Salomon, J.; Enjalbert, J.; Flutre, T.

The genetics of interspecific groups remains largely unexplored, despite the central role of social (or indirect) genetic effects in shaping phenotypic expression within communities. Intercropping, i.e. the simultaneous cultivation of multiple crop species in the same field, offers a powerful model to harness these interspecific social effects. Such species mixtures provide well-documented agricultural benefits, yet few breeding frameworks have integrated the genetics of social interactions. Here, we address this gap by extending quantitative genetic theory to interspecific groups, with intercropping as a concrete and applied model case. We propose a quantitative genetic model that jointly analyzes intra and interspecific interactions within a unifying framework. Breeding values are decomposed into a direct component, shared in mono and mixed-crops, an interspecific social component corresponding to the effect of one species on another, and an intraspecific component that captures the social effects within a mono-genotypic stand of cloned plants. Statistically, this consists in simultaneously fitting several linear mixed models, one per stand type, all having direct breeding values in common. As no open-source software can fit such a complex mixed model, we provide such an implementation in R/C++. Simulations across various genetic (co)variance structures and sparse experimental designs showed accurate estimation of all genetic (co)variances and breeding values. With an incomplete, yet balanced design combining sole crops and intercrops, genetic gains in both systems were achievable simultaneously, enabling breeding strategies that progressively integrate intercropping into existing, sole-crop-only schemes. More broadly, this framework allows dissecting direct and social genetic effects when genotypes are observed in mono- and mixed- species situations, cultivated or not.