François Bordeyne
email: fbordeyne@sb-roscoff.fr

Dominique Davoult

Aline Migné

Euriell Bertaud

Du Chazaud

Cédric Leroux

Pascal Riera

Euriell Bertaud Du Chazaud

Trophic structure of two intertidal Fucus spp. communities along a vertical gradient: Similarity and seasonal stability evidenced with δ13C and δ15N

Keywords: Stable isotopes, intertidal zonation, seasons, trophic groups HIGHLIGHTS

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INTRODUCTION

Along intertidal rocky shores of temperate areas, sheltered habitats are usually dominated by canopy-forming brown algae (Phaeophyceae) that can cover almost all the substratum. These species are established along a vertical gradient and are typically associated with numerous species of primary producers and consumers in such a way that intertidal rocky shores are composed of a succession of distinct communities from high to low tide levels [START_REF] Raffaelli | Intertidal ecology[END_REF]. Trophic structure of these intertidal communities has been the focus of intensive research during the past decades, due to the emergence of the stable isotopic approach (e.g. [START_REF] Dauby | Trophic relationships within intertidal communities of the Brittany coasts: a stable carbon isotope analysis[END_REF][START_REF] Sarà | Sources of organic matter for intertidal consumers on Ascophyllum-shores (SW Iceland): a multistable isotope approach[END_REF][START_REF] Riera | Trophic ecology of the rocky shore community associated with the Ascophyllum nodosum zone (Roscoff, France): A δ 13 C vs δ 15 N investigation[END_REF][START_REF] Duarte | Effects of alga Fucus serratus decline on benthic assemblages and trophic linkages at its retreating southern range edge[END_REF]. To our knowledge, only one study was however carried out in the context of vertical zonation [START_REF] Steinarsdóttir | Trophic relationships on a fucoid shore in south-western Iceland as revealed by stable isotope analyses, laboratory experiments, field observations and gut analyses[END_REF]). Tidal zonation is, yet, expected to be a significant driver of community trophic structure. For instance, shore level usually controls resource access for primary producers (e.g. CO 2 /HCO 3 -and nutrients, [START_REF] Raven | Ecophysiology of photosynthesis in macroalgae[END_REF], sessile fauna (as some species can only feed when immersed, [START_REF] Raffaelli | Intertidal ecology[END_REF]) and mobile fauna (as the amount of available food might decrease from low to high shore levels, [START_REF] Underwood | Microalgal food and the growth of the intertidal gastropods Nerita atramentosa Reeve and Bembicium nanum (Lamarck) at four heights on a shore[END_REF]. Trophic relationships are considered as an important component of community functioning and should be defined more accurately in the context of tidal zonation. The use of stable isotopes seems particularly powerful for this purpose, as they act as chemical tracers of energy flow (Peterson & Fry 1987[START_REF] Fry | Stable Isotope Ecology[END_REF]). Thus, δ 13 C of a consumer usually provides information about its diet sources while its δ 15 N value is often related to its trophic position in the food web [START_REF] Zanden | Variation in δ 15 N and δ 13 C trophic fractionation: Implications for aquatic food web studies[END_REF][START_REF] Caut | Variation in discrimination factors (Δ 15 N and Δ 13 C): the effect of diet isotopic values and applications for diet reconstruction[END_REF]).

In temperate areas, abiotic factors such as light and temperature display significant seasonal fluctuations. As a consequence, intertidal communities show seasonal pattern in their metabolism [START_REF] Golléty | Benthic metabolism on a sheltered rocky shore: role of the canopy in the carbon budget[END_REF][START_REF] Bordeyne | Metabolic activity of intertidal Fucus spp. communities: evidence for high aerial carbon fluxes displaying seasonal variability[END_REF], as well as in their species richness and/or abundance [START_REF] Rindi | Composition and spatio temporal variability of the epiphytic macroalgal assemblage of Fucus vesiculosus Linnaeus at Clare Island, Mayo, western Ireland[END_REF][START_REF] Dethier | Seasonal stresses shift optimal intertidal algal habitats[END_REF]. These seasonal fluctuations potentially influence species interactions and may therefore lead to modification in their food webs. Furthermore, seasonal changes in isotopic composition of both primary producer and consumer species are regularly evidenced in coastal communities [START_REF] Nordström | Temporal variability of a benthic food web: patterns and processes in a low-diversity system[END_REF][START_REF] Hyndes | The magnitude of spatial and temporal variation in δ 15 N and δ 13 C differs between taxonomic groups: Implications for food web studies[END_REF], including intertidal habitats [START_REF] Golléty | Complexity of the food web structure of the Ascophyllum nodosum zone evidenced by a δ 13 C and δ 15 N study[END_REF][START_REF] Ouisse | Food web analysis in intertidal Zostera marina and Zostera noltii communities in winter and summer[END_REF]. These changes, which could be related to numerous biotic and abiotic factors [START_REF] Jennings | Body-size dependent temporal variations in nitrogen stable isotope ratios in food webs[END_REF][START_REF] Vanderklift | Variation in δ 13 C and δ 15 N of kelp is explained by light and productivity[END_REF][START_REF] Viana | Experimental assessment of the macroalgae Ascophyllum nodosum and Fucus vesiculosus for monitoring N sources at different time-scales using stable isotope composition[END_REF], may also reflect important modifications in the trophic structure of these communities over time [START_REF] Mcmeans | Food web structure in temporally-forced ecosystems[END_REF].

In this context, it appears essential to understand how seasonal variations can structure the food webs of benthic communities, and also how these communities respond to existing environmental variations [START_REF] Hyndes | The magnitude of spatial and temporal variation in δ 15 N and δ 13 C differs between taxonomic groups: Implications for food web studies[END_REF].

Using a δ 13 C and δ 15 N approach, this study focuses on the main taxa inhabiting two communities that are established at adjacent tidal levels. These two communities, widespread in temperate rocky shores, are respectively dominated by the canopy-forming species Fucus vesiculosus Linnaeus and Fucus serratus Linnaeus. This study aimed to describe the trophic structure of these communities at four periods of the year, assuming that the alternation of seasons is likely to generate significant fluctuations of food webs. Comparisons between communities were also carried out to test the hypothesis that food webs vary according to the tidal level.

MATERIAL AND METHODS

Study site

The study site is located in front of the Station Biologique de Roscoff, in the southwestern part of the English Channel (Brittany, France) (48°43.743'N, 3°59.407'W). It consisted of an intertidal boulder reef subjected to semi-diurnal tidal cycle, with maximal amplitude of about 9 m. This semi-sheltered rocky shore is characterized by a vertical succession of communities dominated by canopy-forming Phaeophyceae, where the Fucus vesiculosus and F. serratus communities are characteristic of the mid-intertidal (3.0 to 4.0 m above chart datum) and low mid-intertidal (2.5 to 3.0 m above chart datum) respectively. These communities are mainly composed of dense Fucus spp. canopies, covering up to 100 % of the substratum, which are associated with miscellaneous epibionts (i.e. algae and sessile invertebrates directly attached to the Fucus, see [START_REF] Wahl | Marine Hard Bottom Communities: Patterns, Dynamics, Diversity, and Change[END_REF]. They are also made up of sub-canopy and encrusting algae, as well as microphytobenthos, and phytoplankton during high tide. Finally, these communities also support a diverse pool of mobile invertebrates [START_REF] Raffaelli | Intertidal ecology[END_REF], Migné et al. 2015).

Sampling and preparation for stable isotopes analysis

For both F. vesiculosus and F. serratus communities, the most representative taxa of food sources (i.e. erect and encrusting algae, and epilithon) and consumers were collected by hand during low tide, in four successive seasons (September and December 2013 and March and June 2014, see Supplementary material for the list of sampled taxa). After collection, samples were frozen at -18 °C for later processing. Particular attention was taken to collect consumers from the main trophic groups (filter-feeders, grazers and predators), based on literature knowledge (e.g. [START_REF] Dauby | Trophic relationships within intertidal communities of the Brittany coasts: a stable carbon isotope analysis[END_REF][START_REF] Riera | Trophic ecology of the rocky shore community associated with the Ascophyllum nodosum zone (Roscoff, France): A δ 13 C vs δ 15 N investigation[END_REF][START_REF] Golléty | Complexity of the food web structure of the Ascophyllum nodosum zone evidenced by a δ 13 C and δ 15 N study[END_REF]. Stable isotope data for marine suspended particulate organic matter (POM) were obtained from the SOMLIT network, in a place located at approximately 600 m of our study site (Estacade sampling point, Roscoff, France, data available at http://somlit-db.epoc.u-bordeaux1.fr/bdd.php).

