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Keywords: nutrient flows, agro-food systems, nitrogen, agent-based model, circular flows, agro-industrial ecology, local scale, organic waste recycling Premièrement, les directeurs et chercheurs, Laurence, Bruno

Feeding the growing global population in a context of global change raises new challenges for agriculture regarding its production efficiency and impacts on natural resources.

Solutions for towards farming sustainability require to improve nutrient and biomass recycling in agro-food systems, i.e. to move from linear to more circular flows of fertilizers, crop products, feedstuff, by-products and organic wastes. Innovative tools exploring material exchanges between farms and their upstream and downstream partners in agrofood systems at the local scale are needed. In the present work, the state of the art about analysis methods, models and environmental tools addressing nutrient and biomass flows at different scales is reviewed. The FAN ("Flows in Agricultural Network") model, an agent-based model that simulates a range of material flows among farms and their partners within agricultural districts is developed. FAN processes are explained in details and a sensitivity analysis to some key variables is performed. In addition, the FAN model is applied to a French case-study to assess the performances of contrasted scenarios aiming to enhance nutrient use efficiency, recycling strategies, biogas production and system redesign. The outcomes from the scenario simulation are analyzed are assessed in terms of food provisioning, nutrient cycling and greenhouse gas emissions. This work shows the usefulness of prospective, agent-based tools for greater farming and food-chain sustainability, to design and evaluate collective solutions for circular economy and to account for interactions among economic actors within complex agro-food systems.

Résumé de la thèse

Nourrir une population mondiale croissante dans un contexte de changements globaux pose de nouveaux défis à l'agriculture en termes d'efficience de production et d'impacts environnementaux. Rendre les systèmes agro-alimentaires plus soutenables nécessite de mieux recycler la biomasse et les nutriments, c'est-à-dire de tendre vers des flux de fertilisants, de produits végétaux, d'aliments du bétail, de coproduits et de déchets plus circulaires. À ce titre, il est nécessaire de développer de nouveaux outils pour mieux explorer et évaluer les échanges de matières entre les fermes et leurs partenaires

Introduction What the current issues related to material flows in agro-food systems are and how the present work is going to address them.

Agriculture altered global biogeochemical cycles

Population growth and consumption are driving increasing demands on agriculture and natural resources [START_REF] Godfray | Food security: the challenge of feeding 9 billion people[END_REF]. In this context, it has become one of the greatest challenges of this century to meet society's growing food needs while simultaneously reducing agriculture's environmental burden [START_REF] Cumming | Implications of agricultural transitions and urbanization for ecosystem services[END_REF][START_REF] Erb | Complexity of the international agro-food trade network and its impact on food safety[END_REF][START_REF] Fedoroff | Radically rethinking agriculture for the 21st century[END_REF][START_REF] Mouël | How can we feed the world in 2050? A review of the responses from global scenario studies[END_REF]. Studies on sustainability have pointed out agriculture to be one of the major natural resource user [START_REF] Ellis | Used planet: A global history[END_REF], chiefly land and water, and, at the same time, to be one of the major causes of environmental pollution [START_REF] Tilman | Forecasting agriculturally driven global environmental change[END_REF]. Increasing meat in human diets has fostered livestock population globally, despite the fact that the sustainability of animal production still remains under concern [START_REF] Wirsenius | How much land is needed for global food production under scenarios of dietary changes and livestock productivity increases in 2030?[END_REF]. Overall, agriculture impact drives the planet beyond its safe operating space for several ecological processes such as land-use, climate change, biodiversity, and, especially, global biogeochemical cycles [START_REF] Rockstrom | A safe operating space for humanity[END_REF][START_REF] Steffen | Planetary boundaries: Guiding human development on a changing planet[END_REF]. Indeed, one of the major issues of the global change is the alteration of the biogeochemical cycles due to nutrient management in agriculture, in particular linked to fertilizers use and livestock wastes management that severely impact the environment [START_REF] Bouwman | Human alteration of the global nitrogen and phosphorus soil balances for the period 1970-2050[END_REF]. In the case of fertilizers, intense production and extraction induced the democratization of mineral fertilizers in agriculture [START_REF] Dawson | Fertilizer availability in a resource-limited world: Production and recycling of nitrogen and phosphorus[END_REF]. Regarding nitrogen (N), since the Haber-Bosch process, i.e., industrial synthesize of ammonia, was invented, it has resulted in around half of humanity being depend on it to feed on [START_REF] Erisman | How a century of ammonia synthesis changed the world[END_REF]. Widespread mineral N over-fertilization practices in agriculture have resulted in an extremely low nitrogen use efficiency [START_REF] Braun | Reactive nitrogen in the environment: too much or too little of a good thing (UNEP/Earthprint)[END_REF]. Reactive nitrogen has affected the global nitrogen cycle in atmospheric, aquatic and terrestrial pools [START_REF] Gruber | An Earth-system perspective of the global nitrogen cycle[END_REF], by greatly increasing transfer and emissions since pre-industrial times (Figure 1. ). Another key fertilizer is phosphorus, that is derived from phosphate rock, a non-renewable resource which current global reserves may be depleted [START_REF] Bennett | A broken biogeochemical cycle[END_REF][START_REF] Cordell | The story of phosphorus: Global food security and food for thought[END_REF]. Similarly to nitrogen, its use remains inefficient in many agroecosystems [START_REF] Macdonald | Agronomic phosphorus imbalances across the world's croplands[END_REF]. The massive use of fertilizers have triggered great losses to the atmosphere [START_REF] Sutton | Too much of a good thing[END_REF], in particular as greenhouse gases [START_REF] Carlson | Greenhouse gas emissions intensity of global croplands[END_REF][START_REF] Sanz-Cobena | Strategies for greenhouse gas emissions mitigation in Mediterranean agriculture: A review[END_REF] and as nutrient leaching that triggers algae bloom and water eutrophication [START_REF] Conley | Controlling eutrophication: nitrogen and phosphorus[END_REF][START_REF] Paerl | Algal blooms: Noteworthy nitrogen[END_REF].

Organic fertilization may play a crucial role as an alternative to non-renewable mineral fertilizers through manure recycling [START_REF] Jensen | Animal manure fertilizer value, crop utilisation and soil quality impacts[END_REF][START_REF] Rufino | Manure as a key resource within smallholder farming systems: Analysing farm-scale nutrient cycling efficiencies with the NUANCES framework[END_REF]. Yet, management of livestock dejections has become a challenge in many parts of the world, where animal excreta accumulates in soils and water [START_REF] Chen | Estimating nutrient releases from agriculture in China: An extended substance flow analysis framework and a modeling tool[END_REF]Leip et al., 2015a). In addition, livestock production drives severe environmental problems, especially in terms of greenhouse gas emissions [START_REF] Herrero | Biomass use, production, feed efficiencies, and greenhouse gas emissions from global livestock systems[END_REF]. The reliance on massive nutrient and biomass material inflows are linked to environmental issues that need to be addressed [START_REF] Vitousek | Nutrient imbalances in agricultural development[END_REF]. Therefore, solutions for more sustainable food systems should involve alternatives combining both the way farming activity is performed and the use and allocation of the agricultural materials produced (Foley et al., 2011a).

Agro-food system dependency on linear flows

Current farming productions have become dependent on numerous agro materials as inputs via national and international trade [START_REF] Fader | Spatial decoupling of agricultural production and consumption: quantifying dependences of countries on food imports due to domestic land and water constraints[END_REF]. This high dependency is quite recent in the history of agriculture and has evolved together with farming specialization at both the farm and the regional scales [START_REF] Billen | The food-print of Paris: long-term reconstruction of the nitrogen flows imported into the city from its rural hinterland[END_REF][START_REF] Carmo | The NPK soil nutrient balance of Portuguese cropland in the 1950s: The transition from organic to chemical fertilization[END_REF]. The reliance of agricultural management on external inputs is especially intense in the case of livestock systems, usually by sourcing animal feed from crops produced elsewhere [START_REF] Lambin | Global land use change, economic globalization, and the looming land scarcity[END_REF]. Not only are global inflows coming to satisfy livestock systems, but also arable crop farming systems are highly dependent on mineral fertilizer flows [START_REF] Cordell | The story of phosphorus: Global food security and food for thought[END_REF][START_REF] Galloway | Transformation of the Nitrogen Cycle: Recent Trends, Questions, and Potential Solutions[END_REF][START_REF] Potter | Characterizing the spatial patterns of global fertilizer application and manure production[END_REF]. Indeed, globalization has enabled the creation of an interconnected agricultural system that sources land and materials in distant places linked by the global markets [START_REF] Liu | Framing sustainability in a telecoupled world[END_REF]. Such global interconnection is resulting in massive global exchanges of nutrients and biomass materials at the global scale (Figure 2), i.e., exchanges of food, feed, forage, and fertilizers (Lassaletta et al., 2014a;[START_REF] Macdonald | Rethinking agricultural trade relationships in an era of globalization[END_REF]. This strong dependency on input flows is also found in small specialized regions relying on nutrient and material flows at more regional, subnational scale [START_REF] Le Noë | How the structure of agro-food systems shapes nitrogen, phosphorus, and carbon fluxes: The generalized representation of agrofood system applied at the regional scale in France[END_REF]. Describing those global input and product flows as 'linear flows' is appropriate because, in a large part, the nutrients they contain are not returned where they were extracted [START_REF] Schipanski | The influence of agricultural trade and livestock production on the global phosphorus cycle[END_REF]. The importance of resources shared between farms, their food chain partners and consumers is driving new pathways for the study of agriculture and societies activities together [START_REF] Tilman | Global diets link environmental sustainability and human health[END_REF]. In this sense, some authors proposed their consideration through a systematic integration of a larger 'agro-food system' that involves, not only farms, but also the food and agricultural activities (i.e., exchanges, processing, consumption) linked to the farming production and the ecological system where they are developed [START_REF] Billen | A biogeochemical view of the global agrofood system: Nitrogen flows associated with protein production, consumption and trade[END_REF]. Actually, the material flows between the agents of the agro-food system are key drivers of the current challenges on food security, biogeochemical balances and systems stability (Ercsey-Ravasz et al., 2012). Many agro-food systems are ultimately relying on nonrenewable sources of nutrients, usually fertilizers. The increasing connectivity created by these 'linear material flows' may support access to resources at lower prices, yet it does it at the cost of decreased local self-sufficiency and destabilization of biogeochemical cycles.

Circular flows in agro-food systems as a local solution

As seen before, these constant use of linear flows exacerbate the reliance of farming systems on external nutrient inputs, yet, it does it triggering great losses to the environment. In contrast to linear flows, the development of 'circular flows' that are based on the local production and consumption of resources while reducing losses, needs to be encouraged [START_REF] Madelrieux | Écologie et économie des interactions entre filières agricoles et territoire: quels concepts et cadre d'analyze?[END_REF]. Enhancing material exchanges in 'circular flows' by closing material loops, limiting travel distances and associated energy costs and emissions can help to advance towards the sustainability of the agro-food systems [START_REF] El-Chichakli | Five cornerstones of a global bioeconomy[END_REF] and renew governance of food chains [START_REF] Brullot | Stratégies d'acteurs et gouvernance des démarches d'écologie industrielle et territoriale[END_REF]. Still, these flows need the cooperation of the actors within agrofood chains, e.g., through linking their material production and needs in local networks [START_REF] Durand | L'application du principe de proximité dans la gestion des déchets: divergence d'enjeux sociaux, techniques et environnementaux[END_REF]. Some examples of more 'circular flows' can be reached by promoting crop-livestock integration [START_REF] Moraine | Farming system design for innovative crop-livestock integration in Europe[END_REF][START_REF] Regan | Does the recoupling of dairy and crop production via cooperation between farms generate environmental benefits? A case-study approach in Europe[END_REF], biogas energy production [START_REF] Lorenz | Current EU-27 technical potential of organic waste streams for biogas and energy production[END_REF] and efficient waste recycling [START_REF] Alvarenga | Sewage sludge, compost and other representative organic wastes as agricultural soil amendments: Benefits versus limiting factors[END_REF][START_REF] Bodirsky | Reactive nitrogen requirements to feed the world in 2050 and potential to mitigate nitrogen pollution[END_REF][START_REF] Metson | Feeding the corn belt: opportunities for phosphorus recycling in US agriculture[END_REF]. Material reuse and recycling among economic actors seems a win-win solution to maintain food production while reducing pollution and preserving natural resources [START_REF] Barles | L'écologie territoriale et les enjeux de la dématérialisation des sociétés: l'apport de l'analyze des flux de matières[END_REF].

It is necessary to apply those principles to agro-food systems, concerning food production, food processing, farming practices, interactions between crops and livestock, and wastes management [START_REF] Pagotto | Towards a Circular Economy in Australian Agri-food Industry: An Application of Input-Output Oriented Approaches for Analyzing Resource Efficiency and Competitiveness Potential[END_REF].

However, most studies that addressed the analysis of circular flows have been restricted to input-output tables and static pictures of current flows, as done in substance flow analysis and industrial ecology studies [START_REF] Brunner | Substance flow analysis[END_REF][START_REF] Chertow | Uncovering" Industrial Symbiosis[END_REF]. Additionally, sustainability of farm management practices have been traditionally studied and assessed at the farm scale in detail [START_REF] Bockstaller | Agri-environmental indicators to assess cropping and farming systems: a review[END_REF]). Yet, we need new tools to estimate circular flows in agro-food systems, taking into account interactions among farms and their partners and prospective quantification of flows together with their associated environmental performances.

In particular, models can be very useful to design and assess alternative scenarios of material flows and their consequences for the environment. However, there exist very few studies developing models able to estimate nutrient and material flows and to simulate alternative, circular flows among agents in the agro-food systems. This project aims to fill this gap by conceiving and testing a model simulating flows in agro-food systems that can also be useful to simulate scenarios.

System under study

In this Ph.D. thesis, we aimed to model material flows and cycles developed by human activities related to food production and consumption as well as their associated environmental effects. For this purpose, we were interested in methods analysing flows at different local scales. We defined the local scale as regions or districts in which economic partners are spatially close enough to be connected within biomass and waste exchange networks, while sharing the same natural environment. We excluded long upstream and downstream chains such as global food markets from the scale of analysis, even if their role is important for shifting from global to local flows.

Considering the high diversity of agents in rural agro-food systems, we wondered if some of the mechanics might be to interact with higher levels of actor's organizations, from the farm to the local scale. Our local agro-food systems encompass farms, feed dealers, food consumption, food processing industries, organic wastes managers and fertilizers suppliers (Figure 3). We considered all forms of materials containing nutrients: fertilizers, crop and livestock products, organic wastes, organic and mineral fertilization flows, animal feeding and bedding flows, food processing flows and energy flows of biomass and wastes as well as related nutrient losses and emissions to the environment.

Research questions

With the objective of proposing a robust modelling tool, we formulated the three following questions:

Which approaches already exist in the scientific literature to study the exchange of biomass and nutrient flows in local agro-food systems?

Although going beyond the plot towards larger scales may be useful to better understand circular flows among actors of agro-food systems, studies and terms addressing nutrient flows and exchanges in the scientific literature are vast and sometimes confusing. A state-of-the-art exploration was performed to know if there was already an existing powerful tool for our goal, and if not, to identify the approaches to get inspiration from.

How can we simulate biomass and nutrient exchanges in local agro-food systems?

We wondered about the modelling approaches to estimate and simulate the socioeconomic and agroecological drivers behind material exchanges. This encouraged us to improve existing tools thanks to our literature exploration in order to design a new simulation model.

Can we assess scenarios of alternative material flows in agro-food systems with multiple indicators?

The ultimate goal of a simulation model is to estimate contrasted scenarios of circular flows. This is crucial in order to improve the sustainability of the system locally and to assess their production and environmental outcomes.

Thesis structure

We carried out an exploration of the scientific literature, by reviewing peer-reviewed articles dealing with nutrient and material flows, in different social-ecological and agro-food systems. We classified all the relevant approaches depending on the methods they use to understand, model and represent the conceptual framework of nutrients and biomaterials transfer in both ecological and socio-ecological systems, paying special attention to the latter. We published a review article with the different methods explained in detail, presented in Chapter 1. We found that there are three main approaches (i) those interested in measuring the impact of nutrients flows from human activities on the ecosystems; (ii) originated by the stock-flow systems related to agriculture and ecology and (iii) those simulating multi-agent populations to manage natural resources. We concluded by highlighting the need of a specific tool to simulate the exchanges between individual agents of the agro-food network.

In order to test the viability of an accurate simulation of alternative farming activities and material flows, we selected a case-study by paying special attention to areas affected by issues concerning nutrient management, and also where data was available. We decided to work on the Ribéracois district, where our research unit had previous experience. The Ribéracois is located in the Dordogne department, in the southwest of France. This district exhibits several issues concerning local nutrient and biomass management such as nutrient losses to water sources, difficulties for feeding livestock locally and development of biogas production. Although the boundaries and size of the district were difficult to set, we found that the French local entity 'Communauté de communes du pays de Ribéracois' satisfies a compromise between enough diversity of agents and a reasonable amount data to process in the simulations. The total selected area was around 1000 km 2 , with 635 km 2 of utilizable agricultural area. The district includes approximately 835 farms encompassing a diversity of farming activities, such as arable, dairy, beef production, pig, ovine and horticultural production, in both specialized and mixed crop-livestock farms. The Ribéracois characteristics are further explained in Chapters 2 and 3.

We present a new agent-based model, 'Flows in Agro-food Networks' (FAN) in Chapter 2, which simulates the processing and exchange of fertilizers, feed, food and wastes among farms and with their multiple upstream or downstream partners (feed and fertilizer suppliers, food industries, waste processors, and anaerobic digesters) at the local scale. We developed the FAN model in GAMA 1.7 platform, an opensourced coding environment that supports the use of geographical information systems within the agent-based language GAML. FAN includes a series of environmental indicators that can be used to assess alternative scenarios in terms of ecosystem services, nutrient cycling, and resource autonomy. It also provides a powerful tool to assess opportunities for circular bioeconomy, including by simulating competitions between local and global sourcing of resources in agro-food networks. We used the Ribéracois as a case study in France to demonstrate FAN's dynamics and to explore its sensitivity to key variables.

Finally, we applied FAN to the simulation of alternative scenarios of material exchanges in Ribéracois in Chapter 3. Eight scenarios were implemented following the 'Efficiency, Substitution and Redesign' framework. These scenarios ranged from the introduction of best agricultural management practices, collective solutions including recycling and biogas production, up to complete redesign of the agricultural systems including changes in land-use, livestock population and chemical fertilizer availability. The outcomes of simulating the scenarios were analyzed through an integrated assessment.

Chapter 1 -"Towards an Agro-Industrial Ecology: a review of nutrient flow modelling and assessment tools in agro-food systems at the local scale"

Published in 2016 in Science of the Total Environment, 543, 467-479.

Introduction

The demand for agricultural and natural resources is continually increasing due to global population growth and overall diet transition to higher meat consumption.

Meeting society's growing food needs while simultaneously reducing the environmental impact of agriculture is, undoubtedly, one of the greatest challenges of the century (Foley et al., 2011a); [START_REF] Godfray | Food security: the challenge of feeding 9 billion people[END_REF][START_REF] Makowski | Global agronomy, a new field of research[END_REF].

Nutrients such as nitrogen and phosphorus play a critical role in food production and global food security [START_REF] Erisman | How a century of ammonia synthesis changed the world[END_REF][START_REF] Wetzel | Inorganic nutrients: nitrogen, phosphorus, and other nutrients[END_REF] and have been widely used as fertilizers to sustain high agricultural yields for decades [START_REF] Tilman | Agricultural sustainability and intensive production practices[END_REF]. However, the massive use of fertilizers during the last decades has resulted in dramatic changes in global nutrient cycles. In particular, large nutrient losses from agricultural soils to the environment have resulted in natural ecosystem pollution and the loss of services provided by these ecosystems. For example, the massive use of mineral nitrogen fertilizers has led to dramatic changes in the atmospheric, aquatic and terrestrial pools of the global nitrogen cycle as well as to increased transfers between compartments, compared to pre-industrial times [START_REF] Gruber | An Earth-system perspective of the global nitrogen cycle[END_REF]. This has caused serious ecosystem disturbances, including water eutrophication, soil acidification and greenhouse gas emissions [START_REF] Conley | Controlling eutrophication: nitrogen and phosphorus[END_REF][START_REF] Galloway | Transformation of the Nitrogen Cycle: Recent Trends, Questions, and Potential Solutions[END_REF][START_REF] Sharpley | Managing agricultural phosphorus for protection of surface waters: Issues and options[END_REF]. Similarly, the widespread use of mineral phosphorus fertilizers derived from phosphate rock in industrial agriculture is increasing the risk of depletion of this non-renewable and highly geopolitically-sensitive resource [START_REF] Cordell | The story of phosphorus: Global food security and food for thought[END_REF]. Phosphorus transfers from agricultural lands to water bodies are also known to trigger algae bloom and eutrophication in freshwater ecosystems [START_REF] Conley | Controlling eutrophication: nitrogen and phosphorus[END_REF]. There is, therefore, an urgent need for a drastic increase in use efficiency and recycling of these nutrients, in particular, in areas where food production has been highly intensified.

Large efforts have been made to improve nutrient management in agriculture over the last decades [START_REF] Gerber | Nutrient use efficiency: a valuable approach to benchmark the sustainability of nutrient use in global livestock production?[END_REF]. In the past, this generally involved understanding and modelling nutrient dynamics in the soil-plant system and designing decision tools for fertilization at the field and farm scale [START_REF] Gruhn | Integrated nutrient management, soil fertility, and sustainable agriculture: current issues and future challenges[END_REF][START_REF] Havlin | Soil fertility and fertilizers: An introduction to nutrient management[END_REF][START_REF] Nesme | Are agronomic models useful for studying farmers' fertilization practices?[END_REF]. These tools helped to correct improper management of fertilizers and manure by farmers and to better adjust fertilizer supply to crop requirements at these small spatial scales. However, these approaches were inherently limited since they did not consider some key segments of the nutrient cycles that occur at larger scales, such as material flows (e.g., grain, straw and manure) between farms and their upstream and downstream economic partners (e.g., feed and fertilizer suppliers, grain and livestock product collectors and processors, waste producers, etc.). Such upscaling is in fact needed to improve our understanding of how nutrients flow in and out of farms and, ultimately, into the environment, and to promote more efficient recycling loops in agriculture [START_REF] Nowak | Nutrient recycling in organic farming is related to diversity in farm types at the local level[END_REF].

Industrial ecology emerged during the last decades as a scientific field focused on the interactions between industrial societies and their environment, considering industrial societies as systems [START_REF] Allenby | Industrial ecology[END_REF]. Developing a circular economy that protects finite natural resources by the better closure of materials and energy cycles is at the core of its principles [START_REF] Ayres | A handbook of industrial ecology[END_REF][START_REF] Socolow | Industrial ecology and global change[END_REF].

For that purpose, industrial ecology encompasses a range of approaches ranging from ecology and industrial management to economy and sociology [START_REF] Andrews | Building a micro foundation for industrial ecology[END_REF][START_REF] Boons | The social embeddedness of industrial ecology[END_REF][START_REF] Seuring | Industrial ecology, life cycles, supply chains: differences and interrelations[END_REF]. Numerous approaches have been developed to design recycling loops and to explore circular economy options in industrial social-ecological systems. They include Substance Flow Analysis [START_REF] Brunner | Substance flow analysis[END_REF], Industrial Symbiosis analysis [START_REF] Chertow | Uncovering" Industrial Symbiosis[END_REF] and regional Life Cycle Assessment [START_REF] Frischknecht | Notions on the design and use of an ideal regional or global LCA database[END_REF]. However, these approaches strongly differ in terms of purpose, scope and framework, making the assessment of their advantages and drawbacks to design recycling loops extremely difficult.

Our aim in this paper is to review the different approaches that were designed to analyze, assess and simulate nutrient flows and to explore nutrient recycling scenarios in complex social-ecological systems. We focused our analysis on agro-food systems at the local scale where economic agents may exchange agricultural inputs, products, by-products and waste. We defined the local scale as regions or districts in which economic partners are spatially close enough to be connected within exchange networks while sharing the same natural environment. We excluded long upstream and downstream chains such as global food markets from our analysis (Figure 3).

We argue that agro-food systems have several specificities compared to purely industrial social-ecological systems. These specificities are related to: (i) the strong interactions between farming production processes and the natural environment; (ii) the predominance of diffuse vs. point source pollution in farming operations; (iii) the highly scattered nature of farming enterprises within landscapes; and (iv) the high diversity of farming practices and interactions over time and space. For these reasons, we paid specific attention to environmental assessment approaches that account for diffuse nutrient losses to the environment, and to agent-based models that account for social interactions within complex social systems. We consider this extended set of approaches to be better suited to the analysis of nutrient flows within agro-food chains and to the design of efficient recycling loops in agriculture. In that perspective, we propose to define Agro-Industrial Ecology as the specific application of industrial ecology to farming system analysis (Figure 4). We provide below a comparison of the major approaches that we identified based on their purpose, scope, application context, and environment and actor representation.

