Nabil Majdi

Nicolas Hette-Tronquart
email: nicolas.hette@edu.mnhn.fr

Etienne Auclair

Alexandre Bec

Tiphaine Chouvelon

Bruno Cognie

Michaël Danger

Priscilla Decottignies

Aurélie Dessier

Christian Desvilettes

Michael Danger

Stanislas Dubois

Christine Dupuy

Clémentine Fritsch

Cédric Gaucherel

Mickaël Hedde

Franck Jabot

Sebastien Lefebvre

Martin P Marzloff

Benjamin Pey

Nathalie Peyrard

Thibaut Powolny

Régis Sabbadin

Elisa Thébault

Marie-Elodie Perga

There's no harm in having too much: A comprehensive toolbox of methods in trophic ecology

Keywords:

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

Trophic ecology covers the ecological implications of feeding. As such, it embraces the act of food acquisition and its consequences at the individual, population and community levels up to functional outputs at the scale of the whole ecosystem. The field of trophic ecology, in which the concept of food web is embedded, is broader than organismal detection and the description of inter-species feeding relationships. Briefly, at the smallest organisational levels, feeding is intimately linked to nutrition and ecophysiology, as the quantity and quality of mineral or organic food resources regulates individual survival, growth and fecundity with upscaling effects on population demography [START_REF] Elser | Organism size, life history, and N:P stoichiometry[END_REF]. Except for lithotrophic and saprophytic organisms, food acquisition also implies that feeding interactions generate reciprocal effects on predator and prey demography [START_REF] Lotka | Elements of Physical Biology[END_REF][START_REF] Volterra | Fluctuations in the abundance of a species considered mathematically[END_REF]. Trophic relationships are also responsible for species inter-dependencies and contribute to shaping behaviours, driving phenotype selection and eco-evolutionary feedbacks [START_REF] Post | Eco-evolutionary feedbacks in community and ecosystem ecology: interactions between the ecological theatre and the evolutionary play[END_REF][START_REF] Clinchy | Predator-induced stress and the ecology of fear[END_REF]. A trophic transition can also be biogeochemically regarded as a way to transfer mineral or organic matter between two trophic levels with more-or-less efficiency ("trophic efficiency concept" of [START_REF] Lindeman | The trophic-dynamic aspect of ecology[END_REF], "ecological stoichiometry" see e.g. [START_REF] Elser | Organism size, life history, and N:P stoichiometry[END_REF], or transformations in its biochemical quality ("trophic upgrading": [START_REF] Klein-Breteler | Trophic upgrading of food quality by protozoans enhancing copepod growth: role of essential lipids[END_REF]. The concept of food web brings trophic ecology to the community and ecosystem scales. Food webs allows exploring the network of consumer-resource interactions, considering its assemblage rules and interaction strength and the consequences of network structure to overall community composition and stability, up to emergent properties of the ecosystemlike carbon fixation (see Layman et al., 2015, and ref-erences therein for a synthesis of major concept achievements in food web ecology).

The broadness of trophic ecology implies a diversity of methodologies, along with considerable improvements and developments both in field and laboratory methods. In addition, numerical approaches have flourished and now support trophic ecologists in their efforts to conceptualise their theories and to modify them based on empirical data (e.g. [START_REF] Proulx | Network thinking in ecology and evolution[END_REF][START_REF] D'alelio | Ecological-network models link diversity, structure and function in the plankton food-web[END_REF].

Considering this large and fast-evolving bouquet of methodologies, we felt that an up-to-date overview of existing methods, merging both empirical and numerical technics, has been so far missing. Here, by providing a technical overview, we hope to facilitate both upstream decision-making and the inclusion of a broader diversity of research paths within otherwise well-defined methodological road maps. Nevertheless, we do not pretend to provide either an exhaustive critical review of every method relevant to trophic ecology or systematic pairwise comparisons of all methods. For this, we refer readers to the comprehensive book by [START_REF] Garvey | Trophic Ecology[END_REF] and to more specific methodological reviews referenced hereafter. Because the choice of a method primarily depends on its ability to answer a question at hand, we have structured this review accordingly, grouping the methodologies into four categories based on the trophic ecology question they are most suitable for addressing: (Section 2) empirical detection of predator-prey relationships or food sources, (Section 3) connection of species within networks based on empirical data (inference methods), (Section 4) quantification of the consequences of feeding, from individuals to ecosystems and ( Section 5) testing the implications of trophic interactions (trophic models). For each method, we briefly describe the aims and principles, the advantages and drawbacks, and we include estimates of human and financial costs, as time and money are often decisive in the final choice. Beyond providing a methodological toolbox that will help identify the most appropriate tool (Section 6), we seek to encourage an integrated research strategy that combines approaches (Section 7) and to highlight the conceptual barriers (Section 8) in trophic ecology.

Detecting predator-prey relationships or food sources

Observations of feeding activity

The most straightforward and oldest approach to study feeding interactions relies on observations. Feeding observations can be made with the naked eye and simple equipment (e.g., binoculars) or using sophisticated, miniaturised, high-magnification optical devices, including remote underwater video stations, camera traps and drones (e.g. [START_REF] Linchant | Are unmanned aircraft systems (UASs) the future of wildlife monitoring? A review of accomplishments and challenges[END_REF]. This allows large-scale records of feeding behaviours in remote ecosystems that are poorly studied. In addition, animal-borne video systems offer the animal's perspective (e.g. [START_REF] Moll | A new 'view' of ecology and conservation through animal-borne video systems[END_REF]. For microscopic or suspension-feeding animals, most observations are restricted to laboratory conditions, for example using a camera attached to a microscope (e.g. [START_REF] Dupuy | Predation of mudflat meio-macrofaunal metazoans by a calcareous foraminifer, Ammonia tepida (Cushman, 1926)[END_REF] or by in vivo video endoscopy (e.g. [START_REF] Prasetiya | Effect of marennine produced by the blue diatom Haslea ostreariaon behavioral, physiological and biochemical traits of juvenile Mytilus edulisand Crassostrea virginica[END_REF]. To complement direct observations, an emerging approach consists in remotely monitoring multiple biological and environmental factors that constitute surrogates for feeding activity, such as the movements of body parts, oesophageal or gastric temperatures and geographical positions, using animal-attached bio-logging devices (Ropert-Coudert and Wilson, 2005). This should further progress with the transfer of geo-referenced human mobility data analysis techniques to animals [START_REF] Thums | How big data fast tracked human mobility research and the lessons for animal movement ecology[END_REF]. If direct observation of feeding activity is impracticable, food intake can be inferred from the disappearance of food items. For example, suspension-feeder activity is most commonly assessed using food-clearance experiments or flow-through chamber methods (see e.g. [START_REF] Ward | Separating the grain from the chaff: particle selection in suspension-and deposit-feeding bivalves[END_REF]. Different parameters can be obtained this way, such as clearance rate, retention and sorting efficiencies, ingestion, and egestion rates.

Gut content and faeces analysis

Observing the food remains in digestive tracts of animals is the most common approach to get a basic, timely knowledge of predator-prey relationships. Some studies have used massive gut contents datasets to evaluate and compare trophic networks in different ecosystems (e.g. [START_REF] Winemiller | Spatial and temporal variation in tropical fish trophic networks[END_REF]. Especially in fishes, typical methodologies and indices have been developed, and some like the percentage of prey occurrence may emerge as relatively reliable proxies of diet composition (see [START_REF] Baker | Fish gut content analysis: robust measures of diet composition[END_REF]. Rejection pellets and faeces can also be collected and inspected for undigested prey items (e.g. [START_REF] Kusmer | Taphonomy of owl pellet deposition[END_REF]. In most cases, a dietary assessment is based on the recovery of hard/recalcitrant prey parts (e.g. bones, fur, diatom frustules), which makes a reference collection of such parts often necessary to identify the respective prey organism.

The main advantages of this type of dietary analysis consist in: (1) being accessible, (2) being applicable at relatively large spatial and temporal scales and (3) enabling assessments of prey size (e.g. measuring otoliths or vertebrae). Among the main drawbacks are (1) the discrepancies in taxonomic distinctness (as the ingested items can be identified either at the species level or at a higher taxonomic level), (2) the inability to account for labile food items and (3) the requirement of comprehensive taxonomic expertise. (4) Ethical issues are also raised by this approach, particularly when animals must be dissected. Alternative techniques that avoid dissection can be used to recover stomach contents, such as stomach flushing or regurgitation (e.g. [START_REF] Pierce | A review of methods for diet analysis in piscivorous marine mammals[END_REF][START_REF] Legler | The application of stomach-flushing to lizards and anurans[END_REF][START_REF] Duffy | Diet studies of seabirds: a review of methods[END_REF]. In addition, as many microscopic animals have transparent bodies, their gut contents can often be examined under the microscope without dissection. For example, confocal laser scanning microscopy can be used to detect the auto-fluorescence of micro-algal pigments in the gut of rotifers [START_REF] Mialet | Selective feeding of Bdelloid rotifers in river biofilms[END_REF], and chromatography to quantify ingested biomarker pigments extracted from guts (e.g. [START_REF] Majdi | Feeding of biofilm-dwelling nematodes examined using HPLC-analysis of gut pigment contents[END_REF].

Molecular approaches can also be used to decipher ingested prey remains based on the use of specific prey primers to amplify the prey DNA contained in the gut or faeces of the predator followed by (meta)barcoding (for a review see [START_REF] King | Molecular analysis of predation: a review of best practice for DNA-based approaches[END_REF]. The use of molecular gut content has really expanded in recent years and has proved useful to assess, for instance, the diet of minute animals such as soil micro-and meso-arthropods (e.g. [START_REF] Eitzinger | Unveiling soil food web links: new PCR assays for detection of prey DNA in the gut of soil arthropod predators[END_REF][START_REF] Heidemann | Nematode consumption by mite communities varies in different forest microhabitats as indicated by molecular gut content analysis[END_REF], and zooplankton (e.g. [START_REF] Ho | DNA-based study of the diet of the marine calanoid copepod Calanus sinicus[END_REF]. The major advantages of analysing gut content DNA are: (1) high taxonomic resolution without taxonomic expertise, (2) the inclusion of partly digested, unidentifiable prey chunks and, potentially, (3) the acquisition of data on the microbial assemblages ingested or persisting in the gut (i.e. gut microbiomes, see, e.g. [START_REF] Derycke | Coexisting cryptic species of the Litoditis marina complex (Nematoda) show differential resource use and have distinct microbiomes with high intraspecific variability[END_REF]. However, besides substantial costs, there are several disadvantages inherent to molecular approaches, especially (1) high risk of sample contamination and false positives, (2) need for specific primers to identify uncommon prey taxa, (3) absence in public gene repositories of sequence data for the DNA of numerous prey types, (4) bias in quantitative extrapolations due to the differential timing of DNA degradation during digestion or the specificity of certain DNA extraction protocols and (5) the inability to detect cannibalistic behaviour [START_REF] Traugott | Empirically characterising trophic networks: what emerging DNA-based methods, stable isotope and fatty acid analyses can offer[END_REF].

Parasites as biological tags

Since some parasites are transmitted only through food ingestion, they serve as evidence of a feeding interaction and indicate that the host species has fed in geographical areas where the prevalence of this parasite is high. Similarly, accurate information about the feeding grounds and past movements of animal hosts can be surmised based on the presence of multiple parasite species differing in their endemic areas [START_REF] Mackenzie | Parasites as biological tags for stock discrimination of marine fish: a guide to procedures and methods[END_REF]). Yet, to be reliable biological tags, parasites must have: (1) distinct prevalences in different studied areas, (2) limited inter-annual or seasonal variations in those prevalences, (3) a high specificity for the microhabitat within the host's body, (4) a lifespan fitting the aim/scale of the study, (5) no strong pathological effects on the host and (6) preferably, a direct and single-host life cycle (facilitating interpretations). They must also be readily detectable and identifiable. Helminths generally fulfil all of these criteria and are thus the most commonly used trophic tracers (see [START_REF] Mackenzie | Parasites as biological tags in population studies of marine organisms: an update[END_REF].

