Mathematical Models for Gene Flow from GM Crops in the Environment

Risk assessment of gene flow from GM crops into the environment requires both the development of physical transport models and biological models for the assessment of outcrossing probabilities. Our starting point is a Lagrangian approach for pollen dispersal, which describes the concentration statistics in terms of the stochastic properties of the paths of ensembles of particles. Transport of a particle from a location (x’,y’,z’) to a location (x,y,z) is mediated by a probability density or transfer function Q(x,y,z|x’,y’,z’). The transfer function depends on the statistics of the wind field during pollination. The total amount of pollen, which reaches a single plant, is then derived by the integral over all donators. In the context of gene flow, particle transport is but one aspect. The target variable is not primarily pollen density but the amount of outcrossing. The transfer function Q thus has to take into account both transport and biological processes and is devised to combine a transport submodel capable of integrating the statistics of wind velocities, a pollen viability submodel, a phenological submodel, a submodel for pollen redistribution by insects and a pollen competition submodel. Model parameters are estimated from data of outcrossing studies of maize and oil seed rape. The model is then applied to study the effect of field geometries on outcrossing rates.