The relative efficiency of replicates in sweet corn hybrid disease nurseries and posterior probabilities as a measure of confidence in assigning sweet corn hybrids to disease reaction categories

The objectives of this research are to use Monte Carlo methods to determine the effect of replicate number on the absolute and relative ability of disease nurseries to classify hybrids into reaction categories and to calculate posterior probabilities with Bayes' theorem as a measure of confidence in assigning hybrids to reaction categories based on single or multiple trials. For each of three diseases (northern leaf blight, Stewart's wilt, and common rust), 1,000 simulated mean ratings each for 2,365 to 3,527 hybrids were produced as a random draw of two or three replicates. Boundaries for disease reaction categories from resistant (1) to susceptible (9) were assigned for each disease in each trial based on a combination of Waller-Duncan mean separation values, standardized z-scores, disease severity on standard hybrids, and cluster analyses. Simulated hybrid means were compared to the boundaries assigned to reaction categories and frequencies were calculated for the absolute value of the change in reaction compared to the reaction based on the input data. Two replicates appear sufficient in most cases to place hybrids within one category of the reaction based on the input data for the simulation. Data sets were generated using Monte Carlo methods from which to calculate posterior probabilities. For each of the three diseases, two individual trials with the highest and lowest frequency of simulated hybrids assigned to the same category as the reaction based on input means (i.e., the most and least accurate trials, respectively) were selected for the Monte Carlo simulation. Posterior probabilities were calculated from values based on one to four simulated years. Confidence in disease reaction categories to which hybrids were assigned improved when hybrids were evaluated in multiple trials. There is a very high probability in accurate trials that disease reactions reflect the relative disease performance of a hybrid. In less accurate trials, it appears that evaluating hybrids in three or four trials is necessary to achieve a similar level of confidence as a single accurate trial.