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Allowing growers to get free from pesticide use and preserving cultivated genetic resources while limiting the emergence of new diseases is one of the aims of the ongoing agroecological transition. To these ends, cultivar mixtures are an effective and more sustainable solution than pure stands of resistant cultivars, but a lack of understanding persists about how they work. Plant immunity and more specifically immune priming is sometimes mentioned to explain the observed efficiency of mixtures, but its mode of action on epidemics is still poorly known. I thus developed epidemiological models to identify the effects of priming on the effectiveness of mixtures. These models evidence that priming is critical to explain the observed effectiveness of cultivar mixtures.In a mixture of susceptible and resistant cultivars, priming decreases disease prevalence compared to a pure stand of the resistant host. In a mixture of resistant cultivars, priming also reduces the number or resistance genes needed to maintain disease prevalence below an acceptable threshold. In addition, the models make it possible to evaluate in what proportions cultivars should be mixed to optimize mixture efficiency and increase the durability of the resistances used. The variety to be mixed in the greatest proportion is the one that is the least costly for the pathogen to break. These novel theoretical contributions, sometimes counter intuitive but explainable ecologically, highlight how individual immunity scales up at the population level, and encourage future research to best exploit priming in plant protection strategies.; Permettre aux agriculteurs de s’affranchir des pesticides et préserver les ressources génétiques cultivées en limitant l’émergence de nouvelles maladies est l’un des objectifs de la transition agro-écologique. Les mélanges variétaux sont une solution efficace et plus durable que les cultures pures de variétés résistantes pour la maîtrise des épidémies, mais leur fonctionnement est encore mal compris. L’immunité végétale et plus précisément le priming immunitaire est parfois évoqué pour expliquer l’efficacité observée des mélanges, mais son influence sur les épidémies reste peu étudiée. J’ai donc développé des modèles épidémiologiques qui montrent l’impact potentiel du priming dans l’efficacité observée des mélanges variétaux.Dans un mélange de variétés sensibles et résistantes, le priming peut ainsi diminuer la prévalence des maladies comparativement aux cultures pures de variétés résistantes. Dans un mélange de variétés résistantes, le priming réduit également le nombre minimal de gènes de résistance requis pour rester sous un seuil de prévalence acceptable. De plus, les modèles développés permettent d’évaluer les proportions optimales des variétés pour renforcer l’efficacité des mélanges et accroître la durabilité des résistances utilisées. Ils montrent que la variété à insérer en plus grande proportion est la moins coûteuse à contourner pour l’agent pathogène. Ces nouveaux apports théoriques, parfois contre-intuitifs mais explicables écologiquement, soulignent l’importance de l’immunité individuelle à l’échelle de la population, et encouragent de futures recherches pour mieux utiliser le priming dans les stratégies de protection des plantes.

Le modèle spatio-temporel de gestion durable des résistances variétales au phoma SIPPOM-WOSR a été amélioré, en particulier au niveau temps de calcul. Ceci a permis, en collaboration avec des acteurs de terrain, de procéder à des simulations de plusieurs centaines de scénarios. Une synthèse de la démarche et des résultats obtenus en matière d’évolution des populations virulentes avrlm7 de L.maculans est présentée., The spatio-temporal model SIPPOM-WOSR, designed for a durable management of plant resistance to blackleg, has been improved, especially concerning execution time. In collaboration with stakeholders, this allowed the elaboration of several hundred of scenarios, their simulation with the model, and their eventual evaluation with the stakeholders. The approach and the results relative to the evolution of virulent avrlm7 Leptosphaeria maculans population are presented.

National audience; This presentation gives a perspective on the main findings of the economic literature dealing with pest resistance management and on questions for future research. Resistance to pest damage is embedded in some crop varieties, which thereby have an economic advantage over their conventional non-resistant counterparts. But this advantage may be lost over time, as selection pressure causes pest populations to adapt to this resistance. The economic literature has mainly illustrated the examples of resistance to a chemical pesticide or to an insect-resistant transgenic variety (as well as the related case of weed adaptation to a herbicide-tolerant transgenic crop variety on which a total herbicide may be applied). It has explored how to best design the use of pest-toxic varieties over time, which involves an intertemporal trade-off between controlling the pest population now and preserving its susceptibility to the pest-toxic crop in the future. It has also analyzed how to regulate this use, with regulation being motivated by the common-pooled nature of pest population and pest resistance, two detrimental resources exploited by farmers under open access. Besides, it has tackled the issue of how the interest of a social planner in preserving the resistance of a pest-toxic variety compares with that of a monopolist selling the crop variety with patent rights. At last, the literature has looked into the question of possible increasing returns to adoption in disfavor or in favor on pest-toxic varieties. Vanloqueren and Baret (2008) illustrate path-dependent processes and lock-in factors playing against the diffusion of multi-resistant wheat cultivars. In the case of herbicide-tolerant transgenic varieties, which allow the use of a total herbicide to combat weeds, on the contrary, some weed scientists warn on some path-dependence factors that play in favor of increased herbicide use over time to control weeds with herbicide-tolerant varieties (Mortensen et al., 2012).

We examine the optimal time-variant refuge policy to manage pest resistance to Bt crops in a finite-horizon discrete-time model. We identify analytically the intertemporal effects of refuge fields on the pest population and its susceptibility. The shape of the optimal refuge policy and whether or not pest susceptibility should be exhausted completely at the end of the time horizon depend crucially on the values of a cost premium of Bt seeds and the fitness cost of resistance (over-mortality of resistant pests) and are addressed via numerical simulations. We demonstrate the importance of modeling the dynamics of the biological system accurately, of defining a diploid (and not haploid) biological model, and of using a discrete-time (rather than continuous-time) framework.

We consider the use of a genetically modi ed crop to ght a pest population that feeds on the crop. We use an entomological model that captures the diversity of the pest population's gene pool, as well as the level of pest invasion itself. A refuge area is used as an instrument to control the evolution of the susceptibility of the pest's gene pool to the genetically modi ed crop. We characterize the refuge area that minimizes the sum of discounted costs related to the crop damage caused by the pest as well as the supplemental cost of the genetically modi ed crop. The model is calibrated for the use of Bt-corn to ght the European corn borer. Because of the linearity of the objective function, the optimal refuge consists of a bang-bang and a singular control. For the calibrated parameters, as well as reasonable variations of them, the bio-economic system tends to an interior steady state where the level of pest-susceptibility is renewable.However, when the control is restricted to being constant over time, as is currently done in the United States, the system generally tends to a steady state where the susceptibility is completely exhausted. In that case, it takes very particular parameter constellations for the system to reach an interior steady state. We are able to assess,for the calibrated model, the cost reduction attained by using a refuge area that varies over time instead of a time-invariant one.