Joseph M Kenworthy
email: joseph.kenworthy@sb.roscoff.fr

David M Paterson

Melanie J Bishop

Multiple stressor impacts on benthic assemblages

Keywords: Multiple Stressors, Context dependence, Nutrient Enrichment, Disturbance, Macrobenthos, Microphytobenthos, Field Experiments

Stressors to ecological communities often overlap in time and space and may have additive, synergistic or antagonistic effects. Nutrient enrichment and physical disturbance are two commonly co-occurring stressors to estuarine ecosystems, but their combined effects have mainly been investigated in mesocosm experiments of unknown relevance to field scenarios. Here, the interacting effects of these two stressors were examined at two field locations -Botany Bay and Lane Cove, New South Wales, Australia -using a fully orthogonal manipulative experiment. All possible combinations of zero, low and high intensities of nutrient enrichment and physical disturbance on macrofaunal and microphytobenthic communities were examined. Effects of stressors were generally site-specific and additive, differing in terms of magnitude of effects, although some idiosyncratic interactive effects were seen on selected species. Where effects of stressors were observed, nutrient enrichment generally increased microphytobenthic biomass and altered the macrofaunal community structure while physical disturbance produced limited impacts. The divergent results of this and previous mesocosm experiments, which found primarily interactive effects of the stressors, highlights the importance of undertaking field experiments that offer a greater element of realism. Furthermore, this study, in finding differing responses to stressors at the two sites, highlights the importance of environmental context in mediating effects.

Introduction

How organisms respond to naturally occurring and anthropogenic stressors has been a subject that has dominated the marine ecological literature for many decades [START_REF] Dayton | Competition, disturbance and community organization: the provision and subsequentutilization of space in a rocky intertidal community[END_REF][START_REF] Connell | Diversity in Tropical Rain Forests and Coral Reefs High diversity of trees and corals is maintained[END_REF][START_REF] Paine | Intertidal landscapes : disturbance and the dynamics of pattern[END_REF][START_REF] Menge | Community regulation: Variation in disturbance, copetition, and predation in relation to environmental stress and recruitment[END_REF][START_REF] Hall | Physical disturbance and marine benthic communities: life in unconsolidated sediments[END_REF][START_REF] Crain | Interactive and cumulative effects of multiple human stressors in marine systems[END_REF]. Early studies considered the effects of stressors independently from one another and on individual species, yet stressors to natural ecological systems rarely occur singularly [START_REF] Crain | Interactive and cumulative effects of multiple human stressors in marine systems[END_REF], Halpern et al. 2008) and species rarely occur alone. Effects of multiple stressors cannot easily be predicted from the effects of singular stressors because, when combined, they are rarely neutral but have additive, subtractive or synergistic effects [START_REF] Crain | Interactive and cumulative effects of multiple human stressors in marine systems[END_REF][START_REF] Darling | Quantifying the evidence for ecological synergies[END_REF], Bijma et al. 2013). Yet many studies continue to examine the effects of stressors individually and on single species or small sub groups of taxa [START_REF] Crain | Interactive and cumulative effects of multiple human stressors in marine systems[END_REF]. As coastal development and climate change continue to increase the frequency and intensity of stressors [START_REF] Halpern | A Global Map of Human Impact on Marine Ecosystems[END_REF], Bijma et al. 2013) there is need to understand the combined effects of stressors, so as to develop appropriate policy and management strategies to manage and perhaps minimise their impact.

Of the studies that have considered the effects of multiple stressors on organisms, many have been conducted in the controlled environment of experimental mesocosms, with species isolated from their habitats and communities [START_REF] Hicks | Impact of biodiversityclimate futures on primary production and metabolism in a model benthic estuarine system[END_REF][START_REF] Godbold | Habitat structure mediates biodiversity effects on ecosystem properties[END_REF]. Although such studies allow the effects of stressors to be examined in the absence of other confounding influences, the extent to which results can be applied to natural systems is unclear because they fail to take into consideration the role of the environmental and biotic context in mediating stressor impacts. For example, organisms can make use of microhabitats to minimise exposure to stressors [START_REF] Jones | State-dependent habitat selection by an intertidal snail: the costs of selecting a physically stressful microhabitat[END_REF] and, under natural conditions, ecological interactions such as competition, facilitation and predation may dampen or exacerbate stressor impacts (Christensen et al. 2006[START_REF] Hicks | Impact of biodiversityclimate futures on primary production and metabolism in a model benthic estuarine system[END_REF]. In situ mesocosms have been used effectively to add an element of realism to assessments of stressor impacts (e.g. Christensen et al. 2006). Nevertheless, while studies such as these offer interesting insights and explore important relationships between changes in ecosystem function and biodiversity under scenarios of environmental change, they do not represent natural conditions and field studies are still needed as part of the experimental framework (for a review of the topic see [START_REF] Crain | Interactive and cumulative effects of multiple human stressors in marine systems[END_REF]Przeslawski et al. 2015 and references therein).

Estuarine environments are among the most heavily impacted in the world, with greater than 40% of the world's human population living within 100 km of the coast. Among the plethora of stressors affecting these systems on a daily basis, nutrient enrichment and physical disturbances of sediments are often singled out as the most severe [START_REF] Gray | Marine biodiversity patterns, threats and conservation needs[END_REF]. Leaching of nutrients from the terrestrial environment, atmospheric deposition and decomposition are natural sources of nutrient loading in these environments but these can become exacerbated by human influences [START_REF] Nixon | Coastal marine eutrophication -a definition, social causes, and future concerns[END_REF]. For example, the discharge of sewage into aquatic environments, as well as run-off of nutrient-rich fertilisers, cleaning products and animal wastes from the land can enhance delivery of nitrogen and phosphorus to estuarine systems [START_REF] Nixon | Coastal marine eutrophication -a definition, social causes, and future concerns[END_REF], Vitousek et al. 1997a).

Where nitrogen and/or phosphorous is a limiting resource, addition of these nutrients has the potential to greatly stimulate primary productivity (Vitousek et al. 1997a, Cloern 2001). Excess nutrients have been linked to eutrophication events worldwide whereby algal blooms are facilitated, ultimately leading to hypoxic and anoxic conditions through over-stimulation of oxygen-consuming microbial decomposition (Vitousek et al. 1997b).

High human population densities around estuaries also facilitate many small scale disturbances to estuarine sediments through recreation -e.g. boat wake, anchorage, propeller scarring, coastal walking (Bishop 2005[START_REF] Rossi | Human trampling as short-term disturbance on intertidal mudflats: effects on macrofauna biodiversity and population dynamics of bivalves[END_REF]) -and as a consequence of livelihood exploitation -e.g. bait digging, fishing, dredging [START_REF] Wynberg | Disturbance associated with bait-collection for sandprawns (Callianassa kraussi) and mudprawns (Upogebia africana): Long-term effects on the biota of intertidal sandflats[END_REF][START_REF] Somerfield | Interrelationships in community structure between shallow-water marine meiofauna and macrofauna in relation to dredgings disposal[END_REF], Brown & Wilson 1997). These physical disturbances have been widely studied and can lead to the disturbance and redistribution of sediments [START_REF] Hall | Physical disturbance and marine benthic communities: life in unconsolidated sediments[END_REF]. Such disturbances are likely to cause physical damage to sediment-dwelling organisms or burrows [START_REF] Hall | Physical disturbance and marine benthic communities: The effects of mechanical harvesting of cockles on non-target benthic infauna[END_REF]. This physical disturbance has the potential to alter the distribution, abundance and diversity of macrofaunal assemblages [START_REF] Fraterrigo | Disturbance-driven changes in the variability of ecological patterns and processes[END_REF]. At a larger scale, natural events such as storms also cause physical disturbances to sediments although less frequently, offering the potential for recovery of sediment communities between events. These events loosen sediment, making it more susceptible to erosion and further stimulating damaging scour impacts [START_REF] Yeo | Intertidal catastrophes: effect of storms and hurricanes on intertidal benthos of the Minas Basin, Bay of Fundy[END_REF]. While sediment grain size can mediate the effect of disturbance on communities [START_REF] Lindegarth | Patterns of distribution of macro-fauna in different types of estuarine, soft sediment habitats adjacent to urban and non-urban areas[END_REF], grain size itself can also become altered by intense disturbance effects (Bishop 2005) thereby facilitating a change in community structure.

The aim of this study was to explore how the stressors, nutrient enrichment and physical disturbance, interact under natural field conditions. Nutrient enrichment and physical disturbances often overlap in time and space. For example, nutrient enrichment influences whole catchments, within which physical disturbances may also occur at smaller scales. Additionally, storm events that flush nutrient pollution into estuarine and coastal areas may also cause physical disturbance [START_REF] Harris | Shelf and deep-sea sedimentary environments and physical benthic disturbance regimes: A review and synthesis[END_REF]. Despite this, most studies that have examined effects of these stressors on sediment communities have done so independently, and those that have examined interacting effects have done so in small-scale mesocosm experiments (see [START_REF] Widdicombe | The interaction between physical disturbance and organic enrichment: An important element in structuring benthic communities[END_REF], Austen & Widdicombe 2006). According to [START_REF] Huston | A general hypothesis of species diversity[END_REF] dynamic equilibrium model, that posits that larger disturbances will be required to disrupt competitive dominance when productivity is high, the two stressors are predicted to display non-additive effects. Mesocosm experiments provide support for this hypothesis [START_REF] Widdicombe | The interaction between physical disturbance and organic enrichment: An important element in structuring benthic communities[END_REF], Austen & Widdicombe 2006). In buckets, experimental manipulations of nutrient enrichment (via addition of dried and powdered Ascophyllum) and physical disturbance (via surface raking) revealed that diversity was lower than expected when low frequencies of physical disturbance were applied in combination with high levels of organic enrichment or vice versa [START_REF] Widdicombe | The interaction between physical disturbance and organic enrichment: An important element in structuring benthic communities[END_REF], Austen & Widdicombe 2006). Diversity was higher than expected when both disturbance and enrichment were either high or low [START_REF] Widdicombe | The interaction between physical disturbance and organic enrichment: An important element in structuring benthic communities[END_REF]. Despite these results, it is unknown whether these non-additive effects also occur in field systems in which environmental conditions may buffer effects and recruitment of fauna is possible. Here, manipulative field experiments were conducted in two estuaries of eastern Australia to test the hypotheses that (1) the two stressors would display non-additive effects on microphytobenthic and macrofaunal communities, that are not easily predicted from their independent effects and (2) the nature of interactions would vary across field sites that differ in biotic and abiotic conditions.

