J Le Noë

G Billen

F Esculier

J Garnier

Long-term socioecological trajectories of agro-food systems revealed by N and P flows in French regions from 1852 to 2014

We present a quantitative description of the N and P flows characterizing the agro-food system metabolism of 33 agricultural regions in France and their time evolution since the middle of the 19th century. The data were interpreted in terms of connection between crop production, livestock breeding, human nutrition and trade of agricultural goods, and were linked to their historical background. Until the early 20th century, the integrated crop and livestock farming model dominated everywhere, and the slow increase in crop production was only possible because of an increase in livestock density. Specialized cash crop farming systems appeared in the central Paris basin only in the first half of the 20th century together with the increase in the use of industrial fertilizers. Only after WWll, under the pressure of strong interventionist policies, did specialization of French territories lead to five types of systems, favoring their openness and integration into the international market, with harmful environmental impacts. The 1980s were marked by a policy shift towards more liberalism, which reinforced specialization. However, greater environmental concern stabilized or decreased nutrient losses, while maintaining largely open biogeochemical cycles.

Introduction

Today, agriculture is largely responsible for disturbing the nitrogen (N) and phosphorus (P) cycles, which [START_REF] Steffen | Planetary boundaries: guiding human development on a changing planet[END_REF] pointed out as one of the nine earth-system limits. These perturbations are mainly due to the shift from an organic agriculture closely coupling livestock and vegetal production to an industrial agriculture based on mineral fertilization and specialization that has separated crop and livestock farming. The transition from organic fertilization toward mineral-based fertilization was initially made possible by two historical discoveries: (i) the existence of phosphate deposits, in the form of guano in Peru first, and as phosphorus rock in Florida and Morocco thereafter [START_REF] Clark | Ecological imperialism and the global metabolic rift, unequal exchange and the guano/nitrates trade[END_REF][START_REF] Pluvinage | Industrie et commerce des engrais et des anticryptogamiques et insecticides[END_REF] and (ii) the invention of the Haber-Bosh process in 1913 [START_REF] Smil | Enriching the earth: Fritz Haber. Carl Bosch and the Transformation of World Food Production[END_REF]. By the end of the 19 th century, these new farming techniques responded to the problem of soil exhaustion, which had already raised concerns among scientists (e.g., Liebig) as early as 1840 [START_REF] Foster | Marx's Ecology: Materialism and Nature[END_REF]. It also made it possible to better integrate agriculture into the market economy as yields increased with these new means of fertilization, while the need for closing the nutrient loop locally became less stringent. In many places, this implied the progressive specialization of agro-food systems over the course of the 20th century in order to remain competitive and maximize profits [START_REF] Mazoyer | Histoire des agricultures du monde. du Néolithique à la crise contemporaine[END_REF]. In return, decoupling animal and vegetal production resulted in ever-increasing trade flows of agricultural products (Lassaletta et al., 2014a). The consequences for N and P cycles were a complete opening at the global scale [START_REF] Smil | Phosphorus in the environment: natural flows and human interferences[END_REF][START_REF] Galloway | Reactive nitrogen and the world: 200 years of change[END_REF] leading to the eutrophication of water streams [START_REF] Carpenter | Eutrophication of aquatic ecosystems: Bistability and soil phosphorus[END_REF], an increase in NH 3 emissions, which have dangerous side effects for both ecosystems and human health [START_REF] Bouwman | A global high-resolution emission inventory for ammonia[END_REF], and emission of N 2 O, a powerful greenhouse gas [START_REF] Bouwman | Direct emission of nitrous oxide from agricultural soils[END_REF]. Furthermore, the opening of the P cycle also raised the issue of its exhaustion over the more or less long term [START_REF] Elser | Phosphorus cycle: a broken biogeochemical cycle[END_REF] given that it is a limited and nonrenewable resource over the human time scale. As an indispensable element to plant growth, restricted accessibility to P is likely to jeopardize the capacity of agro-food systems to produce enough food for a growing world population, which may generate geopolitical conflicts [START_REF] Cordell | The story of phosphorus: global food security and food for thought[END_REF].

In this context, a number of recent studies have focused on the socioecological metabolism of agro-food systems, applying material, nutrients or energy flow analysis approaches from local to global scales [START_REF] Güldner | Nutrient recycling and soil fertility management in the Course of the industrial transition of traditional, organic agriculture: the case of Bruck Estate, (1787-1906)[END_REF][START_REF] Guzmàn | Spanish agriculture from 1900 to 2008: a long-term perspective on agroecosystem energy from an agroecological approach[END_REF][START_REF] Garnier | Phosphorus budget in the water-agro-food system at nested scales in two contrasted regions of the world (ASEAN-8 and EU-27)[END_REF][START_REF] Garnier | Reconnecting crop and cattle farming to reduce nitrogen losses to river water of an intensive agricultural catchment (Seine basin, France): past, present and future[END_REF][START_REF] Soto | The social metabolism of biomass in Spain, 1900-2008: from food to feed-oriented changes in the agro-ecosystems[END_REF][START_REF] Billen | Grain, meat and vegetables to feed Paris: where did and do they come from? Localising Paris food supply areas from the eighteenth to the twenty-first century[END_REF]. Analyses of socioecological metabolism conducted within a long-term perspective can shed light on the interrelation between human and natural history in the evolution of agro-ecosystems. Material and energy flows embedded in the functioning of agro-food systems are shaped by human activities of extraction, processing and consumption of biomass, but are also mediated by complex and dynamic natural processes such as ammonia volatilization, nitrate leaching and P sorption. Therefore, as stated by [START_REF] Gizicki-Neudlinger | Land, food and labour in pre-industrial agro-ecosystems: a socio-ecological perspective on early 19th century seigneurial systems[END_REF], agricultural systems, perhaps more than any other human activity, need to be considered as "historical phenomen [a] at the intersection of economy and ecology, as a hybrid between nature and culture."

However, to our knowledge few studies within this perspective have examined the case of France, with the exception of the recent article of [START_REF] Harchaoui | Reconstructing production efficiency, land use and trade for livestock systems in historical perspective. The case of France, 1961-2010[END_REF], which analyzed the transformation of livestock breeding and its consequences over land use and agricultural trade in France over the 1961-2010 period. Yet, the national scale adopted in their study is blind to regional disparities and to the structural link between livestock breeding, arable land and grassland production. The case of France is noteworthy because this country is currently one of the main agricultural powers in Europe, the first exporter of cereals in 2014 (FAO, 2017), although the modernization of French agriculture had long lagged behind other Western European countries such as the United Kingdom, The Netherlands, Belgium and Germany [START_REF] Ruttan | Structural retardation and the modernization of French agriculture: a skeptical View[END_REF]. The late modernization of agriculture in France has been studied in great depth by historians [START_REF] Jollivet | La grande transformation de l'agriculture française sous l'oeil du sociologue[END_REF][START_REF] Duby | Histoire de la France rurale, tome III de 1789 à 1914[END_REF][START_REF] Muller | Le technocrate et le paysan: Les lois d'orientation agricole de 1960-1962 et la modernisation de l'agriculture française[END_REF][START_REF] Ruttan | Structural retardation and the modernization of French agriculture: a skeptical View[END_REF][START_REF] Duby | Histoire de la France rurale, tome IV depuis[END_REF] who highlighted the political and economic reasons for this delay. Nevertheless, the consequences of the particular evolution of French agriculture in terms of N and P cycles and environmental and agronomic performance are still lacking in the analysis. Therefore, the present research explored the co-evolution of the different patterns of agro-food systems in terms of N and P cycles in their historical context, applying the Generalized Representation of Agro-Food System (GRAFS) as developed by [START_REF] Billen | A biogeochemical view of the global agro-food system: nitrogen flows associated with protein production, consumption and trade[END_REF][START_REF] Le Noë | How the structure of agro-food systems shapes nitrogen, phosphorus, and carbon fluxes: the generalized representation of agro-food system applied at the regional scale in France[END_REF].

Studying the trajectories of agro-food systems from the perspective of N and P flows is an original prism for such analysis because at the same time it provides information on their degree of openness, their agronomic and environmental performance in terms of N and P use efficiency (NUE and PUE, i.e. the fraction of all N and P inputs that is effectively harvested), and the N and P balances. What are the trajectories that have led to the current agro-food systems at the regional scale? What were the main drivers of these trajectories? What are the environmental consequences? What are the legacies from the previous history on the current state of the system? Answering these questions contributes to responding to the general challenge for future sustainable agricultural production because (i) lessons can be drawn from the past given that traditional agricultural systems relied mainly on nutrient recycling at the farm and regional scale and (ii) designing future patterns of production will require accounting for the effect of agriculture development based on soil fertility, particularly P.

We therefore studied the period from 1852 to 2014. The mid-19th century corresponds to the very beginning of mineral fertilization in France [START_REF] Boulaine | Histoire de la fertilisation phosphatée 1762-1914[END_REF] and also to the beginning of the Napoleonian Second Empire and the documentation of regular and detailed agricultural statistics. In this paper, some concrete findings regarding the evolution of agro-food system for three typical and contrasted French regions are first analyzed in order to capture the main characteristic of these systems. Based on this first analysis, a typology is then developed in order to objectify main types of agro-food system and to further systematize the analysis of regional trajectories. Finally, based on this typology, we investigate the evolution of agro-food systems toward the different types identified, the consequences of these evolutions in terms of N and P fluxes and some interpretations regarding the drivers of these evolutions are proposed based on literature review.

Concepts of the method, data collection and hypothesis

Concepts of the GRAFS approach

The GRAFS approach (Generalized Representation of Agro-Food Systems, [START_REF] Billen | A biogeochemical view of the global agro-food system: nitrogen flows associated with protein production, consumption and trade[END_REF] is a generic biogeochemical approach for describing the agro-food system of a given territory, from the farm [START_REF] Garnier | Reconnecting crop and cattle farming to reduce nitrogen losses to river water of an intensive agricultural catchment (Seine basin, France): past, present and future[END_REF] to the global scale [START_REF] Lassaletta | Nitrogen use in the global food system: past trends and future trajectories of agronomic performance, pollution, trade, and dietary demand[END_REF], by quantifying nutrient fluxes between cropland, permanent grassland, livestock, humans and the natural environment. From the GRAFS perspective, cropping systems are considered to convert nutrient inputs (such as fertilizers, manure, symbiotic N fixation, and atmospheric deposition) into harvestable vegetal products. Crop products can be used (i) to meet the vegetal protein requirements of human nutrition, (ii) to be exported or (iii) to feed livestock, to the extent that they are not fed by grazing on permanent and semi-natural grassland or by imported feedstuffs. The difference between nutrient inputs and outputs informs on the nutrient balance of either crop or grassland soils. More detailed information is provided in Supplementary material SM 1.

