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Abstract: Oil of conventional oilseed rape (OSR) varieties with 7–10% alpha-linolenic acid content (LAC) might oxidize when heated, resulting into an unpleasant odor. Varieties with low (around 3%) LAC have been bred to provide industries with a new raw material for frying media production. However, high-oleic low-linolenic (HOLL) OSR quality could be compromised by conventional OSR through pollen flow or volunteers. Both nearby fields and volunteers of conventional OSR growing in the HOLL field or in its margins could thus be the cause of a reduced quality. Crop management practices such as regional field pattern, crop rotation, weed control and soil tillage might be decisive. The GeneSys model was initially developed to quantify the effects of cropping systems on gene flow between genetically-modified (GM) and non-GM crops. In this work, it was improved and then used to predict LAC of OSR harvests, particularly HOLL ones, in different situations. Field experiments carried out at the experimental station in Changins (VD), Switzerland, in 2005–2006 showed that LAC was controlled by two additive quantitative genes. Consequently, an additive model was used for calculations with GeneSys. Results also showed that beyond a 20m distance, a field of conventional OSR caused only a minor increase in LAC in a neighbouring HOLL OSR field, meaning that it is highly unlikely that pollen dispersal will compromise HOLL OSR quality under farmers’ conditions. These data were also used to evaluate the prediction quality of GeneSys. Briefly, the final LAC was slightly underestimated by the model, especially in the case of a high amount of conventional OSR volunteers leading to high LAC. Both experiments and simulations showed that the presence of volunteers of conventional OSR in the HOLL field had the most dramatic effect. In a short crop rotation, an important amount of volunteers significantly increased the LAC, but this can be controlled by adequate tillage and weed control in other crops of the rotation. Furthermore, in Switzerland, OSR is usually grown with an interval of at least 4 years in normal crop rotations, which is usually enough to prevent major contamination by volunteers if they are correctly managed. [Copyright &y& Elsevier]