Materials and Methods

Study site

Field experiments were conducted between May and September 2012 at two locations within Sydney, New South Wales, Australia: Tambourine Bay within Lane Cove River (33°49'39"S 151°09'38"E); and Woolooware Bay within Botany Bay (34°01'11"S, 151°07'46"E). Sites were unvegetated intertidal mud flats, adjacent to mangrove habitat. Each was within 15 km of the estuary mouth, was situated in a highly urbanised catchment, and had sandy-mud sediments.

Sites were away from storm-water drains, which transport nutrients into estuaries. Although the sites may be subject to some, minimal, trampling and the occasional boat run-aground, neither was subject to background raking or substantial bait-digging prior to experimental intervention.

At an intertidal elevation of ~0.5 m above mean low water springs, 70 square plots (0.5 x 0.5 m in size) were randomly established, and marked by a single post in the upper left corner of the plot.

Each plot was separated by approximately 3 metres.

Experimental approaches

The interactive effect of stressors was determined using a fully orthogonal experimental design with two factors, nutrient enrichment and physical disturbance. Each factor had three levels of disturbance intensity: zero, low or high. Seven plots were randomly assigned to each of the resulting nine experimental treatments. The remaining seven plots were procedural controls for the method of nutrient enrichment (see below).

Physical disturbance was manipulated by raking sediments (50 cm wide rake) to a depth of 2-4 cm.

Raking is one of the most commonly used methods for physically disturbing sediments (e.g. [START_REF] Cowie | Effects of physical disturbance on an estuarine intertidal community: field and mesocosm results compared[END_REF][START_REF] Whomersley | Response of intertidal macrofauna to multiple disturbance types and intensities -an experimental approach[END_REF], and mimics cockle hand raking [START_REF] Kaiser | Disturbance of intertidal soft-sediment benthic communities by cockle hand raking[END_REF][START_REF] Mistri | Disturbance of a soft-sediment meiobenthic community by clam hand raking[END_REF]. For plots assigned to the low or high physical disturbance, an area of approximately 1 m 2 , centring on but extending beyond the experimental plot was raked in a cross-hatched pattern. The low treatment consisted of two strokes of the rake, perpendicular to one another. This level of disturbance has previously been shown to illicit a response from intertidal communities [START_REF] Whomersley | Response of intertidal macrofauna to multiple disturbance types and intensities -an experimental approach[END_REF]. The high treatment consisted of 6 strokes, each stroke perpendicular to the previous. This disturbance was applied at the start of experiment and then monthly, over a four-month period.

Nutrient plots were enriched using Scotts Osmocote Pro, 8-9 month coated fertiliser pellets (N:P:K ratio of 16:4.8:8.3). These pellets which gradually release nutrients provide a controlled method of testing the effects of chronic nutrient enrichment in soft sediment benthic environments without need for replenishment [START_REF] Worm | In situ nutrient enrichment: Methods for marine benthic ecology[END_REF]. Plots were given 0 g (zero), 500 g (low) or 1000 g (high) of fertiliser. The high nutrient treatment was based on the level of nutrient loading that might be experienced in the vicinity of the discharge point of a moderately sized sewage treatment plant [START_REF] Morris | Organic pollution and its effects : a short-term transplant experiment to assess the ability of biological endpoints to detect change in a soft sediment environment[END_REF], 2003a[START_REF] O'brien | Multiple sources of nutrients add to the complexities of predicting marine benthic community responses to enrichment[END_REF]) and the low treatment was set at half of this.

For each of the plots assigned to the high or low nutrient treatment, nutrients were dispensed via five bags per plot, made from nylon panty-hose, among which the fertiliser was evenly distributed. These bags were spread evenly within each plot and were buried approximately 2-4 cm below the surface of the sediment. The nylon provided a fine permeable membrane through which nutrients could leach out into the plots. A procedural control tested for any experimental artefacts associated with burying the fertiliser; for this treatment nylon bags contained sediment in place of fertiliser and were deployed in the same manner as the nutrient treatments. Nylon bags containing slow release fertiliser or sediment (for the procedural control) were added to plots at the start of the experiment.

Sampling

Prior to initial manipulation of stressors, the chlorophyll and organic content of a subset (n = 25) of plots was sampled to determine background conditions at each site. Additionally, the spectral reflectance of the sediment and the macrofaunal community were sampled in each plot immediately prior to the manipulation of stressors. All variables were subsequently sampled monthly, for four months, in the case of sediment properties and at 2 (July) and 4 (September) months for macrofauna. Sampling of chlorophyll a content and spectral reflectance were together used as proxies for the biomass of microphytobenthos [START_REF] Tolhurst | Content versus concentration: Effects of units on measuring the biogeochemical properties of soft sediments[END_REF][START_REF] Kromkamp | Relationship of intertidal surface sediment chlorophyll concentration to hyperspectral reflectance and chlorophyll fluorescence[END_REF]. Sampling was conducted immediately prior to each re-application of the physical disturbance treatment. Sampling at Lane Cove was not possible in the first month following initial disturbance due to large amounts of overlying water caused by a sizable low pressure system. The location of sample collection within each plot at each sampling time was noted, so as to avoid repeated collection of samples from the same area.

The sediment organic content and chlorophyll a concentration was assessed through the contact coring method [START_REF] Ford | Grazing on intertidal microphytobenthos by macrofauna: is pheophorbide a a useful marker?[END_REF] whereby the top 2 mm of the sediment surface was flashfrozen with liquid nitrogen and then freeze dried. A single randomly-positioned 2463 mm 2 core was collected from each plot at each sampling time. Over a period of 48 hours, photosynthetic pigments were extracted from a 200 mg subsample of sediment from each core using 1.5 ml of 90% acetone under dark conditions within a -80 °C freezer. Samples were agitated after 24 hours for 10 seconds by using a vortex mixer. The chlorophyll a concentration of the acetone solution was determined spectrophotometrically using the method of [START_REF] Jeffrey | New spectrophotometric equations for determining chlorophylls a, b, c1 and c2 in higher-plants, algae and natural phytoplankton[END_REF] and the chlorophyll a content of sediment was calculated per unit area (mg m -2 ). A second 2 g subsample of sediment was taken from each contact core to determine the organic content through loss-onignition (450 °C for 4 hours).

An Ocean Optics USB2000 spectroradiometer was used to measure the spectral reflectance of the sediment surface in situ. Reflectance values (R) were made in the visible (675 nm) and infra-red (750 nm) parts of the spectra, and used to calculate the Normalised Difference Vegetation Index (NDVI), a measure of the photosynthetically-related biomass based upon reflectance of chlorophyll a in the sediment [START_REF] Kromkamp | Relationship of intertidal surface sediment chlorophyll concentration to hyperspectral reflectance and chlorophyll fluorescence[END_REF]): NDVI = (R750 -R675) / (R750 + R675) Three measurements were collected per plot allowing an average NDVI to be calculated.

Reflectance measurements were discarded where there was interference from surface water. Nevertheless, at each sampling time measurements from at least n = 3 plots per treatment could be included in the analyses.

One large core (10 cm diameter, 10 cm depth) was collected from each plot to quantify macrofaunal biodiversity each of the sampling times indicated above. Sediment cores were taken from between nylon bags, so as not to disrupt dispense of nutrients. Sediment core samples were sieved through a 500 µm diameter mesh and material retained on the sieve was fixed in 10% buffered formalin. Retained material was subsequently transferred into 70% ethanol and examined under a dissecting microscope to separate fauna from other remaining material. Fauna were identified to species level or morphospecies where this was not possible.

Statistics

Permutational analyses of variance (PERMANOVA: [START_REF] Anderson | A new method for non-parametric multivariate analysis of variance[END_REF], Anderson et al. 2008) were used to analyse univariate and multivariate data. Although initially developed for multivariate application, PERMANOVA can also be run on univariate data (Anderson et al. 2008) and has the advantage over ANOVA that it does not have assumptions regarding the underlying distribution of the data and can be used on any distance matrix (Anderson et al. 2008). Multivariate analyses, using Bray Curtis dissimilarities, were run on macrofaunal composition data. Macrofaunal composition data was square-root transformed prior to PERMANOVA in order to down-weigh the effect of species dominance and ordinated using two-dimensional non-metric multidimensional scaling (nMDS). Univariate tests, using Euclidean distance matrices, were run on each of sediment organic content, chlorophyll a content, NDVI, Shannon's diversity of macrofauna, total abundance of macrofauna, species richness of macrofauna, as well as the abundance of macrofaunal species that were key discriminators of multivariate differences among treatments.

