A diallel mating design (in which each line is crossed with every other line) is a commonly used experimental design for crossing inbred lines (Jenson, 1970). It is the most extensively used design to understand the nature of gene action involved in the expression of quantitative traits (Singulas et al., 1988). It allows estimations of general and specific combining abilities (Singulas et al., 1988). A complete diallel evaluates the variances due to the crosses, parents, and reciprocal effects (Falconer and Makay, 1996). However, Halleur and Miranda (1988) indicated that for ease of management of the crosses, diallel mating design is practically more applicable with few parents.
On the other hand, the North Carolina design I (NC I) which was introduced by Halleur (1992) enables the breeder to test a large number of plants from a population, and is usually important when using an unequal number of parents as male and female. The NC I provides a simple means of estimating additive genetic variance (VA) and dominance variance (VD) by allowing the between families statistics to be subdivided.
The uniqueness of this design is that factors are nested in one another instead of being crossed in a factorial design. Hallauer and Miranda (1988) indicated that NC I is more frequently used in maize breeding than any other mating design other than the diallel.
With the North Carolina design II (NC II) all progeny families obtained from crossing males to females are raised. The NC II design estimates variance components in addition to GCA and SCA. Its major advantage is handling a larger number of parents in each experiment (Singulas et al., 1988). The male and female mean squares are estimated from the GCA, while the interaction between males and females is equivalent to the SCA variance of the diallel analysis (Halleur and Miranda, 1988). Similarly, dominance variance is estimated directly from the mean squares (Falconer and Mackay, 1996).
1.18 Genotype X environment interaction
In addition to genotype and environment main effects, performance of cultivars is also determined by genotype x environment interaction (G x E), which is the differential response of cultivars to environmental changes (Vargas et al., 2001). There are three
35
common types of G x E interaction, namely cultivar x location interaction; cultivar x year interaction; and cultivar x location x year interaction effects (Crossa, 1990). These G x E interactions are explained by variation in weather between and within seasons and soil properties, among other factors. For example, Troyer (1996) reported that cultivar x year interaction was larger than cultivar x location interaction due to differing soil moisture availability at flowering. Crossover interaction is the G x E interaction that changes the rank order for performance of cultivars. At times G x E does not change the rank order except for absolute differences of cultivar performance in the different environments. Crossover interaction causes problems in crop breeding because it impedes selection progress due to changing composition of cultivars selected in different environments (Cooper and Delacy, 1994; Crossa et al., 1995).
1.18.1 Stability of yield and yield components
Stable cultivars have little interaction with environments (Tollenaar and Lee, 2002).
Becker and Leon (1988) defined two types of stability, namely static or dynamic. In static stability, cultivar yield does not change; but with dynamic stability cultivar yield changes in a predictable manner, and its stability is affected by the set of cultivars under evaluation (Becker and Leon, 1988; Tollenaar and Lee, 2002). Thus, static stability is an absolute measure, while dynamic stability is a relative measure. In cultivar selection, the best cultivar should effectively exploit the high inputs under favorable conditions and display acceptable grain yield under relatively low input systems. Finlay and Wilkinson (1963) suggested that dynamic stability could be preferred. This dynamic concept of stability is measured by the regression analysis as described by Finlay and Wilkinson (1963) and is sometimes referred as the parametric statistic.
Lin et al. (1986) reviewed the nonparametric statistics for evaluating G x E. These stability statistics are not influenced by the set of cultivars under evaluation. Lin et al.
(1986) defined a stable cultivar as having a small variance and a similar deviation from the overall mean yield in all the environments. Lin and Binns (1988) also reported the
36
cultivar superiority index, which they defined as the mean square of the differences between the cultivar’s response and the maximum response in different environments.
Grain yield stability is influenced by the genetics of the cultivar. Eberhart and Russell (1966) reported that the use of genetic mixtures rather than homogeneous cultivars reduced G x E interaction due to population buffering in a heterogeneous population.
Lee et al. (2003) reported that double cross hybrids had smaller G x E interaction, than single cross hybrids, which are more homogeneous. However, it is also possible that some single crosses could be more stable than the three-way and double cross hybrids (Eberhart and Russell, 1966). Grain yield stability can be improved through recurrent selection because it is heritable and largely controlled by additive gene action (Lee et al., 2003). In addition, stable cultivars can be identified through multi-location trials in targeted environments (Troyer, 1996). The high grain yield potential and adaptation of Pioneer hybrids to the USA were obtained through extensive multi-location trials (Duvick and Cassman, 1999; Evans and Fischer, 1999). It is, thus, prudent to evaluate regionally important germplasm under varied environments.