In the laboratory, erect algae were carefully cleaned in filtered seawater (0.45 µm) to remove detrital fragments and attached organisms. The encrusting ones were scrubbed in filtered seawater, which was then filtered onto pre-combusted filters (Whatman GF/F glass microfiber filters). In order to remove inorganic carbon of the encrusting Rhodophyceae Phymatolithon lenormandii, HCl 1N was added to seawater prior to filtration. Epilithon was gently removed from small boulders using a smooth brush and collected in filtered seawater, then filtered onto pre-combusted filters. Regarding consumers, organisms belonging to the Cnidaria (except campanulariidae), Mollusca, Arthropoda (except amphipods) and Echinodermata phyla were treated at the individual level, while for colonial taxa (i.e.

campanulariidae, Bryozoa and Ascidiacea), Spirorbis sp. and amphipods, several organisms were pooled together to get enough material for accurate stable isotope analyses. Gastropods were extracted from their shell to take off foot muscle, whereas for decapods, muscle was taken off from their pereiopods. For Asterina gibbosa, amphipods, campanulariidae and polyclinidae, half of the samples were acidified to remove inorganic carbon (HCl 1N) while the other part remained untreated. δ 13 C measurements were performed on acidified samples and δ 15 N on untreated ones, as advised by [START_REF] Schlacher | Effects of acid treatment on carbon and nitrogen stable isotope ratios in ecological samples: a review and synthesis[END_REF]. Finally, all samples were rinsed with distilled water, before being dried (60°C, 48h) and ground to a fine homogeneous powder using an agate mortar and pestle.

Carbon and nitrogen stable isotopes ratios were determined using a Flash EA 1112 CHN analyzer (ThermoFinningan) coupled with a Finnigan Delta Plus mass spectrometer, via a Finnigan Con-Flo III interface. Data are expressed in the standard δ unit:

𝛿𝑋(‰) = �� 𝑅 𝑠𝑎𝑚𝑝𝑙𝑒 𝑅 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 � -1� × 10 3
With X is 13 C or 15 N and R is 13 C/ 12 C ratio for carbon or 15 N/ 14 N ratio for nitrogen.

δ 13 C and δ 15 N were calculated in relation to the certified reference materials Vienna-Pee Dee Belemnite-limestone (V-PDB) and atmospheric di-nitrogen (N 2 ). The V-PDB and N 2 at airscales were achieved using in-house protein standards, calibrated against NBS-19 and IAEA N3 reference materials. The standard deviation of repeated measurements of δ 13 C and δ 15 N values of the laboratory standard was 0.10 ‰ versus V-PDB and 0.05 ‰ versus at-air, respectively.

Taxonomic diversity and density of gastropod grazers

Gastropod grazers (hereafter referred to as "grazers") constitute the most abundant group of consumers in these communities (approx. 95% of the countable fauna) and likely play a significant role in organic matter fluxes within the food webs. The taxonomic diversity of these grazers was monitored in the same areas and at the same periods than sampling for stable isotopes analyses (i.e. September and December 2013, and March and June 2014).

Thus, at each season, grazers were identified at the species level and counted in five replicates of 0.1 m² randomly chosen in each community. To account for spatial variability, intracommunity replicates were 3 to 10 m away one from each other.

Data analysis

The trophic structure of each community, its temporal fluctuations, and the potential trophic relationships between diets and consumers, were investigated by drawing dual-isotope plots at each sampling period. The "community-wide" isotopic metrics developed by [START_REF] Cucherousset | Quantifying the multiple facets of isotopic diversity: new metrics for stable isotope ecology[END_REF] (i.e. isotopic richness, divergence, dispersion, evenness and uniqueness) were used as a complement to these dual-isotope plots. The isotopic richness is related to the area of the bi-dimensional isotopic space that is filled by all the taxa while the isotopic divergence, dispersion, eveness and uniqueness are related to the distribution of taxa in this space, providing information about trophic diversity and redundancy. These metrics have the benefit to be mathematically independent of the number of replicates used and allow accounting for abundance/biomass of taxa, when available. They were calculated at each sampling period and for each community, using the R functions computed by [START_REF] Cucherousset | Quantifying the multiple facets of isotopic diversity: new metrics for stable isotope ecology[END_REF], with R software, version 3.2.2 (R Core Team 2015). Their coefficient of variation across seasons was used to discuss about the seasonal variability in the trophic structure of these two communities.

Bayesian stable isotope mixing models (SIAR, [START_REF] Parnell | Source partitioning using stable isotopes: coping with too much variation[END_REF][START_REF] Parnell | Stable Isotope Analysis in R. Peterson BJ, Fry B[END_REF] were implemented to estimate the relative contribution of food sources to the diet of several consumers, at each season, and for each community. To do so, trophic enrichment factors of 0.28 ± 0.23 ‰ for δ 13 C and of 2.5 ± 0.68 ‰ for δ 15 N were assumed [START_REF] Caut | Variation in discrimination factors (Δ 15 N and Δ 13 C): the effect of diet isotopic values and applications for diet reconstruction[END_REF]). Thus, these mixing models were run for a set of filter-feeders selected for each community, implementing POM and erect algae as potential food sources. Erect algae were used considering that they may be consumed by filter-feeders through detritus [START_REF] Leclerc | Temporal variation in organic matter supply in kelp forests: linking structure to trophic functioning[END_REF], despite that degradation process might affect their isotopic composition [START_REF] Lehmann | Preservation of organic matter and alteration of its carbon and nitrogen isotope composition during simulated and in situ early sedimentary diagenesis[END_REF]. Mixing models were also run for a set of grazers selected for each community, implementing epilithon and erect algae as potential food sources. Grazer selection was realized according to [START_REF] Hawkins | A comparison of feeding mechanisms in microphagous, herbivorous, intertidal, prosobranchs in relation to resource partitioning[END_REF], in such a way that diversity of feeding behaviours and of radula types was maximised. In the F. serratus community, some erect Rhodophyceae were pooled together according to their characteristics, to limit the number of potential food sources [START_REF] Phillips | Best practices for use of stable isotope mixing models in food-web studies[END_REF].

For comparisons between communities, we first calculated the overall level of isotopic overlap between the two communities using the isotopic overlap metrics (isotopic similarity and nestedness) developed by [START_REF] Cucherousset | Quantifying the multiple facets of isotopic diversity: new metrics for stable isotope ecology[END_REF], from the average isotopic signature of each taxon. We also focused on consumer taxa present in both communities (i.e.

shared consumers, see Supplementary Material for their identities). Their average δ 13 C and δ 15 N obtained in the F. vesiculosus community were plotted against those obtained in the F. serratus community. Slopes and intercepts of a Model II regression were then calculated according to the major axis method, using the "lmodel2" R package version 1.7-2 (Legendre 2014), for both δ 13 C Fves vs δ 13 C Fser and δ 15 N Fves vs δ 15 N Fser plots. Student's t-tests were performed to test if slopes and intercepts of regressions were significantly different from 1 and 0, respectively. If not, it would indicate that, on average, the shared consumers' exhibited similar isotopic signature in the two communities.

Focusing on grazers, potential differences between communities were first investigated in terms of taxonomic diversity (i.e. distribution of abundances among taxa) using clustering analysis (group average) and one-way ANOSIM test (for each community, the four seasonal samples were considered as replicates). These analyses were performed on similarity matrix calculated from Bray-Curtis similarity index on square-root transformed abundances, using PRIMER software, version 6.1.12 [START_REF] Clarke | Allochthonous brown algae are the primary food source for consumers in a temperate, coastal environment[END_REF]. Then, potential difference between communities in term of isotopic diversity of grazers was investigated using the isotopic diversity metrics (isotopic richness, divergence, dispersion, evenness and uniqueness, [START_REF] Cucherousset | Quantifying the multiple facets of isotopic diversity: new metrics for stable isotope ecology[END_REF]. These isotopic metrics were calculated at each season and for each community, from grazer isotopic signatures, with and without weighting them by their abundances. Clustering analysis and one-way ANOSIM tests were then performed for each condition on similarity matrices calculated using Bray-Curtis similarity index on the five metrics, following the procedure previously described.