First, for macrofauna and NDVI variables, three-way analyses on time 0 data, collected prior to application of perturbations, and including the factors nutrient enrichment (fixed; 3 levels: zero [HD]) and site (fixed; 2 levels) tested for any pre-existing differences in variables of interest among plots and between sites that coincided with their treatment assignment. Due to only a subset of contact core samples taken in the first month we were unable to run a complete analysis testing differences between treatments for chlorophyll a and organic content, however a one-way analysis was conducted testing for differences between sites. Second, four-way analyses, with the factors time (4 levels for most variables [1, 2, 3, 4 months after perturbation], and 2 levels for macrofauna [2, 4 months]), site (2 levels, random), treatment (2 levels: undisturbed, disturbance control) and plot (random; nested within site and treatment) tested for experimental artefacts of the method of nutrient application. Third, five-factor analyses with the factors site (random, 2 levels); nutrient enrichment (fixed; 3 levels); physical disturbance (fixed; 3 levels); plot (random, 7 levels, nested within site x nutrients x disturbance) and time (random, 2 or 4 levels) tested for interacting effects of the two stressors across both sites and all time periods. The inclusion of plot as a nested factor enabled time to be treated as a repeated measure. Following these analyses pairwise post hoc tests were conducted to identify significant differences between factors. Where the number of possible permutations was lower than 100, Monte Carlo (MC) testing was run to generate p-values from constructed asymptotic permutation distributions for the pseudo-F statistic. All analyses were conducted using the PRIMER v6 statistical program with the PERMANOVA+ addition (Clarke & Gorley 2006, Anderson et al. 2008).

[0N], low [LN], high [HN]), physical disturbance (fixed; 3 levels: zero [0D], low [LD], high
The macrofaunal multivariate analysis revealed large spatial and temporal differences in communities resulting in strong interactions between month and site. These prevented the factors of interest (nutrient enrichment and physical disturbance) from being appropriately tested and so separate tests were run for each month and site using a reduced model including only the factors nutrient enrichment and physical disturbance. Key discriminating species, contributing to multivariate differences in macrofaunal community structure, were identified by SIMPER analysis and were defined as those having a dissimilarity/standard deviation ratio > 1 between nutrient or physical disturbance treatments. Of these, species that were present at both sites were analysed using the complete 5-factor model, with abundances 4 th root transformed. Discriminating species that were unique to a site were analysed under the reduced 2-factor model. Permutational multivariate dispersions (PERMDISP) were analysed alongside the multivariate PERMANOVAs to assess the extent to which any treatment effects were driven by differences in dispersion between treatments and unless otherwise indicated were non-significant.

Results

Microphytobenthic component

Prior to experimental manipulations there were no differences in organic content or chlorophyll a content of sediments between the two sites, although NDVI was significantly greater at Lane Cove than Botany Bay (main effect of site PERMANOVA: p < 0.05; see supplemental materials). Across the two sites, there were no pre-existing differences in NDVI among plots that corresponded to treatment assignments (PERMANOVA p > 0.05, see supplemental materials; insufficient plots were sampled to address this question for organic content and chlorophyll a). At none of the sampling times following application of stressors were there experimental artefacts of the method of fertiliser burial on any of the three variables, organic content, chlorophyll a or NDVI (PERMANOVA p > 0.05; see supplemental material). Organic content did not respond to the addition of stressors at either site (Table 1).By contrast, site-specific effects of stressors on the two measures of MPB biomass, chlorophyll a concentration and NDVI were observed (Table 1). Neither variable displayed interactive effects between the two stressors so additive effects could be interpreted. Chlorophyll a concentration displayed a significant interaction between physical disturbance, site and month (Table 1; Figures 1A,B), whereas there was no effect of physical disturbance on NDVI at either site (Table 1). In Botany Bay (Figure 1A), although a slight negative impact of high physical disturbance on chlorophyll a was observed in August (month 3), prior to September (month 4) the effects of disturbance were non-significant (a posteriori pairwise comparisons p > 0.05; 0D = LD = HD). In September, plots receiving the high physical disturbance treatment had a significantly lower chlorophyll a concentration than those not receiving physical disturbance (t = 1.99, p(perm) = 0.048). There were no differences between the undisturbed and low disturbance treatments (t = 1.59, p(perm) = 0.113), or the low and high disturbance treatments (t = 0.14, p(perm) =0.898). At Lane Cove (Figure 1B), lower levels of chlorophyll were observed in plots receiving high than low physical disturbance in July (month 2; HD < LD, t = 3.42, p(perm) = 0.002), but in August these two treatments did not significantly differ, and there were no significant differences between other pairs of treatments in either July or August (a posteriori pairwise comparisons: p > 0.05). In September, low disturbance resulted in significantly greater concentrations of chlorophyll a than in the undisturbed (t = 2.34, p(perm) = 0.022) or high disturbance treatment (t = 2.97, p(perm) = 0.004), but there was no difference between the high disturbance and undisturbed treatments (t = 0.71, p(perm) = 0.497) (LD > 0D = HD).

Despite chlorophyll a displaying a significant interaction between nutrient addition and month (N x M interaction; Table 1) and a weak trend for a greater concentration of in plots receiving a low or high nutrient addition than no nutrients (Figure 1C, D), in none of the months were significant differences among nutrient treatments found (a posteriori pairwise comparisons: p > 0.05). By contrast, NDVI displayed a significant interaction between nutrient enrichment and site (Table 1), with effects of nutrient enrichment apparent in Botany Bay only (Figure 2). In Botany Bay, plots receiving either a low (t = 2.16, p(perm) = 0.032) or high nutrient addition (t = 2.75, p(perm) = 0.011) had a significantly greater NDVI than unenriched plots. There were no differences between the low and the high treatment (t = 0.63, p(perm) = 0.557) (0N < LN = HN).

Macrofauna

Analysis of macrofaunal community structure prior to manipulations revealed that multivariate community composition differed significantly between the sites (Pseudo-F (1,108) = 31.63, p(perm) = 0.001), with a greater abundance of invertebrates per plot at Lane Cove than Botany Bay (Pseudo-F (1,108) = 3.70, p(perm) = 0.031). Sixty-five species were identified, of which 28 were common between the two sites, 19 species were unique to Botany Bay and 18 were unique to Lane Cove. Shannon Diversity and total plot species richness did not significantly differ between the two sites (PERMANOVA p > 0.05; see supplemental materials). At neither of the sites were there pre-existing differences among plots that corresponded to treatment assignments (see supplemental materials). Furthermore, at none of the sampling times were there experimental artefact associated of the method of nutrient addition on macrofauna (PERMANOVA p > 0.05; see supplemental materials).

In the analysis comparing stressor impacts to macrofauna between the two sites, and across all sampling times, there was no effects of nutrient enrichment or physical disturbance on community composition or biodiversity indices, however there was a significant interaction between month and site (PERMANOVA: p(perm) < 0.05). When sites and times were considered separately, stressor effects on macrofauna could not be distinguished in July (PERMANOVA, p > 0.05) and in September, following four months of continued exposure to stressors, there was no interacting effect of nutrients and physical disturbance on any of the measures of macrofaunal community structure, at either site, allowing interpretation of main effects (Table 2). Whereas the September analysis revealed no effect of physical disturbance on any of the measures of macrofaunal community structure, nutrient enrichment affected multivariate community composition at Botany Bay and at Lane Cove it had a weak, though non-significant effect on this variable (Table 2; Figure 3). At Botany Bay, the highly enriched treatment was significantly different to the unenriched treatment only (t = 1.63, p(perm) = 0.031), with no differences between the low and the highly enriched treatments (t = 1.36, p(perm) = 0.077) or between the low enrichment and unenriched treatments (t = 1.04, p(perm) = 0.386). Additionally at Botany Bay the multivariate dispersions were significantly greater in the enriched plots in comparison to the controls (PERMANOVA, a posteriori tests, 0N < LN = HN; PERMDISP: F(2,58) = 8.94, p(perm) = 0.002). There were no treatment effects on Shannon diversity for either Botany Bay or Lane Cove (Table 2). However, for Lane Cove, there was a treatment effect of nutrient enrichment on the total macrofaunal abundance whereby increasing enrichment caused a decrease in total abundance (Table 2; PERMANOVA, a posteriori tests, 0N > LN > HN). Analysis of dispersions also revealed increased nutrient enrichment significantly decreased the dispersion of abundances at Lane Cove with no differences in dispersion of either low or highly enriched treatment (0N > LN, HN; PERMDISP: F(2,58) = 7.06, p(perm) = 0.027). SIMPER analysis identified six discriminating species contributing most to dissimilarity between nutrient treatments in Botany Bay, four of which coincided with those found in Lane Cove. These were Mysella sp., Mediomastus australiensis, Prionospio sp., and Nephtys australiensis. These species were among the most abundant species found at each site. The additional discriminating species at Botany Bay were Salinator fragilis and Owenia australis. Lane Cove had a total of 12 discriminating species which also included two species of Gammarus amphipods, Oedicerotidae sp. amphipods, Scoloplos sp., Laternula sp., Platynereis uniseris, Australonereis ehlersi and large nematodes.

In repeated measures analyses that included both sites, M. australiensis did not display any significant effects of nutrient enrichment or physical disturbance at either of the sites or at any of the sampling times (Table 3). Nutrient enrichment caused a significant alteration of the abundance of Prionospio sp. at Botany Bay only (nutrient enrichment x site interaction; Table 3; a posteriori pairwise comparisons: p < 0.05; Figure 4). Pairwise comparisons revealed that at Botany Bay, the high nutrient enrichment plots had significantly lower Prionospio sp. abundances than the unenriched plots (t = 2.42, p(perm) = 0.016) whereas there were no significant differences between the unenriched and low enrichment plots, or the low and high enrichment plots (p > 0.05).

Across both sites and all sampling times, there was a significant interaction between nutrient enrichment and physical disturbance for the species N. australiensis (Table 3; Figure 4). There were no significant differences due to the impact of disturbance among plots that received either zero or high enrichment (a posteriori pairwise comparisons: p > 0.05). Among plots that received low nutrient enrichment, abundances of N. australiensis were significantly greater in plots that also received low physical disturbance than those that were not disturbed (LD > 0D; t = 16.64, p(perm) = 0.013), with no significant difference between plots receiving high or low physical disturbance(t = 0.40, p(perm) = 0.829) and between plots receiving high or no physical disturbance (t = 1.94, p(perm) = 0.223). By contrast, among plots receiving high or zero nutrient enrichment, there was no significant effect of physical disturbance on N. australiensis abundance (a posteriori pairwise comparisons: p > 0.05). When the interaction was examined around the other way around, there was no significant effect of nutrient enrichment, within any of the three levels of physical disturbance (a posteriori pairwise comparisons: p > 0.05).

