VIEW ARTICLE

Ecology and Epidemiology

Empirical Estimation of the Asymptotes of Disease Progress Curves and the Use of the Richards Generalized Rate Parameters for Describing Disease Progress. E. W. Park, Graduate research assistant, Agricultural Research Service, U.S. Department of Agriculture, and Department of Plant Pathology, University of Illinois at Urbana-Champaign, Urbana 61801; S. M. Lim, plant pathologist and professor, Agricultural Research Service, U.S. Department of Agriculture, and Department of Plant Pathology, University of Illinois at Urbana-Champaign, Urbana 61801. Phytopathology 75:786-791. Accepted for publication 20 December 1984. This article is in the public domain and not copyrightable. It may be freely reprinted with customary crediting of the source. The American Phytopathological Society, 1985. DOI: 10.1094/Phyto-75-786.

The effect of fixing the asymptote parameter of growth functions at 1 on estimates of the rate parameter and the use of generalized rate parameters proposed by Richards are discussed. When disease progress curves have asymptotes which are less than 1, the asymptote parameter of growth functions needs to be estimated empirically; otherwise, underestimation of the rate parameter of growth functions (e.g., Vanderplank's apparent infection rate, r) and changes in the rank of estimates of the rate parameter may result from fixing the asymptote parameter of growth functions at 1. The use of the weighted mean absolute growth rate and the weighted mean relative growth rate of the Richards function as the “absolute rate of disease progress” (Ra) and the “relative rate of disease progress” (Rr), respectively, is proposed for describing and comparing epidemics with different asymptotes and shapes of disease progress curves. Since they are determined empirically without the unrealistic assumption on the upper limit of disease severity, they provide more accurate information on disease development than Vanderplank's apparent infection rate or the rate parameter of growth functions with the asymptote value of 1. Development of bacterial blight in a soybean field was described using Ra and Rr.