title: A Lévy-flight diffusion model to predict transgenic pollen dispersal.
abstract: The containment of genetically modified (GM) pollen is an issue of significant concern for many countries. For crops that are bee-pollinated, model predictions of outcrossing rates depend on the movement hypothesis used for the pollinators. Previous work studying pollen spread by honeybees, the most important pollinator worldwide, was based on the assumption that honeybee movement can be well approximated by Brownian motion. A number of recent studies, however, suggest that pollinating insects such as bees perform Lévy flights in their search for food. Such flight patterns yield much larger rates of spread, and so the Brownian motion assumption might significantly underestimate the risk associated with GM pollen outcrossing in conventional crops. In this work, we propose a mechanistic model for pollen dispersal in which the bees perform truncated Lévy flights. This assumption leads to a fractional-order diffusion model for pollen that can be tuned to model motion ranging from pure Brownian to pure Lévy. We parametrize our new model by taking the same pollen dispersal dataset used in Brownian motion modelling studies. By numerically solving the model equations, we show that the isolation distances required to keep outcrossing levels below a certain threshold are substantially increased by comparison with the original predictions, suggesting that isolation distances may need to be much larger than originally thought.
authors.affiliation: Institute of Mechanics, Materials and Civil Engineering (IMMC), Université catholique de Louvain, 4 Avenue G. Lemaître, 1348 Louvain-la-Neuve, Belgium.
authors.forename: Valentin
authors.initials: V
authors.lastname: Vallaeys
authors.affiliation: IKBSAS 5 BLDG SCI, University of British Columbia Okanagan, 3333 University Way, Kelowna, British Columbia, Canada V1V 1V7.
authors.forename: Rebecca C
authors.initials: RC
authors.lastname: Tyson
authors.affiliation: Blue Comet Agro Inc., 8345 Canyon View Road, Summerland, British Columbia, Canada V0H 1Z2.
authors.forename: W David
authors.initials: WD
authors.lastname: Lane
authors.affiliation: Institute of Mechanics, Materials and Civil Engineering (IMMC), Université catholique de Louvain, 4 Avenue G. Lemaître, 1348 Louvain-la-Neuve, Belgium.|Earth and Life Institute (ELI), Université catholique de Louvain, 4 Avenue G. Lemaître, 1348 Louvain-la-Neuve, Belgium.|Delft Institute of Applied Mathematics (DIAM), Delft University of Technology, Mekelweg 4, 2628CD Delft, The Netherlands.
authors.forename: Eric
authors.initials: E
authors.lastname: Deleersnijder
authors.affiliation: Earth and Life Institute (ELI), Université catholique de Louvain, Croix du Sud 2 box L7.05.16, 1348 Louvain-la-Neuve, Belgium emmanuel.hanert@uclouvain.be.
authors.forename: Emmanuel
authors.identifier: 0000-0002-8359-868X
authors.initials: E
authors.lastname: Hanert
mesh_terms: D000818:Animals; D001516:Bees / Q000502:physiology*; D008954:Models, Biological; D030821:Plants, Genetically Modified / Q000502:physiology*; D011058:Pollen / Q000502:physiology*; D054817:Pollination / Q000502:physiology*
keywords: anomalous diffusion; bee-mediated pollen dispersal; genetically modified crops; isolation distances; truncated Lévy flights