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Growing mixtures of annual arable crop species or genotypes is a promising way to improve crop production without increasing agricultural inputs. To design optimal crop mixtures, choices of species, genotypes, sowing proportion, plant arrangement, and sowing date need to be made but field experiments alone are not sufficient to explore such a large range of factors. Crop modeling allows to study, understand and ultimately design cropping systems and is an established method for sole crops.Recently, modeling started to be applied to annual crop mixtures as well.Here, we review to what extent crop simulation models and individual-based models are suitable to capture and predict the specificities of annual crop mixtures. We argued that: 1) The crop mixture spatio-temporal heterogeneity (influencing the occurrence of ecological processes) determines the choice of the modeling approach (plant or crop centered). 2) Only few crop models (adapted from sole crop models) and individual-based models currently exist to simulate annual crop mixtures. 3) Crop models are mainly used to address issues related to crop mixtures management and to the integration of crop mixtures into larger scales such as the rotation, whereas individual-based models are mainly used to identify plant traits involved in crop mixture performance and to quantify the relative contribution of the different ecological processes (niche complementarity, facilitation, competition, plasticity) to crop mixture functioning.This review highlights that modeling of annual crop mixtures is in its infancy and gives to model users some important keys to choose the model based on the questions they want to answer, with awareness of the strengths and weaknesses of each of the modeling approaches. The authors declare that they have no conflict of interestDuchene O, Vian J-F, Celette F (2017) Intercropping with legume for agroecological cropping systems: Complementarity and facilitation processes and the importance of soil microorganisms. A review. Agric Dunbabin VM, Postma JA, Schnepf A, et al (2013) Modelling root-soil interactions using threedimensional models of root growth, architecture and function. Plant Soil 372:93-124. Durand J-L, Andrieu B, Barillot R, et al (2016) Designing and improving mixed grasslands: advances made in modelling forage variety performance. Fourrages 21-28 Duru M, Therond O, Fares M (2015) Designing agroecological transitions; A review. Agron Sustain

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The effects of intercropping wheat with faba bean (Denmark, Germany, Italy and UK) and wheat with pea (France), in additive and replacement designs on grain nitrogen and sulphur concentrations were studied in field experiments in the 2002/03, 2003/04 and 2004/05 growing seasons. Intercropping wheat with grain legumes regularly increased the nitrogen concentration of the cereal grain, irrespective of design or location. Sulphur concentration of the cereal was also increased by intercropping, but less regularly and to a lesser extent compared with effects on nitrogen concentration. Nitrogen concentration (g/kg) in wheat additively intercropped with faba bean was increased by 8% across all sites (weighted for inverse of variance), but sulphur concentration was only increased by 4%, so N:S ratio was also increased by 4%. Intercropping wheat with grain legumes increased sodium dodecyl sulphate (SDS)-sedimentation volume. The effect of intercropping on wheat nitrogen concentration was greatest when intercropping had the most deleterious effect on wheat yield and the least deleterious effect on pulse yield. Over all sites and seasons, and irrespective of whether the design was additive or replacement, increases in crude protein concentration in the wheat of 10 g/kg by intercropping with faba bean were associated with 25?30% yield reduction of the wheat, compared with sole-cropped wheat. It was concluded that the increase in protein concentration of wheat grain in intercrops could be of economic benefit when selling wheat for breadmaking, but only if the bean crop was also marketed effectively