EFFECTS OF INITIAL CONDITIONS, SPORULATION RATE, AND SPORE DISPERSAL GRADIENT ON THE SPATIOTEMPORAL DYNAMICS OF PLANT-DISEASE EPIDEMICS

A stochastic model that simulates the spread of disease over space and time was developed to study the effects of initial epidemic condition s (number of initial inocula and their spatial pattern), sporulation r ate, and spore dispersal gradient on the spatio-temporal dynamics of p lant disease epidemics. The spatial spread of disease was simulated us ing a half-Cauchy distribution with median dispersal distance mu (unit s of distance). The rate of temporal increase in disease incidence (be ta(1), per hay) was influenced jointly by mu and by the sporulation ra te lambda (spores per lesion per day). The relationship between beta(1 ) and mu was nonlinear: the increase in beta(1) with increasing mu was greatest when mu was small (i.e., when the dispersal gradient was ste ep). The rate of temporal increase in disease severity of diseased pla nts (beta(S)) was affected mainly by lambda: beta(S) increased directl y with increasing lambda. Intraclass correlation (kappa(t)), the corre lation of disease status of plants within quadrats, increased initiall y with disease incidence, reached a peak, and then declined as disease incidence approached 1.0. This relationship was well described by a p ower-law model that is consistent with the binary form of the variance power law. The amplitude of the model relating kappa(t) to disease in cidence was affected mainly by mu: kappa(t) decreased with increasing mu. The shape of the curve was affected mainly by initial conditions, especially the spatial pattern of the initial inocula. Generally, the relationship of spatial autocorrelation (rho(t,k)), the correlation of disease status of plants at various distances apart, to disease incid ence and distance was well described by a four-parameter power-law mod el. rho(t,k) increased with disease incidence to a maximum and then de clined at higher values of disease incidence, in agreement with a powe r-law relationship. The-amplitude of rho(t,k) was determined mainly by initial conditions and by mu: rho(t,k) decreased with increasing mu a nd was lower for regular patterns of initial inocula. The shape of the rho(t,k) curve was affected mainly by initial conditions, especially the spatial pattern of the initial inocula. At any level of disease in cidence, autocorrelation declined exponentially with spatial lag; the degree of this decline was determined mainly by mu: it was steeper wit h decreasing mu.