Use of the modified gregory model to describe primary disease gradients of wheat leaf rust produced from area sources of inoculum
1989
Mundt, C.C.
Primary disease gradients of wheat (Triticum aestivum) leaf rust (induced by Puccinia recondita) were studied around 3.66- X 3.66-m sources of infection in two fields in both Pendleton and Corvallis, OR. The gradients were described well by the modified Gregory model, y = a(x'+ c)-b, in which y is the number of infections per unit area, 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 of spores, c is a truncation factor that provides for a finite y-intercept when x'= 0, and b is a measure of the steepness of the gradient. The model-fitting showed that the modified Gregory model can be used to describe disease gradients away from area sources of inoculum in addition to gradients away from single source plants, for which the model was originally developed. For the Pendleton data, the truncation factor closely approximated the radius of the source when this parameter was estimated by nonlinear regression. For the Corvallis data, estimated values of c for the two fields were considerably less than the radius of the source. The modified Gregory model always provided a better fit to the data than did the Kiyosawa and Shiyomi model, an exponential function often used to describe gradients because it predicts a finite number of infections or propagules at the source.
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