According to these criteria, we found that these approaches could be classified into three major groups:

(i) Environmental impact assessment tools (Section 2);

(ii) Stock and flow Analysis methods (Section 3);

(iii) Agent-based models (Section 4).

We develop each of these approaches in the following sections. In each section, we describe the major characteristics of each approach, giving examples of studies with a brief contextualisation, highlighting their relevance and their key features.

Finally, we present a comparison of their potential for modelling nutrient flows and for designing recycling loops in agro-food systems (Section 5) and a conclusion (Section 6). Although classifying approaches may be debatable at some level, we distinguished between tools, methods and models. Depending on their final purpose, we considered tools to be usage-oriented, methods to be analysis-oriented, and models to be prediction-oriented. Even though the boundaries of these terms might be fuzzy, we decided to consider models only if they are based on complex numerical calculations to predict future events.

Environmental Impact Assessment Tools

The first group we identified is related to the environmental impact assessment of agro-food systems. These tools have a clear focus on nutrient losses from agricultural land to the natural environment. These approaches often use nutrient emission indicators that we classified into two categories, depending on the way they estimate impacts. These categories are "real nutrient flow indicators" when nutrient flows and production processes are co-located; and "virtual nutrient flow indicators" when nutrient flows and production processes are spatially disconnected.

Real nutrient flow indicators

In this category, we aggregated different approaches aimed at quantifying nutrient losses from agricultural lands to the environment, e.g., to estimate nitrate leaching to water bodies or nitrous oxide (N2O) emissions to the atmosphere. These approaches have a strong biophysical background and are clearly focused on agroecosystem processes, whereas they do not generally take economic agents other than farms into account. Most of these indicators are based on simple statistical calculations -such as N2O emissions as a linear or exponential function of nitrogen fertilizer supplied [START_REF] Philibert | Quantifying uncertainties in N 2 O emission due to N fertilizer application in cultivated areas[END_REF] -but some of them are based on more sophisticated models that incorporate several natural and anthropogenic drivers such as soil, climate and farming practices [START_REF] Brisson | An overview of the crop model STICS[END_REF]. Many of those indicators have been developed at the field scale, but some upscaling has in fact been attempted to address larger systems such as districts and regions. Among them, we highlighted two widespread approaches that appear to be relevant to assess nutrient flows: environmental risk mapping and integrated assessment of agricultural systems.

The environmental risk mapping approach aims to establish pollution risk maps, generally for one specific pollutant. It uses geographical information systems to superimpose several sets of spatial information underlying the environmental risk, e.g., soil, climate, elevation, land-use, farming practices, etc. [START_REF] Lahr | Environmental risk mapping of pollutants: State of the art and communication aspects[END_REF]. Several cases exist in the literature concerning nutrients, including soil phosphorus fertility depletion [START_REF] Brown | Soil phosphorus fertility degradation: A geographic information system-based assessment[END_REF], nitrogen flows within landscapes [START_REF] Theobald | Modelling nitrogen fluxes at the landscape scale[END_REF] and nitrate leaching risk [START_REF] Assimakopoulos | A GIS-based fuzzy classification for mapping the agricultural soils for N-fertilizers use[END_REF]. This approach is adapted when risk mapping can be accurately assessed by just superimposing information about biophysical context, land-use and management practices. However, it does not account for complex interactions in management practices, nor for the role of agents and their social organization in that pollution.

The integrated assessment of agricultural systems aims to estimate agricultural impacts on the environment within a multi-criteria perspective. While different impacts are considered, nutrient losses to the environment are almost always considered. In contrast with the previous approach, nutrient losses are often considered in a sophisticated way by accounting for multiple farming practices and their potential interactions. Although there is a wide variety of tools that could be used [START_REF] Bockstaller | Agri-environmental indicators to assess cropping and farming systems: a review[END_REF], most of them bring together a set of agroenvironmental indicators. The INDIGO® tool, for example, is a wide-ranging set of indicators capable of evaluating farm sustainability based on farming practices such as crop rotation, fertilization, irrigation and pesticide use [START_REF] Bockstaller | Evaluation agri-environnementale des systèmes de culture: la méthode INDIGO®[END_REF]. Ultimately, these indicators can serve as multi-criteria decision-making tools that support farmers' groups and policy-makers [START_REF] Sadok | Ex ante Assessment of the Sustainability of Alternative Cropping Systems: Implications for Using Multi-criteria Decision-Aid Methods-A Review[END_REF]. Most of these tools have been designed at the field or farm scale, whereas very few have been designed at the district scale. In addition, this approach is usually based on local or multi-local data, but is rarely spatialised. [START_REF] Payraudeau | Environmental impact assessment for a farming region: a review of methods[END_REF] provided one of the very few reviews of the application of those tools at different regional scales, including examples at the local scale. They concluded that different indicators of nutrient losses to the environment could be identified, but the clarification of their position in the cause-effect chain related to farming practices is strongly recommended (Figure 5). Overall, a key asset of real nutrient flow indicators is their ability to integrate both soil and climate conditions together with farming practices to accurately estimate diffuse nutrient losses from agriculture. Such indicators are therefore of critical importance to capture the complex interactions between farming systems and their natural environment and to accurately estimate nutrient losses in social-ecological systems. However, these indicators remain strongly focused on agro-ecosystems and do not consider economic agents other than farms: since they do not address nutrient losses from other agents, in particular, from point sources, these indicators are therefore not appropriate to assess total nutrient losses within complete agro-food systems. In addition, their focus on the agricultural production segment of agro-food chains makes them inappropriate to explore opportunities for designing recycling loops among agents and their environment.

Virtual nutrient flow indicators

In this category, we aggregated indicators used to estimate nutrient flows related to product development, use and disposal. Here, nutrient flows and production processes can be spatially disconnected: in addition to direct (on-site and internal) emissions or resource use, these indicators also account for indirect (off-site, external, embodied, upstream and downstream) emissions or resource use. This category encompasses two major groups of indicators: nutrient footprints and Life

Cycle Assessment (LCA). Although several definitions exist, footprint approaches usually encompass nutrient losses occurring upstream of a given product. In contrast, LCA encompasses all nutrient losses that may occur upstream and downstream along a product chain, i.e., through the whole life cycle of a product, including during product use and disposal.

Footprint indicators have been widely used to estimate single environmental impacts of a given product or activity. The carbon footprint remains the most widespread of these: it estimates the total amount of greenhouse gas emissions that are directly and indirectly caused by an activity or that are accumulated over the life stages of a good or a service, expressed in kg of CO2-equivalent [START_REF] Wiedmann | A definition of 'carbon footprint[END_REF]. Some studies considered a spatial scale dimension in LCA assessments. In that case, all consumption activities within a defined area are taken into account and equated into a single element, such as estimating carbon footprints of regions and countries by input-output tables [START_REF] Wiedmann | A review of recent multi-region input-output models used for consumption-based emission and resource accounting[END_REF]. Similar footprint indicators have been developed concerning nutrients. Nitrogen footprint indicators [START_REF] Andrews | Our nitrogen 'footprint': the need for increased crop nitrogen use efficiency[END_REF][START_REF] Galloway | Transformation of the Nitrogen Cycle: Recent Trends, Questions, and Potential Solutions[END_REF] have already been applied to European food products [START_REF] Leip | The nitrogen footprint of food products in the European Union[END_REF]. Similarly, phosphorus footprint indicators [START_REF] Macdonald | Embodied phosphorus and the global connections of United States agriculture[END_REF][START_REF] Matsubae | Virtual phosphorus ore requirement of Japanese economy[END_REF][START_REF] Metson | The role of diet in phosphorus demand[END_REF][START_REF] Wang | The phosphorus footprint of China's food chain: implications for food security, natural resource management, and environmental quality[END_REF] follow mineral phosphorus consumption paths in agro-food chains. They can be used to estimate the contribution of specific regions to the global depletion of non-renewable phosphate rock resources. When applied to nutrients, these indicators are able to estimate nutrient pollution along agro-food chains, and to aggregate local and remote impacts within a globally sensitive context.

Life Cycle Assessment (LCA) assesses all environmental impacts associated with a product or a process by accounting for and evaluating its resource consumption and pollutant emissions during its life stages [START_REF] Guinée | Handbook on life cycle assessment operational guide to the ISO standards[END_REF]. When applied to nutrients, LCA uses nitrogen and phosphorus footprint indicators, in particular, to estimate the risks of water eutrophication. For food production systems, the analysis includes not only on-farm activities, but impacts related to the production of farm inputs such as fertilizers, seeds and imported feed as well. LCA has been widely used to study food production systems [START_REF] Roy | A review of life cycle assessment (LCA) on some food products[END_REF] where further research has been carried out to quantify fertilization impacts [START_REF] Van Zeijts | Fitting fertilization in LCA: allocation to crops in a cropping plan[END_REF]. Despite the fact that LCA is usually applied to a specific production process [START_REF] Haas | Life cycle assessment framework in agriculture on the farm level[END_REF], it has recently been applied to landscapes and districts. In that case, LCA either focuses on a specific production process or accounts for any activities that take place in the area considered [START_REF] Loiseau | Adapting the LCA framework to environmental assessment in land planning[END_REF]. Examples of the former include the comparison of the environmental performance of fossil fuels vs. local biomass and biofuel production in New York State [START_REF] Heller | Life cycle assessment of a willow bioenergy cropping system[END_REF], Spain [START_REF] Butnar | Life-cycle assessment of electricity from biomass: Case studies of two biocrops in Spain[END_REF][START_REF] Gasol | LCA of poplar bioenergy system compared with Brassica carinata energy crop and natural gas in regional scenario[END_REF] and China [START_REF] Ou | Energy consumption and GHG emissions of six biofuel pathways by LCA in (the) People's Republic of China[END_REF]. Examples of the latter include territorial LCA applied to a university campus in Barcelona (Lopes Silva et al., 2014) and to a French Mediterranean region [START_REF] Loiseau | Implementation of an adapted LCA framework to environmental assessment of a territory: Important learning points from a French Mediterranean case study[END_REF]. Through these examples we can observe that LCA assesses multiple environmental impact categories and that it is powerful enough to account for a set of diverse activities within the same area.

Compared to real flow indicators, virtual flow indicators are able to consider nutrient losses to the environment related to inputs and outputs occurring on upstream or downstream farms. They, therefore, provide integrated assessment of resource use efficiency throughout complex production chains. However, estimations of nutrient losses to the environment are generally not site-specific or spatially explicit, which limits their accuracy. Finally, although these indicators have some potential to estimate nutrient losses and resource use along agro-food chains, they have rarely been applied to complex social-ecological systems such as agent networks at the local scale.

Stock and Flow Analysis Methods

The second group of approaches we identified is related to the calculation of stocks and flows of substances, materials or energy through social-ecological systems within territories. In these methods, the system under study is described in terms of storage and transfer of conservative energy or matter flowing in, out and through the system. These stock and flow methods are widely used to represent and sometimes model nutrient cycles within complex social-ecological systems, with the specific objective of identifying losses and accumulations occurring within the systems. Such methods belong to the family of mathematical input-output models applied to system dynamics [START_REF] Miller | Input-output analysis: foundations and extensions[END_REF]. They aim to integrate the socioeconomic dimension into ecological system analysis [START_REF] Folke | Resilience: the emergence of a perspective for social-ecological systems analyzes[END_REF], with a particular focus on resource and substance flows through human activities.

Basically, stock-flow methods break down the systems under study into compartments. Those compartments usually aggregate major physical or economic agents within the study area considered, whereas one or several compartments represent the environment. Major flows among compartments are then identified and represented by arrows in a specific graphical schematisation. Those flows are generally quantified by multiplying material flows by their specific nutrient content but they may sometimes be calculated by differences with other flows based on the mass conservation law [START_REF] Chen | Anthropogenic cycles of the elements: A critical review[END_REF].

All the stock and flow methods refer to some substance flow analysis principles (Section 3.1). However, other related approaches exist with specific objectives and contexts. They yield different sub-groups and names such as: urban metabolism, when applied to cities; industrial symbiosis, when applied to clusters of industries with an optimisation objective; and integrated crop-livestock system analyzes, when applied to mixed farming systems. Although some overlap exists between these methods, we develop each of these sub-groups, along with some examples, in Sections 3.2, 3.3 and 3.4.

Substance Flow Analysis

Substance Flow Analysis (SFA) is a generic method to quantify substance or material flows and stocks in various contexts and scales [START_REF] Van Der Voet | Substance flow analysis methodology[END_REF]. Although SFA can be applied to very detailed systems, a classical characteristic of most SFAs is the aggregation of all physical or economic agents with similar properties into single compartments. For example, all industries with similar input use and output production are aggregated into the same compartment, whereas soils, crops and animals are aggregated into "soils", "crops" and "animal" compartments, respectively, each of them having stocks where substances may accumulate or be depleted. This aggregation strategy makes SFA different from industrial symbiosis or crop-livestock systems analysis where each economic agent is represented individually. When modelling nutrients along social-ecological systems, such system analysis is used to reveal where nutrients may accumulate and be transferred to the environment.

To better illustrate the schematic representation of nutrient cycles in SFA, we selected the analysis of the phosphorus cycle at the national scale in France [START_REF] Senthilkumar | Phosphorus recovery and recycling from waste: An appraisal based on a French case study[END_REF]. In this study, all physical agents (agricultural soils, crops, animals, landfills and water bodies) and economic agents (food/feed industry, municipal waste and human populations) were aggregated depending on their characteristics and their input/output properties (Figure 6). In addition, recycling flows and losses were estimated, highlighting the efficiency properties of the system.

In this case, agricultural soils, water bodies and landfills were clearly major phosphorus sinks at the country scale. SFA principles were applied to nutrient cycles at different spatial scales from districts to cities, basins, landscapes, regions and countries. Some examples include nutrient flows applied to specific economic sectors in different parts of the world, such as a the steel industry [START_REF] Jeong | Substance flow analysis of phosphorus and manganese correlated with South Korean steel industry[END_REF], municipal waste [START_REF] Sokka | Flows of nitrogen and phosphorus in municipal waste: a substance flow analysis in Finland[END_REF] and the trout fish sector [START_REF] Asmala | Closing a loop: substance flow analysis of nitrogen and phosphorus in the rainbow trout production and domestic consumption system in Finland[END_REF]. Nutrient analysis using SFA methods has been applied to cities [START_REF] Li | Phosphorus flow analysis of civil food production and consumption system[END_REF][START_REF] Ma | Nitrogen flow analysis in Huizhou, south China[END_REF][START_REF] Schmid Neset | The flow of phosphorus in food production and consumption -Linköping, Sweden, 1870-2000[END_REF][START_REF] Yuan | Understanding the anthropogenic phosphorus pathway with substance flow analysis at the city level[END_REF] and to landscapes [START_REF] Liu | Substance flow analysis on phosphorus cycle in Dianchi basin, China[END_REF]. Finally, Substance Flow Analysis has been widely used for phosphorus analysis at the country scale, frequently considering agro-food systems [START_REF] Antikainen | Stocks and flows of nitrogen and phosphorus in the Finnish food production and consumption system[END_REF][START_REF] Chen | Estimating nutrient releases from agriculture in China: An extended substance flow analysis framework and a modeling tool[END_REF][START_REF] Cooper | A substance flow analysis of phosphorus in the UK food production and consumption system[END_REF][START_REF] Cordell | Phosphorus flows through the Australian food system: Identifying intervention points as a roadmap to phosphorus security[END_REF][START_REF] Matsubae-Yokoyama | A material flow analysis of phosphorus in Japan[END_REF]Senthilkumar et al., 2012a[START_REF] Senthilkumar | Conceptual design and quantification of phosphorus flows and balances at the country scale: The case of France: DESIGN OF P FLOWS FOR FRANCE[END_REF]. These examples illustrate the broad spectrum of the SFA application contexts, from industrial chains and economic sectors, to cities, landscapes or countries.

By providing a robust framework for analysing nutrient flows and stocks under different material forms within social-ecological systems across different scales, SFA methods are a critical element for assessing and modelling nutrient cycles within agro-food systems. They provide the possibility to follow nutrient paths under different material forms. This feature is essential to the study of mixed contexts where materials easily change their forms, as often happens in agro-food systems where farming, industrial and natural pools of nutrients are observed together.

Their system representation also provides a sound basis for calculating nutrient budgets at the district scale and for deriving estimations of nutrient losses. However, the aggregation strategy, which is often a core principle of SFA approaches, is clearly a limitation to the simulation of detailed flows among different economic agents. In addition, their often static basis is a limitation to the dynamic simulation of nutrient flows within complex and interacting social-ecological systems.

Urban Metabolism

Considering cities as super-organisms, urban metabolism analysis aims to quantify material and energy flows in, out and through the area under study. Appearing between the 1960s and the 1970s [START_REF] Duvigneaud | Études écologiques de l'écosystème urbain bruxellois: contributions no 1 à 4 (Société royale de botanique de Belgique)[END_REF][START_REF] Wolman | The metabolism of cities[END_REF], urban metabolism analysis methods were originally limited to black-box models and inputoutput accounting [START_REF] Kennedy | The study of urban metabolism and its applications to urban planning and design[END_REF]. Nowadays, urban metabolism analysis are inspired by other complex approaches such as ecological networks, substance flow analysis and environmental assessment methods [START_REF] Zeeman | Urban metabolism: A review of research methodologies[END_REF]. Urban metabolism usually considers flows and stocks from different materials, substances and energy among very different urban compartments (industries, households, infrastructures, environmental entities, etc.). In some occasions, system representation in urban metabolism might be very similar to those used for natural food webs by categorising the different urban sectors into "producers" (e.g., the environment as the supplier of natural resources), "consumers" (e.g., productive and domestic activities), and "reducers" (e.g., pollution clean-up activities): such system representation was adopted in urban metabolism studies of the water cycle in Beijing [START_REF] Zhang | Ecological network analysis of an urban water metabolic system: Model development, and a case study for Beijing[END_REF].

Nutrient budgeting has been extensively considered in urban metabolism approaches. Nutrient budgets integrate inputs and outputs from and to different urban compartments that often include households, industries and environmental entities. For instance, nitrogen budgets were assessed in Toronto [START_REF] Forkes | Nitrogen balance for the urban food metabolism of Toronto, Canada[END_REF], Phoenix [START_REF] Baker | Nitrogen balance for the Central Arizona-Phoenix (CAP) ecosystem[END_REF] and Paris [START_REF] Barles | Feeding the city: food consumption and flow of nitrogen, Paris, 1801-1914[END_REF][START_REF] Barles | Urban metabolism of Paris and its region[END_REF][START_REF] Billen | The food-print of Paris: long-term reconstruction of the nitrogen flows imported into the city from its rural hinterland[END_REF], and in Chinese urban food systems [START_REF] Li | Urban phosphorus metabolism through food consumption[END_REF]. Carbon, nitrogen and phosphorus flows have been assessed in Minnesota [START_REF] Fissore | Carbon, nitrogen, and phosphorus fluxes in household ecosystems in the Minneapolis-Saint Paul, Minnesota, urban region[END_REF]. Moreover, landscape metabolism includes examples of nitrate flows and emissions in Central

Europe [START_REF] Haag | Landscape fate of nitrate fluxes and emissions in Central Europe: A critical review of concepts, data, and models for transport and retention[END_REF] and in Hungarian lowlands [START_REF] Oláh | Improving landscape nitrogen metabolism in the Hungarian lowlands[END_REF]. These examples show that although urban metabolism studies focusing on nutrients can target the same objectives as the SFA methods applied to cities, they may not consider a whole mass balance since some flows are sometimes not quantified and do not always follow elements along their whole cycle.

Some urban metabolism studies may consider nutrient flows together with other material flows such as water, energy and greenhouse gas emissions. Although urban metabolism remains far from agro-food chain assessment, some key ideas such as the conceptualisation of urban actors as producers, consumers and reducers (or waste recyclers) are of primary importance to simulate nutrient flows within agrofood systems that include several trophic and product transformation levels.

However, the poor mechanistic basis underlying urban metabolism may prevent their use for exploring and simulating options for more efficient recycling loops within social-ecological systems.

Industrial Symbiosis Analysis

Industrial symbiosis analysis aims to understand how economic agents can be integrated within clusters to better close material, nutrient and energy cycles. By looking for optimised exchanges and the use of raw materials, products, by-products and waste among agents, it searches for closed loops of materials and energy [START_REF] Chertow | INDUSTRIAL SYMBIOSIS: Literature and Taxonomy[END_REF]. Industrial symbiosis analysis is therefore an essential method for the circular economy and geographic proximity.

A key asset of industrial symbiosis is the ability to consider different kinds of industries, i.e., not only farms but their upstream and downstream partners as well, and to make their specific input demands and supply capacities explicit. An additional asset of these methods is their ability to cover different types of materials, substances (e.g., water, nutrients and carbon) or energy (e.g., heat and electricity) flows that may be converted into each other. By analysing how, and with what degree of efficiency, these different resources are processed, produced and transformed within clusters of agents, efficient recycling loops can be designed at the local scale.

However, industrial symbiosis analyzes are merely descriptive since they represent static, actual flows among industries and activities, although they have the potential to design dynamic predictive models. In addition, this method strongly focuses on economic agents, but only provides rough estimations, if any, of nutrient losses to the environment.

One of the paradigmatic examples of industrial symbiosis is the Danish industrial park of Kalundborg [START_REF] Ehrenfeld | Industrial ecology in practice: the evolution of interdependence at Kalundborg[END_REF]. This case study includes several economic agents such as a refinery, a power plant, a gypsum plant and enzymatic industries, numerous local farms and a municipality. As indicated in Figure 7, numerous recycling loops are highlighted but nutrient losses to the environment are not explicitly estimated. In classic examples of industrial symbiosis, organic compounds are rarely at the core of industrial symbiosis analysis. They are generally considered as by-products or waste from bio-refineries, agro-industries or organic-oriented chemical industries, and they end up as fertilizers for local farmers [START_REF] Beers | Industrial symbiosis in the Australian minerals industry: the cases of Kwinana and Gladstone[END_REF][START_REF] Ehrenfeld | Industrial ecology in practice: the evolution of interdependence at Kalundborg[END_REF]. However, some studies have focused more specifically on nutrient flows related to organic compounds: examples of such studies are related to biofuels [START_REF] Martin | Improving the environmental performance of biofuels with industrial symbiosis[END_REF][START_REF] Ometto | The benefits of a Brazilian agroindustrial symbiosis system and the strategies to make it happen[END_REF]; to the forestry and paper industries [START_REF] Korhonen | Regional industrial ecology: examples from regional economic systems of forest industry and energy supply in Finland[END_REF][START_REF] Sokka | Industrial symbiosis contributing to more sustainable energy use -an example from the forest industry in Kymenlaakso, Finland[END_REF]; to pharmaceutical, cogeneration and wastewater treatment [START_REF] Chertow | Industrial symbiosis in Puerto Rico: Environmentally related agglomeration economies[END_REF]; to algae cultivation through wastewater treatment [START_REF] Soratana | Evaluating industrial symbiosis and algae cultivation from a life cycle perspective[END_REF]; and to food processing industries such as sugar refineries [START_REF] Zhu | Industrial Symbiosis in China: A Case Study of the Guitang Group[END_REF] and an agro-food cluster [START_REF] Simboli | The potential of Industrial Ecology in agri-food clusters (AFCs): A case study based on valorisation of auxiliary materials[END_REF]. Industrial symbiosis approaches have been applied to farming systems, e.g., to couple aquaculture, crops and livestock [START_REF] Dumont | Prospects from agroecology and industrial ecology for animal production in the 21st century[END_REF], and to smallholder farms in Liberia [START_REF] Alfaro | Applying Industrial Symbiosis to Smallholder Farms: Modeling a Case Study in Liberia, West Africa[END_REF]. There is thus a great potential to apply industrial symbiosis analysis to agro-food chains, in particular, when economic agents strongly interact within a given district [START_REF] Nowak | Nutrient recycling in organic farming is related to diversity in farm types at the local level[END_REF].

The multi-resource and multi-agent approach of industrial symbiosis analysis can indeed serve as a guideline for designing recycling loops in agro-food chains, even though nutrient losses are hardly considered.

