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 stochasti c model to study the effects of initial conditions (number of plants initia lly 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 mu (units of dista nce). A total of 54 different quadrat types, including 23 distinct sizes ra nging from 4 to 144 plants, were used to sample the simulated epidemics. A symmetric form of the binary power law with two parameters (alpha, beta) wa s fitted to the sampled epidemic data using each of the 54 quadrats for eac h replicate simulation run. The ct and beta estimates were highly correlate d positively with each other, and their estimates were comparable to those estimated from observed epidemics. Intraclass correlation (kappa) was calcu lated for each quadrat type; kappa decreased exponentially with increasing quadrat size. An asymmetric form of the binary power law with three paramet ers (alpha(1), beta(1), beta(2)) was used to relate kappa to the disease in cidence (p); beta(1) was highly correlated to beta: beta(1) approximate to beta - 1. In general, initial conditions and quadrat size affected alpha, b eta, alpha(1), beta(1), and beta(2) greatly. The parameter estimates increa sed 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 mu. Compared wi th initial conditions and quadrat size, the overall effects of mu and quadr at shape were generally small, although within each quadrat size and initia l condition they could be substantial. Quadrat shape had the greatest effec t when the quadrat was long and thin. The relationship of the index of disp ersion (D) to p and quadrat size was determined from the alpha and beta est imates. 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.