A Modification of Gregory's Model For Describing Plant Disease Gradients

Abstract

Gregory proposed that plant disease gradients can be described by the equation y = ax-b in which y is the number of infections per unit area at distance x from the inoculum source (with x = 0 defined as the boundary between source and receptor plants), a is the number of infections per unit area at one unit of distance from the source, and b is a measure of the steepness of the gradient. The model does not predict a finite number of infections at the source and, therefore, has not been used in computerized simulators in which it is necessary to calculate the amount of autoinfection on source plants. We modified Gregory''s model to y = a(x'' + c) in which a is the number of infections per unit area at 1 - c units of distance from the source, x'' is the distance from the center of the source to the center of a receptor, and c is a truncation factor that provides for a finite y-intercept when x'' = 0. The modified model produces curves with shapes similar to those produced by Gregory''s original model, but predicts a finite amount of infection on source plants. The modified Gregory model was fit to data from primary disease gradients of oat crown rust, common maize rust, and bean rust by using nonlinear regression. For oat crown rust and maize rust, and model adequately described the gradients and provided reasonable estimates of autoinfection. The model fit the bean rust data less well and overpredicted autoinfection on source plants. Values of c estimated by regression were approximately equal to the radius of the source plant for all 3 diseases.