Integrated Crop-Livestock System Analysis

Integrated crop-livestock system analysis aims to represent and simulate nutrient flows through material exchanges among complementary farming enterprises. When applied to the district scale, they focus on flows between livestock and arable farms through feedstuff (e.g., cereals and straw) and organic fertilizers (e.g., animal manure and crop residues) [START_REF] Thornton | Integrated crop-livestock simulation models for scenario analysis and impact assessment[END_REF]. Although these approaches focus on organic materials in agricultural contexts, their system representation may be similar to Industrial symbiosis analysis since both represent detailed flows between partners at the local scale. Nevertheless, crop-livestock system analysis often uses more complex approaches such as mechanistic or dynamic models to derive flows among system components. For example, they may include crop models to simulate crop growth response to fertilizer application or livestock models to simulate manure production in response to livestock feed. Crop-livestock system analyzes have been used, for example, to assess farming system sustainability [START_REF] Bonaudo | Agroecological principles for the redesign of integrated croplivestock systems[END_REF], farming diversification [START_REF] Sulc | Integrated crop-livestock systems in the US Corn Belt[END_REF], and resource use efficiency [START_REF] Cortez-Arriola | Resource use efficiency and farm productivity gaps of smallholder dairy farming in North-west Michoacán[END_REF]. These methods have been widely applied to improve African smallholder crop-livestock systems in terms of soil carbon, nitrogen and phosphorus management [START_REF] Alvarez | Whole-farm nitrogen cycling and intensification of crop-livestock systems in the highlands of Madagascar: An application of network analysis[END_REF][START_REF] Barrett | Natural resources management in African agriculture: Understanding and improving current practices[END_REF][START_REF] Bouwman | Exploring global changes in nitrogen and phosphorus cycles in agriculture induced by livestock production over the 1900-2050 period[END_REF][START_REF] Giller | Communicating complexity: Integrated assessment of trade-offs concerning soil fertility management within African farming systems to support innovation and development[END_REF][START_REF] Manlay | Spatial carbon, nitrogen and phosphorus budget in a village of the West African savanna-II. Element flows and functioning of a mixed-farming system[END_REF]) and can also be spatialised [START_REF] Bellassen | Multi-criteria spatialization of soil organic carbon sequestration potential from agricultural intensification in Senegal[END_REF]. Major progress on nutrient analysis and modelling has been made within the NUANCES Project (Nutrient Use in Animal and Cropping systems -Efficiencies and Scales), where not only actual nutrient flows were analyzed, but also dynamically simulated under different scenarios (Rufino et al., 2011[START_REF] Rufino | Manure as a key resource within smallholder farming systems: Analysing farm-scale nutrient cycling efficiencies with the NUANCES framework[END_REF][START_REF] Tittonell | Carbon and nutrient losses during manure storage under traditional and improved practices in smallholder croplivestock systems-evidence from Kenya[END_REF]Tittonell et al., , 2009a;;[START_REF] Van Wijk | Identifying key entry-points for strategic management of smallholder farming systems in sub-Saharan Africa using the dynamic farm-scale simulation model NUANCES-FARMSIM[END_REF]. In these examples, complex crop-livestock models were applied to study nutrient flows among African smallholder farmers and the environment. Many crop-livestock models have been applied in developing countries where access to chemical fertilizers is limited and waste management is, instead, a key issue. In most cases, farm typologies are a prerequisite to identify and model the different agents and their material exchange strategies according to their farming systems (Figure 8). A definitive asset of crop-livestock analysis methods is their strong biophysical and biotechnical background: by incorporating mechanistic models that simulate crop and herd processes and management, they provide realistic representations of farming systems. They thus represent a critical element in the simulation of nutrient flows within and between farming systems in a given territory. However, their strong focus on farms limits their possibility to simulate nutrient flows within complex agro-food systems that involve upstream and downstream economic partners.

Agent-Based Models

The third group of approaches we identified consists of a diverse research domain related to artificial intelligence based on the concept of "agents" [START_REF] Niazi | Agent-based computing from multi-agent systems to agent-based models: a visual survey[END_REF]. Agent-based models are computerised simulations of a number of stakeholders, decision-makers and institutions that are formally represented in the model and that interact through prescribed rules. Agent-based models were originally developed for the artificial intelligence field, which aimed to reproduce the knowledge and decision-making of several heterogeneous agents that are embedded in and that interact with a dynamic environment. When these agents need to coordinate to jointly solve planning problems, they generally have learning capacities that adapt in response to changes in the environment [START_REF] Bonabeau | Agent-based modeling: Methods and techniques for simulating human systems[END_REF].

These models offer a better comprehension of the agents' roles and the consequences of their actions within interconnected agent networks. They help to improve stakeholders' knowledge, to facilitate their dialogue and to negotiate from different viewpoints and conflicting objectives [START_REF] Barnaud | Multi-agent simulations to explore rules for rural credit in a highland farming community of Northern Thailand[END_REF]. They have been used in a wide range of disciplines, from social and economic behaviour to species networks.

So far, agent-based models have been used for many kinds of resources, but not directly for nutrient cycle modelling. To remain consistent with our objective, which is to simulate nutrient flows through complex agro-food systems, we limited our analysis to two application contexts of agent-based models: those applied to natural resource management and those applied to industrial symbiosis.

Agent-based models have been applied to natural resource management to better understand the role of actors within a district on the conservation of these resources [START_REF] Janssen | Complexity and ecosystem management: the theory and practice of multi-agent systems[END_REF]. The interactions of the social agents with their dynamic environment are at the core of these models. According to Bousquet and Le Page management in order to estimate or negotiate water demand for irrigation between farmers [START_REF] Athanasiadis | A hybrid agent-based model for estimating residential water demand[END_REF][START_REF] Becu | Agent based simulation of a small catchment water management in northern Thailand: description of the CATCHSCAPE model[END_REF][START_REF] Feuillette | SINUSE: a multi-agent model to negotiate water demand management on a free access water table[END_REF]. Agentbased models have also been used to simulate farmers' assimilation of technological innovation, public policies or changes in resource availability [START_REF] Mathevet | Agent-based simulations of interactions between duck population, farming decisions and leasing of hunting rights in the Camargue (Southern France)[END_REF].

These models have also served as platforms in participatory analysis, such a roleplaying game to simulate land-use [START_REF] Castella | Participatory simulation of land-use changes in the northern mountains of Vietnam: the combined use of an agent-based model, a role-playing game, and a geographic information system[END_REF] or water management [START_REF] Gaudou | The MAELIA Multi-Agent Platform for Integrated Analysis of Interactions Between Agricultural Land-Use and Low-Water Management Strategies[END_REF]. Concerning agro-food-systems, [START_REF] Schreinemachers | An agent-based simulation model of humanenvironment interactions in agricultural systems[END_REF] showed how to couple farmers' decision-making simulations with biophysical models, thus accounting for strong interactions between farmers' investment decisions and crop dynamics (Figure 9). In this study, they developed an agentbased model to understand how agricultural technology, market dynamics, environmental change and policy intervention affect farm households and their agroecological resources. Agent-based models can also be applied to industrial symbiosis aiming to simulate industrially transformed materials among network exchanges of industries [START_REF] Axtell | Agent-Based Modeling and Industrial Ecology[END_REF][START_REF] Kraines | Applying Agent-based Simulation in Industrial Ecology[END_REF]. This type of models goes beyond the static approach of industrial symbiosis analysis: it considers how agents adapt to different environmental, social and economic conditions. However, very little research exists on agent-based models applied to the symbiosis within agro-food production systems.

A significant example is the study of pulp and paper industries and oilseed crops [START_REF] Bichraoui | Agent-based Modelling Simulation for the Development of an Industrial Symbiosis -Preliminary Results[END_REF] where driving forces that promoted industrial symbiosis under different scenarios were identified, although no ecological and farming dynamics were included. Another example is related to the BIOMAS Project [START_REF] Guerrin | Modélisation des flux de biomasse et des transferts de fertilité[END_REF], which aimed to model organic matter exchange between horticultural farms, animal farms and wastewater treatment stations.

By accounting for interactions among a wide variety of economic actors, agent-based models are clearly essential in simulating material exchanges within complex socialecological systems. Their ability to address different economical or environmental contexts is an additional asset to realistically simulate decision making of interacting agents. However, their often limited biophysical background means that their ability to simulate nutrient flows within agro-food chains requires significant adaptation efforts.

Discussion

In the previous sections, we reviewed three main approaches that help to simulate nutrient flows in agro-food systems. In this section, we provide an overall comparison of those approaches in terms of purpose, scope and framework (Table 1Table 1.) and in terms of scale and agent modelling (Figure 10). We then discuss their interest for modelling nutrient flows in agro-food systems at the local scale. As a receptor or impacted compartment. Some of its features may be taken into account (soil, climate)

As one or several physical compartments (soil, water, air) that exchange substances with economic compartments

As a surrounding context with sensitive resources

How are the agents represented?

Through their activities and practices

As aggregated compartments supplying or receiving flows

As autonomous, interacting decisionmakers

What is the spatial scale?

From plot to farm, sometimes extended to larger scales (Env. Risk Mapping) or to production chains (LCA, Footprints)

From local to global (districts or cities)

Mostly local (districts, cities or regions)

What is the time scale?

From day to year year From day to year How is the system dynamics?

Generally static, based on empirical (e.g., footprints, LCA) or mechanistic data (e.g., as a function of climatic conditions or farming practices)

Generally static and sometimes dynamic

Dynamic through stochastic simulation of social and natural processes and decision-making Globally, they are Tools (although sometimes based on encapsulated models)

Analysis methods, but sometimes models as well Models Our analysis revealed that each of the approaches that we considered in the previous sections has its pros and cons when simulating nitrogen or phosphorus cycles in complex agro-food systems. For instance, our analysis highlighted the fact that environmental assessment tools are indispensable to account for the critical segment of nutrient cycles that is related to losses to the environment. However, these tools remain clearly focused on a short segment of the agro-food chain, namely the agricultural production segment, making them inappropriate to link these losses to the complex functioning of the local agro-food chain or to design recycling loops among economic agents within districts.

In contrast, stock and flow analysis methods are more ubiquitous and can be applied to a vast range of spatial scales, from cities and districts to regions and countries (Figure 10). Moreover, these methods generally embed a large number of economic agents that are more or less aggregated. The degree of aggregation varies from no aggregation (e.g., in industrial symbiosis), to large aggregation based on input/output typology (e.g., in SFA and Crop-Livestock System Analysis). This makes stock and flow analysis methods capable of simulating material exchanges within longer segments of the agro-food chain (e.g., including farms and their upstream and downstream partners) (Figure 10). However, our analysis also revealed that the interactions between economic agents and their environment are generally poorly considered in these methods, leading to rough estimations of nutrient losses from agro-food activities to the environment. In addition, stock and flow analysis methods are often static and rarely spatially explicit, thus providing limited opportunities to dynamically explore alternative scenarios of agro-food chains that could promote resource conservation and recycling.

Finally, although stock and flow methods represent a progress in conceptualising agents' practices compared to environmental impact assessment tools, our analysis showed that agent-based models provide unique opportunities to simulate dynamic interactions among economic agents within a district (Figure 10). Conceptualising autonomous and decision-making agents makes it possible to take the interactions among agents and with the environment into account (Table 1). However, our analysis highlighted the fact that nutrient losses to the environment are generally simulated on a simple basis. In addition, modelling the specific decision-making of the different agents remains a challenge.

Although the aim of all of these approaches is sustainability, it is not surprising that Ecology to study agro-food systems sustainability and food chain cycles.

Conclusion and perspectives

Rural districts are characterised by a high number of individual and interacting agents, i.e., numerous individual, autonomous and scattered farms; input suppliers; agricultural product collectors and processors; waste managers; etc. By contributing to material exchanges, all of these agents control some segments of the global nitrogen and phosphorus cycle. Designing agro-food systems that efficiently recycle nutrient resources and limit their losses to the environment therefore requires the consideration of these different agents. This is even reinforced by the fact that agricultural production systems are increasingly specialised and embedded in long supply chains, leading to more extensive material exchanges within food chains.

Actually, nutrient recycling opportunities at the farm scale might be limited in the future and there is the additional need to explore recycling loops at the local scale.

While classical analysis methods provided by industrial ecology may be of great help to simulate material exchanges among economic agents, their inability to account for agricultural processes in terms of ecological dynamics and agent behaviour makes them poorly adapted for exploring realistic scenarios of agro-food system organization. The same holds true for agent-based models that often have a very limited capacity to accurately simulate diffuse nutrient losses to the environment and material exchanges among agents.

Indeed, coupling a consistently mechanistic natural environment with an unpredictable socio-economic system necessarily requires complex tools, analysis and models. For instance, coupling stock and flow and environmental assessment tools would help to link nutrient losses to the environment with material exchanges within food chains. Similarly, coupling stock-flow methods with agent-based models would help to link exchanges within food chains to agent decision-making and their corresponding driving forces. Due to their complete accounting of system functioning, stock-flow methods appear to be a critical element in nutrient modelling at the local scale. However, such couplings remain challenging in terms of system representation (e.g., to have a correspondence between decision-makers and stockflow compartments) and in terms of system spatialisation (e.g., to have a correspondence between stock-flow compartments and accurate estimation of nutrient losses to the environment). The fact that each of the methods, tools and models presented above has its own limitations means that none alone is able to accurately simulate nutrient cycling in agro-food systems alone. In contrast, we consider that linking stock and flow, environmental impact and stakeholders' decision-making approaches would be of great help to explore and assess innovative scenarios of agro-food systems. We believe that the development of an Agro-Industrial Ecology capable of linking complex environmental assessment, socioeconomic agent interactions and farming decision-making would be an essential approach to address the global challenges concerning nutrient management today.

Introduction

Improving resource-use efficiency in agriculture is crucial to reducing pressures on natural resources while simultaneously enhancing agricultural productivity [START_REF] Erb | Complexity of the international agro-food trade network and its impact on food safety[END_REF]Foley et al., 2011b). Food systems in many regions are increasingly comprised of highly specialised farms connected to global markets, which can create spatial disconnects between food consumers and agriculture's environmental impacts [START_REF] Liu | Framing sustainability in a telecoupled world[END_REF]. Globalization has also resulted in massive exchanges of food, feed, forage, and fertilizers in agriculture (Lassaletta et al., 2014a;[START_REF] Macdonald | Rethinking agricultural trade relationships in an era of globalization[END_REF], and such 'linear' flows among regions can exacerbate reliance of local farming systems on external inputs by decreasing the potential for local recycling [START_REF] Schipanski | The influence of agricultural trade and livestock production on the global phosphorus cycle[END_REF][START_REF] Tittonell | Farming systems ecology: Towards ecological intensification of world agriculture[END_REF]. The reliance of agricultural management on external inputs of fertilizers is especially pervasive in livestock farming systems [START_REF] Herrero | Biomass use, production, feed efficiencies, and greenhouse gas emissions from global livestock systems[END_REF], and has been acknowledged as key drivers of water eutrophication [START_REF] Leip | Impacts of European livestock production: nitrogen, sulphur, phosphorus and greenhouse gas emissions, land-use, water eutrophication and biodiversity[END_REF]) and greenhouse gas emissions [START_REF] Carlson | Greenhouse gas emissions intensity of global croplands[END_REF]. While the increasing connectivity created by global material flows via trade may support increased access to resources at lower prices, it does so potentially at the cost of decreased local self-sufficiency and import dependency [START_REF] Fader | Spatial decoupling of agricultural production and consumption: quantifying dependences of countries on food imports due to domestic land and water constraints[END_REF][START_REF] Le Noë | How the structure of agro-food systems shapes nitrogen, phosphorus, and carbon fluxes: The generalized representation of agrofood system applied at the regional scale in France[END_REF]. In contrast, greater reliance on local materials exchange ('circular' flows) can help to promote crop-livestock integration [START_REF] Moraine | Farming system design for innovative crop-livestock integration in Europe[END_REF][START_REF] Regan | Does the recoupling of dairy and crop production via cooperation between farms generate environmental benefits? A case-study approach in Europe[END_REF], biogas energy production [START_REF] Lorenz | Current EU-27 technical potential of organic waste streams for biogas and energy production[END_REF] and efficient waste recycling [START_REF] Alvarenga | Sewage sludge, compost and other representative organic wastes as agricultural soil amendments: Benefits versus limiting factors[END_REF][START_REF] Bodirsky | Reactive nitrogen requirements to feed the world in 2050 and potential to mitigate nitrogen pollution[END_REF][START_REF] Metson | Feeding the corn belt: opportunities for phosphorus recycling in US agriculture[END_REF]. Such 'closed-loop' approaches are key for more sustainable and autonomous bio-economy patterns in agro-food systems [START_REF] El-Chichakli | Five cornerstones of a global bioeconomy[END_REF][START_REF] Scarlat | The role of biomass and bioenergy in a future bioeconomy: policies and facts[END_REF].

Designing and assessing alternative scenarios of material flows within local agro-food systems can help decision-makers to identify the feasibility and pathways to move towards a circular economy [START_REF] Ingrao | Agricultural and forest biomass for food, materials and energy: bio-economy as the cornerstone to cleaner production and more sustainable consumption patterns for accelerating the transition towards equitable, sustainable, post fossil-carbon societies[END_REF][START_REF] Smith | Addressing policy challenges for more sustainable local-global food chains: Policy frameworks and possible food "futures[END_REF]. However, assessment of alternative scenarios is challenged by the complex nature of agro-food networks [START_REF] Fernandez-Mena | Towards an Agro-Industrial Ecology: A review of nutrient flow modelling and assessment tools in agro-food systems at the local scale[END_REF], which involve flows and relationships among different economic agents in the food production sector (e.g., farms, fertilizer and feed suppliers, slaughterhouses, food processors, and waste managers).

Modelling interactions by simulating material exchanges among economic agents in agro-food networks is an approach that helps to design, quantify and assess the potential socioeconomic and ecological benefits of social change towards circular economy patterns [START_REF] Elsawah | A methodology for eliciting, representing, and analysing stakeholder knowledge for decision making on complex socio-ecological systems: From cognitive maps to agent-based models[END_REF][START_REF] Filatova | Spatial agent-based models for socio-ecological systems: Challenges and prospects[END_REF][START_REF] Page | Agent-based modelling and simulation applied to environmental management[END_REF]. Agent-based modelling is a particularly important as a tool that enables simulation of complex material flows among a range of economic agents and to assess the potential outcomes of different scenarios on multiple environmental indicators [START_REF] Fernandez-Mena | Towards an Agro-Industrial Ecology: A review of nutrient flow modelling and assessment tools in agro-food systems at the local scale[END_REF].

At present, only a relatively small number of studies have applied agent-based modelling to agrofood systems. These studies have typically focused on specific aspects of the agro-food systems, rather than integrating across multiple agro-food system sectors and activities. For example, past agent-based modelling has been applied to the study of environmental changes in farming systems [START_REF] Acosta-Michlik | Assessing vulnerability of selected farming communities in the Philippines based on a behavioural model of agent's adaptation to global environmental change[END_REF][START_REF] Murray-Rust | Conceptualising the analysis of socio-ecological systems through ecosystem services and agent-based modelling[END_REF][START_REF] Schreinemachers | An agent-based simulation model of humanenvironment interactions in agricultural systems[END_REF]; agricultural markets and policies [START_REF] Bert | Simulating agricultural land rental markets by combining agent-based models with traditional economics concepts: The case of the Argentine Pampas[END_REF][START_REF] Schouten | Comparing two sensitivity analysis approaches for two scenarios with a spatially explicit rural agent-based model[END_REF]; landuse change [START_REF] Groeneveld | Theoretical foundations of human decisionmaking in agent-based land use models -A review[END_REF][START_REF] Le | Land Use Dynamic Simulator (LUDAS): A multi-agent system model for simulating spatio-temporal dynamics of coupled humanlandscape system: 2. Scenario-based application for impact assessment of land-use policies[END_REF]; agricultural water management [START_REF] Becu | Agent based simulation of a small catchment water management in northern Thailand: description of the CATCHSCAPE model[END_REF][START_REF] Gaudou | The MAELIA Multi-Agent Platform for Integrated Analysis of Interactions Between Agricultural Land-Use and Low-Water Management Strategies[END_REF]; urban and agricultural waste management [START_REF] Bichraoui | Agent-based Modelling Simulation for the Development of an Industrial Symbiosis -Preliminary Results[END_REF][START_REF] Courdier | Agent-based simulation of complex systems: application to collective management of animal wastes[END_REF][START_REF] Xu | Understanding the mechanism of food waste management by using stakeholder analysis and social network model: An industrial ecology perspective[END_REF]; and rural livelihoods and self-sufficiency [START_REF] Iwamura | Agentbased modeling of hunting and subsistence agriculture on indigenous lands: understanding interactions between social and ecological systems[END_REF][START_REF] Magliocca | Exploring agricultural livelihood transitions with an agent-based virtual laboratory: global forces to local decision-making[END_REF][START_REF] Villamor | Biodiversity in rubber agroforests, carbon emissions, and rural livelihoods: An agentbased model of land-use dynamics in lowland Sumatra[END_REF]. To our knowledge, agent-based models have not yet been applied to simulate material flows across a broader range of components in agro-food networks, including multiple agents and a wide range of exchanged materials. This more holistic analysis is, however, key to assess alternative agricultural development strategies, waste recycling, and environmental impacts related to circular economy.

Here, we present an agent-based model, "Flows in Agro-food Networks" (FAN), which facilitates the simulation of multiple types of material exchanges across upstream and downstream agents in local scale agro-food networks. Multiple types of biomass materials containing nutrients are considered in FAN, i.e. fertilizers, forage, feed, food and wastes, in order to simulate the effect of contrasted scenarios of material exchanges. We developed the FAN model in GAMA 1.7 platform [START_REF] Drogoul | Gama: multi-level and complex environment for agent-based models and simulations[END_REF][START_REF] Grignard | GAMA 1.6: Advancing the art of complex agent-based modeling and simulation[END_REF][START_REF] Taillandier | GAMA: a simulation platform that integrates geographical information data, agent-based modeling and multiscale control[END_REF], an open-sourced coding environment that supports the use of geographical information systems within the agent-based language GAML. In this paper, we present and illustrate FAN's features, and how the model can be applied to assess outcomes arising from multi-agent interactions in terms of local food and bioenergy production, nutrient cycling, greenhouse gas emissions, and other indicators of environmental quality under user-defined scenarios. We also use a case study of a district in

France to examine the model sensitivity for its key input variables.

FAN Model Overview

In this section, we use the Overview Design concepts and Details "ODD" protocol for agent-based model descriptions (Grimm et al. 2006;2010) to outline the FAN model, including the model purpose, scope, and agents' characteristics. We also introduce the mechanisms involved in the material exchanges through individual decision-making processes and social simulation. Each of the sub-sections further describes the modelling approach used in FAN, from the model conception, to the submodel and processes simulated. The GAML code for FAN and its attached files are provided in the supplementary materials (Supplementary Materials File 1).

Purpose

We developed FAN in order to simulate material flows among economic agents in local agro-food networks. We define agro-food networks as encompassing various activities related to food production and consumption at local scales (Figure 3). They include farming activities and losses to the environment at the farm scale, interactions between farms and their partners through material exchanges, as well as waste and by-product recycling. In FAN, food, feed and wastes are processed and exchanged among farms, and their upstream and downstream partners that have direct connections to farms in the agro-food network. These partners include feed and fertilizer suppliers, food industries, waste processors, and anaerobic digesters. Their features are presented in the next section.

The key foundations for developing more closed-loop agro-food systems can be simulated by focusing on individual agent choices (e.g., for sourcing different materials) across the local network or via exchanges with global markets. The main variables driving these exchange processes in FAN are choices between organic versus chemical fertilizer use, use of crop products for human food, animal feeding or biomass-based energy production, and by-product and waste management strategies. In turn, the model can be parameterized in order to simulate alternative scenarios and their assessment in terms of various environmental indicators, including greenhouse gas emission, nutrient losses, and ecosystem service proxies that result from material exchanges among agents.

Entities, state variables and scales

FAN was developed for application to local or sub-regional case studies (e.g., ≈1,000 km 2 ).

Although many agent-based models have been developed for applications to specific geographical contexts, FAN can be adapted for its use in a variety of rural and agricultural case studies where core input data is available. Key requirements include data on land use, livestock numbers and feed rations, as well as crop yields and fertilization rates. Here, we conduct sensitivity analysis by applying FAN to an agricultural case study for a sub-region of southwestern France with about 835 farms (Ribéracois district in the department of Dordogne, ~1,000 km 2 ; see Section 3.1).

Although we carried out surveys of major farm partners such as feed and food collectors and food industries in order to guide the development of FAN, the scale and number of farms is large enough to make unfeasible gather surveys of farmers individually. For this reason, FAN is able to generate synthetic populations of agents based on general data collected in public statistics providing land-use and livestock in farms.

In FAN, points and vectors are used to represent agents and flows, rather than as raster grid cells that are common in agent-based models (e.g., [START_REF] Grimm | Pattern-oriented modeling of agent-based complex systems: lessons from ecology[END_REF][START_REF] Rebaudo | Agent-based modeling of human-induced spread of invasive species in agricultural landscapes: insights from the potato moth in Ecuador[END_REF]. As a result, agent attributes, such as the land use of each farm, are stored as attributes. The model is therefore able to take into account the geographic location of the agents (represented as points), flows between agents (represented as vectors), and to distribute these points according to specific addresses or randomly. Simulation of larger and smaller areas is also possible with FAN, as well as the use of different numbers of agents. In FAN, the eight farm functional groups are created based on local farming typologies, each one having its own surface, land-use and livestock number of heads. Each farm agent may find partners to exchange with, depending on whether they are supplying or demanding specific materials (boxes in Figure 12) and if these materials are exchanged in the network or not.

Although the model focusses on local-scale exchanges within the specified study area, agents can also exchange with global markets outside of the system boundaries. Global markets in FAN represent unidirectional supplies with (i) fertilizers, competing with local organic fertilizers; (ii) feed (cereals, oilseeds and pulses) and forage (such as dry alfalfa), compensating local deficit for feed requirements; and (iii) digestible biomass, compensating local deficit for anaerobic digestion.

