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-M² where M is disease mean. For the scale 0–10 or percentage [0–100]. the functions are V_max= 10M-M² or V_max=100M-M², respectively. A variance-mean relationship is dis-tributed within the region defined by the V,_max function. Third, a spatio-temporal 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 inreased as the dispersal capacity decreased. The variance values inreased when pattern of mitial 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 epi-demics started from situations having the same degree of aggregation but different geographic distributions for initial inoculum, the variance-mean relationships weredifferent. Variance values varied greatly even the degree of aggregation was constant. The inportance of these results in relation to interpretation of field experiments was discussed.