Mysella sp. displayed a three-way interaction between nutrient enrichment, physical disturbance and month, with no differences between sites (Table 3; Figure 4). Among unenriched plots, there was no significant effect of physical disturbance in either of the months (a posteriori pairwise comparisons: p > 0.05). Among plots subjected to low nutrient enrichment, abundances were greater in plots receiving high than no physical disturbance in each of the months (HD > 0D; July: t = 21.30, p(MC) = 0.037; September: t = 19.32, p(MC) = 0.031) and in July, there was also a significant difference between the high and low disturbance treatment (HD > LD; t = 22.42, p(MC) = 0.037) but all other pairwise comparisons were non-significant (p > 0.05). Among plots receiving high nutrient enrichment, plots receiving high physical disturbance had greater abundances of Mysella sp. than undisturbed plots in July (HD > 0D; t = 31.87, p(MC) = 0.017), whereas in September, highly disturbed plots contained fewer individuals than those that were undisturbed (HD < 0D; t = 12.33, p(MC) = 0.049), with no other pairwise comparisons between levels of physical disturbance significant for either of the sampling times (p > 0.05). Examining the interaction around the other way, in July, plots receiving no physical disturbance had lower abundances of Mysella sp. when they received low as compared to no nutrient enrichment(0N > LN; t = 51.61, p(MC) = 0.013), but other pairwise contrasts revealed no other significant differences (a posteriori pairwise comparisons: p > 0.05). In September, both the low and high nutrient treatments had lower abundances of Mysella sp. in comparison to the unenriched treatment (low: t = 17.51, p(MC) = 0.33; high: t = 41.83, p(MC) = 0.017) but did not significantly differ from one another (0N > LN = HN; t = 0.04, p(MC) = 0.977). There was no effect of nutrient enrichment on Mysella sp. among plots receiving low or high physical disturbance (a posteriori pairwise comparisons: p > 0.05).

Few of the species that were key discriminating taxa at only one of the two sites displayed significant responses to stressors (see supplemental materials: Table S4). At Lane Cove, Scoloplos sp. displayed a significant interaction between nutrient enrichment and physical disturbance (Pseudo-F(2,52) = 2.91, p(perm) = 0.039; Figure 5A). Among plots subjected to zero physical disturbance, plots receiving low (t = 2.23, p(perm) = 0.034) and high (t = 2.13, p(perm) = 0.050) nutrient contained fewer Scoloplos sp. than those receiving zero enrichment, with no differences between the low and high nutrient treatments (0N > LN = HN). By contrast, among plots receiving low or high physical disturbance, there was no effect of nutrient enrichment (PERMANOVA a posteriori tests: p > 0.05). When the interaction was examined around the other way, among plots subjected to zero nutrient enrichment, high physical disturbance resulted in significantly fewer Scoloplos sp. as compared to undisturbed controls (0D > HD; t = 2.46, p(perm) = 0.030) whereas there were no differences between plots receiving low and no disturbance (t = 2.38, p(perm) = 0.064) or low and high disturbance (t = 0.12, p(perm) = 0.99). Among plots receiving low or high nutrient enrichment, there was no significant effect of disturbance on Scoloplos sp. (PERMANOVA a posteriori tests: p > 0.05). At Lane Cove, nematodes displayed a significant main effect of nutrient enrichment only (Pseudo-F(2,52) = 3.25, p(perm) = 0.045; Figure 5B) whereby abundance decreased with increasing nutrient enrichment (0N > LN > HN; PERMANOVA a posteriori tests: p < 0.05).

Discussion

The limited number of mesocosm studies focussing on the interaction between physical disturbance and nutrient enrichment have highlighted the potential for interactions between these two stressors [START_REF] Widdicombe | The interaction between physical disturbance and organic enrichment: An important element in structuring benthic communities[END_REF], Austen & Widdicombe 2006). This study sought to expand upon this earlier work by examining the interaction between nutrient enrichment and physical disturbance, under larger-scale field conditions that offer an element of ecological realism To our knowledge, it represented the first field-based study to examine the multiple effects of these two stressors in an intertidal sedimentary habitat (but see [START_REF] Rossi | Small-scale disturbance and increased nutrients as influences on intertidal macrobenthic assemblages: Experimental burial of wrack in different intertidal environments[END_REF] for a discussion on the impacts of organic matter burial that result both from physical disturbance of sediments and nutrient enrichment during decay). It found site-specific effects of nutrient enrichment and physical disturbance, with limited interactions between stressors. The study thereby demonstrates the role environmental context plays on mediating the impact of multiple stressors, and raises the possibility that communities may be more resilient to increased stress than can be predicted from laboratory studies alone.

Of the two stressors examined by this study, nutrient enrichment generally elicited stronger ecological responses than physical disturbance. Eastern Australian estuaries are, in general, oligotrophic and phosphorus-limited (Bishop et al. 2006[START_REF] Scanes | Evaluation of the utility of water quality based indicators of estuarine lagoon condition in NSW, Australia[END_REF][START_REF] Kelaher | Positive responses of a seagrass ecosystem to experimental nutrient enrichment[END_REF].

In nutrient-limited systems such as these, nutrient enrichment typically stimulates bottom-up responses of the MPB [START_REF] O'brien | Multiple sources of nutrients add to the complexities of predicting marine benthic community responses to enrichment[END_REF][START_REF] Pascal | Response of the benthic food web to short-and long-term nutrient enrichment in saltmarsh mudflats[END_REF]. This growth may then lead to cascading positive effects on higher trophic levels [START_REF] York | Trophic responses to nutrient enrichment in a temperate seagrass food chain[END_REF]). Nevertheless, because excess primary production can also result in deterioration of sediment conditions through overstimulation of oxygen-consuming bacteria, the effects of nutrient enrichment on macrofaunal abundance and richness can range from positive (Morris & Keough 2003a, b) to negative [START_REF] Fitch | Effective methods for assessing ecological quality in intertidal softsediment habitats[END_REF], Botter-Carvalho et al. 2014), depending on the level of enrichment and environmental conditions [START_REF] Pearson | Macrobenthic succession in relation to organic enrichment and pollution of the marine environment[END_REF].

In the present study, an effect of nutrient enrichment on MPB was identified at both study sites (although effects were stronger in Botany Bay), and the effect was positive, in agreement with mesocosm studies (e.g. [START_REF] Sundback | Effects of multiple stressors on marine shallow-water sediments: Response of microalgae and meiofauna to nutrient-toxicant exposure[END_REF]. While nutrient additions acted to alter macrofaunal community structure at each of the sites, effects were weaker than expected, with few species significantly affected by stressors, and the nature of effects variable between these. It has been hypothesised that estuarine communities have an inherent ability to resist stress at levels that would push other aquatic systems over a threshold, and which are above and beyond that which they are subjected to daily (e.g. salinity fluctuations, tides, and emersion periods; see [START_REF] Elliott | Challenging paradigms in estuarine ecology and management[END_REF]. Within nature, biotic interactions may reduce the impacts of nutrient enrichment. The limited effects of nutrient enrichment observed in this study indicate there could be a mix of top down and bottom up effects impacting the community. Although in nutrientlimited systems, nutrient enrichment facilitates autotrophic growth, this effect can become masked by top down processes where increased productivity is matched by increased grazing pressure [START_REF] Pascal | Response of the benthic food web to short-and long-term nutrient enrichment in saltmarsh mudflats[END_REF]. Alternatively, the weak effects of nutrient enrichment observed in the present study may be a function of other abiotic and biotic characteristics of the sites, an aspect that would be controlled for in closed systems. Sedimentary grain size and starting community composition can play an important role in interpreting how communities will respond to stressors [START_REF] Lindegarth | Patterns of distribution of macro-fauna in different types of estuarine, soft sediment habitats adjacent to urban and non-urban areas[END_REF][START_REF] Rossi | Small-scale disturbance and increased nutrients as influences on intertidal macrobenthic assemblages: Experimental burial of wrack in different intertidal environments[END_REF][START_REF] Whomersley | Response of intertidal macrofauna to multiple disturbance types and intensities -an experimental approach[END_REF]). The relatively weak effects of nutrient enrichment detected in this study are consistent with largerscale surveys that indicate that nutrient enrichment is potentially a weak driver of change in benthic community composition in comparison to environmental characteristics, such as grain size [START_REF] Nicastro | Weak and habitat-dependent effects of nutrient pollution on macrofaunal communities of Southeast Australian estuaries[END_REF]. Alternatively, the weak effects of nutrient enrichment seen in this study may reflect the small scale of manipulations. Larger-scale disturbances alter system dynamics ultimately impacting recovery and community resilience [START_REF] Ellis | Broad-scale disturbance of intertidal and shallow sublittoral soft-sediment habitats; Effects on the benthic macrofauna[END_REF].

Both MPB and macrofauna displayed a limited to neutral response to physical disturbance despite predictions, based on previous field studies, of negative effects of this stressor from destruction of sediment structure, burrows and damage to softer-bodied species [START_REF] Hall | Physical disturbance and marine benthic communities: life in unconsolidated sediments[END_REF], Brown & Wilson 1997[START_REF] Hall | Physical disturbance and marine benthic communities: The effects of mechanical harvesting of cockles on non-target benthic infauna[END_REF][START_REF] Dernie | Recovery rates of benthic communities following physical disturbance[END_REF][START_REF] Rossi | Human trampling as short-term disturbance on intertidal mudflats: effects on macrofauna biodiversity and population dynamics of bivalves[END_REF]). Community or species-specific responses to physical disturbance have been previously noted to vary according to environmental context [START_REF] Whomersley | Response of intertidal macrofauna to multiple disturbance types and intensities -an experimental approach[END_REF] and previous mesocosm experiments have found that, in line with predictions of the Dynamic Equilibrium Hypothesis [START_REF] Huston | A general hypothesis of species diversity[END_REF], the effects of physical disturbance vary across productivity gradients caused by nutrient enrichment [START_REF] Widdicombe | The interaction between physical disturbance and organic enrichment: An important element in structuring benthic communities[END_REF], Austen & Widdicombe 2006). Consistent with the Dynamic Equilibrium Hypothesis, a number of macrofaunal species in this study displayed responses to physical disturbance that varied according to the prevailing levels of nutrient enrichment. Overall, however, the number of species exhibiting such a non-additive responses was few, and nutrient enrichment was the dominant stressor impacting community composition in these systems.