When local agents are connected to the global market, FAN assumes that they have access to an unlimited supply (e.g., fertilizer supply from the global markets is not constrained).

Process overview and scheduling

Since the core purpose of FAN is to simulate local-scale material flows in agro-food networks, here we present how the related processes are scheduled and what rules govern the types and magnitude of these flows. The steps of the model represent different production and exchange activities during a simulation cycle, equivalent to a year (Figure 13).

The simulation cycle begins with the production of fertilizing materials such as manure, digestates and sewage by farms, anaerobic digesters and wastewater treatment plants. These fertilizing materials are then applied to agricultural soils according to each farm's nutrient demand. Chemical fertilizers can also be used by farms. Excess manure may be saved for bioenergy production by anaerobic digesters. Subsequently, each farm's crop production is calculated as a function of fertilizing material inputs to soils through a simple linear yieldresponse model. Animal feed requirements are estimated according to species-specific feed demand, and crop products are exchanged in order to meet these animal requirements. Once feed and forage requirements are satisfied, livestock production is calculated.

After total crop and animal production has been computed, fruits, vegetables, and animal products are exchanged with local food industries, where they are processed, generating processed food and food wastes. Finally, once food wastes have been exchanged with livestock farms and anaerobic digesters, the latter results in bioenergy production. Note that global markets can create competition with local materials (e.g., imported chemical fertilizers can compete with local manures for fertilizing soils) or can compensate local production deficits (e.g., in feedstuff and forage to meet animal requirements). When exchanging each material, the choice of partners in the network is made based on the weight calculated according to Equation 1. Calculating this weight helps to rank each pair of agents combining a supplier (i) and a demander (j) willing to exchange.

Weighti,j= Proximityi,j * Supply-Demand Ratioi,j * Preference (Equation 1)

Where:

 Proximity = ( 1 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑠 𝑖,𝑗
𝑎 ); with Distanceij the distance in km between agents i and j; a is a user-defined exponential of distance accounting for local transportation issues and a key factor when allocating biomass [START_REF] Görgüner | A transport cost-based optimization for recycling of municipal sludge through application on arable lands[END_REF][START_REF] Metson | Feeding the corn belt: opportunities for phosphorus recycling in US agriculture[END_REF];

 Supply-Demand Ratio = ( min|𝛹𝑆 𝑖 ,𝛹𝐷 𝑗 | max [𝛹𝑆 𝑖 ,𝛹𝐷 𝑗 ]
) where 𝛹𝑆 𝑖 , 𝛹𝐷 𝑗 are the potential supply and demand of the agents, respectively, in kg of materials. This ratio accounts for matching potentials among agents, which has been acknowledged to be significant driver of material exchanges [START_REF] Zhao | Research on Integration of Livestock Products Supply Chain Based on the Optimal Match Between Supply and Demand[END_REF]. This ratio is only applied to local biomass exchanges (i.e., it is not applied to commodities that are sourced from the global market);

 Preference coefficients [0-1] are simulation artefacts that we created to orient agents in a context where a specific material type or use is preferred, (e.g., because markets make it cheaper or regulation compulsory). These preference coefficients are used to represent agent behavior in a context where different material types can serve the same usage (e.g., both mineral fertilizers and animal manure can be used to fertilize soils) or a given material can serve different usages (e.g., animal manure can serve to fertilize soils and to be used as substrate by anaerobic digesters).

The factors that we have simulated (e.g., distance, supply-demand ratio, preference coefficients) drive the possibilities to initiate an exchange with one agent rather than with another one (Figure 14). While in theory Equation 1 applies to any potential supplier or demander, we added three additional variables to better mimic real-world processes and to limit the duration of calculations. First, a 'Disposition to exchange' variable helps to set the proportion of farms that are willing to exchange their biomass, including manure, forage and straw. This variable assumes the possibility that not all farmers are interested in exchanging products with no clear price in the economic market, i.e., biomass and wastes. Moreover, in order to consider temporal dimensions of agent relationships, after the first year, the number of agents keeping their previous year partner is proportional to the 'Fidelity' variable. 'Fidelity' accounts for the agents keeping the same partner as the previous year for each specific use, and it also includes the idea of the low variability of farmer partners in reality, and the low network exploration. Finally, transportation distance is limited using a 'radius of action' that sets the maximum distance over which a given material can be transported. The radius of action is applied to bulky biomass materials including manure, sewage sludge, grass, silage maize, legume fodder. For a given supplier (or demander), this radius of action de facto excludes any potential demander (or supplier, respectively) that is located beyond its value (Figure 14). Another process used to govern exchanges is the adaptation of our local network market to either a buyers' or a sellers' market depending on the relative number of 'suppliers' (𝛹S) versus 'demanders' (𝛹D) present in the network. For instance, if forage demanders are more numerous than suppliers, FAN lets suppliers initiate the material exchange process, and vice versa. Therefore, the corresponding material flows occur one by one, allowing to recalculate weights with the remaining of the agents in the network if they still need to exchange materials. FAN makes use of this simple stochastic method to create partner couples as we understand that there is a high variability in partnership establishment in the real world that may not be fully captured by this model.

Note that FAN does not explicitly include prices or economic factors, since many biomass materials (e.g., forage, manure, food processing wastes) do not have a clear market value. Further consideration of economic modelling processes was considered beyond the scope of the model at this stage, and so our focus is on the biophysical and social factors that may drive materials flows at the local level. Instead, we include various simulation mechanisms and decision-making variables that can mimic market contexts when prices, costs, subsidies and farming strategies may interact. These mechanisms and variables include the radius of action, farm fidelity to their partners, their relative disposition to exchange and the set of preference coefficients for specific material uses. Note also that the exchange processes are organized to allow for different uses for a given material depending on agent preferences. This is simulated through the substitutability of interchangeable materials for the same use and, symmetrically, through the partition of a given material into different uses. Such substitutability was related in our model to chemical fertilizers and organic wastes; grains; forage; other crops and animal products and food wastes. Forage & feed Grass forage-digestion preference coef.

[0-1] ratio 100

Radius of action for grass km 50

Radius of action for silage maize km 20

Food wastes

Fruits & vegetables wastes for digestion preference coef.

[0-1] ratio 0.5

Fruits & vegetables wastes for animal by products pref. coef.

[0-1] ratio 0.5

Design Concepts

Model presentations following the ODD protocol commonly include design concepts [START_REF] Grimm | The ODD protocol: a review and first update[END_REF], which we describe below with specific focus on those relevant to FAN.

Basic principles. The FAN model design follows an intermediate geographic scale in which farms and their partners are connected through a series of rules that govern decisions about materials exchange. The concept and theory behind FAN are related to the fact that agents exchange a series of materials based on their (negative or positive) potential, becoming suppliers or demanders. In FAN, we hypothesized that this potential results from both agronomic constraints (which are well represented) together with economic constraints (only considered through proxies).

Emergence The model provide emergent, poorly predictable results about competition among agents and among uses related to material flows. Other emergent results are related to deficits that may occur as a result of competition phenomena, or accumulation of wastes by specific agents (e.g., accumulation of animal manure within livestock farms that did not identify demanding partners). Such emergent results may also arise due to altering system attributes by the user, i.e., by modifying farm behavior or farm features.

Objectives. Basically, the objective of each agent is to achieve material exchange and production.

That is, for suppliers to maximize the amount of materials that can be supplied, and, for demanders, to maximize the amount of material that can be collected. For instance, farms aim to both satisfy their fertilizing material, animal feed, forage and straw requirements by collecting appropriate materials from suppliers and to avoid animal manure accumulation on their land by exchanging their surplus. Regarding their partners, anaerobic digesters aim to complete their capacity, while food industries, grain collectors, wastewater treatment plants and slaughterhouses aim to get rid of their wastes and avoid their accumulation.

Sensing. Any agent in the model can sense any of the variables used in Equation 1. These variables relate to the potential supply and demand of all the agents and for all the considered materials, the geographic location of all the agents (calculated by Euclidian distance), their history of material exchanges and their preference related to substitutable products. The fact that each agent can sense these variables helps to identify the best partnership and to maximize material exchanges.

Interaction. Most interactions among agents are direct, through material exchanges among agents. However, some interactions can also be indirect through some specific resources for which competition among agents occurs. Considering these two types of interaction is key to reveal unexpected processes and material exchanges.

Stochasticity. Although the model is clearly deterministic, we added a small stochastic effect in the process related to the selection of pairs of partners. A random choice of pair of partners is made by the model proportionally to the weights determined for the whole set of potential pairs of partners. While we considered that the set of variables used in Equation 1 is relevant to mimic the fact that two agents become partners, we acknowledge that this set may not capture all the socio-economic processes that determine such relationships. These un-captured processes -which we consider beyond the scope of FAN-are accounted for by adding stochasticity to the model.

Observation. At the end of each cycle (year), a set of outputs is generated by the model, including food and energy production on one side and greenhouse gas emissions, nutrient cycling and resources use on the other side. Outcomes for these environmental indicators are described in next section, and some of them are used in the Sensitivity Analysis, in Section 3.

Submodels

Initialization. In order to initialise FAN, a synthetic farm population was created based on the average features of different farm types. Farms were indeed classified according to their main agricultural productions into different farm types and, for each farm type, we calculated the mean and standard deviation of (i) the total farm area; (ii) the farm's land-use distribution and (iii) the farm's livestock number. Then, to create the synthetic population of farms, for each farm type, we first used a normal distribution of the farms' area centered on the mean observed value. We then distributed land-use and livestock numbers to the farms proportionally to their area. Other existing partners are placed using points (as a shapefile), and anaerobic digesters are distributed uniformly across the landscape. Each agent is supposed to have a null stock at the initialization.

Fertilizing material application to soils, crop production and nutrient losses. Although in some minor cases crop production could be phosphorus-limited, we considered that nitrogen (N) was clearly the most limiting factor of crop production in this area [START_REF] Mueller | Tree species effects on coupled cycles of carbon, nitrogen, and acidity in mineral soils at a common garden experiment[END_REF]. In simulations, crop yields thus vary with N applications to soils through organic and mineral fertilization, N fixation by legumes, atmospheric deposition and soil organic matter mineralization. Crop yield response to N application was considered to be linear up to a certain N application level, after which it reaches a plateau corresponding to the observed regional yields.

This approach was justified by the fact that fertilization excess usually occurs in the considered region [START_REF] Lassaletta | 50 year trends in nitrogen use efficiency of world cropping systems: the relationship between yield and nitrogen input to cropland[END_REF]. Losses of N are estimated in the model through (i) leaching as the surplus of N application relative to crop uptake, (ii) N volatilization from organic fertilizing material storage and application and (iii) N2O emissions from soils to the atmosphere. Users can define the fertilization application rates by following a simple N budget based on crop nutrient uptake, by using observed fertilization doses, or by setting fertilization restriction policies.

Livestock feed, forage, bedding and production. Once crops are produced, animal requirements are estimated based on observed feed rations, forage use for ruminants, and straw for bedding that are applied in France [START_REF] Agreste | Les dossiers n°21[END_REF]. These requirements are first supposed to be satisfied with inner farm production. However, if inner farm production fail to satisfy those animal requirements, the model simulates exchanges with others farms, feed suppliers or with the global market. In FAN, forage requirements per ruminant are linearly proportional to their production within a range of variation of ±10 % around the average forage consumption reported in statistical data [START_REF] Devun | Alimentation des bovins: rations moyennes et autonomie alimentaire[END_REF]. Finally, ruminant meat and milk production are proportional to the forage consumption.

Waste and by-product production. Waste and by-product production from food industries were determined by using food processing ratios (in %) both from local surveys and national data and by applying these ratios to the amount of raw products (e.g., live animals, raw milk, grains, fruits and vegetables) entering food industries. Although food processing wastes are demanded for energy production by the anaerobic digesters, non-animal food wastes such as fruits and vegetable wastes are also demanded by farms for animal feeding. In addition, animal manure production was determined by using excretion rates per animal type (in kg N per animal and per year) collected from national databases (Table 2) that were multiplied by the number of livestock of each farm. Fresh digestates from anaerobic digesters were estimated proportionally to the amount of materials entering anaerobic digesters.

Bioenergy production. In FAN, the number and capacity of anaerobic digesters can be defined by the user. Anaerobic digesters are supplied according to average composition of the feedstock observed in France. According to the French environmental and energy agency 'ADEME', in 2013, the average composition of feedstock was 68% manure, 17% green biomass (grass, energy and inter crops), and 15% food processing wastes. The energy produced by anaerobic digesters was modelled proportionally to the digestible potential of material inputs. We estimated a production of 42.02 m 3 of biogas, with 34% of electric yield equivalent to 85.73 kWh of electricity per tonne of feedstock mix (ADEME, 2013;[START_REF] Pöschl | Evaluation of energy efficiency of various biogas production and utilization pathways[END_REF].

Environmental extension. The outputs from FAN can be used not only to calculate food and energy production, but also to assess various environmental indicators, including greenhouse gas emissions from agricultural activities and material transportation, nutrient losses to water bodies, and other ecosystem services (Table 3). Greenhouse gas (GHG) emissions from agricultural activities were estimated by using IPCC methods (IPCC Guidelines, 2006)

Food and feed Autonomy

Feed and Forage autonomy Food and feed production equivalents Total production in each district divided by average citizen consumption and average livestock requirements

Nutrient Cycles in Fertilization

Fertilization inputs and crop outputs Use of N from: chemical fertilizers; recycled sewage sludge Potential local flows (fertilization, bioenergy, animal feeding).

% N recycled N losses N use

Input Data and Initialization

For application of FAN, various input data are required to characterize the agents and to define the key processes that are considered. Characterizing the agents required specific data about their size (e.g., total area and livestock number for farms or energy production capacity for anaerobic digesters), their main activities (expressed in land use and livestock distribution per farm type for farms) and geographic location. Regarding the latter, the model allows for random spatial distribution of the agents or distribution according to a user-defined map. Defining the key processed considered in the model requires local, regional or national data concerning production rates (e.g., crop and animal potential yields); feed requirements for livestock and anaerobic digesters; waste and by-product production from production activities. We collected these data from French national, regional and local statistics (see Table 4 for some key examples).

Nevertheless, it is recommended that users compile the best available data for application to case studies in other countries. This data gathering was obtained both from public data coming from farming extension programs as well as agricultural census.

Parameter Value and units Source

Land As mentioned before, we aimed to simultaneously calculate the probability of all possible exchanges before starting allocating material flows. Yet, the exchanges carried out are not the always optimum ones, because although the occurrence of the exchanges is proportional to the probability of becoming partners (Eq. 1, Chapter 2), we introduced a stochastic element through the Mersenne Twister algorithm included in GAMA platform, the most popular pseudorandom number generator (Matsumoto and Nishimura, 1998). This stochasticity is a typical characteristic of agent based models, aiming to simulate social complex behavior [START_REF] Bonabeau | Agent-based modeling: Methods and techniques for simulating human systems[END_REF].

Economic factors such as prices of materials and transportation costs were not included explicitly in FAN. Indeed, further consideration of economic modelling processes was considered beyond the scope of the model at this stage. Instead, hypothetical market contexts where mimicked as a combination of prices, costs, subsidies and farming strategies. Thus, we included various simulation mechanisms and decision-making variables that are able to recreate these kind of contexts. The parameters and variables used in the exchanges are discussed as follows. They include: the radius of action, farm fidelity to their partners, their relative disposition to exchange and the set of preference coefficients for specific material uses.

-

Exchanges parameters

Radius of action is the distance that a material can travel, they restrict farther exchanges that therefore implicitly more costly. To apply a value, we consulted both the local managers and scientific literature. In literature, although few papers addressed the question, values for manure ranged from 5 to 40 km, depending on the area under study and the humidity of the materials, being distances farther for dry products and shorter for wet ones (Dagnall et al., 2000;Nowak et al., 2013a;Riaño and García-González, 2014). Contrasting with local managers, larger distances were travelled by sludge and sometimes dry digestates, up to 80-100 km. In FAN, there are no different categories for wet and dry organic wastes, since their mass is accounted in dry matter and their volume converted in fresh mass for digestion. A radius of action of 15 km was set for manure and digestates (that in our simulations are being recycled more locally) and 80 km for sewage sludge. Forages were known to be transported to close locations (10-50 km), limiting local forage up to 50 km, except for dry legume forage such as alfalfa, that could come from more than 500 km away, and thus we considered it as a global market product. To progress into circular economy, more information about materials transportation for recycling and allocation is needed.

Fidelity was set as the percentage of farms keeping the same partner each year and therefore repeating the same exchange. This parameter aimed to account for the historical links between real partners. No information about it was founded in the literature. A default value of 50 % of farms keeping the same partner each year was set for the scenarios simulations. Nevertheless, the sensitivity analysis showed a negligible effect of the fidelity factor on the exchanges.

Disposition to exchange wastes and biomass is the number of farms willing to locally exchange their forages, their manure and their straw. For instance, higher disposition to exchange wastes and biomass increases the number of farms that are offering and seeking for manure. This may be used to represent a context where organic fertilization is encouraged, or where manure recycling for energy or fertilization becomes an imperative, as applied in the scenarios.

Preference coefficients are parameters affecting the ranking result of a given material flow in the probability of becoming partners (Eq. 1, Chapter 2). They aim to represent the substitutability of interchangeable materials for the same use and, symmetrically, the partition of a given material into different uses. Such substitutability was related in our model to chemical and organic fertilizers and wastes; forages; other crops and animal products and food wastes for different uses including fertilization, bioenergy and animal feeding or bedding. We did not find similar coefficients in the literature. Although these coefficients can be considered as a modelling artefact, they were useful when imitating a context where some uses or materials are favored, as applied in the scenarios.

-Simulating FAN production of crops, animal, wastes and energy

Due to the complexity of agro-food systems, some simplifications were, however, necessary in the model. Those simplifications mostly concern production estimations, in particular crop yield response to fertilization and livestock yield response to animal feeding.

Since we are addressing nutrient materials reuse and recycling, we considered that nitrogen (N) was the of crop production driver in FAN. Even if in some minor cases phosphorus limitations may occur, most agronomists confer N the most important nutrient role in crop production [START_REF] Mueller | Tree species effects on coupled cycles of carbon, nitrogen, and acidity in mineral soils at a common garden experiment[END_REF], especially in organic farming systems (Nowak et al., 2013a(Nowak et al., , 2013b)).

However, other well-known drivers of crop production have a great importance in crop production [START_REF] Brisson | An overview of the crop model STICS[END_REF], both biophysical (rainfall, temperature) and management practices (plant pests and diseases, weeds, tillage, crop rotations) are out of the scope of the present work. Thus, in FAN simulations, crop yields vary with N applications calculated as a function of fertilizing N inputs to soils through a simple linear yield-response model ending in a plateau. For the moment, we preferred to simplify this response linearly, despite the fact that a curve response is more accurate and should be applied in the future (Godard et al., 2008). In addition, once loses are accounted, all N applied to soils was considered to be available for crop growth. This simplification avoids N mineralization dynamics across time, especially important in organic fertilization (Kaur et al., 2008).

Regarding livestock production, we considered a wide range of animal categories, helping to better estimate the meat production and animal requirements. They include calves, goat and sheep kids, sows, lambs and fattening pigs. Their feed requirements are estimated based on observed average feed rations that are applied in France per livestock category and year. However, each farm has its own specific rations depending on their own and their neighbors land use, therefore, more specific rations could be applied to the case studies. In our case study, farms locally exchanged cereals, oilseeds and by-products, and imported soybean, that was the only missing feed in the area. Straw local exchanges for bedding is also simulated in FAN, although we did not make any changes on this material in the scenarios. Contrary to feed, we observed that fixing forage rations to their average forage consumption reported in French statistical data forced too many forage exchanges between farms in Ribéracois. When farms were seeking for an exact quantity of forage, the number of exchanges was overestimated. In order to solve this issue, we set an internal range of variation of ±10 % around the average forage rations, and therefore we linked in a linear proportion forage intake to ruminant meat and milk production (Vasta et al., 2008).

Waste and by-product production from food industries was determined by using food processing ratios (in %) both from local surveys and national data and by applying these ratios to the amount of raw products (e.g., live animals, raw milk, grains, fruits and vegetables) entering food industries. When simulating our case study, we got strong difficulties to gather waste generation, recycle and disposal data from local food industries. In consequence, we applied national statistics from the corresponding production sector. The collaboration of local food industries would have been crucial to obtain access to food processing wastes related data. Alternative sources and mix compositions of feedstock for bioenergy could also be applied in the future.

-Simulating FAN environmental outputs FAN can assess various environmental indicators, including greenhouse gas emissions from agricultural activities and material transportation, nutrient losses to water bodies, and some other proxies to estimate ecosystem services.

Greenhouse gas emissions from some agricultural activities, including CH4 from enteric fermentation, CH4 from manure storage and N2O from fertilizers application and indirect leaching emissions, were estimated by using emission factors from the 1 st tier IPCC methods. However, improving their estimation by using the 2 nd or the 3 rd tier would be highly recommended. In addition, C stored in grasslands estimated by applying the C stored in grasslands from [START_REF] Soussana | Mitigating the greenhouse gas balance of ruminant production systems through carbon sequestration in grasslands[END_REF], was key factor of system emissions improvement, yet, it presented lower values when other methods, such as the one presented in Chang et al., (2015), were applied. Scientific discussion concerning the estimation of C storage in grasslands are still running, so doing a FAN model update in consequence will be needed.

Concerning the Nitrogen budget estimation, soils were considered in steady state, neutralizing N inputs from crop residues, N immobilization and N soil mineralization. Still, accounting for these processes will demand gathering data by sampling N in soil organic matter for the case study simulated. N atmospheric deposition was neglected but could help to improve the N budget calculation. As previously mentioned, going further in the N dynamics will help to better estimate N availability for crop intake.

FAN Model Exploration

In this section, we provide an example of the application of FAN to a case study in France. We conducted a sensitivity analysis on the model in order to explore how FAN outcomes respond to changes in parameterization, as well as to evaluate the model's internal consistency. Sensitivity analysis is especially insightful for this study as FAN contains several variables that reflect behavioral characteristics, which were not empirically derived and therefore cannot be calibrated to fit known values.

Case-study presentation

We used a test case in the southwest of France in order to conduct the sensitivity analysis of FAN.

This case study corresponds to the 'Ribéracois' sub-region (in Dordogne, France), which we refer to as a 'district' herein ( Figure 20). The Ribéracois has a total area of around 1000 km 2 , an area slightly smaller than the average county in the US 1642 km 2 (US Census, 2010). There are approximately 835 farms that include a diversity of farming activities, such as arable, dairy, beef production, pig, ovine and horticultural production, in both specialised and mixed crop-livestock farms. There are a number of upstream and downstream partners of farms that operate across the district. These partners include three large companies that collect cereals and process feed, two milk industries, two slaughterhouses, several small fruits and vegetables industries, four wastewater treatment plants and some projects of anaerobic digestion. Data on average farm land-use and livestock units per farm type was collected from Agreste database and from interviews with the local extension services (e.g., Chamber of Agriculture, agricultural cooperatives). Exact location of farms was not available, but because the distribution of the different farm types inside withindistrict subzones was available, the farms were randomly located inside each subzone.

Variables explored in Sensitivity Analysis

The sensitivity analysis was performed by selecting a set of key variables that we expect to have the greatest influence on the model outputs. These variables include: (see Table 2 for the full list of variables).

 The exponential of the distance in the proximity term of Equation 1 (parameter "a") that sets the limitation related to material transportation.

 The fidelity coefficient, that represents the percentage of farms keeping the same partner each year.

 The disposition to exchange biomass between farms that represents the percentage of farms willing to exchange their biomass.

 The preference coefficients, accounting for the likeability of farms to select a material for a specific purpose. Here we tested those related to manure for both fertilization and digestion uses, as well as the coefficient related to chemical fertilizer use and to grass digestion.

We also tested other variables related to the model application to different case studies, such as the number of farms, the radius of action for materials exchanged between farms, or the capacity of anaerobic digestion. Since these variables had little influence, we decided not include them in the results shown in this section. The related results showed that changing the radius of action of materials can help to simulate alternative recycling scenarios where agents can allocate their ressources farther. Structural changes such as the number of farms can drastically change the number of flows without changing environmental performance or any other results.

For each variable, we explored a range of values that corresponded to 0.1; 0.5; 1; 1.5 and 2 times the default value (Table 2). The model was run over a period of five annual time steps (i.e., 5 years), and the data from the last year was retained. We then calculated the annual average of the 5 years for each output. In order to minimize randomness related to farm spatial distribution and farm size around average farm type size, we used 30 repetitions of these model runs to test each value. Additionally, the random seed was kept along the values tested to avoid the pseudorandomness of the initialisation. We focus our analysis on fertilizing materials (manure, digestates, mineral fertilizer) and livestock feeding (forage, by-products and straw) flows.

