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The structural pattern of infectivity matrices, which contains infection data resulting from inoculations of a set of hosts by a set of parasites, is a key parameter for our understanding of biological interactions and their evolution. This pattern determines the evolution of parasite pathogenicity and host resistance, the spatiotemporal distribution of host and parasite genotypes, and the efficiency of disease control strategies. Two major patterns have been proposed for plant-virus genotype infectivity matrices. In the gene-for-gene model, infectivity matrices show a nested pattern, where the host ranges of specialist virus genotypes are subsets of the host ranges of less specialized viruses. In contrast, in the matching-allele (MA) model, each virus genotype is specialized to infect one (or a small set of) host genotype(s). The corresponding infectivity matrix shows a modular pattern where infection is frequent for plants and viruses belonging to the same module but rare for those belonging to different modules. We analyzed the structure of infectivity matrices between Potato virus Y (PVY) and plant genotypes in the family Solanaceae carrying different eukaryotic initiation factor 4E (eIF4E)-coding alleles conferring recessive resistance. Whereas this system corresponds mechanistically to an MA model, the expected modular pattern was rejected based on our experimental data. This was mostly because PVY mutations involved in adaptation to a particular plant genotype displayed frequent pleiotropic effects, conferring simultaneously an adaptation to additional plant genotypes with different eIF4E alleles. Such effects should be taken into account for the design of strategies of sustainable control of PVY through plant varietal mixtures or rotations. IMPORTANCE The interaction pattern between host and virus genotypes has important consequences on their respective evolution and on issues regarding the application of disease control strategies. We found that the structure of the interaction between Potato virus Y (PVY) variants and host plants in the family Solanaceae departs significantly from the current model of interaction considered for these organisms because of frequent pleiotropic effects of virus mutations. These mutational effects allow the virus to expand rapidly its range of host plant genotypes, make it very difficult to predict the effects of mutations in PVY infectivity factors, and raise concerns about strategies of sustainable management of plant genetic resistance to viruses.