While small scale disturbances such as raking and trampling sediments have been shown to negatively impact sediment communities in other studies [START_REF] Rossi | Human trampling as short-term disturbance on intertidal mudflats: effects on macrofauna biodiversity and population dynamics of bivalves[END_REF][START_REF] Whomersley | Response of intertidal macrofauna to multiple disturbance types and intensities -an experimental approach[END_REF], the spatial scale and frequency of raking may simply not have been great enough to elicit a strong response in the communities examined here. In this experiment, plots were less than 1 m in diameter, allowing species to rapidly recolonise from outside affected areas (see [START_REF] Lee | Short-term response of estuarine sandflat trophodynamics to pulse anthropogenic physical disturbance: Support for the Intermediate Disturbance Hypothesis[END_REF]. This small scale of physical disturbance might be analogous to that caused by clam raking, by boat-run up on intertidal sediments or by propeller scaring. However, for disturbances, such as storms, that cause physical disturbance at the scale of the entire site, movement of species between affected areas would not be possible. Treatment effects at this level are likely to facilitate the selection for more resilient organisms that are able to tolerate stressors [START_REF] Sanford | Local adaptation in marine invertebrates[END_REF]. The relatively (low) monthly frequency of raking may also have contributed to the weak to absent responses of taxa to physical disturbance. The frequency of disturbance is an important factor determining the magnitude of impact [START_REF] Connell | Diversity in Tropical Rain Forests and Coral Reefs High diversity of trees and corals is maintained[END_REF][START_REF] White | Natural disturbance and patch dynamics: an introduction[END_REF], with infrequent disturbances providing opportunity for organisms to recolonise in between, particularly if the spatial scale of the disturbance is small, but frequent disturbances preventing recovery before the next perturbation. Nevertheless, in Northern Europe, a single raking event covering an area of 36 m 2 , that perturbed large benthic species, had ecological impacts that extended a year [START_REF] Kaiser | Disturbance of intertidal soft-sediment benthic communities by cockle hand raking[END_REF]. Impacts are, therefore, likely to be dependent on the size and scale of the raking event, as well as the species present. Although the physical disturbance imposed by repeatedly sampling of sediments may have complicated results by leading to small scale disturbance across all experimental plots, irrespective of disturbance treatment (Lindegarth and Underwood 2000), we were careful to sample different areas on each sampling date.

Within the literature, there are many examples of context dependent effects of manipulations, even across geographically proximate and/or environmentally similar locations (e.g [START_REF] Whomersley | Response of intertidal macrofauna to multiple disturbance types and intensities -an experimental approach[END_REF][START_REF] Kelaher | Positive responses of a seagrass ecosystem to experimental nutrient enrichment[END_REF][START_REF] Gladstone-Gallagher | Response of temperate intertidal benthic assemblages to mangrove detrital inputs[END_REF]. In this study, the differing response between the two sites to environmental perturbations may be a direct effect of environmental differences between sites, or an indirect effect arising from differences in their community composition. Although the two sites did not differ in background sediment organic content or chlorophyll concentration and were selected to be of similar grain size, other environmental variables are likely to have differed. Botany Bay is a large industrial area with a history of contamination whereas Lane Cove is surrounded by bushland and is used for recreational purposes such as bushwalking, boating and fishing. Habitat characteristics such as grain size, organic content and water content mediate the speed of benthic recovery from perturbations [START_REF] Dernie | Recovery rates of benthic communities following physical disturbance[END_REF]. Additionally, under natural conditions, habitat heterogeneity can buffer against treatment effects [START_REF] Godbold | Habitat structure mediates biodiversity effects on ecosystem properties[END_REF] or lead to substantial background variation, against which treatment effects are hard to detect (Bulling et al. 2008). Community structure may mediate stressor impacts by dictating the functional capability of the ecosystem, and the ways in which species may interact to buffer the effects of stressors (Bulling et al. 2008[START_REF] Godbold | Relative importance of biodiversity and the abiotic environment in mediating an ecosystem process[END_REF]. Additionally, differences between the sites in background stressors may have contributed to the differing sensitivity of their communities to the experimental perturbations. Background stress can mediate how a system will respond to further stress via two main mechanisms. First, prevailing stress may select for organisms that have enhanced resistance to local stressors and so are able to withstand further disturbance [START_REF] Sanford | Local adaptation in marine invertebrates[END_REF]. Second, prevailing stressors can determine how far away a system is from a tipping-point beyond which the application of additional stress pushes the system over a threshold value, resulting in a system collapse [START_REF] Pearson | Macrobenthic succession in relation to organic enrichment and pollution of the marine environment[END_REF][START_REF] Whomersley | Response of intertidal macrofauna to multiple disturbance types and intensities -an experimental approach[END_REF]. How far away systems are from tipping points is related to the conditions to which fauna are adapted and the trade-offs they have made either through evolutionary or local adaptations [START_REF] Sanford | Local adaptation in marine invertebrates[END_REF], Botero et al. 2015). In dynamic environments subjected to multiple stressors such as estuaries, it would be expected that communities are dominated by species that are resilient to perturbation [START_REF] Sanford | Local adaptation in marine invertebrates[END_REF].

Only where stressors exceed the threshold of resilience is there system collapse or change to another stable state.

Although previous mesocosm studies have identified interactions between nutrient enrichment and physical disturbance (e.g. [START_REF] Widdicombe | The interaction between physical disturbance and organic enrichment: An important element in structuring benthic communities[END_REF], our study demonstrates that the results of such studies cannot necessarily be used to infer responses of benthic communities to stressors in the field. While some studies have found agreement between the outcomes of field and mesocosm experiments (e.g. [START_REF] Sundback | Effects of multiple stressors on marine shallow-water sediments: Response of microalgae and meiofauna to nutrient-toxicant exposure[END_REF], mesocosm studies can never completely replicate the natural environment and conclusions about the way in which multiple stressors interact can differ between these approaches (Przelawski et al. 2005;[START_REF] Crain | Interactive and cumulative effects of multiple human stressors in marine systems[END_REF][START_REF] Alsterberg | Multiple stressors and multifunctionality: limited effects on an illuminated benthic system[END_REF]. For example, [START_REF] Cowie | Effects of physical disturbance on an estuarine intertidal community: field and mesocosm results compared[END_REF] observed a negative effect of physical disturbance on the macrofauna in both experimental mesocosms and in situ treatments; however, the strength of the decline of species was greater in mesocosm experiments. Adverse effects are likely to be amplified in mesocosm studies due to the stress imposed on organisms as a consequence of handling and containment in confined conditions, and because processes such as recruitment that act to weaken impacts in field scenarios cannot always occur (see [START_REF] Cowie | Effects of physical disturbance on an estuarine intertidal community: field and mesocosm results compared[END_REF]. The heterogeneity of environments such as mudflats and the patchiness of species can contribute to the differing responses observed between laboratory and mesocosm studies [START_REF] Crain | Interactive and cumulative effects of multiple human stressors in marine systems[END_REF], or even between different field sites [START_REF] Norkko | Conditional responses to increasing scales of disturbance, and potential implications for threshold dynamics in softsediment communities[END_REF]. While mesocosms provide a controlled environment, there is a growing evidence that environmental context (such as prevailing nutrient status) are often the determinant factors governing how systems will respond to stress [START_REF] Sundback | Combined nutrient-toxicant effects on a shallow-water marine sediment system:sensitivity and resilience of ecosystem functions[END_REF][START_REF] Kelaher | Positive responses of a seagrass ecosystem to experimental nutrient enrichment[END_REF][START_REF] O'connor | Environmental context determines multi-trophic effects of consumer species loss[END_REF]. Thus it follows that while mesocosm and laboratory experiments are often a quick and simple tool in understanding the consequences of change, these experiments should be utilised to formulate theories to be tested empirically (see Benton et al. 2007), field experiments must be used to determine true impacts of stressors under naturally occurring conditions. Furthermore, the implications of multiple stressor impacts are well known to vary depending upon the experimental protocol (laboratory/mesocosm; see Crain et al. 2008 and references therein) or the responses measured [START_REF] Alsterberg | Multiple stressors and multifunctionality: limited effects on an illuminated benthic system[END_REF]. The differing method of nutrient enrichment between our study, which applied fertiliser to plots, and the previous mesocosm studies that enriched sediments via application of dried and ground-up Ascophyllum [START_REF] Widdicombe | The interaction between physical disturbance and organic enrichment: An important element in structuring benthic communities[END_REF], Austen & Widdicombe 2006), may have contributed to differences in the conclusions of these. Similarly, the differing frequency of physical disturbance between our study, which raked plots monthly, and the mesocosm experiments, that raked plots daily to monthly [START_REF] Widdicombe | The interaction between physical disturbance and organic enrichment: An important element in structuring benthic communities[END_REF], Austen & Widdicombe 2006) may also have led to differences.