We selected output variables that were helpful to understand how the material flows were affected by the user-defined variables and to test their capacity to simulate contrasted situations. The output variables that we considered were as follows:

• The number of local flows within the district. Such variable aggregates all the material exchanged or used by the farms for fertilization, animal feeding or energy production within the area under study. We considered that a flow stops when the corresponding material is used to produce either food or energy. Exchanges inflowing or going to the global market were not included. We have classified these flows into (i) local fertilization flows (Figure 7)

including manure, sewage sludge and digestates applied to soils; (ii) animal requirements flows including forage, by-products and straw for bedding; and (iii) energy flows including manure, grass and food processing wastes allocated to anaerobic digesters.

• The average distance in exchanges of manure and grass. This variable was calculated as the average distance travelled in km by a specific material when flowing from one agent to another.

• The CO2 emissions from material transportation by trucks. This variable accounts for the distance travelled by a given material when flowing from one agent to another but also for the weight of the materials transported at each exchange.

Sensitivity Analysis Results

Regarding fertilizing materials (manure, digestates and mineral fertilizer) flows, the results

showed that although the exponential of the distance (proxy for proximity) has an important role, the disposition to exchange biomass between farms clearly drives the amount of manure and consequently of digestates that were exchanged (Figure 17). The preference coefficients for manure and chemical fertilizers almost symmetrically induce and restrict the number of local fertilization flows: they respectively drive the fertilization by using either the manure from local exchanges to fertilize soils or favor chemical fertilizer use (Figure 17). Finally, the fidelity factor does not strongly affect the fertilization flows. When focussing on manure exchanges, we found that, as expected, manure travels greater distances when proximity between partners is not encouraged (low values for exponential of distance), suggesting greater tolerance for long transport distances (Figure 18). We also found that manure travels greater distances when the farm disposition to exchange materials is low. This is probably explained by lower supply of manure when the disposition to exchange material is low, therefore inducing long distances to meet manure demand. Regarding the biomass used for livestock feeding (i.e. forage, straw and by-products), we found that, in contrast, the number of flows of these materials are poorly affected by the considered input variables (proximity, disposition to exchange and fidelity, data not shown). This may be due to the fact that these materials are first exchanged locally among farms, followed by inflows from the global market only when local supply is exhausted. This modelling choice makes the number of local flows sensitive to the farm disposition to exchange materials, but less sensitive to the proximity between partners. This result is also due to the fact that there is no substitution of such materials with other ones or with other uses. Finally, we found that the distance travelled by these materials is clearly reduced when long distances between partners are penalized (high values for the exponential of the distance, Figure 19). However, the disposition to exchange between farms and the fidelity does not affect the distance travelled by these materials between local partners. Sensitivity analysis using FAN shows that fertilization materials are relatively more sensitive in the model than feed materials, which are more dependent on parameters extracted from national and regional databases. Besides, there is a low effect of fidelity variable, which means that lower fidelity values are unlikely to influence the decision of the best agent to exchange with over time.

This is probably because relationships initiated at the first cycle (year) are already close to 'optimal' in FAN.

Conclusion

Understanding how multi-agent behavior affects materials exchange is key to identify the drivers and dynamics of agro-food networks. Although agent-based models related to agricultural systems already exist [START_REF] Iwamura | Agentbased modeling of hunting and subsistence agriculture on indigenous lands: understanding interactions between social and ecological systems[END_REF][START_REF] Schreinemachers | An agent-based simulation model of humanenvironment interactions in agricultural systems[END_REF], to our knowledge FAN is the first model that combines social simulation with the environmental characteristics of farms across a wide range of materials in more complex agro-food networks.

Therefore, one of the core innovations of FAN lies in its ability to simultaneously simulate multiple bio-sourced and biomass materials as a network of local potential exchanges. Another originality of the model lies in the considered system that encompasses a large range of agents.

In total, eight types of agents were considered, which is beyond the agents modelled in other farming agent-based models, (e.g., two in [START_REF] Shastri | Agent-based analysis of biomass feedstock production dynamics[END_REF] for famers and bio-refineries, and five farmer strategies in [START_REF] Valbuena | An agentbased approach to explore the effect of voluntary mechanisms on land use change: A case in rural Queensland, Australia[END_REF]. Considering both a large number of agent types and of material types helped to address an intermediate spatial scale between the farm and the country. Such a sub-regional level is critical because actors are uniquely identified and their potential role in a circular economy can be assessed. In addition, our model was developed by combining multiple approaches in order to address a set of environmental and economic issues to the sustainable development of agriculture in rural areas and the challenges they face in a global market offering manifold farm inputs.

Due to its capacity to account for a large range of economic agents and exchanged materials, FAN can help address several issues related agro-food systems and circular bioeconomy [START_REF] El-Chichakli | Five cornerstones of a global bioeconomy[END_REF][START_REF] Lainez | Spanish strategy on bioeconomy: towards a knowledge based sustainable innovation[END_REF][START_REF] Sarkar | Enabling a Sustainable and Prosperous Future through Science and Innovation in the Bioeconomy at Agriculture and Agri-Food Canada[END_REF]. For example, FAN offers a promising framework and the tools needed to assess alternative agricultural developments strategies, such as the development of localised food production and short supply chains (food autonomy and sovereignty), the better coordination between crop and livestock production at the local scale, the improved recycling, use and disposal of waste and by-products, the decreasing reliance on nonrenewable fertilizer resources, as well as the dependency on international feed imports.

Due to the complexity of agro-food systems, some simplifications were, however, necessary in the model. Those simplifications mostly concern production estimations, in particular crop yield response to fertilization and livestock yield response to animal feeding-as well as, in some cases, waste production from industries (which were estimated from national sources when local were not available). In addition, although we excluded explicit economic variables in FAN, we can still approach contrasted contexts through the use of logistic variables and preferences coefficients for materials or for usages. Concerning the social simulation aspects, FAN does not yet include individual adaptation to dynamic processes [START_REF] Berger | Agent-based Modelling of Climate Adaptation and Mitigation Options in Agriculture[END_REF], that are quite complex to simulate. Individual adaptation could potentially be included in FAN, for instance by allowing farmers to alter land use or livestock populations in response to material availability in the network or after the alteration of global supply chains.

Here, we presented the FAN model as a first attempt to simulate multiple interacting material flows at the local scale, including some global feedbacks. We gave an overview of the model framework, its processes, and an application to a case study in France where we have collected a considerable amount of data that is included in the model (Supplementary Materials File 1).

We presented submodel mechanisms for crop fertilization, animal feeding, food wastes use and bioenergy production. Finally, we presented a sensitivity analysis of FAN, showing its strength when simulating soil fertilization and modulating alternative material uses, including the interactions between local and global markets in environmental policies. FAN features open promising avenues to simulate contrasted scenarios of agro-food networks at the local scale in other regions and case studies in a bioeconomy context.

Introduction

Current agricultural use of resources and impact on ecosystems is driving the planet beyond its safe operating space [START_REF] Godfray | Food security: the challenge of feeding 9 billion people[END_REF][START_REF] Tilman | Global diets link environmental sustainability and human health[END_REF]. In this context, new strategies and regulations are needed to tackle agriculture's pressure on natural resources including land, water, fertilizers and climate [START_REF] Carlson | Greenhouse gas emissions intensity of global croplands[END_REF]Foley et al., 2011c;[START_REF] Pretty | The top 100 questions of importance to the future of global agriculture[END_REF]. In a context where specialized farms rely on outsourced inputs -thus driving imbalances and dependencies globally (Lassaletta et al., 2014a)-some alternatives to the conventional food systems may be found at the local scales. In other words, food chains have to move away from linear towards more close-looped systems [START_REF] Davis | Closing the loop: integrative systems management of waste in food, energy, and water systems[END_REF]. Indeed, reducing agricultural pressure on natural resources can be achieved through a better use of local biomass materials (e.g., feed and forage for livestock as well as wastes for fertilization), by applying circular bioeconomy and agro-industrial ecology principles [START_REF] El-Chichakli | Five cornerstones of a global bioeconomy[END_REF][START_REF] Fernandez-Mena | Towards an Agro-Industrial Ecology: A review of nutrient flow modelling and assessment tools in agro-food systems at the local scale[END_REF][START_REF] Golembiewski | The emerging research landscape on bioeconomy: What has been done so far and what is essential from a technology and innovation management perspective?[END_REF]. To apply these strategies, local material exchanges among farms to better use and recycle local resources need to be included.

Understanding the benefits and limitations of implementing alternative material flow strategies in local agro-food systems can be done by using simulation models together with material flow scenarios [START_REF] Fernandez-Mena | Towards an Agro-Industrial Ecology: A review of nutrient flow modelling and assessment tools in agro-food systems at the local scale[END_REF]. To go further when applying scenarios assessment, we need to better estimate and quantify the both farming production and environmental performance linked to the associated material flows in the agro-food system locally. On one hand, some studies have attempt to do an assessment of alternative scenarios towards sustainable practices in a farming region, such as the scenario assessment of the Montérégie region in Canada [START_REF] Mitchell | The Montérégie Connection: linking landscapes, biodiversity, and ecosystem services to improve decision making[END_REF] and the California Nitrogen Assessment [START_REF] Tomich | The California Nitrogen Assessment: Challenges and solutions for people, agriculture, and the environment[END_REF]), Yet, they did not quantify the flows and the environmental outputs consequence of applying scenarios in these regions. On the other hand, some studies that quantified the outcomes by simulating flows and environmental indicators, such as the assessment of dairy farms in a French region [START_REF] Acosta-Alba | Exploring sustainable farming scenarios at a regional scale: an application to dairy farms in Brittany[END_REF], and the biomass dynamics of crop-livestock systems in a region of Kenya (Tittonell et al., 2009a), only focused on a single specific sector of the food chain within the region studied.

Although few studies have estimated this outputs from different sectors of the food, feed and wastes chains in a region, we need to better account for the interactions involving different farming activities and their upstream and downstream partners. Characterizing the agro-food network as agents interacting is key to represent alternative scenarios of biomass materials management. Agent-based models can be a useful tool to simulate different agents behaviors under alternative scenarios towards sustainability [START_REF] Alonso-Betanzos | Agent-Based Modeling of Sustainable Behaviors[END_REF]. Although there is a large literature on agent-based models applied to land use systems [START_REF] Matthews | Agentbased land-use models: a review of applications[END_REF], very few studies have applied agent based simulations to study alternative scenarios of materials management in agro-food systems at the local scale [START_REF] Fernandez-Mena | Towards an Agro-Industrial Ecology: A review of nutrient flow modelling and assessment tools in agro-food systems at the local scale[END_REF]. In particular, to our knowledge, agent-based models have never been used to simulate alternative scenarios of material exchanges concerning crops, livestock, wastes and bioenergy all together.

In this study, we aimed to simulate alternative scenarios of material flows in a specific farming region. To do so, we applied the FAN ("Flows in Agricultural Networks") agent-based model (Fernandez-Mena et al., submitted) to Ribéracois, a case-study in the southwest of France, described in section 3.2.1. The FAN model is a powerful tool to simulate different scenarios, to assess a range of environmental outputs, and to simultaneously simulate multiple bio-sourced and biomass materials as a network of local potential exchanges. Our scenarios, described in section 3.2.2, deal with good management practices, organic waste recycling, bioenergy production, crop-livestock symbiosis and chemical fertilizers removal. Thanks to FAN simulations, we obtained production and environmental indicators that are presented and discussed in section 3.3. Finally, our scenarios performances are evaluated through various environmental indicators.

Materials and Methods

The Ribéracois case-study

We used a case-study in the southwest of France in order to simulate alternative agro-food scenarios using FAN. This case-study corresponds to the 'Ribéracois' sub-region, which we refer to as a 'district' here. It is located in Dordogne département of the Nouvelle-Aquitaine administrative region, in the southwest of France (Figure 20). Ribéracois has a total area of around 1000 km 2 , with approximately 500 km 2 of utilised agricultural area (UAA), a mean altitude of 80 m, an annual rainfall of around 800 mm, and an average annual temperature of 12.3 °C. In comparison, the surface of Ribéracois district is lightly smaller than the average county in the US (1610 km 2 ).

In Ribéracois, the agricultural census registered 835 farms that include a diversity of farming activities, such as arable, dairy, beef, monogastrics, ovine, and horticultural production (Table 5).

There are a number of upstream and downstream partners of farms that operate across the district. These partners include three large companies that collect cereals and process feed, two milk and cheese industries, two slaughterhouses, several small fruits and vegetables industries, four wastewater treatment plants and 2-3 projects of anaerobic digestion plants. Data on average agricultural land-use and livestock units per farm type was collected from Agreste's database and from interviews with the local extension services (e.g., Chamber of Agriculture, agricultural cooperatives). The exact location of farms was not available, but the number of farms in each farm type (n=8 farm types) and for each of the five subzones that composed the district was available. Farming activities in Ribéracois are quite diversified. Even so, they are challenged by inefficient nutrient and biomass management. Livestock production is concerned by the high volatility of input prizes due to overall deficit in soybean (imported from South America) and alfalfa (imported from the north of France) to meet livestock requirements. Green, renewable energy production through anaerobic digestion is strongly pushed by local authorities. Although there is no biogas plants in the district currently, a few of such plants are expected to develop in the next few years.

Their capacity is estimated as the fourth of the biogas production potential in the area. Horticultural farms 0 0 0 0 0 0 0 0 0 0.5 0

Scenario design and description

In order to design our scenarios, we considered several alternative farming practices and farming network organization, to better couple material cycles and, ultimately, to improve system sustainability. The scenarios were built following the "ESR" framework, i.e., "Efficiency, Substitution and Redesign", which has already been applied to agricultural systems transition towards sustainability [START_REF] Lamine | Transition pathways towards a robust ecologization of agriculture and the need for system redesign. Cases from organic farming and IPM[END_REF][START_REF] Wezel | Agroecological practices for sustainable agriculture[END_REF]. More precisely, the scenarios will be based on the following leverage factors: (i) reduction of fertilization loses by adjusting fertilization rates to crop requirements and by using catch crops [START_REF] Valkama | Meta-analysis of the effects of undersown catch crops on nitrogen leaching loss and grain yields in the Nordic countries[END_REF][START_REF] Valkama | Catch crops as universal and effective method for reducing nitrogen leaching loss in spring cereal production: A meta-analysis[END_REF]; (ii) adjustment of protein intake in cattle feed rations [START_REF] Edouard | Low degradable protein supply to increase nitrogen efficiency in lactating dairy cows and reduce environmental impacts at barn level[END_REF][START_REF] Pellerin | Quelle contribution de l'agriculture française à la réduction des émissions de gaz à effet de serre? Potentiel d'atténuation et coût de dix actions techniques[END_REF]; (iii) exchange organic fertilising materials among farms [START_REF] Nowak | Nutrient recycling in organic farming is related to diversity in farm types at the local level[END_REF]; (iv) setting up biogas plants [START_REF] Mao | Review on research achievements of biogas from anaerobic digestion[END_REF]; (v) enhancing the production of local feed and forage [START_REF] Bonaudo | Agroecological principles for the redesign of integrated croplivestock systems[END_REF][START_REF] Lemaire | Integrated crop-livestock systems: Strategies to achieve synergy between agricultural production and environmental quality[END_REF]; (vi) reducing livestock population [START_REF] Leip | Impacts of European livestock production: nitrogen, sulphur, phosphorus and greenhouse gas emissions, land-use, water eutrophication and biodiversity[END_REF]) and (vii) removing chemical fertilizers [START_REF] Bouwman | Lessons from temporal and spatial patterns in global use of N and P fertilizer on cropland[END_REF]. Although all these drivers can enhance system's environmental performance, interconnected they have different expected effects that are represented in the converted to pulses. Cereals were chosen because they are the most common crop in the area and because they exhibit a large surplus in the district.

S6a. The removal of chemical N fertilizers supply (No Chem. Fert.). In this scenario, chemical fertilizers are not available to fertilize soils. Because the remaining fertilizing sources (manure, digestates and sewage sludge) may not match crop demand, we introduced a simple yield response curve to soil N input in order to simulate yield limitation due to soil fertilization. In this response to N soil inputs, yields decrease linearly from their species-dependent upper value, which is equal to the current average yield.

S5b. Livestock is reduced to half of its initial population and principles of local feed and forage presented in S5a are also applied (C-L Symb. + L/2). In addition, unused silage maize for forage is reduced and replaced by cereals. Grasslands are not modified.

S6b. Livestock is reduced to half of its initial population and chemical fertilizers are removed (No Chem. Fert. + L/2). Changes applied in S5b and S6a are combined.

Variable

FAN outcomes and indicators estimation

The production, environmental losses and environmental efficiency of the different scenarios were assessed through a set of environmental indicators provided by the FAN model. These indicators are necessary pieces for integrated assessment of the scenarios.

They represent crop, livestock, and bioenergy production; feed and forage balance; N flows (inputs, outputs and losses); greenhouse gas emissions and carbon storage in soils; local flows and transportation amounts and distances. In this section, we present those indicators and we also give some clarifications about FAN mechanisms to simulate the related indicators.

Crop Production

Crop production (for food or feed) represents the ultimate goal of farming systems. While crop production is not expected to vary in several scenarios, some scenarios may have an impact on crop yields, in particular when chemical fertilizers are eliminated (S6) or livestock population is reduced (S5b and S6b).

In FAN, crop production is estimated as a result of areas under the different crop species multiplied by their regional yields adjusted by N input to soils. The crops included here were aggregated cereals, oilseeds, pulses, grass, fruits and vegetables, silage maize and legume fodder.

Feed and forage balance

Feed and forage balance indicators are important to see how the animal requirements are locally satisfied and to quantify external inflows (especially for soybean and alfalfa).

Reducing farms dependency on external feed and forage is possible by better integrating crop and livestock production, by applying changes in the crop rotations to fulfil livestock requirements or eventually by reducing livestock population.

In FAN, once crop production is simulated, animal requirements are estimated based on species-based, average national livestock requirements [START_REF] Agreste | Les dossiers n°21[END_REF]. These requirements are supposed to be satisfied, first, by inner farm production and, second, by exchanges with others farms, feed suppliers or with the global market. Forage is estimated in FAN as the addition of grass, silage maize and legume forage. Contrary to feed, forage requirements per ruminant are linearly proportional to their production within a small range of variation around the average forage consumption reported in statistical data [START_REF] Devun | Alimentation des bovins: rations moyennes et autonomie alimentaire[END_REF].

Livestock production

Similarly to crops, livestock is an important part of food production. In addition, although reducing livestock population may have positive impacts on the environment (e.g., in terms of greenhouse gas emissions), it may also generate indirect effects, such as lower crop and energy production due to reduced manure availability.

In FAN, livestock feeding inside the region is assumed, initially with local production and afterwards inflowing feed and forage from global markets. Livestock production is estimated according to French production rates for meat and milk. Therefore, when livestock numbers are not modified, animal production cannot vary, except in a range of ±10 % of ruminants forage intake that affects meat and milk production.

Bioenergy production

In French conditions, the feedstock mix to be fermented is composed of, on average, 68% of manure; 17% of green biomass (considered as grass in FAN) and 15% of food processing wastes, including cereal, milk, fruit and vegetable wastes (ADEME, 2013). The energy produced by anaerobic digesters was modelled proportionally to the digestible potential of material inputs [START_REF] Pöschl | Evaluation of energy efficiency of various biogas production and utilization pathways[END_REF]. The production, per ton of feedstock mix, was estimated to be 42 m 3 of biogas, with 34% of electric yield equivalent to 85.73 kWh of electricity (ADEME, 2013). Anaerobic digesters total capacity was estimated as 225,210 tons of substrate for digestion and was calculated in the model according to total animal manure in the Ribéracois district.

Local flows and transportation

We proposed local flows as network indicators representing exchanges between two agents present within the Ribéracois district. We considered that a flow stops when the corresponding material is used and transformed to produce either food or energy, while exchanges inflowing from or outflowing to the global market were not included.

Estimating the number of local flows is useful to give an insight of local synergies and cooperation.

In FAN model, there are numerous exchanges inside the district. Materials are assumed to be transported by truck from one farm to another, or between farms and their partners.

Material flows were aggregated according to their final use into (i) local fertilization flows including manure, digestates and sewage sludge applied to soils; (ii) energy flows including manure, grass and food processing wastes allocated to anaerobic digesters; and three flows allocated to animal requirements: (iii) feed flows; (iv) forage flows and (v) straw flows for bedding.

N flows

Nitrogen is the most limiting nutrient for crop production [START_REF] Mueller | Tree species effects on coupled cycles of carbon, nitrogen, and acidity in mineral soils at a common garden experiment[END_REF][START_REF] Mueller | A tradeoff frontier for global nitrogen use and cereal production[END_REF]), and at the same time has great impact when lost in large amounts to the environment [START_REF] Bodirsky | Reactive nitrogen requirements to feed the world in 2050 and potential to mitigate nitrogen pollution[END_REF]. Hence there is a need to use appropriate indicators to estimate its use efficiency [START_REF] Godinot | Relative nitrogen efficiency, a new indicator to assess crop livestock farming systems[END_REF][START_REF] Leip | Impacts of European livestock production: nitrogen, sulphur, phosphorus and greenhouse gas emissions, land-use, water eutrophication and biodiversity[END_REF]. Because our scenarios were oriented toward maximizing organic fertilization, two indicators were proposed:

𝑁 𝑜𝑟𝑔 𝑎𝑝𝑝𝑙𝑖𝑒𝑑 % = 𝑁 𝑜𝑟𝑔

;

Eq. 3 "N org applied %" accounts for all non-mineral sources in the total N added to soils, whereas "N org exchanged %", takes into account only the part of organic N that was exchanged between two agents before being used for fertilization. Note that, in FAN, there is no soil mineralization accounted for since the organic carbon soil dynamics is considered to be at steady state. In addition, all N applied is considered to be available for crop intake at an annual time scale.

Greenhouse Gas Emissions

Greenhouse gas (GHG) emissions and carbon sequestration indicators are necessary to estimate mitigation of agriculture's impact on climate change [START_REF] Lipper | Climate-smart agriculture for food security[END_REF]. Two GHG balances were estimated: (i) one including only in site emissions, and (ii) one also including induced and avoided emissions. In the C balance estimates, emissions were considered to be positive, whereas C stored and CO2 avoided were considered to be negative. Indirect emissions were only considered if they were linked to materials inflowed to the area under study and were in our case those related to fertilizers production and feed importation. Additionally, is important to notice that emissions induced by producing the same amount of food or feed elsewhere to compensate for lower production in the study area were not considered.

In FAN, GHG emissions (expressed in CO2 equivalent) from livestock enteric fermentation, manure management and soil fertilizers applications were calculated from emissions factor of first and second tier of IPCC, ( 2006). The CH4 emissions when anaerobic digestion is implement are considered to be reduced as 10% of the initial emissions [START_REF] Zeeman | Urban metabolism: A review of research methodologies[END_REF]. CO2 emissions from truck transportation and induced emissions from fertilizers and imported feed were estimated using emissions factors from ADEME, (2016). CO2 avoided emissions from biogas produced were estimated according to the average CO2 emissions per kWh in France and Europe (European Environmental Agency, 2014). A soil organic matter dynamics model, inspired by the Hénin and Dupuis model (1945), was used to estimate carbon storage in soils by accounting for soil organic matter stock, C humification following organic material inputs and CO2 from organic matter mineralisation. Finally, carbon stored in grasslands has been calculated considering data from [START_REF] Soussana | Mitigating the greenhouse gas balance of ruminant production systems through carbon sequestration in grasslands[END_REF]. Animal respiration is not considered in this C balance.

Results

Here we discuss the FAN simulation results estimated through the various indicators presented above. These indicators cover food and energy production, environmental performance and district autonomy. We show annual results as the average of the 5 th year simulation (n=30 repetitions).

Crop Production

Simulation results showed that crop production is not affected in the first four scenarios, because no changes were applied to land-use or fertilizers availability (Figure 23). Crops demanding high N inputs (cereals, oilseeds, fruits and vegetables…) decreased their production to half their initial values in scenarios with no chemical fertilizer (No Chem. 3.

Livestock production

Results showed that livestock production remains constant until scenarios where livestock is halved (C-L Symb. + L/2; No Chem. Fert. + L/2). In these last two scenarios, pig and poultry production is reduced to half of the value observed in the baseline scenarios (Figure 24). However, livestock reduction did not affect ruminant meat production in the same way, because these animals can benefit from the higher forage availability that, in turn, increases productivity per animal. Those two effects compensate each other, as it is remarkable for beef meat production. Besides, even if crop production is lower in scenario without chemical fertilizers, livestock in FAN are fed in priority including by importing feed and forage to reach animal minimum requirements.

Feed and forage balance

Results showed that cereals and oilseeds are always in surplus after feeding animals in the district (Figure 25, left panel). However, their production decreased in scenarios of crop-livestock symbiosis, due to the competition for land with pulses, and also in scenarios

Bioenergy production

FAN estimated the anaerobic digesters total capacity to amount to 225,210 tons of substrate for digestion in the BIOGAS scenario (Figure 26). This capacity dropped to half when livestock population is reduced due to lower manure availability, which is the limiting factor of digestible biomass in our model. Results showed that biogas production was over 9,042,148 m 3 in BIOGAS scenario, decreasing to half of that value when reducing livestock population. The biogas produced in the BIOGAS scenario was estimated as 18.4

GWh of electricity, without taking into account the associated heat production.

