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 reproductive number, 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 a maximum 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.

#### Hermiston 2002 stripe rust disease gradient

This file contains the disease gradient data from Hermiston 2002 experiment for stripe rust on wheat. The experiments were reported in [Sackett, K. E., and C. C. Mundt. 2005. Primary disease gradients of wheat stripe rust in large field plots. Phytopathology 95:983–91.] 1st column: distance from the source of infection in feet. 2nd column: distance from the source of infection in meters. 3rd, 4th, 5th columns disease severity (percentage of leaf area infected) measurements in three replicate plots. This disease gradient is plotted in Figure 2(a).

hermiston2002_repl.dat

#### Madras 2002 stripe rust disease gradient

This file contains the disease gradient data from Madras experiment for stripe rust on wheat. The experiments were reported in [Sackett, K. E., and C. C. Mundt. 2005. Primary disease gradients of wheat stripe rust in large field plots. Phytopathology 95:983–91.] 1st column: distance from the source of infection in feet. 2nd column: distance from the source of infection in meters. 3rd, 4th, 5th columns disease severity (percentage of leaf area infected) measurements in three replicate plots. This disease gradient is plotted in Figure 2(b).

madras2002_repl.dat

#### Dose response dependence for stripe rust controlled by epoxiconazole

Dose response dependence for stripe rust controlled by the fungicide epoxiconazole (Opus). The data was reported in the Home Grown Cereal Authority (HGCA) report n. 488 "Fungicide performance on winter wheat" (Ref. Bounds et al 2012 in the manuscript), Figure 15. The first column represents the fungicide dose as a proportion of the full label rate. The second column represents severity of stripe rust as percentage of the total leaf area. The results are averages over the two consecutive seasons, 2008 and 2009. This data is plotted in Fig. 5(a) of the manuscript.

epoxiconazole_2008_2009_dr.dat

#### R0 as a function of the field size for exponential dispersal kernel

The file represents the basic reproductive number, R0, as a function of the field size for exponential dispersal kernel. 1st column distance [m]; 2nd column R0. Spatial grid 60x60 gridpoints. Plotted as solid curve in Fig. 1 (up to values of d of about 193 m). The data was generated by numerical solution of Eq. (6) in the manuscript.

r0_vs_d_exp_finescale.dat

#### R0 as a function of the field size for exponential dispersal kernel, large field sizes and higher spatial resolution

The file represents the basic reproductive number, R0, as a function of the field size for exponential dispersal kernel. 1st column distance [m]; 2nd column R0. Spatial grid 150x150 gridpoints. Plotted as solid curve in Fig. 1 (up to values of d of about 193 m). The data was generated by numerical solution of Eq. (6) in the manuscript.

r0_vs_d_exp_large_d.dat

#### basic reproductive number, R0, as a function of the field size for modified power law 2 dispersal kernel.

The file represents the basic reproductive number, R0, as a function of the field size for exponential dispersal kernel. 1st column distance [m]; 2nd column R0. Spatial grid 120x120 gridpoints (d from 0 m to 100 m) 150x150 gridpoints (d from 110 m to 250 m). Plotted as dashed curve in Fig. 1. The data was generated by numerical solution of Eq. (6) in the manuscript.

r0_vs_d_pl2.dat

#### R0 as a function of the field size for gaussian dispersal kernel

The file represents the basic reproductive number, R0, as a function of the field size for Gaussian dispersal kernel. 1st column distance [m]; 2nd column R0. Spatial grid 120x120 gridpoints. Plotted as dotted curve in Fig. 1. The data was generated by numerical solution of Eq. (6) in the manuscript.

r0_vs_d_gauss.dat

#### R0, as a function of the field size for power law 2 dispersal kernel, parameters for Madras 2002 experiment

The file represents the basic reproductive number, R0, as a function of the field size for power law 2 dispersal kernel, parameters for Madras 2002 experiment. 1st column distance [m]; 2nd column R0. Spatial grid 120x120 gridpoints. Plotted as points on the dashed blue curve in Fig. 3. The data was generated by numerical solution of Eq. (6) in the manuscript.

r0_vs_d_madr2002.dat

#### R0, as a function of the field size for power law 2 dispersal kernel, parameters for Hermiston 2002 experiment.

The file represents the basic reproductive number, R0, as a function of the field size for power law 2 dispersal kernel, parameters for Hermiston 2002 experiment. 1st column distance [m]; 2nd column R0. Spatial grid 120x120 gridpoints, except for last 3 points with 180x180 grid. Plotted as points on solid red curve in Fig. 3. The data was generated by numerical solution of Eq. (6) in the manuscript.

r0_vs_d_herm2002.dat

#### R0, as a function of the field aspect ratio for 4 ha field area, power law 2 dispersal kernel, parameters for Hermiston 2002 experiment.

