Analysis of variance-mean relationships of plant diseases

Disease variance-mean relationships and the underlying mechanisms were examined using three approaches. First, data on four foliar diseases were collected. The variance of a disease increased geometrically, reached the maximum, and decreased geometrically when disease means were low, mediate, and high, respectively. There were great variations of variance values in the mediate ranges. Second, it was mathematically proven that the variance of a disease has an upper limit of variance (V-max) that follows a quadratic function. When a disease is rated in a range from 0 to C, the upper limit of variance (V-max) follows a quadratic function as V-max = CM-M(2) where M is disease mean. For the scale 0-10 or percentage [0-100], the functions are V-max = 10M-M(2) or V-max = 100M-M(2), respectively. A variance-mean relationship is distributed within the region defined by the V,, function. Third, a spatiotemporal simulation model was used to examine the effect of three spatial components, dispersal capacity, aggregation of initial inoculum, and geographic distribution of initial inoculum, on disease variance-mean relationship. The variance values increased as the dispersal capacity decreased. The variance values increased when pattern of initial inoculum changed from regular pattern to aggregation or as the degree of aggregation increased. There was an interactive effect between the two components on the variance values. Furthermore, when epidemics started from situations having the same degree of aggregation but different geographic distributions for initial inoculum, the variance-mean relationships were different. Variance values varied greatly even the degree of aggregation was constant. The importance of these results in relation to interpretation of field experiments was discussed.