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A model of pollen–mediated gene flow for oilseed rape

The development of genetically modified (GM) crops has precipitated the need for risk assessment and regulation of pollen–mediated gene flow. In response to this need we present a mathematical model to predict the spatial distribution of outcrossing between progenitor populations of oilseed rape. The model combines the processes of pollen dispersal and pollination, resulting from wind and insect activity. It includes the effects of post–pollination reproductive processes by relating the number of progeny to both pollen deposition and competition at the stigma. Predictions compare well with a range of experimental results for different–sized GM source crops (i.e. 0.0064–0.8 ha) and non–GM target crops with different fertilities (i.e. self–fertile to 80% male–sterile). For these comparisons, we represent the variation caused by wind and insect exposure as a constrained set of random functions and limit the range of insect transport to typical plant–scale distances. In addition, the model is used to examine the relative sensitivity to the factors that determine gene flow. Target–crop fertility and source–crop size are shown to be more important than other factors, including background pollen and the natural range of insect activity. The concept of isolation distance to regulate gene flow is most effective for self–fertile target crops, but is ineffective for male–sterile target crops with low background pollen.