Dispersal of Windborne Spores - Densities, Heavy Tails and Spatial Configurations.

Ander Stockmarr, Danish Veterinary Institute, Denmark.

e-mail: sta@vetinst.dk

The spatial dispersal of fungal spores from a point source may, through simple homogeneity assumptions, be described by a Cox process, ie. a Poisson process with randomized intensity. The parameters to be modelled here are spore release, dispersal through a dispersal kernel (or spatial probabilistic density), and spore survival. The many choices in this model lies in how the dispersal kernel is chosen, and the talk will devote itself to this subject. A central point in the study of spore dispersal is whether this is best described through a exponentially decreasing density, or a 'polynomially decreasing' density, ie. the density is the reciprocal of a polynomial, with much heavier tails, allowing longdistance dispersal and diffuse spatial patterns of dispersed spores, which over generations lead to secondary foci. Until recently, these two scenarios has been modelled as separate phenomenons, but a new modelling framework for particle dispersal given in Stockmarr (2002), which gives rise to both exponentially decreasing and polynomially decreasing two-dimensional densities has been developed, based on the theory of diffusions. The framework will be investigated through the time to deposition, and it is shown how this concept is equivalent to the deposition rate for fungal spores. I shall consider special cases where parameter values for wind and gravitation lead to exponentially/polynomially decreasing densities, and formulas for two- and one-dimensional densities of deposited spores are given explicitly in terms of parameters for diffusion, wind, gravitation and spore release height. Finally, advantages of the mathematical toolbox that is opened through diffusion modelling is discussed.