RESULTS

Trophic structure of Fucus spp. communities and seasonal variability

For each community, primary sources were distributed over a large range of δ 13 C over the sampling seasons. For the F. vesiculosus community, Caulacanthus ustulatus, POM and epilithon were the most 13 C-depleted sources, and displayed δ 13 C ranging from -20.3 to -24.0 ‰, according to sampling seasons. Ascophyllum nodosum, F. vesiculosus, Ulva spp. and Hildenbrandia rubra were more 13 C-enriched and showed δ 13 C values ranging from -13.0 to -18.4 ‰, according to sampling seasons. These sources were mainly discriminated by their δ 15 N, with A. nodosum and F. vesiculosus being on average more 15 N-depleted (5.1 to 7.4 ‰)

than Ulva spp. and H. rubra (6.2 to 8.9 ‰, Figure 1). For the F. serratus community, C. ustulatus, Chondracanthus acicularis, POM and epilithon were the most 13 C-depleted sources, and displayed δ 13 C values ranging from -19.5 to -25.0 ‰, according to sampling seasons. The other sources were more 13 C-enriched (-14.8 to -19.9 ‰). Among them, F. serratus was the most 15 N-depleted (3.0 to 5.7 ‰), while Ulva spp., H. rubra, Mastocarpus stellatus and P. lenormandii were more closely related (δ 15 N ranging from 6.5 to 9.7 ‰, Figure 2). Regarding consumers, filter-feeders were on average the most 13 Cdepleted, with δ 13 C values ranging from -16.5 to -20.8 ‰ for the F. vesiculosus community and from -15.2 to -21.2 ‰ for the F. serratus community, according to sampling seasons. In comparison, grazers were more 13 C-enriched, with values ranging from -13.9 to -16.4 ‰ for the F. vesiculosus community and from -13.1 to -17.0 ‰ for the F. serratus community, according to sampling seasons. Predators occupied the top of the food webs, and were the most 15 N-enriched consumers. They displayed δ 15 N values ranging from 9.2 to 13.0 ‰ for the F. vesiculosus community (filter-feeders and grazers: 7.2 to 10.8 ‰, Figure 1) and from 7.7 to 14.0 ‰ for the F. serratus community (filter-feeders and grazers: 6.0 to 10.3 ‰, Figure 2), according to sampling seasons.

The five isotopic metrics showed low variability across seasons, as their coefficient of variation varied between 3.8 and 14.6% in the F. vesiculosus community and between 2.4 and 25.4% in the F. serratus community (Table 1). Only isotopic richness and uniqueness of the F. serratus community exhibited a coefficient of variation higher than 15%. This was mainly due to the high 13 C and/or 15 N depletions of two basal sources in some seasons (i.e. epilithon was 13 C and 15 N depleted in both December and March, and F. serratus was 15 N depleted in March, Figure 2).

Relative contributions of potential food sources to the diet of consumers were highly variable between sampling seasons (Table 2). In the F. vesiculosus community, the contribution of POM to the diet of filter-feeders was maximal in September and June (17.2 to 49.4% on average) and minimal in December and March (8.8 to 13.1% on average). In contrast, erect macroalgae were the main resources to filter-feeders in December and March (86.9 to 91.2% on average, Table 2). For grazers, no clear seasonal trend in diet was evidenced, even though Ulva spp. and F. vesiculosus constituted their main trophic resources in March (27.0 to 77.6% on average) and in June (42.9 to 71.2% on average), respectively. In the F. serratus community, the contribution of POM to the diet of filter-feeders was maximal in September and June (29.5 to 77.6% on average) and minimal in December and March (6.1 to 16.1% on average) as well. Erect macroalgae were their main resources in December and March (83.9 to 93.9% on average, Table 2). No clear seasonal trend in diet of grazers was evident, even though F. serratus constituted their main trophic resources in June (69.2 to 86.3% on average).

Comparisons between communities

No seasonal trend in trophic structure has been observed for these two intertidal communities.

As well, when comparisons between communities were performed at each season, any difference were evidenced, neither considering the functional isotopic space of whole communities (i.e. high isotopic similarity and isotopic nestedness), nor considering the isotopic composition (δ 13 C and δ 15 N) of consumers species present in both communities.

Therefore, comparisons between communities were performed using an average isotopic signature of each taxon, obtained after pooling the stable isotope values of the different sampling periods. Considering these year-round means in isotopic signature, the two communities presented an isotopic similarity of 0.779 and an isotopic nestedness of 0.894 (Figure 3). Almost all the taxa (43 of 52) were included in the intersection of the two isotopic spaces. Regarding the consumers shared by the two communities, the model II regressions of dual plots exhibited significant Pearson's coefficient (For δ 13 C Fves vs δ 13 C Fser , n = 14, R = 0.876, p < 0.001; for δ 15 N Fves vs δ 15 N Fser , n = 14, R = 0.953, p < 0.001) (Figure 4). The slopes of regressions were equal to 1.2 and 1.0 for δ 13 C Fves vs δ 13 C Fser and δ 15 N Fves vs δ 15 N Fser , respectively, while intercepts were equal to 2.9 and 0.3, respectively. These slopes and intercepts were not significantly different from 1 and 0, respectively (For δ 13 C Fves vs δ 13 C Fser , t = 1.42, p = 0.091 for the slope and t = 1.49, p = 0.080 for the intercept; for δ 15 N Fves vs δ 15 N Fser , t = 0.13, p = 0.450 for the slope and t = 0.40, p = 0.349 for the intercept).

In both communities, Gibbula spp., Littorina spp. and Patella vulgata were the most dominant taxa of grazers: G. umbilicalis being the most abundant species in the F. vesiculosus community (96 to 208 individuals per m²) and G. pennanti was most abundant species in the F. serratus community (130 to 508 individuals per m², Table 3). Clustering analysis performed on the taxonomic diversity of grazers discriminated the two communities (Figure 5a), which were significantly different according to the ANOSIM test (R = 0.75, p = 0.029).

When performed on isotopic diversity metrics, these analyses did not allow to significantly discriminate the two communities, neither when they were conducted on unweighted data (ANOSIM test, R = 0.26, p = 0.083, Figure 5b), nor when conducted on data weighted by abundance of grazers (ANOSIM test, R = 0.12, p = 0.229, Figure 5c).

DISCUSSION

Trophic structure of Fucus spp. communities

By analysing isotopic composition of the main taxa inhabiting the Fucus vesiculosus and F. serratus communities, we attempted to depict their global trophic structure. At each season and in each community, groups of consumers were discriminated as filter-feeders, grazers and predators, despite some overlap in their isotopic signatures. As expected, filter-feeders were the most 13 C-depleted consumers, while predators were the most 15 N-enriched and occupied the top of the food webs. Both sources and consumers were distributed over large δ 13 C and δ 15 N ranges, suggesting that the Fucus spp. communities are characterized by a complex trophic structure [START_REF] Golléty | Complexity of the food web structure of the Ascophyllum nodosum zone evidenced by a δ 13 C and δ 15 N study[END_REF]. This complexity may have been however

underestimated during this study, as the ultimate top predators of these communities (i.e.

fishes and shore birds, [START_REF] Ellis | Regulation of intertidal food webs by avian predators on New England rocky shores[END_REF], as well as one potential food source (epibiotic biofilms) were not sampled. Despite that, the large δ 15 N range of consumers (i.e. δ 15 N extended over 4.7 to 7.4 ‰ according to the sampling period) reveals the presence of several trophic levels within the Fucus spp. communities. The heterogeneous distribution in δ 15 N of primary consumers prevented, however, to attribute an accurate trophic position to each consumer [START_REF] Post | Using stable isotopes to estimate trophic position: models, methods, and assumptions[END_REF][START_REF] Riera | Trophic ecology of the rocky shore community associated with the Ascophyllum nodosum zone (Roscoff, France): A δ 13 C vs δ 15 N investigation[END_REF]. As well, their large δ 13 C range is characteristic of the occurrence of several trophic pathways, as previously reported in rocky shore habitats [START_REF] Golléty | Complexity of the food web structure of the Ascophyllum nodosum zone evidenced by a δ 13 C and δ 15 N study[END_REF][START_REF] Leclerc | Temporal variation in organic matter supply in kelp forests: linking structure to trophic functioning[END_REF]. This likely results from the high diversity of food sources and feeding behaviors of invertebrates [START_REF] Riera | Trophic ecology of the rocky shore community associated with the Ascophyllum nodosum zone (Roscoff, France): A δ 13 C vs δ 15 N investigation[END_REF], which are favored by the multitude of microhabitats that usually characterized rocky shores [START_REF] Schaal | A seasonal stable isotope survey of the food web associated to a peri-urban rocky shore[END_REF][START_REF] Schaal | Microscale variations of food web functioning within a rocky shore invertebrate community[END_REF].

