensurate modulation vector Qn = ± 5 6 ⁄ a* + 1 2 ⁄ b*, taking into account 2 orthorhombic twin domains, each forming up to 4 monoclinic domains, which are almost perfectly superimposed due to the minor deviation of the monoclinic angle from 90°. As a consequence all domains result in an almost perfect merohedical overlay of all satellite reflections as further outlined in ref 22 . The satellite reflections were all assumed to have the same intensity. As prepared Pr2NiO4+d in air shows an extra oxygen stoichiometry of d = 0.25 adapting a monoclinic symmetry (space group F112/m, with lattice parameters a = 5.3977(3) Å, b = 5.4540(3) Å, c = 12.4362(10) Å, g = 90.03°(1)). Storing under ambient conditions leads to a topotactic release of the O-stoichiometry towards Pr2NiO4.225 with a = 5.3945(4) Å, b = 5.4538(4) Å, c = 12.4408(10)Å, g = 90.07(1)°. While the changes in the lattice parameters are only marginal, the respective change of the modulation vector ordering from Qn = ± 7 9 ⁄ a* + 5 9 ⁄ b* towards Qn = ± 5 6 ⁄ a* + 1 2 ⁄ b* clearly indicates a distinct oxygen ordering. For Pr2NiO4.25, the space group of the modulated structure is P112/m(αß0)(00), a subgroup of the standard setting P2/m. The oxygen release towards Pr2NiO4.225 yields a different oxygen ordering scheme, resulting in a more complex symmetry with a (3+2)-dimensional super space description. With the general scattering vector G = ha* + kb* + lc* +m1Qn + m2qn with 0 ≤ |m1|≤ 6 and 0 ≤ |m2|≤ 1, n symbolizes the number of the twin individuals, ranging between 1 £ n £ 4.With qn = ±0.25a* + 0.25b* + 0.5c*, the (3+2) super space group thus becomes P112/m(α1ß10)(0s)(α2ß21/2)(00). Interestingly, both phases appear to be line phases, despite the only narrow difference in their respective oxygen stoichiometry.1

Fig. S7 :

 S7 Fig. S7: Schematic presentation of the two anti phase domains in Pr2NiO4.0 showing a different tilt direction for the NiO6 octahedra.

Table of

 of Contents. Long-range domain ordering observed by in situ single crystal synchrotron diffraction during the electrochemical reduction of Pr 2 NiO 4.225 towards Pr 2 NiO 4.0 at room temperature showing periodicities of 70 Å.

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Supplementary information:

(a) (b) (c) (f) ) (k) ) (l) ) (m) ) (g) ) (h) ) (i) ) (d) ) (e) ) (n) ) (o) ) (j) )

h (r.l.u.) k (r.l.u.)

Fig. S5a: reconstructed (hk0)-plane for the Pr2NiO4.10 phase, indicating the presence of several superstructure reflections in agreement with the P42/ncm space group (red), while a few weak reflections marked in green violate the reflection conditions h + k = 2n. The blue circles belong to the NiO intergrowth phase, which turns out to be present in all Pr2NiO4+d crystals as an unavoidable fraction as described in ref [START_REF] Jeen | Reversible redox reactions in an epitaxially stabilized SrCoO x oxygen sponge[END_REF] . The NiO reflections are already present in the starting phase and persist to the fully reduced Pr2NiO4.0 phase.