Additive Main Effects and Multiplicative Interaction Analysis of Two International Maize Cultivar Trials

Abstract

The methodology used by the International Maize and Wheat Improvement Center (CIMMYT) to develop and improve its maize (Zea mays L.) germplasm involves evaluation of families or experimental varieties in extensive international testing trials. The genotype‐environmental interaction is produced by differential genotypic responses to varied environmental conditions. Its effect is to limit the accuracy of yield estimates and complicate the identification of specific genotypes for specific environments. The objective of this study was to use the Additive Main effects and Multiplicative Interaction (AMMI) method, with additive effects for genotypes and environments and multiplicative terms for genotype‐environment interaction, for analyzing data from two international maize cultivar trials. Results from the first trial were: (i) predictive assessment selected AMMI with one principal component axis, (ii) AMMI increased the precision of yield estimates equivalent to increasing the number of replications by a factor of 4.30, (iii) AMMI provided much insight into genotype‐environment interactions, and (iv) AMMI selected a different highest‐yielding genotype than did treatment means in 72% of the environments. Results for the second trial were that predictive assessment selects the AMMI with none of the principal component axes, which increased precision equivalent to increase the number of replications by a factor of 2.59.

Use of AMMI and other stability statistics in the simultaneous selection of rice genotypes for yield and stability under direct-seeded conditions

“…The AMMI method is used for three main purposes. The first is that the model diagnoses other models; secondly, AMMI clarifies GEI and summarizes patterns and relationships of G and E (Zobel et al, 1988;Crossa et al, 1990), and the third use is the accuracy of yield estimates (Zobel et al, 1988;Crossa et al, 1990). The GEI was further partitioned by PCA (Table 3 and Figure 1).…”

“…The importance of GEI in national cultivar evaluation and breeding programs has been demonstrated in almost all major crops (Najafian et al, 2010;Zali et al, 2011). Various statistical methods/ models (parametric and non-parametric), concepts, and definitions of stability have been described over the years by many researchers (Lin et al, 1986;Becker and Léon, 1988;Crossa et al, 1990;Lin and Binns, 1994;Hussein et al, 2000;Mohammadi and Amri, 2008;Mohammadi et al, 2010). The model used for GEI is similar to a static or biological concept of stability (Becker and Léon, 1988) and the parameters used in the study are the coefficient of determination (Ri 2 ) (Pinthus, 1973), coefficient of variability (CVi) (Francis and Kannenberg, 1978), and the genotypic variances across environments (Si 2 ) (Roemer, 1917).…”

“…Similarly, another model is the dynamic or agronomic concept of stability (Becker and Léon, 1988) where the parameters used are the regression coefficient (bi) (Finlay and Wilkinson, 1963) and Shukla's stability variance (σi 2 ) (Shukla, 1972), the regression coefficient (bi), and deviation from regression (Sd i 2 ) (Eberhart and Russell, 1966;Perkins and Jinks, 1968). The main problem with stability statistics is that a single model cannot provide an accurate picture because of the genotype's multivariate response to varying environments (Lin et al, 1986), whereas stability indices are usually univariate (Gauch, 1988;Crossa et al, 1990).…”

“…Among the multivariate methods, the additive main effects and multiplicative interaction (AMMI) analysis is widely used for GEI investigation. This method has been effective because it captures a large portion of the GEI sum of squares; it clearly separates main and interaction effects and often provides meaningful interpretation of data to support a breeding program such as genotype stability (Gauch and Zobel, 1989;1996;1997;Crossa et al, 1990). The AMMI model combines ANOVA for the genotype and environment main effects with principal components analysis of GEI (Zobel et al, 1988;Gauch and Zobel, 1996).…”

Grain yield performance and flowering synchrony of CIMMYT’s tropical maize (Zea mays L.) parental inbred lines and single crosses

“…Simple linear correlation between GY and AD was carried out using PROC CORR of SAS. Based on results of ANOVA indicating significant G 9 E for GY in the trials, Additive Main effects and Multiplicative Interaction (AMMI) analysis (Crossa et al 1990) was used to assess G 9 E and stability of genotypes. The AMMI analysis uses principal component analysis (PCA) to decompose the multiplicative effects (G 9 E) into a number of interaction principal component axes (IPCA).…”