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Monte Carlo Distributions of Parameters Relating to a Superiority Measure for Cultivar Assessment

Statistical Res. Section, Res. Program Service, Agriculture Canada, Ottawa, ON, Canada K1A 0C6

^* Corresponding author.

A cultivar x location trial is the standard method for providing data by which new cultivars are assessed. To measure a test cultivar's general adaptability in such a trial, a superiority measure (designated as its P_i value) has been defined as the distance mean square between the test cultivar and the maximum yield at that particular location. A cultivar is considered to be better adapted if its P_i value is small. However, the distribution of differences from the maximum yield at each location in the context of cultivar x location data is unknown. This creates difficulties in measuring the difference between the cultivar mean and the mean of the maximum, and testing the pairwise interaction sum of squares between the maximum and the test cultivar. A computer program for Monte Carlo simulation can obtain approximations to the distribution of differences between the maximum location mean and a cultivar mean. This is then used to obtain probability intervals for comparing cultivar means with the location maximum. Approximate distributions are obtained for the P_i value and the pairwise genotype x environment interaction between the cultivar and the location maxima.

Received for publication May 26, 1992.