Conclusions

This study analysed the combined impact of selected multiple stressors -nutrient enrichment and physical disturbance -in a field setting. While both stressors have been previously identified to be detrimental to communities, and in mesocosm experiments produce non-additive effects, the combined impacts observed in this study were weak, mainly additive (at least at the chosen levels of stress), and mediated by environmental context. The differing results of this in situ study to those of previous mesocosm experiments, and the site-specificity of effects, highlight the important role that abiotic and biotic features of the environment play in mediating stressor effects. Furthermore, the resilience of benthic communities will determine their response to

  multiple stressors. The minor responses observed within this study highlight that benthic sedimentary communities are more resilient to increased stress than previous studies would indicate. Studies are now needed that examine which aspects of the environment or community are most important in mediating stressor impacts. Anderson M, Gorley RN, Clarke RK (2008) Permanova+ for Primer: Guide to Software and Statistical Methods. Austen MC, Widdicombe S (2006) Comparison of the response of meio-and macrobenthos to disturbance and organic enrichment. J Exp Mar Bio Ecol 330:96-104 Benton TG, Solan M, Travis JMJ, Sait SM (2007) Microcosm experiments can inform global ecological problems. Trends Ecol Evol 22:516-521 Bijma J, Pörtner H-O, Yesson C, Rogers AD (2013) Climate change and the oceans-what does the future hold? Mar Pollut Bull 74:495-505 Bishop MJ (2005) Compensatory effects of boat wake and dredge spoil disposal on assemblages of macroinvertebrates. Estuaries 28:510-518 Bishop MJ, Kelaher BP, Smith MPL, York PH, Booth DJ (2006) Ratio-dependent response of a temperate Australian estuarine system to sustained nitrogen loading. Oecol 149:701-708 Bishop MJ, Kelaher BP (2013) Context-specific effects of the identity of detrital mixtures on invertebrate communities. Ecol Evol 3:3986-3999 Botero CA, Weissing FJ, Wright J, Rubenstein DR (2015) Evolutionary tipping points in the capacity to adapt to environmental change. Proc Natl Acad Sci USA 112:184-189 Botter-Carvalho ML, Carvalho PVVC, Valença APMC, Santos PJP (2014) Estuarine macrofauna responses to continuous in situ nutrient addition on a tropical mudflat. Mar Pollut Bull 83:214-23 Brown B, Wilson WH (1997) The role of commercial digging of mudflats as an agent for change of infaunal intertidal populations. J Exp Mar Bio Ecol 218:49-61 Bulling MT, Solan M, Dyson KE, Hernandez-Milian G, Luque P, Pierce GJ, Raffaelli D, Paterson DM, White PCL (2008) Species effects on ecosystem processes are modified by faunal responses to habitat composition. Oecologia 158:511-520 Christensen MR, Graham MD, Vinebrooke RD, Findlay DL, Paterson MJ, Turner M a. (2006) Multiple anthropogenic stressors cause ecological surprises in boreal lakes. Glob Chang Biol 12:2316-2322 Clarke K, Gorley R (2006) PRIMER v6: User Manual/Tutorial. PRIMER-E, Plymouth. Cloern J (2001) Our evolving conceptual model of the coastal eutrophication problem. Mar Ecol Prog Ser 210:223-253 Table 1: PERMANOVA analyses examining the interacting effects of Nutrients (the macrofaunal community at sites within Botany Bay and Lane Cove estuaries. Nutrient enrichment and physical disturbance factors contained 3 levels of applied stress (zero, low or high) over 4 months (M). n=5-7 for all treatments levels

Figure 1 :

 1 Figure 1: Mean (+/-SE) chlorophyll a concentration (mg m -2 ) of surface sediments in

Figure 2 :

 2 Figure 2: Mean (+/-SE) normalised difference vegetation index (NDVI) at sites in Botany Bay (BB)

Figure 3 :Figure 4 :

 34 Figure 3: Two-dimensional nMDS configuration displaying macrofaunal composition at Botany Bay

Figure 5 :Figure

 5 Figure 5: Mean (+/-SE) abundance of A) Scoloplos sp. and B) nematodes in experimental plots at

  Figure 3:

  Figure 4:

Figure

  Figure 5:


Magali Guénot
email: magali.guenot@gmail.com

L'histoire de l'art à l'épreuve de l'analyse statistique implicative : l'exemple de la structure iconique de l'image médiévale

L'analyse d'une série d'images est devenue monnaie courante dans les recherches en histoire de l'art et archéologie. En iconographie médiévale, les travaux de Jérôme Baschet ont été porteurs : à force de diagrammes, il préconise l'utilisation des statistiques pour mettre en lien par exemple la fréquence d'un thème en fonction des époques. De cette démarche découle une réflexion sur l'influence du contexte de création de l'oeuvre au Moyen Age. Dans le cadre d'une thèse sur les représentations de l'Ascension du Christ au Moyen Age, nous nous sommes tournée vers les statistiques pour obtenir de premières hypothèses de travail. Une problématique sur la structure iconique de l'image, c'est-à-dire son agencement interne, s'est dégagée. Plus spécifiquement, nous souhaitons déterminer en quoi les différences de traitement du Christ, référence iconique de l'image, portent à conséquence sur l'analyse iconographique. Pour ce faire, il est primordial de vérifier la connexion de certains signifiants de l'image entre eux : le signifié provenant du résultat obtenu infirme, confirme ou oriente une hypothèse d'interprétation. L'analyse statistique implicative est un atout majeur pour mener ce type de recherche. Le travail préliminaire de la base de données permet une première appréciation de l'image. De premières statistiques sont réalisées, donnant lieu à des pistes de réflexion. Certaines variables sont sélectionnées pour être croisées grâce à la mise en oeuvre de l'analyse statistique implicative. Par le biais de l'analyse statistique implicative, deux groupes se forment. Ils établissent deux types de structure iconique, à partir desquels l'ajout de variables fait intervenir d'autres croisements. Les nouveaux résultats favorisent et affinent la réflexion sur les répercussions de l'organisation spatiale de l'image dans l'interprétation de cette dernière.

ABSTRACT -The use of serial analysis is a current practice in history of art and archaeology. In medieval iconography, the researches of Jérôme Baschet have been successful: using bar charts, he recommends for instance the use of statistics to link the frequency of a theme according to periods. Thus, a food of thought about the influence of the context of creation of a work of art at the Middle Age can appear. Writing a thesis about representations of Christ during the Middle Age, we turned to statistics to get first hypothesis of works. A problematic on iconic structure, i.e. its internal construction, freed itself. More specifically, we want to establish how how the different ways treating Christ's figure -

Introduction

L'analyse d'une série d'images est une pratique répandue en iconographie médiévale. Elle aborde des thèmes de nature différente : sujet, technique, aire géographique ou chronologique etc. L'étude des représentations de l'Ascension du Christ s'inscrit dans ce type de recherches1 . L'ampleur du champ d'étude a justifié le recours aux statistiques, dont l'usage dans ce domaine est avéré depuis les travaux initiateurs de Jérôme Baschet [START_REF] Baschet | Inventivité et sérialité des images médiévales. Pour une approche iconographique élargie[END_REF]. Les résultats obtenus ont fait naître des questions, auxquelles les statistiques classiques ne permettent pas de répondre : les nouvelles problématiques apparues nécessitent de mettre en lien plusieurs données. L'analyse statistique implicative (A.S.I.) intervient alors pour tester la connexion entre plusieurs éléments, tout en conservant une sécurité par l'indice de confiance que le chercheur fixe lui-même. Pour ce faire, il a fallu s'approprier un vocabulaire technique et appréhender le logiciel CHIC, qui autorise l'application de l'A.S.I. La méthode intégrée, elle a été mise en pratique sur différentes problématiques comme l'importance de la structure iconique dans l'interprétation iconographique, à savoir comment la manière de disposer les éléments influe sur le sens global de l'image. Le présent article expose les résultats de cette recherche, à partir d'un cas d'étude : le lien entre la position, la présentation et les actions du Christ dans l'image.

Il semble important de présenter dans un premier temps l'iconographie médiévale, avant de situer nos travaux dans ce champ disciplinaire. Dans un second temps, "Quaderni di Ricerca in Didattica (Mathematics)", n°20 suppl 1, 2010 G.R.I.M. (Department of Mathematics, University of Palermo, Italy) A.S.I. 5 Proceedings 5-7-November 2010

Magali Guénot 499 sera abordée l'A.S.I. au sein de la recherche entreprise : la mise en application, les résultats, et les applications ultérieures envisageables.

. L'image médiévale : du catalogue d'oeuvres à l'analyse statistique

L'image médiévale a longtemps souffert de nombreux préjugés. Les oeuvres représentant essentiellement des thèmes bibliques2 , elle a été vue comme un moyen d'apprendre la Bible à une population qualifiée à tort d'analphabète. L'avancée des recherches a mis en évidence la complexité de l'image médiévale. Au fur et à mesure, deux types de recherches principaux se sont dégagés : l'étude sérielle et la monographie.

. Définition de l'iconographie médiévale

L'iconographie médiévale est l'étude et l'interprétation des images au Moyen Age.

Cette discipline naît à la fin du XIXe siècle, lors de la redécouverte du Moyen Age.

L'image médiévale est alors perçue comme une simple illustration du texte, et est appelée Bible des illettrés (Mâle, 1986, p.370). Cette idée est aujourd'hui révolue. Il confirme cet article par la publication d'un ouvrage consacré au thème iconographique du sein d'Abraham [START_REF] Baschet | Le Sein du père : Abraham et la paternité dans l'Occident médiéval[END_REF]. L'analyse sérielle est selon lui le moyen, dans un premier temps, de montrer la diversité de l'image médiévale.

Dans un second temps, elle permet de relier entre eux des aspects multiformes de l'iconographie médiévale (Baschet 2000, p.26) 2). La principale difficulté est donc de mettre en lien ces images.

  figure christique. Ne bénéficiant pas de la performance des outils actuels, les chercheurs étaient limités dans leurs démarches, aussi bien dans la collecte d'oeuvres pour effectuer leurs corpus que dans l'utilisation des statistiques. Celle-ci connaît un essor grâce aux travaux de Jérôme Baschet. Historien médiéviste, il présente sa thèse sur les représentations du Jugement dernier. Il est alors confronté à un corpus d'images conséquent, de plus de deux cents oeuvres. Réfléchissant au moyen de mener de manière plus performante une étude sur une série d'images, il écrit un premier article en 1996 sur ce qu'il nomme l'analyse sérielle, à savoir l'étude d'une série d'images ayant en commun un thème, une technique etc.

