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This article in CS

  1. Vol. 39 No. 4, p. 955-967
    Received: July 2, 1998

    * Corresponding author(s): JCROSSA@CIMMYT.MX


Using Partial Least Squares Regression, Factorial Regression, and AMMI Models for Interpreting Genotype × Environment Interaction

  1. Mateo Vargas,
  2. José Crossa ,
  3. Fred A. van Eeuwijk,
  4. Martha E. Ramírez and
  5. Ken Sayre
  1. P rograma de Estadística del Instituto de Socioeconomía, Estadística e Informáitica (ISEI), Colegio de Postgraduados, CP 56230, Montecillo, Mexico, and International Maize ad Wheat Improvement Center (CIMMYT), Lisboa 27, Apdo. Postal 6-641, 06600 Mexico, D.F., Mexico;
    B iometrics and Statistics Unit, CIMMY, Lisboa 27, Apdo. Postal 6-641, 06600 Mexico, D.F., Mexico;
    D ep. of Agricultural, Environmental and Systems Technology, Wageningen Agricultural Univ., Dreijenlaan 4, 6703 HA Wageningen, the Netherlands;
    P rograma de Estadística del Instituto de Socioeconomía, Estadistica e Informática (ISEI), Colegio de Postgraduados, CP 56230, Montecillo, Mexico;
    W heat Program, CIMMYT, Lisboa 27, Apdo. Postal 6-641, 06600 Mexico, D.F., Mexico.



Partial least squares (PLS) and factorial regression (FR) are statistical models that incorporate external environmental and/or cultivar variables for studying and interpreting genotype × environment interaction (GEl). The Additive Main effect and Multiplicative Interaction (AMMI) model uses only the phenotypic response variable of interest; however, if information on external environmental (or genotypic) variables is available, this can be regressed on the environmental (or genotypic) scores estimated from AMMI and superimposed on the AMMI biplot. The objectives of this study with two wheat [Triticum turgidum (L.) var. durum] field trials were (i) to compare the results of PLS, FR, and AMMI on the basis of external environmental (and cultivar) variables, (ii) to examine whether procedures based PLS, FR, and AMMI identify the same or a different subset of cultivar and/or environmental covariables that influence GEI for grain yield, and (iii) to find multiple FR models that include environmental and cultivar covariables and their cross products that explain a large proportion of GEI with relatively few degrees of freedom. Results for the first trial showed that AMMI, PLS, and FR identified similar cultivar and environmental variables that explained a large proportion of the cultivar × year interaction. Results for the second wheat trial showed good correspondence between PLS and FR for 23 environmental covariables. For both trials, PLS and FR complement each other and the AMMI and PLS biplots offered similar interpretations of the GEl. The FR analysis can be used to confirm these results and to obtain even more parsimonious descriptions of the GEL

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