Mixing models also highlighted the occurrence of several trophic pathways in fucoid communities. Thus, filter-feeders were supposed to rely mainly on POM and on several species of erect algae through the detrital pathway. As well, the diet of grazers was mainly based on a mix of different species of algae (i.e. Fucus, Ulva spp., A. nodosum, M. stellatus).

According to these results, filter-feeders and grazers can be considered as generalist species.

Therefore, Fucus species did not constitute the cornerstone of these food webs, supplying the vast majority of organic carbon for primary consumers (with the exception of June for grazers), as we might reasonably expect from their abundance (i.e. 1.50 to 11.80 kg of fresh weight m -2 for Fucus canopies; 0.02 to 0.28 kg of fresh weight m -2 for all other erect macroalgae, Bordeyne et al., unpublished data). However, fucoid species are usually considered to have poor nutritional values and can induce anti-grazing defence that may repel primary consumers [START_REF] Molis | Inducible responses in the brown seaweed Ecklonia cava: the role of grazer identity and season[END_REF]. Therefore, primary consumers may show food preference toward more nutritional species [START_REF] Lubchenco | Plant species diversity in a marine intertidal community: importance of herbivore food preference and algal competitive abilities[END_REF][START_REF] Littler | The evolution of thallus form and survival strategies in benthic marine macroalgae: field and laboratory tests of a functional form model[END_REF][START_REF] Watson | Dietary preferences of the common periwinkle, Littorina littorea (L.)[END_REF], despite their lower abundance. Epibiotic biofilms, while not sampled here, may also constitute a complementary trophic resource for some species of grazers, notably those living on fucoid fronds such as Littorina obtusata (see Norton et al. 1990 and references therein). Interestingly, according to its isotopic signature and the results of mixing models, the introduced alga C. ustulatus has very low contribution to the diet of grazers. This species, first recorded close to our study site almost 30 years ago [START_REF] Rio | Apparition du Caulacanthus ustulatus (Rhodophyta, Gigartinales) dans la Manche occidentale[END_REF], was suggested to be unpalatable for native consumers due to production of secondary metabolites [START_REF] Smith | The non-native turf-forming alga Caulacanthus ustulatus displaces space-occupants but increases diversity[END_REF]). However, filter-feeders may rely on this species through the detrital pathway. Finally, we should mention that the wide ranges in specific contributions obtained from mixing models reveal some uncertainties, and have to be considered with caution [START_REF] Phillips | Best practices for use of stable isotope mixing models in food-web studies[END_REF].

Seasonal variability of trophic structure

The year-round analysis of the isotopic composition of the main taxa inhabiting the F. vesiculosus and F. serratus communities revealed an overall preservation of their food webs across seasons. This trend, depicted by comparing the biplots drawn at each season, was supported by the low values of the coefficient of variation across seasons for isotopic diversity metrics, especially in the F. vesiculosus community. Such preservation of trophic structure across seasons has already been noticed for a Fucus-dominated community [START_REF] Schaal | A seasonal stable isotope survey of the food web associated to a peri-urban rocky shore[END_REF], even though the studied community was subjected to a strong anthropogenic pressure, which may have influenced isotopic composition of both sources [START_REF] Viana | Experimental assessment of the macroalgae Ascophyllum nodosum and Fucus vesiculosus for monitoring N sources at different time-scales using stable isotope composition[END_REF] and consumers [START_REF] Warry | Nitrogen stable isotope values of large-bodied consumers reflect urbanization of coastal catchments[END_REF]. Thus, the year-round preservation of food webs we observed in non-impacted fucoid communities could have major implications regarding our knowledge of their dynamics. Indeed, temporal modification of species richness and/or abundance is generally considered as a key process in temperate habitats [START_REF] Dethier | Seasonal stresses shift optimal intertidal algal habitats[END_REF] and could potentially lead to a seasonality in resource availability, as observed in the Arctic environments. Such seasonality finally leads to large modifications of food webs in these extreme environments [START_REF] Forest | The annual cycle of particulate organic carbon export in Franklin Bay (Canadian Arctic): Environmental control and food web implications[END_REF][START_REF] Darnis | Current state and trends in Canadian Arctic marine ecosystems: II. Heterotrophic food web, pelagic-benthic coupling, and biodiversity[END_REF]). In the present study, however, most of the common macroalgae are perennial (e.g. Fucus spp., M. stellatus),

providing constant resources for grazers, despite the fall to spring decrease in abundance of ephemeral alga Ulva spp. [START_REF] Migné | Effect of canopy removal on a rocky shore community metabolism and structure[END_REF]. Therefore, grazers do not need to switch their diet over the course of the year, explaining their temporal conservation within food webs. In contrast, filter-feeders showed a partial switch in diet over the year, according to the results of mixing models. They were found to rely mainly on phytoplankton-dominated POM during summer and on macroalgae-derived organic matter during winter, which is consistent with seasonal variations in abundance of phytoplankton observed close to our study area (SOMLIT data). Such switch in diet has already been observed in kelp forests of Brittany [START_REF] Leclerc | Temporal variation in organic matter supply in kelp forests: linking structure to trophic functioning[END_REF], and strengthens the idea that macroalgae-derived detritus are a significant food source for filter-feeders [START_REF] Sarà | Sources of organic matter for intertidal consumers on Ascophyllum-shores (SW Iceland): a multistable isotope approach[END_REF][START_REF] Clarke | Allochthonous brown algae are the primary food source for consumers in a temperate, coastal environment[END_REF][START_REF] Schaal | A seasonal stable isotope survey of the food web associated to a peri-urban rocky shore[END_REF][START_REF] Miller | Kelp as a trophic resource for marine suspension feeders: a review of isotope-based evidence[END_REF]. They are therefore suggested to be opportunistic species relying on the most abundant food source [START_REF] Ricciardi | Global patterns of macroinvertebrate biomass in marine intertidal communities[END_REF][START_REF] Schaal | A seasonal stable isotope survey of the food web associated to a peri-urban rocky shore[END_REF]. In spite of this temporal diet variability, the average trophic position of this functional group in the two communities remained unchanged, and filter-feeders stayed 13 C-depleted compared to grazers, all over the year. The relative seasonal conservation of predators within the food webs was probably due to the seasonal consistency of their potential diet (i.e. primary consumers) but should also result from a relative degree of omnivory and opportunism [START_REF] Thompson | Trophic levels and trophic tangles: the prevalence of omnivory in real food webs[END_REF][START_REF] Silva | Use of the intertidal zone by mobile predators: influence of wave exposure, tidal phase and elevation on abundance and diet[END_REF][START_REF] Duarte | Effects of alga Fucus serratus decline on benthic assemblages and trophic linkages at its retreating southern range edge[END_REF]. Finally, the overall preservation of trophic structure across seasons observed despite some seasonal changes in taxonomic diversity of consumers, suggests that some redundancy in the feeding behaviour of these species [START_REF] Hawkins | A comparison of feeding mechanisms in microphagous, herbivorous, intertidal, prosobranchs in relation to resource partitioning[END_REF][START_REF] Golléty | Complexity of the food web structure of the Ascophyllum nodosum zone evidenced by a δ 13 C and δ 15 N study[END_REF]) helps to keep a relative food web stability over time [START_REF] Christie | Macrophytes as habitat for fauna[END_REF]).

The high degree of conservation of their trophic structures exhibited by fucoid communities during the sampling year could lead to further new insights about dynamics of these habitats.

These results should, however, be complemented by the addition of densities or biomasses for each taxa, as this may thoroughly modify the vision we have of trophic relationships [START_REF] Rigolet | Investigating isotopic functional indices to reveal changes in the structure and functioning of benthic communities[END_REF].

