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Effects of Quadrat Size and Shape, Initial Epidemic Conditions, and Spore Dispersal Gradient on Spatial Statistics of Plant Disease Epidemics

The spatiotemporal spread of plant diseases was simulated using a stochastic model to study the effects of initial conditions (number of plants initially infected and their spatial pattern), spore dispersal gradient, and size and shape of sampling quadrats on statistics describing the spatiotemporal dynamics of epidemics. The spatial spread of disease was simulated using a half-Cauchy distribution with median dispersal distance μ (units of distance). A total of 54 different quadrat types, including 23 distinct sizes ranging from 4 to 144 plants, were used to sample the simulated epidemics. A symmetric form of the binary power law with two parameters (α, β) was fitted to the sampled epidemic data using each of the 54 quadrats for each replicate simulation run. The α and β estimates were highly correlated positively with each other, and their estimates were comparable to those estimated from observed epidemics. Intraclass correlation (κ) was calculated for each quadrat type; κ decreased exponentially with increasing quadrat size. An asymmetric form of the binary power law with three parameters (α ₁, β₁, β₂) was used to relate κ to the disease incidence (p); β1 was highly correlated to β: β1 ≈ β - 1. In general, initial conditions and quadrat size affected α, β, α₁, β₁, and β₂ greatly. The parameter estimates increased as quadrat size increased, and the relationships were described well by a linear regression model on the logarithm of quadrat size with the slope or intercept parameters dependent on initial conditions and μ. Compared with initial conditions and quadrat size, the overall effects of μ and quadrat shape were generally small, although within each quadrat size and initial condition they could be substantial. Quadrat shape had the greatest effect when the quadrat was long and thin. The relationship of the index of dispersion (D) to p and quadrat size was determined from the α and β estimates. D was greatest when p was 0.5 and decreased when p approached 0 or 1. It increased with quadrat size and the rate of the increase was maximum when p was 0.5 and decreased when p approached 0 or 1.