Coupling disease-progress-curve and time-of-infection functions for predicting yield loss of crops

A general approach was developed to predict the yield loss of crops in relation to infection by systemic diseases. The approach was based on two premises: (i) disease incidence in a population of plants over time can be described by a nonlinear disease progress model, such as the logistic or monomolecular; and (ii) yield of a plant is a function of time of infection (t) that can be represented by the (negative) exponential or similar model (ζ(t)). Yield loss of a population of plants on a proportional scale (L) can be written as the product of the proportion of the plant population newly infected during a very short time interval (X'(t)dt) and ζ(t), integrated over the time duration of the epidemic. L in the model can be expressed in relation to directly interpretable parameters: maximum per-plant yield loss (α, typically occurring at t = 0); the decline in per-plant loss as time of infection is delayed (γ; units of time^-1); and the parameters that characterize disease progress over time, namely, initial disease incidence (X₀), rate of disease increase (r; units of time^-1), and maximum (or asymptotic) value of disease incidence (K). Based on the model formulation, L ranges from αX₀ to αK and increases with increasing X₀, r, K, α, and γ^-1. The exact effects of these parameters on L were determined with numerical solutions of the model. The model was expanded to predict L when there was spatial heterogeneity in disease incidence among sites within a field and when maximum per-plant yield loss occurred at a time other than the beginning of the epidemic (t > 0). However, the latter two situations had a major impact on L only at high values of r. The modeling approach was demonstrated by analyzing data on soybean yield loss in relation to infection by Soybean mosaic virus, a member of the genus Potyvirus. Based on model solutions, strategies to reduce or minimize yield losses from a given disease can be evaluated.