A mathematical method for estimating patterns of flower‐to‐flower gene dispersal from a simple field experiment

Summary Pollination is a principal means of gene dispersal in animal‐pollinated plants. Theoretically, gene dispersal can be predicted from pollinator movements and their associated patterns of flower‐to‐flower gene dispersal, or paternity shadow, but quantifying the paternity shadow under field conditions is problematic. We developed a mathematical method to quantify the paternity shadow from a simple field experiment by initially stating the problem in matrix algebra, then using a least‐squares regression to find the paternity shadow that best explained the observed spatial distribution of gene dispersal, given the observed pollinator movements. We applied the method to data on the dispersion of a marker gene along rows of oilseed rape (Brassica napus) pollinated by bumble bees (Bombus spp.) and thereby produced the first field‐based paternity shadow. When coupled with observed movements of bumble bees, this paternity shadow explained virtually all (r2 = 90%) of the dispersion of the marker gene. Close similarity between our result and a paternity shadow obtained for B. napus in a separate laboratory experiment suggests that the paternity shadow is a fundamental attribute of the Bombus–B. napus interaction.