The use of parasites as trophic tracers has thus far been limited to marine ecosystems, but, given the ubiquity of parasites [START_REF] Marcogliese | Parasites: small players with crucial roles in the ecological theater[END_REF], implementation of this method in other ecosystems is certainly possible (see [START_REF] Holmstad | Parasite tags in ecological studies of terrestrial hosts: a study on ptarmigan (Lagopusspp.) dispersal[END_REF]. Additional advantages of parasites are that they provide information even when their host's stomach is empty [START_REF] Baldwin | Expanding the foraging history of juvenile Pacific salmon: combining stomach-content and macroparasitecommunity analyses for studying marine diets[END_REF]) and indicate long-term feeding, as they can accumulate in their hosts for months or longer [START_REF] Marcogliese | Parasite communities as indicators of ecosystem stress[END_REF]. However, this method also requires that the animals are killed and dissected, the method is time-consuming and considerable taxonomic expertise is required. Some of these shortcomings might be overcome using DNA barcoding, which is inexpensive (~5€/parasite), or by coupling behavioural and molecular approaches [START_REF] Poulin | Parasite manipulation of host behavior: an update and frequently asked questions[END_REF]. However, the use of a parasite as a biological tag relies on an at least partial understanding of the parasite's life cycle, which probably explains their use mostly in fish species so far.

Tracers of biomass

Trophic tracers of biomass origin are elements or molecules that an organism can gain only from its trophic resources. The presence of a tracer in the biomass of an organism indicates the consumption and assimilation of a resource containing that tracer, as well as whether and how much the different trophic resources have contributed to the biomass of the organism (or its targeted tissue), provided that the potential resources differ in their tracer composition. Moreover, the presence of a tracer not only reflects the consumption of a resource, it can also provide an information on how the tracer is retained and transferred within the consumer, such as by selective digestion or assimilation [START_REF] Gannes | Stable isotopes in animal assumptions, caveats, and a call for more laboratory experiments[END_REF] or routing to different tissues [START_REF] Carleton | Should we use one-, or multi-compartment models to describe 13C incorporation into animal tissues?[END_REF].

Stable isotope composition of bulk tissues

One of the most common trophic-tracer-based methods is the determination of the stable isotope composition of bulk tissues, such as muscle, blood, liver, feather, hair, fin, or whole organism. In trophic ecology, C, N and S are the tracers most frequently used in stable isotopic analysis (SIA) [START_REF] Fry | Stable Isotope Ecology[END_REF], but H/D and O isotopes are also employed [START_REF] Vander Zanden | Expanding the isotopic toolbox: applications of hydrogen and oxygen stable isotope ratios to food web studies[END_REF]. The method is based on predictable differences (trophic discrimination factors, TDFs) between the isotopic composition of an organism and that of its food resources. For C and S, the difference is limited and these elements are mainly used to trace the origins of the food resources from which the consumers' biomass has been synthesized [START_REF] Boecklen | On the use of stable isotopes in Trophic Ecology[END_REF], whereas the TDF for N is larger, allowing its use in estimates of trophic position [START_REF] Post | Using stable isotopes to estimate trophic position: models, methods, and assumptions[END_REF]. However, the variability in the TDFs depending on environments, trophic levels, taxa, tissues, etc. [START_REF] Bond | Recent Bayesian stable-isotope mixing models are highly sensitive to variation in discrimination factors[END_REF]) is a potential confounding factor, that has been highlighted in several studies (e.g. [START_REF] Bastos | Are you what you eat? Effects of trophic discrimination factors on estimates of food assimilation and trophic position with a new estimation method[END_REF]. In addition, the high variability of stable isotope compositions in space and time (e.g. [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] must also be considered. Several tools are used to analyse stable isotope data. Their most recent versions generally adopt a similar Bayesian approach to account for the sources of uncertainty (e.g. [START_REF] Parnell | Bayesian stable isotope mixing models[END_REF] and include associated confidence intervals. Bayesian approaches also allow introducing informative priors, increasing the accuracy and precision of the estimates. We distinguished three main types of tools: (1) those devoted to the estimation of trophic position (e.g. tRophicPosition, [START_REF] Quezada-Romegialli | tRophicPosition: Bayesian trophic position calculation with stable isotopes[END_REF], (2) isotopic metrics to measure specimen or species positions in the isotopic space and to compare the variability of isotopic signatures across individuals, populations and communities (SIBER, [START_REF] Jackson | Comparing isotopic niche widths among and within communities: SIBER -Stable Isotope Bayesian Ellipses in R[END_REF][START_REF] Cucherousset | Quantifying the multiple facets of isotopic diversity: new metrics for stable isotope ecology[END_REF] and (3) mixing models to estimate the contribution of each potential trophic resource to the biomass of an organism (see [START_REF] Philips | Converting isotope values to diet composition: the use of mixing models[END_REF] for a review). The relevance of SIA-derived results is thus strongly tied to isotopic discrimination between resources, the spatial and temporal variability of the isotopic compositions captured by resource/consumer sampling and an accurate estimate of the TDF. SIA is not well suited to situations involving large numbers of potential resources (e.g. [START_REF] Robinson | Stable isotope mixing models fail to estimate the diet of an avian predator[END_REF]. The integration of the food isotopic signal into the consumer's tissue depends of the rate at which tissue are renewed, by somatic growth or metabolic tissue replacement (which determines isotopic turnover). Issues related to isotopic turnover thereby limit the relevance of the method for individuals (i.e. adults) or seasons of reduced somatic growth (gonadic growth or maintenance metabolism, [START_REF] Perga | Are fish what they eat' all year round?[END_REF]. Issues related to differential isotopic routing [START_REF] Gannes | Natural abundance variations in stable isotopes and their potential uses in animal physiological ecology[END_REF][START_REF] Del Rio | Isotopic ecology ten years after a call for more laboratory experiments[END_REF] and unequal TDF in plant versus animal food sources [START_REF] Perga | Laboratory measures of isotope discrimination factors: comments on Caut, Angulo & Courchamp[END_REF]) also limit the detection of omnivory for individuals and species exploiting both plant and animal resources. As a result, SIA enables quantitative estimates of elemental fluxes within the different steps and habitats of a food web, but it is a less than ideal method with which to assess the diversity and specificity of a consumer's diet.

When natural isotope abundance does not provide the necessary discrimination between sources, for example, to overcome uncertainties linked to TDF variability, small quantities of isotopically labelled sources (stable or radioactive) can be injected in-or ex-situ to track C and/or N pathways. This method of isotope labelling, or Stable Isotope Probing (SIP) aims to track the integration of the labelled elements within food webs [START_REF] Pace | Does terrestrial organic carbon subsidize the planktonic food web in a clear-water lake?[END_REF]. Primary producers can be selectively labelled through addition of 13 C-enriched bicarbonate/carbon dioxide or 15 N-enriched ammonium or nitrate directly in situ (see e.g. [START_REF] Middelburg | The fate of intertidal microphytobenthos carbon: an in situ 13 C-labeling study[END_REF] to track the fate of primary production through food webs. Similarly, SIP based on dissolved organic matter (e.g. [START_REF] Hall | The trophic significance of bacteria in a detritus-based stream food web[END_REF], phytodetritus (e.g. [START_REF] Scharnweber | Whole-lake experiments reveal the fate of terrestrial particulate organic carbon in benthic food webs of shallow lakes[END_REF] or animal faeces (e.g. [START_REF] Dungait | Tracking the fate of dung-derived carbohydrates in a temperate grassland soil using compound-specific stable isotope analysis[END_REF] are used to label microbial decomposers and the fate of dead organic matter through "brown" food webs. The mode (single addition, pulse chase, or constant levels) and the duration (a few hours to several months) at which the label is introduced into the system determine the time and scale at which the fate of the labelled substrate is tracked (from microbial interactions up to the whole ecosystem), and eventually to document the dynamics of the processes (when performed in pulse chase) (e.g. [START_REF] Maxfield | Stable isotope switching (SIS): a new stable isotope probing (SIP) approach to determine carbon flow in the soil food web and dynamics in organic matter pools[END_REF]. If studies using isotope labelling are relieved from the issues of TDF uncertainties encountered for SIA in natural abundances, they also suffer for issues related to isotope routing. Indeed, structural components of plant material behave differently than metabolic components in terms of microbial utilisation, grazing, and assimilation (see e.g. [START_REF] Soong | Design and operation of a continuous 13 C and 15 N labeling chamber for uniform or differential, metabolic and structural, plant isotope labeling[END_REF]. The success of isotope-labelling experiments is thereby strongly tied to the ability to uniformly label throughout the food source, or instead to differentially label the structural and metabolic components of the source [START_REF] Soong | Design and operation of a continuous 13 C and 15 N labeling chamber for uniform or differential, metabolic and structural, plant isotope labeling[END_REF]. SIP studies have proven powerful in documenting microbial involvement in biogeochemical processes in soils and sediments and in quantifying the trophic links between the microbial and macro-faunal worlds (e.g. [START_REF] Crotty | Using stable isotopes to differentiate trophic feeding channels within soil food webs[END_REF][START_REF] Middelburg | Stable isotopes dissect aquatic food webs from the top to the bottom[END_REF].

Fatty acid trophic biomarkers

Since the early 1980s, fatty acids (FAs) have been widely used to study predator-prey relationships and to trace the origin and transfer of organic matter in food webs [START_REF] St-John | Lipid biomarkers: linking the utilization of frontal plankton biomass to enhanced condition of juvenile North Sea cod[END_REF]. The use of FAs as trophic markers relies on the specific FA patterns exhibited by basal resources that are then transferred to and identifiable in consumers. As such, FAs have been analysed in many species to infer feeding relationships in aquatic environments for example [START_REF] Arts | Lipids in aquatic ecosystems[END_REF]. They are increasingly used to shed light on feeding channels in soil environments (e.g. Ruess et al., 2007). Most often, this method requires tracing specific FAs of prey that cannot be synthesized de novo by the targeted community of consumers/predators (e.g. 16:4ω3 for chlorophytes, 16:4ω1 for diatoms, 22:1ω11 biomarker for Calanoid copepods). The detection of those prey-specific FAs in the tissues of consumers/predators thus reveals the assimilation pathway of the prey. However, many fatty acids (e.g. 16:0, 18:0, 18:3ω3, 18:2ω6) occur in a wide range of organisms restraining the accuracy of the approach [START_REF] Dalsgaard | Fatty acid trophic markers in the pelagic marine environment[END_REF]. For this matter, the comparison of FA ratios can improve the interpretation of results [START_REF] Parrish | Lipids in marine ecosystems[END_REF]. For example tracking the16:1ω7/16:0 ratio for diatoms or the 22:6ω3/20:5ω3 ratio for chrysophytes can be used to demonstrate that these microalgae are assimilated by zooplanktonic microcrustaceans [START_REF] Desvilettes | Use of fatty acids for the assessment of zooplankton grazing on bacteria, protozoans and microalgae[END_REF][START_REF] Pepin | Late autumn condition of Calanus finmarchicus in the northwestern Atlantic: evidence of size-dependent differential feeding[END_REF]. Indeed, the reliability of FA-based trophic markers requires in-depth knowledge of the lipid metabolism of both primary producers and the targeted animal species as a prerequisite. However, while these metabolic processes may obscure the identification of actual food resources, FA-based methods generally provide sufficient information on foraging patterns.