The efficiency of feed and grazing conversion into consumable animal proteins (meat, milk and eggs) determines the amount of excreted N, a part of which can be recycled into cropland as manure, making cropland fertility partly dependent on transfers from permanent grassland. The fishery and aquaculture sector also contributes, providing animal proteins for human nutrition, but is considered in our analysis as a separate system for the sake of simplicity. Nutrient losses to the environment occur at each stage of the chain, particularly through leaching and volatilization from cropland, loss from animal excreta and waste from food processing and, finally, from human excretion. Storage in the soil pool is also a possible fate for nutrients.

The GRAFS representation enables to draw direct links between different aspects of the agro-food system, e.g., the link between livestock breeding, grassland areas, and forage crops and the link between fertilization of cropland and grassland and environmental nutrient losses. GRAFS also provides some key indicators for analyzing agrofood systems from both the environmental and agronomic perspectives. A full description of the GRAFS methodology has been provided by Le [START_REF] Le Noë | How the structure of agro-food systems shapes nitrogen, phosphorus, and carbon fluxes: the generalized representation of agro-food system applied at the regional scale in France[END_REF]. Hereafter, we only provide a synthetic description of the main hypotheses and data sources to establish GRAFS for past and current times. A more detailed description of the method is provided in SM1. In this study, we applied the approach to 33 regions defined by Le [START_REF] Le Noë | La place du transport de denrées agricoles dans le cycle biogéochimique de l'azote en France : un aspect de la spécialisation des territoires[END_REF] for 22 dates from 1852 to 2014.

Data collection for past and present

Human population and consumption

Total, urban and rural population figures at the "département" (Nuts 3) level are provided by the French National Institute for Statistics and Economic Studies (INSEE, 2017) for the census years, every 5 years from 1852 to 2014, interpolated to the years of the survey. The changes in the human diet in France over the last two centuries were investigated from different data sources and archives [START_REF] Philippe | Une opération pilote : l'étude du ravitaillement de Paris au temps de Lavoisier[END_REF][START_REF] Toutain | La consommation alimentaire en France de 1789 à 1964[END_REF][START_REF] Barles | Feeding the city: food consumptiona nd flow of nitrogen, Paris, 1801-1914[END_REF][START_REF] Afssa | Enquête Individuelle Nationale des consommations Alimentaires (INCA 2)[END_REF][START_REF] Chatzimpiros | Les empreintes environnementales de l'approvisionnement alimentaire: Paris, ses viandes et lait, XIXe-XXIe siècles. Architecture, aménagement de l'espace[END_REF]INSEE, 2017). The conversion coefficients used to translate consumption of each food item into N and P were taken from several databases including CIQUAL (https://pro.anses.fr/tableciqual/ ), Diet Grail (http://dietgrail.com) and USDA (http://ndb.nal.usda. gov). These coefficients were provided in detail by Le Noë et al (2017).

Livestock metabolism

Animal production and livestock numbers for different age classes and animal categories were provided in carcass weight equivalent by annual agricultural statistics, available online at http://agreste. agriculture.gouv.fr/la-statistique-agricole/, starting in 1970. For earlier periods, data were obtained from nondigitized official registers (available from Gallica.bnf.fr). Meat, milk and egg production in terms of N and P were derived from these sources following the same procedure as described by Le [START_REF] Le Noë | How the structure of agro-food systems shapes nitrogen, phosphorus, and carbon fluxes: the generalized representation of agro-food system applied at the regional scale in France[END_REF]. We considered that there was no temporal evolution in the N and P contents of animal organs.

Total excretion in terms of N was estimated from numbers of livestock following a procedure similar to Le Noë et al. ( 2017), yet temporal evolution was considered.

Total ingestion in terms of N was taken as the sum of total production and excretion. However, part of the N excreted was considered lost by direct volatilization in the form of ammonia. Ammonia volatilization factors depended on manure management which was also documented.

For the sake of consistency between N and P fluxes, total P ingestion was calculated from the P/N ratio of the different types of ingested feed and from the estimated use of P feed additives after 1946. Subsequently, total excretion in terms of P was estimated as the difference between P ingestion and animal production in terms of P. More information regarding hypotheses and data compilation for livestock metabolism is specified in SM1.

Input to cropland and permanent grassland

Application rates of N and P mineral fertilizers to agricultural land were taken from Unifa (2016) (Union des Industries de la Fertilisation) at the "département" scale from 1970 to 2014. For the 1929-1965 period, the application rate of N and P fertilizers was provided at the "département" scale by annual agricultural statistics. Prior to 1929, fertilization data did not appear in annual agricultural statistics and were obtained at the national level from the compilation of various sources including [START_REF] Pluvinage | Industrie et commerce des engrais et des anticryptogamiques et insecticides[END_REF] and [START_REF] Duby | Histoire de la France rurale, tome III de 1789 à 1914[END_REF] (see SM1 for further details).

To assess the distribution of total fertilizer use among crop-and grasslands, we used regional data available from special surveys on grassland fertilization carried out by Agreste (Enquêtes Pratiques) in 1958, 1982[START_REF] Mazoyer | Histoire des agricultures du monde. du Néolithique à la crise contemporaine[END_REF]and 2011. No mineral fertilization of grassland was considered prior to 1955 [START_REF] Richard | Physionomie de la fertilisation en France[END_REF].

For wet and dry N atmospheric deposition (under reduced and oxidized forms), we used the values provided by EMEP (2006) at the scale of 50 × 50-km grids from 1981 to 2014, assuming even distribution at the regional scale. We calculated the N atmospheric deposition considering a variable background level of N deposition for the 1852-1981 period following the long-term trend established by [START_REF] Ruoho-Airola | Atmospheric nutrient input to the Baltic Sea from 1850 to 2006: a reconstruction from modeling results and historical data[END_REF] for Rothamsted and adding the livestock contribution proportional to livestock density at each period (see SM1 for further details on calculation).

The rate of atmospheric P deposition was taken as 0.4 kg P ha -1 yr -1 , based on the measurements of [START_REF] Némery | Phosphorus budget in the Marne Watershed (France): urban vs. diffuse sources, dissolved vs. particulate forms[END_REF] and [START_REF] Némery | Origin and fate of phosphorus in the Seine watershed (France) : agricultural and hydrographic P budgets[END_REF] for the Seine Basin, ranging from 0.28 to 0.52 kg P ha -1 yr -1 . We assumed even distribution across landscapes and geographical areas and used the same rate of P deposition over the course of the whole period studied.

Symbiotic N 2 fixation over arable land was estimated according to the relationship linking N fixation to yields (Y) for grain and forage legumes [START_REF] Anglade | Relationships for estimating N2 fixation in legumes: incidence for N balances of legume-based cropping systems in Europe[END_REF]Lassaletta et al., 2014b). For permanent grassland, we assumed legumes to be responsible for 25% of the total production. The same procedure was used across the entire period studied.

N and P inputs through seeds were estimated as a variable percentage of N and P in harvest based on different sources (Chamber of Agriculture of the Manche "département": http://www.chambreagriculture-50.fr/cultures/cereales/semis-des-cereales/; [START_REF] Agreste | La statistique agricole[END_REF][START_REF] Toutain | La consommation alimentaire en France de 1789 à 1964[END_REF]. All details on calculation are provided in SM 1.

N and P inputs to cropland or grassland via animal manure were calculated according to the same procedure as described by Le Noë et al. (2017). Briefly, the fate of N and P embedded in livestock excretion depends on the time spent by livestock outdoors (direct excretion) versus indoors and on the type of manure management for excrement collected indoors. For each type of animal and each region, the available amount of livestock excrement remaining after losses is allocated between grassland and cropland according to the following rules:

(1) direct excretion during grazing is allocated to both temporary and permanent grassland pro rata to their respective surface area; (2) excretion indoor is allocated to cropland.

N and P inputs to cropland through recycling of human excreta was calculated based on an estimated rate of human waste recycling, differing for urban and rural populations, and varying regionally and throughout the whole period [START_REF] Esculier | The biogeochemical imprint of human metabolism in Paris Megacity: a regionalized analysis of a water-agro-food system[END_REF] (see SM1 for further details in Supplementary material).

Output from cropland and permanent grassland

Crop-and grassland production was the mass harvested or grazed in wet weight or dry weight depending on the product, provided by annual agricultural statistics. The conversion of vegetal production from mass unit to ktN yr -1 and ktP yr -1 was based on coefficients for 36 different types of vegetal products gathered by Lassaletta et al. (2014a, Suppl Mat, compiling FAO data). With too few trials investigating possible historical evolution of mineral content of crops, we considered that N and P content in harvested or grazed products did not change over the course of the period investigated.

Hypotheses regarding the allocation of crop-and grassland production between the local human population, livestock production and export to other French or foreign regions to livestock are explained in SM1.

N and P balances in cropland and grassland

The N balance was defined as the sum of N inputs through mineral fertilizers, manure after NH 3 volatilization, symbiotic fixation by legumes, sludge, seeds and atmospheric deposition, minus N output through crop harvesting. The N balance on arable land represents a potential loss to the environment, either as N 2 , N 2 O and NO emissions or as N leaching [START_REF] Benoit | Nitrous oxide emissions and nitrate leaching in an organic and a conventional cropping system (Seine basin, France)[END_REF]; part of the N balance can also be stored in the SOM pool. By contrast, below a threshold of about 100 kg N ha -1 yr -1 , the N balance in grassland is mostly stored or denitrified instead of being leached to groundwater [START_REF] Billen | The nitrogen cascade from agricultural soils to the sea: modelling N transfers at regional watershed and global scales[END_REF].

Similarly, the annual soil P balance was calculated considering P inputs through mineral fertilizers, manure, sludge, seeds, and atmospheric deposition, and P output through harvest. Contrary to N, P leaching is generally low because phosphate anions are strongly sorbed onto soil particles and tend to precipitate with Ca 2+ cations. Most of the time erosion is the dominant loss process [START_REF] Kronvang | Phosphorus losses at the catchment scale within Europe: an overview[END_REF]. Therefore, in a first approximation, we considered positive P balances to indicate potential P accumulation in soils (with possible subsequent P losses through erosion), while negative P balances revealed P removal from the soil pool [START_REF] Garnier | Phosphorus budget in the water-agro-food system at nested scales in two contrasted regions of the world (ASEAN-8 and EU-27)[END_REF].

