Effect of pollinator abundance on self-fertilization and gene flow: application to GM canola

Cross-pollination from fields of transgenic crops is of great public concern. Although cross-pollination in commercial canola (Brassica napus) fields has been empirically measured, field trials are expensive and do not identify the causes of cross-pollination. Therefore, theoretical models can be valuable because they can provide estimates of cross-pollination at any given site and time. We present a general analytical model of field-to-field gene flow due to the following competing mechanisms: the wind, bees, and autonomous pollination. We parameterize the model for the particular case of field-to-field cross-pollination of genetically modified (GM) canola via the wind and via bumble bees (Bombus spp.) and honey bees (Apis mellifera). We make extensive use of the large data set of bee densities collected during the recent U.K. Farm Scale Evaluations. We predict that canola approaches almost full seed set without pollinators and that autonomous pollination is responsible for ≥25% of seed set, irrespective of pollinator abundance. We do not predict the relative contribution of bees vs. the wind in landscape-scale gene flow in canola. However, under model assumptions, we predict that the maximum field-to-field gene flow due to bumble bees is 0.04% and 0.13% below the current EU limit for adventitious GM presence for winter- and spring-sown canola, respectively. We predict that gene flow due to bees is ~3.1 times higher at 20% compared to 100% male-fertility, and due to the wind, 1.3 times higher at 20% compared to 100% male-fertility, for both winter- and spring-sown canola. Bumble beemediated gene flow is ~2.7 times higher and wind-mediated gene flow ~1.7 times lower in spring-sown than in winter-sown canola, regardless of the degree of male-sterility. The model of cross-pollination due to the wind most closely predicted three previously published observations: field-to-field gene flow is low; gene flow increases with the proportion of plants that are male-sterile; and gene flow is higher in winter- than in spring-sown canola. Our results therefore suggest that the wind, not bees, is the main vector of long-distance gene flow in canola.