<p>Appendix S1: calibration of the relationship between production </p><p> and agricultural intensity</p><p>At the level of the SAR, agricultural production was described as the ratio between the total edible energy from cereals, industrial crops, products from ruminants, and utilized agricultural area, expressed in gigacalories/ha. All agricultural data were drawn from national agricultural statistics</p><p>(Agreste 2014). Data for crop surfaces and numbers of animals were taken from the 2000 and 2010 agricultural censuses and estimates for 2006 were obtained by interpolation. Data on crop and animal production were taken from 2006 annual statistics, but were available only at the Nomenclature of</p><p>Territorial Units of Statistics 3 (NUTS 3) level with a mean area of 5776.8 km 2. They were disaggregated at the SAR level using the 2006 estimations for crop surfaces and animal populations.</p><p>Crop yield and animal productivity were assumed to be constant within each NUTS 3 region.</p><p>Production data were then converted into energy values using conversion coefficients (ANSES 2013;</p><p>FAO 2003). An estimation of the energy value of the crops fed to livestock on the farm was subtracted from the total energy value. This subtraction was based on animal numbers and average feed rations to livestock (Devun and Guinot 2012).</p><p>Generalized Additive Models were used to determine the relationship between food production and agricultural intensity (IC/ha indicator, which was the only explanatory variable) at the national scale and across SARs. Several degrees of freedom were tested and a cubic relationship was selected</p><p>(Fig. 1a) based on the Akaike Information Criterion (AIC). The details of this statistical relationship are provided in Table S1.1.</p><p>� Leave-one-out cross n F p-value Explained deviance validation error 578 56.32 < 0.001 49% 4% Table S1.1: Performance summary of the generalized additive models linking IC/ha agricultural intensity indicator to food production.</p><p>References</p><p>Agreste (2014) Ministère de l’agriculture, de l’agroalimentaire et de la forêt - Service de la statistique et de la prospective </p><p> http://www.agreste.agriculture.gouv.fr/. Accessed 15 November 2014.</p><p>ANSES (2013). Ciqual French food composition table version 2013. https://pro.anses.fr/TableCIQUAL/. Accessed 25 June </p><p>2014.</p><p>Devun, J., Guinot, C. (2012) Alimentation des bovins : Rations moyennes et autonomie alimentaire. Institut de l'Elevage, </p><p>Paris.</p><p>FAO (2003). Les bilans alimentaires, Manuel. Food and Agriculture Organization of the United Nations, Rome, Italy.</p><p>�</p>