Feed trade

For the 1981-2014 period, the net import of animal feed was obtained from the complete matrix of animal feed exchanged between the 33 French agricultural regions from the analysis of the SitraM database on commodity transport of the French Ministry of the Environment, using the methodology of [START_REF] Silvestre | Évaluation de la provenance des marchandises consommées par un territoire: AmstraM, une application de webmapping basée sur les statistiques de transport et de production[END_REF]. For the 1961-1981 period, we used the data on feed import at the national scale provided by the FAO (2017). We assumed that the distribution of imported feed from abroad between the 33 French agricultural regions during this latter period followed the same pattern as in 1981, the earlier date documented in SitraM. Before 1961, we considered imported feed to be insignificant, based on the very low volume of imported feed reported by the FAO (2017) at the beginning of the 1960s.

Uncertainty

Some assumptions in the GRAFS approach, such as those ranking of priorities for allocating nutrients flows between grassland, arable land, livestock and human population, might be a source of bias in our results. It is rather difficult to quantitatively assess this kind of uncertainty, which is part of the construction of the approach itself.

By contrast, operational uncertainties in the data and parameters used can be quantitatively assessed, as described in Le [START_REF] Le Noë | How the structure of agro-food systems shapes nitrogen, phosphorus, and carbon fluxes: the generalized representation of agro-food system applied at the regional scale in France[END_REF]. We used the Monte Carlo method to generate random samples of values for each primary data and each parameter, considering their own level of uncertainty, which can differ over the time period covered by the study. The model's intermediate variables (such as vegetal or animal production in N and P) and outputs (such as N or P balances) were computed in accordance to the Monte Carlo simulation of the primary data [START_REF] Loucks | Model sensitivity and uncertainty analysis[END_REF]. We thus generated a distribution of the main variables and outputs of the model by bootstrapping the Monte Carlo simulation with replacements (1000 replicates). The uncertainty for each variable and parameter was given by the standard error of the mean of the 1000 replicates.

Results and discussion

3.1. Regional features revealed by the GRAFS approach 3.1.1. Changes in the overall metabolism of three typical regions Fig. 1 shows the temporal evolution of N flows in agro-food systems for three typical but contrasted French regions: Picardy, Brittany and Loire Amont. In 1852, all three regions were characterized by selfsufficiency for crop, grass and livestock production, which was just enough to fulfil the local human demand. The only exogenous inputs to arable land and grassland were symbiotic N fixation and atmospheric deposition, and total inputs were close to balance with N output through harvest. Consequently N balance over arable land was very low (5 ± 7, 1 ± 5 and 1 ± 3 kg N ha -1 yr -1 for Picardy, Loire Amont and Brittany, respectively), while the P balance was almost balanced in Brittany and Loire Amont but slightly negative over arable land in Picardy (-2 ± 1 kg P ha -1 yr -1 ), indicating that soil P was being mined at a time when P enrichment of soil was low, which challenged the sustainability of the agro-food system. Mining in soil fertility around the mid-19th century has also been reported in other studies [START_REF] Güldner | Nutrient recycling and soil fertility management in the Course of the industrial transition of traditional, organic agriculture: the case of Bruck Estate, (1787-1906)[END_REF].

The cases of Picardy and Loire Amont, regions that already had a significant excess of crop and livestock production with respect to their local livestock and human population requirements, would suggest that these products already had the status of a commodity. This hypothesis would be particularly relevant for Picardy, where the additional production was likely exported to the nearby Paris food market, leading to a negative P balance. Brittany showed complete self-subsistence since no products had to be imported or exported. Nevertheless, although some differences can be observed, the overall similarity between agrofood systems is striking.

Over one century later, the situation had drastically changed. The GRAFS of the three regions considered in 1970 (Fig. 1) showed contrasted production patterns, although the common features of the evolution of these agro-food systems can be found in the increased recourse to both N and P mineral fertilizers and the overall intensification of internal and external nutrient flows. This happened concomitantly with a sharp decrease in the contribution of symbiotic N fixation to overall inputs (Fig. 2). This stressed out the preeminent role that legume crops had in the previous periods, when they provided both direct fertilization to cropland and indirect fertilization through manure input by fed livestock. In Picardy, arable crop production doubled together with the stagnation of livestock density and the local human population, generating an increased crop surplus with more than 80% of the production being available for exportation. Simultaneously, N and P balance over arable land rose significantly, reaching 57 ± 8 kg N ha -1 yr -1 and 46 ± 1 kg P ha -1 yr -1 , respectively. The apparent specialization in crop production in Picardy was accompanied by a significant decrease of NUE and PUE from 85 ± 13% and 160 ± 29% in 1852 to 66 ± 4% and 27 ± 2% in 1970, respectively. In Brittany, the complementarity between livestock, arable land and grassland continued to be effective since animal excretion and N symbiotic fixation still made up more than 60 ± 3% of arable land fertilization, while livestock were mainly fed from arable land and grassland. However, imported feed was already needed to meet the requirement of increasing livestock. The agro-food system therefore turned from a complete self-sustaining regime in 1852 to a clear system of interdependence for both vegetal and animal production. The consequences of these changes in terms of environmental and agronomic performance was an increase in N and P balances over arable land, reaching 29 ± 11 kg N ha -1 yr -1 and 37 ± 3 kg P ha -1 yr -1 and the concomitant drop in NUE and PUE from 96 ± 16% and 118 ± 26% in 1852 to 81 ± 7% and 35 ± 3% in 1970, respectively. The case of Loire Amont in 1970 showed much smaller changes compared to the situation of 1852. The recycling of N within the agro-food system continued to make up most arable land and grassland fertilization together with N symbiotic fixation, while livestock production was still self-reliant. Paradoxically, this region showed relatively low environmental and agronomic performance since N and P balances over arable land reached 77 ± 10 kg N ha -1 yr -1 and 39 ± 3 kg P ha -1 yr -1 , while NUE and PUE decreased from 89 ± 15% and 118 ± 35% in 1852 to 49 ± 4% and 21 ± 2% in 1970, respectively.

Finally, the GRAFS for 2010 confirmed the trends observed in the 1970s, namely the increased specialization in crop and livestock farming for Picardy and Brittany, respectively, and the continued integrated crop and livestock farming in Loire Amont. In Picardy, grassland was less than 15 ± 0.4% of the utilized agricultural area (UAA) and N mineral fertilizer contributed 73 ± 2% to total fertilization of arable land. The case of Brittany is particularly striking in that the agrofood system was almost entirely dedicated to livestock production, with 77 ± 3% of the arable production used for livestock ingestion and more than 55 ± 3% of animal feed being imported. Moreover, although Loire Amont was still characterized by apparently integrated crop and livestock farming, the livestock production was henceforth dependent on imported feed.

Overall, the evolution of these agro-food systems can be analyzed as three aspects of the same process: the progressive expansion of a "metabolic rift" [START_REF] Foster | Marx and the Rift in the Universal Metabolism of Nature[END_REF] mostly captured, in the present study, through the rising openness of N and P cycles with increasing dependence on external inputs and a growing share of the production being exported.

Historical legacy of P

Long-term accumulation (or depletion) of P in arable land, calculated by summing up annual P balances of cropland over the whole period covered, revealed both similar and contrasted patterns in Picardy, Loire Amont and Brittany (Fig. 3). In all cases the late 19th and early 20th centuries were characterized by the continuous mining of P reserves, indicating that inputs could not compensate for output. This trend was clearly reversed after WWII when a substantial P stock had accumulated until the 1990s. Yet for the recent period, due to a large reduction in mineral fertilizers, Picardy again showed a net mining of the cumulated P balance, while it plateaued for Loire Amont. By contrast, Brittany continued to accumulate P in arable land. Again, this particularity can be explained by the huge amount of P inputs through animal excretion due to the concentration of livestock breeding in the region. For the case of Brittany, P inputs through manure originated, to a large extent, from feed import from South America [START_REF] Le Noë | Phosphorus management in cropping systems of the Paris Basin: from farm to regional scale[END_REF]. Our estimations of P balances over arable land for these three regions were in accordance with two other studies on France, which also indicated a sharp rise of P in arable land at the turn of the 1960s [START_REF] Ringeval | Contribution of anthropogenic phosphorus to agricultural soil fertility and food production[END_REF] and their relative stagnation in the last two decades [START_REF] Senthilkumar | Regional-scale phosphorus flows and budgets within France: the importance of agricultural production systems[END_REF]. Our results highlighted that, according to their specific trajectories, French regions have constituted their own P legacy, deriving from three main sources: (i) a transfer of fertility from the local permanent grassland, (ii) the importation of mineral fertilizers mainly from foreign mining resources and (iii) a transfer of fertility from arable land of feed-exporting regions. In the future, although anthropogenic P accumulated in agricultural soil should contribute to sustaining plant growth for some years [START_REF] Ringeval | Contribution of anthropogenic phosphorus to agricultural soil fertility and food production[END_REF], a possible shortage of P [START_REF] Cordell | The story of phosphorus: global food security and food for thought[END_REF] could threaten the ecological maintenance of agricultural soil. Regions that benefited from high P fertilization rates in the past will thus take advantage of their past legacy in the future, whereas regions that have historically exported nutrients could suffer from the unpaid cost of ecological soil degradation. Such historically unequal exchanges have been defined as ecological debt by several authors [START_REF] Roberts | Ecologically unequal Exchange, ecological debt, and climate justice[END_REF][START_REF] Clark | Ecological imperialism and the global metabolic rift, unequal exchange and the guano/nitrates trade[END_REF].

Typology of the different kinds of agro-food systems

The GRAFS approach could provide as many monographs as regions considered. To systemize the analysis of our results and to obtain an objective assessment of the trajectories of the 33 French regions, we chose here to aggregate these regions according to similarities in their production pattern. This typology corresponds to an algorithm that filters various results provided by the GRAFS analysis and subsequently defines each region as belonging to an agro-food system type. The choice of criteria and thresholds is necessarily somewhat arbitrary, minimized by a thorough analysis of the raw results. The analysis of the three typical trajectories of agro-food systems (Fig. 1) indicated that specialization and intensification were the two main changes captured through the GRAFS approach. Such a typology can help characterize the structure of an agro-food system based on the trajectories' degree of specialization, openness or self-reliance and inter-connections between crop, grassland and livestock breeding.

