5. Structure of the dissertation
1.11 Genotype by environment interaction in maize
The phenotype of an individual is determined by the genotype, environment and the interaction between genotype and environment (Martin, 2004). Genotype X environment interaction (GXE) causes complications in selecting hybrids for broad adaptation (Martin, 2004; Abdurahman, 2009; Babić et al., 2011). The relationship between phenotypic and genotypic values is impaired by the large GXE interaction (Ilker, 2011), hence the role of GXE interaction must be quantified in order to devise a breeding strategy. Genotype X Environment interaction is very important in sub-Saharan Africa because of fluctuation in environmental conditions, drought, low soil fertility, non-uniform management practices
and occurrence of diseases and pests (Martin, 2004). GXE is quantified by conducting multi- environment testing.
I. Crossing over interaction
Crossing over of genotypes is change in a genotype’s rank from one environment to another (Crossa, 1990; Abdurahman, 2009). Crossa (1990) further explained that in crossing over, genotypic differences vary in direction among environments whereas; with non-crossing over genotypes reflects differences in magnitudes but not in direction. An appropriate stable cultivar which is capable of using resources that are available in high yielding environments, while maintaining above average performance in all other environments can also be identified (Nagabushan, 2008; Kandus et al., 2010). On the other hand, adaptability refers to the capacity of genotypes to give high yield under specific conditions. Cross over interaction delays the breeding progress as different sets of genotypes are selected in each environments (Abdurahman, 2009). Therefore there is a need to breed for genotypes with a wide adaptability to withstand different environmental conditions. Breeding for specifically adapted genotypes could also be an option; however, it is not durable because environmental conditions on the same locations change from year to year.
II. Analysis of Genotype X Environment interaction
Analysis of variance
Kandus et al. (2010) reported that combined ANOVA is frequently used to identify the existence of GXE interaction in multi-environmental experiments. Nonetheless, combined analysis has limitations that it assumes homogeneity of variance among environments required to determine differences among genotype differences (Kandus et al., 2010). Even though this analysis manage to determine the variance due to genotype, environment and the GXE interaction, it does not explore the response of the genotypes in the non-additive term (Kandus et al., 2010). Stability analysis is a tool that provides a general solution for the response of the genotypes to environmental change (Crossa, 1990; Kandus et al., 2010) .
Non-parametric test
The non-parametric statistics for GXE interaction based on ranks provide a useful alternative to parametric statistics, if the breeder is only interested in the existence of rank order differences over different environments (Martin, 2004). The rank order provides the breeder with the information of genotypes which are well ranked in all environments and those which are specifically well ranked in one environment. Principal component analysis (PCA) has more advantages than regression methods, because the regression method uses one statistic, the regression coefficient, to describe the pattern of response of a genotype across environments, and most of the information is wasted in accounting for deviations (Martin, 2004). On the other hand, PCA overcomes this difficulty by providing the scores on the PCA to describe the response pattern of genotypes (Crossa, 1990). The scores allows depicting GXE interactions into two dimensions (biplot) and identifying the factor responsible for the interaction (Abdurahman, 2009). The biplots provide a clear picture of genotypes and environments which are stable and the association between this. It also has the ability to group similar genotypes and environments in terms of stability. Crossa (1990) pointed out that the aim of principal analysis is to transform the data from one set of coordinate axes to another, which preserves as much as possible the original configuration of the set of points and concentrates most of the data structure in the first principal component axes. This analysis assumes that the original variables define a Euclidean space and similarity between individuals is measured as Euclidian distance (Crossa, 1990). As a result the structure of a two-way genotype-environment analysis data matrix is subspace of fewer dimensions (Crossa, 1990). Other methods can be used to group similar genotypes and environments, for example, Martin (2004) defined cluster analysis as a numerical classification technique that defines groups of clusters of individuals. There are two types of classification, non- hierarchical which assigns each item to a class and hierarchical groups which assigns the individuals into clusters and arranges these into a hierarchy for the purpose of studying relationships in the data (Crossa, 1990).
Additive Main effect and Multiplicative Interaction
The Additive Main effect and Multiplicative Interaction (AMMI) model encompasses several sources such as genotype main effect, environment main effect and the interaction with 0-F interaction’s PCA axes (IPCA) and can thus be used to predict GXE (Crossa, 1990; Babić et al., 2011). Crossa (1990) mentioned that the AMMI model is used for model diagnosis to clarify GXE and to improve accuracy of yield estimates. Additionally, Babić et al. (2011) mentioned that the greatest benefit of AMMI is better understanding of genotypes, environments and the complex of their interactions. This basically helps in allocating genotypes to environments they are adapted to and in identifying the best environment for evaluation of genotypes. AMMI models can range from AMMI(1), AMMI(2) to AMMI(n), depending on the number of principal components used to study the interaction (Kandus et al., 2010). In the current study the AMMI-2 model was adopted.
1.12 Cultivar superiority and rank analysis
The stability of genotypes is studied by using simple and effective methods such as cultivar superiority and ranking methods. Lin and Binns (1988) defined a superior cultivar as one with a performance near the maximum in various environments. The genotypes are characterised with a parameter (Pi) by associating stability with productivity (Lin and Binns, 1988), in this way genotypes which are stable and high yielding can be identified. In other words this helps in identifying and separating genotypes with dynamic and homeostatic stability. Furthermore, cultivar superiority provides information on the general and specific adaptability of a genotype, whereas ranking method only provides information on generally good performers of the genotype across environments (Makanda, 2009). Thus, cultivar superiority is more useful because it measures both the performance and stability of the genotype. Basically Pi was defined as superiority index of the ith cultivar relative to the genotype with maximum performance in each environment and it is used to assess the superiority of the cultivar (Moremoholo and Shimelis, 2009). The smaller the value of Pi, the less is the distance to the genotype with maximum yield and the better the genotype.