Analysis and interpretation of genotype by environment interaction using additive main effect and multiplicative interaction (AMMI) model

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One very important activity in plant breeding is to test a wide range of genotypes in a wide diversity of environments. Environment refers to site, year or a combination of site and year. The objective of the plant breeder is to select superior genotypes. The plant breeder however is usually confronted with the problem of genotype by environment interaction which complicates selection of superior genotypes. Genotype by environment (GE) interaction is a situation in which the performance of genotypes varies across different environments. GE interaction makes it inadequate for the plant breeder to recommend a particular genotype because its mean yield over the environments tested is high; it might have produced outstanding yield in some sites and performed poorly when grown in a particular site. Several statistical methods have been proposed for the analysis of GE interaction. In recent years one of the most popular methodologies is the additive main effect and multiplication interaction (AMMI) model (Gauch, 1988) which was originally proposed by GolIob (1968) and Mandel (1971). This thesis is concerned with the analysis of GE data using the AMMI model. The performance of the AMMI model is investigated by comparing genotypic correlations and their respective sums of squares using real data sets with the objective of highlighting the “optimism” associated with the fitting of the model. Results have shown that the interaction matrix exhibits high correlations between the genotype vectors which when ignored leads to optimism in the fitting sums of squares. This has prompted the development of the complement index vector as an alternative fitting procedure. The performance of the new approach is evaluated using real data sets.
A thesis submitted to the Department of Mathematics in partial fulfilment of the requirements for a Master of Science degree in Mathematics, 2004