For this purpose, we defined biogeochemical criteria to check the level of interaction between arable land, livestock and grassland, based on nutrient fluxes or flux ratios. The ratio between arable crop production and livestock excretion was used as an indicator of the dominance of crop production over livestock breeding. The share of manure in arable land fertilization and the proportion of local arable production in livestock feeding were both used as indicators of the connection between crop and livestock farming. The proportion of grass in livestock feeding was taken as an indicator of the connection between grassland production and livestock production. Finally, the livestock density and the share of imported feed in livestock feeding were considered as indicative of the specialization in livestock production and the dependence of livestock production on feed supply. The typology was established based on N production and fertilization data, but the subsequent analysis can also account for P management in each of the different types of region defined. The decision tree accordingly represents the differentiation logic, criteria and thresholds used (Fig. 4).

The agro-food system types can be literally defined as follows: (i) "Arable crop" systems are characterized by the dominance of arable crop production over livestock breeding; (ii) "Intensive livestock farming" systems are characterized by high livestock density and dependence on feed import. However, the connection between arable and livestock production exists in this system through the high proportion of manure in arable land fertilization. By contrast, (iii) "Extensive integrated crop and livestock farming" systems are defined by the connection between livestock, grass and crop production through the double criteria of a large share of grass in livestock feeding and a significant contribution of manure to arable land fertilization. Systems defined as (iv) "Intensive integrated crop and livestock farming" are characterized by the connection between livestock and arable production through either the significant contribution of manure in arable land fertilization and/or the high proportion of local arable production in livestock feeding. However, the share of grass in livestock feeding is of lesser importance compared to systems defined as extensive integrated crops and livestock farming. Lastly, (v) "Intensive crops-extensive livestock farming" systems are characterized by the connection between livestock and grassland production owing to the significant proportion of grass in livestock feeding, while the link between livestock and arable land production is weak, since manure plays only a minor role in arable land fertilization and local arable land production contributes only marginally to livestock feeding. Consequently, arable land is mainly fertilized by mineral fertilizers, which justify the first term "intensive crops" for this type of system.

All criteria gathered regions with a homogeneous production pattern; however, the internal variability among regions belonging to the same type was sometimes concealed. For instance, in 1929, the average yield of arable land, a parameter that was not included in our typology, reached 50 ± 15 and 54 ± 9 kg N ha -1 yr -1 in regions of extensive and intensive integrated crops and livestock farming, respectively. In 1989, the average yield of arable land of the different regions was 130 ± 15 kg N ha -1 yr -1 for Arable crops, 97 ± 23 kg N ha -1 yr -1 , and 97 ± 21 kg N ha -1 yr -1 for Extensive and Intensive integrated crops and livestock farming, and 81 ± 38 kg N ha -1 yr -1 for Intensive crops-extensive livestock farming. The variability of individual regional values around the mean emphasized the need for a dual approach: at the regional level to describe specific trajectories and at the national level to analyze the overall evolution of production patterns toward specialization or continued integrated crops and livestock. In the next section we did not discuss the variability within each type of region but provided uncertainty values as calculated by the Monte Carlo procedure (see Section 2.3).

Trajectories of agro-food systems

In view of the above, we can now trace the evolution the agro-food system of the 33 regions in France toward specialization or continued integrated crop and livestock farming (Figs. 5a-d and Figure 6). Putting the changes captured within their political and economic context should allow us to identify the drivers of these changes together with their impact on N and P fluxes in agro-food systems. In the following, N and P fluxes are therefore analyzed under their dual, social and material, dimension.

1852-1906: the dominance of integrated crop-livestock farming

Integrated crop and livestock farming was the rule everywhere during the late 19th century (Fig. 6), because fertilization mainly relied on manure recycling and symbiotic N fixation. Therefore, the progressive intensification of production with increasing yields occurring during this period (Fig. 5b) was only driven by an increase of livestock density with the increase in forage crops and grassland. The agricultural system in this period therefore fully obeyed the well-established paradigm that crop production can only be improved by increasing manure resources [START_REF] Krausmann | Milk, manure and muscle power. Livestock and the transformation of preindustrial agriculture in Central Europe[END_REF]. At the farm scale, diversification of production was also the best suited way to cope with pests, disease and weather and ensure the subsistence of the farm while multiplying possible outlets. As long as technical possibilities remained limited, integrating crop and livestock was inherent in farming systems [START_REF] Antoine | Specialisation in rural history: towards a definition[END_REF]. The visible shift from intensive integrated crop and livestock farming to extensive integrated crops and livestock farming systems between 1852 and 1906 (Fig. 6) also reflects the increase in grassland area as a corollary of the growing importance of livestock breeding activities. The integrated crop and livestock farming model was also well adapted to respond to a growing demand for animal protein whose distribution became physically possible with the development and extension of the railway network (Freycinet plan in 1878). Consequently, animal production, which had long been a "necessary evil" (cf. Lavoisier 1791), started to become a marketable product. The expansion of the railway in the late 19th century also engendered the emergence of a national market for food products by opening up isolated rural regions. As a consequence, price differentials between regions lessened: for instance, the maximum difference among "départements" in the price of wheat shifted from 70% in the mid-19th century to less than 10% in 1913 [START_REF] Duby | Histoire de la France rurale, tome III de 1789 à 1914[END_REF].

The slow increase in productivity of French agriculture, essentially driven by an increase in manure production rather than by the recourse to industrial fertilizers, contrasted with the development of agriculture in England and Germany during this period [START_REF] Duby | Histoire de la France rurale, tome III de 1789 à 1914[END_REF][START_REF] Muller | Le technocrate et le paysan: Les lois d'orientation agricole de 1960-1962 et la modernisation de l'agriculture française[END_REF]. [START_REF] Duby | Histoire de la France rurale, tome IV depuis[END_REF] interpreted this delay in French agriculture to result from the structure of agriculture in France at these times that was well adapted to the needs of a national economy that matched the place France held in the world economy. Until the end of WWII the economic power of France in global capitalism arose mostly from its financial role as an international banking power. According to Fig. 4. Decision tree representing the elaboration of a typology of agricultural regions in France. [START_REF] Duby | Histoire de la France rurale, tome III de 1789 à 1914[END_REF], with their savings, peasants contributed almost one-third of the surplus money that could be appropriated through the banking channel and invested in the industrial sector and, above all, invested abroad as loans. For this reason, there was no political will in France to enhance labor productivity by mechanization or other forms of modernization, since this would have resulted in an increased rural exodus and a shift of peasant savings to investments. The protectionist measures implemented by the French Minister of Agriculture Jules Méline between 1884 and 1892 and until the beginning of WWI offered a sort of artificial prosperity to farmers, who were ensured outlets for their production without improving labor productivity through mechanical and chemical modernization; instead, famers could fulfil their dream of purchasing land [START_REF] Duby | Histoire de la France rurale, tome III de 1789 à 1914[END_REF]. The limited rate of fertilization induced by this slow modernization resulted in very high NUE and PUE, a low N balance and a slightly negative P balance (Fig. 5c andd), indicating that the intensification of agricultural production led to loss of soil fertility, with only quite limited inputs of exogenous fertilizers.

The results could provide the impression of uniformity in the agricultural production pattern in the 1852-1906 period. However, some areas within a region, such as the Rennes Basin in Brittany, were already in a process of specialization in the sense that their local production was already dedicated to exportation [START_REF] Cocaud | A early form of specialized agriculture in Western France[END_REF], while others remained behind this movement. In total, the perspective adopted in this study revealed that, despite a possible patchwork of farming, the overall regional structure of agro-food systems led to similar biogeochemical patterns.

1906-1946: timid beginnings of crop specialization

For the same reasons as those explained in section 3.3.1, and in spite of the major crises of WWI and 1929, the inter-war period continued to be characterized by the near homogeneity of integrated crop-livestock farming. Self-subsistence was still perceived as the best protection against poverty and integrated crops and livestock farming thus remained the best-suited system. This assumption can be confirmed by the figures of on-farm consumption in 1938: 30% of the pork meat, 30% of the dairy products, 40% of the eggs, 20% of the wine and 10% of the wheat harvest were consumed on the farm [START_REF] Duby | Histoire de la France rurale, tome IV depuis[END_REF]. Nevertheless, the very beginning of regional specialization in crop production around the Ile-de-France region was already visible (Fig. 6). Following Von Thünen's theory, the specialization in cash crop production in this area should be attributed to the closeness of Paris; however, other factors such as proximity to the Seine River or the establishment of a complex commercial network also explain the geography of specialization [START_REF] Antoine | Specialisation in rural history: towards a definition[END_REF].

During this period, N mineral fertilization clearly rose in regions specialized in arable crops, shifting from almost zero at the end of WWI to 9.9 ± 0.9 kg N ha -1 yr -1 in 1929 and then 14 ± 1.2 kg N ha -1 yr -1 in 1946. By contrast, in regions of integrated crops and livestock farming, N mineral fertilization rose more slowly. Between 1929 and 1946, the rates of N mineral fertilizer over arable land shifted from 4 ± 0.4 kg N ha -1 yr -1 and 8.5 ± 0.8 kg N ha -1 yr -1 to 5.5 ± 0.6 kg N ha -1 yr -1 and 6.7 ± 0.7 kg N ha -1 yr -1 in regions of extensive and intensive integrated crops and livestock farming, respectively. Regarding P, rates of mineral fertilization increased considerably between 1906 and 1929 but then slightly decreased between 1929 and 1946, probably due to the economic difficulties arising from the economic crisis and WWII (8.7 ± 0.7, 8.5 ± 0.7 and 9.2 ± 0.8 kg P ha -1 yr -1 in 1929 and 7.5 ± 0.6, 7.1 ± 0.6 and 6.3 ± 0.5 kg P ha -1 yr -1 in 1946 for arable crops, extensive and intensive integrated crops and livestock farming systems, respectively). Although it was limited, the progress in the use of mineral fertilizers during the inter-war periods has been mainly attributed to the popularization of new technical possibilities provided by industry and national syndicates for mineral fertilizers, such as the propaganda created in 1920 [START_REF] Duby | Histoire de la France rurale, tome IV depuis[END_REF]. Furthermore, modernization was triggered after WWI resulting from the losses of millions of peasants killed in combat in WWI; increasing the productivity of agricultural labor was therefore a necessity. However, the role of the state remained limited to the creation of the national Grain Board in 1936 by the Front Populaire, allowing farmers to be involved in the fixation of wheat prices. In the absence of national policy, the investment in new technical equipment remained limited and more than two-thirds of peasant debts involved land acquisition.

