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Heterosis, or hybrid vigour, is said to occur when F1 individuals exhibit increased performance for a number of traits compared to their parental lines. Improved traits can include increased size, better yield, faster development and a higher tolerance to pathogens or adverse conditions. The molecular basis for the phenomenon remains disputed, despite many decades of theorising and experimentation. In this study, we add a genetics layer to a constraint-based model of plant (Arabidopsis) primary metabolism and show that we can realistically reproduce and quantify heterosis in a highly complex trait (the rate of biomass production). The results demonstrate that additive effects coupled to the complex patterns of epistasis generated by a large metabolic network are sufficient to explain most or all the heterosis seen in typical F1 hybrids. Such models provide a simple approach to exploring and understanding heterosis and should assist in designing breeding strategies to exploit this phenomenon in the future.