Assembling spatially explicit landscape models of pollen and spore dispersal by wind for risk assessment

Models of windblown pollen or spore movement are required to predict gene flow from genetically modified (GM) crops and the spread of fungal diseases. We suggest a simple form for a function describing the distance moved by a pollen grain or fungal spore, for use in generic models of dispersal. The function has power-law behaviour over sub-continental distances. We show that air-borne dispersal of rapeseed pollen in two experiments was inconsistent with an exponential model, but was fitted by power-law models, implying a large contribution from distant fields to the catches observed. After allowance for this ‘background’ by applying Fourier transforms to deconvolve the mixture of distant and local sources, the data were best fit by power-laws with exponents between 1.5 and 2. We also demonstrate that for a simple model of area sources, the median dispersal distance is a function of field radius and that measurement from the source edge can be misleading. Using an inverse-square dispersal distribution deduced from the experimental data and the distribution of rapeseed fields deduced by remote sensing, we successfully predict observed rapeseed pollen density in the city centres of Derby and Leicester (UK).

[1]  H. Mccartney Deposition of Erysiphe graminis Conidia on a Barley Crop II. Consequences for Spore Dispersal , 1987 .

[2]  R. Clarke,et al.  Long distance seed dispersal by wind: measuring and modelling the tail of the curve , 2000, Oecologia.

[3]  G. Giddings Modelling the spread of pollen from Lolium perenne. The implications for the release of wind-pollinated transgenics , 2000, Theoretical and Applied Genetics.

[4]  J. Osborne,et al.  A model of pollinator‐mediated gene flow between plant populations with numerical solutions for bumblebees pollinating oilseed rape , 2002 .

[5]  D. Aylor,et al.  The Role of Intermittent Wind in the Dispersal of Fungal Pathogens , 1990 .

[6]  M. J. Wilkinson,et al.  Risks from transgenic crops , 1996, Nature.

[7]  J. Gupta A Theoretical Framework , 1997 .

[8]  G. W. Snedecor Statistical Methods , 1964 .

[9]  Christian Damgaard,et al.  Gene flow of oilseed rape (Brassica napus) according to isolation distance and buffer zone , 2005 .

[10]  B. Godelle,et al.  A pollen-dispersal experiment with transgenic oilseed rape. Estimation of the average pollen dispersal of an individual plant within a field , 1998, Theoretical and Applied Genetics.

[11]  Per Løfstrøm,et al.  An Improved Dispersion Model for Regulatory Use — The OML Model , 1992 .

[12]  Stephen R. Baillie,et al.  Modeling large-scale dispersal distances , 2002 .

[13]  C. Lavigne,et al.  High diversity of oilseed rape pollen clouds over an agro‐ecosystem indicates long‐distance dispersal , 2005, Molecular ecology.

[14]  D. Peart The Quantitative Representation of Seed and Pollen Dispersal , 1985 .

[15]  The microbiology of the atmosphere , 1973 .

[16]  Cyril Dutech,et al.  Using genetic markers to estimate the pollen dispersal curve , 2004, Molecular ecology.

[17]  Jeremy Sweet,et al.  Hybridization Between Brassica napus and B. rapa on a National Scale in the United Kingdom , 2003, Science.

[18]  S. Pacala,et al.  SEEDLING RECRUITMENT IN FORESTS: CALIBRATING MODELS TO PREDICT PATTERNS OF TREE SEEDLING DISPERSION' , 1994 .

[19]  S. Levin,et al.  Mechanistic Analytical Models for Long‐Distance Seed Dispersal by Wind , 2005, The American Naturalist.

[20]  Dennis Wheeler,et al.  Regional Climates of the British Isles , 2002 .

[21]  H. A. Mccartney,et al.  Deposition of Erysiphe graminis Conidia on a Barley Crop , 1987 .

[22]  William H. Press,et al.  Numerical recipes in C. The art of scientific computing , 1987 .

[23]  M. Wilkinson,et al.  Assessing the risks of wind pollination from fields of genetically modified Brassica napus ssp. oleifera , 1995, Euphytica.

[24]  Simon A. Levin,et al.  A Theoretical Framework for Data Analysis of Wind Dispersal of Seeds and Pollen , 1989 .

[25]  R. Rabbinge,et al.  Ability of the Gaussian plume model to predict and describe spore dispersal over a potato crop , 2002 .

[26]  I. Skogsmyr Gene dispersal from transgenic potatoes to conspecifics: a field trial , 1994, Theoretical and Applied Genetics.

[27]  William H. Press,et al.  The Art of Scientific Computing Second Edition , 1998 .

[28]  A. Stockmarr The distribution of particles in the plane dispersed by a simple 3-dimensional diffusion process , 2002, Journal of mathematical biology.

[29]  F. B. Smith,et al.  UK-ADMS: A new approach to modelling dispersion in the earth's atmospheric boundary layer , 1994 .

[30]  Weili Zhao Wind , 1978, Ecologics.

[31]  E. Shields,et al.  An aerobiological framework for assessing cross-pollination in maize , 2003 .

[32]  W. Press,et al.  Numerical Recipes in C++: The Art of Scientific Computing (2nd edn)1 Numerical Recipes Example Book (C++) (2nd edn)2 Numerical Recipes Multi-Language Code CD ROM with LINUX or UNIX Single-Screen License Revised Version3 , 2003 .

[33]  Farm Buildings,et al.  Ministry of Agriculture, Fisheries and Food- , 1956 .

[34]  J. Perry,et al.  Sensitive dependencies and separation distances for genetically modified herbicide-tolerant crops , 2002, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[35]  P. A. Prince,et al.  Lévy flight search patterns of wandering albatrosses , 1996, Nature.

[36]  H. R. Olesen,et al.  The Danish Gaussian Air Pollution Model (Oml): Description, Test and Sensitivity Analysis in View of Regulatory Applications , 1986 .

[37]  J. Metz,et al.  Focus expansion in plant disease. III: Two experimental examples , 1988 .

[38]  J. Perry,et al.  Farm-scale evaluation of GM crops explained , 1999, Nature.

[39]  J. Mesquida,et al.  ÉTUDE DE LA DISPERSION DU POLLEN PAR LE VENT ET DE L'IMPORTANCE DE LA POLLINISATION ANÉMOPHILE CHEZ LE COLZA (BRASSICA NAPUS L., VAR. OLEIFERA METZGER) , 1982 .

[40]  N. R. Sackville Hamilton,et al.  The release of genetically modified grasses. Part 2: the influence of wind direction on pollen dispersal , 1997, Theoretical and Applied Genetics.

[41]  Christopher Preston,et al.  Pollen-Mediated Movement of Herbicide Resistance Between Commercial Canola Fields , 2002, Science.

[42]  L. De Meester,et al.  Regional structuring of genetic variation in short-lived rock pool populations of Branchipodopsis wolfi (Crustacea: Anostraca) , 2000, Oecologia.

[43]  Janneke HilleRisLambers,et al.  Seed Dispersal Near and Far: Patterns Across Temperate and Tropical Forests , 1999 .