Comparisons between communities

By analysing isotopic composition of taxa living in these communities, we had the prospect to do comparisons in the context of vertical zonation of intertidal habitats. Using communitywide metrics, we highlighted an important similarity in the average trophic structure of the two Fucus spp. communities. This was supported by the large number of taxa present in the common isotopic space. Despite some differences in the species richness and composition between these two communities (Davoult et al., unpublished data), they shared a roughly similar isotopic functional space, suggesting that the same trophic functions are undertaken by different species in the F. vesiculosus and F. serratus communities. This is consistent with the fact that intertidal communities are mostly composed of generalists and opportunistic species, that rely mainly on the most abundant food sources [START_REF] Steinarsdóttir | Trophic relationships on a fucoid shore in south-western Iceland as revealed by stable isotope analyses, laboratory experiments, field observations and gut analyses[END_REF]. Such plasticity in diet could favour growth rates of consumers, as demonstrated by [START_REF] Lee | Feeding and reproductive performace of the harpacticoid Tisbe carolinensis (Copepoda, Crustacea) in four algal cultures[END_REF], providing them some benefit in intertidal habitats. However, the two Fucus spp. communities exhibited significant differences in their photosynthetic activity over the year [START_REF] Bordeyne | Metabolic activity of intertidal Fucus spp. communities: evidence for high aerial carbon fluxes displaying seasonal variability[END_REF], potentially leading to important differences in the amount of carbon accumulation at the base of the food webs, and in carbon fluxes toward top predators. Again, further investigations taking into account taxon abundances are needed to understand more faithfully the trophodynamics of these communities.

Although the F. vesiculosus and F. serratus communities exhibit some differences in their specific composition, several taxa of consumers live commonly in the two communities.

These taxa were found to exhibit, on average, similar isotopic composition, whether they were found in the F. vesiculosus community or in the F. serratus one. [START_REF] Steinarsdóttir | Trophic relationships on a fucoid shore in south-western Iceland as revealed by stable isotope analyses, laboratory experiments, field observations and gut analyses[END_REF] observed a similar pattern on a few number of invertebrate species from Icelandic coast.

These results are particularly interesting since most of the considered taxa are sessile or slow moving invertebrates. Therefore, this suggests that they used similar diet resources in both locations. The case of the green crab Carcinus maenas is slightly different, as for this highly mobile species, migration toward higher intertidal levels for foraging activity has been shown to be usual during high tide [START_REF] Silva | Use of the intertidal zone by mobile predators: influence of wave exposure, tidal phase and elevation on abundance and diet[END_REF]. This species can thus be considered as a coupler that underlie landscape level food webs, as defined by [START_REF] Rooney | A landscape theory for food web architecture[END_REF].

Diversity monitoring highlighted significant differences in the composition of grazers between the two communities, in accordance with the tidal control of species distribution and abundances [START_REF] Raffaelli | Intertidal ecology[END_REF]. However, when considering isotopic composition, no significant difference between communities was evidenced, whether the abundance of grazers is accounted for or not. These results suggest that the two groups of grazers exhibited similar trophic functions within the two communities, despite some differences in species identities and abundances. Besides, within each community, the diversity of radula types and feeding mechanisms described for these grazers indicated that some functional complementarity occurs (for instance, P. vulgata is considered as a scraper of hard substrata, while Gibbula spp. seem rather to brush algae, [START_REF] Hawkins | A comparison of feeding mechanisms in microphagous, herbivorous, intertidal, prosobranchs in relation to resource partitioning[END_REF], and is likely to promote species coexistence in relatively high abundances.

By focusing on grazers, the present study confirms that considering species abundance or biomass in association with stable isotope approach is a fresh opportunity to bring some new insights about community functioning [START_REF] Cucherousset | Quantifying the multiple facets of isotopic diversity: new metrics for stable isotope ecology[END_REF][START_REF] Rigolet | Investigating isotopic functional indices to reveal changes in the structure and functioning of benthic communities[END_REF]. In this study, this approach allowed us to exclude significant difference in the trophic structure of grazers between the two communities, as discussed before. Without this, any evident conclusion would have been drawn, as the doubt could still subsist with a p-value of 0.08 (obtained for unweighted isotopic data of grazers), especially when specific composition and abundance varied between the two communities.

Conclusion

This study highlighted that the two widespread Fucus vesiculosus and F. serratus communities exhibited trophic structures that remained highly conserved over a year, despite some seasonal fluctuations in physiological processes and in species composition and abundance. Thus, such food web approaches should be carried on, not only at the seasonal scale but also at various temporal scales [START_REF] Mcmeans | Food web structure in temporally-forced ecosystems[END_REF], to better understand the dynamics of food webs, especially according to the specific features of their environment.

Furthermore, the two Fucus spp. communities exhibited similar trophic structure while they are located at different shore levels and exhibit some differences in their specific composition.

In this context of vertical zonation, it would be interesting to go further, and for instance have a look to the specific composition and food webs of several communities dominated by canopy-forming macroalgae that are established on the whole intertidal gradient.

Figure 1 :

 1 Figure 1: Mean ± SE of δ 15 N (‰) vs δ 13 C (‰) for primary producers and consumers of the

Figure 2 :

 2 Figure 2: Mean ± SE of δ 15 N (‰) vs δ 13 C (‰) for primary producers and consumers of the

Figure 3 :

 3 Figure 3: Annual mean of scaled δ 15 N vs scaled δ 13 C for primary producers and consumers of

Figure 4 :

 4 Figure 4: Annual mean of a) δ 13 C ± SE (‰) of shared taxa obtained in the F. vesiculosus community vs those obtained in the F. serratus community, and of b) δ 15 N ± SE (‰) of

Figure 5 :

 5 Figure 5: Dendrograms from clustering analyses conducted on the grazers' data; a) on square-

Table 1 :

 1 Isotopic diversity metrics calculated at each season and for each community, and their associated coefficient of variation (CV, in %).

		Date	Sept	Dec	March	June	CV
		Isotopic richness	0.590	0.565	0.528	0.413	13.3
	F. vesiculosus community	Isotopic divergence 0.765 Isotopic dispersion 0.607	0.729 0.535	0.695 0.429	0.743 0.461	3.8 13.1
		Isotopic eveness	0.785	0.791	0.774	0.844	4.0
		Isotopic uniqueness 0.455	0.349	0.394	0.500	14.6
		Date	Sept	Dec	March	June	CV
		Isotopic richness	0.269	0.415	0.389	0.308	25.4
	F. serratus community	Isotopic divergence 0.709 Isotopic dispersion 0.503	0.701 0.334	0.681 0.400	0.722 0.447	2.4 14.3
		Isotopic eveness	0.828	0.737	0.743	0.801	5.4
		Isotopic uniqueness 0.538	0.274	0.249	0.425	25.2

Table 2 :

 2 Ranges (1 st -99 th percentiles) and mean of potential contributions (%) of primary sources to the diet of several species of filter-feeders and grazers, according to SIAR mixing models. Analyses were carried out for each community and during all sampling seasons.

Table 3 :

 3 Abundance of grazers recorded at each period of observation in the two communities.

		Date	Sept	Dec	March	June
		Gibbula cineraria	0	2	0	2
		Gibbula pennanti	58	170	32	226
	F. vesiculosus	Gibbula umbilicalis	208	106	174	96
	community	Littorina littorea	6	12	16	2
		Littorina obtusata	172	76	118	86
		Littorina saxatilis	4	0	0	0
		Patella vulgata	32	62	20	22
		Date	Sept	Dec	March	June
		Gibbula cineraria	20	26	54	26
		Gibbula pennanti	130	430	508	240
	F. serratus	Gibbula umbilicalis	36	38	24	46
	community	Lamellaria perspicua	0	4	0	0
		Littorina obtusata	94	80	70	18
		Patella vulgata	2	12	36	32
		Tricolia pullus	0	0	2	0

ACKNOLEDGMENTS

The authors thank the SOMLIT network for providing isotopic data of particulate organic matter of our study area. Two anonymous reviewers and the associate editor are thanked for constructive comments. This work benefited from the support of the Brittany Regional Council and of the French Government through the National Research Agency with regard to the investment expenditure programme IDEALG ANR-10-BTBR.

Supplementary material 2: Mean ± SE (‰) of δ 13 C and δ 15 N of sources and consumers of the F. serratus community, with the number of replicates (n) analysed for each sampling period (September and December 2013 and March and June 2014). Groups: ER = Erect alga; EN = Encrusting alga; G = Grazer; FF = Filter-feeder; P = Predator.


