Department of Plant Pathology, The Ohio State University, Wooster 44691.
Seventy-seven studies reporting Fusarium head blight disease index (Y; mean percentage of diseased spikelets per spike) and wheat yield (W; MT/ha) were analyzed to determine the relationship between W and Y, and to assess the degree of variation for the relationship among studies. A linear random-coefficient model—comprising a population-average intercept and slope, a random residual term, and random effects of study on the intercept and slope (best linear unbiased predictors; BLUPs)—was successfully fitted to the data using maximum likelihood. From the predicted random effects, study-specific intercepts and slopes were obtained, and both population-average and subject-specific predictions of yield were determined. The estimated population-average intercept (expected yield when disease symptoms were not present) was 4.10 MT/ha, and the population-average slope was 0.038 MT/ha per unit increase of disease index. Wheat class had a significant effect on the intercept but not on the slope, with soft-red winter wheat having, on average, 0.85 MT/ha higher yield than spring wheat. Based on the estimates of the among-study variances, there was high variation in the effects of study on the intercept, but substantially lower variation in the effects of study on the slope. Thus, although one cannot predict with accuracy the actual wheat yield in a field or plot based on disease index using population-average results, one can predict with accuracy the decline in yield at a given level of disease index using the population-average slope. Through the modeling results, predicted relative yield (as a percentage of yield when disease is not present) can be determined, as well as predicted disease index at which a prespecified level of yield (or yield loss) is expected to occur. The predicted reduction in yield on a percentage scale was greater for spring than for soft-red winter wheat, on average, because of the lower estimated intercept in absolute units for spring wheat.
Additional keywords:empirical Bayes model, hierarchical linear model, linear mixed model, studentized residual plot.