Effects of Initial Epidemic Conditions, Sporulation Rate, and Spore Dispersal Gradient on the Spatio-Temporal Dynamics of Plant Disease Epidemics

Abstract

ABSTRACT A stochastic model that simulates the spread of disease over space and time was developed to study the effects of initial epidemic conditions (number of initial inocula and their spatial pattern), sporulation rate, and spore dispersal gradient on the spatio-temporal dynamics of plant disease epidemics. The spatial spread of disease was simulated using a half-Cauchy distribution with median dispersal distance mu (units of distance). The rate of temporal increase in disease incidence (beta(I), per day) was influenced jointly by mu and by the sporulation rate lambda (spores per lesion per day). The relationship between beta(I) and mu was nonlinear: the increase in beta(I) with increasing mu was greatest when mu was small (i.e., when the dispersal gradient was steep). The rate of temporal increase in disease severity of diseased plants (beta(S)) was affected mainly by lambda: beta(S) increased directly with increasing lambda. Intraclass correlation (kappa(t)), the correlation of disease status of plants within quadrats, increased initially with disease incidence, reached a peak, and then declined as disease incidence approached 1.0. This relationship was well described by a power-law model that is consistent with the binary form of the variance power law. The amplitude of the model relating kappa(t) to disease incidence 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 incidence and distance was well described by a four-parameter power-law model. rho(t,k) increased with disease incidence to a maximum and then declined at higher values of disease incidence, in agreement with a power-law relationship. The amplitude of rho(t,k) was determined mainly by initial conditions and by mu: rho(t,k) decreased with increasing mu and 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 incidence, autocorrelation declined exponentially with spatial lag; the degree of this decline was determined mainly by mu: it was steeper with decreasing mu.