Diego Carnevale
email: carnevalediego.carnevale@unine.ch

Srinivas Chinthalapalli

Geoffrey Bodenhausen

Exciting wide NMR spectra of static solid samples with weak radiofrequency fields 1 Exciting wide NMR spectra of static solid samples with weak radiofrequency fields

Keywords: NMR Spectroscopy, Solid-State NMR of Static Samples, DANTE, Hydration Water, Dipolar Interactions, Quadrupolar Interactions, Dipolar Echoes, Quadrupolar Echoes, Solid Echoes

Trains of short pulses in the manner of 'delays alternating with nutations for tailored excitation' (DANTE) have been applied to the Pake patterns of protons of water molecules trapped in a static powdered sample of barium chlorate monohydrate. The spin dynamics in the course of such experiments have been investigated by means of numerical simulations and compared with the ideal refocusing that can be achieved under magic-angle spinning. Solid echoes yield essentially undistorted lineshapes, in contrast to direct excitation without refocusing that leads to severe dispersions of the phases because of inhomogeneous interactions such as homonuclear dipolar couplings and anisotropic chemical shifts. The selectivity of DANTE sequences allows one to access 'slices' of the Pake pattern that can be related to particular crystallite orientations. Single-crystal spectra can therefore be extracted from powder spectra. A similar behavior is expected for both dipolar and quadrupolar echoes.

Introduction

Solid-state NMR is an invaluable tool for the structural characterization of systems where diffraction techniques are less effective due to dynamics or to a lack of long-range order. Valuable insight into dynamic processes such as chemical exchange and molecular reorientation can be obtained. When the interactions that affect nuclear spins in solids are anisotropic, [START_REF] Duer | Solid-State NMR Spectroscopy: Principles and Applications[END_REF] this results in static NMR lineshapes commonly referred to as 'powder patterns' that are inhomogeneously broadened. In samples spinning about the magic-angle, the properties of DANTE trains [START_REF] Bodenhausen | [END_REF]3] of radiofrequency (rf) pulses applied in a rotor-synchronized fashion have been thoroughly investigated. [4][5][6][7][8] In this paper, we turn our attention to the application of such pulse trains to static samples that are subject to inhomogeneous broadening. DANTE sequences can offer both a uniform broadband excitation extending over several MHz, and the selective excitation of chosen frequency ranges extending over a few kHz. These paradoxical features are particularly appealing to study samples that are subject to large inhomogeneous interactions, such as hyperfine couplings in paramagnetic systems, or dipolar interactions. [6,7] For the latter interactions, a spin system comprising only isolated pairs of nuclear spins, like water trapped in gypsum (CaSO4) [10] offers an instructive example. We have investigated the protons of water trapped in barium chlorate monohydrate, Ba(ClO3)2.H2O. [9] The distance between the two protons belonging to a given water molecule is ca. 1.6 Å, leading to a homonuclear dipolar coupling constant of ca. 30 kHz, giving rise to a nearly ideal Pake pattern [10]. The distance between two neighboring water molecules in Ba(ClO3)2.H2O is ca. 4.8 Å, resulting in intermolecular dipolar couplings below 1 kHz which barely affect the Pake pattern.

If one combines DANTE pulse trains with sample rotation about the magic angle, there is a synergy between the mechanical rotation, which refocuses the spatial parts of anisotropic interactions of rank 2 (but not of second-order quadrupolar couplings) to form rotational echoes, and the nutation due to the rf pulses that affects the spin part of the interactions. [6] Neglecting homogeneous losses, this allows one to excite a coherence (transverse magnetization) through the cumulative effects of small flip angles in a uniform manner over several MHz, provided all inhomogeneous interactions can be refocused by rotation about the magic angle.

In static samples, on the other hand, there are of course no rotational echoes, and it is far from obvious that the cumulative effects of a train of pulses can excite a coherence. In this study, we investigate some properties of both excitation and refocusing by DANTE pulse trains applied to static samples. The spin dynamics that occur during the pulse trains are analyzed by means of numerical simulations. The refocusing properties of DANTE echoes in static samples are compared with echoes of equivalent experiments performed under magic-angle spinning (MAS), where full refocusing can be achieved. The comparison serves as a test for our experiments in static samples. Applications to the Pake pattern of Ba(ClO3)2.H2O show how DANTE trains can be used to extract spectra corresponding to single crystals with different orientations with respect to the external magnetic field.

Results and discussion

In previous studies we have introduced the nomenclature to describe DANTE pulse trains applied to samples that are spinning at the magic angle, N being the number of rf pulses per rotor period and K the number of rotor periods that corresponds to the length of the entire pulse train, which therefore comprises M = K  N pulses. [6] In static samples, where the concept of a rotor period is meaningless, a DANTE train   solid echo scheme, one can use a

         10 10 D D x sequence (or                      M p M x p
) comprising two DANTE combs, both with M = 10, a delay between the two DANTE trains that may be set to   = 0, and step the relative phase  of the two  In order to understand the differences between static and spinning samples, we performed numerical simulations for a spin system comprising two equivalent dipolar-coupled I = 1/2 spins.

D

refocusing train, while alternately adding and subtracting the signals. As has been shown elsewhere for the excitation,6 each pulse acts on a rotational echo so that a cumulative effect is observed, generating the full signal intensity corresponding to a 90 pulse, i.e., at the end of the first

  F Tr t F       F I S    
Half-way during the sequence, provided coherence selection by phase cycling ensures that p = +1  p = -1, the signal drops to zero. This is due to the fact that p = +1 coherence (i.e., 〈𝐹 -〉) is selected during the first half of the echo whereas p = -1 (i.e., 〈𝐹 + 〉) is selected during the second half of the echo. In other words, no p = -1 coherence is present after the first block

x D , 10 1
, since phase cycling cancels this coherence order. In contrast, during the second block . During the first x D 10 train, as expected, no cumulative effect is observed since there are no rotational echoes. In the intervals between the pulses, the inhomogeneous interaction causes a dephasing of the p = +1 coherence and each pulse acts on partially dephased coherences, which, in contrast to spinning samples, results in a failure to build up any signal. As one can appreciate from Fig 1(b) and 1(c), the signal intensity created by the first pulse is = 0.31 in both spinning and static samples.  Surprisingly, after the p = +1  p = -1 transfer, half-way during the sequence, one observes a completely different profile, with a cumulative effect that leads to a build-up of the signal similar to that of the spinning case. In the intervals between the pulses, one observes an increase in signal intensity. This is solely due to free evolution under inhomogeneous interactions and merely resembles the refocusing effect due to the mechanical rotation observed in the spinning case of The spectra are highly distorted as a result of the dephasing that occurs during the  intervals between pulses. A simulation of an ideal Pake pattern is overlaid in (f) with a vertical scaling factor. Figures 1(g),(h) and (i) show, from left to right, the spectra that would result if one acquired the signal after 'truncated' spin echo sequences (g)

         1 10 D D x , (h)          5 10 D D x and (i)          10 10 D D x
, respectively, as indicated by black arrows in Fig. In order to obtain insight into the spin dynamics during a DANTE echo sequence applied to a static sample, we shall consider the shortest possible DANTE sequence

         2 2 D D x that   Tr t F    
can be seen as analogous to a solid echo. For the sake of comparison with the ideal case of a complete refocusing, the MAS condition will also be considered. A scheme depicting the pulse sequence, with its corresponding coherence transfer pathway, is shown in Fig. 2(a), for 0    . The relevant state of the system is indicated by the index (n). We chose a model system comprising two equivalent 1 = 0  p = +1, the rephasing effect during the second train with p = +1  p = -1 and the ability of the dipolar interaction to increase the signal intensity under free evolution. This latter feature may be seen as a partial refocusing of the internal interactions. We monitored the relevant singlequantum matrix elements before and after each rf pulse and at the end of the echo, as indicated by numbers in brackets in Fig 2(a). The state of the system at point (n) of the pulse sequence is described by , with the propagator U = for the interaction , which can be either an rf-pulse or a dipolar coupling, described either by the Hamiltonian or by . Since we make use of ideal (infinitely short) pulses, no interaction other than the rf pulse can take place between states (2) and (3). Therefore, rather than 'at time (n)', we shall speak of 'at point (n)' of the pulse sequence shown in Fig. 2(a). In the spinning case, at points (2), ( 4), ( 6) and ( 8), a rotational echo is formed and the dipolar interaction is fully refocused by the mechanical rotation and can therefore be completely ignored. Therefore, in the spinning case it can be shown that , , and . In the static case, on the other hand, one finds the following expressions:

(1)

    † 1 n U n U      exp iH      1 cos sin rf x y H F F         2 / 2 3cos 1 3 D z z H d I S IS          12 2 FF       34 2 FF       56 1 1 2 FF         78 1 FF     1 2 F   (2) (3) (4) (5) (6) (7)
.