In spite of the development of mineral fertilizer, arable crop yields stagnated, although disparities between the different types of agro-food systems showed better performance in regions of arable crop with average yields over arable land of 67 ± 4, 47 ± 3 and 51 ± 3 kg N Fig. 5. Evolution in the five different types of regions considered for France over the 1852-2014 period. a. Livestock density (LU haUAA -1 ); b. yield of arable land (kgN ha -1 yr -1 ); c. rate of N synthetic fertilizer application over arable cropland (kgN ha -1 yr -1 ); d. N balance of arable land (kgN ha -1 yr -1 ); e. P balance of arable land (kgP ha -1 yr -1 ). ha -1 yr -1 for arable crops, extensive and intensive integrated crops and livestock farming systems, respectively (Fig. 5a). The combination of stagnant yield and little progress in terms of N fertilization resulted in a progressive increase in N balance over arable land, but this remained quite low (Fig. 5c). Similarly, the slight decline in P mineral fertilization between 1929 and 1946 led to reduced, but still positive, P balances for cropland in all types of regions.

Interestingly, regions that specialized were also among those identified by [START_REF] Bonnin | Explaining the decrease in the genetic diversity of wheat in France over the 20th century[END_REF] as presenting the greatest loss of wheat genetic diversity, promoted by intensification and integration of crop production to market. However, their study showed that other regions had already been concerned by losses in wheat genetic diversity since 1912, mainly the Paris basin and the northwest quadrant. It is therefore possible that regions such as Picardie, Eure and Champagne-Ardennes-Yonne were already on the path toward arable crop intensification, as will be confirmed in the next section. .3.3. 1946-1978: the expansion of crop specialization and the great acceleration

3

The three decades following WWII were marked by the expansion of arable crop system around the Paris Basin and the development of a new type of agro-food system defined in our typology as intensive crops-extensive livestock farming. The use of synthetic fertilizer started to increase from the end of WWII and exploded at the beginning of the 1960s, generating high N and P balances over arable land (Fig. 5c andd) and grassland. This trend was not specific to France: similar patterns also occurred in other European countries [START_REF] Bouwman | Lessons from temporal and spatial patterns in global use of N and P fertilizer on cropland[END_REF]. The degree of openness of N and P cycles strongly depended on the type of agro-food system. Regions of arable crops exported most of their vegetal production and relied almost completely on N and P mineral fertilizers to compensate for export through harvest. Regions of intensive crops-extensive livestock farming relied mainly on N and P mineral fertilizer for arable land production but retained significant livestock farming where animals were mainly fed on permanent grassland. In this type of region, the complementarity between arable land, grassland and livestock production was giving way to a disconnection of animal and crop production. Along with the expansion of agricultural specialization, regions defined as extensive and intensive integrated crop and livestock farming still existed, with strongly interlinked N and P flows through arable land, grassland and livestock production, but were characterized by an intensification of both arable land and livestock production (Fig. 5a,b) and an increased use of synthetic fertilizer, particularly P. Therefore, although specialization only concerned crop production, intensification of arable production was occurring everywhere with increased yield. Densification of livestock production was also characteristic of this period, except for regions specialized in crop production (Fig. 5b). As a consequence, N and P balances rose sharply from the beginning of the 1960s in all types of region, resulting in a rapid decrease in NUE and PUE.

These far-reaching changes in the intensity and nature of N and P fluxes in the different types of agricultural systems in French regions have to be linked to their historical background. In the post-WWII context, France was completely devastated and almost everything had to be rebuilt. Consequently, France had to live on credit and its commercial balance was strongly budget-deficit. By comparison with previous periods, the economic situation of France in the world economy had completely changed [START_REF] Duby | Histoire de la France rurale, tome IV depuis[END_REF]. A voluntarist policy was thus implemented to find a new acceptable place for the French economy within Europe, implying an enormous increase in agricultural production, in order not only to meet domestic demand, but also to become a net exporter on the international agricultural market [START_REF] Jollivet | La grande transformation de l'agriculture française sous l'oeil du sociologue[END_REF]. The Monnet Plan (1945) followed by the Marshall Plan (1947) thus explicitly aimed at improving labor productivity in agriculture in order to export food products, accelerate the rural exodus and free labor for employment in industry, as well as making agriculture an important outlet for the mineral and machine industry [START_REF] Duby | Histoire de la France rurale, tome IV depuis[END_REF]. To reach that goal, the French government implemented a strong policy of popularization and education in the countryside and developed new land ownership legislation that favored the development of the medium-sized farm, eliminating the smallest and least competitive landowners while avoiding the concentration of land in the hands of non-farmers, which would have led to the development of wage-earning in the agricultural sector [START_REF] Duby | Histoire de la France rurale, tome IV depuis[END_REF]. The implementation of the European common market in 1957 fostered the modernization of agriculture by protecting internal European markets with custom barriers. Later on, the implementation of the Common Agricultural Policy beginning in 1962 ensured that farms adopted modernization to remain viable by providing them outlets for food products [START_REF] Bureau | La politique agricole commune[END_REF].

Therefore, modernization of agriculture in France was stimulated through propaganda and economic incentives but was constrained by laws restricting and regulating access to land, reinforcing the competition between farmers who had to modernize to survive. This fierce competition combined with modernization is probably the main factor explaining the expansion of crop specialization during the 1946-1981 period [START_REF] Jollivet | La grande transformation de l'agriculture française sous l'oeil du sociologue[END_REF]. Machines, fertilization and herbicides were first designed for arable land to facilitate crop specialization. Furthermore, cereals producers were the main beneficiaries of the French government and European subsidies through price setting of wheat and export subsidies [START_REF] Bureau | La politique agricole commune[END_REF]. Therefore, the great acceleration in crop specialization, the increasing openness of N and P fluxes in agrofood systems and the dependency on external inputs were driven by economic interests and by the political commitment on the part of the French government and the Common Agriculture Policy.

1978-2014: livestock specialization and the rational use of fertilizers

The most recent period from 1978 until the present was characterized by the continuous development of specialized arable crop systems together with the emergence of a new type of agro-food system, i.e., "intensive livestock farming" (see Fig. 6). At the same time, regions defined as intensive crops-extensive livestock farming declined, either as a result of a lower rate of mineral fertilizer, which gave greater weight to manure recycling on arable land and grassland and therefore led to the conversion of this type of region into an integrated crop and livestock farming system, or because they turned into specialized arable crop system. The 1980s marked the beginning of intensive livestock farming in the west of France. Poultry and pig breeding were the most emblematic of this new form of industrial breeding, which were no more than factories converting vegetal proteins into animal proteins [START_REF] Duby | Histoire de la France rurale, tome IV depuis[END_REF]. The consequences in terms of N and P fluxes were an increased dependence upon feed import and a structural excess of N and P inputs through manure to arable land and grassland, generating high N and P balances, although moderate mineral fertilization has reduced these balances over the two last decades (Fig. 5d).

Indeed, this period also showed a deep inversion in the trends of mineral fertilization. At the same time, arable yields kept rising, although at a slower rate than in the previous period. As a consequence, the N and P balances on arable land steadily decreased. In regions of arable crops, P balances have even become increasingly negative over the two last decades. As pointed out in a previous study [START_REF] Le Noë | Phosphorus management in cropping systems of the Paris Basin: from farm to regional scale[END_REF], this could probably be achieved without loss in crop yield due to the huge soil P legacy built up between 1960 and 1990. This decreasing trend is taking place in all types of regions and started by the end of the 1970s. It coincided with the second oil crisis, which generated a peak in energy prices and therefore in the price of N and P fertilizers [START_REF] Mew | Phosphate rock costs, prices and resources interaction[END_REF]. With the 2007-2008 food crisis, phosphate rock and fertilizer prices increased by 700% in 14 months [START_REF] Cordell | The story of phosphorus: global food security and food for thought[END_REF], probably contributing to reinforcing the decline in P mineral fertilizer use. After the 2000 s the decline in N and P mineral fertilizer use might also be attributed to the implementation of agro-environmental measures introduced at the European level through a series of successive European directives gathered within the Water Framework Directive in 2000 [START_REF] Bureau | La politique agricole commune[END_REF]. The consequences of these changes were the increase of NUE and PUE in every type of region except intensive livestock farming regions.

Summarizing the changes during this period, regional specialization strengthened while N and P inputs through mineral fertilizers decreased but the ever-growing dependence for both inputs and outlets, increased the openness of N and P cycles. On the economic side, policies progressively shifted from interventionism and support to production to give way to greater liberalism by lowering and sometimes eliminating customs barriers. The Common Agricultural Policy separated subsidies from the volume of production, which instead became indexed on the surface area farmed and herd size. The aim was to incite farmers to adapt to international competition [START_REF] Bureau | La politique agricole commune[END_REF] which subsequently reinforced these specialized production patterns and fully integrated agriculture into the market economy.

Conclusion

The GRAFS approach was implemented herein to study the longterm evolution of agricultural production patterns in the regions of France for the first time. The associated changes in N and P flows and balances over arable land and grassland were analyzed. In the mid-19 th century, the production patterns of regional agricultural systems were quite homogeneous. Integrated crop and livestock farming systems were the rule everywhere and manure recycling was the main source of agricultural land fertilization. However, at the beginning of the 20th century, the sustainability of this farming system began to be jeopardized by the mining of soil nutrient stocks, especially P. Over the course of the 20th century, this situation shifted toward more contrasted production patterns. This became particularly true after the Second World War: modernization of agriculture contributed to the emergence of specialized cereal cropping systems in the most fertile plains of the North of France, exporting a large fraction of their cereal production. This trend was characterized by a decreased connection to livestock. The significant rupture after 1946, which accentuated the openness of regional agro-food system, was promoted by the increased recourse to mineral fertilizers and the subsequent separation of crop and animal production in regions on a path to specialization. The consequences for N and P cycles varied, depending on the specific trajectory of each region. Overall, regions of intensive cropping revealed the highest degree of openness through crop exportation, while the region of intensive livestock farming was characterized by a growing reliance on feed importation and over-fertilization of arable land through manure inputs. However, all regions intensified their production during the second half of the 20th century by increasing rates of mineral fertilizer inputs. As a result, arable yield rose, as did the N and P balances. The rise of fertilizer prices together with the implementation of agro-environmental measures over the last two decades resulted in the lowering of N and P balances, the latter being even negative in regions specialized in crop production. However, as long as the agro-food system remains specialized, possible changes through improved fertilization will be limited by the inefficiency of nutrient recycling at the regional level.

