Guilding marks on stability and genotype-environment interaction analyses in plant breeding

In plant breeding studies, different statistical stabilities between genotypes or genotype-environment interactions (GEI) must often be considered since genotype responses differ from one environment to another. This paper reviews the statistical techniques used in recent literature up to 1996 and the most recent developments are described. First, stability concepts are reviewed and genotype-environment interaction is defined according to the following notation: (formula, see attached document) where E [Y ge] is the expectation of a given observation Yge for genotype g and environment e, μ is the grand mean, αg is the genotype main effect, βe environment main effect and αβge is the interaction between genotype and environment, defined as the complement from the additive model (μ + αg + βe). Then, main statistical methods are presented and classified from an interpreting point of view into five main approaches: (1) Uniparametric approaches: stability or GEI is described with a single parameter. Environmental variance can be set so as to differ for each genotype, which was first introduced by Roemer (1917, cited from Becker and Léon, 1988) and written as follows: (formula, see attached document) μ and αg have the same meaning as in the first model and σ2g are variance parameters associated with each genotype.The joint regression model, first proposed by Yates and Cochran (1938), which uses environment main effect as a pseudo covariate for modelling the interaction term, also belongs to this category: (formula, see attached document) where ρg is the genotype slope or genotype regression coefficient that describes the genotype response to environment potentiality estimated by βe, its main effect. Other terms of the model, E [Yge ], μ and αg are defined as in the first model. This family of models is attractive for the simplicity of its interpretations. Most authors have concluded that these models oversimplify and have added new parameters such as goodness of fit. This leads to more sophisticated families of models. (2) Multiparametric fixed approaches: GEI is modelled by means of several parameters associated with each genotype. There are two basic models: biadditive (or AMMI) models and factorial regression models. They can be extended and combined in several ways, see Gauch (1992) and van Eeuwijk et al (1996). The multiplicative model is written: (formula, see attached document) where λ1 is the singular value that accounts for the interactive part explained