To date, most studies using FA have been qualitative with the presence/absence of a source-specific FA being used as an indicator of the existence of a trophic interaction between this source and the consumer under study. A Quantitative FA Signature Analysis (QFASA) has been more recently developed to enable the estimation of the propor tions of different sources in a predator's diet [START_REF] Iverson | Quantitative fatty acid signature analysis: a new method of estimating predator diets[END_REF]. Basically, the FA signatures of consumers are modelled as a mixture of the FA signatures of major food resources, which provides a quantitative estimate of the proportions of those resources. The method is based on the calculation of the statistical distance between predator FA signatures and mean prey FA signatures. The predator's FA patterns are corrected according to the degree of modification linked to its FA metabolism. Calibration coefficients are then necessary and calculated using experimental diet studies. These studies are designed to assess the selective retention of dietary fatty acids, to detect fatty acid bioconversion or de novo synthesis. The acceptance of this method by researchers studying the trophic ecology of marine mammals for example will likely be broadened by the recent development of a dedicated R-package [START_REF] Bromaghin | QFASAR: quantitative fatty acid signature analysis with R[END_REF]. According to [START_REF] Happel | Evaluating quantitative fatty acid signature analysis (QFASA) in fish using controlled feeding experiments[END_REF], however, as for mixing models in SIA, the use of QFASA should be limited to the predators that consume a small number of species and that can be studied experimentally as well as in the wild.

Compound specific isotopic analyses (CSIA)

Combining detection of biomarkers (lipids and amino-acids mainly, but also amino-sugars) to stable isotope analyses, CSIA is able to trace the sources and pathways of numerous natural as well as anthropogenic organic compounds. In ecology, first utilizations of CSIA focused on chemotaxonomic markers of microorganisms. Although the role of microorganisms is crucial in processing and transferring organic matter in food webs, their isotopic signatures were rarely reported due to the difficulty of isolating specific microbial biomass from natural samples. Using 13 C labelled substrates [START_REF] Boschker | Direct linking of microbial populations to specific biogeochemical processes by 13C-labelling of biomarkers[END_REF] described a CSIA approach to directly link specific microbial processes with the organism involved, based on the stable carbon isotope labelling of individual lipid biomarkers. In the same way, [START_REF] Werne | Molecular isotopic tracing of carbon flow and trophic relationships in a methane-supported benthic microbial community[END_REF] followed the 13 C depleted signal of methane in cold seep sediment through different specific microbial markers and could trace with smart elegance the flow of methane-derived-carbon through anaerobic methane-oxidizing archaea (archeol and sn-3-hydroxyarchaeol) into sulfate-reducing bacteria (C15 and C17 iso and anteiso fatty acids, dialkyl glycerol diethers), as well as into aerobic methane-oxidizing bacteria (diploptene, diplopterol) up to bacterivorous ciliates (tetrahymanol). Stable isotope probing of amino-sugars is regarded as a promising tool to investigate fungal-bacterial interactions in soils [START_REF] Bodé | Stable isotope probing of amino sugarsa promising tool to assess microbial interactions in soils[END_REF]. Thus, CSIA can be used successfully for elucidating source and fate of naturally or artificially labelled substrates.

In other cases, the isotopic fractionation between substrates and chemotaxonomic markers must be known. Food webs studies have thus applied CSIA on essential lipid compounds such PUFA or sterols by assuming that TDFs would be negligible. However, an unpredictable fractionation ranging from 0‰ to 4‰ still occurs during trophic transfer of essential lipid compounds such sterols [START_REF] Chamberlain | Lipid content and carbon assimilation in Collembola: implications for the use of compound-specific carbon isotope analysis in animal dietary studies[END_REF] or PUFA [START_REF] Bec | Assessing the reliability of fatty acid-specific stable isotope analysis for trophic studies[END_REF][START_REF] Gladyshev | Stable isotope fractionation of fatty acids of Daphnia fed laboratory cultures of microalgae[END_REF]. Moreover, the intermolecular variability of δ 13 C values within the same sample may be relatively high, thereby challenging again data interpretation. For example, the difference between fatty acids δ 13 C values within a single cultivated alga may be up to 7.6‰ [START_REF] Schouten | Biosynthetic effects on the stable carbon isotopic compositions of algal lipids: implications for deciphering the carbon isotopic biomarker record[END_REF]. Thus, interpretation of CSIA data could be constrained in case the potential endmembers are not sufficiently isotopically different. However, when the conditions are met, CSIA could trace limiting compounds and eventually detect minor food sources unseen by classical methods. For example, CSIA has revealed an uncoupling between essential compounds and major organic matter transfers highlighting functional importance of minor food sources of great nutritional importance [START_REF] Koussoroplis | Nutritional importance of minor dietary sources for leaping grey mullet Liza saliens (Mugilidae) during settlement: insights from fatty acid d13C analysis[END_REF]. An increasing attention is now being paid to amino acids-CSIA since [START_REF] Mcclelland | Trophic relationships and the nitrogen isotopic composition of amino acids in plankton[END_REF] showed that the δ 15 N values of some amino acids such phenylalanine in consumers are very similar to those in the producers while the δ 15 N values of other amino Majdi et al. Food Webs xxx (2018) xxx-xxx acids such glutamic acid become enriched in 15 N with each trophic transfer. Thus, due to this differential 15 N enrichment with trophic transfer, δ

U N C O R R E C T E D P R O O F N.
15 N of amino acids in a consumer provide a measurement of the δ 15 N baseline as well as its trophic position.

Coupled with stable isotopic probing (also coined SIP), ribosomal RNA or DNA can also be used as integrative tracers. 13 C-or 15 N-labelled RNA or DNA is heavier and can be separated from unlabelled material using isopycnic ultracentrifugation, for example. Further amplification and barcoding of the isolated fractions allows an organism associated with the assimilation of a specific resource or organic contaminant to be identified [START_REF] Neufeld | Methodological considerations for the use of stable isotope probing in microbial ecology[END_REF]. In microbial ecology, this is a promising approach to detect specific functional guilds of microbes (e.g. methanotrophic bacteria), but it can also be scaled-up to other consumers, such as fungi and flagellates, to reveal matter flows in microbial food webs [START_REF] Lueders | Stable isotope probing of rRNA and DNA reveals a dynamic methylotroph community and trophic interactions with fungi and protozoa in oxic rice field soil[END_REF].

Contaminants as trophic tracers

Both trace metals (inorganic elements) and xenobiotic organic compounds can fulfil the role of trophic tracers [START_REF] Ramos | Trace me if you can: the use of intrinsic biogeochemical markers in marine top predators[END_REF] when these contaminants enter trophic pathways and differentially bio-accumulate in food sources or prey and consequently in consumers or top predators (e.g. [START_REF] Walters | The dark side of subsidies: adult stream insects export organic contaminants to riparian predators[END_REF][START_REF] Pitt | Polychlorinated biphenyl bioaccumulation patterns among Lake Erie lower trophic level consumers reflect species ecologies[END_REF]. Selected contaminants can thus be used to infer trophic relationships, including the prey preferences of consumers/predators, foraging areas or food webs exploited by different individuals or populations (e.g., [START_REF] Larsson | Differences in uptake of persistent pollutants for predators feeding in aquatic and terrestrial habitats[END_REF][START_REF] Deshpande | Polychlorinated biphenyls and organochlorine pesticides as intrinsic tracer tags of foraging grounds of bluefin tuna in the northwest Atlantic Ocean[END_REF] and even trophic positions and organic matter flux when bio-magnification occurs [START_REF] Kelly | Food web-specific biomagnification of persistent organic pollutants[END_REF]. Therefore, these indirect tracers can be particularly helpful when there is inherent difficulty of direct observations of trophic relationships (e.g., for marine species). Another advantage of using contaminants in a trophic perspective is that it also informs on the contamination status of the species and food webs of concern, which may be very interesting for ecotoxicological and/or conservation biology perspectives as well. For example, a survey of cadmium (Cd) in common dolphins from the North-East Atlantic allowed neritic and oceanic populations to be distinguished based on the Cd concentrations in their kidneys (long-term accumulation organ in mammals) and their distinct preferential prey [START_REF] Lahaye | Long-term dietary segregation of short-beaked common dolphins (Delphinus delphis) in the Bay of Biscay determined using cadmium as an ecological tracer[END_REF]. Cephalopods and especially oceanic squids (i.e. the preferential prey of oceanic dolphins compared to neritic ones) indeed display very high burden of this metal relative to fish prey species, and were thus proved to constitute a significant vector of Cd for their predators [START_REF] Caurant | Cadmium contamination in pilot whales Globicephala melas: source and potential hazard to the species[END_REF][START_REF] Bustamante | Cephalopods as a vector for the transfer of cadmium to top marine predators in the north-East Atlantic Ocean[END_REF].

However, while monitoring contaminants can yield information on both trophic interactions and matter fluxes, good knowledge of the contaminants' characteristics (biogeochemical cycles, the distribution and persistence of the contaminant in organisms and the environment), the target organism's biology, and the structure of food webs are essential. Another prerequisite is an obvious source of the contaminant and its clear partitioning. In fact, contaminants are rarely used alone as trophic tracer tools, and rather complement other intrinsic trophic markers such as C, N, S isotopic ratios or FA profiles (e.g., [START_REF] Krahn | Use of chemical tracers in assessing the diet and foraging regions of eastern North Pacific killer whales[END_REF][START_REF] Hebert | Biochemical tracers reveal intra-specific differences in the food webs utilized by individual seabirds[END_REF][START_REF] Praca | Toothed whales in the northwestern Mediterranean: insight into their feeding ecology using chemical tracers[END_REF]. For example, in prey with similar FA but different contaminant profiles, use of the latter allows the discrimination of different diets in the predator (while the use of FA alone did not). Nevertheless, the use of contaminants as trophic tracers requires that the analysed tissues be carefully chosen, because the type of tissue strongly influences the turnover rate of the contaminant-containing compound, which in turn modifies the integration time of the contaminant itself. Finally, like parasites-based approaches, the toxic effects of a contaminant may alter the feeding strategy of the organism. However, as long as the contaminants are able to track these potentially altered foraging behaviours, they fulfil their role as trophic tracers. With the recent development and improvement of modelling tools such as the "Ecotracer" module [START_REF] Walters | Ecotracer: analyzing concentration of contaminants and radioisotopes in an aquatic spatial-dynamic food web model[END_REF] in the Ecopath with Ecosim software package (see Sections 3.3 and 5.1), the potential of contaminants as trophic tracers could be further extended.

Connecting species within networks from ecological data (inference methods)

Because establishing complete inventories of trophic interactions within a system is virtually impossible, inference methods can be used to reconstruct trophic networks when the ecological datasets are incomplete [START_REF] Jordano | Sampling networks of ecological interactions[END_REF]. Inference methods are thus specifically useful when empirical approaches (such as those described in Section 2) cannot be implemented to assess trophic interactions. In that case, inference methods combine empirical data about the community composition (mostly occurrence/abundance of the different species) and theoretical knowledge about trophic ecology (e.g. trophic behaviour of the species) to infer the trophic interactions within the community. It is worth noting that inference methods were not specifically developed for trophic interactions, but for all kinds of interactions (from causal relationships among variables, to social networks). Several ways are available to infer interactions (e.g. using Gaussian distributions, logical interaction rules or likelihood postulates), each leading to a different method that can be applied to trophic interactions. In the following, we only focus on the inference methods that are mainly used in the reconstruction of trophic networks.

Graphical models

A Graphical model is a probalistic model using a graph to represent the dependencies among variables. In the case of trophic networks, the variables are species abundances or occurrences and the edges in the graph can be interpreted as trophic interactions. Generally, the graph structure is given by expert knowledge, and graphical models are used to make predictions about species persistence. Conversely, it is also possible to learn the graph structure, in our case the trophic network, using empirical data. The principle is to draw an edge between two species in the community, whenever their abundances/occurrences are not independent. Two main kinds of graphical models are used in trophic ecology: Gaussian Graphical Models (GGMs) [START_REF] Højsgaard | Gaussian graphical models[END_REF] and Bayesian Networks (BNs) [START_REF] Jensen | Bayesian Networks and Decision Graphs[END_REF].