This study demonstrates the value of adopting a long-term perspective to articulate a vision of how production pattern changes and environmental and agronomic performances are related. The analysis of these changes in light of their political and economic contexts, based on the existing literature, showed that changes in production patterns as well as their consequences on N and P flows and agro-environmental performances should be mostly attributed to external factors related to political choices and modes of insertion within the market economy, rather than to mechanisms endogenous to agricultural production itself. Material flow analysis was shown to be a way to capture both the biophysical processes governing agricultural production and its impact on natural resources and the environment. At the same time, analyzing social, economic and political processes, based on the existing literature, allowed determining the controlling factor of how these processes evolve. A holistic approach linking the materiality of agricultural production to its political and economic logic was therefore indispensable to understand past changes for a vision of possible transformations of agro-food systems in the future. More generally, the present study stressed out the artificiality of the distinction between "natural" and "anthropic" fluxes and the need for coupling quantitative and qualitative approaches. This, in turn, implies to reconsider the duality between nature and culture around which the human and social sciences on the one hand and the natural sciences on the other hand, are divided. Hence, this study should also be an incentive for further interdisciplinary collaboration at least in the fields of ecology, agronomy and environmental sustainability.

Fig. 1 .

 1 Fig. 1. GRAFS-based N flows for Picardy, Loire-Amont and Brittany in 1852, 1970 and 2010. Fluxes of animal and vegetal import/export relate to trade fluxes of agricultural production with other French regions or foreign countries. Fluxes of Symbiotic N fixation and atmospheric deposition derive from the atmosphere which can be considered as the "surrounding environment". Fluxes of synthetic fertilizer mostly originate from industrial sector, mostly outside of the region and can be seen as external fluxes. N balance represents a potential loss to the hydrospheric or atmospheric surrounding environment through lixiviation and gaseous emission, although part of the N balance remains in the soil of the region.

Fig. 2 .

 2 Fig. 2. Features of the agricultural systems of Picardy, Loire Amont and Brittany over time. a. Agricultural production; b. type of N fertilization; c. origin of livestock feed.

Fig. 3 .

 3 Fig. 3. Cumulated P balance over arable land in the course of the 1852-2014 period in Brittany, Loire Amont and Picardy. Error bars provide uncertainties as calculated by the Monte Carlo analysis.

Fig. 6 .

 6 Fig. 6. Chronology of the different types of agricultural regions in France over the 1852-2014 period. A: Alpes; Al: Alsace; AL: Aveyron-Lozère; AR: Ain-Rhône; B: Bourgogne; Br: Bretagne; C-A-Y: Champagne-Ardennes-Yonne; CC: Cantal-Corrèze; CdA: Côte d'Azur; CO: Calvados-Orne; DL: Dordogne-Lot; E: Eure; E&L: Eure-et-Loire; Gar: Garonne; Gd J: Grand Jura; Gd M: Grand Marseille; Gde L: Grande Lorraine; G-H: Gard-Hérault; Gir: Gironde; I-D-A: Isère-Drôme-Ardèche; IdF: Ile de France; L Am: Loire Amont; L Av: Loire Aval; Lan: Landes; LC: Loire Centrale; M: Manche; N-PdC: Nord Pas-de-Calais; Pic: Picardie; Pocc: Pyrénées Occidentales; POr: Pyrénées Orientales; S: Savoie; VC: Vendée-Charentes.

Acknowledgements

We greatly acknowledge the PIREN-Seine (CNRS) and RESET projects for their financial support. Thanks are also due to the Fédération Ile-de-France de Recherche pour l'Environnement (FIRE) for providing an interdisciplinary framework that was beneficial for this work and Marie Silvestre for analyzing the SITRAM database. We are grateful to Dr. Laurent Herment (EHESS) for helpful bibliographic indications regarding fertilization in the 19 th century. Julia Le Noë's PhD is granted by the Ecole Doctorale Géosciences, Ressources Naturelles et Environnement (GRNE, ED 398).

Appendix A. Supplementary data

Supplementary material related to this article can be found, in the online version, at doi:https://doi.org/10.1016/j.agee.2018.06.006.


Xi Wang

Marc Christie

Eric Marchand

MULTIPLE LAYERS OF CONTRASTED IMAGES FOR ROBUST FEATURE-BASED VISUAL TRACKING

Keywords: keypoint detection, contrast enhancement, SLAM

Feature-based SLAM (Simultaneous Localization and Mapping) techniques rely on low-level contrast information extracted from images to detect and track keypoints. This process is known to be sensitive to changes in illumination of the environment that can lead to tracking failures. This paper proposes a multi-layered image representation (MLI) that computes and stores different contrast-enhanced versions of an original image. Keypoint detection is performed on each layer, yielding better robustness to light changes. An optimization technique is also proposed to compute the best contrast enhancements to apply in each layer. Results demonstrate the benefits of MLI when using the main keypoint detectors from ORB, SIFT or SURF, and shows significant improvement in SLAM robustness.

INTRODUCTION

Research in visual tracking systems such as SLAM and SfM (Structure from Motion) has led to mature technologies exploited in industrial-level systems. Except for direct methods working on the analysis of changes in pixel gradients, the majority of visual SLAMs rely on corner detection with extractors that extract keypoints (KP) and descriptors that identify and match the extracted KPs over different frames.

Unfortunately, the corner detection process and consequently the matching problem are strongly dependent on the illumination condition at the moment of capturing images and generally make a brightness constancy assumption. Although the matching process usually relies on gradient information that is more or less independent from intensity, SLAM and SfM methods still suffer from illumination changes at different degrees (see Fig. 1) and may yield inaccurate maps and even tracking failures during the tracking process [START_REF] Pascoe | Nid-slam: Robust monocular slam using normalised information distance[END_REF][START_REF] Seonwook | Illumination change robustness in direct visual slam[END_REF].

Robustness to light changing conditions is therefore a central issue that has received increased attention. The issue has often been tackled at the extractor level by searching an optimal contrast threshold in the KP extractor with respect to the current lighting condition. For example, in SuperFast [START_REF] Florentz | Superfast: Model-based adaptive corner detection for scalable robotic vision[END_REF] the FAST contrast threshold -a threshold value that triggers a brighter, darker or similar decision on per-pixel comparisonis dynamically computed using a feedback-like optimization method that yields a new threshold value per region in the image. Lowering the threshold however tends to generate a large number of KPs that influence the computational capacity of other processes, and the proposed technique requires specific adaptations to be applied to other KP detectors. Another possibility is to apply image transformations (eg. contrast enhancers) on captured images before applying KP detectors. Interestingly, it has been demonstrated that KP extractors gain significant performance by using HDR (High Dynamic Range) images as input, converted to SDR (Standard Dynamic Range) images through tone-mapping operators [START_REF] Rana | Evaluation of feature detection in hdr based imaging under changes in illumination conditions[END_REF][START_REF] Přibyl | Feature point detection under extreme lighting conditions[END_REF]. Among these techniques, a learning-based optimal tone-mapping operator has been proposed for SIFTlike detectors [START_REF] Rana | Learning-Based Tone Mapping Operator for Image Matching[END_REF]. But the high computational cost and specific HDR devices are required, as well as HDR-customized extractors hamper the wider applicability of such approaches. In comparison, for SDR images, research has mainly focused on contrast enhancement operators for aesthetic and perceptional goals through changes in the exposure times [START_REF] Yuan | Automatic exposure correction of consumer photographs[END_REF] which remain limited in addressing robustness of KP tracking.

For direct and semi-direct SLAM methods, i.e. methods that rely on analysis of pixel intensities rather than extracting intermediate features, robustness to illumination changes has been addressed by optimizing an affine brightness transfer transformation between consecutive frames [START_REF] Engel | Direct sparse odometry[END_REF][START_REF] Engel | LSD-SLAM: Large-scale direct monocular SLAM[END_REF]. Using mutual information instead of photometric error as the metric during the optimization process of pose estimation has also demonstrated its benefits [START_REF] Caron | Direct model based visual tracking and pose estimation using mutual information[END_REF][START_REF] Pascoe | Nid-slam: Robust monocular slam using normalised information distance[END_REF]. While exhibiting a good robustness to illumination changes, these methods remain computationally expensive.

In this paper, a new representation -multi-layered image (MLI) -is proposed to improve the robustness of visual tracking systems like SLAM. We first analyze the reasons for which KP extraction fails. We then present our MLI representation that relies on different contrast-enhanced versions of the same image. We design an optimization technique to compute the best contrast enhancements to perform and we demonstrate how MLI boosts performance of traditional KPs extractors/descriptors, and lead to significant improvements on the robustness of a state-of-the-art visual SLAM system.

ISSUES WITH CONTRAST ENHANCERS

Except for HDR images, the majority of contrast enhancement techniques can be defined as continuous monotone surjective mappings from domain interval [0, 1] to codomain interval [0, 1] that transform a given image to a (more) contrasted version. Typically, the classical S-Curve Tone Mapping method [START_REF] Yuan | Automatic exposure correction of consumer photographs[END_REF] is used to correct underexposure and overexposure regions in images, by applying a per-pixel function.

However, by using such transformations the improvement of the contrast in one region must necessarily be paid for by a reduction of the contrast in another region (see examples of S-Curves in Fig. 2). Given that most keypoint detection techniques are based on analysis of finite local differences in contrasts, contrast enhancement tends to increase the detection of keypoints by passing some internal thresholds, while contrast compression leads to the opposite. We illustrate this through the example of a synthetic scene shot in different lighting conditions [START_REF] Peris | Towards a simulation driven stereo vision system[END_REF]. The ORB detector [START_REF] Rublee | Orb: An efficient alternative to sift or surf[END_REF] is used to extract and match keypoints between a well-lit given reference image (see Fig. 1 a) and an image from the same viewpoint with only a flashlight illuminating the scene. The ORB detector with default parameters only finds a few matched keypoints between the two images (i.e. keypoints extracted and described as being the same at the same image locations). Interestingly by applying different S-Curve transformations (see Fig. 2), the total number of keypoint matches increases while ORB detector loses already matched keypoints from previous transformations. This empirically shows (i) that a single contrast enhancer only represents a partial solution to keypoint robustness, and that (ii) improving extraction by contrast-enhancement also improves matching.

