  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.
