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

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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 μ (units of distance). The rate of temporal increase in disease incidence (βI, per day) was influenced jointly by μ and by the sporulation rate λ (spores per lesion per day). The relationship between βIand μ was nonlinear: the increase in βIwith increasing μ was greatest when μ was small (i.e., when the dispersal gradient was steep). The rate of temporal increase in disease severity of diseased plants (βS) was affected mainly by λ: βSincreased directly with increasing λ. Intraclass correlation (κt), 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 κtto disease incidence was affected mainly by μ: κtdecreased with increasing μ. 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 (ρt,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. ρt,kincreased 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 ρt,kwas determined mainly by initial conditions and by μ: ρt,kdecreased with increasing μ and was lower for regular patterns of initial inocula. The shape of the ρt,kcurve 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 μ: it was steeper with decreasing μ.