MULTI-LAYERED IMAGE

The idea of Multi-Layered Image (MLI) is to generate k contrast enhancements of a given image into k image layers on which keypoint detection will be performed. The contrast enhancement technique relies on a saturated affine brightness transfer per-pixel function (SAT). We use a SAT form that defines a contrast band u = (a, b) which conveniently models the lower cut point (a) and higher cut point (b) of the saturation, with a linear interpolation between a and b on pixel intensity i (see Fig. 3). A given contrast u = (a, b) is defined in a contrast space Γ ⊆ R 2 , where Γ is the space of all contrast bands where b > a.

f SAT (i, (a, b) ) = min(max(0, i/(b -a)), 1) (1)
Parameters a and b naturally represent the band region where the contrast is enhanced, which motivated the choice of this operator compared to S-Curve. To ensure enhancement or compression of contrasts, we define the range of values for

u = (a, b) as a ∈ [-∞, 1] and b ∈ [0, ∞].
The computation of a layer k in our MLI representation is performed by applying the following operator M LI k on all pixel intensities of the image using a contrast band u k . A MLI is therefore represented as a set of k image layers where M LI k (I) = f SAT (I, u k ) for an image I, where f SAT (I, u k ) is the application of f SAT on all pixels of I.

LOW-CORRELATED CONTRAST SPACE

To address the issue of robustness, the key challenge is therefore to generate different layers such that each layer has the lowest correlation with the others in terms of detected keypoints (i.e. aiming at providing new keypoints in each layer).

In other terms, we are looking at computing a set of contrast band parameters such that each contrast band yields an image containing newly matched keypoints with the reference image (the initial lighting condition).

This paper proposes a technique to compute the optimal contrast bands together with a stopping criterion on the number of layers required, given a reference image I * representing a given lighting condition and a camera image I in another lighting condition. The first layer is computed by selecting a contrast band u i that maximizes the correspondence of keypoints between the reference image I * and the contrastenhanced image f SAT (I, u i ). The other layers are computed by selecting contrast bands that provide the lowest correlation (in terms of correspondence between keypoints) with the current contrast band. More formally we start by defining the KP-correspondence set between two images. Given S * the set of KPs extracted from a reference image I * (and respectively S from I), the KP-correspondence S Cor is the set of KPs in S * for which there is a correspondence in S, i.e. for which there is a keypoint at a similar location in image I:

S Cor = {x * | x * ∈ S * , x ∈ S, x * -x < } (2)
This definition expresses the repeatability ratio [START_REF] Schmid | Evaluation of interest point detectors[END_REF] between two sets of keypoints from two different images, a wellknown metric in visual tracking [START_REF] Gauglitz | Evaluation of interest point detectors and feature descriptors for visual tracking[END_REF], that measures the ratio of KPs appearing at similar positions on both images, over the number of keypoints in the first image:

Card({x * ∈ S * , x ∈ S, s.t. x * -x < }) Card(S * ) (3)
Given a KP extractor e, we define a band-correspondence set S u Cor as the KP-correspondence set between a SAT contrastenhanced version of I and a reference image I * given u:

S u Cor = {x * | x * ∈ e(I * ), x ∈ e(f SAT (I, u)), x * -x < } (4)
Intuitively, this means the more keypoints there are in this band correspondence set, the better is the contrast band u in yielding an image containing corresponding keypoints with a reference image. We therefore express the cardinality of this set

M Cor : Γ ⊆ R 2 → R as M Cor (u) = Card(S u
Cor ). The global maximum of this function represents the optimal contrast band u in terms of KP-correspondence and is used to compute the first layer of our MLI.

We then need a way to compute new contrast bands with low-correlation in the contrast space u ∈ Γ. We define a covariance-like method on S u

Cor that provides a co-Correspondence set S u1,u2

coCor . This co-Correspondence computes the corresponding keypoints between two contrast bands u 1 and u 2 and a reference image I * . We similarly define its cardinality

M coCor : Γ × Γ ⊆ R 2 × R 2 → R. S u1,u2 coCor = {x 1 ∈ S u1 Cor |x 2 ∈ S u2 Cor , x 1 -x 2 < } (5) Algorithm 1 Optimal MLI 1: i ← 0; C 0 (u) ← M Cor (u); 2: while i = 0 or C i (u i ) > k * C i-1 (u i-1 ) do 3: u i ← argmax u (C i (u)) 4: C i+1 (u) ← C i (u) -M ui sim (u)
5:

i ← i + 1 6: end while

Using this co-correspondence definition we can compute how much a given contrast-band u r yields information similar to all the other contrast bands, i.e. the number of KPs generated by this contrast-band also found in others. This similarity measure M ur sim : Γ ⊆ R 2 → R is expressed as:

M ur sim (u) = Card(S ur,u coCor ) (7)
A low similarity represents a low correlation between the contrast bands. Using these definitions, the computation of the different contrast bands consists in applying a sequence of two stage operations (see Alg. 1). The first stage selects an optimal contrast band u that maximizes a cost function C(u), i.e. maximizes the correspondences between reference image I * and f SAT (I, u). The second stage then updates the cost function by subtracting the similarity M ui sim between the current contrast band u i and all others (ensuring a low correlation). The algorithm terminates when the new iteration yields information proportionally lower than the previous one using a factor k. The algorithm is illustrated in Fig. 4 using the FAST extractor [START_REF] Rosten | Machine learning for high-speed corner detection[END_REF], and the ground truth is ensured by calculating BRIEF descriptor [START_REF] Calonder | Brief: Binary robust independent elementary features[END_REF]. Again we reuse the data set of New Tsukuba [START_REF] Peris | Towards a simulation driven stereo vision system[END_REF]. For the purpose of illustration, Γ is defined as a discrete sampling space between [-0.5, 1.5] × [-0.5, 1.5]. Images (a) and (c) represent the landscape of the cost functions C i (u) and similarities M ui sim (u) of the previous optimal contrast band in each iteration. We observe that the maximums of C i (u) change every iteration after updating by a subtraction with M sim . As one can see in the third iteration (Fig. 4.b), extract more KPs with low-correlation between the layers. This empirically shows that instead of intuitively or programmatically decreasing the thresholds parameters of detectors, an optimization scheme to compute the optimal contrast bands in each layer improves the correspondence of keypoints with a reference image.

EVALUATIONS AND EXPERIMENTS

We compare the use of MLI with classical detectors/descriptors: ORB [START_REF] Rublee | Orb: An efficient alternative to sift or surf[END_REF], SIFT [START_REF] Lowe | Distinctive image features from scaleinvariant keypoints[END_REF] and SURF [START_REF] Bay | Surf: Speeded up robust features[END_REF] on the NewTsukuba Data set [START_REF] Peris | Towards a simulation driven stereo vision system[END_REF]. We measure the repeatability (cf. eq. 3) and the matching ratio by matching descriptors on feature points between a reference image I * and new images I from the same viewpoint and different lighting conditions. For each condition, the optimal values of the contrast bands are computed by using the algorithm defined in Alg 1. The measures reported in Table 1 show that MLI improves repeatability and matching ratio across all detectors, despite different detection methods and default threshold parameters. This demonstrates the wide applicability of our approach.

We then compare the use of MLI on visual SLAM tasks in different lighting conditions. We choose ORB-SLAM [START_REF] Mur-Artal | Orbslam: A versatile and accurate monocular slam system[END_REF] to implement our MLI representation. We tested two sequential videos from a combination of four different lighting conditions. The experiment consisted in localizing and tracking the camera from the second video sequence against the keyframes generated from the first video sequence (in a way similar to NID-SLAM [START_REF] Pascoe | Nid-slam: Robust monocular slam using normalised information distance[END_REF]). The measured value is the success rate, i.e. the percentage of the frames from second video successfully tracked against keyframes created from the first video.

The optimal contrast bands of the MLIs of each illumination condition (first video to second video) are computed by Algo. 1 over 5 sample images in the test set. Comparison is performed between standard ORB-SLAM [START_REF] Mur-Artal | Orbslam: A versatile and accurate monocular slam system[END_REF], our MLI implemented ORB-SLAM and reported results of monocular visual SLAM NID-SLAM [START_REF] Pascoe | Nid-slam: Robust monocular slam using normalised information distance[END_REF] which demonstrated a good performance against illumination changing environments. Two to three layers are used in the experiments. The MLI approach is significantly more robust than the default ORB implementation (see Table 2), especially in difficult situations (Lamps to Flashlights, Daylight to Flashlight). Our approach also compares very favourably with NID-SLAM, displaying similar or better performances for a lower computational cost (keypoint extraction only represents 3 to 5% of computation time in ORB [START_REF] Mur-Artal | Orbslam: A versatile and accurate monocular slam system[END_REF], limiting the impact of MLI cost). Typically the Lamps to Flashlight failed to track all keyframes with both ORB and NID (0%) and successfully tracked 94.2% of the keyframes with our MLI approach. Table 2. SLAM keyframe retrieval success rate between our MLI implementation, default ORB SLAM and NID SLAM.

V 2 V

CONCLUSION

We have introduced a novel multi-layered image representation to address robustness of keypoint tracking in light changing conditions. Each layer is a contrast-enhanced version of an original image, computed in a way to improve the detection and matching of keypoints. We proposed a method to compute optimal parameters for each layer and demonstrated the benefits of our approach on keypoint detection tasks and SLAM applications. While the proposed solution pre-computes the optimal contrast bands to apply, we are currently exploring an adaptive computation of such transforms.

Fig. 1 .

 1 Fig. 1. ORB keypoint extractor and descriptor on different lighting conditions (images a and b). Only a few keypoints are matched between (a) and (b) using ORB (i.e. same position, same descriptor), compared to our MLI method (image d).

Fig. 2 .

 2 Fig. 2. Matching KPs with ORB detector between a reference image (see Fig. 1 a) and different S-Curve tone mapped versions of an image in a different lighting condition. Each tone-mapping provides newly matched KPs (blue) while losing others (orange).

Fig. 3 .

 3 Fig. 3. Using SAT function with different contrast bands to generate a multi-layered image representation (MLI).

7 :Fig. 4 .

 74 Fig. 4. Evolution of MLI layers: (a)(c) represent heatmaps of cost function C i (u) and similarity M ui sim (u) in each iteration. (b) demonstrates accumulated matched ORB KPs against reference image from every iteration represented with different colors. In each heatmap, vertical and horizontal axis represents u = (a, b) respectively with a < b.

Table 1 .