The numerical values of these expectation values are given in Table 1 for d = 10 kHz, p = 1 s and intervals between pulses  = 100 s -p = 99 s. Equation 8 reveals that the dipolar interaction is not fully refocused at the end of a DANTE solid echo sequence. The rf pulses in the second refocusing DANTE train have different effects under spinning and static conditions, i.e., in the spinning case, the rf pulses lead to an increase of I  whereas, in the static case, the rf pulses result in a decrease of SQ coherence. This can be estimated by the variation of the relevant expectation values between points (4) and (5) = 0.2929 and -0.1527, for spinning and static cases, respectively, or between points ( 6) and (7) = 0.7071 and -0.3491, for spinning and static cases, respectively. These effects are highlighted by dashed arrows in Fig. 2 (b). Therefore, the descriptor evaluated during rf pulses in the second DANTE train of the solid echo sequence is always positive under MAS and always negative in static samples.

During the first DANTE train of the echo sequence on the other hand, is always

  2 3 2 cos 4 d F         3 3 1 cos 4 d F         4 33 cos cos 42 dd F                    5 1 3 3 2 2 cos cos 4 4 2 dd F                            6 1 3 3 9 1 cos 2 1 cos 2 1 cos 4 4 2 4
d d d F                                  2 7 33 cos cos 84 dd F                  22 8 1 3 3 3 9 cos cos cos 2sin 2 8 4 2 8 d d d d F                                      5,4' F     7,6 F     ,1 nn F      ,1 nn F   
positive during the pulses in both spinning and static samples. Furthermore, and only during the second refocusing train of rf pulses, the inhomogeneous dipolar interaction increases the projection onto the transverse plane during free evolution in static samples. This can be appreciated between points ( 5) and ( 6), where one finds = 0.4794. By contrast, in the intervals between rf pulses, this descriptor always vanishes under MAS, since two consecutive points, say ( 5) and ( 6), correspond to tops of rotational echoes, where all inhomogeneities are refocused. In the single-crystal case of Fig. 7) and ( 8) results in = -0.0213. This is in disagreement with what can be seen between points ( 5) and ( 6). However, we find that, when extensive powder averaging is performed, the descriptor evaluated in the intervals between rf pulses is always positive in static samples during the second train of a DANTE solid echo sequence. This latter feature is ensured by coherence transfer selection and reflects the partial refocusing effect of the second DANTE pulse train. As previously highlighted by the simulations of Fig. 1, at the end of the solid echo sequences, the DANTE trains indeed allow one to acquire reasonably undistorted lineshapes in static samples.

  6,5 F     8,7 F     ,1 nn F   
These spectra show that, by means of DANTE pulse trains, one can selectively excite 'slices' across an inhomogeneous lineshape. This amounts to say that a chosen 'window' of crystallite orientations within a powder pattern can be selectively excited and explored.

Figure 4 shows experimental spectra analogous to those of Fig. 3, with the exception that a roughly 4-fold weaker rf-field strength of 1 = 26 kHz (90 = 9.6 s) was used in a solution-state NMR spectrometer. The lower rf amplitude leads to the slightly distorted powder pattern of Fig.

4(a)

, where the shoulders of the Pake pattern are less pronounced compared to those of Fig. 3(a).

On the other hand, the DANTE spectra of Fig. 4(b-d) obtained with 1 = 26 kHz are substantially identical to those of Fig. 3(b-d), obtained 1 = 114 kHz. Subtle differences in the relative intensities of the peaks of Figs. 3 and4 are ascribed to variations in T1 observed for crystallites of BaClO3.H2O

with different orientations 15 bearing in mind that different recovery delays of 5 and 10 s were used in the experiments of Figs. 3 and4. These observations confirm that DANTE echo trains may be used to excite and refocus inhomogeneously broadened lines with line widths that greatly exceed the strength of the field. [6] When dealing with an isolated dipolar-coupled spin pair, as in our case, each single crystal gives rise to a doublet with a splitting determined by the magnitude of the coupling constant d and the angle  subtended between the main axis of the dipolar tensor and the external magnetic field. The two transitions of the doublet have frequencies where iso is the chemical shift, assumed to be isotropic. It is worth bearing in mind at this point that each single transition of the doublet is 'shared' by each of the two spins. In fact, if one could detect only one of the two protons, one would obtain exactly the same Pake pattern with half the intensity, i.e.,

. The splitting is maximum when  = 0, i.e., , vanishes at the magic angle  = 54.7, and becomes negative for  = 90,

  2 3 2 d D     
. Between the inner 'horns' of the pattern, each doublet can correspond to two different orientations. By contrast, outside these 'horns', near the 'shoulders', each doublet corresponds to a crystallite with a unique orientation. One can choose the parameters of a DANTE static echo sequence so as to obtain spectra that correspond either to a unique or to two crystal

    2 3 3cos 1 / 4 D iso d               22 F t I t S t       03 D d  
orientations by setting the carrier frequency νrf and the delay τ between adjacent pules according to:

(9)     1 cos 3 2 3 2 1       d . (10)
A system made up of a single isolated spin S = 1/2, subject to an anisotropic interaction such as a chemical shift anisotropy, would produce a powder lineshape made up of a single peak (rather than a doublet) for each crystal orientation. In such cases, each peak resulting from a DANTE echo can be ascribed to a single crystallite orientation. Thus DANTE-based techniques allow one to detect a subspectrum corresponding to a particular range of crystallite orientations. In spectra such as those shown in Fig. 3(b-d) and 4(b-d), one expects a range of crystallite orientations to contribute to the signal. The 'purity' of DANTE signals in terms of the number of that contribute depends on the width of the rf spikelets resulting from the DANTE trains. This width is determined by the total length of the rf sequence and, in the case of the solid echoes in this work, is proportional to (2M) -1 .

Figure 5 shows spectra which demonstrate how DANTE echoes may be tuned so as to explore particular sets of crystallite orientations. In Fig. 5(a), the static pattern obtained with a conventional solid echo is shown to guide the eye. Figure 5(b) shows that a 'horns-only' DANTE spectrum may be obtained by an appropriate choice of the carrier frequency and pulse interval. A 'single-shoulder' spectrum is shown in Fig. 5(e). In the latter case, a single transition of a doublet associated with a single crystal is excited. The carrier frequency is indicated by black arrows when different from 0 Hz.

      2 3 3cos 1 4 D rf iso d           
The necessity to resort to a second DANTE train for refocusing is demonstrated in Figure 6.

In (a), a spectrum obtained with a

         10 10 D D x
echo is shown. This is in very good agreement with the simulation of Fig. 1(i). Figure 6(b) shows the spectrum resulting from a single    x D 10 train, i.e., when no refocusing train is used. The lineshape obtained in the latter case is characterized by distortions that are in very good agreement with the simulations shown in Fig. 1(f). The partial failure to refocus the dipolar interactions in static samples at the end of a DANTE solid echo sequence results in distortions of the spectra that are analogous to those obtained if one inserts a long 'dead time' before starting signal acquisition. However, as may be appreciated in the experimental spectra of Figures 3(b-d) and 4(b-d), the extent of dephasing is perfectly acceptable in our case.