Considering an annual electricity consumption of 4679 kWh per household in France, bioenergy production in the Ribéracois could satisfy the demand of 3942 households, which represents almost one third of the Ribéracois total population.

N cycle

Concerning N inputs to soil, results showed the highest mineral fertilizer use in the BAU scenario, whereas fertilizer use exhibited a strong decrease when adjusting fertilization to crop needs in BMP scenario, as well as in the remaining scenarios (Figure 29). After EXCH scenario, N mineral remain low, since organic fertilization is privileged through preference coefficients. However, N mineral increases when reducing livestock in C-L Symb. + L/2 since the area under crops with strong N demand such as cereals increases.

The N from animal excreta (collected in barns) allocated to crop fertilization only satisfies half of crop requirements, however, it is initially reduced with protein intake, and finally proportionally reduced to livestock heads in C-L Symb. + L/2 and No Chem. Fert. + L/2 scenarios. The N fixed by legumes is particularly remarkable when crop-livestock symbiosis is applied, that fostered pulses production. In addition, when implementing digesters in BIOGAS scenario, the N added by digested green biomass and food processing wastes behaves as a new input of nitrogen to the system under study. This source of N comes from the fermentation of wastes not mobilized in the previous scenarios, where grass and food processing wastes did not have any fertilization role. Finally, sewage sludge inflows play a small role in the overall N inputs. Regarding N losses, N leaching is very high in the BAU scenario, but applying BMP works as a great option to reduce N losses. In fact, best management practices have a double effect on N losses: on one hand, N fertilization rates are adjusted to crop needs; on the other hand, they introduce catch crops that reduce on average 50% of the N leached.

Besides, N volatilization (as NH3 and NOx gases produced during manure storage and fertilizers application) losses are directly linked to N inputs. Volatilization losses increased considerably when anaerobic digestion is applied, due to higher ammonia emissions, approaching one third of total N applied to soils [START_REF] Ni | Analysis of ammonia losses after field application of biogas slurries by an empirical model[END_REF]. Finally, although N2O direct and indirect emissions remain a small proportion of N in any scenario, they have a great impact on greenhouse gas emissions. Along the scenarios, the relative importance of organic N in total inputs to soils increased (Figure 30). The fact of adding more N to the system through the digestion of green biomass and food processing wastes after the BIGOAS scenario, and the addition of pulses fixing N in C-L Symb., was important in this process. Still, when mineral fertilizers were an option for farms, its use reached, at least, half of the total N inputs to soils. In scenarios where N organic fertilization was the only option, (i.e. No Chem. Fert.), the total N available in the district was not enough to satisfy total crop N demand plus losses to the environment, therefore limiting crop yields.

Figure 30. N indicators from FAN scenario outputs, expressed in percentage of N. "N org applied %" accounts for all organic sources in the N added to soils, whereas "N org exchanged %", takes into account only the part of organic N that was exchanged between two agents before used for fertilization, see 2 and 3.

Greenhouse Gas Emissions

Results of FAN simulations showed that greenhouse gas in site emissions (in CO2 eq.)

decreased from the BAU to the last scenario (Figure 31). Most of CO2 eq. was emitted from livestock and fertilizer management, including through CH4 from both enteric fermentation and manure storage and through N2O from fertilizer management and application. These emissions were substantially reduced when reducing livestock or removing chemical fertilizers. In addition, anaerobic digesters help to reduce most of CH4 Results including both in and off site emissions showed higher emissions for all the scenarios, except the No Chem. Fert. scenarios that avoided chemical fertilizers synthesis emissions (Figure 32). CO2 avoided emissions by biogas production in France are quite low. This is explained by the low CO2 emissions of nuclear power that is the main source of electricity in the country. The amount of avoided CO2 thanks to anaerobic digestion would be around four times higher if emissions per kWh of electricity produced in Europe were considered instead. Total CO2 eq. emissions are the addition of all in and off site emissions of CO2 eq. in FAN

and the subtractions of the CO2 eq. avoided or stored as C in soils. Results showed that globally the scenarios have improved total CO2 eq. emissions progressively (Figure 33).

The CO2 emissions in BAU were estimated as 93,938 tons of CO2 eq. per year. Thanks to the application of progressive solutions, CO2 emissions were reduced in the further When comparing CO2 emissions to food produced in terms of calories and energy, the progressive pattern of improvement across the scenarios is maintained (Figure 34).

Initially, emissions are reduced in BMP by reducing N losses and some feed imports. Then, anaerobic digestion implementation in BIOGAS scenario also presents a difference with previous scenarios in terms of efficiency. Surprisingly, when comparing No Chem. Fert.

and C-L Symb + L/2, we observe that removing fertilizers or reducing livestock alone presents the same effect. Finally, the No Chem. Fert. + L/2 scenario exhibited a negative GHG budget, i.e., net avoided emissions while producing food.

Discussion and Conclusion

In this work we showed how FAN, a model combining an agent-based model with an agroecological model, was helpful for obtaining unexpected outcomes under different constraints. The agent-based core helped to simulate exchanges, quantifying them and especially locating them [START_REF] Drogoul | Gama: multi-level and complex environment for agent-based models and simulations[END_REF]. These exchanges were especially important to simulate animal feeding and other requirements, as well as local collective solutions including recycling and biogas. On the other hand, the agroecological core of the model was useful to both estimate food and a set of environmental indicators [START_REF] Bonaudo | Agroecological principles for the redesign of integrated croplivestock systems[END_REF][START_REF] Wezel | Agroecological practices for sustainable agriculture[END_REF]. However, some FAN limitations lay on the non-consideration of socioeconomic and ecological barriers related to some alternative scenarios. The former include farmers' willingness to implement the solutions proposed in the various scenarios and their transition cost. The latter would require to better explore how the solutions proposed in the various scenarios are applied more precisely. For instance, we assumed that the adjustment of the N fertilization, or the substitution of chemical for organic fertilizers are straightforward. However, adjusting fertilizer rates is not easy without technical assistance and incentives and that direct substitution of chemical fertilizers is difficult in terms of availability and soil dynamics [START_REF] Carmo | The NPK soil nutrient balance of Portuguese cropland in the 1950s: The transition from organic to chemical fertilization[END_REF][START_REF] Černý | Mineral and organic fertilization efficiency in long-term stationary experiments[END_REF].

After applying the scenarios with FAN, we showed that, strictly applied as in BMP scenario, best management practices are very effective to reduce nutrient losses and GHG emissions. Although low progress was shown by the organic wastes exchanges EXCH scenario on GHG, because of higher truck transportation, the efficiency of nutrient use increased. The implementation of anaerobic digesters in BIOGAS scenario significantly decreased GHG emissions, even if more truck transportation was necessary, but this balance was compensated by the production of renewable energy collaborated. The symbiosis of crops and livestock in C-L Symb through, not only manure recycling for fertilization, but also local feeding, exhibited less greenhouse gas emissions than previous scenarios even if greater truck transportation was needed, thanks to the elimination of long protein feed chains. Livestock division scenarios C-L Symb. + L/2 and drastic reduction in GHG emissions, generate some strong costs and drawbacks. In particular, it compromises organic fertilizer availability, biomass inputs for anaerobic digestion and grassland role in carbon sequestration in soils. Finally, despite its low food production, the No Chem. Fert. + L/2 scenario, seems to be minimizing environmental impacts.

In this study, we applied an integrated assessment approach using FAN outputs to better study the cross-sectional outcomes of the scenarios. Globally, we observed that the environmental performances improved along with the application of the scenarios. This verifies our hypothesis on the progressive order of measures and solutions implemented in the scenarios. We showed that the scenarios performing more exchanges, i.e., EXCH, BIOGAS and C-L Symb., proved to be a good compromise for increasing environmental performance with agents' coordination without radically modifying farming systems.

Actually, only some small land-use changes were applied to pulses along with recycling and anaerobic digesters. Recycling for fertilization, energy and animal feeding is possible

and has still a large potential, even if the investment costs are quite high especially for anaerobic digestion equipment. Autonomy also showed a potential to increase in the area by better integrating crops and livestock, both for feeding and for soil fertilization. The system redesign in the last scenarios evidenced the need to rethink our agro-food systems to minimize our environmental impact. Nevertheless, some of these scenarios are less productive in terms of food, from both crop and livestock production. Indeed, the removal of chemical fertilizers and reduction of livestock population are significantly drastic

To come back to the reasons that stimulated this Ph.D., we discuss here the initial methodological that we made in this original research project and we outline its contributions. This overall discussion will first situate our research approach within the scientific literature and the current terminology. We will then justify the choice of the specific case-study and system's scale. We will argue about the originality carried out by the FAN model, its assumptions, limitations and related modelling decisions. We will comment the application of FAN to the simulation of scenarios and to their integrated assessment. Finally, we will discuss FAN future applications and perspectives, in particular by providing recommendations for its improvement.

Our approach in reference to the state of the art

We are in a stage where human trace on the planet becomes more and more important, the so-called "Anthropocene" [START_REF] Smith | The onset of the Anthropocene[END_REF]. In this context, the traditional empirical approaches in science have lead into more integrated ways of observing natural and human activities, and their links through the study of environmental management [START_REF] Mitchell | Resource & environmental management[END_REF], ecosystem services [START_REF] Braat | The ecosystem services agenda: bridging the worlds of natural science and economics, conservation and development, and public and private policy[END_REF], social-ecological systems [START_REF] Binder | Comparison of frameworks for analyzing social-ecological systems[END_REF] and resilience [START_REF] Olsson | Why resilience is unappealing to social science: Theoretical and empirical investigations of the scientific use of resilience[END_REF]. We acknowledged the need to work in this direction through the study of the links between agriculture, environment and society. We believe that our work comes to reinforce this framework, by proposing a social-ecological model that assesses development alternatives in local agro-food system.

In fact, our work appears in a context where more and more studies are showing the issues of agro-food systems and their links with resources management, economic activities, and the global environmental change [START_REF] Carlson | Greenhouse gas emissions intensity of global croplands[END_REF][START_REF] Fader | Spatial decoupling of agricultural production and consumption: quantifying dependences of countries on food imports due to domestic land and water constraints[END_REF]Foley et al., 2011a;[START_REF] Steffen | Planetary boundaries: Guiding human development on a changing planet[END_REF]. Although many publications address this question at the global scale [START_REF] Erb | Complexity of the international agro-food trade network and its impact on food safety[END_REF][START_REF] Mouël | How can we feed the world in 2050? A review of the responses from global scenario studies[END_REF]), considering regional food chains and local agro-food systems remains of great importance. This local scale is especially important because it provides specific guidance and solutions [START_REF] Mascarenhas | The role of common local indicators in regional sustainability assessment[END_REF]. Indeed, there is an imperative need to investigate not only the causes and the magnitude of the impacts, but also pathways for new solutions, by exploring and assessing the different alternatives that we locally have to make agro-food systems evolve.

Undoubtedly, the scientific community plays a crucial role on our knowledge about these issues, by warning about the impact of agricultural activities and proposing innovative solutions to seek for food security and sustainability [START_REF] Fao | The State of Food Insecurity in the World[END_REF][START_REF] Hedger | Progress on agriculture in the UN climate talks: How COP21 can ensure a food-secure future[END_REF].

Scientific fields and terminologies

To start our research work, we decided to explore the vast scientific literature about nutrient and material flows with a focus on local agro-food systems. Because we found several terms addressing similar things, we decided to gather them under the same umbrella that we called "Agro-Industrial Ecology". We presented this concept as an essential approach to address the local biomass and nutrient management issues, capable of linking complex environmental assessment, socio-economic agent interactions and farming decision-making. This concept was inspired from different fields studying material flows. In particular, we grounded our thinking into the "Industrial Ecology" scientific discipline [START_REF] Allenby | Industrial ecology[END_REF] that was framed by engineers to study how to couple material flows between stakeholders in the so-called "Industrial Symbiosis" [START_REF] Chertow | Uncovering" Industrial Symbiosis[END_REF]. We also got inspiration from the "Urban and Landscape Metabolism" [START_REF] Zeeman | Urban metabolism: A review of research methodologies[END_REF], the "Crop-Livestock Models" (Tittonell et al., 2009c) and from the "Substance Flow Analysis" that focusses on single element flows present in different materials and economic sectors. The Agro-Industrial Ecology field encompasses a local scale together with actors' explicit representation and modelling and agro-ecological methodologies, as presented in Chapter 2. These methodologies include both ecological tools and social models in a deeper way that Industrial Ecology studies have done so far.

This new approach was proposed in response to the need of sharing a common framework between agronomists and ecologists working with nutrient and material flows in sustainable agro-food systems. This concept is challenged by the emergence of two new popular terms closer to economy: "Bioeconomy" [START_REF] El-Chichakli | Five cornerstones of a global bioeconomy[END_REF] and "Circular

Economy" [START_REF] Ghisellini | A review on circular economy: the expected transition to a balanced interplay of environmental and economic systems[END_REF][START_REF] Murray | The Circular Economy: An Interdisciplinary Exploration of the Concept and Application in a Global Context[END_REF]. The former embraces all initiatives related to bio-sourced material efficient use and recycling, while the latter expands the idea of circular material flows to all sort of material types and production sectors. These two terms are even sometimes combined as "Circular Bioeconomy" [START_REF] Mohan | A circular bioeconomy with biobased products from CO 2 sequestration[END_REF].

Still, their definition is not clarified yet properly [START_REF] Sauvé | Environmental sciences, sustainable development and circular economy: Alternative concepts for trans-disciplinary research[END_REF] and probably a reciprocal integration of these terms will be needed [START_REF] D'amato | Green, circular, bio economy: A comparative analysis of sustainability avenues[END_REF]. In the future, we bet that Agro-Industrial Ecology can remain a specific field of agricultural application for closing material loops between partners of the agro-food systems, being at the same time compatible with both the Bioeconomy and the Circular Economy terms that target larger applications.

Case study issues, scale and data collection

In this PhD, we have decided to develop a model of material flows at the local scale, with a special focus on the areas with major environmental and agronomic issues. In fact, most agricultural areas in the European Union present modern agro-food systems with major issues related to nutrient and material management, especially high nutrient losses from fertilization and livestock excretions [START_REF] Stoate | Ecological impacts of early 21st century agricultural change in Europe-a review[END_REF][START_REF] Tuominen | Contribution of throughflows to the ecological interpretation of integral network utility[END_REF][START_REF] Velthof | Integrated assessment of nitrogen losses from agriculture in EU-27 using MITERRA-EUROPE[END_REF][START_REF] Vitousek | Human domination of Earth's ecosystems[END_REF]. In parallel to FAN conception and testing, we explored several case studies of local agro-food systems with strong issues related to nutrient and material management. Among them, the Ribéracois was chosen as being the closest case study to our institution, an area where we already had some experience (e.g., in [START_REF] Nowak | Nutrient recycling in organic farming is related to diversity in farm types at the local level[END_REF]. In the Ribéracois district, there are, in addition, farming issues related to the preservation of high quality livestock production, and grassland conservation. Livestock farmers face some great economic difficulties due to milk quota liberalization, high volatility of input price and encouragement to intensify farming systems. There is therefore a will to explore options to diversify the farming systems of the district, to cut Exchanges with partners outside from the area were considered as exchanges with the global markets. In terms of spatial scale, our goal was to delimit an area that could be easily represented in the FAN model, with an administrative status, a project and where data was available. A French département, (e.g., Dordogne) could have been a good scale since the administrative delimitation is quite clear and extension services work at this scale. However, because the area and the number of agents were too large to be implemented in FAN (the Dordogne presents 9060 km² of total area and more than 5000 farms), we decided to consider smaller scales. In that perspective, we paid some interest to the 'small, historical farming regions' ("petite région agricole") that were originally defined based on homogeneous farming systems and land-use but without administrative unity. We also paid attention to the "communautés de communes" that correspond to local development projects lead by aggregation of municipalities. We therefore decided to limit our case studies to 1000 km2, a surface in between both entities, where 835 farms and several partners where operating. At the scale we considered, farms land-use and livestock data were available from surveys carried out every 10 years by the statistical service of the French Ministry of Agriculture, Agreste. Since very few data were available regarding flows between farms and with their partners, we decided to directly inquire the actors concerned. Our experience was that local agronomists, more used to work at the total Dordogne area, had difficulties to provide accurate data at the scale we were working. In addition, private food and feed companies, fertilizer suppliers and other partners were not willing to share their materials and wastes flows data, or they did not have account for this data.

In our work, we dared to create boundaries in inlands farming areas to define a local scale, setting an example for future studies. Nevertheless, the size of what we called "local scale" remains quite ambiguous and should be defined according to each project needs. Moreover, collaboration between researchers, local managers, and private companies, seems fundamental for accurately study local agro-food systems.

Building a material flows agent-based model

After having reviewed the mechanisms used in the different approaches that study material and nutrient flows, we confirmed that stock-flow methods are crucial to analyze substance flows, due to their complete accounting of whole system functioning. However, stock-flow methods have commonly been applied at large scales, where agents' characterization is merely an aggregation of individuals and the impact on the environment is roughly measured. Indeed, coupling a mechanistic natural environment with an unpredictable socio-economic system necessarily requires complex tools, analysis and models (An, 2012;[START_REF] Chen | Coupled natural and human systems: a landscape ecology perspective[END_REF]. We therefore hypothesized that coupling stock and flow with environmental assessment tools would help to link nutrient losses to the environment coming from the agro-food system and that coupling them with agent-based models would help to better account for agent decisions in flows and their corresponding driving forces. Therefore, we concluded Chapter 1 stating that linking stock and flow with environmental impact and agents-decision models approaches would be of great help to simulate and assess alternative nutrient and biomass material flows in agro-food systems.

This objective was materialized in the conception and application of the FAN model that couples these three approaches. Nonetheless, such coupling was challenging for four reasons: the agent representation, their decision making, the environmental dynamics and the system spatialization.

In terms of agent representation, contrary to stock-flow methods that aggregate agents driving material flows, agent based models represent individual agents. In other words, they simulate a so called "artificial population" that represents the actual one. In the case of FAN, the model is able to build an artificial population of farms and their partners based on the characteristics provided in the data gathered. Yet, a small level of aggregation was somehow applied when characterizing farm agents around a typology. This conceptualization is similar as the one used in crop-livestock models, a useful way to qualitatively understand a large diversity of farm features. Upstream and downstream farm partners were however represented individually.

In terms of decision making, stock-flow methods describe static situations defined in a specific context and constrain, i.e., they mostly represent material flows as they actually occur. In contrast, in agent based models interactions between agents to decide where to allocate material flows in sequenced steps is a must have. This is the case in FAN, where most flows are set by a ranking that each agent does. They calculate the appropriate agent to exchange with according to favorable conditions (historical, supply-demand ratio, disposition to exchange, location, etc.), as explained in Chapter 2.

In terms of environmental dynamics, whereas most environmental assessment indicators try to integrate empirical data from losses in dynamic systems, stock-flow methods estimates the flows released to the ecosystems thanks to historical data or emission factors. In the present work, the gathering of empirical data from material wastes, nutrient losses and emissions was out of the project scope. Hence, FAN was parametrized based on statistical data for waste production, such as sewage sludge and food waste production at the national scale, and based on emission factors for loses, such as those provided by IPCC or ADEME. Yet, a vast range of nutrient losses and greenhouse gas emissions was taken into account. This diversity in the elements considered, goes further than the single element flows commonly studied in stock-flow methods.

In terms of system spatialization, all stock-flow systems and most environmental assessment tools do not account for agent location or geographical characteristics of the environment. In contrast, agent based models can locate agents accurately if data is available, especially for small numbers. In FAN, this approach was partially implemented: artificial agents were located by scattering farms with their corresponding land-use and livestock in specific sub-zones of the district. This approach was key to consider major logistic and environmental constrains.

The FAN model discussion

As shown in our review of the literature, only a relatively small number of studies have applied agent-based modelling to agro-food systems [START_REF] Schreinemachers | An agent-based simulation model of humanenvironment interactions in agricultural systems[END_REF].

They have typically focused on specific aspects of the agro-food systems, rather than integrating across multiple agro-food system activities and sectors [START_REF] Acosta-Michlik | Assessing vulnerability of selected farming communities in the Philippines based on a behavioural model of agent's adaptation to global environmental change[END_REF][START_REF] Bert | Simulating agricultural land rental markets by combining agent-based models with traditional economics concepts: The case of the Argentine Pampas[END_REF][START_REF] Bichraoui | Agent-based Modelling Simulation for the Development of an Industrial Symbiosis -Preliminary Results[END_REF][START_REF] Courdier | Agent-based simulation of complex systems: application to collective management of animal wastes[END_REF][START_REF] Groeneveld | Theoretical foundations of human decisionmaking in agent-based land use models -A review[END_REF][START_REF] Iwamura | Agentbased modeling of hunting and subsistence agriculture on indigenous lands: understanding interactions between social and ecological systems[END_REF][START_REF] Murray-Rust | Conceptualising the analysis of socio-ecological systems through ecosystem services and agent-based modelling[END_REF][START_REF] Schouten | Comparing two sensitivity analysis approaches for two scenarios with a spatially explicit rural agent-based model[END_REF].

However, to our knowledge, agent-based models have not been applied to simulate material flows across a broader range of components in agro-food networks, including multiple agents and a wide range of exchanged materials. This more holistic analysis is important to assess alternative agricultural development strategies, such as waste recycling, and environmental impacts related to agro-industrial ecology and circular economy. So far, FAN is the first model that combines social simulation with the environmental characteristics of farms across a wide range of materials in complex agrofood networks.

One of FAN's most important strengths lies in its utility to simulate what we called the "local scale", by addressing an intermediate spatial scale between the farm and the subnational region or the country. Such a sub-regional level is critical because actors are uniquely identified and their potential role in a circular economy can be assessed. In addition, the FAN model was developed by combining multiple approaches in order to address a set of environmental and agronomic issues to the sustainable development of agriculture in rural areas and the challenges they face in global markets offering manifold farm inputs. This allows FAN to be used to assess scenarios of circular economy by simulating material flows in local agro-food systems.

Indeed, to address the local scale, FAN encompasses a wide range of agents and material types. In total, eight types of agents were considered, which is beyond the number of agents modelled in other farming agent-based models, (e.g., two in [START_REF] Shastri | Agent-based analysis of biomass feedstock production dynamics[END_REF] for famers and bio-refineries, and five farmer strategies in [START_REF] Valbuena | An agentbased approach to explore the effect of voluntary mechanisms on land use change: A case in rural Queensland, Australia[END_REF]. In addition, the difficulty of acquiring individual data for numerous farm agents (>800 in our casestudy) make agent typologies useful to create artificial agent populations. In FAN, farm typologies help to build a farm population distributed around the average characteristics of each farm type. However, each farm was defined as belonging to a generic agent called "farm" in the model. This conception strategy differs from that commonly used in agentbased models, where agent classes are set with specific characteristics, making, for instance, dairy farms having a defined number of dairy cows, and restricting to no beef cattle or pig in the farm. In our case, typologies help to integrate a vast flexibility of farm features, in a way that, even if arable farms can have some dairy cows, only farms having dairy cows can produce milk. In addition, FAN can simulate multiple bio-sourced and biomass materials, including wastes and fertilizers, crops and feed, livestock and meat, straw and crop residues. These materials correspond to those usually found in western livestock and arable farming systems. In the future, FAN should be able to integrate more specific categories of crop and materials, such as different fruits and vegetables, depending on the case study applications. Similarly, more waste characteristics could be included in cases with specific food industries.

Another core innovation of FAN lies in its ability to simultaneously simulate farms' interaction as a local network of potential exchanges. In numerous agent based models, individual actions are carried out one by one, starting by a random agent. Yet, we know that, in reality, several actions can be carried out simultaneously by different agents. For instance, two farms can negotiate their exchange of grains while two other farms can negotiate the same thing at the same time. To approach this complex phenomena, we developed a way in which the calculation of all the exchange possibilities was done first.

Then, the actual exchanges were selected through a stochastic choice based on several parameters.

Explicit economic factors such as material prices and transportation costs were not directly used to determine the exchanges in FAN. Despite the fact that innovative, sustainable systems enhance circular waste flows to avoid material losses, energy consumption, and waste disposal, the prices of wastes and the cost of recycling have been poorly studied [START_REF] Higashida | Determinants of trade in recyclable wastes: evidence from commodity-based trade of waste and scrap[END_REF][START_REF] Iacovidou | Metrics for optimising the multi-dimensional value of resources recovered from waste in a circular economy: A critical review[END_REF]. In the case of agro-food systems, most biomass materials (e.g., forage, manure, food processing wastes) do not always have a defined value in the market, and their costs and prices may vary depending on subsidies and local farming strategies [START_REF] Dietrich | Crop and Plant Biomass as Valuable Material for BBB. Alternatives for Valorization of Green Wastes[END_REF]. In our case-study, the difficulty in obtaining farmers disposition to assume recycling costs and the lack of waste prices data was confirmed by interviewing local agronomists and extension services. For all these reasons, economic factors such as prices of materials and transportation costs were not included explicitly in FAN. Instead, we included some innovative simulation mechanisms that were able to indirectly recreate these processes, namely the radius of action, the fidelity, the disposition to exchange and the preference coefficients. Although these coefficients can be considered as modelling artefacts, they were useful to imitate a context where some uses or materials are favored, as applied in the scenarios.

