An investigation of multi-attribute genotype response across environments using three-mode principal component analysis

Abstract

SummaryThe usefulness of three-mode principal component analysis to explore multi-attribute genotype-environment interaction is investigated. The technique provides a general description of the underlying patterns present in the data in terms of interactions of the three quantities (attributes, genotypes, and environments) involved. As an example, data from an Australian experiment on the breeding of soybean lines are treated in depth.

A multi-trait multi-environment QTL mixed model with an application to drought and nitrogen stress trials in maize (Zea mays L.)

“…Well known examples of such models are the regression on the mean model (Finlay and Wilkinson 1963) and the Additive Main effects and Multiplicative Interaction effects model, or, AMMI model, (Gollob 1968;Gabriel 1978;Gauch 1988). Fixed multiplicative models can be generalised to multi-trait GEI analysis, for example in the form of three-mode principal components (Kroonenberg and Basford 1989;Basford et al 1991;Crossa et al 1995). By determining low dimensional approximations (principal components) to the structure present in the three classification modes of genotypes, environments, and traits, GEI patterns across traits can be studied (van Eeuwijk and Kroonenberg 1995;Varela et al 2006).…”

Ecotype differentiation of Ribes rubrum in Norway

“…Correlations between characters are established enabling early selection (Acquaah et al ., 1992) . Specific combining ability can be understood and Cluster I I 1 exploited (Kroonenberg & Basford, 1989) . Variation in crossing can be increased by choosing parents from different clusters (Dale et al ., 1993 ;Ajmone-Marsan et al ., 1992 ;Souza & Sorrells, 1989) .…”

Multivariate Analyses to Display Interactions between Environment and General or Specific Combining Ability in Hybrid Crops

“…Therefore, several solutions have to be inspected to come to an adequate description of a dataset (Kroonenberg, 1983, chap. 2; Kroonenberg and Basford, 1989).…”

“…If F × E, M × E and/or F × M × E interactions explain a large portion of the variance in a half‐sib mating design study (i.e., GCA F × E, GCA M × E and/or SCA × E interactions are important), then it would be useful to examine the three‐way matrix of F × M × E means. Three‐mode PCA (Tucker, 1966; Kroonenberg, 1983), an extension of the standard PCA to handle such three‐way datasets, has been used for handling genotypes, environments, and attributes simultaneously (Kroonenberg and Basford, 1989; Basford et al, 1990; Chapman et al, 1997; de la Vega et al, 2002; Bertero et al, 2004), allowing an examination of the relationships between genotypes and attributes associated with specific patterns of environmental variability. In the same way, we propose that three‐mode PCA can be used to display the relationships between female and male inbred lines associated with predictable or unpredictable environmental contrasts.…”