engleski

AMMI model analyses of data sets with large amount of missing cells

Variety trials usually result in data sets with certain amount of missing cells (genotype x environment combinations). Each year some varieties complete the testing, others are withdrawn, and new varieties enter the trials. In Croatia, a variety is present in trials for, at most three years, except for the few standard varieties (checks), present in every environment throughout the years. Therefore, variety trials with four cereal crops, used in this research, contained only Ż (one third) of the possible treatments (genotype x environment combinations). Fitting AMMI (Additive Main effect and Multiplicative Interaction) models to these unbalanced data employed the EM (Expectation-Maximization) algorithm. Detecting the best model from the resulting family of models required assessment of postdictive and predictive accuracy. For most of the calculations we used MATMODEL (Gauch, 1998), as well as SAS software. Spring oats data set of 13 genotypes and 28 environments is best fitted with AMMI1 model. It has the smallest RMSPD (root mean square prediction difference, recovers most of the pattern, and its residual RMS (root mean square) is 5% of the grand mean. Larger, barley data sets &#8211 ; ; spring barley 39 G x 29 E and winter barley 44 G x 25 E are best fitted with AMMI4 or AMMI5 models, according to their RMSPD and pattern recovery. Finally, winter wheat data set, being the largest with 238 genotypes and 31 environment, could not be fitted even with AMMI7 model. All data sets have 66-69% of missing cells, but differed in size and genotype/environment ratio. Smallest data set has less genotypes than environments, being best fitted with AMMI1 model. Fitting larger data sets with more genotypes than environments (up to 7 times) required complex models with 5-7 IPCA axes. Hence, for these data sets AMMI analysis does not offer convenient interpretation of complex interaction patterns. However, predictive accuracy of these models, based on their successful pattern recovery (even complex like in these data sets), enables their use in selection.

variety trials; AMMI; EM; MATMODEL; RMSPD

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