Effects of prevailing wind direction on spatial statistics of plant disease epidemics

A stochastic simulation model was used to study the effects of the strength of prevailing wind (W), the size/ shape (Q) of sampling quadrats and their orientation in relation to the prevailing wind direction (D) on spatial statistics describing plant diseases. Spore dispersal followed a half-Cauchy distribution with median distance mu, which depended on simulated wind speed. The relationship of spatial autocorrelation at distance k (rho (k)) to disease incidence (p) and distance was well described by a four-parameter (alpha, beta (1), beta (2), beta (3)) power-law model at a given p, rhok declined exponentially with distance. A total of 35 different quadrat sizes, ranging from 4 to 432 plants, were used to sample the simulated epidemics for estimating intraclass correlation (kappa). The kappa -values decreased exponentially with increasing quadrat size, a binary power law model with three parameters (alpha, beta (4), beta (5)) successfully related kappa to p. In general, the effect of W and D was greatest on the parameters; alpha, beta (1), beta (2) and beta (3). The effect of W on alpha, beta (1), beta (2) and beta (3) depended critically on the spatial pattern of initial infected plants (Y) W had greatest effect for the random pattern. In contrast, the main effect of D and its interaction with W on the parameters alpha, beta (1), beta (2) and beta (3) were large and consistent over different initial conditions. Variations in alpha (1), beta (4) and beta (5) were predominantly due to Y and Q. Only for beta (5) under the clumped pattern was the effect of W very large. For the parameters alpha (1), beta (4) and beta (5) there was a large interaction among W, Q and D for the clumped and regular patterns. As expected, in general, the effect of D increased with increasing prevailing wind strength, quadrat size and quadrat length width ratio. Using square quadrats reduced significantly the effect of W on the parameters alpha (1), beta (4) and beta (5); however, the effect of W on beta (5) was still very large for the clumped pattern. Sampling perpendicular to the prevailing wind direction generally resulted in larger differences in the nine estimated parameters.