With GGMs, independence between two species is assessed from the empirical data with the precision matrix (i.e. the inverse of the covariance matrix of the model). The resulting network is an undirected interaction network whose edges are weighted by the coefficient of the precision matrix. Expert knowledge is then required to determine the nature and the direction of the inferred interactions (trophic or non-trophic links). In addition, it is often necessary to limit the number of inferred interactions to the most relevant ones. To do so, GGMs are coupled with sparse regularisation techniques, such as the graphical LASSO (for Least Absolute Shrinkage and Selection Operator; [START_REF] Friedman | Sparse inverse covariance estimation with the graphical lasso[END_REF]. [START_REF] Faisal | Inferring species interaction networks from species abundance data: a comparative evaluation of various statistical and machine learning methods[END_REF] tested different GGM procedures on large-scale spatial data sets describing abundance records for 39 species of European Warblers. They were able to reconstruct in silico the ecological networks, and from the inferred networks, they could compare the relative role of bioclimatic versus biotic interactions on the species spatial distribution.

Unlike GGMs, BNs and their temporally explicit extension, dynamic-BNs [START_REF] Dean | A model for reasoning about persistence and causation[END_REF] rely on directed graphs. Concretely, it means that an edge can be interpreted directly as a predation link. BNs also differ from GGMs by the learning process of the graph. In the case of BNs, every possible graph is used to assess species abundances/occurrences. Then, each graph receives a score, depending on both the fit between observed and inferred abundances/occurrences Majdi et al. Food Webs xxx (2018) xxx-xxx and graph complexity. Scores are calculated using different statistical score functions (e.g. Bayesian information criterion), but the underlying principle is the same: to find a graph (in our case a trophic network) that maximises the score, exactly or approximately. In trophic ecology, BNs and dynamic-BNs have been successfully applied to infer feeding interactions among species based on synthetic data [START_REF] Aderhold | Hierarchical Bayesian models in ecology: reconstructing species interaction networks from nonhomogeneous species abundance data[END_REF], by combining expert knowledge and field data, such as long-term catches per unit effort of fisheries [START_REF] Trifonova | Spatio-temporal Bayesian network models with latent variables for revealing trophic dynamics and functional networks in fisheries ecology[END_REF], or based on the presence-absence time series of a fish community [START_REF] Sander | Ecological network inference from long-term presence-absence data[END_REF].

U N C O R R E C T E D P R O O F N.

Logic-based approaches

Logic-based approaches differ from graphical models by the way they reconstruct trophic networks. The principle is not based on statistical approaches, but on a set of logical rules (in the form of: "if" premise "then" consequence) that is used to reconstruct trophic networks. The main advantage of such approaches is to establish the rules by combining background knowledge about the species and their environment and empirical data. In trophic ecology, two techniques are commonly used to determine the set of logical rules: Inductive logic programming [START_REF] Muggleton | Inductive logic programming[END_REF] when background knowledge is available; or meta-interpretive learning [START_REF] Muggleton | Meta-interpretive learning: application to grammatical inference[END_REF] when background knowledge is incomplete or lacking, (e.g. when the trophic ecology of the species is not known and is actually the object of the attention). Logic-based approaches have been successfully employed to automatically generate trophic networks. For instance, [START_REF] Bohan | Automated discovery of food webs from ecological data using logic-based machine learning[END_REF] reconstruct the trophic network of invertebrate communities within arable fields in Great Britain, using logic-based machine-learning algorithms, species occurrence data and background knowledge, such as species body-size and functional groups.

Linear inverse inference

In linear inverse inference, trophic networks are represented in a steady state, as static webs of model compartments (e.g. species or group of species) that are linked together by linear interactions [START_REF] Van Oevelen | Quantifying food web flows using linear inverse models[END_REF]. The approach is particularly suited to infer the magnitude of missing interactions, a very common situation in many ecosystems given the high-dimensionality of trophic networks and the scarcity of information across all trophic levels. Linear inverse inference estimates the missing interactions by ensuring mass-balance across all compartments. Practically, different kinds of techniques can be used (see [START_REF] Van Oevelen | Quantifying food web flows using linear inverse models[END_REF] to select the set of parameters that produce the best fit between the modelled abundances (or biomasses) of each compartment and empirical observations. The Ecopath software (see [START_REF] Christensen | Ecopath II -a software for balancing steady-state ecosystem models and calculating network characteristics[END_REF] constitutes a typical example of this approach. In addition, linear inverse inference can be coupled with ecological stoichiometry or stable isotopic analysis to further constrain the solution range of the reconstructed food webs. For instance, [START_REF] Pacella | Incorporation of diet information derived from Bayesian stable isotope mixing models into mass-balanced marine ecosystem models: a case study from the Marennes-Oléron estuary, France[END_REF] associated isotope data with linear inverse modelling to reconstruct the feasible food webs within the Marennes-Oléron intertidal seagrass bed.

Approximate Bayesian computation

Bayesian inference methods rely on the computation of a likelihood, which is the probability density of the observed data under the studied model. It is associated with the parameter values of the model. As a likelihood computation is not always possible, approximate Bayesian methods can be used instead, with the most common one being the Approximate Bayesian Computation (ABC). This approach originates from the field of population genetics [START_REF] Tavaré | Inferring coalescence times from DNA sequence data[END_REF] but it has been successfully applied in trophic ecology to decipher the im pacts of trophic interactions on the spatial structure of communities (e.g. [START_REF] Jabot | Bitrophic interactions shape biodiversity in space[END_REF]. In an ABC, the likelihood computation step is replaced by intensive simulations of the model with variable parameter values, so as to select the values that lead to the best match between simulations and empirical data. ABC can be further coupled to efficient algorithms, such as sequential or traditional Markov Chain Monte Carlo methods [START_REF] Jabot | EasyABC: performing efficient approximate Bayesian computation sampling schemes using R[END_REF]. This approach was used to evidence the presence of density-dependent dispersal in spatially distributed food webs, as well as its implication for food web spatial structure [START_REF] Melián | Dispersal dynamics in food webs[END_REF].

Quantifying the consequences of feeding from individuals to ecosystems

Ecophysiological markers

Nutritional status and/or body condition can be assessed using diverse types of information, such as foraging success or the energy stored by individuals (Schulte- [START_REF] Schulte-Hostedde | Evaluating body condition in small mammals[END_REF]. Using ecophysiological approaches among others, nutritional status and body condition can be helpful to (1) infer feeding activities and foraging history of individuals and populations, and (2) the consequences of trophic relationships and availability of resources on individual health and fitness as well as population and community dynamics. Despite the existence of extremely invasive or lethal methods currently available to assess body condition, body composition and nutritional status, non-lethal techniques are increasingly used. As described in recent reviews, these techniques include body condition indices, body fluid biochemistry, chemical dilution techniques (isotope dilution: change in concentration of isotopes of hydrogen and/or oxygen in body water, and gas dilution: change in concentration of lipid soluble gas), electrical approaches such as body electrical conductivity and bioelectrical impedance, scanning methods (e.g. magnetic resonance imaging, ultrasound scanning, dual-energy X-ray absorptiometry, computed tomography), molecular analyses (e.g. gene expression) and measurements of stress hormones and immune responses [START_REF] Stevenson | Condition indices for conservation: new uses for evolving tools[END_REF][START_REF] Wilder | Moving beyond body condition indices as an estimate of fitness in ecological and evolutionary studies[END_REF].

In addition, animal performance (i.e. various life-history traits related to fitness, such as survival, development rate and growth, resistance to starvation, tests of stamina, and reproductive success) can be measured. These data are often used to assess the physical condition of the animal, or to evaluate the "quality" of its food and/or habitat and determining factors of trophic interactions or driver of diet selection [START_REF] Harrison | Carry-over effects as drivers of fitness differences in animals: carry-over effects in animal populations[END_REF][START_REF] Jakob | Estimating fitness: a comparison of body condition indices[END_REF][START_REF] Raubenheimer | Organismal stoichiometry: quantifying non-independence among food components[END_REF][START_REF] Visanuvimol | How dietary phosphorus availability during development influences condition and life history traits of the cricket, Acheta domesticas[END_REF]. Metabolism is also a physiological indicator; it can be determined directly through calorimetry, and indirectly through respirometry, which measures the basal metabolic rate (at rest) or the maximum oxygen consumption rate during forced exercise [START_REF] Sadowska | Laboratory model of adaptive radiation: a selection experiment in the bank vole[END_REF][START_REF] Urrejola | Diet-induced developmental plasticity in life histories and energy metabolism in a beetle[END_REF]. Among this wide range of techniques, our focus here is on those most widely used, easy to conduct, least invasive and least expensive, namely, body condition indices and body fluid biochemistry.

Body condition

Body composition, or the amount of fat vs. fat-free body mass, is probably one of the most direct indicators of body condition. It provides a quantitative assessment of energy storage because lipid stores constitute the principal form of energy reserves in animals [START_REF] Schulte-Hostedde | Evaluating body condition in small mammals[END_REF][START_REF] Walsberg | Evaluation of a nondestructive method for determining fat stores in small birds and mammals[END_REF]. Thus, the body's energy reserves are measured through analyses of body fat content or body composition. The latter is mostly based on two or three compartments: fat mass, lean dry mass/water mass and protein and ash mass [START_REF] Jakob | Estimating fitness: a comparison of body condition indices[END_REF][START_REF] Peig | New perspectives for estimating body condition from mass/ length data: the scaled mass index as an alternative method[END_REF][START_REF] Reynolds | Evaluation of total body electrical conductivity to estimate body composition of a small mammal[END_REF][START_REF] Schulte-Hostedde | Restitution of mass-size residuals: validating body condition indices[END_REF]. Alternative, but destructive methods, that can Majdi et al. Food Webs xxx (2018) xxx-xxx be conducted in study designs based on carcass collection for instance include the sampling and weighing of specific subcutaneous fat depots during dissection or the use of complementary somatic indices such as those of the liver or pancreas [START_REF] Stevenson | Condition indices for conservation: new uses for evolving tools[END_REF]. However, such methods are tedious, time-consuming and intrusive as well as destructive.

U N C O R R E C T E D P R O O F N.
Consequently, other methods have been proposed to measure body composition or fat stores, notably total body electrical conductivity [START_REF] Reynolds | Evaluation of total body electrical conductivity to estimate body composition of a small mammal[END_REF][START_REF] Walsberg | Evaluation of a nondestructive method for determining fat stores in small birds and mammals[END_REF], magnetic resonance imaging [START_REF] Mcguire | Quantitative magnetic resonance: a rapid, noninvasive body composition analysis technique for live and salvaged bats[END_REF] and body composition modelling [START_REF] Molnar | A body composition model to estimate mammalian energy stores and metabolic rates from body mass and body length, with application to polar bears[END_REF]. In certain taxonomic groups (such as birds), subcutaneous adipose depots can be assessed by simple visual inspection [START_REF] Labocha | Morphometric indices of body condition in birds: a review[END_REF], whereas others (small mammals) require simple measurements, such as pelvic circumference, considered representative of fat content [START_REF] Labocha | Which body condition index is best?[END_REF]. In microscopic organisms, coherent anti-Stokes Raman spectroscopy can be used to non-invasively observe lipid droplets in tissues (e.g. [START_REF] Fueser | Analyzing life-history traits and lipid storage using CARS microscopy for assessing effects of copper on the fitness of Caenorhabditis elegans[END_REF].

