Invasiveness of plant pathogens depends on the spatial scale of host distribution

Plant diseases often cause serious yield losses in agriculture. A pathogen's invasiveness can be quantified by the basic reproductive number, R₀. Since pathogen transmission between host plants depends on the spatial separation between them, R₀ is strongly influenced by the spatial scale of the host distribution. We present a proof of principle of a novel approach to estimate the basic reproductivenumber, R₀, of plant pathogens as a function of the size of a field planted with crops and its aspect ratio. This general approach is based on a spatially explicit population dynamical model. The basic reproductive number was found to increase with the field size at small field sizes and to saturate to a constant value at large field sizes. It reaches amaximum in square fields and decreases as the field becomes elongated. This pattern appears to be quite general: it holds for dispersal kernels that decrease exponentially or faster, as well as for fat-tailed dispersal kernels that decrease slower than exponential (i.e., power-law kernels). We used this approach to estimate R₀ in wheat stripe rust(an important disease caused by Puccinia striiformis), where we inferred both the transmission rates and the dispersal kernels from the measurements of disease gradients. For the two largest datasets, we estimated R₀ of P. striiformis in the limit of large fields to be of the order of 30. We found that the spatial extent over which R₀ changes strongly is quite fine-scaled (about 30 m of the linear extension of the field). Our results indicate that in order to optimize the spatial scale of deployment of fungicides or host resistances, the adjustments should be made at a fine spatial scale. We also demonstrated how the knowledge of the spatial dependence of R₀ can improve recommendations with regard to fungicide treatment.