Using partial least squares regression, factorial regression, and AMMI models for interpreting genotype x environment interaction

Partial least squares (PLS) and factorial regression (FR) are statistical m odels that incorporate external environmental and/or cultivar variables for studying and interpreting genotype x environment inter action (GEI), The A dditive Main effect and Multiplicative Interaction (AMMI) model uses only t he phenotypic response variable of interest; however, if information on ext ernal environmental (or genotypic) variables is available, this can be regr essed on the environmental (or genotypic) scores estimated from AMMI and su perimposed on the AMMI biplot. The objectives of this study with two wheat [Triticum turgidum (L.) var. durum] field trials were (i) to compare the re sults of PLS, FR, and AMMI on the basis of external environmental land cult ivar) variables, (ii) to examine whether procedures based on PLS, FR, and A MMI identify the same or a different subset of cultivar and/or environmenta l covariables that influence GEI for grain yield, and (iii) to find multipl e FR models that include environmental and cultivar covariables and their c ross products that explain a large proportion of GEI with relatively few de grees of freedom. Results for the first trial showed that AMMI, PLS, and FR identified similar cultivar and environmental variables that explained a l arge proportion of the cultivar X year interaction Results for the second w heat trial showed good correspondence between PLS and FR for 23 environment al covariables. For both trials, PLS and FR complement each other and the A MMI and PLS biplots offered similar interpretations of the GEI. The FR anal ysis can be used to confirm these results and to obtain even more parsimoni ous descriptions of the GEI.