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CROP BREEDING & GENETICS

Generalizing the Sites Regression Model to Three-Way Interaction Including Multi-Attributes

^a Departamento de Matemática del Instituto Nacional de Ciencias Agrícolas, La Habana, Carretera Tapaste, Km 3 1/2, San José de Las Lajas, Apdo. Postal 32700, Habana, Cuba
^b Biometrics and Statistics Unit of the Crop Research Informatics Lab (CRIL), International Maize and Wheat Improvement Center (CIMMYT), Apdo. Postal 6-641, Mexico, D.F., Mexico
^c Dep. of Genetics and Plant Breeding, Institute of Agricultural Sciences, Banaras Hindu Univ., Varanasi 221 005, India; present address: CIMMYT South Asia Regional Office, P.O. Box 5186, Kathmandu, Nepal
^d Dep. of Plant and Soil Sciences and Dep. of Statistics, Univ. of Kentucky, Lexington, KY 40546-0312
^e Global Wheat Program, International Maize and Wheat Improvement Center (CIMMYT), Apdo. Postal 6-641, Mexico, D.F., Mexico

^* Corresponding author (j.crossa{at}cgiar.org).

When a multienvironment trial (MET) is established across several locations and years, the interaction is referred to as a three-way array. Three-way interaction can be studied by means of three-way principal components analysis. In this study, the three-way principal components analysis is adapted to the sites regression model (three-way SREG). The three-way SREG with location and year combines the effects of genotype, genotype x location, genotype x year, and genotype x location x year. The objective of this study is to show how the three-way SREG can be put to practical use in agriculture and breeding. We utilized two wheat (Triticum aestivum L) data sets that have already been used for fitting a three-way additive main effects and multiplicative interaction model. One data set had genotype (25) x location (4) x sowing times (4) and eight attributes, and the other data set included genotype (20) x irrigation level x year on grain yield. The three-way SREG applied simultaneously to eight attributes facilitates the interpretation of genotypic performance for all traits in specific locations and across locations for a selected sowing time. Results of the three-way SREG for both data sets show the different response patterns of genotypes for locations and sowing dates (Data Set 1), as well as genotypic responses across irrigation levels in different years (Data Set 2). Using Data Set 1, we show that fitting a three-way data structure to a three-way SREG model is more effective for detecting important interaction patterns than using the two-way SREG.

Abbreviations: AF, postanthesis drought stress • AMMI, additive main effect and multiplicative interaction • BF, preanthesis drought stress • CS, continuous drought stress • GE, genotype x environment interaction • GGE, genotype main effects and genotype x environment interaction • GLY, genotype x location x year • MET, multienvironment trial • NS, well-watered or nonstressed • SREG, sites regression model • SVD, singular value decomposition