An empirical model for pollen-mediated gene flow in wheat

The extent of pollen-mediated gene flow (PMGF) in wheat (Triticum spp. L.) as a function of distance from a pollinator source has been measured in recent field studies. Wheat is primarily self-pollinated; however, some cross-pollination can occur depending on biological, agronomic, and environmental factors. The complexity of these interactions restricts attempts to develop a workable mechanistic model; therefore, we pursued an entirely empirical modeling approach. We fit a simple empirical regression model to all available observed data and then used it to make general predictions about the effects of field size, blending at harvest, and isolation distances on PMGF in wheat. The empirical model was derived by fitting a least squares regression line to the gene flow data when plotted as the logarithm of PMGF versus the square root distance from the edge of the source field. Linear behavior was observed when either the maximum or mean PMGF was plotted in this manner. A "General Wheat Model" (GWM) of this same mathematical form is given which provides a conservative ("high-end") prediction of PMGF in the general case: PMGF (%) = 10(-(0.2 root x)), where PMGF is the percent gene flow at a particular point in the field (without blending), and x is the distance (m) from the edge of the source field. The GWM was used to show that the effect of source field size is minimal for sources of 10 ha or larger, where asymptotic levels of PMGF are obtained. The model was also applied to show that harvest-blending produces PMGF at the field level 10 to 50 times lower than the highest level observed at the edge of the receptor field. Significantly, isolation buffers of 0 to 10 m were predicted by the GWM to have only a minimal impact on harvest-blended PMGF, when the receptor field had an overall width of 100 m or greater. Without any isolation buffers, the harvest-blended PMGF between neighboring commercial-sized (> 10 ha) fields was less than 0.1% (well below commercial thresholds for foreign material in wheat seed and grain). This is also well below any existing standards for labeling the presence of approved biotech traits in food or seed distributed or sold as conventional.