Body condition indices based on morphometrics have also been developed. Most discriminate between the mass of the individual associated with body structural size (body weight) and the mass related to energy reserves [START_REF] Green | Mass/length residuals: measures of body condition or generators of spurious results?[END_REF][START_REF] Peig | New perspectives for estimating body condition from mass/ length data: the scaled mass index as an alternative method[END_REF][START_REF] Schulte-Hostedde | Restitution of mass-size residuals: validating body condition indices[END_REF]. Accordingly, the greater the body weight is, the larger are the energy reserve, and the better is the body condition. Body condition indices thus allow the relative size of the body's energy stores to be computed, taking into account body structural size components. Historically, this was achieved using the residuals of the regression (typically, ordinary least squares regression) between body weight and some index of body size, or by calculating the scaled mass index [START_REF] Green | Mass/length residuals: measures of body condition or generators of spurious results?[END_REF][START_REF] Peig | New perspectives for estimating body condition from mass/ length data: the scaled mass index as an alternative method[END_REF]Green, 2009, 2010;[START_REF] Schulte-Hostedde | Restitution of mass-size residuals: validating body condition indices[END_REF]. Although much debated [START_REF] Wilder | Moving beyond body condition indices as an estimate of fitness in ecological and evolutionary studies[END_REF], body condition indices based on morphometrics have been, and are still, widely applied [START_REF] Labocha | Which body condition index is best?[END_REF][START_REF] Labocha | Morphometric indices of body condition in birds: a review[END_REF][START_REF] Wilder | Moving beyond body condition indices as an estimate of fitness in ecological and evolutionary studies[END_REF].

Body fluid biochemistry

Several (micro-) nutrients needed to fulfil basic energetic requirements and metabolism cannot be synthesized de novo and can only be acquired from food [START_REF] Kohl | Do wild carnivores forage for prey or for nutrients?[END_REF][START_REF] Mcwilliams | Ecology of vertebrate nutrition[END_REF]. These essential trace elements include dietary minerals (e.g. Cu, Co, Fe, Mn, Mo, Se, Zn), carotenoids, vitamins and some amino acids and FAs [START_REF] Costantini | From molecules to living systems: historical and contemporary issues in oxidative stress and antioxidant ecology: issues in oxidative stress and antioxidant ecology[END_REF][START_REF] Harrison | Carry-over effects as drivers of fitness differences in animals: carry-over effects in animal populations[END_REF][START_REF] Kohl | Do wild carnivores forage for prey or for nutrients?[END_REF][START_REF] Mcwilliams | Ecology of vertebrate nutrition[END_REF]. By measuring the levels of certain metabolites, electrolytes and enzymes, the depletion of some essential or limiting dietary element, and thus the health state (or the presence of food deficiencies) of the individual, can be determined directly. Moreover, information are given on how the resource balance is oriented toward the use (and even storage) of nutrients from the acquired food or toward the mobilisation of endogenous reserves.

With the aid of diagnostic tools similar to those used in human and veterinary medicine, body fluid biochemistry can be used to assess body condition and individual health in other organisms [START_REF] Resano-Mayor | The influence of diet on nestling body condition of an apex predator: a multi-biomarker approach[END_REF][START_REF] Schoepf | The pathophysiology of survival in harsh environments[END_REF], especially for micro-nutriments only acquired by food. Since the late 1990s, interest in non-lethal methods to evaluate the physiological state of individuals has grown and has stimulated the development of technical devices and commercial kits compatible with the measurement of micro-volumes. Thus, biochemical analyses of plasma/serum or hemolymph can be conducted by measuring various markers related to nutrition and digestion, metabolism, nutrient storage, osmoregulation, liver or kidney function and immunity. Specifically, nutritional status and patterns of energy utilisation can be assessed by measuring the levels of the products of intermediary metabolism related to diet and detectable in body fluids. This is the case for total proteins, glucose, albumin, urea, creatinine, uric acid, essential minerals and trace elements. Lipid metabolism can be assessed by measuring the concentrations of lipids and ketones, homeostasis, energetic metabolism or the functioning of tissues involved in digestion based on the activities of specific enzymes (e.g. alkaline phosphatase, lactate dehydrogenase and creatine kinase). There are also markers specifically associated with starvation, such as bile acids, bilirubin and globulin, and those that allow accurate assessments of hepatic, renal and pancreatic function or electrolyte levels (major and dietary minerals). Analyses of body fluids may also target specific micronutrients essential for normal metabolic processes and thus potentially indicative of health status. An example is carotenoids. These fat-soluble pigments originate from plants, algae or fungi but cannot be synthesized de novo by vertebrates, which must acquire them exclusively from dietary sources. Hence, carotenoid-based traits can reveal the foraging ability, resource availability and trophic interactions as well as the nutritional and immune status of their bearers [START_REF] Sternalski | Carotenoids in nestling Montagu's harriers: variations according to age, sex, body condition and evidence for diet-related limitations[END_REF].

The main drawback of these techniques lies in the difficulty of interpreting the data obtained from the battery of markers. The measured parameters must be chosen carefully to obtain convincing evidence of a metabolic pattern or change in nutritional status. Furthermore, some parameters can be interpreted only in the light of variations in others (for instance lipids or hepatic enzymes), and body fluid biochemistry can be affected by several confounding factors in the relationship with food acquisition (for instance, blood/hemolymph metabolite concentrations may change after food ingestion, and age, sex, and reproductive stage can affect metabolic levels and enzymatic activities). Given these considerations, an integrated assessment is critical and should be based on the use of several body fluid biomarkers, other metrics of body condition and could be dependant of individual and ecological factors as well [START_REF] Resano-Mayor | The influence of diet on nestling body condition of an apex predator: a multi-biomarker approach[END_REF][START_REF] Wilder | Moving beyond body condition indices as an estimate of fitness in ecological and evolutionary studies[END_REF]. Changes in physiological conditions are not always food-related but may be driven by other abiotic stressors (e.g. temperature changes, contaminants) that might be considered carefully but that are important in trophic ecology as well as to get further insights into the consequences of the interactions between environmental factors and trophic relationships (see for instance [START_REF] Bustnes | Multiple stressors in a top predator seabird: potential ecological consequences of environmental contaminants, population health and breeding conditions[END_REF]. Such issues are raising growing interest within the framework of stress ecology. Nutritional ecology is one side within trophic ecology framework that is perhaps not enough considered to build integrated approaches and may deserve further attention in studies on food webs and trophic ecology [START_REF] Raubenheimer | Nutrition, ecology and nutritional ecology: toward an integrated framework[END_REF].

Trait-based trophic ecology

Focusing on functional features rather than on taxa helps describing biodiversity from a functional point of view [START_REF] Levine | Ecology: a trail map for trait-based studies[END_REF]. Trait-based approaches can be an adequate theoretical framework for understanding and predicting food webs dynamics and properties [START_REF] Bartomeus | A common framework for identifying linkage rules across different types of interactions[END_REF][START_REF] Gravel | The meaning of functional trait composition of food webs for ecosystem functioning[END_REF]. Thus, trait-based trophic ecology investigates both (1) trophic interactions per se and (2) their ecosystem implications. First, functional traits allow inferences regarding the most probable interactions occurring within a community. A common first approach uses phenological traits or ecological preferences to detect species that co-occur and to discard unlikely trophic interactions [START_REF] González-Varo | The labile limits of forbidden interactions[END_REF]. The morphological and/or physiological traits of the co-occurring partners are then used to infer the probability of realised trophic interactions (see [START_REF] Gravel | The meaning of functional trait composition of food webs for ecosystem functioning[END_REF] for a useful framework distinguishing foraging, vulnerability and consumption traits). Because determining all interactions among individuals, even in simple systems, is fairly unattainable, narrowing those interactions using functional traits provides an alternative and can make the mechanistic underpinnings of interactions understandable (e.g. [START_REF] Ibanez | Plant functional traits reveal the relative contribution of habitat and food preferences to the diet of grasshoppers[END_REF]. In addition, functional traits enable the different dimensions of the trophic niche to be investigated individually or simultane Majdi et al. Food Webs xxx (2018) xxx-xxx ously by examining the morphological, physiological, phenological and behavioural determinants of the trophic niche of a particular species (e.g. [START_REF] Spitz | Let's go beyond taxonomy in diet description: testing a trait-based approach to prey-predator relationships[END_REF]. Two tenets of functional-trait-based approaches are essential in interpreting the implications of the identified trophic interactions. First, 'response and effect traits' link the response of individuals to higher trophic levels or to environmental stressors with the potential effects on lower trophic levels. For instance, plant diversity changes affects functional diversity of arthropods across trophic levels [START_REF] Ebeling | Plant diversity induces shifts in the functional structure and diversity across trophic levels[END_REF] which might affect ecosystem processes. Second, functional-trait-based approaches can explicitly address intra-specific variability at the individual level [START_REF] Albert | When and how should intraspecific variability be considered in trait-based plant ecology?[END_REF][START_REF] Rota | Phenotypic determinants of inter-individual variability of litter consumption rate in a detritivore population[END_REF] and the findings then scaled up to the community and ecosystem levels (e.g. [START_REF] Lavorel | How fundamental plant functional trait relationships scale-up to trade-offs and synergies in ecosystem services[END_REF].

U N C O R R E C T E D P R O O F N.
The development of functional-traits-based approaches in trophic ecology is still hampered by several limitations and drawbacks, but with recent progress these are being overcome e.g. by using methodological standardization [START_REF] Moretti | Handbook of protocols for standardized measurement of terrestrial invertebrate functional traits[END_REF]. Further, it remains difficult to assess the strength of species interactions (the direct effect that species have on their mutual demography). Nevertheless, it is possible to estimate functional food web relationships by distinguishing (1) the life-history traits which may modulate the strength of an interaction on population growth, from (2) the topological traits which may modulate the pairwise interactions between the predator and its prey, and from (3) the consumption traits which may modulate the per capita interaction strength [START_REF] Gravel | The meaning of functional trait composition of food webs for ecosystem functioning[END_REF], see also [START_REF] Brousseau | Trait matching and phylogeny as predictors of predator-prey interactions involving ground beetles[END_REF]. Additionally, the correlation between individual traits and how this lack of independence among traits reflects phylogenetic (evolutionary) constraints remain poorly understood [START_REF] Poff | Functional trait niches of north American lotic insects: traits-based ecological applications in light of phylogenetic relationships[END_REF]. Thus, the validity of linking traits to actual trophic functions continues to be a source of debate, as the causal link between them is often far from obvious, quite variable, and/or has yet to be definitively demonstrated.

Ecological stoichiometry (ES)

The consequences of elemental imbalances in ecosystems can be explored using ES approaches, in which the elemental compositions of heterotrophic organisms (generally expressed as C:N or C:P ratios) are considered as far less variable than those of primary producers, at least for most similarly sized taxa [START_REF] Persson | To be or not to be what you eat: regulation of stoichiometric homeostasis among autotrophs and heterotrophs[END_REF]. Based on the law of conservation of matter, ES approaches can predict how organisms are influenced by the mismatch between consumer demand and the elemental supply available in resources [START_REF] Sterner | Ecological Stoichiometry: The Biology of Elements from Molecules to the Biosphere[END_REF]. At the ecosystem scale, measuring imbalances can be used to estimate nutrient transfer efficiency and secondary production [START_REF] Cebrian | Producer nutritional quality controls ecosystem trophic structure[END_REF]. In the presence of excess elements in their food, consumers make use of several coping strategies such as: (1) selecting food with elemental ratios close to their requirements and/or (2) eating food of different qualities but assimilating only those elements that fulfil their requirements while rejecting those available in excess. In the latter case, mass balance models can estimate the amount of excess elements released. Experimental measurements of metazoan's nitrogen and phosphorus excretion rates showed that animals can supply nutrients at rates similar to those of other major nutrient sources and support a large portion of primary production by nutrient recycling [START_REF] Vanni | Nutrient cycling by animals in freshwater ecosystems[END_REF][START_REF] Vanni | Stoichiometry of nutrient recycling by vertebrates in a tropical stream: linking species identity and ecosystem processes[END_REF]. Excreted elements reduce nutrient limitations and impact ecosystem processes in a predictable manner [START_REF] Danger | Food-web structure and functioning of temperate and tropical lakes: a stoichiometric viewpoint[END_REF]. Accordingly, ES is a powerful conceptual framework for predicting both the consequences of resource ingestion on consumers' life history traits and the ecosystem consequences of elemental imbalances. To date, most ES studies have focused on C, N and P; however, the consideration of other essential elements (e.g. As or Cu, see [START_REF] Karimi | Beyond macronutrients: element variability and multielement stoichiometry in freshwater invertebrates[END_REF] might provide a better understanding of nutrient transfer and the potential limitations for consumer growth or ecological processes [START_REF] Welti | Bridging food webs, ecosystem metabolism, and biogeochemistry using ecological stoichiometry theory[END_REF].

