Methods for estimating epidemiological effects of quantitative resistance to plant diseases

A model developed by R.C. Lewontin relating rate of population increase to key parameters of the organism's fecundity curve is described and adapted for use with plant pathogenic fungi. For diseases such as cereal rusts, rice blast, and powdery mildew and downy mildew of cucumber, the sporulation curves for the pathogens have been shown to follow an approximately triangular pattern. In the Lewontin model the key features of the pattern are: A, the time from inoculation to first sporulation (i.e. latent period); T, the time of peak spore production per day; W, the time at which sporulation ceases; and S, the area of the triangle (total reproduction per generation). For exponential increase, the values of A, T, W, and S are related to r ₁, the rate of population increase, according to the following equation: $$\begin{gathered} \gamma ^2 (W - A)/2S = [(e^{ - rA} - e^{ - rT} )/(T - A)] \hfill \\ {\text{ + }}[(e^{ - rW} - e^{ - rT} )/(W - T)] \hfill \\ \end{gathered} $$ This equation was used to generate families of curves showing effects on r ₁ of changes in the position of the triangle (altering latent period) or area (altering reproduction per generation). Data for barley leaf rust, oat crown rust, wheat leaf rust, wheat stem rust, rice blast, cucumber downy mildew, and cucumber powdery mildew were analyzed according to the model to show the effects of different components of resistance on r ₁ for each disease. Predictions from the model for barley leaf rust were compared with published data for components of resistance and rates of disease increase for eight barley cultivars. For cultivars of similar crop canopy type (two cultivars sparse; six cultivars, dense canopies), the predicted r ₁ values closely corresponded to observed values. Applications of the model to cultivar mixtures and to integrated control (involving protectant fungicides in combination with quantitative resistance) are also discussed.