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Effects of Initial Epidemic Conditions, Sporulation Rate, and Spore Dispersal Gradient on the Spatio-Temporal 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 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 (β_I, per day) was influenced jointly by μ and by the sporulation rate Λ (spores per lesion per day). The relationship between β_I and μ was nonlinear: the increase in β_I with 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 (β_S) was affected mainly by Λ: β_S increased directly with increasing Λ. Intraclass correlation (κ_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 κ_t to disease incidence was affected mainly by μ: κ_t decreased 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 (ρ_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. ρ_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 ρ_t,k was determined mainly by initial conditions and by μ: ρ_t,k decreased with increasing μ and was lower for regular patterns of initial inocula. The shape of the ρ_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 μ: it was steeper with decreasing μ.