International audienceWhen a long line of stationary touching balls is hit on its end by another ball, the line fragments: some balls fly off at the far end, some in the middle hardly move, and the impacting ball rebounds backwards taking with it some nearby balls. Two laws for the contact force are studied, both elastic and cohesionless. First a simple law linear in the compression and then the nonlinear 3 over 2-power law of Hertz for touching spheres. For the linear force and for a line of N balls being impacted by a ball at velocity V, {1.5N1/3balls} fly off from the far end, the furthest at a velocity {1.4VN-1/6}, the others at similar but slower speeds, while the majority rebound, the impacting ball at {-0.13V} and the nth from the end at a velocity {-0.16Vn-5/6at} large n. For the nonlinear Hertz law, only two balls fly off from the far end with significant velocities, at {0.986V} and {0.149V}, the majority hardly move, and a few rebound, the impacting ball at {-0.07V} and the nth from the end at a velocity {-0.084Ve-0.55n.

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The use of cultivar mixtures to control foliar fungal diseases is well documented for windborne diseases, but remains controversial for splash-dispersed diseases. To try to improve this strategy, a cultivar mixture was designed consisting of two wheat cultivars with contrasted resistance to Mycosphaerella graminicola, responsible for the rainborne disease septoria tritici blotch (STB), in a 1:3 susceptible:resistant ratio rather than the 1:1 ratio commonly used in previous studies. The impact of natural STB epidemics in this cultivar mixture was studied in field experiments over 4 years. Weekly assessments of the number of sporulating lesions, pycnidial leaf area and green leaf area were carried out on the susceptible cultivar. In years with sufficient STB pressure, disease impacts on the susceptible cultivar in the mixture were always significantly lower than in the pure stand (e.g. 42% reduction of pycnidial leaf area for the three upper leaves in 2008 and 41% in 2009). In years with low STB pressure (2010 and 2011), a reduction of disease impacts was also shown but was not always significant. After major rainfall events, the number of sporulating lesions observed on the susceptible cultivar after one latent period was reduced on average by 45% in the mixture compared to the pure stand. All the measurements showed that a susceptible cultivar was consistently protected, at least moderately, in a mixture under low to moderate STB pressure. Therefore, the results prove that the design of an efficient cultivar mixture can include the control of STB, among other foliar diseases.

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

Cultivar mixtures slow polycyclic epidemics but may also affect the evolution of pathogen populations by diversifying the selection pressures exerted by their plant hosts at field scale. We compared the dynamics of natural populations of the fungal pathogen Zymoseptoria tritici in pure stands and in three binary mixtures of wheat cultivars (one susceptible cultivar and one cultivar carrying the recently broken‐down Stb16q gene) over two annual field epidemics. We combined analyses of population “size” based on disease severity, and of population “composition” based on changes in the frequency of virulence against Stb16q in seedling assays with more than 3000 strains. Disease reductions were observed in mixtures late in the epidemic, at the whole‐canopy scale and on both cultivars, suggesting the existence of a reciprocal protective effect. The three cultivar proportions in the mixtures (0.25, 0.5, and 0.75) modulated the decrease in (a) the size of the pathogen population relative to the two pure stands, (b) the size of the virulent subpopulation, and (c) the frequency of virulence relative to the pure stand of the cultivar carrying Stb16q. Our findings suggest that optimal proportions may differ slightly between the three indicators considered. We argue potential trade‐offs that should be taken into account when deploying a resistance gene in cultivar mixtures: between the dual objectives “efficacy” and “durability,” and between the “size” and “frequency” of the virulent subpopulation. Based on current knowledge, it remains unclear whether virulent subpopulation size or frequency has the largest influence on interepidemic virulence transmission.

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The fungus Leptosphaeria maculans causes blackleg (phoma stem canker), one of the most serious diseases of oilseed rape. The role of pycnidiospores produced during asexual reproduction is poorly documented and limits the understanding of the pathogen's population dynamics. The objectives of this study were to assess rain-splash dispersal of pycnidiospores of L. maculans from phoma leaf spots, and transmission of the disease from oilseed rape stubble carrying pycnidia. The work was conducted in still air with either a drop generator or a rain simulator. The impact of simulated incident drops on phoma leaf spots resulted in the dispersal of L. maculans pycnidiospores within splash droplets. Ninety per cent of the spores were collected within 14 cm of the source and a few were regularly observed up to 40 cm. Pycnidiospores produced on oilseed rape stubble and dispersed by simulated rain infected oilseed rape trap plants in a spatial pattern that matched the spatial dispersal of the pycnidiospores. In the field, rain-splash dispersal of pycnidiospores could increase the pathogen population and may enhance sexual reproduction by facilitating the mating of initially spatially separated isolates of opposite mating type.