 1 /100 100/100 100/100 63.6/21.2 36.2/21.5 50.1/20.0 21.1/0.8 22.2/0.5 28.6/1.1 52.3/5.8 43.0/11.3 48.6/5.9 M 100/100 100/100 100/100 85.3/38.7 64.1/37.3 75.4/34.4 35.7/1.6 39.8/1.1 49.8/2.2 67.6/8.4 50.9/13.8 56.7/8.4 Fluorescent D 63.7/21.2 48.7/27.2 63.2/22.8 100/100 100/100 100/100 7.0/0.3 33.3/1.0 44.4/1.5 49.8/9.1 54.5/16.9 59.7/8.4 Repeatability/matching ratio evaluation between MLI (M) and default single image (D) in percentage.

	cam	ref		Daylight			Fluorescent			Lamps			Flashlight
			ORB	SIFT	SURF	ORB	SIFT	SURF	ORB	SIFT	SURF	ORB	SIFT	SURF
	Daylight D 100M 72.3/34.7 61.2/34.7 76.6/30.7 100/100 100/100 100/100 13.8/0.4 51.0/1.6 65.7/2.0 66.2/13.9 60.8/21.5 65.4/13.4
	Lamps	D 4.2/0.9	2.0/1.2	3.1/1.7	1.4/0.5	2.1/1.4	3.6/1.7 100/100 100/100 100/100 4.4/1.0	1.2/0.5	3.8/0.8
			M 64.6/20.0 46.9/24.0 62.1/21.8 66.6/21.8 47.0/26.7 60.7/25.9 100/100 100/100 100/100 56.8/6.7 41.3/14.2 46.2/9.0
	Flashlight D 34.0/5.3 12.2/5.4 16.4/5.3 32.4/7.6 11.3/6.3 16.2/6.2 14.6/0.5 5.1/0.0 12.1/0.2 100/100 100/100 100/100
			M 58.1/11.8 31.4/11.8 44.6/11.4 61.4/16.6 30.5/15.0 44.0/13.5 18.4/0.5 16.4/0.5 35.0/0.8 100/100 100/100 100/100

1

  Daylight Fluo Lamps Flash NID ORB MLI NID ORB MLI NID ORB MLI NID ORB MLI Daylight 99.3 100 100 96.7 96.2 98.4 73.9 97.6 53.6 74.6 79.8 77.1 Fluo 95.0 88.1 95.1 99.7 100 100 85.3 93.9 100 95.8 100 100 Lamps 88.3 55.7 93.3 93.6 79.8 93.4 93.1 100 100 84.3 37.9 96.8 Flash 23.8 30.7 77.6 92.2 90.6 93.6 0.00 0.00 94.2 92.0 100 99.3


The molecular self-assembly of preformed complexes in soft conditions is an interesting alternative to more energyconsuming routes generally used in solid-state chemistry in order to obtain functional materials. In recent years, strong research efforts have been devoted to the design of functional coordination polymers and metal organic frameworks.

Cyanide coordination chemistry nicely illustrates the efficiency of the self-assembly synthetic approach. In fact, the existence of numerous stable polycyanido-metallates [M(CN) n ] mbuilding blocks (M: transition metal), allows the tuning of the electronic properties and the architecture of the resulting selfassembled materials. [START_REF] Alexandrov | [END_REF] The strength of the M-CN-M' bridges can also confer structural robustness to the obtained networks. Finally, the cyanide bridges promote efficient electronic couplings between the metal ions it links, which can lead to interesting magnetic, optical or electronic properties.

3

In this context, a large number of Prussian Blue Analogues (PBAs) and cyanide-bridged frameworks have been studied for many kinds of application including catalysis, 4 bio-sensing, [START_REF]Advanced Biomaterials and Biodevices[END_REF] gas storage, [START_REF] Kaye | [END_REF] etc.

The use of cyanido complexes, [M(L)(CN) n ] m-, which contain ancillary ligand (L), has permitted the preparation of new architectures, in particular the design of molecular materials that exhibit reduced dimensionality. 7 The fac-[Fe III (Tp)(CN) 3 ] complex (Tp: hydrotris(pyrazolyl)borate) that we first described in 2002 has been particularly used in this context.

The Tp -ligand belongs to the well-known scorpionate ligand family that can be easily functionalized, [START_REF]Scorpionates II, chelating borate ligands, C. Pettinari[END_REF] allowing the adjustment of its electronic and steric properties. This anisotropic building block [START_REF] Ridier | [END_REF] In this paper, we selected as a model compound a simple and known one dimensional (1D) material of formula

{[Fe III (Tp)(CN) 3 ] 2 [Ni II (H 2 O) 2 ]} n , which contains the versatile [Fe III/II (Tp)(CN) 3 ]
-building block. We expected that, while this building block exhibits a higher redox potential relative to the parent [Fe III/II (CN) 6 ]

3-/4-, which could lead to higher reaction voltage, the lower dimensionality and open framework should confer more flexibility to the framework and more space to permit easier ion (de)intercalation. The questions we wanted to address were as follows: are lower dimensional cyanidebased materials still robust enough to reversibly insert alkali ions? Is the electronic conductivity of the 1D material high enough (compare to 3D phases) for it to act as a cathode? Can the scorpionate-based subunits be reversibly oxidized/reduced in the solid state? We thus report here the electrochemical Li 1b, grey) that was previously reported by You et al. 14 The hydrated compound 1 can also be obtained by a single-crystal to single-crystal phase transition. The XRD analysis revealed that methanol in the single crystal of 1' is completely replaced by water after 3 days in ambient atmosphere to give 1 (Fig. S1, supporting information). The calculated XRD pattern based on the crystal structure of 1 matches the pattern measured for the precipitated material (Fig. 1b, blue). 12 However, most of the {Fe III (Tp)(CN) 3 } -units in the pristine compound undergoes reversible redox reaction associated with Li + (de)intercalation.

+ (de)intercalation properties of the {[Fe(Tp)(CN) 3 ] 2 [Ni(H 2 O) 2 ]} chain compound. The 1D cyanide-bridged compound {[Fe III (Tp)(CN) 3 ] 2 [Ni II (H 2 O) 2 ]}•4H
Indeed, X-ray absorption near edge structure (XANES) spectroscopy shows that the main peak position of the Fe Kedge shifts to lower energy after Li + intercalation, and shifts back to the original position after Li + deintercalation (Fig. 3a).

The XANES spectra at the Ni K-edge do not show any shift of the main peak position during Li + (de)intercalation (Fig. 3b).

These results confirm that the reversible redox reaction in 1 occurs on the [Fe III/II (Tp)(CN) 3 ] -/2-building block. To the best of our knowledge, this result is the first demonstration of a reversible Li + (de)intercalation in a 1D cyanide-bridged molecular material obtained by self-assembly of preformed building blocks. The magnetic measurements before and after Li + (de)intercalation were studied using ex-situ SQUID measurements (Fig. 4). The observed magnetic behaviour of 1 (Fig. S7-S9, supporting information) is typical of a ferromagnetic chain. The observed ferromagnetic coupling is as predicted on the basis of simple orbital symmetry consideration: the unpaired electron of the iron(III) centre is described by a t 2g type magnetic orbital (π symmetry) whereas the two unpaired electrons of the nickel(II) centre are in two e g orbitals (σ symmetry). The Field-Cooled and Zero-Field Cooled magnetization (FC-ZFC) curves (Fig. 4 andS7) indicate the occurrence of magnetic ordering at 5 K due to interchains interactions. Overall, the magnetic properties of the pristine compound 1 are similar to those observed for 1' reported by You et al. 19 Indeed, the FC-ZFC curves for the lithiated sample (Fig. 4) do not show an abrupt increase of magnetization, indicating the disappearance of the magnetic order. Importantly, the ferromagnetic transition occurring at 5 K is recovered after Li + deintercalation. This shows that the material still behaves as interacting ferromagnetic chains, and thus the 1D Fe 2 Ni framework is maintained, even though electrochemical Li + intercalation induces the loss of the crystallinity. The Fe K-edge extended X-ray fine structure (EXAFS) spectra before and after Li + intercalation (Fig. S10, supporting information) also indicate that the Fe coordination sphere is not significantly altered.

In summary, we have shown that our synthetic approach based on the self-assembly of tailored cyanide building blocks in soft conditions is valid to obtain molecular material capable of ion storage. The [Fe(Tp)(CN) 3 ]

-is a novel versatile building unit to design electrochemically-active molecule-based magnetic materials. We are now focusing our efforts on the use of modified Fe building blocks with higher redox potentials.

[

  Fe III (Tp)(CN) 3 ] -Scorpionate-based Complex as a Building Block for designing Ion-Storage Hosts (Tp: hydrotrispyrazolylborate) which can be viewed as a lower dimensional model of Prussian blue analogues, was investigated as a lithium-ion storage host.

13

 13

Figure 1 .

 1 Figure 1. (a) Perspective view of the crystal structure of 1. (b) (i) Calculated powder Xray diffraction pattern from the single-crystal structure of 1' (grey). (ii) Experimental powder X-ray diffraction pattern of the air-dried crystals of 1' (green). (iii) Calculated powder X-ray diffraction pattern from the single-crystal structure of 1 (blue). (iv) Experimental powder X-ray diffraction pattern of the directly precipitated powder (orange).

Figure 2 . 4 (

 24 Figure 2. Open circuit potentials of 1 in a 1M LiClO4/PC electrolyte. The inset shows the cyclic voltammetry during the second cycle at the scan rate of 0.2 mV/s.

Figure 3 .

 3 Figure 3. Ex situ X-ray absorption spectra for (a) Fe and (b) Ni K-edges of 1 upon (de)lithiation.

Figure 4 .

 4 Figure 4. Magnetic property changes of 1 upon (de)lithiation. The black arrows indicate the ferromagnetic transition temperature.

14 After 1 . 6

 1416 Li + intercalation per {Fe 2 Ni} unit, most paramagnetic low-spin Fe III ions are reduced to diamagnetic low-spin Fe II . Therefore, the material does not behave as a ferromagnetic chain and the magnetic order disappears.

This work was financially supported by the ANR-JST Strategic International Collaborative Research Program (SICORP), Molecular Technology, Molecular Materials for Magnesium Batteries (MoMa). X-ray absorption spectroscopy was conducted under the approval of the Photon Factory Program Advisory Committee (Proposal 2016G031). We thank B. Baptiste from IMPMC for initial PXRD measurements.

Conflicts of interest

There are no conflicts to declare.

Notes and references ‡Electronic supplementary information (ESI) available: Experimental section, crystal structure, ex situ XRD patterns, magnetic properties, FT-IR, TGA, and EXAFS measurements.