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The effect of spatial scales on the reproductive fitness of plant pathogens

Plant diseases often cause serious yield losses in agriculture. A pathogen's reproductive fitness 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 scales of pathogen dispersal and the spatial scales of the host population. 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 a maximum in quadratic 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 pathogen caused by Puccinia striiformis), since disease gradients for this pathogen were thoroughly measured over large distances [Sackett and Mundt, Phytopathology, 95, 983 (2005)]. For the two largest datasets, we estimated R0 in the limit of large fields to be of the order of 50. These estimates are consistent with independent field observations [Cowger et al. (2005), Phytopathology, 95, 97282; Farber et al. (2013), Phytopathology, 103, 41]. We present a proof of principle of a novel approach to estimate the basic reproductive number, R0, of plant pathogens using wheat stripe rust as a case study. 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.