1.18.2 Additive Main Effects and Multiplicative Interaction (AMMI) model
Data from multi-location trials help researchers estimate yield more accurately, select better production alternatives, and understand the interaction of yield with environments. In breeding programs it is of interest to decide whether observed stability differences are due to chance or statistically significance difference. Significance testing is strongly advisable to determine the quality of stability estimates (Crossa et al., 1995).
A broad range of multivariate methods can be used to analyze multi-location yield trial data to asses yield stability. Although some of them overcome the limitations of linear regression, the results are often difficult to interpret in relation to GEI. Multivariate techniques are widely applied in stability analysis to investigate multivariate response of genotypes to environments. Among the multivariate analysis techniques, AMMI model is the powerful method in assessing GEI and stability or adaptation of genotypes from
37
multi-environment trials. AMMI is essentially effective where the assumption of linearity of responses of genotype to a change in environment is not fulfilled, which is an important aspect in stability analysis. The results can be graphed in a useful biplot that shows both main and interaction effects for both genotypes and environments (Gauch and Zobel, 1996).
The integration of certain ordination methods into “pattern” analysis and the bi-plot method are valuable tools for grouping environments or genotypes showing similar response patterns. The combination of analysis of variance and principal component analysis in the AMMI model, along with the prediction assessment, is a valuable approach for understanding genotype x environment interaction and obtaining better yield estimates. Agronomic predictive assessment with AMMI can be used to analyze the results of trials (Chukan, 2010).
AMMI analysis is helpful to choose the most stable hybrid and to group hybrids with a location where they have good specific adaptability. Adaptation to unsuitable conditions would also be shown. Thus the AMMI model was proved to be a useful tool in diagnosing the G x E interaction patterns and improving the accuracy of the response estimates in these trials. It provided more precise estimates of the true yield potential of both cultivars and specific environments where individual tests were evaluated.
Increased accuracy in selection could help researchers identify specific cultivars with competitive yields across diverse environments (Zerihun, 2011).
1.18.3 GGE biplot analysis
The GGE (genotype and genotype by environment interaction) biplot analysis is increasingly being used in GEI studies in plant breeding research (Butran et al., 2004;
Samonte et al., 2005). Visualization of “which won where” pattern of multi environment yield trial (MEYT) data is necessary for studying the possible existence of different mega environments (Gauch and Zobel, 1997; Yan et al., 2000; Yan, 2001). The polygon
38
view of a biplot is the best way to visualize the interaction patterns between genotypes and environments (Yan and Kang, 2003) to show the presence or absence of cross over GEI which is helpful in estimating the possible existence of different mega environments (Gauch and Zobel, 1997; Yan and Rajcan, 2002; Yan and Tinker, 2006).
The polygon is formed by connecting the markers of genotypes that are further away from the biplot origin such that all genotypes are contained in the polygon (Kaya et al., 2006). The genotypes which are located on vertices of the polygon formed are either the best or poorest in one or more environments (Yan et al., 2000; Yan and Rajcan, 2002; Yan and Tinker, 2006). The vertex genotypes in each sector is also the best genotype for sites whose markers fell into the respective sector so that sites within the same sector share the same winning genotype (Yan, 1999; 2002; Yan et al., 2000). On the biplot, rays or lines that are drawn perpendicular to the sides of the polygon divide it into sectors.
1.18.4 Regression approach and its limitations in stability analysis
Crossa (1990) reviewed the limitations of regression analysis of stability. He reported that with few cultivars (less than 15) the mean of cultivars would not be independent of the marginal means of the environments. The regression analysis is not effective in the absence of a linear relationship between cultivar x environment interaction and the environmental means. Stability of a cultivar measured by regression analysis of a few and/or extreme environments would not provide reliable information, due to the high levels of bias. In the same vein, stability of a cultivar depends on the set of cultivars evaluated; hence application of the results from a regression analysis is limited to the specific set of environments and cultivars evaluated. Alternatives to the regression analysis are several nonparametric statistics. Huehn (1990) reviewed the rank analyses used in studying G x E interactions. These statistics have some advantages over the regression analysis such as reduction of bias caused by outlying cultivars and they are easy to interpret. In addition, the assumptions about the distribution of data, homogeneity of variances and linearity are not required for rank analyses (Huehn, 1990).