A mechanistic model to predict transgenic seed contamination in bee-pollinated crops validated in an apple orchard

The adventitious presence of transgene containing seed in conventional crops is an issue of considerable interest; a model to predict levels will aid regulators and help to address concerns of farmers and consumers. While outcrossing levels have been described in crops such as rape that are wind-pollinated, or both wind- and insect-pollinated, much less is known about pollen dispersal in exclusively insect-pollinated crops. In this paper, we develop a mechanistic model for pollen movement that is based on a description of bee movement through space. Our model is a system of diffusion-based partial differential equations that we use to predict percent transgenic seed at arbitrary distances from a transgenic source under different planting scenarios. We present a two-pronged study, in which the mathematical modelling work is informed by experimental work. The latter was carried out in an apple orchard with a row of 200 transgenic source trees carrying the GUS marker gene. Fruit from neighbouring conventional trees was gathered at distances ranging from 3.5m to 183m, and the seeds were extracted and germinated. Percent transgenic seed at each location was determined by testing the seedlings for the presence of the GUS marker gene. We use the experimental data to validate and parameterize the model, and then run model simulations to determine expected percent transgenic seed in various linear landscapes. We find that the percent transgenic seed in neighbouring conventional trees and orchards is a function of the size of each orchard block and the distance between them. The model explicitly shows the effect of overlapping transgenic and nontransgenic pollen distributions in setting seed distributions, and also shows the value of buffer rows in reducing outcrossing levels in neighbouring crops. The model parameters can be adjusted to suit particular crops and locations, and may be useful for determining plausible distributions on transgenic seed plantings needed to allow for an adventitious presence of, for example, 0.9%.