ABSTRACT
SUMMARY. In this paper, we compared the theoretical aspects and applications of two-way mixed models, viz., Scheffe-Calinski’s (S-C) model and Shukla’s (Sh) model. Both models were considered in their basic form and as multiplicative, joint regression models. Despite the different observed co variance matrices in pairs of both basic and regres sion models, they adequately described performance (stability) of geno types in randomly chosen environments. The statistical tools (estimators and tests) developed in the respective models (both basic and joint re gression) are optimal or have desirable properties. The models may be re garded as pairs of alternative, realistic, and of similar statistical and practical efficiency, approaches to analyzing genotype means (across en vironments) and phenotypic stability of two-way data. [Article copies avail able fo r a fee from The Haworth Document Delivery Service: I-8OO-HAWORTH. E-mail address: <docde livery @ haworthpress.com> Website: <https://www. HaworthPress.com> © 2005 by The Haworth Press, Inc. All rights reserved.]
KEYWORDS. Genotype-by-environment interaction, joint regression analysis, mixed two-way models, stability analysis
INTRODUCTION
Evaluation and interpretation of crop genotype-environment interac tions are often accomplished through phenotypic stability analyses of genotypes, which may be simply referred to as stability analyses (Lin et al., 1986; Becker and Leon, 1988; Lin and Binns, 1994; Kang, 1998; Piepho and van Eeuwijk, 2002). Stability analyses are usually conducted on multi-environment, two-way data, e.g., genotype-by-environment data. Environments may be locations in a given year or location-by-year combinations (Denis etal., 1997; Piepho, 1998; Annicchiarico, 2002ab; Piepho and van Eeuwijk, 2002). In most statistical approaches to stabil ity analysis, various forms of stability statistics are used to judge stabil ity of performance of studied genotypes (Lin et al., 1986; Becker and Leon, 1988; Kang, 1998; Piepho, 1998). These stability measures may be based on one of two model groups for genotype-by-environment classification. The first basic model in each group is a modification of the classic (with equal observation variances and covariances within any given environment) mixed model of variance analysis for two-way classification. The other models in the groups, called joint regression models, are extensions of the first respective basic models. Modifica tions and extensions of the models involve providing more appropriate assumptions for random effects in genotype-environment interaction analyses as well as allowing for regression procedures in interpreting the interaction.