The file represents the basic reproductive number, R0, as a function of the field aspect ratio for 4 ha field area, power law 2 dispersal kernel, parameters for Hermiston 2002 experiment. 1st column field aspect ratio; 2nd column R0. Spatial grid 150x150 gridpoints. Plotted as points on the solid yellow curve in Fig.4(a). The data was generated by numerical solution of Eq. (6) in the manuscript.

r0_vs_arat_herm2002_4ha.dat

#### R0 as a function of the field aspect ratio for 1 ha field area, power law 2 dispersal kernel, parameters for Hermiston 2002 experiment.

The file represents the basic reproductive number, R0, as a function of the field aspect ratio for 1 ha field area, power law 2 dispersal kernel, parameters for Hermiston 2002 experiment. 1st column field aspect ratio; 2nd column R0. Spatial grid 150x150 gridpoints. Plotted as points on the dashed blue curve in Fig.4(a). The data was generated by numerical solution of Eq. (6) in the manuscript.

r0_vs_arat_herm2002_1ha.dat

#### R0 as a function of the field aspect ratio for 0.2 ha field area, power law 2 dispersal kernel, parameters for Hermiston 2002 experiment.

The file represents the basic reproductive number, R0, as a function of the field aspect ratio for 0.2 ha field area, power law 2 dispersal kernel, parameters for Hermiston 2002 experiment. 1st column field aspect ratio; 2nd column R0. Spatial grid 150x150 gridpoints. Plotted as points on the dash-dotted red curve in Fig.4(a). The data was generated by numerical solution of Eq. (6) in the manuscript.

r0_vs_arat_herm2002_0.2ha.dat

#### R0 as a function of the field aspect ratio for 0.2 ha field area, power law 2 dispersal kernel, parameters for Hermiston 2002 experiment.

The file represents the basic reproductive number, R0, as a function of the field aspect ratio for 0.2 ha field area, power law 2 dispersal kernel, parameters for Hermiston 2002 experiment. 1st column field aspect ratio; 2nd column R0. Spatial grid 150x150 gridpoints. Plotted as points on the dotted orange curve in Fig.4(a). The data was generated by numerical solution of Eq. (6) in the manuscript.

r0_vs_arat_herm2002_0.1ha.dat

#### R0 as a function of the field aspect ratio for 4 ha field area, power law 2 dispersal kernel, parameters for Madras 2002 experiment.

The file represents the basic reproductive number, R0, as a function of the field aspect ratio for 4 ha field area, power law 2 dispersal kernel, parameters for Madras 2002 experiment. 1st column field aspect ratio; 2nd column R0. Spatial grid 150x150 gridpoints. Plotted as points on the solid yellow curve in Fig.4(b). The data was generated by numerical solution of Eq. (6) in the manuscript.

r0_vs_arat_madr2002_4ha.dat

#### R0 as a function of the field aspect ratio for 1 ha field area, power law 2 dispersal kernel, parameters for Madras 2002 experiment.

The file represents the basic reproductive number, R0, as a function of the field aspect ratio for 1 ha field area, power law 2 dispersal kernel, parameters for Madras 2002 experiment. 1st column field aspect ratio; 2nd column R0. Spatial grid 150x150 gridpoints. Plotted as points on the dashed blue curve in Fig.4(b). The data was generated by numerical solution of Eq. (6) in the manuscript.

r0_vs_arat_madr2002_1ha.dat

#### R0, as a function of the field aspect ratio for 0.2 ha field area, power law 2 dispersal kernel, parameters for Madras 2002 experiment.

The file represents the basic reproductive number, R0, as a function of the field aspect ratio for 0.2 ha field area, power law 2 dispersal kernel, parameters for Madras 2002 experiment. 1st column field aspect ratio; 2nd column R0. Spatial grid 150x150 gridpoints. Plotted as points on the dash-dotted red curve in Fig.4(b). The data was generated by numerical solution of Eq. (6) in the manuscript.

r0_vs_arat_madr2002_0.2ha.dat

#### R0, as a function of the field aspect ratio for 0.1 ha field area, power law 2 dispersal kernel, parameters for Madras 2002 experiment.

The file represents the basic reproductive number, R0, as a function of the field aspect ratio for 0.1 ha field area, power law 2 dispersal kernel, parameters for Madras 2002 experiment. 1st column field aspect ratio; 2nd column R0. Spatial grid 150x150 gridpoints. Plotted as points on the dotted orange curve in Fig.4(b). The data was generated by numerical solution of Eq. (6) in the manuscript.

r0_vs_arat_madr2002_0.1ha.dat