FigureFigure 3 .Figure 4 .Figure 5 .Figure 6 .

 3456 Figure 1a et b. Bible, Troyes, abbaye de Saint-Loup, vers 1185-1195. Paris, bibliothèque Sainte-Geneviève, ms 0010, f.209v (Paris, Bibliothèque Sainte-Geneviève ©).

L"

  'image constitue l'individu de référence. Une base de données est créée, qui soumet la représentation à une série de questions, sous forme de variables et de modalités de variables. Ce processus est destiné à dresser les caractéristiques de chaque image. On obtient ce que l'on peut nommer une carte d'identité : chaque image est considérée comme un individu unique, pour l'instant sans connexion avec les autres. Des variables ne concernent pas l'iconographie directement. Elles interviennent toutefois dans le traitement iconique ou iconographique du thème car l'image se construit aussi en fonction d'éléments extrinsèques. Il peut s'agir de la technique employée : une sculpture demande un travail sur la matière, plus ou moins malléable, et joue sur la lumière à travers les modelés utilisés, tandis que la peinture prend en compte les couleurs sur une surface plane. Le public est aussi considéré dans la conception picturale. L'accès aux manuscrits est restreint : ce sont surtout des hommes d'Église, et une iconographie spécifique est utilisée. Certains cependant seront exposés lors de cérémonies religieuses "Quaderni di Ricerca in Didattica (Mathematics)", n°20 suppl 1, 2010 G.R.I.M. (Department of Mathematics, University of Palermo, Italy) A.S.I. 5 Proceedings 5-7-November 2010 spécifiques, telles que la Nativité ou Pâques. Ils ne seront pas ouverts mais les plats de reliure seront offerts à la vue de tous et soumis à des actes de vénération 17 . Autre facteur extérieur portant à conséquence sur l'image : les conflits politiques ou théologiques qui l'ont vue naître. L'image est à cette époque un medium utilisé pour véhiculer des messages. Elle se dote souvent d'un double sens subtil, accessible aux personnes visées, créant une ambiguïté dans son message initial. C'est pourquoi il est nécessaire de déterminer l'origine géographique et la période de conception, tant elles peuvent influer sur le parti pris iconographique d'un thème. Une fois renseignés ces éléments, une première ébauche de l'image se dessine. Vient ensuite le travail sur l'image en elle-même. Chaque élément signifiant composant l'image a été disséqué pour obtenir la description la plus fine possible : les anges volent-ils ? Quelles formes adoptent les nuées ? etc. Au final, trente-trois variables ont été définies : elles comptent jusqu'à vingt-deux modalités pour certaines. Quelques unes sont quantitatives, mais la majorité est qualitative : il s'agit de livrer une description juste de l'image. Le raisonnement s'est effectué jusqu'à présent image par image dans la description, puis élément signifiant par élément signifiant pour déterminer les modalités principales (voir figures 3 à 5). Des problématiques se font jour, nécessitant de regrouper plusieurs signifiants : dans quelle mesure font-ils sens lorsque certains sont réunis ? Les données à disposition se révèlent suffisamment complètes et complexes pour utiliser l'A.S.I. 4.2 . Choix de la problématique Parmi les problématiques dégagées, l'une porte sur la structure iconique de l'image. Ce terme concerne l'organisation physique de l'image. Suivant la disposition des éléments les uns par rapport aux autres ou leur traitement pictural, la vision de l'épisode sera différente et partant, son interprétation. De plus, se pose la question du support : ce dernier induit des caractéristiques spécifiques, mais favorisent-elles des mises en formes ? Intéressons-nous alors au traitement du Christ. Axe vertical de la structure, il en constitue l'élément référentiel. Il crée un rapport à l'épisode totalement différent suivant s'il est représenté de face, de profil ou de trois-quarts, en train de monter ou 17 Un plat de reliure en contact avec un public est soumis à ses baisers et caresses. Il en résulte une patine effaçant les détails, comme le plat de reliure dit des Scènes de la Passion, réalisé vers l'an mil et conservé à Paris (France), au musée du Louvre. "Quaderni di Ricerca in Didattica (Mathematics)", n°20 suppl 1, 2010 G.R.I.M. (Department of Mathematics, University of Palermo, Italy) A.S.I. 5 Proceedings 5-7-November 2010 au contraire statique. Peut-on relier ces différences de traitement du Christ à la nature du support ? Privilégient-elles l'intervention ou non d'autres éléments ? Par exemple, la présence de la main de Dieu ou de la croix du Christ découlent-elles directement de telle position ou action du Christ ? La déduction de l'existence de telles connexions entre les éléments permettra alors de démontrer le rôle déterminant de la structure iconique dans l'interprétation iconographique de l'image : le signifié est accentué par la jonction d'éléments signifiants. Avant toute interprétation, il faut donc mettre en place une méthode de travail qui permette de valider cette hypothèse. 4.3 Méthodologie En premier lieu, il convient de cibler les éléments que nous voulons voir apparaître dans la base de données de référence utilisée dans le traitement statistique envisagé. Nous ne pensons plus par image mais par connexion d'éléments signifiants. Dans la base de données, ce ne sont plus les images mais les éléments qui sont fractionnés en variables. La perception de l'image change en fonction des éléments ajoutés ou enlevés. Dans la transcription, si l'on se trompe dans la reconnaissance d'un élément signifiant, l'analyse est fausse. La structure iconique est modifiée selon la modulation d'un élément, ce qui a pour conséquence une interprétation iconographique différente. Mépriser la combinaison des éléments signifiants peut aboutir à une mauvaise lecture de l'image. Souhaitant déterminer si la position du Christ provoque des réactions en chaîne sur l'image, nous limitons la base de données aux entrées « position du Christ », « présentation du Christ », « action du Christ », « croix du Christ » et « main de Dieu ». A titre d'expérience, nous ajoutons également les « objets ». Voici les transcriptions : Quaderni di Ricerca in Didattica (Mathematics)", n°20 suppl 1, 2010 G.R.I.M. (Department of Mathematics, University of Palermo, Italy) A.S.I. 5 Proceedings 5-7-November 2010 Lettre enluminée Pleine page Plat de reliure Tympan Il est possible désormais de mettre en pratique les croisements voulus. A cet effet, il faut appréhender le logiciel CHIC. Parmi les possibilités de mises en graphique, nous optons pour le graphe implicatif. Dans un premier temps, il importe de choisir les modalités que nous souhaitons croiser. L'avantage réside dans la possibilité de combiner les croisements au gré des observations. De plus, le fait de déterminer soi-même l'indice de confiance est un atout majeur : nous pouvons moduler l'indice et observer les nouveaux liens se tisser entre les signifiants. Nous décidons de ne pas baisser l'indice de confiance en deçà de 95%. En revanche, les fermetures transitives seront intégrées, afin d'avoir une appréciation plus juste. Nous procèderons par étape afin de constater l'évolution des regroupements de variables et les incidences sur l'interprétation de l'image. Penchons-nous sur la figure du Christ pour établir les liens entre sa position, sa présentation et son action (figure 7).

Figure 7 .Figure 8 .Figure 9 .Figure 10 .

 78910 Figure 7. Position, présentation et action du Christ, indice d'implication : 0,99. L'apparition de deux groupes distincts invite à approfondir les liens entre signifiants.

  Elle peut aussi témoigner de la coégalité du Père et du Fils : lors de l'Ascension, le Quaderni di Ricerca in Didattica (Mathematics)", n°20 suppl 1, 2010 G.R.I.M. (Department of Mathematics, University of Palermo, Italy) A.S.I. 5 Proceedings 5-7-November 2010 spectateur émet une appréciation esthétique personnelle. A celle-ci, se joignent ses propres connaissances culturelles et intellectuelles, qui lui permettent d'analyser et d'interpréter l'objet d'étude. Cependant, le danger principal est de décrire ce que l'on veut voir et non de voir ce qui est figuré. Si le chercheur se réfère uniquement à ses observations esthétiques personnelles, il risque de ne prendre en compte que les exemples qui favoriseront son analyse. Reprenons l'exemple de la position du Christ. Nous souhaitons démontrer que lorsque le Christ est de profil, il monte. Nous prendrons plus difficilement en compte les représentations sur lesquelles il est de face mais effectue un mouvement ascendant, levant les bras au ciel par exemple. Une partie du raisonnement sera amputée, ce qui mettra à mal l'hypothèse d'une action du Christ uniquement lorsque celui-ci est de profil. Pour recourir à ce système de statistiques, l'objet d'étude doit être suffisamment significatif. Le corpus se compose de 245 oeuvres 16 . Elles ont pour seul point commun le thème de représentation, en l'occurrence l'Ascension du Christ.

	plusieurs données entre elles, d'en déduire les liens de cause à effet, en calculant
	les contradictions intervenant dans chaque sélection.
	L'ampleur du sujet ainsi que les problématiques envisagées justifient l'application
	Christ révèle à tous sa double nature, ce qui l'autorise à avoir un contact charnel de l'analyse statistique implicative. Il a d'abord fallu évaluer la substance en
	avec son Père. La relation privilégiée entre le Père et le Fils est par ce biais fonction de la méthode : si elle n'était pas assez étoffée, les résultats risquaient
	suggérée. d'être décevants. Une fois assurée de la compatibilité entre les deux, nous nous
	Enfin, elle montre la destination du Christ et induit sa place : il est désormais dans sommes approprié l'outil, puis nous avons déterminé une problématique afin de
	le ciel, assis à la droite de Dieu, comme l'indique le passage de l'Évangile selon mettre en avant l'intérêt que représente le recours à l'analyse statistique implicative
	saint Marc 14 . La présence de la main de Dieu peut alors annoncer l'intronisation du dans notre domaine de recherche.
	Christ au ciel dans la continuité de son Ascension.
	L'utilité des statistiques classiques dans l'iconographie sérielle n'est plus à 4.1 . Conditions réunies
	Le chercheur se base alors sur ses propres observations. Les risques sont
	nombreux, au premier chef desquels la subjectivité. Cette dernière est
	incontournable en histoire de l'art : il est impossible de se départir entièrement
	d'un jugement personnel dans cette discipline, puisque face à une oeuvre, le

démontrer. Il devient possible de mieux apprécier la variété iconographique d'un thème. Des permanences iconographiques se dégagent grâce aux statistiques, de même que des éléments plus spécifiques. Ces constatations guident la réflexion, qui se trouve ainsi facilitée. Elles donnent naissance à de nouvelles hypothèses que les statistiques classiques ne permettent cependant pas de vérifier.