FAN was shown to be useful to estimate food production and waste recycling. Nonetheless, as mentioned in FAN discussion of Chapter 2, there is room for progress in this field.

Concerning crops, some improvements can be applied to the simulation of crop response to N fertilization. Similarly, there are also further steps to make to better simulate how feeding rations determine livestock productivity. In the case of bioenergy production, although anaerobic digester supply is modelled based on the average composition of feedstock observed in France, it would be of especial interest to test different compositions of feedstock as digester inputs.

Finally, FAN proved to be used not only to calculate food and energy production, but also to assess various environmental indicators, including greenhouse gas emissions from agricultural activities and material transportation, nutrient losses to water bodies, and some other proxies to estimate ecosystem services. By considering them all at the same time, FAN provides guidance for an integrated environmental assessment. Yet, since we assumed important simplifications, there is also margin for improvement. In particular, by approaching national emission factors for greenhouse gases and by going further in the N dynamics will help to better estimate N availability for crop intake. Additionally, more indicators could potentially be added, inside farms, such as machinery combustion, energy use for heating and pesticides use; and outside farms, such as specific food processing emissions and losses, integration of trees and forest areas in the landscape, etc.

Scenarios simulation and assessment

The design and simulation of contrasted Agro-Industrial Ecology scenarios is a key target when progressing towards circular economy. These scenarios aimed to mimic contexts that may be encouraged by agrarian policies and regional management. Concerning the scenarios conceptualization, we inspired from the framework efficiency, substitution and redesign to apply measures and technologies towards more sustainable farming. After observing the results of the simulations, we confirmed that agro-food systems improved performance progressively along with the scenarios. Indeed, some of the changes applied in the system are win-win solutions. For instance, increasing efficiency and local recycling help to reduce input costs and to produce additional income by reusing wastes or producing renewable energy. On the contrary, chances concerning system redesign are not easily applicable without a compensation.

By implementing the simulations, we showed how FAN was helpful for obtaining unexpected outcomes under different constrains. On one hand, the agent-based core helped to simulate exchanges, quantifying them and especially locating them. These exchanges were especially important to simulate animal feeding and other requirements, as well as local collective solutions including recycling and biogas. On the other hand, the agroecological core was useful to both estimate food and environmental indicators.

The integrated assessment of FAN outputs helped to better study the cross-sectional outcomes of the scenarios. Results showed that best management practices, when strictly applied, can be very efficient for reduce losses and improve nutrient use efficiency. We also showed that local collective solutions through network coordination were effective, and could improve waste recycling for both fertilization and bioenergy production. In addition, these solutions presented less greenhouse gas emissions than previous scenarios even if truck transportation was higher to support them. Finally, we showed that the most environmental performant scenario implied the reduction of livestock heads, and therefore meat and milk production, plus the reduction of crop and bioenergy production due to lower livestock manure availability.

In the scenarios, we included at the same time policy measurements, food chain reorganization and farm structure modification. Under a policy perspective, the strict application of best management practices concerning fertilizer doses, nitrate catch crops and protein feed are urgently needed to preserve fragile natural ecosystems and watersheds. Moreover, local collective solutions seems to be a good option for farms to improve their sustainability and to obtain alternative sources of energy and income.

Finally, drastic changes in farms structure and production seem to be necessary in order to counteract climate change, and improve environmental sustainability. This reason can make society wonder about how to compensate farms for their restructuration. One way may be through monetary compensation from agrarian policies, or introducing sustainable labels in the goods produced (e.g., a circular economy region, climate positive food).

FAN application and improvement perspectives

Undoubtedly, the FAN model features opened promising avenues to simulate contrasted scenarios of agro-food networks at the local scale in other regions and case studies in a circular economy perspective. FAN can be directly applied to other French regions providing land-use and livestock from farms, food processing wastes, sewage sludge and regional yields data. It can also be applied to other contexts in Europe and western farming areas, by providing, on top of the latter, average livestock feed and forage requirements, fertilization rates, bioenergy feedstock composition and perhaps also livestock excreta.

Very different contexts such as southern countries will require additional update of some production parameters, in particular for livestock meat and milk production.

FAN could be applied to other specific crop productions apart arable crops, such as horticulture, tubers, fiber or energetic crops. This goal is still possible by adjusting crop categories and providing their corresponding land-use, fertilization and yield data.

Nonetheless, FAN application remains especially interesting when these productions are related to livestock, since animals are both consuming crop products and providing fertilizing materials for these crops at the same time, with the associated complex materials flows.

Without any doubt, FAN simulations can be improved in the way the model calculates food production and waste recycling. In particular by gathering more accurate data on farms, including individual farm exact structure and location, animal feeding rations, and fertilization practices. Additional information from the private sector concerning actual material flows may help to verify model simulations. Our experience on this issue was deceiving, as very low interest was shown by farming extension services to collaborate on providing their material flows information. More transparency should be demanded by public institutions concerning the companies' activities, including their exchanges, their byproducts and waste production and their emissions.

FAN could be potentially used to simulate alternative scenarios of waste recycling for fertilization and bioenergy production. Concerning fertilization, many improvements in FAN can be done to better account for temporality and nutrient availability, including waste production dates and timing of mineralization. In addition, the diversity of organic fertilizers should be targeted, including different forms of wet and dry products, as well as different mixes with crop materials and compost. Concerning bioenergy production, the role of local food industries may be key to improve wastes recycling in some specific areas.

Although food processing wastes are demanded for energy production by the anaerobic digesters, fats and non-animal food wastes such as milk wastes, fruits and vegetable wastes are also demanded by farms for animal feeding. Besides, by modifying the composition of the anaerobic digester inflows, alternative sources of biomass such as crop residues may be used to obtain bioenergy. Competition for these kinds of waste materials and their use for energy or animal by-products may be an interesting application of FAN simulations.

Concerning the social simulation aspects, FAN does not yet include individual adaptation to dynamic social and ecological processes that are quite complex to simulate [START_REF] Berger | Agent-based Modelling of Climate Adaptation and Mitigation Options in Agriculture[END_REF]. Individual adaptation could potentially be included in FAN, for example by allowing farmers to alter land use or livestock populations in response to material availability in the network or in response to global supply chains. A more complex type of individual adaptation would be the adoption by farms of the changes implemented in the scenarios simulation. In this sense, some farms can be penalized by their pollution, or in difficulty to find specific partners to exchange materials. For instance, the progression to livestock reduction and organic fertilization may pass through a stage of dependency of some farms on others to obtain fertilizers or feed products.

Conclusion

In this Ph.D., we analyzed the scientific literature estimating, simulating and assessing biomass and nutrient flows across several sectors. We highlighted the need of a new tool for simulating circular biomass and nutrient material flows in the Agro-Industrial Ecology. We presented the FAN agent-based model in GAMA platform 1.7, as a first attempt to simulate multiple, interacting material flows at the local scale. We gave an overview of the model framework, its processes, and a sensitivity analysis of some key parameters. We explored different scenarios applying FAN to a case study in France where a considerable amount of data was collected. Finally, we assessed scenarios performance through an integrated assessment of FAN output, including production, network interaction and environmental indicators. In conclusion, the FAN model is proven to be an innovative, prospective tool for the simulation of sustainable agro-food networks at the local scale, confirming the progress that Agro-Industrial Ecology can make to propose more circular flows and other solutions towards agro-food systems' sustainability.

FiguresFigure 1 .

 1 Figures

Figure 4 .

 4 Figure 1. Natural and anthropogenic nitrogen inflows ............................................................ Figure 2. Global food and feed material flows. ........................................................................... Figure 3. Conceptual framework of nutrient and material flows in agro-food system. ....Figure 4. Agro-industrial Ecology conceptual Framework. .....................................................Figure 5. Example of nutrient loss indicators of a farming region ........................................ Figure 6. Substance Flow Analysis of phosphorus in France. ................................................ Figure 7. Industrial symbiosis of Kalundborg Industrial Park ..............................................Figure 8. Example of a crop-livestock model in the Vihiga district. ......................................Figure 9. An agent decision module within an agent-based model. ...................................... Figure 10. Classification of the different approaches. .............................................................. Figure 11. Class diagram in UML. ................................................................................................ Figure 12. Farm agent entities in the model .............................................................................. Figure 13. Process schedule along a cycle of one year. ............................................................. Figure 14. Representation of material flows in FAN ................................................................ Figure 15. Representation of the 'Ribéracois' district ............................................................... Figure 16. Example of simulation of local fertilization flows in Ribéracois. ....................... Figure 17. Variation in the number of local fertilization flows. ............................................. Figure 18. Variations in average distance (in km) when transporting manure. ................ Figure 19. Average distance (in km) of local flows for forage, straw and by-products used by livestock. ........................................................................................................................................Figure 20. Representation of the 'Ribéracois' district.. ............................................................. Figure 21. Expected effects of the leverage factors on the system performances .. ........... Figure 22. Scenarios explored in the Ribéracois case-study using the FAN model. .......... Figure 23. FAN scenarios outputs for crop production ............................................................ Figure 24. FAN scenario outputs for animal production. ........................................................ Figure 25. Feed district balance from FAN scenario outputs. ................................................ Figure 26. Bioenergy production and indicators from FAN scenario outputs ................... Figure 27. Distance of truck transportation inside the district and material mass exchanged ......................................................................................................................................... Figure 28. Number of local flows from FAN scenarios outputs. .......................................... Figure 29. N flows from FAN scenarios output ........................................................................ Figure 30. N indicators from FAN scenario outputs. .............................................................. Figure 31. CO2 eq. emissions (positive) and C stored or CO2 avoided (negative), from FAN scenarios output in kg of CO2 equivalents per year. .................................................... Figure 32. CO2 eq. in and off site emissions (positive) and C stored expressed as CO2 avoided (negative), from FAN scenario outputs. ......................................................................Figure 33. Total CO2 Emissions from FAN scenario outputs, ..............................................Figure 34. Kg CO2 eq. emitted or stored (in and off site). .....................................................

Figure 5 .

 5 Figure 1. Natural and anthropogenic nitrogen inflows ............................................................ Figure 2. Global food and feed material flows. ........................................................................... Figure 3. Conceptual framework of nutrient and material flows in agro-food system. ....Figure 4. Agro-industrial Ecology conceptual Framework. .....................................................Figure 5. Example of nutrient loss indicators of a farming region ........................................ Figure 6. Substance Flow Analysis of phosphorus in France. ................................................ Figure 7. Industrial symbiosis of Kalundborg Industrial Park ..............................................Figure 8. Example of a crop-livestock model in the Vihiga district. ......................................Figure 9. An agent decision module within an agent-based model. ...................................... Figure 10. Classification of the different approaches. .............................................................. Figure 11. Class diagram in UML. ................................................................................................ Figure 12. Farm agent entities in the model .............................................................................. Figure 13. Process schedule along a cycle of one year. ............................................................. Figure 14. Representation of material flows in FAN ................................................................ Figure 15. Representation of the 'Ribéracois' district ............................................................... Figure 16. Example of simulation of local fertilization flows in Ribéracois. ....................... Figure 17. Variation in the number of local fertilization flows. ............................................. Figure 18. Variations in average distance (in km) when transporting manure. ................ Figure 19. Average distance (in km) of local flows for forage, straw and by-products used by livestock. ........................................................................................................................................Figure 20. Representation of the 'Ribéracois' district.. ............................................................. Figure 21. Expected effects of the leverage factors on the system performances .. ........... Figure 22. Scenarios explored in the Ribéracois case-study using the FAN model. .......... Figure 23. FAN scenarios outputs for crop production ............................................................ Figure 24. FAN scenario outputs for animal production. ........................................................ Figure 25. Feed district balance from FAN scenario outputs. ................................................ Figure 26. Bioenergy production and indicators from FAN scenario outputs ................... Figure 27. Distance of truck transportation inside the district and material mass exchanged ......................................................................................................................................... Figure 28. Number of local flows from FAN scenarios outputs. .......................................... Figure 29. N flows from FAN scenarios output ........................................................................ Figure 30. N indicators from FAN scenario outputs. .............................................................. Figure 31. CO2 eq. emissions (positive) and C stored or CO2 avoided (negative), from FAN scenarios output in kg of CO2 equivalents per year. .................................................... Figure 32. CO2 eq. in and off site emissions (positive) and C stored expressed as CO2 avoided (negative), from FAN scenario outputs. ......................................................................Figure 33. Total CO2 Emissions from FAN scenario outputs, ..............................................Figure 34. Kg CO2 eq. emitted or stored (in and off site). .....................................................

Figure 6 .

 6 Figure 1. Natural and anthropogenic nitrogen inflows ............................................................ Figure 2. Global food and feed material flows. ........................................................................... Figure 3. Conceptual framework of nutrient and material flows in agro-food system. ....Figure 4. Agro-industrial Ecology conceptual Framework. .....................................................Figure 5. Example of nutrient loss indicators of a farming region ........................................ Figure 6. Substance Flow Analysis of phosphorus in France. ................................................ Figure 7. Industrial symbiosis of Kalundborg Industrial Park ..............................................Figure 8. Example of a crop-livestock model in the Vihiga district. ......................................Figure 9. An agent decision module within an agent-based model. ...................................... Figure 10. Classification of the different approaches. .............................................................. Figure 11. Class diagram in UML. ................................................................................................ Figure 12. Farm agent entities in the model .............................................................................. Figure 13. Process schedule along a cycle of one year. ............................................................. Figure 14. Representation of material flows in FAN ................................................................ Figure 15. Representation of the 'Ribéracois' district ............................................................... Figure 16. Example of simulation of local fertilization flows in Ribéracois. ....................... Figure 17. Variation in the number of local fertilization flows. ............................................. Figure 18. Variations in average distance (in km) when transporting manure. ................ Figure 19. Average distance (in km) of local flows for forage, straw and by-products used by livestock. ........................................................................................................................................Figure 20. Representation of the 'Ribéracois' district.. ............................................................. Figure 21. Expected effects of the leverage factors on the system performances .. ........... Figure 22. Scenarios explored in the Ribéracois case-study using the FAN model. .......... Figure 23. FAN scenarios outputs for crop production ............................................................ Figure 24. FAN scenario outputs for animal production. ........................................................ Figure 25. Feed district balance from FAN scenario outputs. ................................................ Figure 26. Bioenergy production and indicators from FAN scenario outputs ................... Figure 27. Distance of truck transportation inside the district and material mass exchanged ......................................................................................................................................... Figure 28. Number of local flows from FAN scenarios outputs. .......................................... Figure 29. N flows from FAN scenarios output ........................................................................ Figure 30. N indicators from FAN scenario outputs. .............................................................. Figure 31. CO2 eq. emissions (positive) and C stored or CO2 avoided (negative), from FAN scenarios output in kg of CO2 equivalents per year. .................................................... Figure 32. CO2 eq. in and off site emissions (positive) and C stored expressed as CO2 avoided (negative), from FAN scenario outputs. ......................................................................Figure 33. Total CO2 Emissions from FAN scenario outputs, ..............................................Figure 34. Kg CO2 eq. emitted or stored (in and off site). .....................................................

Figure 18 .

 18 Figure 1. Natural and anthropogenic nitrogen inflows ............................................................ Figure 2. Global food and feed material flows. ........................................................................... Figure 3. Conceptual framework of nutrient and material flows in agro-food system. ....Figure 4. Agro-industrial Ecology conceptual Framework. .....................................................Figure 5. Example of nutrient loss indicators of a farming region ........................................ Figure 6. Substance Flow Analysis of phosphorus in France. ................................................ Figure 7. Industrial symbiosis of Kalundborg Industrial Park ..............................................Figure 8. Example of a crop-livestock model in the Vihiga district. ......................................Figure 9. An agent decision module within an agent-based model. ...................................... Figure 10. Classification of the different approaches. .............................................................. Figure 11. Class diagram in UML. ................................................................................................ Figure 12. Farm agent entities in the model .............................................................................. Figure 13. Process schedule along a cycle of one year. ............................................................. Figure 14. Representation of material flows in FAN ................................................................ Figure 15. Representation of the 'Ribéracois' district ............................................................... Figure 16. Example of simulation of local fertilization flows in Ribéracois. ....................... Figure 17. Variation in the number of local fertilization flows. ............................................. Figure 18. Variations in average distance (in km) when transporting manure. ................ Figure 19. Average distance (in km) of local flows for forage, straw and by-products used by livestock. ........................................................................................................................................Figure 20. Representation of the 'Ribéracois' district.. ............................................................. Figure 21. Expected effects of the leverage factors on the system performances .. ........... Figure 22. Scenarios explored in the Ribéracois case-study using the FAN model. .......... Figure 23. FAN scenarios outputs for crop production ............................................................ Figure 24. FAN scenario outputs for animal production. ........................................................ Figure 25. Feed district balance from FAN scenario outputs. ................................................ Figure 26. Bioenergy production and indicators from FAN scenario outputs ................... Figure 27. Distance of truck transportation inside the district and material mass exchanged ......................................................................................................................................... Figure 28. Number of local flows from FAN scenarios outputs. .......................................... Figure 29. N flows from FAN scenarios output ........................................................................ Figure 30. N indicators from FAN scenario outputs. .............................................................. Figure 31. CO2 eq. emissions (positive) and C stored or CO2 avoided (negative), from FAN scenarios output in kg of CO2 equivalents per year. .................................................... Figure 32. CO2 eq. in and off site emissions (positive) and C stored expressed as CO2 avoided (negative), from FAN scenario outputs. ......................................................................Figure 33. Total CO2 Emissions from FAN scenario outputs, ..............................................Figure 34. Kg CO2 eq. emitted or stored (in and off site). .....................................................

Figure 19 .

 19 Figure 1. Natural and anthropogenic nitrogen inflows ............................................................ Figure 2. Global food and feed material flows. ........................................................................... Figure 3. Conceptual framework of nutrient and material flows in agro-food system. ....Figure 4. Agro-industrial Ecology conceptual Framework. .....................................................Figure 5. Example of nutrient loss indicators of a farming region ........................................ Figure 6. Substance Flow Analysis of phosphorus in France. ................................................ Figure 7. Industrial symbiosis of Kalundborg Industrial Park ..............................................Figure 8. Example of a crop-livestock model in the Vihiga district. ......................................Figure 9. An agent decision module within an agent-based model. ...................................... Figure 10. Classification of the different approaches. .............................................................. Figure 11. Class diagram in UML. ................................................................................................ Figure 12. Farm agent entities in the model .............................................................................. Figure 13. Process schedule along a cycle of one year. ............................................................. Figure 14. Representation of material flows in FAN ................................................................ Figure 15. Representation of the 'Ribéracois' district ............................................................... Figure 16. Example of simulation of local fertilization flows in Ribéracois. ....................... Figure 17. Variation in the number of local fertilization flows. ............................................. Figure 18. Variations in average distance (in km) when transporting manure. ................ Figure 19. Average distance (in km) of local flows for forage, straw and by-products used by livestock. ........................................................................................................................................Figure 20. Representation of the 'Ribéracois' district.. ............................................................. Figure 21. Expected effects of the leverage factors on the system performances .. ........... Figure 22. Scenarios explored in the Ribéracois case-study using the FAN model. .......... Figure 23. FAN scenarios outputs for crop production ............................................................ Figure 24. FAN scenario outputs for animal production. ........................................................ Figure 25. Feed district balance from FAN scenario outputs. ................................................ Figure 26. Bioenergy production and indicators from FAN scenario outputs ................... Figure 27. Distance of truck transportation inside the district and material mass exchanged ......................................................................................................................................... Figure 28. Number of local flows from FAN scenarios outputs. .......................................... Figure 29. N flows from FAN scenarios output ........................................................................ Figure 30. N indicators from FAN scenario outputs. .............................................................. Figure 31. CO2 eq. emissions (positive) and C stored or CO2 avoided (negative), from FAN scenarios output in kg of CO2 equivalents per year. .................................................... Figure 32. CO2 eq. in and off site emissions (positive) and C stored expressed as CO2 avoided (negative), from FAN scenario outputs. ......................................................................Figure 33. Total CO2 Emissions from FAN scenario outputs, ..............................................Figure 34. Kg CO2 eq. emitted or stored (in and off site). .....................................................

Figure 20 .

 20 Figure 1. Natural and anthropogenic nitrogen inflows ............................................................ Figure 2. Global food and feed material flows. ........................................................................... Figure 3. Conceptual framework of nutrient and material flows in agro-food system. ....Figure 4. Agro-industrial Ecology conceptual Framework. .....................................................Figure 5. Example of nutrient loss indicators of a farming region ........................................ Figure 6. Substance Flow Analysis of phosphorus in France. ................................................ Figure 7. Industrial symbiosis of Kalundborg Industrial Park ..............................................Figure 8. Example of a crop-livestock model in the Vihiga district. ......................................Figure 9. An agent decision module within an agent-based model. ...................................... Figure 10. Classification of the different approaches. .............................................................. Figure 11. Class diagram in UML. ................................................................................................ Figure 12. Farm agent entities in the model .............................................................................. Figure 13. Process schedule along a cycle of one year. ............................................................. Figure 14. Representation of material flows in FAN ................................................................ Figure 15. Representation of the 'Ribéracois' district ............................................................... Figure 16. Example of simulation of local fertilization flows in Ribéracois. ....................... Figure 17. Variation in the number of local fertilization flows. ............................................. Figure 18. Variations in average distance (in km) when transporting manure. ................ Figure 19. Average distance (in km) of local flows for forage, straw and by-products used by livestock. ........................................................................................................................................Figure 20. Representation of the 'Ribéracois' district.. ............................................................. Figure 21. Expected effects of the leverage factors on the system performances .. ........... Figure 22. Scenarios explored in the Ribéracois case-study using the FAN model. .......... Figure 23. FAN scenarios outputs for crop production ............................................................ Figure 24. FAN scenario outputs for animal production. ........................................................ Figure 25. Feed district balance from FAN scenario outputs. ................................................ Figure 26. Bioenergy production and indicators from FAN scenario outputs ................... Figure 27. Distance of truck transportation inside the district and material mass exchanged ......................................................................................................................................... Figure 28. Number of local flows from FAN scenarios outputs. .......................................... Figure 29. N flows from FAN scenarios output ........................................................................ Figure 30. N indicators from FAN scenario outputs. .............................................................. Figure 31. CO2 eq. emissions (positive) and C stored or CO2 avoided (negative), from FAN scenarios output in kg of CO2 equivalents per year. .................................................... Figure 32. CO2 eq. in and off site emissions (positive) and C stored expressed as CO2 avoided (negative), from FAN scenario outputs. ......................................................................Figure 33. Total CO2 Emissions from FAN scenario outputs, ..............................................Figure 34. Kg CO2 eq. emitted or stored (in and off site). .....................................................

Figure 33 .

 33 Figure 1. Natural and anthropogenic nitrogen inflows ............................................................ Figure 2. Global food and feed material flows. ........................................................................... Figure 3. Conceptual framework of nutrient and material flows in agro-food system. ....Figure 4. Agro-industrial Ecology conceptual Framework. .....................................................Figure 5. Example of nutrient loss indicators of a farming region ........................................ Figure 6. Substance Flow Analysis of phosphorus in France. ................................................ Figure 7. Industrial symbiosis of Kalundborg Industrial Park ..............................................Figure 8. Example of a crop-livestock model in the Vihiga district. ......................................Figure 9. An agent decision module within an agent-based model. ...................................... Figure 10. Classification of the different approaches. .............................................................. Figure 11. Class diagram in UML. ................................................................................................ Figure 12. Farm agent entities in the model .............................................................................. Figure 13. Process schedule along a cycle of one year. ............................................................. Figure 14. Representation of material flows in FAN ................................................................ Figure 15. Representation of the 'Ribéracois' district ............................................................... Figure 16. Example of simulation of local fertilization flows in Ribéracois. ....................... Figure 17. Variation in the number of local fertilization flows. ............................................. Figure 18. Variations in average distance (in km) when transporting manure. ................ Figure 19. Average distance (in km) of local flows for forage, straw and by-products used by livestock. ........................................................................................................................................Figure 20. Representation of the 'Ribéracois' district.. ............................................................. Figure 21. Expected effects of the leverage factors on the system performances .. ........... Figure 22. Scenarios explored in the Ribéracois case-study using the FAN model. .......... Figure 23. FAN scenarios outputs for crop production ............................................................ Figure 24. FAN scenario outputs for animal production. ........................................................ Figure 25. Feed district balance from FAN scenario outputs. ................................................ Figure 26. Bioenergy production and indicators from FAN scenario outputs ................... Figure 27. Distance of truck transportation inside the district and material mass exchanged ......................................................................................................................................... Figure 28. Number of local flows from FAN scenarios outputs. .......................................... Figure 29. N flows from FAN scenarios output ........................................................................ Figure 30. N indicators from FAN scenario outputs. .............................................................. Figure 31. CO2 eq. emissions (positive) and C stored or CO2 avoided (negative), from FAN scenarios output in kg of CO2 equivalents per year. .................................................... Figure 32. CO2 eq. in and off site emissions (positive) and C stored expressed as CO2 avoided (negative), from FAN scenario outputs. ......................................................................Figure 33. Total CO2 Emissions from FAN scenario outputs, ..............................................Figure 34. Kg CO2 eq. emitted or stored (in and off site). .....................................................