Resource quality

Parameters other than the C:N:P ratios of resources can influence consumers' growth and physiological status as well as the efficiency of nutrient and energy transfer into food webs. These include several essential compounds as crucial drivers of diet selection [START_REF] Kohl | Do wild carnivores forage for prey or for nutrients?[END_REF]. For example, the lack of certain polyunsaturated FAs of the ω3 series and/or phytosterols limits Daphnia growth and/or reproduction (e.g. [START_REF] Martin-Creuzburg | Colimitation of a freshwater herbivore by sterols and polyunsaturated fatty acids[END_REF]). Micronutrients are another example and include carotenoids, described in Section 4.1.2. These pigments are important stimulators of immune responses and show antioxidant properties (e.g. [START_REF] Lucas | Differential effects of specific carotenoids on oxidative damage and immune response of gull chicks[END_REF]. Integrative approaches that include large classes of biochemical compounds (proteins, lipids, glucids) have been proposed to relate resource composition and organism fitness within a conceptual framework referred to as "nutritional geometry" [START_REF] Simpson | A multi-level analysis of feeding behaviour: the geometry of nutritional decisions[END_REF]. Its advantage is that it directly relates consumers' feeding strategies to their life history traits (e.g. optimal carbohydrate/protein ratios that optimize either individual growth or reproduction) and thus nutritional geometry allows evolutionary questions to be explicitly related to trophic ecology. Moreover, a combination of all of these resource-quality-based approaches has been proposed [START_REF] Sperfeld | Bridging ecological stoichiometry and nutritional geometry with homeostasis concepts and integrative models of organism nutrition[END_REF] and is a promising methodological strategy for research in trophic ecology.

Testing the implications of trophic interactions (trophic models)

While inference methods are used to reconstruct trophic interactions within community (Section 3), modelling approaches presented in this section allow investigations of the consequences of feeding interactions on various ecosystem features, ranging from population to ecosystem dynamics. The assumptions underlying the different models include continuous/discrete, mechanistic/statistical and individual-/population-based systems. The common goal is to simulate food web functioning from a set of given conditions, such as network structure, which can in some cases be determined through inference methods. Modelling approaches can be used to investigate the potential implications of feeding interactions in terms of community dynamics and/or organic matter/energy transfers (e.g. [START_REF] Rall | Food-web connectance and predator interference dampen the paradox of enrichment[END_REF] and thus contribute to an improved understanding and management of ecosystems. The use of models also allows the testing of hypotheses that cannot be tested in natural systems (e.g. [START_REF] Gaucherel | Understand ecosystem regime shifts by modelling ecosystem development using Boolean networks[END_REF] as well as the formulation of predictions regarding ecosystem responses to management decisions (e.g. [START_REF] Marzloff | Modelling marine community responses to climate-driven species redistribution to guide monitoring and adaptive ecosystem-based management[END_REF]. In this section, we present the main modelling approaches currently used for hypotheses testing in trophic ecology.

Ordinary differential equations and qualitative models

Ordinary differential equations (ODEs) simulating species dynamics, such as the Lotka-Volterra equations, can be adapted for food web models. The latter have been central to understanding indirect interactions in food webs and in studying the consequences of predator-prey interactions on population dynamics (e.g. [START_REF] Rall | Food-web connectance and predator interference dampen the paradox of enrichment[END_REF]. Food web models based on ODEs allow investigations of the relationship between food web complexity and stability (e.g. [START_REF] Mccann | The more food webs change, the more they stay the same[END_REF]. During the last two decades, models based on ODEs have been expanded to include allometric constraints on species traits, such as metabolic rates and feeding rates, leading to the so-called bioenergetic or allometric trophic network model [START_REF] Brose | Predicting the consequences of species loss using size-structured biodiversity approaches[END_REF]. Ecosim, the time dynamic simulation module associated with Ecopath, is a well- Majdi et al. Food Webs xxx (2018) xxx-xxx known application of this approach and it is commonly used to explore policy options in the ecosystem-based management of fisheries, such as the effects of fishing on ecosystems and the establishment of marine protected areas (see [START_REF] Walters | Structuring dynamic models of exploited ecosystems from trophic mass-balance assessments[END_REF].

U N C O R R E C T E D P R O O F N.
Qualitative modelling focuses on the feedback structure of food webs and is used to assess both stability and ecosystem responses to perturbations [START_REF] Puccia | Qualitative Modeling of Complex Systems: An Introduction to Loop Analysis and Time Averaging[END_REF]. This method, which is also based on ODEs, is particularly well suited for trophic ecology studies, as it does not rely on the quantification of all trophic interactions within a system. Indeed, based only on qualitative assessments of the interactions among major trophic compartments (e.g. positive, neutral or negative), qualitative models of food webs can provide a general understanding of ecosystem stability and dynamics based on network topology [START_REF] Hulot | Functional diversity governs ecosystem response to nutrient enrichment[END_REF]. For instance, they can be used to predict the overall responses of a community to long-term disturbances, as the spatial shift of multiple marine species due to ocean warming (e.g. [START_REF] Marzloff | Modelling marine community responses to climate-driven species redistribution to guide monitoring and adaptive ecosystem-based management[END_REF]. However, the predictions are most useful for simple networks (<15 nodes) as they become ambiguous in more complex systems (e.g. [START_REF] Dambacher | Qualitative stability and ambiguity in model ecosystems[END_REF].

Statistical approaches

Statistical approaches are based on graphical models (see Section 3.1), but in the present case, the graph structure (i.e. the trophic network) is known and is not an output of the model. Trophic interactions are represented as edges in the graph and are interpreted as statistical interactions between species by the model. Using the resulting graph, statistical approaches are able to model the probability of species persistence, explicitly, without a mechanistic model of the extinction dynamics. Unlike Lotka-Volterra or structural food-web models that are based on material fluxes, statistical approaches can be built from simple "on-field" observations of individual occurrence. The required experimental set-up is thus simpler than the one for computing the parameters and structure of Lotka-Volterra or structural models. Another advantage is the possibility to evaluate the resilience of trophic networks using the probabilities of species persistence, and not only the trophic structure. [START_REF] Mcdonald-Madden | Using food-web theory to conserve ecosystems[END_REF] adopted this approach to study the conservation management of 6 real food webs (the Alaskan, Baltic Sea, Lake Vattern, Cheasapeake Bay, Arizona Montane forest and Long Island Salt Marsh food webs) and 40 hypothetical food webs. The resulting predictions allow estimating the effect of management strategy directly at the scale of food-web and their study provide a computationally efficient way of identifying the important species to manage in large food webs.

Discrete approaches

In discrete approaches, networks of trophic interactions are represented by systems made of distinct and separate components, and characterised by temporally distinct and separated events (e.g. [START_REF] Campbell | A network model for plant-pollinator community assembly[END_REF]. As such, discrete approaches, more than classical trophic models, are particularly appropriate to consider complex interaction networks (i.e. networks with a high number of direct and indirect processes), while their behaviour remain under rigorous control. A strong advantage of discrete models is thus the possibility to model the evolution of trophic networks over time. Studying ecosystem trajectories constitutes a potential fruitful research avenue for discrete approaches that could help identifying sustainable paths (the ecosystem is able to persist and evolve) from dead-ends (the ecosystem disappears or is stuck in a specific state with less interacting species). [START_REF] Gaucherel | Understand ecosystem regime shifts by modelling ecosystem development using Boolean networks[END_REF] followed such an approach, using Boolean networks, to study the trajectories of a theoretical termite colony. By removing different numbers and types of nodes, the authors simulated different disturbances of the colony and examine the effects on the interaction net work. By doing so, they showed that the colony was highly sensitive to the trophic part of the interaction network. In addition, this example illustrates the conceptual shift permitted by discrete approaches toward broader (spatial and temporal) scales of ecological processes [START_REF] Wallach | Trophic cascades in 3D: network analysis reveals how apex predators structure ecosystems[END_REF].

Individual-based models

In an individual-based model (IBM), each individual and its associated behaviour are represented, which allows interactions among individuals to be approximated. IBMs are commonly used in ecology [START_REF] Grimm | Pattern-oriented modeling of agent-based complex systems: lessons from ecology[END_REF]. An important research activity surrounding IBMs consists in understanding how patterns at the population or community scale emerge from the interactions among individuals [START_REF] Durrett | The importance of being discrete (and spatial)[END_REF]. In trophic ecology, IBMs can be used to reveal the consequences of intraspecific variations in diet on community trophic structure [START_REF] Bolnick | Why intraspecific trait variation matters in community ecology[END_REF] or eco-evolutionary dynamics [START_REF] Melián | Eco-evolutionary dynamics of individual-based food webs[END_REF]. Another application consists in scaling from trait-based interactions between individuals to the global structure of ecological networks [START_REF] Jabot | Bitrophic interactions shape biodiversity in space[END_REF].

Dynamic energy and mass budget approaches

The dynamic energy and mass budget (DEB) theory describes the organisation of metabolism within organisms [START_REF] Sousa | From empirical patterns to theory: a formal metabolic theory of life[END_REF] by modelling its quantitative facets (assimilation rate, growth/maintenance, and maturity/reproduction) based on common rules of allocation and the processes occurring at the organism level. Standard DEB model consists in a system of three ordinary differential equations following first order dynamics. Assimilated products first enter a reserve pool which is then mobilized to fuel two pathways following the kappa rule: a fixed kappa fraction is allocated to perform growth and maintenance and the remaining fraction (1-kappa) is available for maturity (i.e. increase of complexity and its maintenance) and reproduction ( Van der Meer, 2006). A set of 12 primary parameters is calibrated from life history traits and univariate data [START_REF] Lika | The "covariation method" for estimating the parameters of the standard Dynamic Energy Budget model I: philosophy and approach[END_REF]. Common model inputs are temperature and food availability and outputs are size, shape, full life cycle dynamics, reproduction rate and composition of the organism (C, H, O, N). Standard DEB models (one reserve, isometric organism) are commonly used at the level of the individual organism (e.g. [START_REF] Grangeré | Modelling the spatial heterogeneity of ecological processes in an intertidal estuarine bay: dynamic interactions between bivalves and phytoplankton[END_REF] but they can be scaled up to population level [START_REF] Martin | Dynamic energy budget theory meets individual-based modelling: a generic and accessible implementation[END_REF] or to food web and ecosystem levels including trophic interactions (e.g. [START_REF] Marques | Can we reach consensus between marine ecological models and DEB theory? A look at primary producers[END_REF]. Interesting applications of DEB models in trophic ecology are related to diet reconstructions [START_REF] Picoche | Towards the determination of mytilus edulis food preferences using the Dynamic Energy Budget (DEB) Theory[END_REF], the effect of food stoichiometry on growth [START_REF] Muller | Stoichiometric food quality and herbivore dynamics[END_REF], the effect of prey selection on organism bioenergetics [START_REF] Lavaud | Feeding and energetics of the great scallop, Pecten maximus, through a DEB model[END_REF] and spatio-temporal dynamics of predator-prey interaction [START_REF] Grangeré | Modelling the spatial heterogeneity of ecological processes in an intertidal estuarine bay: dynamic interactions between bivalves and phytoplankton[END_REF]. With some more parameters, they also include the dynamics of body isotope composition [START_REF] Pecquerie | The impact of metabolism on stable isotope dynamics: a theoretical framework[END_REF] and thus offer promising perspectives in understanding metabolically induced variations in TDFs and in the dynamics of isotope incorporation [START_REF] Emmery | Understanding the dynamics of δ13C and δ15N in soft tissues of the bivalve Crassostrea gigas facing environmental fluctuations in the context of dynamic energy budgets (DEB)[END_REF], in turn allowing better inferences using natural stable isotope ratios.