Conclusions

We have analyzed the response to DANTE trains of rf pulses applied to static samples in

Experimental details

A sample of ca. 50 mg Ba(ClO3)2.H2O (Alfa Aesar) was kept under vacuum (ca. 10 Pa) overnight prior to the experiments in order to minimize the adsorbtion of water which leads to a sharp isotropic peak in the middle of the Pake pattern. All 1 H spectra of Figure 3 excited with "hard" rf pulses have been recorded at the EPFL on a Bruker 400 spectrometer (9.4 T) with an Avance-II console, using 3.2 mm rotors in a triple resonance MAS probe designed for lowtemperature measurements near 100 K, but used at room temperature without microwave irradiation and without spinning. The rf-field amplitude was 1 = 114 kHz. A recycling delay of 5 s was used. All 1 H spectra of Figures 4, 5 and 6 excited with "soft" rf pulses have been recorded at the University of Neuchâtel on a Bruker 400 spectrometer (9.4 T) with an Avance-II console, using 5 mm tubes in a triple resonance probe designed for solution-state NMR. The rf-field amplitude was 1 = 26 kHz. A recycling delay of 10 s was used. All solid echoes were phase cycled for the selection of the p = 0  p = 1  p = -1 pathway by nesting Exorcycle [16] and Cyclops to produce an overall 16-step phase cycle. The delay between the two DANTE trains was 0    , in all cases. Numerical simulations were performed with SIMPSON, [18] using 2000 crystal orientations sampled with the REPULSION scheme. [19] Table 1 Expectation values of relevant operators at selected points in the pulse sequence

         2 2 D D x
of Fig. 2, evaluated using Equations [START_REF] Bodenhausen | [END_REF](3)(4)(5)(6)(7)(8). The relevant parameters are d = -10 kHz, 1 = 125 kHz, p = 1 s,  = 100 s -p = 99 s and   = 0. Pulses are considered as ideal with a vanishing duration. A single crystal is assumed, with the principal axis of the dipolar tensor perpendicular to the external magnetic field B0.

  n F  2 2 2 1 1 / 2  1 1 / 2 

  scheme used to excite solid echoes with  = /2.11,12 By themselves, such experiments cannot simultaneously refocus both linear interactions (chemical shifts) and quadratic interactions (dipolar or quadrupolar couplings).13 This can however be achieved by combining a solid echo sequence with a suitable prescription for cycling the phase  14. By analogy to the familiar          90 90 x solid echo scheme, one can use a

10 D

 10 blocks to refocus both chemical shifts and dipolar or K N D quadrupolar interactions. To this effect, one must select the coherence transfer pathway p = 0  p = +1  p = -1.13 The length p of the individual pulses must be p = 90/M, or, equivalently, their nutation angles must be = 2190/M = /(2M). If the individual pulses have a cumulative effect, each D10 train corresponds to a /2 pulse, and the 

Figure 1 (

 1 Figure 1(b) shows a simulation of the behavior of single-quantum (SQ) coherences IS   in a spinning sample in the course of the solid echo sequence          , 10 1

D

  block leads to a build-up of coherence with order p = -1 by conversion from the coherence with order p = +1 generated by the first x D , 10 1 block, owing to the cumulative effect.



D 10 1 D

 101 , p = -1 coherence is generated from the p = +1 coherence selected during the first block. At the end of the second  , block, the signal intensity is = 1, i.e., half of what was obtained after stems from the fact that we consider a solid echo rather than a Carr-Purcell echo. The dashed line in Fig. 1(b) passes through points at which the acquisition of FID's could by started (just before each pulse in the train) and indicates how the signal intensity of the resulting spectra would vary during such hypothetical experiments.

Figure 1 (

 1 Figure 1(c) shows a profile analogous to that of Fig. 1(b) that one obtains for a static nonspinning sample with the sequence         

Fig. 1 (

 1 Fig. 1(b). The dashed line has the same meaning as in Fig 1(b). It is interesting to note that, in contrast to the spinning case, where each pulse leads to a signal increase, in the static case each pulse results in a loss of signal during the second refocusing train. This decrease in intensity is

  left to right, one can appreciate the increase in signal intensity as the second DANTE train approaches a cumulative nutation angle of 90. The spectrum of Fig. 1(i) results from a complete  echo sequence. As expected, one observes three peaks corresponding to three rf spikelets spaced by 1/ = 30.03 kHz. Their envelope can be compared with the ideal static Pake pattern (red line) which extends over ca. 100 kHz. The intensities of the three peaks nicely reproduce that of the envelope of the static powder pattern.

  H spins with a homonuclear dipolar coupling d = -10 kHz, appropriate for a single crystal with a dipolar tensor perpendicular to the external magnetic field, and ideal pulses with flip angles  = /4 and delays between the pulses  = 100 s. No shift interaction was included for simplicity. The profiles obtained, assuming proper selection of the change in coherence order, are shown in Fig 2(b) with black and red lines for spinning (rot = 10 kHz) and static samples, respectively. Even with these drastic simplifications, the peculiar features highlighted in the profile of Fig 1(c) are preserved, i.e., the dephasing during the first train with p

  2(b), and in contrast to what was observed in the powder average of Fig 1(b), the last free evolution interval between (

Figure 3 (

 3 Figure3(a) shows an experimental solid-echo spectrum of the protons of water in a static sample of barium chlorate monohydrate (BaClO3.H2O). An almost ideal Pake pattern is observed, thus confirming, as discussed above, that intermolecular dipolar couplings can be neglected and that the two-spin system can be assumed to be isolated. The asymmetry in the shoulders of the pattern (the low-frequency or right-hand side being more pronounced than the high-frequency side) is due to the shielding anisotropy of the protons. Figures 3(b), (c) and (d), show solid echo spectra obtained with different spin-echo sequences          5 5 D D x

Figure 5 (

 5 Figure 5(c) shows that a 'single-horn' spectrum may be obtained simply by decreasing the pulse intervals used in (b).Figure 5(d) shows a 'shoulders-only' spectrum of the Pake pattern of Fig.

Figure 5 (

 5 d) shows a 'shoulders-only' spectrum of the Pake pattern of Fig.5(a). Near the shoulders, doublets associated with single-crystallite orientations may be explored.

  solid-state NMR spectroscopy. In contrast to MAS experiments, where it is possible to use a single rotor-synchronized DANTE train for direct excitation without resorting to refocusing, in static samples one can only obtain reasonably undistorted lineshapes if one uses spin echoes that are refocused by a second DANTE pulse train. This has been shown both by numerical simulations and by experiments performed on the protons of hydration water in barium chlorate monohydrate. The spectral bandwidths that one can access with DANTE techniques in static samples open up new ways for exploring the responses of selected crystallites in powder samples.

Figure 1 ((

 1 Figure 1 (a) Scheme representing a solid echo experiment comprising two D10 DANTE sequences for excitation and refocusing, i.e., either a

Figure 2 (

 2 Figure 2 (a) Scheme representing a solid echo experiment comprising two D2 DANTE sequences, with corresponding coherence transfer pathway diagram. (b) Numerical simulations of the experiment shown in (a) for spinning (

Figure 3 (

 3 Figure 3 (a) Experimental static lineshape due to pairs of dipolar-coupled protons in a static nonspinning sample of barium chlorate monohydrate, obtained by Fourier transformation of the decaying half of a solid echo excited by a conventional 90 o --90 o - sequence with 90 o pulses of 2.2 s duration and = 50 s. (b-d) Spectra obtained by Fourier transformation of the decaying halves of solid echoes excited by DANTE sequences (b)

Figure 4 (

 4 Figure 4 (a) Experimental static lineshape due to pairs of dipolar-coupled protons in a static nonspinning sample of barium chlorate monohydrate, obtained by Fourier transformation of the decaying half of a solid echo excited by a conventional

Figure 5 (

 5 Figure 5 (a) Experimental static lineshape as in Fig. 3(a) shown for comparison. (b-e) Spectra obtained by Fourier transformation of the decaying halves of solid echoes excited by DANTE sequences (b)

  Figure 6 (a) Experimental static lineshape obtained with a sequence

  4(c) shown for comparison. (b) Experimental spectrum resulting from a single DANTE sequence with  + p = 33.33 s,  ' = 0 and p = 0.96 s, with a weak rf-field 1 = 26 kHz. The recycling delay was 10 s and 16 transients were averaged in all cases. The carrier frequency was set to 0 Hz in both (a) and (b). No line broadening was applied. Zero-th and first-order phase corrections were -303 and 308, and -288 and 308°, in (a) and (b), respectively.

Acknowledgements

This work was supported by the Swiss National Science Foundation (SNSF), the Ecole Polytechnique Fédérale de Lausanne (EPFL), the University of Neuchâtel, the Neuchâtel Platform of Analytical Chemistry (NPAC), the Swiss Commission for Technology and Innovation (CTI) and the European Research Council (ERC, project 'Dilute para-water').