The dispersal of pollen from a Lolium perenne source has previously been described using various Gaussian plume models which take distance and wind direction into account. One of these models is used here to calculate, using integration, possible pollen deposition onto small conspecific populations a kilometer from the source. The percentage of immigrant pollen is compared for six different sets of parameter values previously estimated from pollen-dispersal experiments. The source size is then scaled up to simulate what might happen if transgenic ryegrass was grown on a large scale. In this case it is seen that small conspecific populations might, in some conditions, be swamped by immigrant pollen, even if they are not directly downwind of the source. The implications of this are discussed in terms of assessing and managing the risks of releasing wind-pollinated transgenic crops.