Pollen dispersal of oilseed rape: estimation of the dispersal function and effects of field dimension

Summary 1. Debate continues regarding the ecological impacts of genetically modified (GM) crops and their coexistence with non-GM crops in Europe. In this debate, quantitative predictions of gene dispersal by pollen are necessary, and as a result numerous plot-to-plot gene flow experiments have been performed with various crops. However, plot-to-plot cross-pollination rates (CPR) depend on spatial configuration of plots, implying that (i) they are difficult to compare among experiments and (ii) functions directly fitted on CPR data are inappropriate for predictions in other spatial contexts. 2. Modelling pollen dispersal via an individual dispersal function (IDF) circumvents these problems by accounting for spatial designs. We detail for oilseed rape how this approach can be used to both estimate an IDF from field data and predict CPR between two neighbouring fields of various sizes and shapes. Predictions were used to investigate the sensitivity of CPR to the family of IDF, the uncertainty in parameter estimates and the effects of field dimensions and isolation distances. 3. We fitted a range of families of IDF, including several types of tails, on previously published data. The best IDF was a fat-tailed power-law function, meaning frequent long-distance dispersal. 4. The choice of IDF appeared crucial when predicting CPR between fields, occasionally being even more important than the distance between fields. Width of the source field and depth of the recipient field were next in importance. When approximated CPR were calculated without considering field dimensions, using distance between field centres gave better performance than field margins. 5. Synthesis and applications. This study demonstrates the value of IDF for quantitative predictions of pollen flow in variable spatial configurations. A spatially explicit model of agro-ecosystems used to define management rules for the commercial release of GM crops in Europe already employs IDF but underestimates long-distance dispersal for oilseed rape. These new parameter estimates will refine the performance of these models. Moreover, the detailed guidelines for estimating an IDF should encourage such statistical analysis of other dispersal data, enabling comparisons of dispersal data obtained for different environments and species and providing new IDF for management models.