Figure 34 .

 34 Figure 1. Natural and anthropogenic nitrogen inflows ............................................................ Figure 2. Global food and feed material flows. ........................................................................... Figure 3. Conceptual framework of nutrient and material flows in agro-food system. ....Figure 4. Agro-industrial Ecology conceptual Framework. .....................................................Figure 5. Example of nutrient loss indicators of a farming region ........................................ Figure 6. Substance Flow Analysis of phosphorus in France. ................................................ Figure 7. Industrial symbiosis of Kalundborg Industrial Park ..............................................Figure 8. Example of a crop-livestock model in the Vihiga district. ......................................Figure 9. An agent decision module within an agent-based model. ...................................... Figure 10. Classification of the different approaches. .............................................................. Figure 11. Class diagram in UML. ................................................................................................ Figure 12. Farm agent entities in the model .............................................................................. Figure 13. Process schedule along a cycle of one year. ............................................................. Figure 14. Representation of material flows in FAN ................................................................ Figure 15. Representation of the 'Ribéracois' district ............................................................... Figure 16. Example of simulation of local fertilization flows in Ribéracois. ....................... Figure 17. Variation in the number of local fertilization flows. ............................................. Figure 18. Variations in average distance (in km) when transporting manure. ................ Figure 19. Average distance (in km) of local flows for forage, straw and by-products used by livestock. ........................................................................................................................................Figure 20. Representation of the 'Ribéracois' district.. ............................................................. Figure 21. Expected effects of the leverage factors on the system performances .. ........... Figure 22. Scenarios explored in the Ribéracois case-study using the FAN model. .......... Figure 23. FAN scenarios outputs for crop production ............................................................ Figure 24. FAN scenario outputs for animal production. ........................................................ Figure 25. Feed district balance from FAN scenario outputs. ................................................ Figure 26. Bioenergy production and indicators from FAN scenario outputs ................... Figure 27. Distance of truck transportation inside the district and material mass exchanged ......................................................................................................................................... Figure 28. Number of local flows from FAN scenarios outputs. .......................................... Figure 29. N flows from FAN scenarios output ........................................................................ Figure 30. N indicators from FAN scenario outputs. .............................................................. Figure 31. CO2 eq. emissions (positive) and C stored or CO2 avoided (negative), from FAN scenarios output in kg of CO2 equivalents per year. .................................................... Figure 32. CO2 eq. in and off site emissions (positive) and C stored expressed as CO2 avoided (negative), from FAN scenario outputs. ......................................................................Figure 33. Total CO2 Emissions from FAN scenario outputs, ..............................................Figure 34. Kg CO2 eq. emitted or stored (in and off site). .....................................................

Figure 1 .

 1 Figure 1. Natural and anthropogenic nitrogen inflows on the left, and flows of reactive Nitrogen on the right in terrestrial, oceanic and atmospheric ecosystems (units are in Teragrams of Nitrogen per year). On the left, green arrows represent natural sources and purple arrows represent anthropogenic sources. On the right, colors represent different forms of reactive N. Figure adapted from Fowler et al., (2013).

Figure 2 .

 2 Figure 2. Global food and feed material flows, expressed in Gigagrams of Nitrogen per year, from (Lassaletta et al., 2014a). Only flows higher than 90 GgN are represented.

Figure 3 .

 3 Figure 3. Conceptual framework of nutrient and material flows in agro-food system at the local scale. System boundaries are indicated by the dotted box. Arrows represent flows, solid lines represent material exchanges, and dotted lines represent losses to the environment. Adapted from Fernandez-Mena et al. (2016).

Figure 4 .

 4 Figure 4. Agro-industrial Ecology conceptual Framework: factors, drivers and tools.

Figure 5 .

 5 Figure 5. Example of nutrient loss indicators of a farming region according to their position in the cause-effect chain linking production practices to their impacts (from Payraudeau and van der Werf, 2005).

Figure 6 .

 6 Figure 6. Substance Flow Analysis of phosphorus in France (from Senthilkumar et al., 2014). Values are phosphorus (P) flows in kt P y -1 for the year 2006. Losses are indicated in orange and recycling routes are indicated in red. Only flows greater than 5 kt P y -1 are represented.

Figure

  Figure 7. Industrial symbiosis of Kalundborg Industrial Park, Denmark (Jacobsen, 2006).

Figure 8 .

 8 Figure 8. Example of a crop-livestock model in the Vihiga district, Kenya. The different material flows among farms are strongly related to the differences in farm types. Dotted lines stand for occasional flows (from Tittonell et al., 2009).

(

  2004), multi-agent systems help researchers in the field of ecosystem management to go beyond the role of individual agents: they help to understand the role of agents' interactions and organization (spatial, networks, hierarchies) in natural resource conservation. Due to the scattered nature of farming operations in agro-food chains, such models are clearly helpful to improve resource management in farming systems. In addition, Delmotte et al., (2013) showed the high adaptability of the agent-based modelling approach to develop participatory assessment of scenarios. In such an approach, different interacting agents (such as farmers, water managers, policy makers or managers of protected areas) are asked to validate the conceptual model and to discuss the different model outputs. Here, agent-based models clearly serve as a means for supporting discussions between possibly conflicting actors. Agent-based models have been extensively developed in relation to agricultural systems and resource management. Due to the scattered presence of farmers and agents among landscapes, these agent-based models are helpful to improve resource management, land-use and farming systems. In these models, the capacity to simulate actors' decision-making in a realistic way and natural processes at the same time remains challenging. Numerous examples exist in relation to water

Figure 9 .

 9 Figure 9. An agent decision module within an agent-based model (Schreinemachers and Berger, 2011a). Proceeding in annual time steps, the agent decision module goes through three phases (investment, production and consumption) and includes specific criteria, resources, periods and feedback.

Figure 10 .

 10 Figure 10. Classification of the different approaches based on how agents are represented (on the Y axis) and the spatial extent of the systems studied (on the X axis).

  each of these ways to estimate nutrient flows has specific advantages and drawbacks when we consider the background of the research teams working on them. On the one hand, industrial ecology tools such as LCA or industrial symbiosis analyzes were originally developed by engineers, indicating a greater interest in technological innovations of industrial and manufactured products and less emphasis on environmental features and ecological processes. On the other hand, agronomists have been more likely to use integrated assessments of agricultural systems, as well as crop-livestock system analyzes, showing a clear focus on farming activities, with less attention to the behaviour of economic agents, product chains and technological innovations. In the case of agent-based models, a rich multidisciplinary of backgrounds exists, including computer scientists, economists, sociologists and other environmental modellers. Although some ecologists and environmental scientists are already working together within different teams, a big effort has to be made to encompass all of these different perspectives of sustainability. Hence, we encourage the contribution and cooperation of the different domains through Agro-Industrial

  The agent population is composed of eight main types of agents, as represented by the agent class diagram in Figure 11. They include agricultural production (farms, feed and forage collectors), food industries (milk & cheese industries, slaughterhouses, and fruits & vegetables industries), waste managers (anaerobic digesters, wastewater treatment plants), and fertilizer wholesalers. We additionally use an intermediary conceptual agent ('Partner', white box in Figure 11) as a modelling tool to allow these agents to simultaneously demand and supply materials on each round of exchanges. Although farms are classified into eight different functional groups according to their characteristics (in terms of area, land-use and livestock numbers), all farm agents are capable of a set of defined actions while their annual production is based on their individual agent attributes. For instance, during a simulation, all farms conduct the action of animal feeding at the same time (regardless of the farm type), but farms that do not have animals remain unchanged by this action.

Figure 11 .

 11 Figure 11. Class diagram in UML (Unified Modelling Language). Agents are represented in boxes with their attributes listed in the middle and their typical actions in the bottom. The eight farm agent functional groups are depicted in green. Solid arrows with hollow white ends represent belongings to a more general category (e.g., an 'arable farm' is an extension of the broader 'farm' class). Dashed arrows indicate actions as specified in angle quotation marks (<<>>).

Figure 12 .

 12 Figure 12. Farm agent entities in the model and their possible interactions and material exchanges with the local and global markets. Solid boxes represent the various types of farm features and white boxes represent the materials that farm agents (8 functional groups) can exchange within the local network. White arrows represent in-farm interactions, black thin arrows stand for interactions with the market (supply or demand of materials) and large black arrows stand for actual flows in and out the farm. Note that some exchanges are bidirectional (fertilizers and animal requirements) while some are unidirectional (foodstuff).

Figure 13 .

 13 Figure 13. Process schedule along a cycle of one year. Linear arrows represent material flows interacting at different steps. Arrow loops at steps 1, 2, and 4 represent the materials exchange processes between agents within the network.

Figure 14 .

 14 Figure 14. Representation of material flows in FAN. Farms are represented as small circles (green for arable, red for cattle, blue for dairy and orange for monogastrics). Arrows represent flows of materials: manure flows are in brown, chemical fertilizers in purple, grass flows in green, cereals flows in orange, oilseeds in yellow, milk in blue, meat in red and food processing wastes in pink. Flows crossing the system boundary represent exchanges with the Global Market. Examples of the radius of action for manure and sewage sludge are show by the dotted circles. WWT stands for Wastewater Treatment plant.

Figure 15 .

 15 Figure 15. Representation of the 'Ribéracois' district. On the left, location of the district in France. On the right, graphical representation of the district in GAMA platform. Farms are represented by circles colored depending on their main production (green for arable; blue for dairy; red for beef cows; purple for mixed cattle; black for mixed crop-livestock; yellow for horticultural; orange for pig and grey for ovine and caprine). Squares represent food industries (yellow: feed collectors; blue: milk and cheese industries; green: fruits and vegetables industries; red: slaughterhouse).

Figure 16 .

 16 Figure 16. Example of simulation of local fertilization flows in Ribéracois.

Figure 17 .

 17 Figure 17. Variation in the number of local fertilization flows in relation to different values of exponential of distance (proxy for proximity), the disposition to exchange between farms, farms fidelity to the same partner and preference coefficients for chemical fertilizer and manure for fertilization use.

Figure 18 .

 18 Figure 18. Variations in average distance (in km) when transporting manure. The variables explored are: exponential of distance (proxy for proximity), the disposition to exchange between farms, farms fidelity to the same partner and preference coefficients for chemical fertilizer and manure for fertilization use.

Figure 19 .

 19 Figure 19. Average distance (in km) of local flows for forage, straw and by-products used by livestock. The explored variables are: the exponential of distance (proxy for proximity); the disposition to exchange biomass and the fidelity.

Figure 20 .

 20 Figure 20. Representation of the 'Ribéracois' district. On the left, location of the district in Dordogne, France. On the right, graphical representation of the district in FAN. Farms are represented by circles coloured with their typology (green for arable; blue for dairy; red for beef cows; purple for mixed cattle; black for mixed crop-livestock; yellow for horticultural; orange for monogastrics and grey for ovine and caprine). Squares represent food industries (yellow: feed collectors; blue: milk industries; green: fruits and vegetables industry; red: slaughterhouse).

  Figure 21.

Figure 21 .

 21 Figure 21. Expected effects of the leverage factors (boxes) on the system performances (circles). Arrows represent interactions between leverage factors

Figure 22 .

 22 Figure 22. Scenarios explored in the Ribéracois case-study using the FAN model. The S5b scenario is Crop-Livestock Symbiosis and livestock is reduced to half of the initial population and the S6b Scenario is No Chemical Fertilizer and livestock is reduced to half too.

  Fert.), especially when reducing livestock (+ L/2). Yet, pulses and grass are not affected since they are not fertilized with chemical sources in FAN and because they are assumed to get enough N through biological fixation. Cereal production decreased in Crop-Livestock Symbiosis scenarios (C-L Symb) when incorporating more pulses in crop rotations at the expense of cereals, but they increased in the scenario reducing livestock (C-L Symb. + L/2) due to the replacement of silage maize by cereals. Although pulse production increased when integrating crops and livestock (C-L Symb), there were no changes in grass and legume forage areas as there was enough of these products to meet animal forage requirements in the district.

Figure 23 .

 23 Figure 23. FAN scenarios outputs for crop production in the Ribéracois, in gigagrams (or kilotons) of crop products per year. Scenarios names are presented in Figure 3 and Table3.

Figure 24 .

 24 Figure 24. FAN scenario outputs for animal production in the Ribéracois, in megagrams (or tons) of meat and gigagrams (or kilotons) of milk per year.

Figure 25 .

 25 Figure 25. Feed district balance from FAN scenario outputs, calculated as the difference between feed produced and consumed by animals in the Ribéracois district, in Gigagrams per year. Forage district balance (on the right) is the difference between the forage produced (as grass, silage maize and legume forage), and the forage consumed in the district.

Figure 26 .Figure 27 .Figure 28 .

 262728 Figure 26. Bioenergy production and indicators from FAN scenario outputs. District anaerobic digestion capacity is the sum of all digesters capacity in terms of substrate digested. Biogas produced after digestion is expressed in m3 and the electricity recovered is expressed in kWh.

  , crop N demand varies only when changing land-use. Since legume crops are not fertilized in FAN, crop N demand decreases when replacing cereals with pulses in C-L Symb., which are less demanding. Still, when reducing livestock, cereals increased and pulses are lesser. Notice that crop N demand is not necessarily N harvested by crops but the necessary N seek for crop maximum yields. As shown in Crop production results, N inputs in scenarios without chemical fertilizers were not enough to satisfy N crop demand for maximum yields.

Figure 29 .

 29 Figure 29. N flows from FAN scenarios output, in kg of N per year. N inputs to the system are on the left, and N outputs and losses on the right.

  storage, significantly improving the balance. Enhancing materials exchanged inside the district only slightly increases CO2 emission from truck transportation. Finally, C storage by grasslands plays an important mitigation role in CO2 balance, by compensating enteric fermentation emissions.

Figure 31 .

 31 Figure 31. CO2 eq. emissions (positive) and C stored or CO2 avoided (negative), from FAN scenarios output in kg of CO2 equivalents per year.

Figure 32 .

 32 Figure 32. CO2 eq. in and off site emissions (positive) and C stored expressed as CO2 avoided (negative), from FAN scenario outputs (in kg of CO2 equivalents per year).

Figure 34 .

 34 Figure 34. Kg CO2 eq. emitted or stored (in and off site) from FAN scenario outputs, in kg of CO2 equivalents emitted per Gigagram of protein and Teracalorie of Metabolisable Energy (ME) in food produced per year.

  into their input and material costs and to derive new income from alternative sources such as renewable energy production. The development of local feed and forage production and of biogas plants are options that are already considered and discussed by breeders and local extension services.However, we faced several challenges to define what a local scale is and what its boundaries are. In Chapter 1, we defined the local scale as regions or districts in which economic partners are spatially close enough to be connected within exchange networks, while sharing the same natural environment. This definition resulted in including direct upstream and downstream partners of farms that operate across the district. We therefore excluded external agents connected to the global markets and long distance national markets. Only agents present within the area were considered as local partners.

Table 1 .Comparison of the different approaches according to their purpose, scope and framework.

 1

	Environmental Impact Assessment Tools	Stock and Flow Analysis methods	Agent-Based Models

Table 2 . User-defined variables and their default values in the model Variable name Units Default value Network features

 2

	Exponential of the distance (a) in Proximity Equation 1	-	a=1
	Fidelity	% farms	50
	Disposition to exchange between farms	% farms	50
	District capacity of anaerobic digestion	kg of materials	60000
	Number of farms	-	850
	Chemical and organic fertilizers
	Sludge for fertilization preference coefficient	[0-1] ratio	0.5
	Manure for direct fertilization preference coef.	[0-1] ratio	0.5
	Manure for anaerobic digestion preference coef.	[0-1] ratio	0.5
	Chemical fertilizer pref. coef.	[0-1] ratio	0.5
	Digestates pref. coef.	[0-1] ratio	0.5
	Radius of action for manure	km	15
	Radius of action for sewage sludge & digestates	km	80

Table 3 . Examples of the various environmental indicators that can be estimated by FAN's submodels.

 3 , including soil emissions and carbon storage, livestock enteric fermentation and emissions related to organic fertilizing material storage and application. GHG emissions from material transportation were estimated by emission factors from average truck and boat emissions per kg of material

	transported (IPCC, 2013) for local and global materials flows respectively. Additionally, potential
	GHG emissions avoided by biogas production emissions are estimated (European Environmental
	Agency, 2014). A soil organic matter dynamics model, inspired by Hénin and Dupuis, (1945), was
	used to estimate carbon storage in soils by accounting for soil organic matter stock, carbon
	humification following organic material inputs and organic matter mineralisation. Human and
	animal average food and feed consumption equivalents were used as a proxy to estimate food and
	feed autonomy indicators (FAO, 2010). The environmental outputs for all indicators are included
	in the code provided (Supplementary Materials File 1), but are not further detailed in this
	paper.
	Activity or	Indicators calculated by the model	Estimation method
	environmental
	component
	Crop production	Grains:	Land use and regional yields
		Cereals, Oilseeds, Pulses.
		Other crops:
		Fruits & Legumes
		Forage:
		Grass, Silage Maize and Legume forage.
	Livestock	Beef meat	Number of heads and average
	production	Sheep & Goat meat	national yields
		Pork meat
		Chicken meat
		Cow milk
		Goat milk

Table 4 . Key input data and sources for main important processes in FAN submodels.

 4

		See model included files
	-use and livestock in farms	(ha of crops and livestock heads.	Agreste (Ministry of Agriculture, France)
		farm -1 )
	Crop regional yields	See model included files (kg of crop. ha -1 . year -1 )	Agreste (Ministry of Agriculture, France)
	N in animal excreta	See model included files (kg N. animal head -1 )	COMIFER, 2013a
	N content in crops	See model included files (kg N. kg harvested crop -1 )	COMIFER, 2013b
	Average N dose in arable crops	151 kg N. ha -1 . year -1	Agreste (Ministry of Agriculture, France)
	N in solid digestates, based on a national average	N = 5,7% (kg N. kg dM -1 . year -1 )	Houot , 2014

Table 5 . Farm types and their land-use and livestock characteristics in Ribéracois (Agreste, 2010).

 5 Besides, the half south of Ribéracois area, where arable crops are predominant, is concerned by the Nitrate

	Vulnerable Directive since 2015 (DREAL, 2016). Still, high fertilization rates are applied overall
	the district, i.e., around 160 kg N/(ha.year) for arable crops, leading to high nutrient losses
	through various nitrogen pathways.

in and off site emissions balance (in kg-CO2 eq/year)

	-100000000 -80000000 -60000000 -40000000 -20000000 0 20000000 40000000 60000000 80000000 100000000	CO2 total in and off site emissions BMP mineralisation CO2 soil and residues EXCH CO2 BAU by storing C in CO2 sinked arable lands BIOGAS C-L Symb CO2 sinked by storing C in grasslands No Chem Fert CO2 from total N2O emissions Figure 33.	CO2 from CH4 enteric fermentation C-L Symb + L/2 CO2 from CH4 manure storage No Chem Fert + L/2 CO2 from truck transport	CO2 avoided emissions in France by bioenergy produced	CO2 induced by synthesis of N chemical fertilizers	CO2 induced by imported feed
		scenarios, for example down to half the initial emissions in the BIOGAS scenario. Finally,
		removing livestock and chemical fertilizers, in No Chem. Fert. + L/2, has a potential net
		storage of 19,256 tons of CO2 eq. per year.

Total CO2 Emissions from FAN scenario outputs, in kg of CO2 equivalents per year.

Acknowledgements / Remerciements / Agradecimientos

This work was funded by INRA (Division of Environment and Agronomy) and Bordeaux Sciences Agro. I received additional financial support for an international mobility in Canada from Labex COTE of University of Bordeaux, and from Agreenium, France. I also carried a collaboration with other researchers, including Graham K. MacDonald from

Chapter 2 -"Flows in Agro-food Networks (FAN): An agent-based model to simulate material flows in agriculture at the local scale"

Submitted in 2017 to Environmental Modelling and Software, under review.

Chapter 3 -

Can changes in material flow networks at the local scale reduce environmental impacts of agro-food systems while maintaining food and energy production? FAN model exploration of different scenarios in the Ribéracois case study.

To be submitted to Agricultural Systems or to Regional Environmental Change.

In the last chapter we presented the FAN model and we explored its sensitivity to some key variables. We highlighted its novelty and its potential to simulate material flows among a large range of economic agents in agro-food chains. We also discussed its ability to be used to assess alternative situations of biomass exchanges among economic agents. In the current chapter we present an application of FAN to the simulation of contrasted scenarios related to material exchanges among economic actors at the local scale. In particular, we focus on the assessment of these scenarios through a large set of indicators related to agricultural production, local trade, nutrient cycling and greenhouse gas budget. In the close future, this chapter will be submitted to Agricultural Systems or to Regional Environmental Change.

Abstract

New strategies and regulations are needed to tackle agriculture's pressure on natural resources.

In particular, agro-food chains have to move away from linear towards more close-looped systems by applying circular bioeconomy and agro-industrial ecology principles. Characterizing the agrofood network as agents interacting is key to explore alternative scenarios of biomass management at the local scale. Agent-based models can be efficient tools to simulate different agents' behaviors under alternative scenarios. In this study, we use the FAN ("Flows in Agricultural Networks") agent-based model to study alternative scenarios of materials management in agro-food systems at the local scale. FAN was applied to the Ribéracois, a case-study in the southwest of France, to simulate and assess a set of contrasted scenarios ranging from good management practices, organic waste recycling, bioenergy production, crop-livestock symbiosis to chemical fertilizers removal. The scenarios outcomes are assessed in terms of food and feed production, nutrient cycling and greenhouse gas budget. The environmental performance of the scenarios increased progressively through their application. However, several variables showed that this progression was not straightforward and sometimes food production could be drastically reduced. This information gave an insight on how different strategies can make agro-food systems change and adapt to local environmental issues.

The scenarios were designed in an aggregative manner, i. e. each scenario applies the changes already implemented in the previous one. The scenario specific characteristics are the following: S1. The "Business As Usual" (BAU) situation, represents the current farming practices, its production and impacts. It is considered as the baseline situation. Its parameters are set to their default values (Table 6).

S2. The adoption of "Best Management Practices" (BMP) by farms. In this scenario, farms aim to reduce their environmental pressure by applying some soft managing measurements that are commonly recommended in agrarian extension [START_REF] Baumgart-Getz | Why farmers adopt best management practice in the United States: A meta-analysis of the adoption literature[END_REF]. In particular, the nitrogen fertilization application rate is adjusted to the crop nutrient requirements plus some unavoidable loses including N volatilisation and moderate N leaching. Farms are also asked to use catch crops in order to additionally reduce N loses through leaching. Animal diets are also adjusted by slightly reducing protein feed intake according to protein use efficiency recommendations.

S3. The fostering of exchanges among economic partners network (EXCH) including local forage and organic waste recycling for fertilization as a substitute of mineral fertilizers.

Here, all farms are disposed to exchange materials with their partners. In addition, the preference coefficient for using manure and sewage sludge as organic fertilizers is increased to its maximum. S4. The implementation of biogas (BIOGAS) production plants up to their maximum potential. In this scenario, ten anaerobic digester units are simulated to ferment biomass materials in order to produce electricity and heat from biogas (CH4 + CO2). Consequently, farms are assumed to give their manure to the digesters, getting back similar amounts of nitrogen as digestates to fertilize soils. Similarly to manure, farms will offer their digestates surplus to other farms in the network, also favoured to be chosen rather than the chemical fertilizers through preference coefficients. The digestion of other digestible materials -grass and food processing wastes-is also favoured by using preference coefficients.

S5a. A complete crop-livestock symbiosis (C-L Symb.) through local feed and forage production. In this scenario, arable production is adjusted to meet livestock demand in terms of crop and forage products. As a consequence, if forage deficit exists, some cereal area is converted to temporary grass production in order to compensate such deficit.

Similarly, if any feed deficit exists -in particular in terms of pulses-cereal surfaces are The scenarios were built in FAN by changing specific parameters of the model (Table 7).

We hypothesised greater environmental benefits for scenarios that requested profound agro-food chain changes (i.e. for 'Redesign-like' scenarios). We performed 30 simulations of each scenarios by running each scenario until its 5 th year. Overall, more sustainable food and renewable bioenergy production seem possible in Ribéracois district without compromising environmental impact. Thanks to the FAN model, we were able to account for complex interactions between the leverage factors applied resulting in different food production and environmental performance. This work gives an insight of how different solutions seeking sustainability in agro-food systems may bring to very different outputs. Future agricultural and environmental policies may be able to take into account simulations from predictive tools like FAN.

Discussion and Conclusion