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Incidence and Density Relationships of Powdery Mildew on Apple

The relationships between disease incidence and colony density and between leaf and shoot disease incidences for apple powdery mildew were investigated over four seasons in order to derive a simple relationship for predicting density using incidence. The Neyman type A distribution generally provided a good fit to the observed number of colonies per leaf and shoot, and provided a significantly better fit than the Poisson distribution, indicating a degree of aggregation of mildew colonies. In general, Taylor's power-law satisfactorily described the observed variance-mean relationship for colony density; however, Taylor's power-law broke down at very high levels of mean density. Incidence of leaf infection could be determined based on average number of colonies per leaf assuming a fixed variance-mean relationship and a Neyman type A distribution for colony density. Regression models using the complemen- tary log-log transformation of incidence also provided accurate predictions of leaf (or shoot) disease incidence from colonies per leaf (or per shoot). Similar accuracies of these incidence-density models suggested that variance-mean ratio of colony density was more or less constant over time. Unlike the case with colony density, the number of mildewed leaves per shoot generally had a random pattern, as indicated by the good fit of the binomial distribution. Thus, it was possible to estimate the leaf incidence of the youngest unrolled leaves on a shoot using the shoot incidence. It is argued that the leaf incidence-density relationships developed in the present study may be used in making practical disease management decisions.