A comprehensive toolbox of methods

Trophic ecology is a vibrant field of research supported, as discussed extensively above, by a diverse and ever-growing array of methodological tools. For ecologists seeking to answer specific trophic questions, we examine this set of tools (Table 1) based on our own experience and background (Fig. 1). For the empirical methods, our discussion includes the results of a multiple correspondence analysis (MCA) based on an evaluation of the price, investment, and affinities of each method with key criteria, such as the observational scale, organi

U N C O R R E C T E D P R O O F Table 1
Synthesis of the main advantages and drawbacks of several methods commonly used in trophic ecology. Expert assessment of empirical methods according to 12 variables is also shown: price, investment (is it a turnkey method? or does it require further development?), observational scale (from microscopic to large organisms), organisational level (from individuals to ecosystem), type of ecological question (interaction vs. flux of energy/matter), and type of produced data (qualitative vs. quantitative). 0 indicates "not adapted" and 1 indicates "strong affinity". The exceptions are the variables "price" and "investment", where 0 and 1 stand for "low" and "high" respectively, and the "data" variable, where 0 and 1 stand for "qualitative" and "quantitative" data respectively. sational level, type of ecological question to be tackled and the type of data produced (Fig. 1A; the procedure is detailed in the Appendix). The first axis of the MCA was mainly driven by the type of ecological question and the second axis was related to the investment needed to implement the methods. On the same figure (Fig. 1A), we also displayed the methods' affinity with organisational level and a rough evaluation of their costs. We completed this analysis with a subjective classification of the various trophic models (after C. Gaucherel and E. Thébault, pers. com.). On the resulting Fig. 1B, we focused on the models' affinity with the type of ecological question and organisational level for the sake of consistency with the classification of empirical methods. Not included into this classification were inference methods, because they could not be discriminated by these two axes. The resulting roadmap (Fig. 1A andB) provides an overview of the affinities of the methods for the different criteria. As an example, from Fig. 1A it can be deduced that the use of observational methods is more appropriate than stoichiometry if the nature of feeding interactions is the subject of interest. This visual overview also highlights the gaps (i.e. the absence of available method to address a specific issue), such as the modelling of fluxes at the integrated scale of ecosystems (and not only between species, see Fig. 1B). An advantage of the roadmap is that it facilitates the selection of the best combination of methods with which to investigate (or triangulate) a specific issue in trophic ecology (see below).

Detecting

U N C O R R E C T E D P R O O F
U N C O R R E C T E D P R O O F

Interconnecting approaches to advance ecological research

The abundance of methods currently available to trophic ecologists offers opportunities such as the triangulation referred to by [START_REF] Munafò | Robust research needs many lines of evidence[END_REF], i.e. the intentional use of multiple approaches which complementarity offers less-biased, multiple lines of evidence. In other words, combining two or more methods allow overcoming the shortfalls of each one alone, and initiating interdisciplinary collaborations that will enrich our knowledge and perspectives. More than combining several methods at the same integration level (e.g. SIA + FA + Gut contents), we recommend more interconnection of approaches, for example by creating first a topology using traits, then modelling and using ingestion/assimilation tracers as validations. Only a few comparative studies of methodologies have been published (but see [START_REF] Nielsen | Diet tracing in ecology: method comparison and selection[END_REF], in the following we present several examples in which complementary methods were merged or interconnected successfully and led to novel insights.

Combinations of methods have been used to improve empirical descriptions of food webs, especially as there are recurring issues related to the integration of trophic processes over time. These can be addressed by complementary approaches. For example, while assimilation tracers such as isotopes and FAs are regularly combined, the addition of complementary behavioural observations and ingestion tracers would favour the emergence of comprehensive theories and models describing tropho-dynamics in food webs (e.g. [START_REF] Woodward | Climate change and freshwater ecosystems: impacts across multiple levels of organization[END_REF][START_REF] Mcmeans | The adaptive capacity of lake food webs: from individuals to ecosystems[END_REF]. Direct field records (motion-sensitive cameras, [START_REF] Robinson | Stable isotope mixing models fail to estimate the diet of an avian predator[END_REF] are also useful additional measurements to obtain inferred food webs with a much better temporal accuracy. At the individual level, SIAs can be coupled to DNA-based analyses of gut contents to enable the detection of possible cannibalistic behaviour, as this is not possible with molecular methods [START_REF] Traugott | Empirically characterising trophic networks: what emerging DNA-based methods, stable isotope and fatty acid analyses can offer[END_REF], and to overcome the lack of dietary resolution inherent to stable isotope methods (e.g. [START_REF] Hambäck | Spatial subsidies in spider diets vary with shoreline structure: complementary evidence from molecular diet analysis and stable isotopes[END_REF].

Other examples show that interconnecting trait-based concepts with stable isotope methods sheds light on the interplay between interactions and fluxes. In fact, this has contributed to the emergence of the concept of isotopic trophic niches (Bowes et al., 2017, and references therein). Also, placing predator-prey functional traits (e.g. predator biting force vs. prey cuticle toughness) within a phylogenetic framework (e.g. evolutionary distance between trophic levels) can give rise to models of predator-prey interactions [START_REF] Brousseau | Trait matching and phylogeny as predictors of predator-prey interactions involving ground beetles[END_REF]. Observational data can contribute to inference methods and models to obtain a characterisation of the ecosystem-level properties emerging from trophic interactions (e.g. [START_REF] Pacella | Incorporation of diet information derived from Bayesian stable isotope mixing models into mass-balanced marine ecosystem models: a case study from the Marennes-Oléron estuary, France[END_REF][START_REF] De Vries | Soil food web properties explain ecosystem services across European land use systems[END_REF]. For example, a Bayesian model using topology and isotopes was specifically dedicated for the elucidation of trophic strengths in trophic networks (IsoWeb, [START_REF] Kadoya | IsoWeb: a Bayesian isotope mixing model for diet analysis of the whole food web[END_REF]. Models tested against empirical data can be employed to reveal the mechanisms operating within food Majdi et al. Food Webs xxx (2018) xxx-xxx webs and to re-assess the relevant level of complexity (guilds) at which food webs should be scrutinised in the field [START_REF] Hulot | Functional diversity governs ecosystem response to nutrient enrichment[END_REF]. Theoretical modelling and empirical data, connected through a trait-based approach to species and metabolic rates within allometric trophic networks, can successfully reproduce complex multi-species dynamics in natural environments [START_REF] Boit | Mechanistic theory and modelling of complex food-web dynamics in Lake Constance[END_REF]. Among the most recent attempts involve hybrid modelling, in which models of the overall dynamics of the ecosystem are combined realistic individual-based models to link responses at the individual and population levels [START_REF] Strauss | The power of hybrid modelling: an example from aquatic ecosystems[END_REF]. Also worthy of mention are stoichiometry-based approaches, which offer a powerful and promising perspective from which to extend our knowledge about food webs to include biogeochemical consequences and effects on ecosystem services [START_REF] Boit | Mechanistic theory and modelling of complex food-web dynamics in Lake Constance[END_REF][START_REF] Strauss | The power of hybrid modelling: an example from aquatic ecosystems[END_REF]. A stoichiometric-trait-based approach was recently described [START_REF] Meunier | From elements to function: toward unifying ecological stoichiometry and trait-based ecology[END_REF], although it requires further development [START_REF] Welti | Bridging food webs, ecosystem metabolism, and biogeochemistry using ecological stoichiometry theory[END_REF]. Multivariate DEB models (several substrates, or/and reserves and structures) offer new perspectives to integrate nutritional geometry and ecological stoichiometry into a metabolic theory through the concept of organisms' homeostasis [START_REF] Sperfeld | Bridging ecological stoichiometry and nutritional geometry with homeostasis concepts and integrative models of organism nutrition[END_REF]. Capturing complex trophic interactions within or between species could then be modelled by embedding multivariate DEB models in agent-based modelling approaches [START_REF] Sperfeld | Bridging ecological stoichiometry and nutritional geometry with homeostasis concepts and integrative models of organism nutrition[END_REF]. Finally, DEB models estimate key morphological traits, such as size, weight, shape, ingestion rates, and range of temperature tolerance. By doing so, they provide connections to biophysical models (e.g. temperature, wind speed and radiation) and to nutritional geometry that allow modelling trophic and ecological niches of organisms [START_REF] Kearney | Modelling the ecological niche from functional traits[END_REF].

U N C O R R E C T E D P R O O F N.

Including the microbial world in trophic ecology

The microbial world has long been treated almost independently from the macroscopic world [START_REF] Prosser | The role of ecological theory in microbial ecology[END_REF]. Conversely, studies of microbial diversity do not explicitly consider the concepts of trophic ecology. The emergence of molecular approaches has enabled microbial cryptic diversity to be revealed through genomics, by mapping co-occurrence networks within microbial communities [START_REF] Barberán | Using network analysis to explore co-occurrence patterns in soil microbial communities[END_REF][START_REF] Peura | Resistant microbial cooccurrence patterns inferred by network topology[END_REF]. However, the implications of the results in terms of trophic interactions within microbial communities or in relation to the metazoan food web remain poorly explored [START_REF] Peura | Resistant microbial cooccurrence patterns inferred by network topology[END_REF]. On the other hand, trophic ecology has not yet explicitly integrated the role and contribution of complex microbial communities even though the participation of microbes in aquatic and marine food webs was described more than four decades ago [START_REF] Pomeroy | The ocean's food web, a changing paradigm[END_REF], and heterotrophic protists have been recognized as the major grazers in the oceans [START_REF] Calbet | Phytoplankton growth, microzooplankton grazing, and carbon cycling in marine systems[END_REF][START_REF] Sherr | Heterotrophic dinoflagellates: a significant component of microzooplankton biomass and major grazers of diatoms in the sea[END_REF]. Bacterial and micro-eukaryotic communities are for the most part included in food web models as broad, unresolved taxonomic or functional groups, with very few exceptions [START_REF] Peura | Resistant microbial cooccurrence patterns inferred by network topology[END_REF][START_REF] D'alelio | Ecological-network models link diversity, structure and function in the plankton food-web[END_REF][START_REF] Weitere | The food web perspective on aquatic biofilms[END_REF]. Furthermore, estimates of trophic chain length fail to consider heterotrophic microbes [START_REF] Post | Using stable isotopes to estimate trophic position: models, methods, and assumptions[END_REF], while recent CSIA-based assessments register heterotrophic microbes in food webs at the same trophic positions as animals [START_REF] Steffan | Microbes are trophic analogs of animals[END_REF].

