Using a spatial and stage-structured invasion model to assess the spread of feral populations of transgenic oilseed rape

The risk of roadside verge invasion by transgenic plants is favoured when a cultivated species can persist outside fields as feral populations. We chose oilseed rape as a model species to evaluate the spread of genetically modified herbicide tolerant (GMHT) feral populations under selection pressure (herbicide spraying) in the medium term. We developed a stepwise invasion model that combines stage-structured dynamics (via a leslie matrix) and seed dispersal (via a mixture of two kernels) within an integro-differential equation. Modelling choices were made to conform to our intention to obtain methodological insight about the necessity to integrate long-distance seed dispersal in models of gene flow among oilseed rape. We thus assumed that roadside verges are a one-dimensional and uniformly suitable habitat and that events of dispersal and demography are deterministic. We performed elasticity analyses of population growth rate and invasion speed to highlight the determinants of population demography and spread. Rare events of long-distance dispersal controlled population spread. The risk of road verge invasion by feral populations of GMHT oilseed rape under selection pressure is thus real and does exist, since it was proved experimentally that oilseed rape can be dispersed by vehicles. Models of oilseed rape should then include long-distance seed dispersal otherwise they would underestimate feral population spread. Population growth rate and invasion speed depended on the same demographic transitions, i.e. those including local recruitment (local production of new individuals), but not on the persistence of seeds in the seed bank. Therefore, plant sterilisation would be more efficient to limit feral population spread than selection of cultivars without seed dormancy. The assumptions made about habitat continuity and homogeneity were consistent in the framework of this stepwise approach. However, integrating habitat heterogeneity and stochasticity would improve this invasion model.