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Exponential and Power-Law Contact Distributions Represent Different Atmospheric Conditions

December 2011 , Volume 101 , Number  12
Pages  1,465 - 1,470

A. M. Reynolds

Rothamsted Research, Harpenden, Hertfordshire, AL5 2JQ, UK.

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Accepted for publication 12 July 2011.

It is well known that the dynamics of plant disease epidemics are very sensitive to the functional form of the contact distribution—the probability distribution function for the distance of viable fungal spore movement until deposition. Epidemics can take the form of a constant-velocity travelling wave when the contact distribution is exponentially bounded. Fat-tailed contact distributions, on the other hand, lead to epidemic spreads that accelerate over time. Some empirical data for contact distributions can be well represented by negative exponentials while other data are better represented by fat-tailed inverse power laws. Here we present data from numerical simulations that suggest that negative exponentials and inverse power laws are not competing candidate forms of the contact distribution but are instead representative of different atmospheric conditions. Contact distributions for atmospheric boundary-layers with stabilities ranging from strongly convective (a hot windless day time scenario) to stable stratification (a cold windy night time scenario) but without precipitation events are calculated using well-established state-of-the-art Lagrangian stochastic (particle tracking) dispersal models. Contact distributions are found to be well represented by exponentials for strongly convective conditions; a –3/2 inverse power law for convective boundary-layers with wind shear; and by a –2/3 inverse power law for stably stratified conditions.

Additional keywords: atmospheric dispersion, dispersal patterns, Lagrangian stochastic modeling, plant disease epidemics.

© 2011 The American Phytopathological Society