Consequently, our understanding of the "green" and "brown" food webs, including the tropho-dynamic processes of the detritusphere, emphasised already by [START_REF] Lindeman | The trophic-dynamic aspect of ecology[END_REF], remains deficient, and the potential contribution of the topology of microbial and metazoan networks to ecosystem stability and resilience barely known [START_REF] Peura | Resistant microbial cooccurrence patterns inferred by network topology[END_REF]. Several recent methodological developments may be the first steps in ground-breaking advances in our understanding of micro-macro food webs: (1) Recent developments in DNA-SIP [START_REF] Pepe-Ranney | Unearthing the ecology of soil microorganisms using a high resolution DNA-SIP approach to explore cellulose and xylose metabolism in soil[END_REF] and RNA-SIP [START_REF] Kramer | Resource partitioning between bacteria, fungi, and protists in the detritusphere of an Agricultural Soil[END_REF] allow the tracking and identification of microbial metabolisers of organic substrates up to primary consumers (see Section 2.4.3), thereby improving empirical de scriptions of the links within prokaryotes and protists but also allowing a quantification of the connection to higher trophic levels. (2) By taking advantage of the surge of metagenomic and metatranscriptomic approaches, microbial ecologists have been able to link microbial genetic diversity with the functionalities and biogeochemical processes determined in field samples (see Morales and Holben, 2011 and references therein). (3) Information on taxon-specific feeding selection and the rates measured in experimental settings from microbial and metazoan organisms can be used as input in Ecopath-like food web models adapted to explicitly include highly resolved protozoan contributors [START_REF] D'alelio | Ecological-network models link diversity, structure and function in the plankton food-web[END_REF]. These models can then be applied to explore the functional consequences of the switches in microbial food web structure on the overall trophic transfer of matter across the micro-macro continuum [START_REF] D'alelio | Ecological-network models link diversity, structure and function in the plankton food-web[END_REF]. Ecological stoichiometry [START_REF] Welti | Bridging food webs, ecosystem metabolism, and biogeochemistry using ecological stoichiometry theory[END_REF] or the application of trait-based approaches to microorganisms [START_REF] Litchman | Microbial resource utilization traits and trade-offs: implications for community structure, functioning, and biogeochemical impacts at present and in the future[END_REF] may serve as a bridge between the microbial food web and the energetics and biogeochemistry of the ecosystem, while allometric scaling could connect processes at the food web scale, thus merging the "green" and "brown" food chains (e.g. [START_REF] Mulder | Connecting the green and brown worlds: allometric and stoichiometric predictability of above-and below-ground networks[END_REF].

For trophic ecologists, these elements well evidence the so-far-unrealised opportunity to fully consider vertical biodiversity based on an explicit representation of the micro-and macroscopic actors and their roles. With the improvement of the collaboration between microbiologists and trophic ecologists many long-standing questions will finally be answered and "complexity made simple" [START_REF] Pomeroy | Caught in the food web: complexity made simple?[END_REF].

Conclusion

In a world of fast and dynamical changes in environmental conditions, there is a crucial need to understand and anticipate changes in biodiversity in both space and time. Direct effects of changes in physical factors on species depend on specific tolerance, physiological acclimation, phenotypic plasticity and evolutionary processes [START_REF] Angert | Climate change and species interactions: ways forward[END_REF], likely to create local changes of biodiversity such as spatial redistribution of species [START_REF] Marzloff | Modelling marine community responses to climate-driven species redistribution to guide monitoring and adaptive ecosystem-based management[END_REF]. Yet, evidences are piling that indirect effects of global changes through alterations in species interactions overweight direct effects (see [START_REF] Holt | Trophic interactions and range limits: the diverse roles of predation[END_REF][START_REF] Angert | Climate change and species interactions: ways forward[END_REF], or that species range shifting can induce new trophic cascades, inflating the ecological consequences of multiple species redistribution [START_REF] Marzloff | Modelling marine community responses to climate-driven species redistribution to guide monitoring and adaptive ecosystem-based management[END_REF]. Such observations of the crucial role of feeding interactions in the biodiversity response to global changes place trophic ecology at the core of the issue (see R. Holt contribution to Nature 2020 visions, Norvig et al., 2010). Recent conceptual and methodological developments in trophic ecology now allow to explore all the dimensions of such changes, but also to draw cross-scale linkages, at least for some pilot sites and case studies. Numerical improvements and machine-learning technics offer the opportunity to test theories and capitalize on these laboriously obtained field-or lab-data by expanding the time-and space scales of processes and predictions [START_REF] Faisal | Inferring species interaction networks from species abundance data: a comparative evaluation of various statistical and machine learning methods[END_REF][START_REF] Angert | Climate change and species interactions: ways forward[END_REF]. We hope this synthesis will convince our colleagues that we have at hand the perfect toolbox to finally deal with the enormous complexity of trophic implications.

  Fig. 1. (A) Multiple correspondence analysis showing the general distribution of empirical methods used in trophic ecology (see Table1for data and abbreviations). Arrows indicate the affinity of the methods with the selected features: organisational level (from individuals to ecosystems), ecological questions (interaction vs. flux of energy/matter), or commitment of budget, time and efforts (investment, price). Observational scale (i.e. microscopic to macroscopic) was mostly discriminated by axis 4, not shown here, but scores are in appendix. (B) Subjective classification of trophic models based on their affinity with the organisational level and ecological question (after C.Gaucherel and E. Thébault, pers. com.). ODE: ordinary differential equation, IBM: individual-based model, DEB: dynamic and mass budget.

Table 1 (

 1 Continued)

	Detecting prey-predator relationships, or food sources	Price	Investment	Micro	Small	Large	Individual	Population	Community	Ecosystem	Interaction	Flux	Data	Advantages	Drawbacks
	Compound-Specific Isotopic Analysis Contaminants	1 1	1 1	0 1		1 1	1 1	1 1	1 1	1 1	0 0	0 1	1 1	1 0	Integrative tracers when coupled with a labeling/Target analysis promising in Microbial Ecology/Ideally it can trace limiting compounds and eventually detect minor food sources unseen by classical methods/Better knowledge in fractionation and turnover times for specific compounds Might trace spatio-temporal ingestion and assimilation depending on the persistence of compounds within tissues (e.g. lipophilic contaminants might biomagnify along food chains)/Potentially information on foraging area, and on contamination status of species and ecosystems	Needs a good understanding of the biochemical and physiological pathways in investigated organisms or tissues/Relatively expensive Needs a source of contamination/ Biases due to side-effects on health and behaviour/Needs knowledge of contaminants' biogeochemical cycle, distribution and persistence in organisms and in the environment/ Relatively expensive
	Connecting species within networks from ecological data (inference methods)	Advantages								Drawbacks
	Gaussian graphical models Bayesian networks & dynamic Bayesian networks Logic-based approaches Linear inverse inference Approximate Bayesian computation	Popular framework to infer interactions among continuous variables/Obtained precision matrix is a direct proxy of network structure Adapted to class-occurrence data/Suitable to represent directed interactions (trophic, parasitic…)/Can be used to infer ecosystem static states or dynamics/Numerous heuristics are available to reach efficient approximate inference Adapted to qualitative data/Can incorporate background (expert) knowledge on the interactions/ Describes directed interactions/Requires relatively less data than others Particularly suited to infer the magnitude of missing interactions based on simple assumptions Replaces the step of likelihood computation by simulations of the model with variable parameter values	The network is undirected (unlike trophic/parasitic relations)/High computational complexity (sparse matrix inversion)/Unsuitable for classes-occurrence observations/Assume a Gaussian distribution of interactions Not adapted to continuous observations/Exact inference is out of reach given the combinatorial nature of the underlying optimization problem. The learnt network describes "deterministic" interactions/Accuracy of learning is hard to validate because the learning process is rather "black box" Relies on a known network topology and on the static assumption of mass balance between all network compartments at equilibrium. Requires substantial computing time
	Quantifying the consequences of feeding from individuals to ecosystems	Price	Investment	Micro	Small	Large	Individual	Population	Community	Ecosystem	Interaction	Flux	Data	Advantages	Drawbacks
	Body composition	1	1		1	1	1	1	1	0	0	0	1	1	Measuring energy storage is one of the most direct and quantitative indicator of body condition	Dissection might be time-consuming and tedious/Alternative techniques are less invasive but more expensive and require further development

Table 1 (

 1 Continued)

	Quantifying the consequences of feeding from individuals to ecosystems	Price	Investment	Micro	Small	Large	Individual	Population	Community	Ecosystem	Interaction	Flux	Data	Advantages	Drawbacks
	Body condition indices Body fluid biochemistry Traits Ecological Stoichiometry Resource quality	0 1 0 0 1	0 1 0 0 0	0 0 1 1 1	1 1 1 1 1	1 1 1 1 1	1 1 0 1 1	1 1 1 1 1	0 0 1 1 0	0 0 0 1 0	0 0 1 0 0	1 1 0 1 1	1 1 0 1 1	Cheap/Estimation of energy storage/Applicable in situ and in the lab from various data sources/ Can be non-lethal (allometry) and applied on endangered wildlife Integrative assessment of physiological state (health, diet deficiencies) Cheap/Morphological repositories widespread/Adapted for paleo-trophic ecology/Useful to infer the dimension of trophic niches Cheap/Permits to scale up processes from molecules to ecosystems, from physiology to ecosystem functioning/Predictive Essential compounds are key drivers of diet selection along the life of an organism/Existence of a "nutritional geometry" framework	Indirect measure, non-specific marker of trophic interactions/Large temporal variations (e.g. depending on annual and circadian cycle) Physiological state can be affected by other factors than nutritional stress/ Difficult interpretation that needs integrated assessment (combination of markers)/Expensive/Less suitable on small animals Difficult to assess strength in species interactions/Little understanding of how traits are inter-correlated/Little consensus and practical guidance in methodology Cannot be used as a tracer of biomass/ Sometimes too general and missing important information (e.g. nature of C compounds) Young field of research/Needs integrative, and thus potentially expensive, measures
	Testing the implications of trophic interactions (trophic models)	Advantages								Drawbacks
	Ordinary Differential Equations and qualitative models Statistical approaches Discrete approaches Individual-based models Dynamic energy and mass budget approaches	Understanding of indirect interactions and species dynamics in food webs/Qualitative models useful when the quantification of each trophic interaction is unreachable/Useful to investigate potential consequences of perturbations on food web functioning and stability Can be built from simple field observations of individual occurrences/Useful to evaluate management strategies dedicated to increase food web resilience (operational models) Adapted to discrete and qualitative interactions/Well adapted to large interaction networks, whatever the nature of components and processes/No need of calibration, except the expert knowledge defining the model/Relevant to deduce all possible trajectories and stabilities the system may experience. Help understanding how patterns emerge from inter-individual interactions/Able to scale up from trait-based interactions to structure of ecological networks Model the quantitative facets of metabolism by depicting rules of allocations and processes at the organism level/Application to diet reconstructions	ODE models for large food webs often require a disproportionate number of parameters, and all parameter combinations are impossible to test through sensitivity analysis/Predictions of the effects of perturbations with qualitative models become ambiguous for large networks (< 15 nodes) Not process-based, thus no mechanistic understanding/Dependent on collected data (over-and under-fitting) Hardly adapted to continuous quantitative abundances, biomasses or fluxes in the network Often require very intensive numerical simulations (calibration and validation stages)/Not adapted to heavy individual or multiscale networks/Hardly provide rigorous and demonstrated analyses Huge personal investment required/Decreasing interest when used for complex applications at community or ecosystem levels

Acknowledgements

This contribution is a collective effort by the French network for trophic ecology (GRET: Groupe de Recherche en Ecologie Trophique), supported by CNRS, INEE and INRA as GDR 3716. We are grateful to

Conflict of interest

The authors have no competing interests to declare. Majdi et al. Food Webs xxx (2018) xxx-xxx the numerous members of the GRET who attended workshops in Toulouse and Nantes, where fruitful discussions led to this review. We address many thanks to Craig Layman for his helpful comments on a previous draft of our manuscript. MEP proposed this review and NM, NHT and MEP led, organized and completed the writing. CG provided helpful support for Sections 3 and 5, and ET, AB and MD for Section 7.

All authors contributed critically to the drafts and gave final approval of the manuscript publication.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https:// doi.org/10.1016/j.fooweb.2018.e00100.