3.2 . Limites

Ce type de statistiques offre des résultats bruts. A partir des variables sélectionnées, elles présentent des données exactes : elles informent quantitativement. Chaque résultat correspond à la somme de la variable sur la totalité du corpus. Il détermine la position ou la présentation la plus fréquente du Christ. Devant ces données, le chercheur émet de premières hypothèses. Puis il peut vouloir mettre en connexion plusieurs variables. Par exemple, à la suite des premières conclusions tirées des statistiques, nous avons ainsi voulu savoir s'il existait des liens de cause à effet entre la présence de la main de Dieu, le Christ de profil et l'action de ce dernier. A ce stade de la demande, il s'est avéré impossible de créer une telle chaîne d'incidence entre plusieurs variables.

uniquement sa nature divine, ce qui amène le concile de Chalcédoine à statuer sur la question en 451. 14 Donc le Seigneur Jésus, après leur avoir parlé, fut enlevé au ciel et s'assit à la droite

de Dieu, Mc 16, 19

.

"

Ensuite, quand bien même le chercheur arrive à passer au-delà de ses appréciations subjectives, il manquera à son raisonnement les contre-exemples lui permettant d'appuyer son argumentaire car comme le souligne Bernard Darras, Si toutes les connaissances sont vraies tant qu'elles résistent à la falsification, les connaissances sont scientifiquement vraies tant qu'elles s'exposent à la falsification

(Darras 2006, p.25)

. C'est donc en considérant les contre-exemples que peut se forger l'enquête 15 : ils permettent de mettre à l'épreuve la viabilité de l'hypothèse en fonction de leur importance. En effet, ils peuvent être l'exception qui confirme la règle, ou ils peuvent révéler une anomalie dans l'hypothèse du chercheur s'ils sont trop nombreux. Cependant, les statistiques classiques ne les prennent pas en compte.

Il s'agit d'une thèse entreprise en

sous la direction de Nicolas Reveyron, professeur d'histoire de l'art et d'archéologie médiévale à l'Université Lumière Lyon 2. Regroupant quelques trois cents images de ce thème, elle couvre tout l'Occident médiéval (hormis l'Italie), du IXe au XIIIe siècle. L finalité est de déterminer les caractéristiques et les originalités du thème.

Nombre d'oeuvres médiévales ont disparu. Il existait un art laïque, mais n'étant doté d'aucune valeur sacrée, il a été plus facilement l'objet de destructions au fil des siècles. Il reste donc peu de témoignage de cette forme artistique.

L'on songe à la mosaïque de la basilique Saint-Clément de Rome, réalisée au XIIe siècle, véritable manifeste de la légitimité de l'Église sur le pouvoir temporel lors de la Querelle des Investitures qui sévissait à la même période. Nous renvoyons à l'article d'Hélène Toubert.

Le subjectile est le support accueillant l'image.

La principale limite de l'iconographie sérielle est l'exhaustivité du corpus. Dans une telle étude, on ne peut prétendre à un corpus définitif, en raison du nombre d'oeuvres détruites, disparues ou détériorées. C'est pourquoi il est nécessaire de concevoir le catalogue le plus complet possible au moment de la recherche, pour obtenir une vision relativement réaliste de la création artistique.

L'ecclésiologie est une discipline de la théologie s'intéressant à la naissance et l'évolution de l'Église.

La mandorle est la forme d'amande entourant le Christ. Elle est un truchement iconographique permettant de montrer la double nature du Christ.

Les Actes des apôtres tout comme la majorité des textes ne font aucune allusion à la Vierge. Quant à saint Paul, il se convertit au christianisme après l'Ascension. Leur présence marque l'indépendance de l'image par rapport aux sources textuelles, en transcendant l'interprétation de la scène par cette double présence.

Magali Guénot

Enfin, une image existe rarement seule au Moyen Age. Elle s'intègre le plus souvent dans ce que l'on nomme un programme iconographique, à savoir la réunion de plusieurs scènes obéissant à une pensée construite, politique ou théologique. Ce programme peut s'entendre à l'échelle de l'objet : un plat de reliure en ivoire peut accueillir plusieurs scènes, un portail d'église joue avec les différents supports dont il bénéficie(chapiteaux, tympan, piédroits) pour donner naissance à un programme iconographique. Mais il a parfois une logique spatiale beaucoup plus vaste : les peintures murales d'une nef d'église demande au spectateur de se déplacer pour en apprécier la teneur 9 . Le prieuré d'Anzy-le-Duc illustre aussi cette problématique. Il possède trois tympans répartis à l'échelle non de l'église, mais du prieuré, ce qui demande de considérer les images dans une réflexion non seulement iconographique, mais aussi spatiale : le portail de l'Ascension ne peut donc s'interpréter seul, sans quoi sa lecture serait diminuée, voire faussée. Chaque image de l'Ascension connaît donc un contexte de création qui lui est propre. Ce dernier contribue à la manière de représenter la scène. Par-delà l'image en elle-même, à savoir son support et son iconographie, il prend en compte des éléments extérieurs tels que la spatialité de l'image. Par exemple, une image à l'entrée de l'église, sur un portail, est exposée à la vue de tous. Elle se chargera de significations autres dans le choeur de l'église, fréquenté essentiellement par les officiants. De plus, elle est en connexion avec d'autres images, qui font sens les unes en fonction des autres. Deux pôles apparaissent alors. Le premier consiste à présenter une typologie de l'Ascension en son ensemble : une étude globale est entreprise, dépouillant chaque oeuvre de sa spécificité. Le second rend à chacune son caractère unique et propose, pour les représentations les plus emblématiques, une analyse spécifique. L'étude globale est une analyse sérielle. Les éléments composant l'image sont désolidarisés puis observés de la manière la plus objective possible. Une base de données est ainsi créée. L'image est l'individu de référence. Après une observation générale (type de subjectile, origine, datation), la base met au jour quatre groupes principaux : les témoins, les anges, le Christ et les éléments complétant l'image. Au9 Nous citerons les peintures murales de Saint-Savin-sur-Gartempe (Christe 1999) : couvrant la totalité de la voûte de la nef, ainsi que l'avant-nef et le choeur de l'édifice, elles obéissent à une organisation spatiale qui oblige le spectateur à se déplacer et à prendre en compte la place des images dans l'édifice.

Un sacramentaire est un livre à l'usage du célébrant, réunissant diverses pièces nécessaires à l'office comme les prières. Le plat de reliure, quant à lui, est la couverture des manuscrits, en ivoire ou en orfèvrerie pour les plus précieux : il fait l'objet d'un décor soigné, avec une iconographie élaborée.

Du grec θος -Dieu et φαυος -manifestation, la théophanie désigne une manifestation de Dieu. Dieu tuerait n'importe quel homme le verrait tant sa transcendance est puissante. Aussi, pour montrer la participation de Dieu à un événement, les textes sacrés font mention de nuées divines masquant Dieu au regard des hommes, et les images ont recours à la main droite sortant de nuées ou du ciel.

Un ivoire du IVe siècle réalisé à Rome, aujourd'hui conservé à la Bayerische Staatsbibliothek de Munich, de même que les portes en bois de la basilique Sainte-Sabine de Rome datées du Ve siècle, figurent le Christ montant au ciel saisissant la main de Dieu.

Hérésie née au IVe siècle, l'arianisme ne reconnaît pas la nature divine du Christ : il est condamné en 325 lors concile de Nicée. Le monophysisme pour sa part voit en Jésus-Christ

3. L'application de l'A.S.I.La masse de documents à disposition autorisait l'utilisation de statistiques. Nous nous sommes d'abord servie des statistiques classiques. Les résultats obtenus ont donné lieu à de nouvelles questions, auxquelles lesdites statistiques ne pouvaient répondre. L'A.S.I. s'est alors imposée comme une méthode de travail de premier ordre : elle réunit en effet les conditions de recherches indispensables au chercheur en sciences humaines, à savoir le recoupement de variables et la prise en compte des contre-exemples. A cette étape de la recherche, elle autorise le croisement de15 Nous entendons ce terme dans le sens que lui donne Bernard Darras, à savoir comme une démarche de l'esprit en recherche(Darras 2006, p.30).

Ce nombre correspond aux premières applications de l'A.S.I. à notre thèse. Nous avons désormais atteint le seuil de 300 subjectiles à l'heure actuelle, mais la base destinée à l'A.S.I. a été arrêtée à 245, pour des raisons pratiques.

"Quaderni di Ricerca in Didattica (Mathematics)", n°20 suppl 1, 2010 G.R.I.M. (Department of Mathematics, University of Palermo, Italy) A.S.I. 5 Proceedings 5-7-November 2010 Remerciements Je tiens à exprimer ma gratitude à Jean-Claude Régnier, professeur à l'université Lumière Lyon 2 (UMR 5191 ICAR), pour m'avoir dévoilé avec patience les arcanes de l'A.S.I., et épaulée dans mes recherches. Ma dette à son égard n'a d'égal que l'estime que je lui porte.